,the ,notebooks of ,leonardo ,da ,vinci ,volume #a ,translated by ,jean ,paul ,richter #ahhh ,,preface4 ,a singular fatality has ruled the destiny of nearly all the most famous of ,leonardo da ,vinci's works4 ,two of the three most important were never completed1 obstacles having arisen during his life-time1 which obliged him to leave them unfinished2 namely the ,sforza ,monument and the ,wall-painting of the ,battle of ,anghiari1 while the third--the picture of the ,last ,supper at ,milan--has suffered irremediable injury from decay and the repeated restorations to which it was recklessly subjected during the ,x,v,i,ith and ,x,v,i,i,ith centuries4 ,nevertheless1 no other picture of the ,renaissance has become so wellknown and popular through copies of every description4 ,vasari says1 and rightly1 in his ,life of ,leonardo1 that he laboured much more by his word than in fact or by deed1 and the biographer evidently had in his mind the numerous works in ,manuscript which have been preserved to this day4 ,to us1 now1 it seems almost inexplicable that these valuable and interesting original texts should have remained so long unpublished1 and indeed forgotten4 ,it is certain that during the ,x,v,ith and ,x,v,i,ith centuries their exceptional value was highly appreciated4 ,this is proved not merely by the prices which they commanded1 but also by the exceptional interest which has been attached to the change of ownership of merely a few pages of ,manuscript4 ,that1 notwithstanding this eagerness to possess the ,manuscripts1 their contents remained a mystery1 can only be accounted for by the many and great difficulties attending the task of deciphering them4 ,the handwriting is so peculiar that it requires considerable practice to read even a few detached phrases1 much more to solve with any certainty the numerous difficulties of alternative readings1 and to master the sense as a connected whole4 ,vasari observes with reference to ,leonardos writing3 he wrote backwards1 in rude characters1 and with the left hand1 so that any one who is not practised in reading them1 cannot understand them4 ,the aid of a mirror in reading reversed handwriting appears to me available only for a first experimental reading4 ,speaking from my own experience1 the persistent use of it is too fatiguing and inconvenient to be practically advisable1 considering the enormous mass of ,manuscripts to be deciphered4 ,and as1 after all1 ,leonardo's handwriting runs backwards just as all ,oriental character runs backwards--that is to say from right to left--the difficulty of reading direct from the writing is not insuperable4 ,this obvious peculiarity in the writing is not1 however1 by any means the only obstacle in the way of mastering the text4 ,leonardo made use of an orthography peculiar to himself2 he had a fashion of amalgamating several short words into one long one1 or1 again1 he would quite arbitrarily divide a long word into two separate halves2 added to this there is no punctuation whatever to regulate the division and construction of the sentences1 nor are there any accents--and the reader may imagine that such difficulties were almost sufficient to make the task seem a desperate one to a beginner4 ,it is therefore not surprising that the good intentions of some of ,leonardo s most reverent admirers should have failed4 ,leonardos literary labours in various departments both of ,art and of ,science were those essentially of an enquirer1 hence the analytical method is that which he employs in arguing out his investigations and dissertations4 ,the vast structure of his scientific theories is consequently built up of numerous separate researches1 and it is much to be lamented that he should never have collated and arranged them4 ,his love for detailed research--as it seems to me--was the reason that in almost all the ,manuscripts1 the different paragraphs appear to us to be in utter confusion2 on one and the same page1 observations on the most dissimilar subjects follow each other without any connection4 ,a page1 for instance1 will begin with some principles of astronomy1 or the motion of the earth2 then come the laws of sound1 and finally some precepts as to colour4 ,another page will begin with his investigations on the structure of the intestines1 and end with philosophical remarks as to the relations of poetry to painting2 and so forth4 ,leonardo himself lamented this confusion1 and for that reason ,i do not think that the publication of the texts in the order in which they occur in the originals would at all fulfil his intentions4 ,no reader could find his way through such a labyrinth2 ,leonardo himself could not have done it4 ,added to this1 more than half of the five thousand manuscript pages which now remain to us1 are written on loose leaves1 and at present arranged in a manner which has no justification beyond the fancy of the collector who first brought them together to make volumes of more or less extent4 ,nay1 even in the volumes1 the pages of which were numbered by ,leonardo himself1 their order1 so far as the connection of the texts was concerned1 was obviously a matter of indifference to him4 ,the only point he seems to have kept in view1 when first writing down his notes1 was that each observation should be complete to the end on the page on which it was begun4 ,the exceptions to this rule are extremely few1 and it is certainly noteworthy that we find in such cases1 in bound volumes with his numbered pages1 the written observations3 turn over1 ,this is the continuation of the previous page1 and the like4 ,is not this sufficient to prove that it was only in quite exceptional cases that the writer intended the consecutive pages to remain connected1 when he should1 at last1 carry out the often planned arrangement of his writings8 ,what this final arrangement was to be1 ,leonardo has in most cases indicated with considerable completeness4 ,in other cases this authoritative clue is wanting1 but the difficulties arising from this are not insuperable2 for1 as the subject of the separate paragraphs is always distinct and well defined in itself1 it is quite possible to construct a well-planned whole1 out of the scattered materials of his scientific system1 and ,i may venture to state that ,i have devoted especial care and thought to the due execution of this responsible task4 ,the beginning of ,leonardo's literary labours dates from about his thirty-seventh year1 and he seems to have carried them on without any serious interruption till his death4 ,thus the ,manuscripts that remain represent a period of about thirty years4 ,within this space of time his handwriting altered so little that it is impossible to judge from it of the date of any particular text4 ,the exact dates1 indeed1 can only be assigned to certain note-books in which the year is incidentally indicated1 and in which the order of the leaves has not been altered since ,leonardo used them4 ,the assistance these afford for a chronological arrangement of the ,manuscripts is generally self evident4 ,by this clue ,i have assigned to the original ,manuscripts now scattered through ,england1 ,italy and ,france1 the order of their production1 as in many matters of detail it is highly important to be able to verify the time and place at which certain observations were made and registered4 ,for this purpose the ,bibliography of the ,manuscripts given at the end of ,vol4 ,,ii1 may be regarded as an ,index1 not far short of complete1 of all ,leonardo s literary works now extant4 ,the consecutive numbers 7from #a to #aeff7 at the head of each passage in this work1 indicate their logical sequence with reference to the subjects2 while the letters and figures to the left of each paragraph refer to the original ,manuscript and number of the page1 on which that particular passage is to be found4 ,thus the reader1 by referring to the ,list of ,manuscripts at the beginning of ,volume ,i1 and to the ,bibliography at the end of ,volume ,,ii1 can1 in every instance1 easily ascertain1 not merely the period to which the passage belongs1 but also exactly where it stood in the original document4 ,thus1 too1 by following the sequence of the numbers in the ,bibliographical index1 the reader may reconstruct the original order of the ,manuscripts and recompose the various texts to be found on the original sheets--so much of it1 that is to say1 as by its subject-matter came within the scope of this work4 ,it may1 however1 be here observed that ,leonardo s ,manuscripts contain1 besides the passages here printed1 a great number of notes and dissertations on ,mechanics1 ,physics1 and some other subjects1 many of which could only be satisfactorily dealt with by specialists4 ,i have given as complete a review of these writings as seemed necessary in the ,bibliographical notes4 ,in #afea1 ,raphael ,trichet ,dufresne1 of ,paris1 published a selection from ,leonardo's writings on painting1 and this treatise became so popular that it has since been reprinted about two-and-twenty times1 and in six different languages4 ,but none of these editions were derived from the original texts1 which were supposed to have been lost1 but from early copies1 in which ,leonardo's text had been more or less mutilated1 and which were all fragmentary4 ,the oldest and on the whole the best copy of ,leonardo's essays and precepts on ,painting is in the ,vatican ,library2 this has been twice printed1 first by ,manzi1 in #ahag1 and secondly by ,ludwig1 in #ahhb4 ,still1 this ancient copy1 and the published editions of it1 contain much for which it would be rash to hold ,leonardo responsible1 and some portions--such as the very important rules for the proportions of the human figure--are wholly wanting2 on the other hand they contain passages which1 if they are genuine1 cannot now be verified from any original ,manuscript extant4 ,these copies1 at any rate neither give us the original order of the texts1 as written by ,leonardo1 nor do they afford any substitute1 by connecting them on a rational scheme2 indeed1 in their chaotic confusion they are anything rather than satisfactory reading4 ,the fault1 no doubt1 rests with the compiler of the ,vatican copy1 which would seem to be the source whence all the published and extensively known texts were derived2 for1 instead of arranging the passages himself1 he was satisfied with recording a suggestion for a final arrangement of them into eight distinct parts1 without attempting to carry out his scheme4 ,under the mistaken idea that this plan of distribution might be that1 not of the compiler1 but of ,leonardo himself1 the various editors1 down to the present day1 have very injudiciously continued to adopt this order--or rather disorder4 ,i1 like other enquirers1 had given up the original ,manuscript of the ,trattato della ,pittura for lost1 till1 in the beginning of #ahhj1 ,i was enabled1 by the liberality of ,lord ,ashburnham1 to inspect his ,manuscripts1 and was so happy as to discover among them the original text of the best-known portion of the ,trattato in his magnificent library at ,ashburnham ,place4 ,though this discovery was of a fragment only--but a considerable fragment--inciting me to further search1 it gave the key to the mystery which had so long enveloped the first origin of all the known copies of the ,trattato4 ,the extensive researches ,i was subsequently enabled to prosecute1 and the results of which are combined in this work1 were only rendered possible by the unrestricted permission granted me to investigate all the ,manuscripts by ,leonardo dispersed throughout ,europe1 and to reproduce the highly important original sketches they contain1 by the process of photogravure4 ,her ,majesty the ,queen graciously accorded me special permission to copy for publication the ,manuscripts at the ,royal ,library at ,windsor4 ,the ,commission ,centrale ,administrative de l',institut de ,france1 ,paris1 gave me1 in the most liberal manner1 in answer to an application from ,sir ,frederic ,leighton1 ,p4 ,r4 ,a41 ,corresponding member of the ,institut1 free permission to work for several months in their private collection at deciphering the ,manuscripts preserved there4 ,the same favour which ,lord ,ashburnham had already granted me was extended to me by the ,earl of ,leicester1 the ,marchese ,trivulsi1 and the ,curators of the ,ambrosian ,library at ,milan1 by the ,conte ,manzoni at ,rome and by other private owners of ,manuscripts of ,leonardo's2 as also by the ,directors of the ,louvre at ,paris2 the ,accademia at ,venice2 the ,uffizi at ,florence2 the ,royal ,library at ,turin2 and the ,british ,museum1 and the ,south ,kensington ,museum4 ,i am also greatly indebted to the ,librarians of these various collections for much assistance in my labours2 and more particularly to ,monsieur ,louis ,lalanne1 of the ,institut de ,france1 the ,abbate ,ceriani1 of the ,ambrosian ,library1 ,mr4 ,maude ,thompson1 ,keeper of ,manuscripts at the ,british ,museum1 ,mr4 ,holmes1 the ,queens ,librarian at ,windsor1 the ,revd ,vere ,bayne1 ,librarian of ,christ ,church ,college at ,oxford1 and the ,revd ,a4 ,napier1 ,librarian to the ,earl of ,leicester at ,holkham ,hall4 ,in correcting the ,italian text for the press1 ,i have had the advantage of valuable advice from the ,commendatore ,giov4 ,morelli1 ,senatore del ,regno1 and from ,signor ,gustavo ,frizzoni1 of ,milan4 ,the translation1 under many difficulties1 of the ,italian text into ,english1 is mainly due to ,mrs4 ,r4 ,c4 ,bell2 while the rendering of several of the most puzzling and important passages1 particularly in the second half of ,vol4 ,i1 ,i owe to the indefatigable interest taken in this work by ,mr4 ,e4 ,j4 ,poynter ,r4 ,a4 ,finally ,i must express my thanks to ,mr4 ,alfred ,marks1 of ,long ,ditton1 who has most kindly assisted me throughout in the revision of the proof sheets4 ,the notes and dissertations on the texts on ,architecture in ,vol4 ,,ii ,i owe to my friend ,baron ,henri de ,geymuller1 of ,paris4 ,i may further mention with regard to the illustrations1 that the negatives for the production of the photo-gravures by ,monsieur ,dujardin of ,paris were all taken direct from the originals4 ,it is scarcely necessary to add that most of the drawings here reproduced in facsimile have never been published before4 ,as ,i am now1 on the termination of a work of several years' duration1 in a position to review the general tenour of ,leonardos writings1 ,i may perhaps be permitted to add a word as to my own estimate of the value of their contents4 ,i have already shown that it is due to nothing but a fortuitous succession of unfortunate circumstances1 that we should not1 long since1 have known ,leonardo1 not merely as a ,painter1 but as an ,author1 a ,philosopher1 and a ,naturalist4 ,there can be no doubt that in more than one department his principles and discoveries were infinitely more in accord with the teachings of modern science1 than with the views of his contemporaries4 ,for this reason his extraordinary gifts and merits are far more likely to be appreciated in our own time than they could have been during the preceding centuries4 ,he has been unjustly accused of having squandered his powers1 by beginning a variety of studies and then1 having hardly begun1 throwing them aside4 ,the truth is that the labours of three centuries have hardly sufficed for the elucidation of some of the problems which occupied his mighty mind4 ,alexander von ,humboldt has borne witness that he was the first to start on the road towards the point where all the impressions of our senses converge in the idea of the ,unity of ,nature ,nay1 yet more may be said4 ,the very words which are inscribed on the monument of ,alexander von ,humboldt himself1 at ,berlin1 are perhaps the most appropriate in which we can sum up our estimate of ,leonardo's genius3 ,majestati naturae par ingenium4 ,,london1 ,april #ahhc4 ,f4 ,p4 ,r4 ,,contents ,,of ,,volume ,i4 ,,prolegomena ,,and ,,general ,,introduction ,,to ,,the ,,book ,,on ,,painting ,clavis ,sigillorum and ,index of ,manuscripts4--,the author's intention to publish his ,,mss4 7#a74--,the preparation of the ,,mss4 for publication 7#b74--;,admonition to readers 7#c74--,the disorder in the ,,mss4 7#d74--,suggestions for the arrangement of ,,mss4 treating of particular subjects 7#e--h74--;,general introductions to the book on painting 7#i--ac74--,the plan of the book on painting 7#ad--ag74--,the use of the book on painting 7#ah74--,necessity of theoretical knowledge 7#ai1 #bj74--,the function of the eye 7#ba--bc74--,variability of the eye 7#bd74--;,focus of sight 7#be74--;,differences of perception by one eye and by both eyes 7#bf--bi74--,the comparative size of the image depends on the amount of light 7#cj--ci74 ,,ii4 ,,linear ,,perspective ,general remarks on perspective 7#dj--da74--,the elements of perspective3--of the point 7#db--df74--,of the line 7#dg--dh74--,the nature of the outline 7#di74--;,definition of perspective 7#ej74--,the perception of the object depends on the direction of the eye 7#ea74--;,experimental proof of the existence of the pyramid of sight 7#eb--ee74--,the relations of the distance point to the vanishing point 7#ee--ef74--;,how to measure the pyramid of vision 7#eg74--,the production of the pyramid of vision 7#eh--fd74--,proof by experiment 7#fe--ff74--;,general conclusions 7#fg74--,that the contrary is impossible 7#fh74--;,a parallel case 7#fi74--,the function of the eye1 as explained by the camera obscura 7#gj--ga74--,the practice of perspective 7#gb--gc74--,refraction of the rays falling upon the eye 7#gd--ge74--,the inversion of the images 7#gf74--,the intersection of the rays 7#gg--hb74--;,demonstration of perspective by means of a vertical glass plane 7#hc--he47--,the angle of sight varies with the distance 7#hf--hh74--,opposite pyramids in juxtaposition 7#hi74--,on simple and complex perspective 7#ij74--,the proper distance of objects from the eye 7#ia--ib74--,the relative size of objects with regard to their distance from the eye 7#ic--ih74--,the apparent size of objects denned by calculation 7#ii--ajf74--,on natural perspective 7#ajg--aji74 ,,iii4 ,,six ,,books ,,on ,,light ,,and ,,shade ,,general ,,introduction4--,prolegomena 7#aaj74--,scheme of the books on light and shade 7#aaa74--;,different principles and plans of treatment 7#aab--aaf74--;,different sorts of light 7#aag--aah74--;,definition of the nature of shadows 7#aai--abb74--,of the various kinds of shadows 7#abc--abe74--,of the various kinds of light 7#abf--abg74--;,general remarks 7#abh--abi74--;,,first ,,book ,,on ,,light ,,and ,,shade4--,on the nature of light 7#acj--aca74--,the difference between light and lustre 7#acb--ace74--,the relations of luminous to illuminated bodies 7#acf74 --,experiments on the relation of light and shadow within a room 7#acg--adj74--,light and shadow with regard to the position of the eye 7#ada--ade74--,the law of the incidence of light 7#adf--adg74--,,second ,,book ,,on ,,light ,,and ,,shade4--,gradations of strength in the shadows 7#adh--adi74--,on the intensity of shadows as dependent on the distance from the light 7#aej--aeb74--,on the proportion of light and shadow 7#aec--aeg74--,,third ,,book ,,on ,,light ,,and ,,shade4--,definition of derived shadow 7#aeh--aei74--;,different sorts of derived shadows 7#afj--afb74--,on the relation of derived and primary shadow 7#afc--afe74--,on the shape of derived shadows 7#aff--agd74--,on the relative intensity of derived shadows 7#age--agi74--,shadow as produced by two lights of different size 7#ahj--aha74--,the effect of light at different distances 7#ahb74--;,further complications in the derived shadows 7#ahc--ahg74--;,,fourth ,,book ,,on ,,light ,,and ,,shade4--,on the shape of cast shadows 7#ahh--aia74--,on the outlines of cast shadows 7#aib--aie74--,on the relative size of cast shadows 7#aif4 #aig74--;,effects on cast shadows by the tone of the back ground 7#aih74--;,a disputed proposition 7#aii74--,on the relative depth of cast shadows 7#bjj--bjb74--;,,fifth ,,book ,,on ,,light ,,and ,,shade4--,principles of reflection 7#bjc4 #bjd74--,on reverberation 7#bje74--,reflection on water 7#bjf4 #bjg74--;,experiments with the mirror 7#bjh--baj74--;,appendix3--,on shadows in movement 7#baa--bab74--,,sixth ,,book ,,on ,,light ,,and ,,shade4--,the effect of rays passing through holes 7#bac4 #bad74--,on gradation of shadows 7#bae4 #baf74--,on relative proportion of light and shadows 7#baf--bba74 ,,iv4 ,,perspective ,,of ,,disappearance ,definition 7#bbb4 #bbc74--;,an illustration by experiment 7#bbd74--;,a guiding rule 7#bbe74---;,an experiment 7#bbf74--,on indistinctness at short distances 7#bbg--bca74--,on indistinctness at great distances 7#bcb--bcd74--,the importance of light and shade in the ,prospettiva de' perdimenti 7#bce--bci74--,the effect of light or dark backgrounds on the apparent size of objects 7#bdj--bej74--,propositions on ,prospettiva de' perdimenti from ,,ms4 ,c4 7#bej--bfb74 ,v4 ,,theory ,,of ,,colours ,the reciprocal effects of colours on objects placed opposite each other 7#bfc--bga74--;,combination of different colours in cast shadows 7#bgb74--,the effect of colours in the camera obscura 7#bgc4 #bgd74--,on the colours of derived shadows 7#bge4 #bgf74--,on the nature of colours 7#bgg4 #bgh74--,on gradations in the depth of colours 7#bgi4 #bhj74--,on the reflection of colours 7#bha--bhc74--,on the use of dark and light colours in painting 7#bhd--bhf74--,on the colours of the rainbow 7#bhg--bhh74 ,,vi4 ,,perspective ,,of ,,colour ,,and ,,aerial ,,perspective ,general rules 7#bhi--bia74--;,an exceptional case 7#bib74--;,an experiment 7#bic74--,the practice of the ,prospettiva de' colori 7#bid74--,the rules of aerial perspective 7#bie--big74--,on the relative density of the atmosphere 7#bih--bii74--,on the colour of the atmosphere 7#cjj--cjg74 ,,vii4 ,,on ,,the ,,proportions ,,and ,,on ,,the ,,movements ,,of ,,the ,,human ,,figure ,preliminary observations 7#cjh4 #cji74--,proportions of the head and face 7#caj--cah74--,proportions of the head seen in front 7#cai--cba74--,proportions of the foot 7#cbb--cbc74--,relative proportions of the hand and foot 7#cbd74--,relative proportions of the foot and of the face 7#cbe--cbg74--,proportions of the leg 7#cbh--cca74--,on the central point of the whole body 7#ccb74--,the relative proportions of the torso and of the whole figure 7#ccc74--,the relative proportions of the head and of the torso 7#ccd74--,the relative proportions of the torso and of the leg 7#cce4 #ccf74--,the relative proportions of the torso and of the foot 7#ccg74--,the proportions of the whole figure 7#cch--cda74--,the torso from the front and back 7#cdb74--,vitruvius' scheme of proportions 7#cdc74--,the arm and head 7#cdd74--,proportions of the arm 7#cde--cdi74--,the movement of the arm 7#cej--ced74--,the movement of the torso 7#cee--cfa74--,the proportions vary at different ages 7#cfb--cfg74--,the movement of the human figure 7#cfh--cge74--,of walking up and down 7#cge--cgi74--,on the human body in action 7#chj--chh74--,on hair falling down in curls 7#chi74--,on draperies 7#cij--cib74 ,,viii4 ,,botany ,,for ,,painters1 ,,and ,,elements ,,of ,,landscape ,,painting ,classification of trees 7#cic74--,the relative thickness of the branches to the trunk 7#cid--cif74--,the law of proportion in the growth of the branches 7#cig--djb74--,the direction of growth 7#djc--djg74--,the forms of trees 7#djh--daa74--,the insertion of the leaves 7#dab--dai74--,light on branches and leaves 7#dbj--dbb74--,the proportions of light and shade in a leaf 7#dbc--dbf74--,of the transparency of leaves 7#dbg--dbi74--,the gradations of shade and colour in leaves 7#dcj--dcd74--;,a classification of trees according to their colours 7#dce74--,the proportions of light and shade in trees 7#dcf--ddj74--,the distribution of light and shade with reference to the position of the spectator 7#dda--ddc74--,the effects of morning light 7#ddd--ddh74--,the effects of midday light 7#ddi74--,the appearance of trees in the distance 7#dej--dea74--,the cast shadow of trees 7#deb4 #dec74--,light and shade on groups of trees 7#ded--deg74--,on the treatment of light for landscapes 7#deh--dfd74--,on the treatment of light for views of towns 7#dfe--dfi74--,the effect of wind on trees 7#dgj--dgc74--,light and shade on clouds 7#dgd--dgg74--,on images reflected in water 7#dgh74--,of rainbows and rain 7#dgi4 #dhj74--,of flower seeds 7#dha74 ,,ix4 ,,the ,,practice ,,of ,,painting ,i4 ,,moral ,,precepts ,,for ,,the ,,student ,,of ,,painting4--,how to ascertain the dispositions for an artistic career 7#dhb74--,the course of instruction for an artist 7#dhc--dhe74--,the study of the antique 7#dhf4 #dhg74--,the necessity of anatomical knowledge 7#dhh4 #dhi74--;,how to acquire practice 7#dij74--;,industry and thoroughness the first conditions 7#dia--dic47--,the artist's private life and choice of company 7#dic4 #did74--,the distribution of time for studying 7#die-- #dig74--,on the productive power of minor artists 7#dih--eja74--;,a caution against one-sided study 7#ejb74--;,how to acquire universality 7#ejc--ejf74--,useful games and exercises 7#ejg4 #ejh74--;,,ii4 ,,the ,,artist',s ,,studio4--,,instruments ,,and ,,helps ,,for ,,the ,,application ,,of ,,perspective4--,,on ,,judging ,,of ,a ,,picture4--,on the size of the studio 7#eji74--,on the construction of windows 7#eaj--eab74--,on the best light for painting 7#eac--ebj74--,on various helps in preparing a picture 7#eba--ecj74--,on the management of works 7#eca4 #ecb74--,on the limitations of painting 7#ecc--ece74--,on the choice of a position 7#ecf4 #ecg74--,the apparent size of figures in a picture 7#ech4 #eci74--,the right position of the artist1 when painting and of the spectator 7#edj--edg74--;,,iii4 ,,the ,,practical ,,methods ,,of ,,light ,,and ,,shade ,,and ,,aerial ,,perspective4--,gradations of light and shade 7#edh74--,on the choice of light for a picture 7#edi--eed74--,the distribution of light and shade 7#eee--eei74--,the juxtaposition of light and shade 7#efj4 #efa74--,on the lighting of the background 7#efb--efe74--,on the lighting of white objects 7#eff74--,the methods of aerial perspective 7#efg--egj74--;,,iv4 ,,of ,,portrait ,,and ,,figure ,,painting4--,of sketching figures and portraits 7#ega4 #egb74--,the position of the head 7#egc74--,of the light on the face 7#egd--egf74--;,general suggestions for historical pictures 7#egg--eha74--;,how to represent the differences of age and sex 7#ehb4 #ehc74--,of representing the emotions 7#ehd74--,of representing imaginary animals 7#ehe74--,the selection of forms 7#ehf--eia74--;,how to pose figures 7#eib74--,of appropriate gestures 7#eic--fjj74--,v4 ,,suggestions ,,for ,,compositions4--,of painting battle-pieces 7#fja--fjc74--,of depicting night-scenes 7#fjd74--,of depicting a tempest 7#fje4 #fjf74--,of representing the deluge 7#fjg--fji74--,of depicting natural phenomena 7#faj4 #faa74--,,vi4 ,,the ,,artist',s ,,materials4--,of chalk and paper 7#fab--fag74--,on the preparation and use of colours 7#fah--fbg74--,of preparing the panel 7#fbh74--,the preparation of oils 7#fbi--fcd74--,on varnishes 7#fce-- #fcg74--,on chemical materials 7#fch--fej74--,,vii4 ,,philosophy ,,and ,,history ,,of ,,the ,,art ,,of ,,painting4--,the relation of art and nature 7#fea4 #feb74--,painting is superior to poetry 7#fec4 #fed74--,painting is superior to sculpture 7#fee4 #fef74--;,aphorisms 7#feg--fei74--,on the history of painting 7#ffj4 #ffa74--,the painter's scope 7#ffb74 ,x4 ,,studies ,,and ,,sketches ,,for ,,pictures ,,and ,,decorations ,on pictures of the ,madonna 7#ffc74--;,bernardo di ,bandino's portrait 7#ffd74--,notes on the ,last ,supper 7#ffe--ffh74--,on the battle of ,anghiari 7#ffi74--;,allegorical representations referring to the duke of ,milan 7#fgj--fgc74--;,allegorical representations 7#fgd--fgh74--;,arrangement of a picture 7#fgi74--,list of drawings 7#fhj74--,mottoes and ,emblems 7#fha--gjb74 ,the author's intention to publish his ,,mss4 #a4 ,how by a certain machine many may stay some time under water4 ,and how and wherefore ,i do not describe my method of remaining under water and how long ,i can remain without eating4 ,and ,i do not publish nor divulge these1 by reason of the evil nature of men1 who would use them for assassinations at the bottom of the sea by destroying ships1 and sinking them1 together with the men in them4 ,nevertheless ,i will impart others1 which are not dangerous because the mouth of the tube through which you breathe is above the water1 supported on air sacks or cork4 ,footnote3 ,the leaf on which this passage is written1 is headed with the words ,casi #ci1 and most of these cases begin with the word ',come'1 like the two here given1 which are the #bfth and #bgth4 #g4 ,sughero4 ,in the ,codex ,antlanticus #cgg;a2 #aagj;a there is a sketch1 drawn with the pen1 representing a man with a tube in his mouth1 and at the farther end of the tube a disk4 ,by the tube the word ',channa' is written1 and by the disk the word 'sughero'4 ,the preparation of the ,,mss4 for publication4 #b4 ,when you put together the science of the motions of water1 remember to include under each proposition its application and use1 in order that this science may not be useless4-- ,footnote3 ,a comparatively small portion of ,leonardo's notes on water-power was published at ,bologna in #ahbh1 under the title3 ,del moto e misura dell',acqua1 di ,l4 da ,vinci4 ,admonition to readers4 #c4 ,let no man who is not a ,mathematician read the elements of my work4 ,the disorder in the ,,mss4 #d4 ,begun at ,florence1 in the house of ,piero di ,braccio ,martelli1 on the #bbnd day of ,march #aejh4 ,and this is to be a collection without order1 taken from many papers which ,i have copied here1 hoping to arrange them later each in its place1 according to the subjects of which they may treat4 ,but ,i believe that before ,i am at the end of this task ,i shall have to repeat the same things several times2 for which1 ,o reader6 do not blame me1 for the subjects are many and memory cannot retain them all and say3 ',i will not write this because ,i wrote it before4' ,and if ,i wished to avoid falling into this fault1 it would be necessary in every case when ,i wanted to copy a passage that1 not to repeat myself1 ,i should read over all that had gone before2 and all the more since the intervals are long between one time of writing and the next4 ,footnote3 #a4 ,in the history of ,florence in the early part of the ,x,v,ith century ,piero di ,braccio ,martelli is frequently mentioned as ,commissario della ,signoria4 ,he was famous for his learning and at his death left four books on ,mathematics ready for the press2 comp4 ,,litta1 ,famiglie celebri ,italiane1 ,famiglia ,martelli di ,firenze4--,in the ,official ,catalogue of ,,mss4 in the ,brit4 ,mus41 ,new ,series ,vol4 ,i41 where this passage is printed1 ,barto has been wrongly given for ,braccio4 #b4 addi #bb di marzo #aejh4 ,the ,christian era was computed in ,florence at that time from the ,incarnation 7,lady day1 ,march #beth74 ,hence this should be #aeji by our reckoning4 #c4 racolto tratto di molte carte le quali io ho qui copiate4 ,we must suppose that ,leonardo means that he has copied out his own ,,mss4 and not those of others4 ,the first thirteen leaves of the ,,ms4 in the ,brit4 ,mus4 are a fair copy of some notes on physics4 ,suggestions for the arrangement of ,,mss treating of particular subjects47#e-h74 #e4 ,of digging a canal4 ,put this in the ,book of useful inventions and in proving them bring forward the propositions already proved4 ,and this is the proper order2 since if you wished to show the usefulness of any plan you would be obliged again to devise new machines to prove its utility and thus would confuse the order of the forty ,books and also the order of the diagrams2 that is to say you would have to mix up practice with theory1 which would produce a confused and incoherent work4 #f4 ,i am not to blame for putting forward1 in the course of my work on science1 any general rule derived from a previous conclusion4 #g4 ,the ,book of the science of ,mechanics must precede the ,book of useful inventions4--,have your books on anatomy bound6 ,footnote3 #d4 ,the numerous notes on anatomy written on loose leaves and now in the ,royal collection at ,windsor can best be classified in four ,books1 corresponding to the different character and size of the paper4 ,when ,leonardo speaks of 'li tua libri di notomia'1 he probably means the ,,mss4 which still exist2 if this hypothesis is correct the present condition of these leaves might seem to prove that he only carried out his purpose with one of the ,books on anatomy4 ,a borrowed book on ,anatomy is mentioned in ,f4,o4 #h4 ,the order of your book must proceed on this plan3 first simple beams1 then 7those7 supported from below1 then suspended in part1 then wholly suspended4 ,then beams as supporting other weights ,footnote3 #d4 ,leonardo's notes on ,mechanics are extraordinarily numerous2 but1 for the reasons assigned in my introduction1 they have not been included in the present work44 ,general introductions to the book on ,painting 7#i-ac74 #i4 ,,introduction4 ,seeing that ,i can find no subject specially useful or pleasing--since the men who have come before me have taken for their own every useful or necessary theme--,i must do like one who1 being poor1 comes last to the fair1 and can find no other way of providing himself than by taking all the things already seen by other buyers1 and not taken but refused by reason of their lesser value4 ,i1 then1 will load my humble pack with this despised and rejected merchandise1 the refuse of so many buyers2 and will go about to distribute it1 not indeed in great cities1 but in the poorer towns1 taking such a price as the wares ,i offer may be worth4 ,footnote3 ,it need hardly be pointed out that there is in this ',proemio' a covert irony4 ,in the second and third prefaces1 ,leonardo characterises his rivals and opponents more closely4 ,his protest is directed against ,neo-latinism as professed by most of the humanists of his time2 its futility is now no longer questioned4 #aj4 ,,introduction4 ,i know that many will call this useless work ,footnote3 #c4 questa essere opera inutile4 ,by opera we must here understand libro di pittura and particularly the treatise on ,perspective42 and they will be those of whom ,demetrius ,footnote3 #d4 ,demetrio4 ,with regard to the passage attributed to ,demetrius1 ,dr4 ,h4 ,m,,ller ,,str,,bing writes1 ,i know not what to make of it4 ,it is certainly not ,demetrius ,phalereus that is meant and it can hardly be ,demetrius ,poliorcetes4 ,who then can it be--for the name is a very common one8 ,it may be a clerical error for ,demades and the maxim is quite in the spirit of his writings ,i have not however been able to find any corresponding passage either in the ',fragments' 7,c4 ,,muller1 ,orat4 ,att41 ,,ii4 #dda7 nor in the ,supplements collected by ,,dietz 7,rhein4 ,mus41 vol4 #bi1 p4 #ajh74 ,the same passage occurs as a simple ,memorandum in the ,,ms4 ,tr4 #eg1 apparently as a note for this ',proemio' thus affording some data as to the time where these introductions were written4 declared that he took no more account of the wind that came out their mouth in words1 than of that they expelled from their lower parts3 men who desire nothing but material riches and are absolutely devoid of that of wisdom1 which is the food and the only true riches of the mind4 ,for so much more worthy as the soul is than the body1 so much more noble are the possessions of the soul than those of the body4 ,and often1 when ,i see one of these men take this work in his hand1 ,i wonder that he does not put it to his nose1 like a monkey1 or ask me if it is something good to eat4 ,footnote3 ,in the original1 the ,proemio d prospettiva cio dell'uffitio dell'occhio 7see ,no4 #ba7 stands between this and the preceding one1 ,no4 #i4 ,,introduction4 ,i am fully concious that1 not being a literary man1 certain presumptuous persons will think that they may reasonably blame me2 alleging that ,i am not a man of letters4 ,foolish folks6 do they not know that ,i might retort as ,marius did to the ,roman ,patricians ,footnote #ba3 ,come ,mario disse ai patriti ,romani4 ,i am unable to find the words here attributed by ,leonardo to ,marius1 either in ,plutarch's ,life of ,marius or in the ,apophthegmata 7,moralia1 p4#bjb74 ,nor do they occur in the writings of ,valerius ,maximus 7who frequently mentions ,marius7 nor in ,velleius ,paterculus 7,,ii1 #aa to #dc71 ,dio ,cassius1 ,aulus ,gellius1 or ,macrobius4 ,professor ,e4 ,,mendelson of ,dorpat1 the editor of ,herodian1 assures me that no such passage is the found in that author 7communication from ,dr4 ,,muller ,,strubing74 ,leonardo evidently meant to allude to some well known incident in ,roman history and the mention of ,marius is the result probably of some confusion4 ,we may perhaps read1 for ,marius1 ,menenius ,agrippa1 though in that case it is true we must alter ,patriti to ,plebei4 ,the change is a serious one4 but it would render the passage perfectly clear4 by saying3 ,that they1 who deck themselves out in the labours of others will not allow me my own4 ,they will say that ,i1 having no literary skill1 cannot properly express that which ,i desire to treat of ,footnote #bf3 le mie cose 4444 che d'altra parola4 ,this can hardly be reconciled with ,mons4 ,,ravaisson',s estimate of ,l4 da ,vinci's learning4 ,leonard de ,vinci etait un admirateur et un disciple des anciens1 aussi bien dans l'art que dans la science et il tenait a passer pour tel meme aux yeux de la posterite4 ,gaz4 des ,beaux arts4 ,oct4 #ahgg42 but they do not know that my subjects are to be dealt with by experience rather than by words ,footnote #bh3 ,see ,footnote #bf2 and experience has been the mistress of those who wrote well4 ,and so1 as mistress1 ,i will cite her in all cases4 #aa4 ,though ,i may not1 like them1 be able to quote other authors1 ,i shall rely on that which is much greater and more worthy3--on experience1 the mistress of their ,masters4 ,they go about puffed up and pompous1 dressed and decorated with the fruits1 not of their own labours1 but of those of others4 ,and they will not allow me my own4 ,they will scorn me as an inventor2 but how much more might they--who are not inventors but vaunters and declaimers of the works of others--be blamed4 ,,introduction4 ,and those men who are inventors and interpreters between ,nature and ,man1 as compared with boasters and declaimers of the works of others1 must be regarded and not otherwise esteemed than as the object in front of a mirror1 when compared with its image seen in the mirror4 ,for the first is something in itself1 and the other nothingness4--,folks little indebted to ,nature1 since it is only by chance that they wear the human form and without it ,i might class them with the herds of beasts4 #ab4 ,many will think they may reasonably blame me by alleging that my proofs are opposed to the authority of certain men held in the highest reverence by their inexperienced judgments2 not considering that my works are the issue of pure and simple experience1 who is the one true mistress4 ,these rules are sufficient to enable you to know the true from the false--and this aids men to look only for things that are possible and with due moderation--and not to wrap yourself in ignorance1 a thing which can have no good result1 so that in despair you would give yourself up to melancholy4 #ac4 ,among all the studies of natural causes and reasons ,light chiefly delights the beholder2 and among the great features of ,mathematics the certainty of its demonstrations is what preeminently 7tends to7 elevate the mind of the investigator4 ,perspective1 therefore1 must be preferred to all the discourses and systems of human learning4 ,in this branch of science the beam of light is explained on those methods of demonstration which form the glory not so much of ,mathematics as of ,physics and are graced with the flowers of both ,footnote3 #e4 ,such of ,leonardo's notes on ,optics or on ,perspective as bear exclusively on ,mathematics or ,physics could not be included in the arrangement of the libro di pittura which is here presented to the reader4 ,they are however but few44 ,but its axioms being laid down at great length1 ,i shall abridge them to a conclusive brevity1 arranging them on the method both of their natural order and of mathematical demonstration2 sometimes by deduction of the effects from the causes1 and sometimes arguing the causes from the effects2 adding also to my own conclusions some which1 though not included in them1 may nevertheless be inferred from them4 ,thus1 if the ,lord--who is the light of all things--vouchsafe to enlighten me1 ,i will treat of ,light2 wherefore ,i will divide the present work into #c ,parts ,footnote3 #aj4 ,in the middle ages--for instance1 by ,,roger ,,bacon1 by ,,vitellone1 with whose works ,leonardo was certainly familiar1 and by all the writers of the ,renaissance ,perspective and ,optics were not regarded as distinct sciences4 ,perspective1 indeed1 is in its widest application the science of seeing4 ,although to ,leonardo the two sciences were clearly separate1 it is not so as to their names2 thus we find axioms in ,optics under the heading ,perspective4 ,according to this arrangement of the materials for the theoretical portion of the libro di pittura propositions in ,perspective and in ,optics stand side by side or occur alternately4 ,although this particular chapter deals only with ,optics1 it is not improbable that the words partir la presente opera in #c parti may refer to the same division into three sections which is spoken of in chapters #ad to #ag44 ,the plan of the book on ,painting 7#ad--ag74 #ad4 ,,on ,,the ,,three ,,branches ,,of ,,perspective4 ,there are three branches of perspective2 the first deals with the reasons of the 7apparent7 diminution of objects as they recede from the eye1 and is known as ,diminishing ,perspective4--,the second contains the way in which colours vary as they recede from the eye4 ,the third and last is concerned with the explanation of how the objects in a picture ought to be less finished in proportion as they are remote 7and the names are as follows73 ,linear ,perspective4 ,the ,perspective of ,colour4 ,the ,perspective of ,disappearance4 ,footnote3 #ac4 ,from the character of the handwriting ,i infer that this passage was written before the year #adij44 #ae4 ,,on ,,painting ,,and ,,perspective4 ,the divisions of ,perspective are #c1 as used in drawing2 of these1 the first includes the diminution in size of opaque objects2 the second treats of the diminution and loss of outline in such opaque objects2 the third1 of the diminution and loss of colour at long distances4 ,footnote3 ,the division is here the same as in the previous chapter ,no4 #ad1 and this is worthy of note when we connect it with the fact that a space of about #bj years must have intervened between the writing of the two passages4 #af4 ,,the ,,discourse ,,on ,,painting4 ,perspective1 as bearing on drawing1 is divided into three principal sections2 of which the first treats of the diminution in the size of bodies at different distances4 ,the second part is that which treats of the diminution in colour in these objects4 ,the third deals with the diminished distinctness of the forms and outlines displayed by the objects at various distances4 #ag4 ,,on ,,the ,,sections ,,of ,,the ,,book ,,on ,,painting4 ,the first thing in painting is that the objects it represents should appear in relief1 and that the grounds surrounding them at different distances shall appear within the vertical plane of the foreground of the picture by means of the #c branches of ,perspective1 which are3 the diminution in the distinctness of the forms of the objects1 the diminution in their magnitude2 and the diminution in their colour4 ,and of these #c classes of ,perspective the first results from the structure of the eye1 while the other two are caused by the atmosphere which intervenes between the eye and the objects seen by it4 ,the second essential in painting is appropriate action and a due variety in the figures1 so that the men may not all look like brothers1 c4 ,footnote3 ,this and the two foregoing chapters must have been written in #aeac to #aeaf4 ,they undoubtedly indicate the scheme which ,leonardo wished to carry out in arranging his researches on ,perspective as applied to ,painting4 ,this is important because it is an evidence against the supposition of ,h4 ,,ludwig and others1 that ,leonardo had collected his principles of ,perspective in one book so early as before #aejj2 a ,book which1 according to the hypothesis1 must have been lost at a very early period1 or destroyed possibly1 by the ,french 767 in #aejj 7see ,h4 ,,ludwig4 ,l4 da ,vinci3 ,das ,buch van der ,malerei4 ,vienna #ahhb ,,iii1 #g and #h74 ,the use of the book on ,painting4 #ah4 ,these rules are of use only in correcting the figures2 since every man makes some mistakes in his first compositions and he who knows them not1 cannot amend them4 ,but you1 knowing your errors1 will correct your works and where you find mistakes amend them1 and remember never to fall into them again4 ,but if you try to apply these rules in composition you will never make an end1 and will produce confusion in your works4 ,these rules will enable you to have a free and sound judgment2 since good judgment is born of clear understanding1 and a clear understanding comes of reasons derived from sound rules1 and sound rules are the issue of sound experience--the common mother of all the sciences and arts4 ,hence1 bearing in mind the precepts of my rules1 you will be able1 merely by your amended judgment1 to criticise and recognise every thing that is out of proportion in a work1 whether in the perspective or in the figures or any thing else4 ,necessity of theoretical knowledge 7#ai4 #bj74 #ai4 ,,of ,,the ,,mistakes ,,made ,,by ,,those ,,who ,,practise ,,without ,,knowledge4 ,those who are in love with practice without knowledge are like the sailor who gets into a ship without rudder or compass and who never can be certain whether he is going4 ,practice must always be founded on sound theory1 and to this ,perspective is the guide and the gateway2 and without this nothing can be done well in the matter of drawing4 #bj4 ,the painter who draws merely by practice and by eye1 without any reason1 is like a mirror which copies every thing placed in front of it without being conscious of their existence4 ,the function of the eye 7#ba-bc74 #ba4 ,,introduction ,,to ,,perspective3--,,that ,,is ,,of ,,the ,,function ,,of ,,the ,,eye4 ,behold here ,o reader6 a thing concerning which we cannot trust our forefathers1 the ancients1 who tried to define what the ,soul and ,life are--which are beyond proof1 whereas those things1 which can at any time be clearly known and proved by experience1 remained for many ages unknown or falsely understood4 ,the eye1 whose function we so certainly know by experience1 has1 down to my own time1 been defined by an infinite number of authors as one thing2 but ,i find1 by experience1 that it is quite another4 ,footnote #ac3 ,compare the note to ,no4 #gj4 ,footnote3 ,in section #ac we already find it indicated that the study of ,perspective and of ,optics is to be based on that of the functions of the eye4 ,leonardo also refers to the science of the eye1 in his astronomical researches1 for instance in ,,ms4 ,f #be;b ',ordine del provare la terra essere una stella3 ,imprima difinisce l'occhio'1 c4 ,compare also ,,ms4 ,e #ae;b and ,f #fj;b4 ,the principles of astronomical perspective4 #bb4 ,here in the eye forms1 here colours1 here the character of every part of the universe are concentrated to a point2 and that point is so marvellous a thing 444 ,oh6 marvellous1 ,o stupendous ,necessity--by thy laws thou dost compel every effect to be the direct result of its cause1 by the shortest path4 ,these indeed are miracles2444 ,in so small a space it can be reproduced and rearranged in its whole expanse4 ,describe in your anatomy what proportion there is between the diameters of all the images in the eye and the distance from them of the crystalline lens4 #bc4 ,,of ,,the #aj ,,attributes ,,of ,,the ,,eye1 ,,all ,,concerned ,,in ,,painting4 ,painting is concerned with all the #aj attributes of sight2 which are3--,darkness1 ,light1 ,solidity and ,colour1 ,form and ,position1 ,distance and ,propinquity1 ,motion and ,rest4 ,this little work of mine will be a tissue of the studies of these attributes1 reminding the painter of the rules and methods by which he should use his art to imitate all the works of ,nature which adorn the world4 #bd4 ,,on ,,painting4 ,variability of the eye4 #ast4 ,the pupil of the eye contracts1 in proportion to the increase of light which is reflected in it4 #bnd4 ,the pupil of the eye expands in proportion to the diminution in the day light1 or any other light1 that is reflected in it4 #crd4 ,footnote3 #h4 ,the subject of this third proposition we find fully discussed in ,,ms4 ,g4 #dd;a44 ,the eye perceives and recognises the objects of its vision with greater intensity in proportion as the pupil is more widely dilated2 and this can be proved by the case of nocturnal animals1 such as cats1 and certain birds--as the owl and others--in which the pupil varies in a high degree from large to small1 c41 when in the dark or in the light4 #dth4 ,the eye out of doors in an illuminated atmosphere sees darkness behind the windows of houses which nevertheless are light4 #eth4 ,all colours when placed in the shade appear of an equal degree of darkness1 among themselves4 #fth4 ,but all colours when placed in a full light1 never vary from their true and essential hue4 #be4 ,,of ,,the ,,eye4 ,focus of sight4 ,if the eye is required to look at an object placed too near to it1 it cannot judge of it well--as happens to a man who tries to see the tip of his nose4 ,hence1 as a general rule1 ,nature teaches us that an object can never be seen perfectly unless the space between it and the eye is equal1 at least1 to the length of the face4 ,differences of perception by one eye and by both eyes 7#bf-bi74 #bf4 ,,of ,,the ,,eye4 ,when both eyes direct the pyramid of sight to an object1 that object becomes clearly seen and comprehended by the eyes4 #bg4 ,objects seen by one and the same eye appear sometimes large1 and sometimes small4 #bh4 ,the motion of a spectator who sees an object at rest often makes it seem as though the object at rest had acquired the motion of the moving body1 while the moving person appears to be at rest4 ,,on ,,painting4 ,objects in relief1 when seen from a short distance with one eye1 look like a perfect picture4 ,if you look with the eye a1 b at the spot c1 this point c will appear to be at d1 f1 and if you look at it with the eye g1 h will appear to be at m4 ,a picture can never contain in itself both aspects4 #bi4 ,let the object in relief t be seen by both eyes2 if you will look at the object with the right eye m1 keeping the left eye n shut1 the object will appear1 or fill up the space1 at a2 and if you shut the right eye and open the left1 the object 7will occupy the7 space b2 and if you open both eyes1 the object will no longer appear at a or b1 but at e1 r1 f4 ,why will not a picture seen by both eyes produce the effect of relief1 as real relief does when seen by both eyes2 and why should a picture seen with one eye give the same effect of relief as real relief would under the same conditions of light and shade8 ,footnote3 ,in the sketch1 m is the left eye and n the right1 while the text reverses this lettering4 ,we must therefore suppose that the face in which the eyes m and n are placed is opposite to the spectator4 #cj4 ,the comparative size of the image depends on the amount of light 7#cj-ci74 ,the eye will hold and retain in itself the image of a luminous body better than that of a shaded object4 ,the reason is that the eye is in itself perfectly dark and since two things that are alike cannot be distinguished1 therefore the night1 and other dark objects cannot be seen or recognised by the eye4 ,light is totally contrary and gives more distinctness1 and counteracts and differs from the usual darkness of the eye1 hence it leaves the impression of its image4 #ca4 ,every object we see will appear larger at midnight than at midday1 and larger in the morning than at midday4 ,this happens because the pupil of the eye is much smaller at midday than at any other time4 #cb4 ,the pupil which is largest will see objects the largest4 ,this is evident when we look at luminous bodies1 and particularly at those in the sky4 ,when the eye comes out of darkness and suddenly looks up at these bodies1 they at first appear larger and then diminish2 and if you were to look at those bodies through a small opening1 you would see them smaller still1 because a smaller part of the pupil would exercise its function4 ,footnote3 #i4 buso in the ,lomb4 dialect is the same as buco4 #cc4 ,when the eye1 coming out of darkness suddenly sees a luminous body1 it will appear much larger at first sight than after long looking at it4 ,the illuminated object will look larger and more brilliant1 when seen with two eyes than with only one4 ,a luminous object will appear smaller in size1 when the eye sees it through a smaller opening4 ,a luminous body of an oval form will appear rounder in proportion as it is farther from the eye4 #cd4 ,why when the eye has just seen the light1 does the half light look dark to it1 and in the same way if it turns from the darkness the half light look very bright8 #ce4 ,,on ,,painting4 ,if the eye1 when out of doors in the luminous atmosphere1 sees a place in shadow1 this will look very much darker than it really is4 ,this happens only because the eye when out in the air contracts the pupil in proportion as the atmosphere reflected in it is more luminous4 ,and the more the pupil contracts1 the less luminous do the objects appear that it sees4 ,but as soon as the eye enters into a shady place the darkness of the shadow suddenly seems to diminish4 ,this occurs because the greater the darkness into which the pupil goes the more its size increases1 and this increase makes the darkness seem less4 ,footnote #ad3 ,la luce entrer4 ,luce occurs here in the sense of pupil of the eye as in no #ea3 ,c4 ,a4 #hd;b2 #bde;a2 ,i--#e2 and in many other places4 #cf4 ,,on ,,perspective4 ,the eye which turns from a white object in the light of the sun and goes into a less fully lighted place will see everything as dark4 ,and this happens either because the pupils of the eyes which have rested on this brilliantly lighted white object have contracted so much that1 given at first a certain extent of surface1 they will have lost more than #c_/d of their size2 and1 lacking in size1 they are also deficient in seeing power4 ,though you might say to me3 ,a little bird 7then7 coming down would see comparatively little1 and from the smallness of his pupils the white might seem black6 ,to this ,i should reply that here we must have regard to the proportion of the mass of that portion of the brain which is given up to the sense of sight and to nothing else4 ,or--to return--this pupil in ,man dilates and contracts according to the brightness or darkness of 7surrounding7 objects2 and since it takes some time to dilate and contract1 it cannot see immediately on going out of the light and into the shade1 nor1 in the same way1 out of the shade into the light1 and this very thing has already deceived me in painting an eye1 and from that ,i learnt it4 #cg4 ,experiment showing the dilatation and contraction of the pupil1 from the motion of the sun and other luminaries4 ,in proportion as the sky is darker the stars appear of larger size1 and if you were to light up the medium these stars would look smaller2 and this difference arises solely from the pupil which dilates and contracts with the amount of light in the medium which is interposed between the eye and the luminous body4 ,let the experiment be made1 by placing a candle above your head at the same time that you look at a star2 then gradually lower the candle till it is on a level with the ray that comes from the star to the eye1 and then you will see the star diminish so much that you will almost lose sight of it4 ,footnote3 ,no reference is made in the text to the letters on the accompanying diagram4 #ch4 ,the pupil of the eye1 in the open air1 changes in size with every degree of motion from the sun2 and at every degree of its changes one and the same object seen by it will appear of a different size2 although most frequently the relative scale of surrounding objects does not allow us to detect these variations in any single object we may look at4 #ci4 ,the eye--which sees all objects reversed--retains the images for some time4 ,this conclusion is proved by the results2 because1 the eye having gazed at light retains some impression of it4 ,after looking 7at it7 there remain in the eye images of intense brightness1 that make any less brilliant spot seem dark until the eye has lost the last trace of the impression of the stronger light4 ,,ii4 ,linear ,perspective4 ,we see clearly from the concluding sentence of section #di1 where the author directly addresses the painter1 that he must certainly have intended to include the elements of mathematics in his ,book on the art of ,painting4 ,they are therefore here placed at the beginning4 ,in section #ej the theory of the ,pyramid of ,sight is distinctly and expressly put forward as the fundamental principle of linear perspective1 and sections #eb to #eg treat of it fully4 ,this theory of sight can scarcely be traced to any author of antiquity4 ,such passages as occur in ,euclid for instance1 may1 it is true1 have proved suggestive to the painters of the ,renaissance1 but it would be rash to say any thing decisive on this point4 ,leon ,battista ,alberti treats of the ,pyramid of ,sight at some length in his first ,book of ,painting2 but his explanation differs widely from ,leonardo's in the details4 ,leonardo1 like ,alberti1 may have borrowed the broad lines of his theory from some views commonly accepted among painters at the time2 but he certainly worked out its application in a perfectly original manner4 ,the axioms as to the perception of the pyramid of rays are followed by explanations of its origin1 and proofs of its universal application 7#eh--fi74 ,the author recurs to the subject with endless variations2 it is evidently of fundamental importance in his artistic theory and practice4 ,it is unnecessary to discuss how far this theory has any scientific value at the present day2 so much as this1 at any rate1 seems certain3 that from the artist's point of view it may still claim to be of immense practical utility4 ,according to ,leonardo1 on one hand1 the laws of perspective are an inalienable condition of the existence of objects in space2 on the other hand1 by a natural law1 the eye1 whatever it sees and wherever it turns1 is subjected to the perception of the pyramid of rays in the form of a minute target4 ,thus it sees objects in perspective independently of the will of the spectator1 since the eye receives the images by means of the pyramid of rays just as a magnet attracts iron4 ,in connection with this we have the function of the eye explained by the ,camera obscura1 and this is all the more interesting and important because no writer previous to ,leonardo had treated of this subject 7#gj--gc74 ,subsequent passages1 of no less special interest1 betray his knowledge of refraction and of the inversion of the image in the camera and in the eye 7#gd--hb74 ,from the principle of the transmission of the image to the eye and to the camera obscura he deduces the means of producing an artificial construction of the pyramid of rays or--which is the same thing--of the image4 ,the fundamental axioms as to the angle of sight and the vanishing point are thus presented in a manner which is as complete as it is simple and intelligible 7#hf--hi74 ,leonardo distinguishes between simple and complex perspective 7#ij1 #ia74 ,the last sections treat of the apparent size of objects at various distances and of the way to estimate it 7#ib--aji74 ,general remarks on perspective 7#dj-da74 #dj4 ,,on ,,painting4 ,perspective is the best guide to the art of ,painting4 ,footnote3 #dj4 ,compare #ec1 #b4 #da4 ,the art of perspective is of such a nature as to make what is flat appear in relief and what is in relief flat4 ,the elements of perspective--,of the ,point 7#db-df74 #db4 ,all the problems of perspective are made clear by the five terms of mathematicians1 which are3--the point1 the line1 the angle1 the superficies and the solid4 ,the point is unique of its kind4 ,and the point has neither height1 breadth1 length1 nor depth1 whence it is to be regarded as indivisible and as having no dimensions in space4 ,the line is of three kinds1 straight1 curved and sinuous and it has neither breadth1 height1 nor depth4 ,hence it is indivisible1 excepting in its length1 and its ends are two points4 ,the angle is the junction of two lines in a point4 #dc4 ,a point is not part of a line4 #dd4 ,,of ,,the ,,natural ,,point4 ,the smallest natural point is larger than all mathematical points1 and this is proved because the natural point has continuity1 and any thing that is continuous is infinitely divisible2 but the mathematical point is indivisible because it has no size4 ,footnote3 ,this definition was inserted by ,leonardo on a ,,ms4 copy on parchment of the well-known ,trattato d',architettura civile e militare c4 by ,,francesco ,,di ,,giorgio2 opposite a passage where the author says3 ',in prima he da sapere che punto quella parie della quale he nulla--,linia he luncheza senza pieza2 c4 #de4 #a1 ,the superficies is a limitation of the body4 #b1 and the limitation of a body is no part of that body4 #d1 and the limitation of one body is that which begins another4 #c1 that which is not part of any body is nothing4 ,nothing is that which fills no space4 ,if one single point placed in a circle may be the starting point of an infinite number of lines1 and the termination of an infinite number of lines1 there must be an infinite number of points separable from this point1 and these when reunited become one again2 whence it follows that the part may be equal to the whole4 #df4 ,the point1 being indivisible1 occupies no space4 ,that which occupies no space is nothing4 ,the limiting surface of one thing is the beginning of another4 #b4 ,that which is no part of any body is called nothing4 #a4 ,that which has no limitations1 has no form4 ,the limitations of two conterminous bodies are interchangeably the surface of each4 ,all the surfaces of a body are not parts of that body4 ,of the line 7#dg-dh74 #dg4 ,,definition ,,of ,,the ,,nature ,,of ,,the ,,line4 ,the line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object2 and this being its nature it occupies no space4 ,therefore an infinite number of lines may be conceived of as intersecting each other at a point1 which has no dimensions and is only of the thickness 7if thickness it may be called7 of one single line4 ,,how ,,we ,,may ,,conclude ,,that ,a ,,superficies ,,terminates ,,in ,a ,,point8 ,an angular surface is reduced to a point where it terminates in an angle4 ,or1 if the sides of that angle are produced in a straight line1 then--beyond that angle--another surface is generated1 smaller1 or equal to1 or larger than the first4 #dh4 ,,of ,,drawing ,,outline4 ,consider with the greatest care the form of the outlines of every object1 and the character of their undulations4 ,and these undulations must be separately studied1 as to whether the curves are composed of arched convexities or angular concavities4 #di4 ,the nature of the outline4 ,the boundaries of bodies are the least of all things4 ,the proposition is proved to be true1 because the boundary of a thing is a surface1 which is not part of the body contained within that surface2 nor is it part of the air surrounding that body1 but is the medium interposted between the air and the body1 as is proved in its place4 ,but the lateral boundaries of these bodies is the line forming the boundary of the surface1 which line is of invisible thickness4 ,wherefore ,o painter6 do not surround your bodies with lines1 and above all when representing objects smaller than nature2 for not only will their external outlines become indistinct1 but their parts will be invisible from distance4 #ej4 ,definition of ,perspective4 ,drawing is based upon perspective1 which is nothing else than a thorough knowledge of the function of the eye4 ,and this function simply consists in receiving in a pyramid the forms and colours of all the objects placed before it4 ,i say in a pyramid1 because there is no object so small that it will not be larger than the spot where these pyramids are received into the eye4 ,therefore1 if you extend the lines from the edges of each body as they converge you will bring them to a single point1 and necessarily the said lines must form a pyramid4 ,perspective is nothing more than a rational demonstration applied to the consideration of how objects in front of the eye transmit their image to it1 by means of a pyramid of lines4 ,the ,pyramid is the name ,i apply to the lines which1 starting from the surface and edges of each object1 converge from a distance and meet in a single point4 ,perspective is a rational demonstration1 by which we may practically and clearly understand how objects transmit their own image1 by lines forming a ,pyramid 7centred7 in the eye4 ,perspective is a rational demonstration by which experience confirms that every object sends its image to the eye by a pyramid of lines2 and bodies of equal size will result in a pyramid of larger or smaller size1 according to the difference in their distance1 one from the other4 ,by a pyramid of lines ,i mean those which start from the surface and edges of bodies1 and1 converging from a distance meet in a single point4 ,a point is said to be that which having no dimensions cannot be divided1 and this point placed in the eye receives all the points of the cone4 ,footnote3 #ej4 #a-e4 ,compare with this the ,proem4 ,no4 #ba4 ,the paragraphs placed in brackets3 lines #a-i1 #aj-ad1 and #ag--bj1 are evidently mere sketches and1 as such1 were cancelled by the writer2 but they serve as a commentary on the final paragraph1 lines #bb-bi4 #ea4 ,,in ,,what ,,way ,,the ,,eye ,,sees ,,objects ,,placed ,,in ,,front ,,of ,,it4 ,the perception of the object depends on the direction of the eye4 ,supposing that the ball figured above is the ball of the eye and let the small portion of the ball which is cut off by the line s t be the pupil and all the objects mirrored on the centre of the face of the eye1 by means of the pupil1 pass on at once and enter the pupil1 passing through the crystalline humour1 which does not interfere in the pupil with the things seen by means of the light4 ,and the pupil having received the objects1 by means of the light1 immediately refers them and transmits them to the intellect by the line a b4 ,and you must know that the pupil transmits nothing perfectly to the intellect or common sense excepting when the objects presented to it by means of light1 reach it by the line a b2 as1 for instance1 by the line b c4 ,for although the lines m n and f g may be seen by the pupil they are not perfectly taken in1 because they do not coincide with the line a b4 ,and the proof is this3 ,if the eye1 shown above1 wants to count the letters placed in front1 the eye will be obliged to turn from letter to letter1 because it cannot discern them unless they lie in the line a b2 as1 for instance1 in the line a c4 ,all visible objects reach the eye by the lines of a pyramid1 and the point of the pyramid is the apex and centre of it1 in the centre of the pupil1 as figured above4 ,footnote3 #ea4 ,in this problem the eye is conceived of as fixed and immovable2 this is plain from line #aa4 ,experimental proof of the existence of the pyramid of sight 7#eb-ee74 #eb4 ,perspective is a rational demonstration1 confirmed by experience1 that all objects transmit their image to the eye by a pyramid of lines4 ,by a pyramid of lines ,i understand those lines which start from the edges of the surface of bodies1 and converging from a distance1 meet in a single point2 and this point1 in the present instance1 ,i will show to be situated in the eye which is the universal judge of all objects4 ,by a point ,i mean that which cannot be divided into parts2 therefore this point1 which is situated in the eye1 being indivisible1 no body is seen by the eye1 that is not larger than this point4 ,this being the case it is inevitable that the lines which come from the object to the point must form a pyramid4 ,and if any man seeks to prove that the sense of sight does not reside in this point1 but rather in the black spot which is visible in the middle of the pupil1 ,i might reply to him that a small object could never diminish at any distance1 as it might be a grain of millet or of oats or of some similar thing1 and that object1 if it were larger than the said black spot would never be seen as a whole2 as may be seen in the diagram below4 ,let a4 be the seat of sight1 b e the lines which reach the eye4 ,let e d be the grains of millet within these lines4 ,you plainly see that these will never diminish by distance1 and that the body m n could not be entirely covered by it4 ,therefore you must confess that the eye contains within itself one single indivisible point a1 to which all the points converge of the pyramid of lines starting from an object1 as is shown below4 ,let a4 b4 be the eye2 in the centre of it is the point above mentioned4 ,if the line e f is to enter as an image into so small an opening in the eye1 you must confess that the smaller object cannot enter into what is smaller than itself unless it is diminished1 and by diminishing it must take the form of a pyramid4 #ec4 ,,perspective4 ,perspective comes in where judgment fails as to the distance in objects which diminish4 ,the eye can never be a true judge for determining with exactitude how near one object is to another which is equal to it in size1 if the top of that other is on the level of the eye which sees them on that side1 excepting by means of the vertical plane which is the standard and guide of perspective4 ,let n be the eye1 e f the vertical plane above mentioned4 ,let a b c d be the three divisions1 one below the other2 if the lines a n and c n are of a given length and the eye n is in the centre1 then a b will look as large as b c4 c d is lower and farther off from n1 therefore it will look smaller4 ,and the same effect will appear in the three divisions of a face when the eye of the painter who is drawing it is on a level with the eye of the person he is painting4 #ed4 ,,to ,,prove ,,how ,,objects ,,reach ,,the ,,eye4 ,if you look at the sun or some other luminous body and then shut your eyes you will see it again inside your eye for a long time4 ,this is evidence that images enter into the eye4 ,the relations of the distance points to the vanishing point 7#ee-ef74 #ee4 ,,elements ,,of ,,perspective4 ,all objects transmit their image to the eye in pyramids1 and the nearer to the eye these pyramids are intersected the smaller will the image appear of the objects which cause them4 ,therefore1 you may intersect the pyramid with a vertical plane ,footnote #d3 ,pariete4 ,compare the definitions in #he1 #b-e1 #f-bg4 ,these lines refer exclusively to the third diagram4 ,for the better understanding of this it should be observed that c s must be regarded as representing the section or profile of a square plane1 placed horizontally 7comp4 lines #aa1 #ad1 #ag7 for which the word pianura is subsequently employed 7#bj1 #bb74 ,lines #f-ac contain certain preliminary observations to guide the reader in understanding the diagram2 the last three seem to have been added as a supplement4 ,leonardo's mistake in writing t denota 7line #f7 for f denota has been rectified4 which reaches the base of the pyramid as is shown in the plane a n4 ,the eye f and the eye t are one and the same thing2 but the eye f marks the distance1 that is to say how far you are standing from the object2 and the eye t shows you the direction of it2 that is whether you are opposite1 or on one side1 or at an angle to the object you are looking at4 ,and remember that the eye f and the eye t must always be kept on the same level4 ,for example if you raise or lower the eye from the distance point f you must do the same with the direction point t4 ,and if the point f shows how far the eye is distant from the square plane but does not show on which side it is placed--and1 if in the same way1 the point t show s the direction and not the distance1 in order to ascertain both you must use both points and they will be one and the same thing4 ,if the eye f could see a perfect square of which all the sides were equal to the distance between s and c1 and if at the nearest end of the side towards the eye a pole were placed1 or some other straight object1 set up by a perpendicular line as shown at r s--then1 ,i say1 that if you were to look at the side of the square that is nearest to you it will appear at the bottom of the vertical plane r s1 and then look at the farther side and it would appear to you at the height of the point n on the vertical plane4 ,thus1 by this example1 you can understand that if the eye is above a number of objects all placed on the same level1 one beyond another1 the more remote they are the higher they will seem1 up to the level of the eye1 but no higher2 because objects placed upon the level on which your feet stand1 so long as it is flat--even if it be extended into infinity--would never be seen above the eye2 since the eye has in itself the point towards which all the cones tend and converge which convey the images of the objects to the eye4 ,and this point always coincides with the point of diminution which is the extreme of all we can see4 ,and from the base line of the first pyramid as far as the diminishing point ,footnote3 ,the two diagrams above the chapter are explained by the first five lines4 ,they have1 however1 more letters than are referred to in the text1 a circumstance we frequently find occasion to remark4 #ef4 there are only bases without pyramids which constantly diminish up to this point4 ,and from the first base where the vertical plane is placed towards the point in the eye there will be only pyramids without bases2 as shown in the example given above4 ,now1 let a b be the said vertical plane and r the point of the pyramid terminating in the eye1 and n the point of diminution which is always in a straight line opposite the eye and always moves as the eye moves--just as when a rod is moved its shadow moves1 and moves with it1 precisely as the shadow moves with a body4 ,and each point is the apex of a pyramid1 all having a common base with the intervening vertical plane4 ,but although their bases are equal their angles are not equal1 because the diminishing point is the termination of a smaller angle than that of the eye4 ,if you ask me3 ,by what practical experience can you show me these points8 ,i reply--so far as concerns the diminishing point which moves with you --when you walk by a ploughed field look at the straight furrows which come down with their ends to the path where you are walking1 and you will see that each pair of furrows will look as though they tried to get nearer and meet at the farther end4 ,footnote3 ,for the easier understanding of the diagram and of its connection with the preceding ,i may here remark that the square plane shown above in profile by the line c s is here indicated by e d o p4 ,according to lines #a1 #c a b must be imagined as a plane of glass placed perpendicularly at o p4 #eg4 ,how to measure the pyramid of vision4 ,as regards the point in the eye2 it is made more intelligible by this3 ,if you look into the eye of another person you will see your own image4 ,now imagine #b lines starting from your ears and going to the ears of that image which you see in the other man's eye2 you will understand that these lines converge in such a way that they would meet in a point a little way beyond your own image mirrored in the eye4 ,and if you want to measure the diminution of the pyramid in the air which occupies the space between the object seen and the eye1 you must do it according to the diagram figured below4 ,let m n be a tower1 and e f a1 rod1 which you must move backwards and forwards till its ends correspond with those of the tower ,footnote #i3 ,i sua stremi 44 della storre 7its ends 444 of the tower7 this is the case at e f42 then bring it nearer to the eye1 at c d and you will see that the image of the tower seems smaller1 as at r o4 ,then again bring it closer to the eye and you will see the rod project far beyond the image of the tower from a to b and from t to b1 and so you will discern that1 a little farther within1 the lines must converge in a point4 ,the ,production of pyramid of ,vision 7#eh-fj74 #eh4 ,,perspective4 ,the instant the atmosphere is illuminated it will be filled with an infinite number of images which are produced by the various bodies and colours assembled in it4 ,and the eye is the target1 a loadstone1 of these images4 #ei4 ,the whole surface of opaque bodies displays its whole image in all the illuminated atmosphere which surrounds them on all sides4 #fj4 ,that the atmosphere attracts to itself1 like a loadstone1 all the images of the objects that exist in it1 and not their forms merely but their nature may be clearly seen by the sun1 which is a hot and luminous body4 ,all the atmosphere1 which is the all-pervading matter1 absorbs light and heat1 and reflects in itself the image of the source of that heat and splendour and1 in each minutest portion1 does the same4 ,the ,northpole does the same as the loadstone shows2 and the moon and the other planets1 without suffering any diminution1 do the same4 ,among terrestrial things musk does the same and other perfumes4 #fa4 ,all bodies together1 and each by itself1 give off to the surrounding air an infinite number of images which are all-pervading and each complete1 each conveying the nature1 colour and form of the body which produces it4 ,it can clearly be shown that all bodies are1 by their images1 all-pervading in the surrounding atmosphere1 and each complete in itself as to substance form and colour2 this is seen by the images of the various bodies which are reproduced in one single perforation through which they transmit the objects by lines which intersect and cause reversed pyramids1 from the objects1 so that they are upside down on the dark plane where they are first reflected4 ,the reason of this is-- ,footnote3 ,the diagram intended to illustrate the statement 7,pl4 ,,ii ,no4 i7 occurs in the original between lines #c and #d4 ,the three circles must be understood to represent three luminous bodies which transmit their images through perforations in a wall into a dark chamber1 according to a law which is more fully explained in #ge8ha4 ,so far as concerns the present passage the diagram is only intended to explain that the images of the three bodies may be made to coalesce at any given spot4 ,in the circles are written1 giallo--yellow1 bicho--white1 rosso--red4 ,the text breaks off at line #h4 ,the paragraph ,no4#dj follows here in the original ,,ms4 #fb4 ,every point is the termination of an infinite number of lines1 which diverge to form a base1 and immediately1 from the base the same lines converge to a pyramid imaging both the colour and form4 ,no sooner is a form created or compounded than suddenly infinite lines and angles are produced from it2 and these lines1 distributing themselves and intersecting each other in the air1 give rise to an infinite number of angles opposite to each other4 ,given a base1 each opposite angle1 will form a triangle having a form and proportion equal to the larger angle2 and if the base goes twice into each of the #b lines of the pyramid the smaller triangle will do the same4 #fc4 ,every body in light and shade fills the surrounding air with infinite images of itself2 and these1 by infinite pyramids diffused in the air1 represent this body throughout space and on every side4 ,each pyramid that is composed of a long assemblage of rays includes within itself an infinite number of pyramids and each has the same power as all1 and all as each4 ,a circle of equidistant pyramids of vision will give to their object angles of equal size2 and an eye at each point will see the object of the same size4 ,the body of the atmosphere is full of infinite pyramids composed of radiating straight lines1 which are produced from the surface of the bodies in light and shade1 existing in the air2 and the farther they are from the object which produces them the more acute they become and although in their distribution they intersect and cross they never mingle together1 but pass through all the surrounding air1 independently converging1 spreading1 and diffused4 ,and they are all of equal power and value2 all equal to each1 and each equal to all4 ,by these the images of objects are transmitted through all space and in every direction1 and each pyramid1 in itself1 includes1 in each minutest part1 the whole form of the body causing it4 #fd4 ,the body of the atmosphere is full of infinite radiating pyramids produced by the objects existing in it4 ,these intersect and cross each other with independent convergence without interfering with each other and pass through all the surrounding atmosphere2 and are of equal force and value--all being equal to each1 each to all4 ,and by means of these1 images of the body are transmitted everywhere and on all sides1 and each receives in itself every minutest portion of the object that produces it4 ,proof by experiment 7#fe-ff74 #fe4 ,,perspective4 ,the air is filled with endless images of the objects distributed in it2 and all are represented in all1 and all in one1 and all in each1 whence it happens that if two mirrors are placed in such a manner as to face each other exactly1 the first will be reflected in the second and the second in the first4 ,the first being reflected in the second takes to it the image of itself with all the images represented in it1 among which is the image of the second mirror1 and so1 image within image1 they go on to infinity in such a manner as that each mirror has within it a mirror1 each smaller than the last and one inside the other4 ,thus1 by this example1 it is clearly proved that every object sends its image to every spot whence the object itself can be seen2 and the converse3 ,that the same object may receive in itself all the images of the objects that are in front of it4 ,hence the eye transmits through the atmosphere its own image to all the objects that are in front of it and receives them into itself1 that is to say on its surface1 whence they are taken in by the common sense1 which considers them and if they are pleasing commits them to the memory4 ,whence ,i am of opinion3 ,that the invisible images in the eyes are produced towards the object1 as the image of the object to the eye4 ,that the images of the objects must be disseminated through the air4 ,an instance may be seen in several mirrors placed in a circle1 which will reflect each other endlessly4 ,when one has reached the other it is returned to the object that produced it1 and thence--being diminished--it is returned again to the object and then comes back once more1 and this happens endlessly4 ,if you put a light between two flat mirrors with a distance of #a braccio between them you will see in each of them an infinite number of lights1 one smaller than another1 to the last4 ,if at night you put a light between the walls of a room1 all the parts of that wall will be tinted with the image of that light4 ,and they will receive the light and the light will fall on them1 mutually1 that is to say1 when there is no obstacle to interrupt the transmission of the images4 ,this same example is seen in a greater degree in the distribution of the solar rays which all together1 and each by itself1 convey to the object the image of the body which causes it4 ,that each body by itself alone fills with its images the atmosphere around it1 and that the same air is able1 at the same time1 to receive the images of the endless other objects which are in it1 this is clearly proved by these examples4 ,and every object is everywhere visible in the whole of the atmosphere1 and the whole in every smallest part of it2 and all the objects in the whole1 and all in each smallest part2 each in all and all in every part4 #ff4 ,the images of objects are all diffused through the atmosphere which receives them2 and all on every side in it4 ,to prove this1 let a c e be objects of which the images are admitted to a dark chamber by the small holes n p and thrown upon the plane f i opposite to these holes4 ,as many images will be produced in the chamber on the plane as the number of the said holes4 #fg4 ,general conclusions4 ,all objects project their whole image and likeness1 diffused and mingled in the whole of the atmosphere1 opposite to themselves4 ,the image of every point of the bodily surface1 exists in every part of the atmosphere4 ,all the images of the objects are in every part of the atmosphere4 ,the whole1 and each part of the image of the atmosphere is reflected in each point of the surface of the bodies presented to it4 ,therefore both the part and the whole of the images of the objects exist1 both in the whole and in the parts of the surface of these visible bodies4 ,whence we may evidently say that the image of each object exists1 as a whole and in every part1 in each part and in the whole interchangeably in every existing body4 ,as is seen in two mirrors placed opposite to each other4 #fh4 ,that the contrary is impossible4 ,it is impossible that the eye should project from itself1 by visual rays1 the visual virtue1 since1 as soon as it opens1 that front portion of the eye which would give rise to this emanation would have to go forth to the object and this it could not do without time4 ,and this being so1 it could not travel so high as the sun in a month's time when the eye wanted to see it4 ,and if it could reach the sun it would necessarily follow that it should perpetually remain in a continuous line from the eye to the sun and should always diverge in such a way as to form between the sun and the eye the base and the apex of a pyramid4 ,this being the case1 if the eye consisted of a million worlds1 it would not prevent its being consumed in the projection of its virtue2 and if this virtue would have to travel through the air as perfumes do1 the winds would bent it and carry it into another place4 ,but we do in fact see the mass of the sun with the same rapidity as an object at the distance of a braccio1 and the power of sight is not disturbed by the blowing of the winds nor by any other accident4 ,footnote3 ,the view here refuted by ,leonardo was maintained among others by ,bramantino1 ,leonardo's ,milanese contemporary4 ,,lomazzo writes as follows in his ,trattato dell' ,arte della pittura c4 7,milano #aehd4 ,libr4 ,v cp4 ,,xxi73 ,sovviemmi di aver gi letto in certi scritti alcune cose di ,bramantino milanese1 celebratissimo pittore1 attenente alla prospettiva1 le quali ho voluto riferire1 e quasi intessere in questo luogo1 affinch sappiamo qual fosse l'opinione di cosi chiaro e famoso pittore intorno alla prospettiva 4 4 ,scrive ,bramantino che la prospettiva una cosa che contraf il naturale1 e che ci si fa in tre modi ,circa il primo modo che si fa con ragione1 per essere la cosa in poche parole conclusa da ,bramantino in maniera che giudico non potersi dir meglio1 contenendovi si tutta ,parte del principio al fine1 io riferir per appunto le proprie parole sue 7cp4 ,,xxii1 ,prima prospettiva di ,bramantino74 ,la prima prospettiva fa le cose di punto1 e l'altra non mai1 e la terza pi appresso4 ,adunque la prima si dimanda prospettiva1 cio ragione1 la quale fa l'effetto dell' occhio1 facendo crescere e calare secondo gli effetti degli occhi4 ,questo crescere e calare non procede della cosa propria1 che in se per esser lontana1 ovvero vicina1 per quello effetto non pu crescere e sminuire1 ma procede dagli effetti degli occhi1 i quali sono piccioli1 e perci volendo vedere tanto gran cosa1 bisogna che mandino fuora la virt visiva1 la quale si dilata in tanta larghezza1 che piglia tutto quello che vuoi vedere1 ed arrivando a quella cosa la vede dove 3 e da lei agli occhi per quello circuito fino all' occhio1 e tutto quello termine pieno di quella cosa4 ,it is worthy of note that ,leonardo had made his memorandum refuting this view1 at ,milan in #adib #fi4 ,a parallel case4 ,just as a stone flung into the water becomes the centre and cause of many circles1 and as sound diffuses itself in circles in the air3 so any object1 placed in the luminous atmosphere1 diffuses itself in circles1 and fills the surrounding air with infinite images of itself4 ,and is repeated1 the whole every-where1 and the whole in every smallest part4 ,this can be proved by experiment1 since if you shut a window that faces west and make a hole ,footnote3 #f4 ,here the text breaks off4 4 4 ,footnote3 ,compare ,,libri1 ,histoire des sciences mathmatiques en ,italie4 ,tome ,,iii1 p4 #dc4 ,the function of the eye as explained by the camera obscura 7#gj4 #ga74 #gj4 ,if the object in front of the eye sends its image to the eye1 the eye1 on the other hand1 sends its image to the object1 and no portion whatever of the object is lost in the images it throws off1 for any reason either in the eye or the object4 ,therefore we may rather believe it to be the nature and potency of our luminous atmosphere which absorbs the images of the objects existing in it1 than the nature of the objects1 to send their images through the air4 ,if the object opposite to the eye were to send its image to the eye1 the eye would have to do the same to the object1 whence it might seem that these images were an emanation4 ,but1 if so1 it would be necessary to admit that every object became rapidly smaller2 because each object appears by its images in the surrounding atmosphere4 ,that is3 the whole object in the whole atmosphere1 and in each part2 and all the objects in the whole atmosphere and all of them in each part2 speaking of that atmosphere which is able to contain in itself the straight and radiating lines of the images projected by the objects4 ,from this it seems necessary to admit that it is in the nature of the atmosphere1 which subsists between the objects1 and which attracts the images of things to itself like a loadstone1 being placed between them4 ,,prove ,,how ,,all ,,objects1 ,,placed ,,in ,,one ,,position1 ,,are ,,all ,,everywhere ,,and ,,all ,,in ,,each ,,part4 ,i say that if the front of a building--or any open piazza or field--which is illuminated by the sun has a dwelling opposite to it1 and if1 in the front which does not face the sun1 you make a small round hole1 all the illuminated objects will project their images through that hole and be visible inside the dwelling on the opposite wall which may be made white2 and there1 in fact1 they will be upside down1 and if you make similar openings in several places in the same wall you will have the same result from each4 ,hence the images of the illuminated objects are all everywhere on this wall and all in each minutest part of it4 ,the reason1 as we clearly know1 is that this hole must admit some light to the said dwelling1 and the light admitted by it is derived from one or many luminous bodies4 ,if these bodies are of various colours and shapes the rays forming the images are of various colours and shapes1 and so will the representations be on the wall4 ,footnote3 #gj4 #ae--bc4 ,this section has already been published in the ,saggio delle ,opere di ,leonardo da ,vinci ,milan #ahgb1 pp4 #ac1 #ad4 ,g4 ,govi observes upon it1 that ,leonardo is not to be regarded as the inventor of the ,camera obscura1 but that he was the first to explain by it the structure of the eye4 ,an account of the ,camera obscura first occurs in ,,cesare ,,cesarini's ,italian version of ,vitruvius1 pub4 #aebc1 four years after ,leonardo's death4 ,cesarini expressly names ,benedettino ,don ,papnutio as the inventor of the ,camera obscura4 ,in his explanation of the function of the eye by a comparison with the ,camera obscura ,leonardo was the precursor of ,g4 ,,cardano1 ,professor of ,medicine at ,bologna 7died #aegf7 and it appears highly probable that this is1 in fact1 the very discovery which ,leonardo ascribes to himself in section #ba without giving any further details4 #ga4 ,,how ,,the ,,images ,,of ,,objects ,,received ,,by ,,the ,,eye ,,intersect ,,within ,,the ,,crystalline ,,humour ,,of ,,the ,,eye4 ,an experiment1 showing how objects transmit their images or pictures1 intersecting within the eye in the crystalline humour1 is seen when by some small round hole penetrate the images of illuminated objects into a very dark chamber4 ,then1 receive these images on a white paper placed within this dark room and rather near to the hole and you will see all the objects on the paper in their proper forms and colours1 but much smaller2 and they will be upside down by reason of that very intersection4 ,these images being transmitted from a place illuminated by the sun will seem actually painted on this paper which must be extremely thin and looked at from behind4 ,and let the little perforation be made in a very thin plate of iron4 ,let a b e d e be the object illuminated by the sun and o r the front of the dark chamber in which is the said hole at n m4 ,let s t be the sheet of paper intercepting the rays of the images of these objects upside down1 because the rays being straight1 a on the right hand becomes k on the left1 and e on the left becomes f on the right2 and the same takes place inside the pupil4 ,footnote3 ,this chapter is already known through a translation into ,french by ,,venturi4 ,compare his ',essai sur les ouvrages physico-mathmatiques de ,l4 da ,vinci avec des fragments tirs de ses ,manuscrits1 apports de l',italie4 ,lu a la premiere classe de l',institut national des ,sciences et ,arts4' ,paris1 ,an ,v 7#agig74 ,the practice of perspective 7#gb4 #gc74 #gb4 ,in the practice of perspective the same rules apply to light and to the eye4 #gc4 ,the object which is opposite to the pupil of the eye is seen by that pupil and that which is opposite to the eye is seen by the pupil4 ,refraction of the rays falling upon the eye 7#gd4 #ge7 #gd4 ,the lines sent forth by the image of an object to the eye do not reach the point within the eye in straight lines4 #ge4 ,if the judgment of the eye is situated within it1 the straight lines of the images are refracted on its surface because they pass through the rarer to the denser medium4 ,if1 when you are under water1 you look at objects in the air you will see them out of their true place2 and the same with objects under water seen from the air4 ,the intersection of the rays 7#gf-hb74 #gf4 ,the inversion of the images4 ,all the images of objects which pass through a window glass pane from the free outer air to the air confined within walls1 are seen on the opposite side2 and an object which moves in the outer air from east to west will seem in its shadow1 on the wall which is lighted by this confined air1 to have an opposite motion4 #gg4 ,,the ,,principle ,,on ,,which ,,the ,,images ,,of ,,bodies ,,pass ,,in ,,between ,,the ,,margins ,,of ,,the ,,openings ,,by ,,which ,,they ,,enter4 ,what difference is there in the way in which images pass through narrow openings and through large openings1 or in those which pass by the sides of shaded bodies8 ,by moving the edges of the opening through which the images are admitted1 the images of immovable objects are made to move4 ,and this happens1 as is shown in the #ith which demonstrates3 ,footnote #aa3 per la #i;a che dicie4 ,when ,leonardo refers thus to a number it serves to indicate marginal diagrams2 this can in some instances be distinctly proved4 ,the ninth sketch on the page ,w4 ,l4 #ade b corresponds to the middle sketch of the three reproduced4 the images of any object are all everywhere1 and all in each part of the surrounding air4 ,it follows that if one of the edges of the hole by which the images are admitted to a dark chamber is moved it cuts off those rays of the image that were in contact with it and gets nearer to other rays which previously were remote from it c4 ,,of ,,the ,,movement ,,of ,,the ,,edge ,,at ,,the ,,right ,,or ,,left1 ,,or ,,the ,,upper1 ,,or ,,lower ,,edge4 ,if you move the right side of the opening the image on the left will move being that of the object which entered on the right side of the opening2 and the same result will happen with all the other sides of the opening4 ,this can be proved by the #bnd of this which shows3 all the rays which convey the images of objects through the air are straight lines4 ,hence1 if the images of very large bodies have to pass through very small holes1 and beyond these holes recover their large size1 the lines must necessarily intersect4 ,footnote3 #gg4 #b4 ,in the first of the three diagrams ,leonardo had drawn only one of the two margins1 et m4 #gh4 ,necessity has provided that all the images of objects in front of the eye shall intersect in two places4 ,one of these intersections is in the pupil1 the other in the crystalline lens2 and if this were not the case the eye could not see so great a number of objects as it does4 ,this can be proved1 since all the lines which intersect do so in a point4 ,because nothing is seen of objects excepting their surface2 and their edges are lines1 in contradistinction to the definition of a surface4 ,and each minute part of a line is equal to a point2 for smallest is said of that than which nothing can be smaller1 and this definition is equivalent to the definition of the point4 ,hence it is possible for the whole circumference of a circle to transmit its image to the point of intersection1 as is shown in the #dth of this which shows3 all the smallest parts of the images cross each other without interfering with each other4 ,these demonstrations are to illustrate the eye4 ,no image1 even of the smallest object1 enters the eye without being turned upside down2 but as it penetrates into the crystalline lens it is once more reversed and thus the image is restored to the same position within the eye as that of the object outside the eye4 #gi4 ,,of ,,the ,,central ,,line ,,of ,,the ,,eye4 ,only one line of the image1 of all those that reach the visual virtue1 has no intersection2 and this has no sensible dimensions because it is a mathematical line which originates from a mathematical point1 which has no dimensions4 ,according to my adversary1 necessity requires that the central line of every image that enters by small and narrow openings into a dark chamber shall be turned upside down1 together with the images of the bodies that surround it4 #hj4 ,,as ,,to ,,whether ,,the ,,central ,,line ,,of ,,the ,,image ,,can ,,be ,,intersected1 ,,or ,,not1 ,,within ,,the ,,opening4 ,it is impossible that the line should intersect itself2 that is1 that its right should cross over to its left side1 and so1 its left side become its right side4 ,because such an intersection demands two lines1 one from each side2 for there can be no motion from right to left or from left to right in itself without such extension and thickness as admit of such motion4 ,and if there is extension it is no longer a line but a surface1 and we are investigating the properties of a line1 and not of a surface4 ,and as the line1 having no centre of thickness cannot be divided1 we must conclude that the line can have no sides to intersect each other4 ,this is proved by the movement of the line a f to a b and of the line e b to e f1 which are the sides of the surface a f e b4 ,but if you move the line a b and the line e f1 with the frontends a e1 to the spot c1 you will have moved the opposite ends f b towards each other at the point d4 ,and from the two lines you will have drawn the straight line c d which cuts the middle of the intersection of these two lines at the point n without any intersection4 ,for1 you imagine these two lines as having breadth1 it is evident that by this motion the first will entirely cover the other--being equal with it--without any intersection1 in the position c d4 ,and this is sufficient to prove our proposition4 #ha4 ,,how ,,the ,,innumerable ,,rays ,,from ,,innumerable ,,images ,,can ,,converge ,,to ,a ,,point4 ,just as all lines can meet at a point without interfering with each other--being without breadth or thickness--in the same way all the images of surfaces can meet there2 and as each given point faces the object opposite to it and each object faces an opposite point1 the converging rays of the image can pass through the point and diverge again beyond it to reproduce and re-magnify the real size of that image4 ,but their impressions will appear reversed--as is shown in the first1 above2 where it is said that every image intersects as it enters the narrow openings made in a very thin substance4 ,read the marginal text on the other side4 ,in proportion as the opening is smaller than the shaded body1 so much less will the images transmitted through this opening intersect each other4 ,the sides of images which pass through openings into a dark room intersect at a point which is nearer to the opening in proportion as the opening is narrower4 ,to prove this let a b be an object in light and shade which sends not its shadow but the image of its darkened form through the opening d e which is as wide as this shaded body2 and its sides a b1 being straight lines 7as has been proved7 must intersect between the shaded object and the opening2 but nearer to the opening in proportion as it is smaller than the object in shade4 ,as is shown1 on your right hand and your left hand1 in the two diagrams a b c n m o where1 the right opening d e1 being equal in width to the shaded object a b1 the intersection of the sides of the said shaded object occurs half way between the opening and the shaded object at the point c4 ,but this cannot happen in the left hand figure1 the opening o being much smaller than the shaded object n m4 ,it is impossible that the images of objects should be seen between the objects and the openings through which the images of these bodies are admitted2 and this is plain1 because where the atmosphere is illuminated these images are not formed visibly4 ,when the images are made double by mutually crossing each other they are invariably doubly as dark in tone4 ,to prove this let d e h be such a doubling which although it is only seen within the space between the bodies in b and i this will not hinder its being seen from f g or from f m2 being composed of the images a b i k which run together in d e h4 ,footnote3 #ha4 ,on the original diagram at the beginning of this chapter ,leonardo has written azurro 7blue7 where in the facsimile ,i have marked ,a1 and giallo 7yellow7 where ,b stands4 ,footnote3 #ae--bc4 ,these lines stand between the diagrams ,i and ,,iii4 ,footnote3 #bd--ec4 ,these lines stand between the diagrams ,i and ,,ii4 ,footnote3 #ed--ig are written along the left side of diagram ,i4 #hb4 ,an experiment showing that though the pupil may not be moved from its position the objects seen by it may appear to move from their places4 ,if you look at an object at some distance from you and which is below the eye1 and fix both your eyes upon it and with one hand firmly hold the upper lid open while with the other you push up the under lid--still keeping your eyes fixed on the object gazed at--you will see that object double2 one image remaining steady1 and the other moving in a contrary direction to the pressure of your finger on the lower eyelid4 ,how false the opinion is of those who say that this happens because the pupil of the eye is displaced from its position4 ,how the above mentioned facts prove that the pupil acts upside down in seeing4 ,footnote3 #hb4 #ad--ag4 ,the subject indicated by these two headings is fully discussed in the two chapters that follow them in the original2 but it did not seem to me appropriate to include them here4 ,demostration of perspective by means of a vertical glass plane 7#hc-he74 #hc4 ,,of ,,the ,,plane ,,of ,,glass4 ,perspective is nothing else than seeing place or objects behind a plane of glass1 quite transparent1 on the surface of which the objects behind that glass are to be drawn4 ,these can be traced in pyramids to the point in the eye1 and these pyramids are intersected on the glass plane4 #hd4 ,pictorial perspective can never make an object at the same distance1 look of the same size as it appears to the eye4 ,you see that the apex of the pyramid f c d is as far from the object c d as the same point f is from the object a b2 and yet c d1 which is the base made by the painter's point1 is smaller than a b which is the base of the lines from the objects converging in the eye and refracted at s t1 the surface of the eye4 ,this may be proved by experiment1 by the lines of vision and then by the lines of the painter's plumbline by cutting the real lines of vision on one and the same plane and measuring on it one and the same object4 #he4 ,,perspective4 ,the vertical plane is a perpendicular line1 imagined as in front of the central point where the apex of the pyramids converge4 ,and this plane bears the same relation to this point as a plane of glass would1 through which you might see the various objects and draw them on it4 ,and the objects thus drawn would be smaller than the originals1 in proportion as the distance between the glass and the eye was smaller than that between the glass and the objects4 ,,perspective4 ,the different converging pyramids produced by the objects1 will show1 on the plane1 the various sizes and remoteness of the objects causing them4 ,,perspective4 ,all those horizontal planes of which the extremes are met by perpendicular lines forming right angles1 if they are of equal width the more they rise to the level of eye the less this is seen1 and the more the eye is above them the more will their real width be seen4 ,,perspective4 ,the farther a spherical body is from the eye the more you will see of it4 ,the angle of sight varies with the distance 7#hf-hh7 #hf4 ,a simple and natural method2 showing how objects appear to the eye without any other medium4 ,the object that is nearest to the eye always seems larger than another of the same size at greater distance4 ,the eye m1 seeing the spaces o v x1 hardly detects the difference between them1 and the4 reason of this is that it is close to them ,footnote #f3 ,it is quite inconceivable to me why ,m4 ,,ravaisson1 in a note to his ,french translation of this simple passage should have remarked3 ,il est clair que c'est par erreur que ,leonard a crit per esser visino au lieu de per non esser visino4 7,see his printed ed4 of ,,ms4 ,a4 p4 #ch472 but if these spaces are marked on the vertical plane n o the space o v will be seen at o r1 and in the same way the space v x will appear at r q4 ,and if you carry this out in any place where you can walk round1 it will look out of proportion by reason of the great difference in the spaces o r and r q4 ,and this proceeds from the eye being so much below near the plane that the plane is foreshortened4 ,hence1 if you wanted to carry it out1 you would have to arrange to see the perspective through a single hole which must be at the point m1 or else you must go to a distance of at least #c times the height of the object you see4 ,the plane o p being always equally remote from the eye will reproduce the objects in a satisfactory way1 so that they may be seen from place to place4 #hg4 ,how every large mass sends forth its images1 which may diminish through infinity4 ,the images of any large mass being infinitely divisible may be infinitely diminished4 #hh4 ,objects of equal size1 situated in various places1 will be seen by different pyramids which will each be smaller in proportion as the object is farther off4 #hi4 ,perspective1 in dealing with distances1 makes use of two opposite pyramids1 one of which has its apex in the eye and the base as distant as the horizon4 ,the other has the base towards the eye and the apex on the horizon4 ,now1 the first includes the visible universe1 embracing all the mass of the objects that lie in front of the eye2 as it might be a vast landscape seen through a very small opening2 for the more remote the objects are from the eye1 the greater number can be seen through the opening1 and thus the pyramid is constructed with the base on the horizon and the apex in the eye1 as has been said4 ,the second pyramid is extended to a spot which is smaller in proportion as it is farther from the eye2 and this second perspective pyramid results from the first4 #ij4 ,,simple ,,perspective4 ,simple perspective is that which is constructed by art on a vertical plane which is equally distant from the eye in every part4 ,complex perspective is that which is constructed on a ground-plan in which none of the parts are equally distant from the eye4 #ia4 ,,perspective4 ,no surface can be seen exactly as it is1 if the eye that sees it is not equally remote from all its edges4 #ib4 ,,why ,,when ,,an ,,object ,,is ,,placed ,,close ,,to ,,the ,,eye ,,its ,,edges ,,are ,,indistinct4 ,when an object opposite the eye is brought too close to it1 its edges must become too confused to be distinguished2 as it happens with objects close to a light1 which cast a large and indistinct shadow1 so is it with an eye which estimates objects opposite to it2 in all cases of linear perspective1 the eye acts in the same way as the light4 ,and the reason is that the eye has one leading line 7of vision7 which dilates with distance and embraces with true discernment large objects at a distance as well as small ones that are close4 ,but since the eye sends out a multitude of lines which surround this chief central one and since these which are farthest from the centre in this cone of lines are less able to discern with accuracy1 it follows that an object brought close to the eye is not at a due distance1 but is too near for the central line to be able to discern the outlines of the object4 ,so the edges fall within the lines of weaker discerning power1 and these are to the function of the eye like dogs in the chase which can put up the game but cannot take it4 ,thus these cannot take in the objects1 but induce the central line of sight to turn upon them1 when they have put them up4 ,hence the objects which are seen with these lines of sight have confused outlines4 ,the relative size of objects with regard to their distance from the eye 7#ic-ih74 #ic4 ,,perspective4 ,small objects close at hand and large ones at a distance1 being seen within equal angles1 will appear of the same size4 #id4 ,,perspective4 ,there is no object so large but that at a great distance from the eye it does not appear smaller than a smaller object near4 #ie4 ,among objects of equal size that which is most remote from the eye will look the smallest4 ,footnote3 ,this axiom1 sufficiently clear in itself1 is in the original illustrated by a very large diagram1 constructed like that here reproduced under ,no4 #ajh4 ,the same idea is repeated in ,c4 ,a4 ,i a2 ,i a1 stated as follows3 ,infra le cose d'equal grandeza quella si dimostra di minor figura che sara pi distante dall' ochio4-- #if4 ,why an object is less distinct when brought near to the eye1 and why with spectacles1 or without the naked eye sees badly either close or far off as the case may be4 #ig4 ,,perspective4 ,among objects of equal size1 that which is most remote from the eye will look the smallest4 #ih4 ,,perspective4 ,no second object can be so much lower than the first as that the eye will not see it higher than the first1 if the eye is above the second4 ,,perspective4 ,and this second object will never be so much higher than the first as that the eye1 being below them1 will not see the second as lower than the first4 ,,perspective4 ,if the eye sees a second square through the centre of a smaller one1 that is nearer1 the second1 larger square will appear to be surrounded by the smaller one4 ,,perspective--,,proposition4 ,objects that are farther off can never be so large but that those in front1 though smaller1 will conceal or surround them4 ,,definition4 ,this proposition can be proved by experiment4 ,for if you look through a small hole there is nothing so large that it cannot be seen through it and the object so seen appears surrounded and enclosed by the outline of the sides of the hole4 ,and if you stop it up1 this small stopping will conceal the view of the largest object4 ,the apparent size of objects defined by calculation 7#ii-aje7 #ii4 ,,of ,,linear ,,perspective4 ,linear ,perspective deals with the action of the lines of sight1 in proving by measurement how much smaller is a second object than the first1 and how much the third is smaller than the second2 and so on by degrees to the end of things visible4 ,i find by experience that if a second object is as far beyond the first as the first is from the eye1 although they are of the same size1 the second will seem half the size of the first and if the third object is of the same size as the #bnd1 and the #crd is as far beyond the second as the #bnd from the first1 it will appear of half the size of the second2 and so on by degrees1 at equal distances1 the next farthest will be half the size of the former object4 ,so long as the space does not exceed the length of #bj braccia4 ,but1 beyond #bj braccia figures of equal size will lose #b_/d and at #dj braccia they will lose #i_/aj1 and #ai_/bj at #fj braccia1 and so on diminishing by degrees4 ,this is if the picture plane is distant from you twice your own height4 ,if it is only as far off as your own height1 there will be a great difference between the first braccia and the second4 ,footnote3 ,this chapter is included in ,,dufresne',s and ,,manzi',s editions of the ,treatise on ,painting4 ,h4 ,,ludwig1 in his commentary1 calls this chapter eines der wichtigsten im ganzen ,tractat1 but at the same time he asserts that its substance has been so completely disfigured in the best ,,ms4 copies that we ought not to regard ,leonardo as responsible for it4 ,however1 in the case of this chapter1 the old ,,ms4 copies agree with the original as it is reproduced above4 ,from the chapters given later in this edition1 which were written at a subsequent date1 it would appear that ,leonardo corrected himself on these points4 #ajj4 ,,of ,,the ,,diminution ,,of ,,objects ,,at ,,various ,,distances4 ,a second object as far distant from the first as the first is from the eye will appear half the size of the first1 though they be of the same size really4 ,,of ,,the ,,degrees ,,of ,,diminution4 ,if you place the vertical plane at one braccio from the eye1 the first object1 being at a distance of #d braccia from your eye will diminish to #c_/d of its height at that plane2 and if it is #h braccia from the eye1 to #g_/h2 and if it is #af braccia off1 it will diminish to #ae_/af of its height and so on by degrees1 as the space doubles the diminution will double4 #aja4 ,begin from the line m f with the eye below2 then go up and do the same with the line n f1 then with the eye above and close to the #b gauges on the ground look at m n2 then as c m is to m n so will n m be to n s4 ,if a n goes #c times into f b1 m p will do the same into p g4 ,then go backwards so far as that c d goes twice into a n and p g will be equal to g h4 ,and m p will go into h p as often as d c into o p4 ,footnote3 ,the first three lines are unfortunately very obscure4 #ajb4 ,i ,,give ,,the ,,degrees ,,of ,,the ,,objects ,,seen ,,by ,,the ,,eye ,,as ,,the ,,musician ,,does ,,the ,,notes ,,heard ,,by ,,the ,,ear4 ,although the objects seen by the eye do1 in fact1 touch each other as they recede1 ,i will nevertheless found my rule on spaces of #bj braccia each2 as a musician does with notes1 which1 though they can be carried on one into the next1 he divides into degrees from note to note calling them #ast1 #bnd1 #crd1 #dth1 #eth2 and has affixed a name to each degree in raising or lowering the voice4 #ajc4 ,,perspective4 ,let f be the level and distance of the eye2 and a the vertical plane1 as high as a man2 let e be a man1 then ,i say that on the plane this will be the distance from the plane to the #bnd man4 #ajd4 ,the differences in the diminution of objects of equal size in consequence of their various remoteness from the eye will bear among themselves the same proportions as those of the spaces between the eye and the different objects4 ,find out how much a man diminishes at a certain distance and what its length is2 and then at twice that distance and at #c times1 and so make your general rule4 #aje4 ,the eye cannot judge where an object high up ought to descend4 #ajf4 ,,perspective4 ,if two similar and equal objects are placed one beyond the other at a given distance the difference in their size will appear greater in proportion as they are nearer to the eye that sees them4 ,and conversely there will seem to be less difference in their size in proportion as they are remote from the eve4 ,this is proved by the proportions of their distances among themselves2 for1 if the first of these two objects were as far from the eye1 as the #bnd from the first this would be called the second proportion3 since1 if the first is at #a braccia from the eye and the #bnd at two braccia1 two being twice as much as one1 the first object will look twice as large as the second4 ,but if you place the first at a hundred braccia from you and the second at a hundred and one1 you will find that the first is only so much larger than the second as #ajj is less than #aja2 and the converse is equally true4 ,and again1 the same thing is proved by the #dth of this book which shows that among objects that are equal1 there is the same proportion in the diminution of the size as in the increase in the distance from the eye of the spectator4 ,on natural perspective 7#ajg--aji74 #ajg4 ,,of ,,equal ,,objects ,,the ,,most ,,remote ,,look ,,the ,,smallest4 ,the practice of perspective may be divided into 444 parts ,footnote #d3 in 444 parte4 ,the space for the number is left blank in the original41 of which the first treats of objects seen by the eye at any distance2 and it shows all these objects just as the eye sees them diminished1 without obliging a man to stand in one place rather than another so long as the plane does not produce a second foreshortening4 ,but the second practice is a combination of perspective derived partly from art and partly from nature and the work done by its rules is in every portion of it1 influenced by natural perspective and artificial perspective4 ,by natural perspective ,i mean that the plane on which this perspective is represented is a flat surface1 and this plane1 although it is parallel both in length and height1 is forced to diminish in its remoter parts more than in its nearer ones4 ,and this is proved by the first of what has been said above1 and its diminution is natural4 ,but artificial perspective1 that is that which is devised by art1 does the contrary2 for objects equal in size increase on the plane where it is foreshortened in proportion as the eye is more natural and nearer to the plane1 and as the part of the plane on which it is figured is farther from the eye4 ,and let this plane be d e on which are seen #c equal circles which are beyond this plane d e1 that is the circles a b c4 ,now you see that the eye h sees on the vertical plane the sections of the images1 largest of those that are farthest and smallest of the nearest4 #ajh4 ,here follows what is wanting in the margin at the foot on the other side of this page4 ,natural perspective acts in a contrary way2 for1 at greater distances the object seen appears smaller1 and at a smaller distance the object appears larger4 ,but this said invention requires the spectator to stand with his eye at a small hole and then1 at that small hole1 it will be very plain4 ,but since many 7men's7 eyes endeavour at the same time to see one and the same picture produced by this artifice only one can see clearly the effect of this perspective and all the others will see confusion4 ,it is well therefore to avoid such complex perspective and hold to simple perspective which does not regard planes as foreshortened1 but as much as possible in their proper form4 ,this simple perspective1 in which the plane intersects the pyramids by which the images are conveyed to the eye at an equal distance from the eye is our constant experience1 from the curved form of the pupil of the eye on which the pyramids are intersected at an equal distance from the visual virtue4 ,footnote #bd3 la prima di sopra i4 e4 the first of the three diagrams which1 in the original ,,ms41 are placed in the margin at the beginning of this chapter4 #aji4 ,,of ,a ,,mixture ,,of ,,natural ,,and ,,artificial ,,perspective4 ,this diagram distinguishes natural from artificial perspective4 ,but before proceeding any farther ,i will define what is natural and what is artificial perspective4 ,natural perspective says that the more remote of a series of objects of equal size will look the smaller1 and conversely1 the nearer will look the larger and the apparent size will diminish in proportion to the distance4 ,but in artificial perspective when objects of unequal size are placed at various distances1 the smallest is nearer to the eye than the largest and the greatest distance looks as though it were the least of all2 and the cause of this is the plane on which the objects are represented2 and which is at unequal distances from the eye throughout its length4 ,and this diminution of the plane is natural1 but the perspective shown upon it is artificial since it nowhere agrees with the true diminution of the said plane4 ,whence it follows1 that when the eye is somewhat removed from the station point of the perspective that it has been gazing at1 all the objects represented look monstrous1 and this does not occur in natural perspective1 which has been defined above4 ,let us say then1 that the square a b c d figured above is foreshortened being seen by the eye situated in the centre of the side which is in front4 ,but a mixture of artificial and natural perspective will be seen in this tetragon called el main ,footnote #bj3 el main is quite legibly written in the original2 the meaning and derivation of the word are equally doubtful41 that is to say e f g h which must appear to the eye of the spectator to be equal to a b c d so long as the eye remains in its first position between c and d4 ,and this will be seen to have a good effect1 because the natural perspective of the plane will conceal the defects which would otherwise seem monstrous4 ,,iii4 ,six books on ,light and ,shade4 ,linear ,perspective cannot be immediately followed by either the prospettiva de' perdimenti or the prospettiva de' colori or the aerial perspective2 since these branches of the subject presuppose a knowledge of the principles of ,light and ,shade4 ,no apology1 therefore1 is here needed for placing these immediately after ,linear ,perspective4 ,we have various plans suggested by ,leonardo for the arrangement of the mass of materials treating of this subject4 ,among these ,i have given the preference to a scheme propounded in ,no4 ,,iii1 because1 in all probability1 we have here a final and definite purpose expressed4 ,several authors have expressed it as their opinion that the ,paris ,manuscript ,c is a complete and finished treatise on ,light and ,shade4 ,certainly1 the ,principles of ,light and ,shade form by far the larger portion of this ,,ms4 which consists of two separate parts2 still1 the materials are far from being finally arranged4 ,it is also evident that he here investigates the subject from the point of view of the ,physicist rather than from that of the ,painter4 ,the plan of a scheme of arrangement suggested in ,no4 ,,iii and adopted by me has been strictly adhered to for the first four ,books4 ,for the three last1 however1 few materials have come down to us2 and it must be admitted that these three ,books would find a far more appropriate place in a work on ,physics than in a treatise on ,painting4 ,for this reason ,i have collected in ,book ,v all the chapters on ,reflections1 and in ,book ,,vi ,i have put together and arranged all the sections of ,,ms4 ,c that belong to the book on ,painting1 so far as they relate to ,light and ,shade1 while the sections of the same ,,ms4 which treat of the ,prospettiva de' perdimenti have1 of course1 been excluded from the series on ,light and ,shade4 ,footnote ,,iii3 ,this text has already been published with some slight variations in ,dozio's pamphlet ,degli scritti e disegni di ,leonardo da ,vinci1 ,milan #ahga1 pp4 #cj--ca4 ,dozio did not transcribe it from the original ,,ms4 which seems to have remained unknown to him1 but from an old copy 7,,ms4 ,h4 #bbg in the ,ambrosian ,library74 ,,general ,,introduction4 ,prolegomena4 #aaj4 ,you must first explain the theory and then the practice4 ,first you must describe the shadows and lights on opaque objects1 and then on transparent bodies4 ,scheme of the books on ,light and shade4 #aaa4 ,,introduction4 ,having already treated of the nature of shadows and the way in which they are cast ,footnote #b3 ,avendo io tractato4--,we may suppose that he here refers to some particular ,,ms41 possibly ,paris ,c41 ,i will now consider the places on which they fall2 and their curvature1 obliquity1 flatness or1 in short1 any character ,i may be able to detect in them4 ,shadow is the obstruction of light4 ,shadows appear to me to be of supreme importance in perspective1 because1 without them opaque and solid bodies will be ill defined2 that which is contained within their outlines and their boundaries themselves will be ill-understood unless they are shown against a background of a different tone from themselves4 ,and therefore in my first proposition concerning shadow ,i state that every opaque body is surrounded and its whole surface enveloped in shadow and light4 ,and on this proposition ,i build up the first ,book4 ,besides this1 shadows have in themselves various degrees of darkness1 because they are caused by the absence of a variable amount of the luminous rays2 and these ,i call ,primary shadows because they are the first1 and inseparable from the object to which they belong4 ,and on this ,i will found my second ,book4 ,from these primary shadows there result certain shaded rays which are diffused through the atmosphere and these vary in character according to that of the primary shadows whence they are derived4 ,i shall therefore call these shadows ,derived shadows because they are produced by other shadows2 and the third ,book will treat of these4 ,again these derived shadows1 where they are intercepted by various objects1 produce effects as various as the places where they are cast and of this ,i will treat in the fourth ,book4 ,and since all round the derived shadows1 where the derived shadows are intercepted1 there is always a space where the light falls and by reflected dispersion is thrown back towards its cause1 it meets the original shadow and mingles with it and modifies it somewhat in its nature2 and on this ,i will compose my fifth ,book4 ,besides this1 in the sixth ,book ,i will investigate the many and various diversities of reflections resulting from these rays which will modify the original shadow by imparting some of the various colours from the different objects whence these reflected rays are derived4 ,again1 the seventh ,book will treat of the various distances that may exist between the spot where the reflected rays fall and that where they originate1 and the various shades of colour which they will acquire in falling on opaque bodies4 ,different principles and plans of treatment 7#aab--aaf74 #aab4 ,first ,i will treat of light falling through windows which ,i will call ,restricted ,light and then ,i will treat of light in the open country1 to which ,i will give the name of diffused ,light4 ,then ,i will treat of the light of luminous bodies4 #aac4 ,,of ,,painting4 ,the conditions of shadow and light as seen by the eye are #c4 ,of these the first is when the eye and the light are on the same side of the object seen2 the #bnd is when the eye is in front of the object and the light is behind it4 ,the #crd is when the eye is in front of the object and the light is on one side1 in such a way as that a line drawn from the object to the eye and one from the object to the light should form a right angle where they meet4 #aad4 ,,of ,,painting4 ,this is another section3 that is1 of the nature of a reflection 7from7 an object placed between the eye and the light under various aspects4 #aae4 ,,of ,,painting4 ,as regards all visible objects #c things must be considered4 ,these are the position of the eye which sees3 that of the object seen with regard to the light1 and the position of the light which illuminates the object1 b is the eye1 a the object seen1 c the light1 a is the eye1 b the illuminating body1 c is the illuminated object4 #aaf4 ,let a be the light1 b the eye1 c the object seen by the eye and in the light4 ,these show1 first1 the eye between the light and the body2 the #bnd1 the light between the eye and the body2 the #crd the body between the eye and the light1 a is the eye1 b the illuminated object1 c the light4 #aag4 ,,of ,,painting4 ,,of ,,the ,,three ,,kinds ,,of ,,light ,,that ,,illuminate ,,opaque ,,bodies4 ,the first kind of ,light which may illuminate opaque bodies is called ,direct light--as that of the sun or any other light from a window or flame4 ,the second is ,diffused universal light1 such as we see in cloudy weather or in mist and the like4 ,the #crd is ,subdued light1 that is when the sun is entirely below the horizon1 either in the evening or morning4 #aah4 ,,of ,,light4 ,the lights which may illuminate opaque bodies are of #d kinds4 ,these are3 diffused light as that of the atmosphere1 within our horizon4 ,and ,direct1 as that of the sun1 or of a window or door or other opening4 ,the third is ,reflected light2 and there is a #dth which is that which passes through semi transparent bodies1 as linen or paper or the like1 but not transparent like glass1 or crystal1 or other diaphanous bodies1 which produce the same effect as though nothing intervened between the shaded object and the light that falls upon it2 and this we will discuss fully in our discourse4 ,definition of the nature of shadows 7#aai--abb74 #aai4 ,,what ,,light ,,and ,,shadow ,,are4 ,shadow is the absence of light1 merely the obstruction of the luminous rays by an opaque body4 ,shadow is of the nature of darkness4 ,light on an object is of the nature of a luminous body2 one conceals and the other reveals4 ,they are always associated and inseparable from all objects4 ,but shadow is a more powerful agent than light1 for it can impede and entirely deprive bodies of their light1 while light can never entirely expel shadow from a body1 that is from an opaque body4 #abj4 ,shadow is the diminution of light by the intervention of an opaque body4 ,shadow is the counterpart of the luminous rays which are cut off by an opaque body4 ,this is proved because the shadow cast is the same in shape and size as the luminous rays were which are transformed into a shadow4 #aba4 ,shadow is the diminution alike of light and of darkness1 and stands between darkness and light4 ,a shadow may be infinitely dark1 and also of infinite degrees of absence of darkness4 ,the beginnings and ends of shadow lie between the light and darkness and may be infinitely diminished and infinitely increased4 ,shadow is the means by which bodies display their form4 ,the forms of bodies could not be understood in detail but for shadow4 #abb4 ,,of ,,the ,,nature ,,of ,,shadow4 ,shadow partakes of the nature of universal matter4 ,all such matters are more powerful in their beginning and grow weaker towards the end1 ,i say at the beginning1 whatever their form or condition may be and whether visible or invisible4 ,and it is not from small beginnings that they grow to a great size in time2 as it might be a great oak which has a feeble beginning from a small acorn4 ,yet ,i may say that the oak is most powerful at its beginning1 that is where it springs from the earth1 which is where it is largest 7,to return37 ,darkness1 then1 is the strongest degree of shadow and light is its least4 ,therefore1 ,o ,painter1 make your shadow darkest close to the object that casts it1 and make the end of it fading into light1 seeming to have no end4 ,of the various kinds of shadows4 7#abc-abe74 #abc4 ,darkness is absence of light4 ,shadow is diminution of light4 ,primitive shadow is that which is inseparable from a body not in the light4 ,derived shadow is that which is disengaged from a body in shadow and pervades the air4 ,a cast transparent shadow is that which is surrounded by an illuminated surface4 ,a simple shadow is one which receives no light from the luminous body which causes it4 ,a simple shadow begins within the line which starts from the edge of the luminous body a b4 #abd4 ,a simple shadow is one where no light at all interferes with it4 ,a compound shadow is one which is somewhat illuminated by one or more lights4 #abe4 ,,what ,,is ,,the ,,difference ,,between ,a ,,shadow ,,that ,,is ,,inseparable ,,from ,a ,,body ,,and ,a ,,cast ,,shadow8 ,an inseparable shadow is that which is never absent from the illuminated body4 ,as1 for instance a ball1 which so long as it is in the light always has one side in shadow which never leaves it for any movement or change of position in the ball4 ,a separate shadow may be and may not be produced by the body itself4 ,suppose the ball to be one braccia distant from a wall with a light on the opposite side of it2 this light will throw upon the wall exactly as broad a shadow as is to be seen on the side of the ball that is turned towards the wall4 ,that portion of the cast shadow will not be visible when the light is below the ball and the shadow is thrown up towards the sky and finding no obstruction on its way is lost4 #abf4 ,,how ,,there ,,are #b ,,kinds ,,of ,,light1 ,,one ,,separable ,,from1 ,,and ,,the ,,other ,,inseparable ,,from ,,bodies4 ,of the various kinds of light 7#abf1 #abg74 ,separate light is that which falls upon the body4 ,inseparable light is the side of the body that is illuminated by that light4 ,one is called primary1 the other derived4 ,and1 in the same way there are two kinds of shadow3--,one primary and the other derived4 ,the primary is that which is inseparable from the body1 the derived is that which proceeds from the body conveying to the surface of the wall the form of the body causing it4 #abg4 ,how there are #b different kinds of light2 one being called diffused1 the other restricted4 ,the diffused is that which freely illuminates objects4 ,the restricted is that which being admitted through an opening or window illuminates them on that side only4 ,footnote3 ,at the spot marked ,a in the first diagram ,leonardo wrote lume costretto 7restricted light74 ,at the spot ,b on the second diagram he wrote lume libero 7diffused light74 ,general remarks 7#abh4 #abi74 #abh4 ,light is the chaser away of darkness4 ,shade is the obstruction of light4 ,primary light is that which falls on objects and causes light and shade4 ,and derived lights are those portions of a body which are illuminated by the primary light4 ,a primary shadow is that side of a body on which the light cannot fall4 ,the general distribution of shadow and light is that sum total of the rays thrown off by a shaded or illuminated body passing through the air without any interference and the spot which intercepts and cuts off the distribution of the dark and light rays4 ,and the eye can best distinguish the forms of objects when it is placed between the shaded and the illuminated parts4 #abi4 ,,memorandum ,,of ,,things ,i ,,require ,,to ,,have ,,granted ,,as ,,axioms ,,in ,,my ,,explanation ,,of ,,perspective4 ,i ask to have this much granted me--to assert that every ray passing through air of equal density throughout1 travels in a straight line from its cause to the object or place it falls upon4 ,,first ,,book ,,on ,,light ,,and ,,shade4 ,on the nature of light 7#acj4 #aca74 #acj4 ,the reason by which we know that a light radiates from a single centre is this3 ,we plainly see that a large light is often much broader than some small object which nevertheless--and although the rays of the large light are much more than twice the extent of the small body--always has its shadow cast on the nearest surface very visibly4 ,let c f be a broad light and n be the object in front of it1 casting a shadow on the plane1 and let a b be the plane4 ,it is clear that it is not the broad light that will cast the shadow n on the plane1 but that the light has within it a centre is shown by this experiment4 ,the shadow falls on the plane as is shown at m o t r4 ,footnote #ac3 ,in the original ,,ms4 no explanatory text is placed after this title-line2 but a space is left for it and the text beginning at line #ae comes next4 ,why1 to two eyes or in front of two eyes do #c objects appear as two8 ,why1 when you estimate the direction of an object with two sights the nearer appears confused4 ,i say that the eye projects an infinite number of lines which mingle or join those reaching it which come to it from the object looked at4 ,and it is only the central and sensible line that can discern and discriminate colours and objects2 all the others are false and illusory4 ,and if you place #b objects at half an arm's length apart if the nearer of the two is close to the eye its form will remain far more confused than that of the second2 the reason is that the first is overcome by a greater number of false lines than the second and so is rendered vague4 ,light acts in the same manner1 for in the effects of its lines 7rays71 and particularly in perspective1 it much resembles the eye2 and its central rays are what cast the true shadow4 ,when the object in front of it is too quickly overcome with dim rays it will cast a broad and disproportionate shadow1 ill defined2 but when the object which is to cast the shadow and cuts off the rays near to the place where the shadow falls1 then the shadow is distinct2 and the more so in proportion as the light is far off1 because at a long distance the central ray is less overcome by false rays2 because the lines from the eye and the solar and other luminous rays passing through the atmosphere are obliged to travel in straight lines4 ,unless they are deflected by a denser or rarer air1 when they will be bent at some point1 but so long as the air is free from grossness or moisture they will preserve their direct course1 always carrying the image of the object that intercepts them back to their point of origin4 ,and if this is the eye1 the intercepting object will be seen by its colour1 as well as by form and size4 ,but if the intercepting plane has in it some small perforation opening into a darker chamber--not darker in colour1 but by absence of light--you will see the rays enter through this hole and transmitting to the plane beyond all the details of the object they proceed from both as to colour and form2 only every thing will be upside down4 ,but the size of the image where the lines are reconstructed will be in proportion to the relative distance of the aperture from the plane on which the lines fall on one hand and from their origin on the other4 ,there they intersect and form #b pyramids with their point meeting a common apex and their bases opposite4 ,let a b be the point of origin of the lines1 d e the first plane1 and c the aperture with the intersection of the lines2 f g is the inner plane4 ,you will find that a falls upon the inner plane below at g1 and b which is below will go up to the spot f2 it will be quite evident to experimenters that every luminous body has in itself a core or centre1 from which and to which all the lines radiate which are sent forth by the surface of the luminous body and reflected back to it2 or which1 having been thrown out and not intercepted1 are dispersed in the air4 #aca4 ,,the ,,rays ,,whether ,,shaded ,,or ,,luminous ,,have ,,greater ,,strength ,,and ,,effect ,,at ,,their ,,points ,,than ,,at ,,their ,,sides4 ,although the points of luminous pyramids may extend into shaded places and those of pyramids of shadow into illuminated places1 and though among the luminous pyramids one may start from a broader base than another2 nevertheless1 if by reason of their various length these luminous pyramids acquire angles of equal size their light will be equal2 and the case will be the same with the pyramids of shadow2 as may be seen in the intersected pyramids a b c and d e f1 which though their bases differ in size are equal as to breadth and light4 ,footnote3 #ea--ee3 ,this supplementary paragraph is indicated as being a continuation of line #de1 by two small crosses4 ,the difference between light and lustre 7#acb--ace74 #acb4 ,of the difference between light and lustre2 and that lustre is not included among colours1 but is saturation of whiteness1 and derived from the surface of wet bodies2 light partakes of the colour of the object which reflects it 7to the eye7 as gold or silver or the like4 #acc4 ,,of ,,the ,,highest ,,lights ,,which ,,turn ,,and ,,move ,,as ,,the ,,eye ,,moves ,,which ,,sees ,,the ,,object4 ,suppose the body to be the round object figured here and let the light be at the point a1 and let the illuminated side of the object be b c and the eye at the point d3 ,i say that1 as lustre is every where and complete in each part1 if you stand at the point d the lustre will appear at c1 and in proportion as the eye moves from d to a1 the lustre will move from c to n4 #acd4 ,,of ,,painting4 ,heigh light or lustre on any object is not situated necessarily in the middle of an illuminated object1 but moves as and where the eye moves in looking at it4 #ace4 ,,of ,,light ,,and ,,lustre4 ,what is the difference between light and the lustre which is seen on the polished surface of opaque bodies8 ,the lights which are produced from the polished surface of opaque bodies will be stationary on stationary objects even if the eye on which they strike moves4 ,but reflected lights will1 on those same objects1 appear in as many different places on the surface as different positions are taken by the eye4 ,,what ,,bodies ,,have ,,light ,,upon ,,them ,,without ,,lustre8 ,opaque bodies which have a hard and rough surface never display any lustre in any portion of the side on which the light falls4 ,,what ,,bodies ,,will ,,display ,,lustre ,,but ,,not ,,look ,,illuminated8 ,those bodies which are opaque and hard with a hard surface reflect light lustre from every spot on the illuminated side which is in a position to receive light at the same angle of incidence as they occupy with regard to the eye2 but1 as the surface mirrors all the surrounding objects1 the illuminated body is not recognisable in these portions of the illuminated body4 #acf4 ,the relations of luminous to illuminated bodies4 ,the middle of the light and shade on an object in light and shade is opposite to the middle of the primary light4 ,all light and shadow expresses itself in pyramidal lines4 ,the middle of the shadow on any object must necessarily be opposite the middle of its light1 with a direct line passing through the centre of the body4 ,the middle of the light will be at a1 that of the shadow at b4 ,again1 in bodies shown in light and shade the middle of each must coincide with the centre of the body1 and a straight line will pass through both and through that centre4 ,footnote3 ,in the original ,,ms41 at the spot marked a of the first diagram ,leonardo wrote primitiuo1 and at the spot marked c--primitiva 7primary72 at the spot marked b he wrote dirivatiuo and at d deriuatiua 7derived74 ,experiments on the relation of light and shadow within a room 7#acg--adj74 #acg4 ,,shows ,,how ,,light ,,from ,,any ,,side ,,converges ,,to ,,one ,,point4 ,although the balls a b c are lighted from one window1 nevertheless1 if you follow the lines of their shadows you will see they intersect at a point forming the angle n4 ,footnote3 ,the diagram belonging to this passage is slightly sketched on ,pl4 ,,xxxii2 a square with three balls below it4 ,the first three lines of the text belonging to it are written above the sketch and the six others below it4 #ach4 ,every shadow cast by a body has a central line directed to a single point produced by the intersection of luminous lines in the middle of the opening and thickness of the window4 ,the proposition stated above1 is plainly seen by experiment4 ,thus if you draw a place with a window looking northwards1 and let this be s f1 you will see a line starting from the horizon to the east1 which1 touching the #b angles of the window o f1 reaches d2 and from the horizon on the west another line1 touching the other #b angles r s1 and ending at c2 and their intersection falls exactly in the middle of the opening and thickness of the window4 ,again1 you can still better confirm this proof by placing two sticks1 as shown at g h2 and you will see the line drawn from the centre of the shadow directed to the centre m and prolonged to the horizon n f4 ,footnote3 ,b here stands for cerchio del' orizonte tramontano on the original diagram 7the circle of the horizon towards the ,north72 ,a for levante 7,east7 and ,c for ponete 7,west74 #aci4 ,every shadow with all its variations1 which becomes larger as its distance from the object is greater1 has its external lines intersecting in the middle1 between the light and the object4 ,this proposition is very evident and is confirmed by experience4 ,for1 if a b is a window without any object interposed1 the luminous atmosphere to the right hand at a is seen to the left at d4 ,and the atmosphere at the left illuminates on the right at c1 and the lines intersect at the point m4 ,footnote3 ,a here stands for levante 7,east71 ,b for ponente 7,west74 #adj4 ,every body in light and shade is situated between #b pyramids one dark and the other luminous1 one is visible the other is not4 ,but this only happens when the light enters by a window4 ,supposing a b to be the window and r the body in light and shade1 the light to the right hand z will pass the object to the left and go on to p2 the light to the left at k will pass to the right of the object at i and go on to m and the two lines will intersect at c and form a pyramid4 ,then again a b falls on the shaded body at i g and forms a pyramid f i g4 f will be dark because the light a b can never fall there2 i g c will be illuminated because the light falls upon it4 ,light and shadow with regard to the position of the eye 7#ada--ade74 #ada4 ,every shaded body that is larger than the pupil and that interposes between the luminous body and the eye will be seen dark4 ,when the eye is placed between the luminous body and the objects illuminated by it1 these objects will be seen without any shadow4 ,footnote3 ,the diagram which in the original stands above line #a is given on ,plate ,,ii1 ,no #b4 ,then1 after a blank space of about eight lines1 the diagram ,plate ,,ii ,no #c is placed in the original4 ,there is no explanation of it beyond the one line written under it4 #adb4 ,why the #b lights one on each side of a body having two pyramidal sides of an obtuse apex leave it devoid of shadow4 ,footnote3 ,the sketch illustrating this is on ,plate ,,xli ,no #a4 #adc4 ,a body in shadow situated between the light and the eye can never display its illuminated portion unless the eye can see the whole of the primary light4 ,footnote3 ,a stands for corpo 7body71 ,b for lume 7light74 #add4 ,the eye which looks 7at a spot7 half way between the shadow and the light which surrounds the body in shadow will see that the deepest shadows on that body will meet the eye at equal angles1 that is at the same angle as that of sight4 ,footnote3 ,in both these diagrams ,a stands for lume 7light7 ,b for ombra 7shadow74 #ade4 ,,of ,,the ,,different ,,light ,,and ,,shade ,,in ,,various ,,aspects ,,and ,,of ,,objects ,,placed ,,in ,,them4 ,if the sun is in the ,east and you look towards the ,west you will see every thing in full light and totally without shadow because you see them from the same side as the sun3 and if you look towards the ,south or ,north you will see all objects in light and shade1 because you see both the side towards the sun and the side away from it2 and if you look towards the coming of the sun all objects will show you their shaded side1 because on that side the sun cannot fall upon them4 ,the law of the incidence of light4 #adf4 ,the edges of a window which are illuminated by #b lights of equal degrees of brightness will not reflect light of equal brightness into the chamber within4 ,if b is a candle and a c our hemisphere both will illuminate the edges of the window m n1 but light b will only illuminate f g and the hemisphere a will light all of d e4 #adg4 ,,of ,,painting4 ,that part of a body which receives the luminous rays at equal angles will be in a higher light than any other part of it4 ,and the part which the luminous rays strike between less equal angles will be less strongly illuminated4 ,,second ,,book ,,on ,,light ,,and ,,shade4 ,gradations of strength in the shadows 7#adh4 #adi74 #adh4 ,,that ,,portion ,,of ,a ,,body ,,in ,,light ,,and ,,shade ,,will ,,be ,,least ,,luminous ,,which ,,is ,,seen ,,under ,,the ,,least ,,amount ,,of ,,light4 ,that part of the object which is marked m is in the highest light because it faces the window a d by the line a f2 n is in the second grade because the light b d strikes it by the line b e2 o is in the third grade1 as the light falls on it from c d by the line c h2 p is the lowest light but one as c d falls on it by the line d v2 q is the deepest shadow for no light falls on it from any part of the window4 ,in proportion as c d goes into a d so will n r s be darker than m1 and all the rest is space without shadow4 ,footnote3 ,the diagram belonging to this chapter is ,no4 #a on ,plate ,,iii4 ,the letters a b e d and r are not reproduced in facsimile of the original1 but have been replaced by ordinary type in the margin4 #e-ab4 ,the original text of these lines is reproduced within the diagram4--,compare ,no #bge4 #adi4 ,the light which falls on a shaded body at the acutest angle receives the highest light1 and the darkest portion is that which receives it at an obtuse angle and both the light and the shadow form pyramids4 ,the angle c receives the highest grade of light because it is directly in front of the window a b and the whole horizon of the sky m x4 ,the angle a differs but little from c because the angles which divide it are not so unequal as those below1 and only that portion of the horizon is intercepted which lies between y and x4 ,although it gains as much on the other side its line is nevertheless not very strong because one angle is smaller than its fellow4 ,the angles e i will have less light because they do not see much of the light m s and the light v x and their angles are very unequal4 ,yhe angle k and the angle f are each placed between very unequal angles and therefore have but little light1 because at k it has only the light p t1 and at f only t q2 o g is the lowest grade of light because this part has no light at all from the sky2 and thence come the lines which will reconstruct a pyramid that is the counterpart of the pyramid c2 and this pyramid l is in the first grade of shadow2 for this too is placed between equal angles directly opposite to each other on either side of a straight line which passes through the centre of the body and goes to the centre of the light4 ,the several luminous images cast within the frame of the window at the points a and b make a light which surrounds the derived shadow cast by the solid body at the points #d and #f4 ,the shaded images increase from o g and end at #g and #h4 ,footnote3 ,the diagram belonging to this chapter is ,no4 #b on ,plate ,,iii4 ,in the original it is placed between lines #c and #d1 and in the reproduction these are shown in part4 ,the semi circle above is marked orizonte 7horizon74 ,the number #f at the left hand side1 outside the facsimile1 is in the place of a figure which has become indistinct in the original4 ,on the intensity of shadows as dependent on the distance from the light 7#aej-aeb74 #aej4 ,the smaller the light that falls upon an object the more shadow it will display4 ,and the light will illuminate a smaller portion of the object in proportion as it is nearer to it2 and conversely1 a larger extent of it in proportion as it is farther off4 ,a light which is smaller than the object on which it falls will light up a smaller extent of it in proportion as it is nearer to it1 and the converse1 as it is farther from it4 ,but when the light is larger than the object illuminated it will light a larger extent of the object in proportion as it is nearer and the converse when they are farther apart4 #aea4 ,that portion of an illuminated object which is nearest to the source of light will be the most strongly illuminated4 #aeb4 ,that portion of the primary shadow will be least dark which is farthest from the edges4 ,the derived shadow will be darker than the primary shadow where it is contiguous with it4 ,on the proportion of light and shade 7#aec-aeg74 #aec4 ,that portion of an opaque body will be more in shade or more in light1 which is nearer to the dark body1 by which it is shaded1 or to the light that illuminates it4 ,objects seen in light and shade show in greater relief than those which are wholly in light or in shadow4 #aed4 ,,of ,,perspective4 ,the shaded and illuminated sides of opaque objects will display the same proportion of light and darkness as their objects ,footnote #f3 ,the meaning of obbietti 7objects7 is explained in no #aec1 lines #a-d4--;,between the title-line and the next there is1 in the original1 a small diagram representing a circle described round a square44 #aee4 ,,of ,,painting4 ,the outlines and form of any part of a body in light and shade are indistinct in the shadows and in the high lights2 but in the portions between the light and the shadows they are highly conspicuous4 #aef4 ,,of ,,painting4 ,among objects in various degrees of shade1 when the light proceeds from a single source1 there will be the same proportion in their shadows as in the natural diminution of the light and the same must be understood of the degrees of light4 #aeg4 ,a single and distinct luminous body causes stronger relief in the object than a diffused light2 as may be seen by comparing one side of a landscape illuminated by the sun1 and one overshadowed by clouds1 and so illuminated only by the diffused light of the atmosphere4 ,,third ,,book ,,on ,,light ,,and ,,shade4 ,definition of derived shadow 7#aeh4 #aei74 #aeh4 ,derived shadow cannot exist without primary shadow4 ,this is proved by the first of this which says3 ,darkness is the total absence of light1 and shadow is an alleviation of darkness and of light1 and it is more or less dark or light in proportion as the darkness is modified by the light4 #aei4 ,shadow is diminution of light4 ,darkness is absence of light4 ,shadow is divided into two kinds1 of which the first is called primary shadow1 the second is derived shadow4 ,the primary shadow is always the basis of the derived shadow4 ,the edges of the derived shadow are straight lines4 ,footnote3 ,the theory of the ombra dirivativa--a technical expression for which there is no precise ,english equivalent is elaborately treated by ,leonardo4 ,but both text and diagrams 7as ,pl4 ,,iv1 #a-c and ,pl4 ,v7 must at once convince the student that the distinction he makes between ombra primitiva and ombra dirivativa is not merely justifiable but scientific4 ,ombra dirivativa is by no means a mere abstract idea4 ,this is easily proved by repeating the experiment made by ,leonardo1 and by filling with smoke the room in which the existence of the ombra dirivativa is investigated1 when the shadow becomes visible4 ,nor is it difficult to perceive how much of ,leonardo's teaching depended on this theory4 ,the recognised1 but extremely complicated science of cast shadows--percussione dell' ombre dirivative as ,leonardo calls them--is thus rendered more intelligible if not actually simpler1 and we must assume this theory as our chief guide through the investigations which follow4 ,the darkness of the derived shadow diminishes in proportion as it is remote from the primary shadow4 ,different sorts of derived shadows 7#afj-afb74 #afj4 ,,shadow ,,and ,,light4 ,the forms of shadows are three3 inasmuch as if the solid body which casts the shadow is equal 7in size7 to the light1 the shadow resembles a column without any termination 7in length74 ,if the body is larger than the light the shadow resembles a truncated and inverted pyramid1 and its length has also no defined termination4 ,but if the body is smaller than the light1 the shadow will resemble a pyramid and come to an end1 as is seen in eclipses of the moon4 #afa4 ,,of ,,simple ,,derived ,,shadows4 ,the simple derived shadow is of two kinds3 one kind which has its length defined1 and two kinds which are undefined2 and the defined shadow is pyramidal4 ,of the two undefined1 one is a column and the other spreads out2 and all three have rectilinear outlines4 ,but the converging1 that is the pyramidal1 shadow proceeds from a body that is smaller than the light1 and the columnar from a body equal in size to the light1 and the spreading shadow from a body larger than the light2 c4 ,,of ,,compound ,,derived ,,shadows4 ,compound derived shadows are of two kinds2 that is columnar and spreading4 #afb4 ,,of ,,shadow4 ,derived shadows are of three kinds of which one is spreading1 the second columnar1 the third converging to the point where the two sides meet and intersect1 and beyond this intersection the sides are infinitely prolonged or straight lines4 ,and if you say1 this shadow must terminate at the angle where the sides meet and extend no farther1 ,i deny this1 because above in the first on shadow ,i have proved3 that a thing is completely terminated when no portion of it goes beyond its terminating lines4 ,now here1 in this shadow1 we see the converse of this1 in as much as where this derived shadow originates we obviously have the figures of two pyramids of shadow which meet at their angles4 ,hence1 if1 as my opponent says1 the first pyramid of shadow terminates the derivative shadow at the angle whence it starts1 then the second pyramid of shadow--so says the adversary--must be caused by the angle and not from the body in shadow2 and this is disproved with the help of the #bnd of this which says3 ,shadow is a condition produced by a body casting a shadow1 and interposed between this shadow and the luminous body4 ,by this it is made clear that the shadow is not produced by the angle of the derived shadow but only by the body casting the shadow2 c4 ,if a spherical solid body is illuminated by a light of elongated form the shadow produced by the longest portion of this light will have less defined outlines than that which is produced by the breadth of the same light4 ,and this is proved by what was said before1 which is3 ,that a shadow will have less defined outlines in proportion as the light which causes it is larger1 and conversely1 the outlines are clearer in proportion as it is smaller4 ,footnote3 ,the two diagrams to this chapter are on ,plate ,,iv1 ,no4 #a4 ,on the relation of derived and primary shadow 7#afc-afe74 #afc4 ,the derived shadow can never resemble the body from which it proceeds unless the light is of the same form and size as the body causing the shadow4 ,the derived shadow cannot be of the same form as the primary shadow unless it is intercepted by a plane parallel to it4 #afd4 ,,how ,a ,,cast ,,shadow ,,can ,,never ,,be ,,of ,,the ,,same ,,size ,,as ,,the ,,body ,,that ,,casts ,,it4 ,if the rays of light proceed1 as experience shows1 from a single point and are diffused in a sphere round this point1 radiating and dispersed through the air1 the farther they spread the wider they must spread2 and an object placed between the light and a wall is always imaged larger in its shadow1 because the rays that strike it ,footnote3 #g4 ,the following lines are wanting to complete the logical connection4 would1 by the time they have reached the wall1 have become larger4 #afe4 ,any shadow cast by a body in light and shade is of the same nature and character as that which is inseparable from the body4 ,the centre of the length of a shadow always corresponds to that of the luminous body ,footnote #f3 ,this second statement of the same idea as in the former sentence1 but in different words1 does not1 in the original1 come next to the foregoing2 sections #agb and #abg are placed between them44 ,it is inevitable that every shadow must have its centre in a line with the centre of the light4 ,on the shape of derived shadows 7#aff-agd74 #aff4 ,,of ,,the ,,pyramidal ,,shadow4 ,the pyramidal shadow produced by a columnar body will be narrower than the body itself in proportion as the simple derived shadow is intersected farther from the body which casts it4 ,footnote #aff3 ,compare the first diagram to ,no4 #afa4 ,if we here conceive of the outlines of the pyramid of shadow on the ground as prolonged beyond its apex this gives rise to a second pyramid2 this is what is spoken of at the beginning of ,no4 #aff4 #afg4 ,the cast shadow will be longest when the light is lowest4 ,the cast shadow will be shortest when the light is highest4 #afh4 ,both the primary and derived shadow will be larger when caused by the light of a candle than by diffused light4 ,the difference between the larger and smaller shadows will be in inverse proportion to the larger and smaller lights causing them4 ,footnote3 ,in the diagrams ,a stands for celo 7sky71 ,b for cadela 7candle74 #afi4 ,,all ,,bodies1 ,,in ,,proportion ,,as ,,they ,,are ,,nearer ,,to1 ,,or ,,farther ,,from ,,the ,,source ,,of ,,light1 ,,will ,,produce ,,longer ,,or ,,shorter ,,derived ,,shadows4 ,among bodies of equal size1 that one which is illuminated by the largest light will have the shortest shadow4 ,experiment confirms this proposition4 ,thus the body m n is surrounded by a larger amount of light than the body p q1 as is shown above4 ,let us say that v c a b d x is the sky1 the source of light1 and that s t is a window by which the luminous rays enter1 and so m n and p q are bodies in light and shade as exposed to this light2 m n will have a small derived shadow1 because its original shadow will be small2 and the derivative light will be large1 again1 because the original light c d will be large and p q will have more derived shadow because its original shadow will be larger1 and its derived light will be smaller than that of the body m n because that portion of the hemisphere a b which illuminates it is smaller than the hemisphere c d which illuminates the body m n4 ,footnote3 ,the diagram1 given on ,pl4 ,,iv1 ,no4 #b1 stands in the original between lines #b and #g1 while the text of lines #c to #f is written on its left side4 ,in the reproduction of this diagram the letter v at the outer right-hand end has been omitted4 #agj4 ,the shadow m bears the same proportion to the shadow n as the line b c to the line f c4 #aga4 ,,of ,,painting4 ,of different shadows of equal strength that which is nearest the eye will seem the least strong4 ,why is the shadow e a b in the first grade of strength1 b c in the second2 c d in the third8 ,the reason is that as from e a b the sky is nowhere visible1 it gets no light whatever from the sky1 and so has no direct primary light4 b c faces the portion of the sky f g and is illuminated by it4 c d faces the sky at h k4 c d1 being exposed to a larger extent of sky than b c1 it is reasonable that it should be more lighted4 ,and thus1 up to a certain distance1 the wall a d will grow lighter for the reasons here given1 until the darkness of the room overpowers the light from the window4 #agb4 ,when the light of the atmosphere is restricted by an opening and illuminates bodies which cast shadows1 these bodies being equally distant from the centre of the window1 that which is most obliquely placed will cast the largest shadow beyond it4 #agc4 ,these bodies standing apart in a room lighted by a single window will have derivative shadows more or less short according as they are more or less opposite to the window4 ,among the shadows cast by bodies of equal mass but at unequal distances from the opening by which they are illuminated1 that shadow will be the longest of the body which is least in the light4 ,and in proportion as one body is better illuminated than another its shadow will be shorter than another4 ,the proportion n m and e v k bear to r t and v x corresponds with that of the shadow x to #d and y4 ,the reason why those bodies which are placed most in front of the middle of the window throw shorter shadows than those obliquely situated is3--,that the window appears in its proper form and to the obliquely placed ones it appears foreshortened2 to those in the middle1 the window shows its full size1 to the oblique ones it appears smaller2 the one in the middle faces the whole hemisphere that is e f and those on the side have only a strip2 that is q r faces a b2 and m n faces c d2 the body in the middle having a larger quantity of light than those at the sides is lighted from a point much below its centre1 and thus the shadow is shorter4 ,and the pyramid g #d goes into l y exactly as often as a b goes into e f4 ,the axis of every derivative shadow passes through #f #a_/b ,footnote #ca3 passa per #f #a_/b 7passes through #f #a_/b74 ,the meaning of these words is probably this3 ,each of the three axes of the derived shadow intersects the centre 7mezzo7 of the primary shadow 7ombra originale7 and1 by prolongation upwards crosses six lines4 ,this is self evident only in the middle diagram2 but it is equally true of the side figures if we conceive of the lines #d f1 x n v m1 y l k v1 and #d e1 as prolonged beyond the semicircle of the horizon4 and is in a straight line with the centre of the primary shadow1 with the centre of the body casting it and of the derivative light and with the centre of the window and1 finally1 with the centre of that portion of the source of light which is the celestial hemisphere1 y h is the centre of the derived shade1 l h of the primary shadow1 l of the body throwing it1 l k of the derived light1 v is the centre of the window1 e is the final centre of the original light afforded by that portion of the hemisphere of the sky which illuminates the solid body4 ,footnote3 ,compare the diagram on ,pl4 ,,iv1 ,no4 #c4 ,in the original this drawing is placed between lines #c and #bb2 the rest1 from line #d to line #ba1 is written on the left hand margin4 #agd4 ,,the ,,farther ,,the ,,derived ,,shadow ,,is ,,prolonged ,,the ,,lighter ,,it ,,becomes4 ,you will find that the proportion of the diameter of the derived shadow to that of the primary shadow will be the same as that between the darkness of the primary shadow and that of the derived shadow4 ,footnote #f3 ,compare ,no4 #agg4 ,let a b be the diameter of the primary shadow and c d that of the derived shadow1 ,i say that a b going1 as you see1 three times into d c1 the shadow d c will be three times as light as the shadow a b4 ,footnote #h3 ,compare ,no4 #agg4 ,if the size of the illuminating body is larger than that of the illuminated body an intersection of shadow will occur1 beyond which the shadows will run off in two opposite directions as if they were caused by two separate lights4 ,on the relative intensity of derived shadows 7#age-agi74 #age4 ,,on ,,painting4 ,the derived shadow is stronger in proportion as it is nearer to its place of origin4 #agf4 ,,how ,,shadows ,,fade ,,away ,,at ,,long ,,distances4 ,shadows fade and are lost at long distances because the larger quantity of illuminated air which lies between the eye and the object seen tints the shadow with its own colour4 #agg4 a b will be darker than c d in proportion as c d is broader than a b4 ,footnote3 ,in the original ,,ms4 the word lume 7light7 is written at the apex of the pyramid4 #agh4 ,it can be proved why the shadow o p c h is darker in proportion as it is nearer to the line p h and is lighter in proportion as it is nearer to the line o c4 ,let the light a b1 be a window1 and let the dark wall in which this window is1 be b s1 that is1 one of the sides of the wall4 ,then we may say that the line p h is darker than any other part of the space o p c h1 because this line faces the whole surface in shadow of ,footnote3 ,in the original the diagram is placed between lines #bg and #bh4 the wall b s4 ,the line o c is lighter than the other part of this space o p c h1 because this line faces the luminous space a b4 ,where the shadow is larger1 or smaller1 or equal the body which casts it4 ,first of the character of divided lights4 ,footnote #ad3 lumi divisi4 ,the text here breaks off abruptly4 ,,of ,,the ,,compound ,,shadow ,f1 ,r1 ,c1 ,h ,,caused ,,by ,a ,,single ,,light4 ,the shadow f r c h is under such conditions as that where it is farthest from its inner side it loses depth in proportion4 ,to prove this3 ,let d a1 be the light and f n the solid body1 and let a e be one of the side walls of the window that is d a4 ,then ,i say--according to the #bnd proposition3 that the surface of any body is affected by the tone of the objects surrounding it1--that the side r c1 which faces the dark wall a e must participate of its darkness and1 in the same way that the outer surface which faces the light d a participates of the light2 thus we get the outlines of the extremes on each side of the centre included between them4 ,this is divided into four parts4 ,the first the extremes1 which include the compound shadow1 secondly the compound shadow between these extremes4 #agi4 ,,the ,,action ,,of ,,the ,,light ,,as ,,from ,,its ,,centre4 ,if it were the whole of the light that caused the shadows beyond the bodies placed in front of it1 it would follow that any body much smaller than the light would cast a pyramidal shadow2 but experience not showing this1 it must be the centre of the light that produces this effect4 ,footnote3 ,the diagram belonging to this passage is between lines #d and #e in the original4 ,comp4 the reproduction ,pl4 ,,iv1 ,no4 #d4 ,the text and drawing of this chapter have already been published with tolerable accuracy4 ,see ,m4 ,,jordan3 ,das ,malerbuch des ,leonardo da ,vinci4 ,leipzig #ahgc1 ,p4 #ij4 ,,proof4 ,let a b be the width of the light from a window1 which falls on a stick set up at one foot from a c ,footnote #f3 bastone 7stick74 ,the diagram has a sphere in place of a stick44 ,and let a d be the space where all the light from the window is visible4 ,at c e that part of the window which is between l b cannot be seen4 ,in the same way a m cannot be seen from d f and therefore in these two portions the light begins to fail4 ,shadow as produced by two lights of different size 7#ahj4 #aha74 #ahj4 ,a body in light and shade placed between two equal lights side by side will cast shadows in proportion to the amount of light4 ,and the shadows will be one darker than the other in proportion as one light is nearer to the said body than the other on the opposite side4 ,a body placed at an equal distance between two lights will cast two shadows1 one deeper than the other in proportion1 as the light which causes it is brighter than the other4 ,footnote3 ,in the ,,ms4 the larger diagram is placed above the first line2 the smaller one between l4 #d #e4 #aha4 ,a light which is smaller than the body it illuminates produces shadows of which the outlines end within the surface of the body1 and not much compound shadow2 and falls on less than half of it4 ,a light which is larger than the body it illuminates1 falls on more than half of it1 and produces much compound shadow4 ,the effect of light at different distances4 #ahb4 ,,of ,,the ,,shadow ,,cast ,,by ,a ,,body ,,placed ,,between #b ,,equal ,,lights4 ,a body placed between #b equal lights will cast #b shadows of itself in the direction of the lines of the #b lights2 and if you move this body placing it nearer to one of the lights the shadow cast towards the nearer light will be less deep than that which falls towards the more distant one4 ,further complications in the derived shadows 7#ahc-ahg74 #ahc4 ,the greatest depth of shadow is in the simple derived shadow because it is not lighted by either of the two lights a b1 c d4 ,the next less deep shadow is the derived shadow e f n2 and in this the shadow is less by half1 because it is illuminated by a single light1 that is c d4 ,this is uniform in natural tone because it is lighted throughout by one only of the two luminous bodies #aj4 ,but it varies with the conditions of shadow1 inasmuch as the farther it is away from the light the less it is illuminated by it #ac4 ,the third degree of depth is the middle shadow ,footnote #ae3 ,we gather from what follows that q g r here means ombra media 7the middle shadow744 ,but this is not uniform in natural tone2 because the nearer it gets to the simple derived shadow the deeper it is ,footnote #ah3 ,compare lines #aj-ac1 and it is the uniformly gradual diminution by increase of distance which is what modifies it ,footnote #bj3 ,see ,footnote #ah3 that is to say the depth of a shadow increases in proportion to the distance from the two lights4 ,the fourth is the shadow k r s and this is all the darker in natural tone in proportion as it is nearer to k s1 because it gets less of the light a o1 but by the accident of distance it is rendered less deep1 because it is nearer to the light c d1 and thus is always exposed to both lights4 ,the fifth is less deep in shadow than either of the others because it is always entirely exposed to one of the lights and to the whole or part of the other2 and it is less deep in proportion as it is nearer to the two lights1 and in proportion as it is turned towards the outer side x t2 because it is more exposed to the second light a b4 ,footnote3 ,the diagram to this section is given on ,pl4 ,v4 ,to the left is the facsimile of the beginning of the text belonging to it4 #ahd4 ,,of ,,simple ,,shadows4 ,why1 at the intersections a1 b of the two compound shadows e f and m e1 is a simple shadow pfoduced as at e h and m g1 while no such simple shadow is produced at the other two intersections c d made by the very same compound shadows8 ,,answer4 ,compound shadow are a mixture of light and shade and simple shadows are simply darkness4 ,hence1 of the two lights n and o1 one falls on the compound shadow from one side1 and the other on the compound shadow from the other side1 but where they intersect no light falls1 as at a b2 therefore it is a simple shadow4 ,where there is a compound shadow one light or the other falls2 and here a difficulty arises for my adversary since he says that1 where the compound shadows intersect1 both the lights which produce the shadows must of necessity fall and therefore these shadows ought to be neutralised2 inasmuch as the two lights do not fall there1 we say that the shadow is a simple one and where only one of the two lights falls1 we say the shadow is compound1 and where both the lights fall the shadow is neutralised2 for where both lights fall1 no shadow of any kind is produced1 but only a light background limiting the shadow4 ,here ,i shall say that what my adversary said was true3 but he only mentions such truths as are in his favour2 and if we go on to the rest he must conclude that my proposition is true4 ,and that is3 ,that if both lights fell on the point of intersection1 the shadows would be neutralised4 ,this ,i confess to be true if neither of the two shadows fell in the same spot2 because1 where a shadow and a light fall1 a compound shadow is produced1 and wherever two shadows or two equal lights fall1 the shadow cannot vary in any part of it1 the shadows and the lights both being equal4 ,and this is proved in the eighth proposition on proportion where it is said that if a given quantity has a single unit of force and resistance1 a double quantity will have double force and double resistance4 ,,definition4 ,the intersection n is produced by the shadows caused by the light b1 because this light b produces the shadow x b1 and the shadow s b1 but the intersection m is produced by the light a which causes the shadow s a1 and the shadow x a4 ,but if you uncover both the lights a b1 then you get the two shadows n m both at once1 and besides these1 two other1 simple shadows are produced at r o where neither of the two lights falls at all4 ,the grades of depth in compound shadows are fewer in proportion as the lights falling on1 and crossing them are less numerous4 #ahf4 ,why the intersections at n being composed of two compound derived shadows1 forms a compound shadow and not a simple one1 as happens with other intersections of compound shadows4 ,this occurs1 according to the #bnd diagram of this prop4 which says3--,the intersection of derived shadows when produced by the intersection of columnar shadows caused by a single light does not produce a simple shadow4 ,and this is the corollary of the #ast prop4 which says3--,the intersection of simple derived shadows never results in a deeper shadow1 because the deepest shadows all added together cannot be darker than one by itself4 ,since1 if many deepest shadows increased in depth by their duplication1 they could not be called the deepest shadows1 but only part-shadows4 ,but if such intersections are illuminated by a second light placed between the eye and the intersecting bodies1 then those shadows would become compound shadows and be uniformly dark just as much at the intersection as throughout the rest4 ,in the #ast and #bnd above1 the intersections i k will not be doubled in depth as it is doubled in quantity4 ,but in this #crd1 at the intersections g n they will be double in depth and in quantity4 #ahg4 ,,how ,,and ,,when ,,the ,,surroundings ,,in ,,shadow ,,mingle ,,their ,,derived ,,shadow ,,with ,,the ,,light ,,derived ,,from ,,the ,,luminous ,,body4 ,the derived shadow of the dark walls on each side of the bright light of the window are what mingle their various degrees of shade with the light derived from the window2 and these various depths of shade modify every portion of the light1 except where it is strongest1 at c4 ,to prove this let d a be the primary shadow which is turned towards the point e1 and darkens it by its derived shadow2 as may be seen by the triangle a e d1 in which the angle e faces the darkened base d a e2 the point v faces the dark shadow a s which is part of a d1 and as the whole is greater than a part1 e which faces the whole base of the triangle1 will be in deeper shadow than v which only faces part of it4 ,in consequence of the conclusion shown in the above diagram1 t will be less darkened than v1 because the base of the t is part of the base of the v2 and in the same way it follows that p is less in shadow than t1 because the base of the p is part of the base of the t4 ,and c is the terminal point of the derived shadow and the chief beginning of the highest light4 ,footnote3 ,the diagram on ,pl4 ,,iv1 ,no4 #e belongs to this passage2 but it must be noted that the text explains only the figure on the right-hand side4 ,,fourth ,,book ,,on ,,light ,,and ,,shade4 ,on the shape of the cast shadows 7#ahh-aia74 #ahh4 ,the form of the shadow cast by any body of uniform density can never be the same as that of the body producing it4 ,footnote3 ,comp4 the drawing on ,,pi4 ,,xxviii1 ,no4 #e4 #ahi4 ,no cast shadow can produce the true image of the body which casts it on a vertical plane unless the centre of the light is equally distant from all the edges of that body4 #aij4 ,if a window a b admits the sunlight into a room1 the sunlight will magnify the size of the window and diminish the shadow of a man in such a way as that when the man makes that dim shadow of himself1 approach to that which defines the real size of the window1 he will see the shadows where they come into contact1 dim and confused from the strength of the light1 shutting off and not allowing the solar rays to pass2 the effect of the shadow of the man cast by this contact will be exactly that figured above4 ,footnote3 ,it is scarcely possible to render the meaning of this sentence with strict accuracy2 mainly because the grammatical construction is defective in the most important part--line #d4 ,in the very slight original sketch the shadow touches the upper arch of the window and the correction1 here given is perhaps not justified4 #aia4 ,a shadow is never seen as of uniform depth on the surface which intercepts it unless every portion of that surface is equidistant from the luminous body4 ,this is proved by the #gth which says3--,the shadow will appear lighter or stronger as it is surrounded by a darker or a lighter background4 ,and by the #hth of this3--,the background will be in parts darker or lighter1 in proportion as it is farther from or nearer to the luminous body4 ,and3--,of various spots equally distant from the luminous body those will always be in the highest light on which the rays fall at the smallest angles3 ,the outline of the shadow as it falls on inequalities in the surface will be seen with all the contours similar to those of the body that casts it1 if the eye is placed just where the centre of the light was4 ,the shadow will look darkest where it is farthest from the body that casts it4 ,the shadow c d1 cast by the body in shadow a b which is equally distant in all parts1 is not of equal depth because it is seen on a back ground of varying brightness4 ,footnote3 ,compare the three diagrams on ,pl4 ,,vi1 no #a which1 in the original accompany this section4 ,on the outlines of cast shadows 7#aib-aie74 #aib4 ,the edges of a derived shadow will be most distinct where it is cast nearest to the primary shadow4 #aic4 ,as the derived shadow gets more distant from the primary shadow1 the more the cast shadow differs from the primary shadow4 #aid4 ,,of ,,shadows ,,which ,,never ,,come ,,to ,,an ,,end4 ,the greater the difference between a light and the body lighted by it1 the light being the larger1 the more vague will be the outlines of the shadow of that object4 ,the derived shadow will be most confused towards the edges of its interception by a plane1 where it is remotest from the body casting it4 #aie4 ,what is the cause which makes the outlines of the shadow vague and confused8 ,whether it is possible to give clear and definite outlines to the edges of shadows4 ,on the relative size of shadows 7#aif4 #aig74 #aif4 ,,the ,,body ,,which ,,is ,,nearest ,,to ,,the ,,light ,,casts ,,the ,,largest ,,shadow1 ,,and ,,why8 ,if an object placed in front of a single light is very close to it you will see that it casts a very large shadow on the opposite wall1 and the farther you remove the object from the light the smaller will the image of the shadow become4 ,,why ,a ,,shadow ,,larger ,,than ,,the ,,body ,,that ,,produces ,,it ,,becomes ,,out ,,of ,,proportion4 ,the disproportion of a shadow which is larger than the body producing it1 results from the light being smaller than the body1 so that it cannot be at an equal distance from the edges of the body ,footnote #aa3 ,h4 ,,ludwig in his edition of the old copies1 in the ,vatican library--in which this chapter is included under ,nos4 #fab1 #fac and #fad alters this passage as follows3 quella parte ch'e piu propinqua piu cresce che le distanti1 although the ,vatican copy agrees with the original ,,ms4 in having distante in the former and propinque in the latter place4 ,this supposed amendment seems to me to invert the facts4 ,supposing for instance1 that on ,pl4 ,,xxxi ,no4 #c4 f is the spot where the light is that illuminates the figure there represented1 and that the line behind the figure represents a wall on which the shadow of the figure is thrown4 ,it is evident1 that in that case the nearest portion1 in this case the under part of the thigh1 is very little magnified in the shadow1 and the remoter parts1 for instance the head1 are more magnified42 and the portions which are most remote are made larger than the nearer portions for this reason ,footnote #ab3 ,see ,footnote #aa4 ,,why ,a ,,shadow ,,which ,,is ,,larger ,,than ,,the ,,body ,,causing ,,it ,,has ,,ill-,,defined ,,outlines4 ,the atmosphere which surrounds a light is almost like light itself for brightness and colour2 but the farther off it is the more it loses this resemblance4 ,an object which casts a large shadow and is near to the light1 is illuminated both by that light by the luminous atmosphere2 hence this diffused light gives the shadow ill-defined edges4 #aig4 ,a luminous body which is long and narrow in shape gives more confused outlines to the derived shadow than a spherical light1 and this contradicts the proposition next following3 ,a shadow will have its outlines more clearly defined in proportion as it is nearer to the primary shadow or1 ,i should say1 the body casting the shadow2 ,footnote #ad3 ,the lettering refers to the lower diagram1 ,pl4 ,,xli1 ,no4 #e4 the cause of this is the elongated form of the luminous body a c1 c4 ,footnote #af3 ,see ,footnote #ad4 ,effects on cast shadows by the tone of the back ground4 #aih4 ,,of ,,modified ,,shadows4 ,modified shadows are those which are cast on light walls or other illuminated objects4 ,a shadow looks darkest against a light background4 ,the outlines of a derived shadow will be clearer as they are nearer to the primary shadow4 ,a derived shadow will be most defined in shape where it is intercepted1 where the plane intercepts it at the most equal angle4 ,those parts of a shadow will appear darkest which have darker objects opposite to them4 ,and they will appear less dark when they face lighter objects4 ,and the larger the light object opposite1 the more the shadow will be lightened4 ,and the larger the surface of the dark object the more it will darken the derived shadow where it is intercepted4 ,a disputed proposition4 #aii4 ,,of ,,the ,,opinion ,,of ,,some ,,that ,a ,,triangle ,,casts ,,no ,,shadow ,,on ,a ,,plane ,,surface4 ,certain mathematicians have maintained that a triangle1 of which the base is turned to the light1 casts no shadow on a plane2 and this they prove by saying #e that no spherical body smaller than the light can reach the middle with the shadow4 ,the lines of radiant light are straight lines #f2 therefore1 suppose the light to be g h and the triangle l m n1 and let the plane be i k2 they say the light g falls on the side of the triangle l n1 and the portion of the plane i q4 ,thus again h like g falls on the side l m1 and then on m n and the plane p k2 and if the whole plane thus faces the lights g h1 it is evident that the triangle has no shadow2 and that which has no shadow can cast none4 ,this1 in this case appears credible4 ,but if the triangle n p g were not illuminated by the two lights g and h1 but by i p and g and k neither side is lighted by more than one single light3 that is i p is invisible to h g and k will never be lighted by g2 hence p q will be twice as light as the two visible portions that are in shadow4 ,footnote3 #e--f4 ,this passage is so obscure that it would be rash to offer an explanation4 ,several words seem to have been omitted4 ,on the relative depth of cast shadows 7#bjj-bjb74 #bjj4 ,a spot is most in the shade when a large number of darkened rays fall upon it4 ,the spot which receives the rays at the widest angle and by darkened rays will be most in the dark2 a will be twice as dark as b1 because it originates from twice as large a base at an equal distance4 ,a spot is most illuminated when a large number of luminous rays fall upon it4 d is the beginning of the shadow d f1 and tinges c but a little2 d e is half of the shadow d f and gives a deeper tone where it is cast at b than at f4 ,and the whole shaded space e gives its tone to the spot a4 ,footnote3 ,the diagram here referred to is on ,pl4 ,,xli1 ,no4 #b4 #bja4 ,a n will be darker than c r in proportion to the number of times that a b goes into c d4 #bjb4 ,the shadow cast by an object on a plane will be smaller in proportion as that object is lighted by feebler rays4 ,let d e be the object and d c the plane surface2 the number of times that d e will go into f g gives the proportion of light at f h to d c4 ,the ray of light will be weaker in proportion to its distance from the hole through which it falls4 ,,fifth ,,book ,,on ,,light ,,and ,,shade4 ,principles of reflection 7#bjc4 #bjd74 #bjc4 ,,of ,,the ,,way ,,in ,,which ,,the ,,shadows ,,cast ,,by ,,objects ,,ought ,,to ,,be ,,defined4 ,if the object is the mountain here figured1 and the light is at the point a1 ,i say that from b d and also from c f there will be no light but from reflected rays4 ,and this results from the fact that rays of light can only act in straight lines2 and the same is the case with the secondary or reflected rays4 #bjd4 ,the edges of the derived shadow are defined by the hues of the illuminated objects surrounding the luminous body which produces the shadow4 ,on reverberation4 #bje4 ,,of ,,reverberation4 ,reverberation is caused by bodies of a bright nature with a flat and semi opaque surface which1 when the light strikes upon them1 throw it back again1 like the rebound of a ball1 to the former object4 ,,where ,,there ,,can ,,be ,,no ,,reflected ,,lights4 ,all dense bodies have their surfaces occupied by various degrees of light and shade4 ,the lights are of two kinds1 one called original1 the other borrowed4 ,original light is that which is inherent in the flame of fire or the light of the sun or of the atmosphere4 ,borrowed light will be reflected light2 but to return to the promised definition3 ,i say that this luminous reverberation is not produced by those portions of a body which are turned towards darkened objects1 such as shaded spots1 fields with grass of various height1 woods whether green or bare2 in which1 though that side of each branch which is turned towards the original light has a share of that light1 nevertheless the shadows cast by each branch separately are so numerous1 as well as those cast by one branch on the others1 that finally so much shadow is the result that the light counts for nothing4 ,hence objects of this kind cannot throw any reflected light on opposite objects4 ,reflection on water 7#bjf4 #bjg74 #bjf4 ,,perspective4 ,the shadow or object mirrored in water in motion1 that is to say in small wavelets1 will always be larger than the external object producing it4 #bjg4 ,it is impossible that an object mirrored on water should correspond in form to the object mirrored1 since the centre of the eye is above the surface of the water4 ,this is made plain in the figure here given1 which demonstrates that the eye sees the surface a b1 and cannot see it at l f1 and at r t2 it sees the surface of the image at r t1 and does not see it in the real object c d4 ,hence it is impossible to see it1 as has been said above unless the eye itself is situated on the surface of the water as is shown below #ac4 ,footnote3 ,a stands for ochio eye1 ,b for aria air1 ,c for acqua water1 ,d for cateto cathetus4--,in the original ,,ms4 the second diagram is placed below line #ac4 ,experiments with the mirror 7#bjh-baj74 #bjh4 ,,the ,,mirror4 ,if the illuminated object is of the same size as the luminous body and as that in which the light is reflected1 the amount of the reflected light will bear the same proportion to the intermediate light as this second light will bear to the first1 if both bodies are smooth and white4 #bji4 ,describe how it is that no object has its limitation in the mirror but in the eye which sees it in the mirror4 ,for if you look at your face in the mirror1 the part resembles the whole in as much as the part is everywhere in the mirror1 and the whole is in every part of the same mirror2 and the same is true of the whole image of any object placed opposite to this mirror1 c4 #baj4 ,no man can see the image of another man in a mirror in its proper place with regard to the objects2 because every object falls on the surface of the mirror at equal angles4 ,and if the one man1 who sees the other in the mirror1 is not in a direct line with the image he will not see it in the place where it really falls2 and if he gets into the line1 he covers the other man and puts himself in the place occupied by his image4 ,let n o be the mirror1 b the eye of your friend and d your own eye4 ,your friend's eye will appear to you at a1 and to him it will seem that yours is at c1 and the intersection of the visual rays will occur at m1 so that either of you touching m will touch the eye of the other man which shall be open4 ,and if you touch the eye of the other man in the mirror it will seem to him that you are touching your own4 ,appendix3--,on shadows in movement 7#baa4 #bab74 #baa4 ,,of ,,the ,,shadow ,,and ,,its ,,motion4 ,when two bodies casting shadows1 and one in front of the other1 are between a window and the wall with some space between them1 the shadow of the body which is nearest to the plane of the wall will move if the body nearest to the window is put in transverse motion across the window4 ,to prove this let a and b be two bodies placed between the window n m and the plane surface o p with sufficient space between them as shown by the space a b4 ,i say that if the body a is moved towards s the shadow of the body b which is at c will move towards d4 #bab4 ,,of ,,the ,,motion ,,of ,,shadows4 ,the motion of a shadow is always more rapid than that of the body which produces it if the light is stationary4 ,to prove this let a be the luminous body1 and b the body casting the shadow1 and d the shadow4 ,then ,i say that in the time while the solid body moves from b to c1 the shadow d will move to e2 and this proportion in the rapidity of the movements made in the same space of time1 is equal to that in the length of the space moved over4 ,thus1 given the proportion of the space moved over by the body b to c1 to that moved over by the shadow d to e1 the proportion in the rapidity of their movements will be the same4 ,but if the luminous body is also in movement with a velocity equal to that of the solid body1 then the shadow and the body that casts it will move with equal speed4 ,and if the luminous body moves more rapidly than the solid body1 the motion of the shadow will be slower than that of the body casting it4 ,but if the luminous body moves more slowly than the solid body1 then the shadow will move more rapidly than that body4 ,,sixth ,,book ,,on ,,light ,,and ,,shade4 ,the effect of rays passing through holes 7#bac4 #bad74 #bac4 ,,perspective4 ,if you transmit the rays of the sun through a hole in the shape of a star you will see a beautiful effect of perspective in the spot where the sun's rays fall4 ,footnote3 ,in this and the following chapters of ,,ms4 ,c the order of the original paging has been adhered to1 and is shown in parenthesis4 ,leonardo himself has but rarely worked out the subject of these propositions4 ,the space left for the purpose has occasionally been made use of for quite different matter4 ,even the numerous diagrams1 most of them very delicately sketched1 lettered and numbered1 which occur on these pages1 are hardly ever explained1 with the exception of those few which are here given4 #bad4 ,no small hole can so modify the convergence of rays of light as to prevent1 at a long distance1 the transmission of the true form of the luminous body causing them4 ,it is impossible that rays of light passing through a parallel slit1 should not display the form of the body causing them1 since all the effects produced by a luminous body are in fact the reflection of that body3 ,the moon1 shaped like a boat1 if transmitted through a hole is figured in the surface it falls on as a boatshaped object4 ,footnote #h3 ,in the ,,ms4 a blank space is left after this question4 ,why the eye sees bodies at a distance1 larger than they measure on the vertical plane84 ,footnote3 ,this chapter1 taken from another ,,ms4 may1 as an exception1 be placed here1 as it refers to the same subject as the preceding section4 ,on gradation of shadows 7#bae4 #baf74 #bae4 ,although the breadth and length of lights and shadow will be narrower and shorter in foreshortening1 the quality and quantity of the light and shade is not increased nor diminished4 #c,the function of shade and light when diminished by foreshortening1 will be to give shadow and to illuminate an object opposite1 according to the quality and quantity in which they fall on the body4 #e;,in proportion as a derived shadow is nearer to its penultimate extremities the deeper it will appear1 g z beyond the intersection faces only the part of the shadow marked y z2 this by intersection takes the shadow from m n but by direct line it takes the shadow a m hence it is twice as deep as g z4 ,y x1 by intersection takes the shadow n o1 but by direct line the shadow n m a1 therefore x y is three times as dark as z g2 x f1 by intersection faces o b and by direct line o n m a1 therefore we must say that the shadow between f x will be four times as dark as the shadow z g1 because it faces four times as much shadow4 ,let a b be the side where the primary shadow is1 and b c the primary light1 d will be the spot where it is intercepted1f g the derived shadow and f e the derived light4 ,and this must be at the beginning of the explanation4 ,footnote3 ,in the original ,,ms4 the text of ,no4 #beb precedes the one given here4 ,in the text of ,no4 #bae there is a blank space of about four lines between the lines #b and #c4 ,the diagram given on ,pl4 ,,vi1 ,no4 #b is placed between lines #d and #e4 ,between lines #e and #f there is another space of about three lines and one line left blank between lines #h and #i4 ,the reader will find the meaning of the whole passage much clearer if he first reads the final lines #aa--ac4 ,compare also line #d of ,no4 #bgj4 ,on relative proportion of light and shadows 7#baf--bba74 #baf4 ,that part of the surface of a body on which the images reflection from other bodies placed opposite fall at the largest angle will assume their hue most strongly4 ,in the diagram below1 #h is a larger angle than #d1 since its base a n is larger than e n the base of #d4 ,this diagram below should end at a n #d #h4 #d,that portion of the illuminated surface on which a shadow is cast will be brightest which lies contiguous to the cast shadow4 ,just as an object which is lighted up by a greater quantity of luminous rays becomes brighter1 so one on which a greater quantity of shadow falls1 will be darker4 ,let #d be the side of an illuminated surface #d #h1 surrounding the cast shadow g e #d4 ,and this spot #d will be lighter than #h1 because less shadow falls on it than on #h4 ,since #d faces only the shadow i n2 and #h faces and receives the shadow a e as well as i n which makes it twice as dark4 ,and the same thing happens when you put the atmosphere and the sun in the place of shade and light4 #ab ,the distribution of shadow1 originating in1 and limited by1 plane surfaces placed near to each other1 equal in tone and directly opposite1 will be darker at the ends than at the beginning1 which will be determined by the incidence of the luminous rays4 ,you will find the same proportion in the depth of the derived shadows a n as in the nearness of the luminous bodies m b1 which cause them2 and if the luminous bodies were of equal size you would still farther find the same proportion in the light cast by the luminous circles and their shadows as in the distance of the said luminous bodies4 ,footnote3 ,the diagram originally placed between lines #c and #d is on ,pl4 ,,vi1 ,no4 #c4 ,in the diagram given above line #ad of the original1 and here printed in the text1 the words corpo luminoso luminous body are written in the circle m1 luminoso in the circle b and ombroso body in shadow in the circle o4 #bag4 ,,that ,,part ,,of ,,the ,,reflection ,,will ,,be ,,brightest ,,where ,,the ,,reflected ,,rays ,,are ,,shortest4 #b ,the darkness occasioned by the casting of combined shadows will be in conformity with its cause1 which will originate and terminate between two plane surfaces near together1 alike in tone and directly opposite each other4 #d ,in proportion as the source of light is larger1 the luminous and shadow rays will be more mixed together4 ,this result is produced because wherever there is a larger quantity of luminous rays1 there is most light1 but where there are fewer there is least light1 consequently the shadow rays come in and mingle with them4 ,footnote3 ,diagrams are inserted before lines #b and #d4 #bah4 ,in all the proportions ,i lay down it must be understood that the medium between the bodies is always the same4 #b ,the smaller the luminous body the more distinct will the transmission of the shadows be4 #c ,when of two opposite shadows1 produced by the same body1 one is twice as dark as the other though similar in form1 one of the two lights causing them must have twice the diameter that the other has and be at twice the distance from the opaque body4 ,if the object is lowly moved across the luminous body1 and the shadow is intercepted at some distance from the object1 there will be the same relative proportion between the motion of the derived shadow and the motion of the primary shadow1 as between the distance from the object to the light1 and that from the object to the spot where the shadow is intercepted2 so that though the object is moved slowly the shadow moves fast4 ,footnote3 ,there are diagrams inserted before lines #b and #c but they are not reproduced here4 ,the diagram above line #f is written upon as follows3 at ,a lume 7light71 at ,b obbietto 7body71 at ,c ombra d'obbietto 7shadow of the object74 #bai4 ,a luminous body will appear less brilliant when surrounded by a bright background4 #b ,i have found that the stars which are nearest to the horizon look larger than the others because light falls upon them from a larger proportion of the solar body than when they are above us2 and having more light from the sun they give more light1 and the bodies which are most luminous appear the largest4 ,as may be seen by the sun through a mist1 and overhead2 it appears larger where there is no mist and diminished through mist4 ,no portion of the luminous body is ever visible from any spot within the pyramid of pure derived shadow4 ,footnote3 ,between lines #a and #b there is in the original a large diagram which does not refer to this text4 #bbj4 ,a body on which the solar rays fall between the thin branches of trees far apart will cast but a single shadow4 #b ,if an opaque body and a luminous one are 7both7 spherical the base of the pyramid of rays will bear the same proportion to the luminous body as the base of the pyramid of shade to the opaque body4 #d ,when the transmitted shadow is intercepted by a plane surface placed opposite to it and farther away from the luminous body than from the object which casts it it will appear proportionately darker and the edges more distinct4 ,footnote3 ,the diagram which1 in the original1 is placed above line #b1 is similar to the one1 here given on page #gc 7section #abj74--,the diagram here given in the margin stands1 in the original1 between lines #c and #d4 #bba4 ,a body illuminated by the solar rays passing between the thick branches of trees will produce as many shadows as there are branches between the sun and itself4 ,where the shadow-rays from an opaque pyramidal body are intercepted they will cast a shadow of bifurcate outline and various depth at the points4 ,a light which is broader than the apex but narrower than the base of an opaque pyramidal body placed in front of it1 will cause that pyramid to cast a shadow of bifurcate form and various degrees of depth4 ,if an opaque body1 smaller than the light1 casts two shadows and if it is the same size or larger1 casts but one1 it follows that a pyramidal body1 of which part is smaller1 part equal to1 and part larger than1 the luminous body1 will cast a bifurcate shadow4 ,footnote3 ,between lines #b and #c there are in the original two large diagrams4 ,,iv4 ,perspective of ,disappearance4 ,the theory of the ,prospettiva de' perdimenti would1 in many important details1 be quite unintelligible if it had not been led up by the principles of light and shade on which it is based4 ,the word ,prospettiva in the language of the time included the principles of optics2 what ,leonardo understood by ,perdimenti will be clearly seen in the early chapters1 ,nos4 #bbb--bbd4 ,it is in the very nature of the case that the farther explanations given in the subsequent chapters must be limited to general rules4 ,the sections given as #bbg--bca ,on indistinctness at short distances have1 it is true1 only an indirect bearing on the subject2 but on the other hand1 the following chapters1 #bcb--bcd1 ,on indistinctness at great distances1 go fully into the matter1 and in chapters #bce--bci1 which treat ,of the importance of light and shade in the ,perspective of ,disappearance1 the practical issues are distinctly insisted on in their relation to the theory4 ,this is naturally followed by the statements as to the effect of light or dark backgrounds on the apparent size of bodies 7,nos4 #bdj--bej74 ,at the end ,i have placed1 in the order of the original1 those sections from the ,,ms4 ,c which treat of the ,perspective of ,disappearance and serve to some extent to complete the treatment of the subject 7#bea--bfb74 ,definition 7#bbb4 #bbc74 #bbb4 ,,of ,,the ,,diminished ,,distinctness ,,of ,,the ,,outlines ,,of ,,opaque ,,bodies4 ,if the real outlines of opaque bodies are indistinguishable at even a very short distance1 they will be more so at long distances2 and1 since it is by its outlines that we are able to know the real form of any opaque body1 when by its remoteness we fail to discern it as a whole1 much more must we fail to discern its parts and outlines4 #bbc4 ,,of ,,the ,,diminution ,,in ,,perspective ,,of ,,opaque ,,objects4 ,among opaque objects of equal size the apparent diminution of size will be in proportion to their distance from the eye of the spectator2 but it is an inverse proportion1 since1 where the distance is greater1 the opaque body will appear smaller1 and the less the distance the larger will the object appear4 ,and this is the fundamental principle of linear perspective and it follows3--#aa;every object as it becomes more remote loses first those parts which are smallest4 ,thus of a horse1 we should lose the legs before the head1 because the legs are thinner than the head2 and the neck before the body for the same reason4 ,hence it follows that the last part of the horse which would be discernible by the eye would be the mass of the body in an oval form1 or rather in a cylindrical form and this would lose its apparent thickness before its length--according to the #bnd rule given above1 c4 ,footnote #bc3 ,compare line #aa44 ,if the eye remains stationary the perspective terminates in the distance in a point4 ,but if the eye moves in a straight horizontal line the perspective terminates in a line and the reason is that this line is generated by the motion of the point and our sight2 therefore it follows that as we move our sight eye1 the point moves1 and as we move the point1 the line is generated1 c4 ,an illustration by experiment4 #bbd4 ,every visible body1 in so far as it affects the eye1 includes three attributes2 that is to say3 mass1 form and colour2 and the mass is recognisable at a greater distance from the place of its actual existence than either colour or form4 ,again1 colour is discernible at a greater distance than form1 but this law does not apply to luminous bodies4 ,the above proposition is plainly shown and proved by experiment2 because3 if you see a man close to you1 you discern the exact appearance of the mass and of the form and also of the colouring2 if he goes to some distance you will not recognise who he is1 because the character of the details will disappear1 if he goes still farther you will not be able to distinguish his colouring1 but he will appear as a dark object1 and still farther he will appear as a very small dark rounded object4 ,it appears rounded because distance so greatly diminishes the various details that nothing remains visible but the larger mass4 ,and the reason is this3 ,we know very well that all the images of objects reach the senses by a small aperture in the eye2 hence1 if the whole horizon a d is admitted through such an aperture1 the object b c being but a very small fraction of this horizon what space can it fill in that minute image of so vast a hemisphere8 ,and because luminous bodies have more power in darkness than any others1 it is evident that1 as the chamber of the eye is very dark1 as is the nature of all colored cavities1 the images of distant objects are confused and lost in the great light of the sky2 and if they are visible at all1 appear dark and black1 as every small body must when seen in the diffused light of the atmosphere4 ,footnote3 ,the diagram belonging to this passage is placed between lines #e and #f2 it is ,no4 #d on ,pl4 ,,vi4 ,a guiding rule4 #bbe4 ,,of ,,the ,,atmosphere ,,that ,,interposes ,,between ,,the ,,eye ,,and ,,visible ,,objects4 ,an object will appear more or less distinct at the same distance1 in proportion as the atmosphere existing between the eye and that object is more or less clear4 ,hence1 as ,i know that the greater or less quantity of the air that lies between the eye and the object makes the outlines of that object more or less indistinct1 you must diminish the definiteness of outline of those objects in proportion to their increasing distance from the eye of the spectator4 ,an experiment4 #bbf4 ,when ,i was once in a place on the sea1 at an equal distance from the shore and the mountains1 the distance from the shore looked much greater than that from the mountains4 ,on indistinctness at short distances 7#bbg-bca74 #bbg4 ,if you place an opaque object in front of your eye at a distance of four fingers' breadth1 if it is smaller than the space between the two eyes it will not interfere with your seeing any thing that may be beyond it4 ,no object situated beyond another object seen by the eye can be concealed by this nearer object if it is smaller than the space from eye to eye4 #bbh4 ,the eye cannot take in a luminous angle which is too close to it4 #bbi4 ,that part of a surface will be better lighted on which the light falls at the greater angle4 ,and that part1 on which the shadow falls at the greatest angle1 will receive from those rays least of the benefit of the light4 #bcj4 ,,of ,,the ,,eye4 ,the edges of an object placed in front of the pupil of the eye will be less distinct in proportion as they are closer to the eye4 ,this is shown by the edge of the object n placed in front of the pupil d2 in looking at this edge the pupil also sees all the space a c which is beyond the edge2 and the images the eye receives from that space are mingled with the images of the edge1 so that one image confuses the other1 and this confusion hinders the pupil from distinguishing the edge4 #bca4 ,the outlines of objects will be least clear when they are nearest to the eye1 and therefore remoter outlines will be clearer4 ,among objects which are smaller than the pupil of the eye those will be less distinct which are nearer to the eye4 ,on indistinctness at great distances 7#bcb-bcd74 #bcb4 ,objects near to the eye will appear larger than those at a distance4 ,objects seen with two eyes will appear rounder than if they are seen with only one4 ,objects seen between light and shadow will show the most relief4 #bcc4 ,,of ,,painting4 ,our true perception of an object diminishes in proportion as its size is diminished by distance4 #bcd4 ,,perspective4 ,why objects seen at a distance appear large to the eye and in the image on the vertical plane they appear small4 ,,perspective4 ,i ask how far away the eye can discern a non-luminous body1 as1 for instance1 a mountain4 ,it will be very plainly visible if the sun is behind it2 and could be seen at a greater or less distance according to the sun's place in the sky4 ,footnote3 ,the clue to the solution of this problem 7lines #a-c7 is given in lines #d-f1 ,no4 #bcb4 ,objects seen with both eyes appear solid since they are seen from two distinct points of sight separated by the distance between the eyes1 but this solidity cannot be represented in a flat drawing4 ,compare ,no4 #ece4 ,the importance of light and shade in the perspective of disappearance 7#bce-bci74 #bce4 ,an opaque body seen in a line in which the light falls will reveal no prominences to the eye4 ,for instance1 let a be the solid body and c the light2 c m and c n will be the lines of incidence of the light1 that is to say the lines which transmit the light to the object a4 ,the eye being at the point b1 ,i say that since the light c falls on the whole part m n the portions in relief on that side will all be illuminated4 ,hence the eye placed at c cannot see any light and shade and1 not seeing it1 every portion will appear of the same tone1 therefore the relief in the prominent or rounded parts will not be visible4 #bcf4 ,,of ,,painting4 ,when you represent in your work shadows which you can only discern with difficulty1 and of which you cannot distinguish the edges so that you apprehend them confusedly1 you must not make them sharp or definite lest your work should have a wooden effect4 #bcg4 ,,of ,,painting4 ,you will observe in drawing that among the shadows some are of undistinguishable gradation and form1 as is shown in the #crd proposition which says3 ,rounded surfaces display as many degrees of light and shade as there are varieties of brightness and darkness reflected from the surrounding objects4 #bch4 ,,of ,,light ,,and ,,shade4 ,you who draw from nature1 look 7carefully7 at the extent1 the degree1 and the form of the lights and shadows on each muscle2 and in their position lengthwise observe towards which muscle the axis of the central line is directed4 #bci4 ,an object which is so brilliantly illuminated as to be almost as bright as light will be visible at a greater distance1 and of larger apparent size than is natural to objects so remote4 ,the effect of light or dark backgrounds on the apparent size of objects 7#bdj-bej74 #bdj4 ,a shadow will appear dark in proportion to the brilliancy of the light surrounding it and conversely it will be less conspicuous where it is seen against a darker background4 #bda4 ,,of ,,ordinary ,,perspective4 ,an object of equal breadth and colour throughout1 seen against a background of various colours will appear unequal in breadth4 ,and if an object of equal breadth throughout1 but of various colours1 is seen against a background of uniform colour1 that object will appear of various breadth4 ,and the more the colours of the background or of the object seen against the ground vary1 the greater will the apparent variations in the breadth be though the objects seen against the ground be of equal breadth throughout4 #bdb4 ,a dark object seen against a bright background will appear smaller than it is4 ,a light object will look larger when it is seen against a background darker than itself4 #bdc4 ,,of ,,light4 ,a luminous body when obscured by a dense atmosphere will appear smaller2 as may be seen by the moon or sun veiled by mists4 ,,of ,,light4 ,of several luminous bodies of equal size and brilliancy and at an equal distance1 that will look the largest which is surrounded by the darkest background4 ,,of ,,light4 ,i find that any luminous body when seen through a dense and thick mist diminishes in proportion to its distance from the eye4 ,thus it is with the sun by day1 as well as the moon and the other eternal lights by night4 ,and when the air is clear1 these luminaries appear larger in proportion as they are farther from the eye4 #bdd4 ,that portion of a body of uniform breadth which is against a lighter background will look narrower than the rest4 #d e is a given object1 itself dark and of uniform breadth2 a b and c d are two backgrounds one darker than the other2 b c is a bright background1 as it might be a spot lighted by the sun through an aperture in a dark room4 ,then ,i say that the object e g will appear larger at e f than at g h2 because e f has a darker background than g h2 and again at f g it will look narrower from being seen by the eye o1 on the light background b c4 ,footnote #ab3 ,the diagram to which the text1 lines #a-aa1 refers1 is placed in the original between lines #c and #d1 and is given on ,pl4 ,,xli1 ,no4 #c4 ,lines #ab to #ad are explained by the lower of the two diagrams on ,pl4 ,,xli1 ,no4 #d4 ,in the original these are placed after line #ad4 ,that part of a luminous body1 of equal breadth and brilliancy throughout1 will look largest which is seen against the darkest background2 and the luminous body will seem on fire4 #bde4 ,,why ,,bodies ,,in ,,light ,,and ,,shade ,,have ,,their ,,outlines ,,altered ,,by ,,the ,,colour ,,and ,,brightness ,,of ,,the ,,objects ,,serving ,,as ,a ,,background ,,to ,,them4 ,if you look at a body of which the illuminated portion lies and ends against a dark background1 that part of the light which will look brightest will be that which lies against the dark background at d4 ,but if this brighter part lies against a light background1 the edge of the object1 which is itself light1 will be less distinct than before1 and the highest light will appear to be between the limit of the background m f and the shadow4 ,the same thing is seen with regard to the dark side1 inasmuch as that edge of the shaded portion of the object which lies against a light background1 as at l1 it looks much darker than the rest4 ,but if this shadow lies against a dark background1 the edge of the shaded part will appear lighter than before1 and the deepest shade will appear between the edge and the light at the point o4 ,footnote3 ,in the original diagram o is inside the shaded surface at the level of d4 #bdf4 ,an opaque body will appear smaller when it is surrounded by a highly luminous background1 and a light body will appear larger when it is seen against a darker background4 ,this may be seen in the height of buildings at night1 when lightning flashes behind them2 it suddenly seems1 when it lightens1 as though the height of the building were diminished4 ,for the same reason such buildings look larger in a mist1 or by night than when the atmosphere is clear and light4 #bdg4 ,,on ,,light ,,between ,,shadows ,when you are drawing any object1 remember1 in comparing the grades of light in the illuminated portions1 that the eye is often deceived by seeing things lighter than they are4 ,and the reason lies in our comparing those parts with the contiguous parts4 ,since if two separate parts are in different grades of light and if the less bright is conterminous with a dark portion and the brighter is conterminous with a light background--as the sky or something equally bright--1 then that which is less light1 or ,i should say less radiant1 will look the brighter and the brighter will seem the darker4 #bdh4 ,of objects equally dark in themselves and situated at a considerable and equal distance1 that will look the darkest which is farthest above the earth4 #bdi4 ,,to ,,prove ,,how ,,it ,,is ,,that ,,luminous ,,bodies ,,appear ,,larger1 ,,at ,a ,,distance1 ,,than ,,they ,,are4 ,if you place two lighted candles side by side half a braccio apart1 and go from them to a distance #bjj braccia you will see that by the increased size of each they will appear as a single luminous body with the light of the two flames1 one braccio wide4 ,,to ,,prove ,,how ,,you ,,may ,,see ,,the ,,real ,,size ,,of ,,luminous ,,bodies4 ,if you wish to see the real size of these luminous bodies1 take a very thin board and make in it a hole no bigger than the tag of a lace and place it as close to your eye as possible1 so that when you look through this hole1 at the said light1 you can see a large space of air round it4 ,then by rapidly moving this board backwards and forwards before your eye you will see the light increase and diminish4 ,propositions on perspective of disappearance from ,,ms4 ,c4 7#bej-bfb74 #bej4 ,of several bodies of equal size and equally distant from the eye1 those will look the smallest which are against the lightest background4 ,every visible object must be surrounded by light and shade4 ,a perfectly spherical body surrounded by light and shade will appear to have one side larger than the other in proportion as one is more highly lighted than the other4 #bea4 ,,perspective4 ,no visible object can be well understood and comprehended by the human eye excepting from the difference of the background against which the edges of the object terminate and by which they are bounded1 and no object will appear to stand out separate from that background so far as the outlines of its borders are concerned4 ,the moon1 though it is at a great distance from the sun1 when1 in an eclipse1 it comes between our eyes and the sun1 appears to the eyes of men to be close to the sun and affixed to it1 because the sun is then the background to the moon4 #beb4 ,a luminous body will appear more brilliant in proportion as it is surrounded by deeper shadow4 ,footnote3 ,the diagram which1 in the original1 is placed after this text1 has no connection with it4 #bec4 ,the straight edges of a body will appear broken when they are conterminous with a dark space streaked with rays of light4 ,footnote3 ,here again the diagrams in the original have no connection with the text4 #bed4 ,of several bodies1 all equally large and equally distant1 that which is most brightly illuminated will appear to the eye nearest and largest4 ,footnote3 ,here again the diagrams in the original have no connection with the text4 #bee4 ,if several luminous bodies are seen from a great distance although they are really separate they will appear united as one body4 #bef4 ,if several objects in shadow1 standing very close together1 are seen against a bright background they will appear separated by wide intervals4 #beg4 ,of several bodies of equal size and tone1 that which is farthest will appear the lightest and smallest4 #beh4 ,of several objects equal in size1 brightness of background and length that which has the flattest surface will look the largest4 ,a bar of iron equally thick throughout and of which half is red hot1 affords an example1 for the red hot part looks thicker than the rest4 #bei4 ,of several bodies of equal size and length1 and alike in form and in depth of shade1 that will appear smallest which is surrounded by the most luminous background4 #bfj4 ,,different ,,portions ,,of ,a ,,wall ,,surface ,,will ,,be ,,darker ,,or ,,brighter ,,in ,,proportion ,,as ,,the ,,light ,,or ,,shadow ,,falls ,,on ,,them ,,at ,a ,,larger ,,angle4 ,the foregoing proposition can be clearly proved in this way4 ,let us say that m q is the luminous body1 then f g will be the opaque body2 and let a e be the above-mentioned plane on which the said angles fall1 showing plainly the nature and character of their bases4 ,then3 a will be more luminous than b2 the base of the angle a is larger than that of b and it therefore makes a greater angle which will be a m q2 and the pyramid b p m will be narrower and m o c will be still finer1 and so on by degrees1 in proportion as they are nearer to e1 the pyramids will become narrower and darker4 ,that portion of the wall will be the darkest where the breadth of the pyramid of shadow is greater than the breadth of the pyramid of light4 ,at the point a the pyramid of light is equal in strength to the pyramid of shadow1 because the base f g is equal to the base r f4 ,at the point d the pyramid of light is narrower than the pyramid of shadow by so much as the base s f is less than the base f g4 ,divide the foregoing proposition into two diagrams1 one with the pyramids of light and shadow1 the other with the pyramids of light only4 #bfa4 ,among shadows of equal depth those which are nearest to the eye will look least deep4 #bfb4 ,the more brilliant the light given by a luminous body1 the deeper will the shadows be cast by the objects it illuminates4 ,v4 ,theory of colours4 ,leonardo's theory of colours is even more intimately connected with his principles of light and shade than his ,perspective of ,disappearance and is in fact merely an appendix or supplement to those principles1 as we gather from the titles to sections #bfd1 #bfg1 and #bgf1 while others again 7,nos4 #bha1 #bhb7 are headed ,prospettiva4 ,a very few of these chapters are to be found in the oldest copies and editions of the ,treatise on ,painting1 and although the material they afford is but meager and the connection between them but slight1 we must still attribute to them a special theoretical value as well as practical utility--all the more so because our knowledge of the theory and use of colours at the time of the ,renaissance is still extremely limited4 ,the reciprocal effects of colours on objects placed opposite each other 7#bfc-bgb74 #bfc4 ,,of ,,painting4 ,the hue of an illuminated object is affected by that of the luminous body4 #bfd4 ,,of ,,shadow4 ,the surface of any opaque body is affected by the colour of surrounding objects4 #bfe4 ,a shadow is always affected by the colour of the surface on which it is cast4 #bff4 ,an image produced in a mirror is affected by the colour of the mirror4 #bfg4 ,,of ,,light ,,and ,,shade4 ,every portion of the surface of a body is varied in hue by the reflected colour of the object that may be opposite to it4 ,,example4 ,if you place a spherical body between various objects that is to say with direct sunlight on one side of it1 and on the other a wall illuminated by the sun1 which wall may be green or of any other colour1 while the surface on which it is placed may be red1 and the two lateral sides are in shadow1 you will see that the natural colour of that body will assume something of the hue reflected from those objects4 ,the strongest will be given by the luminous body2 the second by the illuminated wall1 the third by the shadows4 ,there will still be a portion which will take a tint from the colour of the edges4 #bfh4 ,the surface of every opaque body is affected by the colour of the objects surrounding it4 ,but this effect will be strong or weak in proportion as those objects are more or less remote and more or less strongly coloured4 #bfi4 ,,of ,,painting4 ,the surface of every opaque body assumes the hues reflected from surrounding objects4 ,the surface of an opaque body assumes the hues of surrounding objects more strongly in proportion as the rays that form the images of those objects strike the surface at more equal angles4 ,and the surface of an opaque body assumes a stronger hue from the surrounding objects in proportion as that surface is whiter and the colour of the object brighter or more highly illuminated4 #bgj4 ,,of ,,the ,,rays ,,which ,,convey ,,through ,,the ,,air ,,the ,,images ,,of ,,objects4 ,all the minutest parts of the image intersect each other without interfering with each other4 ,to prove this let r be one of the sides of the hole1 opposite to which let s be the eye which sees the lower end o of the line n o4 ,the other extremity cannot transmit its image to the eye s as it has to strike the end r and it is the same with regard to m at the middle of the line4 ,the case is the same with the upper extremity n and the eye u4 ,and if the end n is red the eye u on that side of the holes will not see the green colour of o1 but only the red of n according to the #gth of this where it is said3 ,every form projects images from itself by the shortest line1 which necessarily is a straight line1 c4 ,footnote3 #ac4 ,this probably refers to the diagram given under ,no4 #ff4 #bga4 ,,of ,,painting4 ,the surface of a body assumes in some degree the hue of those around it4 ,the colours of illuminated objects are reflected from the surfaces of one to the other in various spots1 according to the various positions of those objects4 ,let o be a blue object in full light1 facing all by itself the space b c on the white sphere a b e d e f1 and it will give it a blue tinge1 m is a yellow body reflected onto the space a b at the same time as o the blue body1 and they give it a green colour 7by the #bnd proposition of this which shows that blue and yellow make a beautiful green c47 ,and the rest will be set forth in the ,book on ,painting4 ,in that ,book it will be shown1 that1 by transmitting the images of objects and the colours of bodies illuminated by sunlight through a small round perforation and into a dark chamber onto a plane surface1 which itself is quite white1 c4 ,but every thing will be upside down4 ,combination of different colours in cast shadows4 #bgb4 ,that which casts the shadow does not face it1 because the shadows are produced by the light which causes and surrounds the shadows4 ,the shadow caused by the light e1 which is yellow1 has a blue tinge1 because the shadow of the body a is cast upon the pavement at b1 where the blue light falls2 and the shadow produced by the light d1 which is blue1 will be yellow at c1 because the yellow light falls there and the surrounding background to these shadows b c will1 besides its natural colour1 assume a hue compounded of yellow and blue1 because it is lighted by the yellow light and by the blue light both at once4 ,shadows of various colours1 as affected by the lights falling on them4 ,that light which causes the shadow does not face it4 ,footnote3 ,in the original diagram we find in the circle e giallo 7yellow7 and the cirle d azurro 7blue7 and also under the circle of shadow to the left giallo is written and under that to the right azurro4 ,in the second diagram where four circles are placed in a row we find written1 beginning at the left hand1 giallo 7yellow71 azurro 7blue71 verde 7green71 rosso 7red74 ,the effect of colours in the camera obscura 7#bgc-bgd74 #bgc4 ,the edges of a colour7ed object7 transmitted through a small hole are more conspicuous than the central portions4 ,the edges of the images1 of whatever colour1 which are transmitted through a small aperture into a dark chamber will always be stronger than the middle portions4 #bgd4 ,,of ,,the ,,intersections ,,of ,,the ,,images ,,in ,,the ,,pupil ,,of ,,the ,,eye4 ,the intersections of the images as they enter the pupil do not mingle in confusion in the space where that intersection unites them2 as is evident1 since1 if the rays of the sun pass through two panes of glass in close contact1 of which one is blue and the other yellow1 the rays1 in penetrating them1 do not become blue or yellow but a beautiful green4 ,and the same thing would happen in the eye1 if the images which were yellow or green should mingle where they meet and intersect as they enter the pupil4 ,as this does not happen such a mingling does not exist4 ,,of ,,the ,,nature ,,of ,,the ,,rays ,,composed ,,of ,,the ,,images ,,of ,,objects1 ,,and ,,of ,,their ,,intersections4 ,the directness of the rays which transmit the forms and colours of the bodies whence they proceed does not tinge the air nor can they affect each other by contact where they intersect4 ,they affect only the spot where they vanish and cease to exist1 because that spot faces and is faced by the original source of these rays1 and no other object1 which surrounds that original source can be seen by the eye where these rays are cut off and destroyed1 leaving there the spoil they have conveyed to it4 ,and this is proved by the #dth proposition1 on the colour of bodies1 which says3 ,the surface of every opaque body is affected by the colour of surrounding objects2 hence we may conclude that the spot which1 by means of the rays which convey the image1 faces--and is faced by the cause of the image1 assumes the colour of that object4 ,on the colours of derived shadows 7#bge4 #bgf74 #bge4 ,,any ,,shadow ,,cast ,,by ,,an ,,opaque ,,body ,,smaller ,,than ,,the ,,light ,,causing ,,the ,,shadow ,,will ,,throw ,a ,,derived ,,shadow ,,which ,,is ,,tinged ,,by ,,the ,,colour ,,of ,,the ,,light4 ,let n be the source of the shadow e f2 it will assume its hue4 ,let o be the source of h e which will in the same way be tinged by its hue and so also the colour of v h will be affected by p which causes it2 and the shadow of the triangle z k y will be affected by the colour of q1 because it is produced by it4 #g ,in proportion as c d goes into a d1 will n r s be darker than m2 and the rest of the space will be shadowless #aa4 f g is the highest light1 because here the whole light of the window a d falls2 and thus on the opaque body m e is in equally high light2 z k y is a triangle which includes the deepest shadow1 because the light a d cannot reach any part of it4 x h is the #bnd grade of shadow1 because it receives only #a_/c of the light from the window1 that is c d4 ,the third grade of shadow is h e1 where two thirds of the light from the window is visible4 ,the last grade of shadow is b d e f1 because the highest grade of light from the window falls at f4 ,footnote3 ,the diagram ,pl4 ,,iii1 ,no4 #a belongs to this chapter as well as the text given in ,no4 #adh4 ,lines #g-aa 7compare lines #h-ab of ,no4 #adh7 which are written within the diagram1 evidently apply to both sections and have therefore been inserted in both4 #bgf4 ,,of ,,the ,,colours ,,of ,,simple ,,derived ,,shadows4 ,the colour of derived shadows is always affected by that of the body towards which they are cast4 ,to prove this3 let an opaque body be placed between the plane s c t d and the blue light d e and the red light a b1 then ,i say that d e1 the blue light1 will fall on the whole surface s c t d excepting at o p which is covered by the shadow of the body q r1 as is shown by the straight lines d q o e r p4 ,and the same occurs with the light a b which falls on the whole surface s c t d excepting at the spot obscured by the shadow q r2 as is shown by the lines d q o1 and e r p4 ,hence we may conclude that the shadow n m is exposed to the blue light d e2 but1 as the red light a b cannot fall there1 n m will appear as a blue shadow on a red background tinted with blue1 because on the surface s c t d both lights can fall4 ,but in the shadows only one single light falls2 for this reason these shadows are of medium depth1 since1 if no light whatever mingled with the shadow1 it would be of the first degree of darkness c4 ,but in the shadow at o p the blue light does not fall1 because the body q r interposes and intercepts it there4 ,only the red light a b falls there and tinges the shadow of a red hue and so a ruddy shadow appears on the background of mingled red and blue4 ,the shadow of q r at o p is red1 being caused by the blue light d e2 and the shadow of q r at o' p' is blue being caused by the red light a b4 ,hence we say that the blue light in this instance causes a red derived shadow from the opaque body q' r'1 while the red light causes the same body to cast a blue derived shadow2 but the primary shadow on the dark side of the body itself is not of either of those hues1 but a mixture of red and blue4 ,the derived shadows will be equal in depth if they are produced by lights of equal strength and at an equal distance2 this is proved4 ,footnote #ec3 ,the text is unfinished in the original4 ,footnote3 ,in the original diagram ,leonardo has written within the circle q r corpo obroso 7body in shadow72 at the spot marked ,a1 luminoso azzurro 7blue luminous body72 at ,b1 luminoso rosso 7red luminous body74 ,at ,e we read ombra azzurra 7blue tinted shadow7 and at ,d ombra rossa 7red tinted shadow74 ,on the nature of colours 7#bgg4 #bgh74 #bgg4 ,no white or black is transparent4 #bgh4 ,,of ,,painting4 ,footnote #b3 ,see ,footnote #c ,since white is not a colour but the neutral recipient of every colour ,footnote #c3 il bianco non e colore ma e inpotentia ricettiva d'ogni colore 7white is not a colour1 but the neutral recipient of every colour74 ,,leon ,,batt4 ,,alberti ,della pittura libro ,i1 asserts on the contrary3 ,il bianco e'l nero non sono veri colori1 ma sono alteratione delli altri colori 7ed4 ,,janitschek1 p4 #fg2 ,vienna #ahgg741 when it is seen in the open air and high up1 all its shadows are bluish2 and this is caused1 according to the #dth prop41 which says3 the surface of every opaque body assumes the hue of the surrounding objects4 ,now this white body being deprived of the light of the sun by the interposition of some body between the sun and itself1 all that portion of it which is exposed to the sun and atmosphere assumes the colour of the sun and atmosphere2 the side on which the sun does not fall remains in shadow and assumes the hue of the atmosphere4 ,and if this white object did not reflect the green of the fields all the way to the horizon nor get the brightness of the horizon itself1 it would certainly appear simply of the same hue as the atmosphere4 ,on gradations in the depth of colours 7#bgi4 #bhj74 #bgi4 ,since black1 when painted next to white1 looks no blacker than when next to black2 and white when next to black looks no whiter than white1 as is seen by the images transmitted through a small hole or by the edges of any opaque screen 444 #bhj4 ,,of ,,colours4 ,of several colours1 all equally white1 that will look whitest which is against the darkest background4 ,and black will look intensest against the whitest background4 ,and red will look most vivid against the yellowest background2 and the same is the case with all colours when surrounded by their strongest contrasts4 ,on the reflection of colours 7#bha-bhc74 #bha4 ,,perspective4 ,every object devoid of colour in itself is more or less tinged by the colour of the object placed opposite4 ,this may be seen by experience1 inasmuch as any object which mirrors another assumes the colour of the object mirrored in it4 ,and if the surface thus partially coloured is white the portion which has a red reflection will appear red1 or any other colour1 whether bright or dark4 ,,perspective4 ,every opaque and colourless body assumes the hue of the colour reflected on it2 as happens with a white wall4 #bhb4 ,,perspective4 ,that side of an object in light and shade which is towards the light transmits the images of its details more distinctly and immediately to the eye than the side which is in shadow4 ,,perspective4 ,the solar rays reflected on a square mirror will be thrown back to distant objects in a circular form4 ,,perspective4 ,any white and opaque surface will be partially coloured by reflections from surrounding objects4 ,footnote #bha4 #bhb3 ,the title line of these chapters is in the original simply pro1 which may be an abbreviation for either ,propositione or ,prospettiva--taking ,prospettiva of course in its widest sense1 as we often find it used in ,leonardo's writings4 ,the title pro has here been understood to mean ,prospettiva1 in accordance with the suggestion afforded by page #aj;b of this same ,,ms41 where the first section is headed ,prospettiva in full 7see ,no4 #id71 while the four following sections are headed merely pro 7see ,no4 #he74 #bhc4 ,,what ,,portion ,,of ,a ,,coloured ,,surface ,,ought ,,in ,,reason ,,to ,,be ,,the ,,most ,,intense4 ,if a is the light1 and b illuminated by it in a direct line1 c1 on which the light cannot fall1 is lighted only by reflection from b which1 let us say1 is red4 ,hence the light reflected from it1 will be affected by the hue of the surface causing it and will tinge the surface c with red4 ,and if c is also red you will see it much more intense than b2 and if it were yellow you would see there a colour between yellow and red4 ,on the use of dark and light colours in painting 7#bhd--bhf74 #bhd4 ,,why ,,beautiful ,,colours ,,must ,,be ,,in ,,the ,,highest ,,light4 ,since we see that the quality of colour is known only by means of light1 it is to be supposed that where there is most light the true character of a colour in light will be best seen2 and where there is most shadow the colour will be affected by the tone of that4 ,hence1 ,o ,painter6 remember to show the true quality of colours in bright lights4 #bhe4 ,an object represented in white and black will display stronger relief than in any other way2 hence ,i would remind you ,o ,painter6 to dress your figures in the lightest colours you can1 since1 if you put them in dark colours1 they will be in too slight relief and inconspicuous from a distance4 ,and the reason is that the shadows of all objects are dark4 ,and if you make a dress dark there is little variety in the lights and shadows1 while in light colours there are many grades4 #bhf4 ,,of ,,painting4 ,colours seen in shadow will display more or less of their natural brilliancy in proportion as they are in fainter or deeper shadow4 ,but if these same colours are situated in a well-lighted place1 they will appear brighter in proportion as the light is more brilliant4 ,,the ,,adversary4 ,the variety of colours in shadow must be as great as that of the colours in the objects in that shadow4 ,,the ,,answer4 ,colours seen in shadow will display less variety in proportion as the shadows in which they lie are deeper4 ,and evidence of this is to be had by looking from an open space into the doorways of dark and shadowy churches1 where the pictures which are painted in various colours all look of uniform darkness4 ,hence at a considerable distance all the shadows of different colours will appear of the same darkness4 ,it is the light side of an object in light and shade which shows the true colour4 ,on the colours of the rainbow 7#bhg4 #bhh74 #bhg4 ,treat of the rainbow in the last book on ,painting1 but first write the book on colours produced by the mixture of other colours1 so as to be able to prove by those painters' colours how the colours of the rainbow are produced4 #bhh4 ,,whether ,,the ,,colours ,,of ,,the ,,rainbow ,,are ,,produced ,,by ,,the ,,sun4 ,the colours of the rainbow are not produced by the sun1 for they occur in many ways without the sunshine2 as may be seen by holding a glass of water up to the eye2 when1 in the glass--where there are those minute bubbles always seen in coarse glass--each bubble1 even though the sun does not fall on it1 will produce on one side all the colours of the rainbow2 as you may see by placing the glass between the day light and your eye in such a way as that it is close to the eye1 while on one side the glass admits the diffused light of the atmosphere1 and on the other side the shadow of the wall on one side of the window2 either left or right1 it matters not which4 ,then1 by turning the glass round you will see these colours all round the bubbles in the glass c4 ,and the rest shall be said in its place4 ,,that ,,the ,,eye ,,has ,,no ,,part ,,in ,,producing ,,the ,,colours ,,of ,,the ,,rainbow4 ,in the experiment just described1 the eye would seem to have some share in the colours of the rainbow1 since these bubbles in the glass do not display the colours except through the medium of the eye4 ,but1 if you place the glass full of water on the window sill1 in such a position as that the outer side is exposed to the sun's rays1 you will see the same colours produced in the spot of light thrown through the glass and upon the floor1 in a dark place1 below the window2 and as the eye is not here concerned in it1 we may evidently1 and with certainty pronounce that the eye has no share in producing them4 ,,of ,,the ,,colours ,,in ,,the ,,feathers ,,of ,,certain ,,birds4 ,there are many birds in various regions of the world on whose feathers we see the most splendid colours produced as they move1 as we see in our own country in the feathers of peacocks or on the necks of ducks or pigeons1 c4 ,again1 on the surface of antique glass found underground and on the roots of turnips kept for some time at the bottom of wells or other stagnant waters we see that each root displays colours similar to those of the real rainbow4 ,they may also be seen when oil has been placed on the top of water and in the solar rays reflected from the surface of a diamond or beryl2 again1 through the angular facet of a beryl every dark object against a background of the atmosphere or any thing else equally pale-coloured is surrounded by these rainbow colours between the atmosphere and the dark body2 and in many other circumstances which ,i will not mention1 as these suffice for my purpose4 ,,vi4 ',prospettiva de' colri' 7,perspective of ,colour7 and ',prospettiva aerea' 7,aerial ,perspective74 ,leonardo distinctly separates these branches of his subject1 as may be seen in the beginning of ,no4 #bie4 ,attempts have been made to cast doubts on the results which ,leonardo arrived at by experiment on the perspective of colour1 but not with justice1 as may be seen from the original text of section #bid4 ,the question as to the composition of the atmosphere1 which is inseparable from a discussion on ,aerial ,perspective1 forms a separate theory which is treated at considerable length4 ,indeed the author enters into it so fully that we cannot escape the conviction that he must have dwelt with particular pleasure on this part of his subject1 and that he attached great importance to giving it a character of general applicability4 ,general rules 7#bhi--bia74 #bhi4 ,the variety of colour in objects cannot be discerned at a great distance1 excepting in those parts which are directly lighted up by the solar rays4 #bij4 ,as to the colours of objects3 at long distances no difference is perceptible in the parts in shadow4 #bia4 ,,of ,,the ,,visibility ,,of ,,colours4 ,which colour strikes most8 ,an object at a distance is most conspicuous1 when it is lightest1 and the darkest is least visible4 ,an exceptional case4 #bib4 ,of the edges outlines of shadows4 ,some have misty and ill defined edges1 others distinct ones4 ,no opaque body can be devoid of light and shade1 except it is in a mist1 on ground covered with snow1 or when snow is falling on the open country which has no light on it and is surrounded with darkness4 ,and this occurs only in spherical bodies1 because in other bodies which have limbs and parts1 those sides of limbs which face each other reflect on each other the accidental hue and tone of their surface4 ,an experiment4 #bic4 ,,all ,,colours ,,are ,,at ,a ,,distance ,,undistinguishable ,,and ,,undiscernible4 ,all colours at a distance are undistinguishable in shadow1 because an object which is not in the highest light is incapable of transmitting its image to the eye through an atmosphere more luminous than itself2 since the lesser brightness must be absorbed by the greater4 ,for instance3 ,we1 in a house1 can see that all the colours on the surface of the walls are clearly and instantly visible when the windows of the house are open2 but if we were to go out of the house and look in at the windows from a little distance to see the paintings on those walls1 instead of the paintings we should see an uniform deep and colourless shadow4 ,the practice of the prospettiva de colori4 #bid4 ,,how ,a ,,painter ,,should ,,carry ,,out ,,the ,,perspective ,,of ,,colour ,,in ,,practice4 ,in order to put into practice this perspective of the variation and loss or diminution of the essential character of colours1 observe at every hundred braccia some objects standing in the landscape1 such as trees1 houses1 men and particular places4 ,then in front of the first tree have a very steady plate of glass and keep your eye very steady1 and then1 on this plate of glass1 draw a tree1 tracing it over the form of that tree4 ,then move it on one side so far as that the real tree is close by the side of the tree you have drawn2 then colour your drawing in such a way as that in colour and form the two may be alike1 and that both1 if you close one eye1 seem to be painted on the glass and at the same distance4 ,then1 by the same method1 represent a second tree1 and a third1 with a distance of a hundred braccia between each4 ,and these will serve as a standard and guide whenever you work on your own pictures1 wherever they may apply1 and will enable you to give due distance in those works4 #ad ,but ,i have found that as a rule the second is #d_/e of the first when it is #bj braccia beyond it4 ,footnote3 ,this chapter is one of those copied in the ,manuscript of the ,vatican library ,urbinas #abgj1 and the original text is rendered here with no other alterations1 but in the orthography4 ,h4 ,,ludwig1 in his edition of this copy translates lines #ad and #ae thus3 ,ich finde aber als ,regel1 dass der zweite um vier ,funftel des ersten abnimmt1 wenn er namlich zwanzig ,ellen vom ersten entfernt ist 7874 ,he adds in his commentary3 ,das ,ende der ,nummer ist wohl jedenfalls verstummelt4 ,however the translation given above shows that it admits of a different rendering4 ,the rules of aerial perspective 7#bie--big74 #bie4 ,,of ,,aerial ,,perspective4 ,there is another kind of perspective which ,i call ,aerial ,perspective1 because by the atmosphere we are able to distinguish the variations in distance of different buildings1 which appear placed on a single line2 as1 for instance1 when we see several buildings beyond a wall1 all of which1 as they appear above the top of the wall1 look of the same size1 while you wish to represent them in a picture as more remote one than another and to give the effect of a somewhat dense atmosphere4 ,you know that in an atmosphere of equal density the remotest objects seen through it1 as mountains1 in consequence of the great quantity of atmosphere between your eye and them--appear blue and almost of the same hue as the atmosphere itself ,footnote #aj3 quado il sole e per leuante 7when the sun is in the ,east74 ,apparently the author refers here to morning light in general4 ,h4 ,,ludwig however translates this passage from the ,vatican copy wenn namlich die ,sonne 7dahinter7 im ,osten steht4 when the sun is in the ,east ,footnote #aa3 ,see ,footnote #aj4 ,hence you must make the nearest building above the wall of its real colour1 but the more distant ones make less defined and bluer4 ,those you wish should look farthest away you must make proportionately bluer2 thus1 if one is to be five times as distant1 make it five times bluer4 ,and by this rule the buildings which above a given line appear of the same size1 will plainly be distinguished as to which are the more remote and which larger than the others4 #bif4 ,the medium lying between the eye and the object seen1 tinges that object with its colour1 as the blueness of the atmosphere makes the distant mountains appear blue and red glass makes objects seen beyond it1 look red4 ,the light shed round them by the stars is obscured by the darkness of the night which lies between the eye and the radiant light of the stars4 #big4 ,take care that the perspective of colour does not disagree with the size of your objects1 hat is to say3 that the colours diminish from their natural vividness in proportion as the objects at various distances dimmish from their natural size4 ,on the relative density of the atmosphere 7#bih--bij74 #bih4 ,,why ,,the ,,atmosphere ,,must ,,be ,,represented ,,as ,,paler ,,towards ,,the ,,lower ,,portion4 ,because the atmosphere is dense near the earth1 and the higher it is the rarer it becomes4 ,when the sun is in the ,east if you look towards the ,west and a little way to the ,south and ,north1 you will see that this dense atmosphere receives more light from the sun than the rarer2 because the rays meet with greater resistance4 ,and if the sky1 as you see it1 ends on a low plain1 that lowest portion of the sky will be seen through a denser and whiter atmosphere1 which will weaken its true colour as seen through that medium1 and there the sky will look whiter than it is above you1 where the line of sight travels through a smaller space of air charged with heavy vapour4 ,and if you turn to the ,east1 the atmosphere will appear darker as you look lower down because the luminous rays pass less freely through the lower atmosphere4 #bii4 ,,of ,,the ,,mode ,,of ,,treating ,,remote ,,objects ,,in ,,painting4 ,it is easy to perceive that the atmosphere which lies closest to the level ground is denser than the rest1 and that where it is higher up1 it is rarer and more transparent4 ,the lower portions of large and lofty objects which are at a distance are not much seen1 because you see them along a line which passes through a denser and thicker section of the atmosphere4 ,the summits of such heights are seen along a line which1 though it starts from your eye in a dense atmosphere1 still1 as it ends at the top of those lofty objects1 ceases in a much rarer atmosphere than exists at their base2 for this reason the farther this line extends from your eye1 from point to point the atmosphere becomes more and more rare4 ,hence1 ,o ,painter6 when you represent mountains1 see that from hill to hill the bases are paler than the summits1 and in proportion as they recede beyond each other make the bases paler than the summits2 while1 the higher they are the more you must show of their true form and colour4 ,on the colour of the atmosphere 7#cjj-cjg74 #cjj4 ,,of ,,the ,,colour ,,of ,,the ,,atmosphere4 ,i say that the blueness we see in the atmosphere is not intrinsic colour1 but is caused by warm vapour evaporated in minute and insensible atoms on which the solar rays fall1 rendering them luminous against the infinite darkness of the fiery sphere which lies beyond and includes it4 ,and this may be seen1 as ,i saw it by any one going up ,footnote #e3 ,with regard to the place spoken of as ,m'oboso 7compare ,no4 #cja line #bj7 its identity will be discussed under ,leonardo's ,topographical notes in ,vol4 ,,ii4 ,monboso1 a peak of the ,alps which divide ,france from ,italy4 ,the base of this mountain gives birth to the four rivers which flow in four different directions through the whole of ,europe4 ,and no mountain has its base at so great a height as this1 which lifts itself almost above the clouds2 and snow seldom falls there1 but only hail in the summer1 when the clouds are highest4 ,and this hail lies unmelted there1 so that if it were not for the absorption of the rising and falling clouds1 which does not happen twice in an age1 an enormous mass of ice would be piled up there by the hail1 and in the middle of ,july ,i found it very considerable4 ,there ,i saw above me the dark sky1 and the sun as it fell on the mountain was far brighter here than in the plains below1 because a smaller extent of atmosphere lay between the summit of the mountain and the sun4 ,again as an illustration of the colour of the atmosphere ,i will mention the smoke of old and dry wood1 which1 as it comes out of a chimney1 appears to turn very blue1 when seen between the eye and the dark distance4 ,but as it rises1 and comes between the eye and the bright atmosphere1 it at once shows of an ashy grey colour2 and this happens because it no longer has darkness beyond it1 but this bright and luminous space4 ,if the smoke is from young1 green wood1 it will not appear blue1 because1 not being transparent and being full of superabundant moisture1 it has the effect of condensed clouds which take distinct lights and shadows like a solid body4 ,the same occurs with the atmosphere1 which1 when overcharged with moisture appears white1 and the small amount of heated moisture makes it dark1 of a dark blue colour2 and this will suffice us so far as concerns the colour of the atmosphere2 though it might be added that1 if this transparent blue were the natural colour of the atmosphere1 it would follow that wherever a larger mass air intervened between the eye and the element of fire1 the azure colour would be more intense2 as we see in blue glass and in sapphires1 which are darker in proportion as they are larger4 ,but the atmosphere in such circumstances behaves in an opposite manner1 inasmuch as where a greater quantity of it lies between the eye and the sphere of fire1 it is seen much whiter4 ,this occurs towards the horizon4 ,and the less the extent of atmosphere between the eye and the sphere of fire1 the deeper is the blue colour1 as may be seen even on low plains4 ,hence it follows1 as ,i say1 that the atmosphere assumes this azure hue by reason of the particles of moisture which catch the rays of the sun4 ,again1 we may note the difference in particles of dust1 or particles of smoke1 in the sun beams admitted through holes into a dark chamber1 when the former will look ash grey and the thin smoke will appear of a most beautiful blue2 and it may be seen again in in the dark shadows of distant mountains when the air between the eye and those shadows will look very blue1 though the brightest parts of those mountains will not differ much from their true colour4 ,but if any one wishes for a final proof let him paint a board with various colours1 among them an intense black2 and over all let him lay a very thin and transparent coating of white4 ,he will then see that this transparent white will nowhere show a more beautiful blue than over the black--but it must be very thin and finely ground4 ,footnote #g3 reta here has the sense of malanno4 #cja4 ,experience shows us that the air must have darkness beyond it and yet it appears blue4 ,if you produce a small quantity of smoke from dry wood and the rays of the sun fall on this smoke1 and if you then place behind the smoke a piece of black velvet on which the sun does not shine1 you will see that all the smoke which is between the eye and the black stuff will appear of a beautiful blue colour4 ,and if instead of the velvet you place a white cloth smoke1 that is too thick smoke1 hinders1 and too thin smoke does not produce1 the perfection of this blue colour4 ,hence a moderate amount of smoke produces the finest blue4 ,water violently ejected in a fine spray and in a dark chamber where the sun beams are admitted produces these blue rays and the more vividly if it is distilled water1 and thin smoke looks blue4 ,this ,i mention in order to show that the blueness of the atmosphere is caused by the darkness beyond it1 and these instances are given for those who cannot confirm my experience on ,monboso4 #cjb4 ,when the smoke from dry wood is seen between the eye of the spectator and some dark space or object1 it will look blue4 ,thus the sky looks blue by reason of the darkness beyond it4 ,and if you look towards the horizon of the sky1 you will see the atmosphere is not blue1 and this is caused by its density4 ,and thus at each degree1 as you raise your eyes above the horizon up to the sky over your head1 you will see the atmosphere look darker blue and this is because a smaller density of air lies between your eye and the outer darkness4 ,and if you go to the top of a high mountain the sky will look proportionately darker above you as the atmosphere becomes rarer between you and the outer darkness2 and this will be more visible at each degree of increasing height till at last we should find darkness4 ,that smoke will look bluest which rises from the driest wood and which is nearest to the fire and is seen against the darkest background1 and with the sunlight upon it4 #cjc4 ,a dark object will appear bluest in proportion as it has a greater mass of luminous atmosphere between it and the eye4 ,as may be seen in the colour of the sky4 #cjd4 ,the atmosphere is blue by reason of the darkness above it because black and white make blue4 #cje4 ,in the morning the mist is denser above than below1 because the sun draws it upwards2 hence tall buildings1 even if the summit is at the same distance as the base have the summit invisible4 ,therefore1 also1 the sky looks darkest in colour overhead1 and towards the horizon it is not blue but rather between smoke and dust colour4 ,the atmosphere1 when full of mist1 is quite devoid of blueness1 and only appears of the colour of clouds1 which shine white when the weather is fine4 ,and the more you turn to the west the darker it will be1 and the brighter as you look to the east4 ,and the verdure of the fields is bluish in a thin mist1 but grows grey in a dense one4 ,the buildings in the west will only show their illuminated side1 where the sun shines1 and the mist hides the rest4 ,when the sun rises and chases away the haze1 the hills on the side where it lifts begin to grow clearer1 and look blue1 and seem to smoke with the vanishing mists2 and the buildings reveal their lights and shadows2 through the thinner vapour they show only their lights and through the thicker air nothing at all4 ,this is when the movement of the mist makes it part horizontally1 and then the edges of the mist will be indistinct against the blue of the sky1 and towards the earth it will look almost like dust blown up4 ,in proportion as the atmosphere is dense the buildings of a city and the trees in a landscape will look fewer1 because only the tallest and largest will be seen4 ,darkness affects every thing with its hue1 and the more an object differs from darkness1 the more we see its real and natural colour4 ,the mountains will look few1 because only those will be seen which are farthest apart2 since1 at such a distance1 the density increases to such a degree that it causes a brightness by which the darkness of the hills becomes divided and vanishes indeed towards the top4 ,there is less mist between lower and nearer hills and yet little is to be distinguished1 and least towards the bottom4 #cjf4 ,the surface of an object partakes of the colour of the light which illuminates it2 and of the colour of the atmosphere which lies between the eye and that object1 that is of the colour of the transparent medium lying between the object and the eye2 and among colours of a similar character the second will be of the same tone as the first1 and this is caused by the increased thickness of the colour of the medium lying between the object and the eye4 #cjg4 ,,of ,,painting4 ,of various colours which are none of them blue that which at a great distance will look bluest is the nearest to black2 and so1 conversely1 the colour which is least like black will at a great distance best preserve its own colour4 ,hence the green of fields will assume a bluer hue than yellow or white will1 and conversely yellow or white will change less than green1 and red still less4 ,,vii4 ,on the ,proportions and on the ,movements of the ,human ,figure4 ,leonardo's researches on the proportions and movements of the human figure must have been for the most part completed and written before the year #adih2 for ,,luca ,,paciolo writes1 in the dedication to ,ludovico il ,moro1 of his book ,divina ,proportione1 which was published in that year3 ,leonardo da venci 444 hauedo gia co tutta diligetia al degno libro de pictura e movimenti humani posto fine4 ,the selection of ,leonardo's axioms contained in the ,vatican copy attributes these words to the author3 e il resto si dira nella universale misura del huomo4 7,,manzi1 p4 #adg2 ,,ludwig1 ,no4 #bfd74 ,,lomazzo1 again1 in his ,idea del ,tempio della ,pittura ,milano #aeij1 cap4 ,,iv1 says3 ,lionardo ,vinci 444 dimostro anco in figura tutte le proporzioni dei membri del corpo umano4 ,the ,vatican copy includes but very few sections of the ,universale misura del huomo and until now nothing has been made known of the original ,,mss4 on the subject which have supplied the very extensive materials for this portion of the work4 ,the collection at ,windsor1 belonging to her ,majesty the ,queen1 includes by far the most important part of ,leonardo's investigations on this subject1 constituting about half of the whole of the materials here published2 and the large number of original drawings adds greatly to the interest which the subject itself must command4 ,luca ,paciolo would seem to have had these ,,mss4 7which ,i have distinguished by the initials ,w4 ,p47 in his mind when he wrote the passage quoted above4 ,still1 certain notes of a later date--such as ,nos4 #cfj1 #cfb and #cfc1 from ,,ms4 ,e1 written in #aeac--ad1 sufficiently prove that ,leonardo did not consider his earlier studies on the ,proportions and ,movements of the ,human ,figure final and complete1 as we might suppose from ,luca ,paciolo's statement4 ,or else he took the subject up again at a subsequent period1 since his former researches had been carried on at ,milan between #adij and #aejj4 ,indeed it is highly probable that the anatomical studies which he was pursuing zvith so much zeal between #aeaj--af should have led him to reconsider the subject of ,proportion4 ,preliminary observations 7#cjh4 #cji74 #cjh4 ,every man1 at three years old is half the full height he will grow to at last4 #cji4 ,if a man #b braccia high is too small1 one of four is too tall1 the medium being what is admirable4 ,between #b and #d comes #c2 therefore take a man of #c braccia in height and measure him by the rule ,i will give you4 ,if you tell me that ,i may be mistaken1 and judge a man to be well proportioned who does not conform to this division1 ,i answer that you must look at many men of #c braccia1 and out of the larger number who are alike in their limbs choose one of those who are most graceful and take your measurements4 ,the length of the hand is #a_/c of a braccio #h inches and this is found #i times in man4 ,and the face ,footnote #g3 ,the account here given of the braccio is of importance in understanding some of the succeeding chapters4 ,testa must here be understood to mean the face4 ,the statements in this section are illustrated in part on ,pl4 ,,xi4 is the same1 and from the pit of the throat to the shoulder1 and from the shoulder to the nipple1 and from one nipple to the other1 and from each nipple to the pit of the throat4 ,proportions of the head and face 7#caj-cah74 #caj4 ,the space between the parting of the lips the mouth and the base of the nose is one-seventh of the face4 ,the space from the mouth to the bottom of the chin c d is the fourth part of the face and equal to the width of the mouth4 ,the space from the chin to the base of the nose e f is the third part of the face and equal to the length of the nose and to the forehead4 ,the distance from the middle of the nose to the bottom of the chin g h1 is half the length of the face4 ,the distance from the top of the nose1 where the eyebrows begin1 to the bottom of the chin1 i k1 is two thirds of the face4 ,the space from the parting of the lips to the top of the chin l m1 that is where the chin ends and passes into the lower lip of the mouth1 is the third of the distance from the parting of the lips to the bottom of the chin and is the twelfth part of the face4 ,from the top to the bottom of the chin m n is the sixth part of the face and is the fifty fourth part of a man's height4 ,from the farthest projection of the chin to the throat o p is equal to the space between the mouth and the bottom of the chin1 and a fourth of the face4 ,the distance from the top of the throat to the pit of the throat below q r is half the length of the face and the eighteenth part of a man's height4 ,from the chin to the back of the neck s t1 is the same distance as between the mouth and the roots of the hair1 that is three quarters of the head4 ,from the chin to the jaw bone v x is half the head and equal to the thickness of the neck in profile4 ,the thickness of the head from the brow to the nape is once and #c_/d that of the neck4 ,footnote3 ,the drawings to this text1 lines #a-aj are on ,pl4 ,,vii1 ,no4 ,i4 ,the two upper sketches of heads1 ,pl4 ,,vii1 ,no4 #b1 belong to lines #aa-ad1 and in the original are placed immediately below the sketches reproduced on ,pl4 ,,vii1 ,no4 #a4 #caa4 ,the distance from the attachment of one ear to the other is equal to that from the meeting of the eyebrows to the chin1 and in a fine face the width of the mouth is equal to the length from the parting of the lips to the bottom of the chin4 #cab4 ,the cut or depression below the lower lip of the mouth is half way between the bottom of the nose and the bottom of the chin4 ,the face forms a square in itself2 that is its width is from the outer corner of one eye to the other1 and its height is from the very top of the nose to the bottom of the lower lip of the mouth2 then what remains above and below this square amounts to the height of such another square1 a b is equal to the space between c d2 d n in the same way to n c1 and likewise s r1 q p1 h k are equal to each other4 ,it is as far between m and s as from the bottom of the nose to the chin4 ,the ear is exactly as long as the nose4 ,it is as far from x to j as from the nose to the chin4 ,the parting of the mouth seen in profile slopes to the angle of the jaw4 ,the ear should be as high as from the bottom of the nose to the top of the eye-lid4 ,the space between the eyes is equal to the width of an eye4 ,the ear is over the middle of the neck1 when seen in profile4 ,the distance from #d to #e is equal to that from s to r4 ,footnote3 ,see ,pl4 ,,viii1 ,no4 ,i1 where the text of lines #c-ac is also given in facsimile4 #cac4 7a b7 is equal to 7c d74 ,footnote3 ,see ,pl4 ,,vii1 ,no4 #c4 ,reference may also be made here to two pen and ink drawings of heads in profile with figured measurements1 of which there is no description in the ,,ms4 ,these are given on ,pl4 ,,xvii1 ,no4 #b4--;,a head1 to the left1 with part of the torso ,w4 ,p4 #e;a1 ,no4 #a on the same plate is from ,,ms4 ,a #b;b and in the original occurs on a page with wholly irrelevant text on matters of natural history4 ,m4 ,,ravaisson in his edition of the ,paris ,,ms4 ,a has reproduced this head and discussed it fully note on page #ab2 he has however somewhat altered the original measurements4 ,the complicated calculations which ,m4 ,,ravaisson has given appear to me in no way justified4 ,the sketch1 as we see it1 can hardly have been intended for any thing more than an experimental attempt to ascertain relative proportions4 ,we do not find that ,leonardo made use of circular lines in any other study of the proportions of the human head4 ,at the same time we see that the proportions of this sketch are not in accordance with the rules which he usually observed 7see for instance ,no4 #caj74 ,the head a f #a_/f larger than n f4 #cae4 ,from the eyebrow to the junction of the lip with the chin1 and the angle of the jaw and the upper angle where the ear joins the temple will be a perfect square4 ,and each side by itself is half the head4 ,the hollow of the cheek bone occurs half way between the tip of the nose and the top of the jaw bone1 which is the lower angle of the setting on of the ear1 in the frame here represented4 ,from the angle of the eye-socket to the ear is as far as the length of the ear1 or the third of the face4 ,footnote3 ,see ,pl4 ,,ix4 ,the text1 in the original is written behind the head4 ,the handwriting would seem to indicate a date earlier than #adhj4 ,on the same leaf there is a drawing in red chalk of two horsemen of which only a portion of the upper figure is here visible4 ,the whole leaf measures #bb #a_/b centimetres wide by #bi long1 and is numbered #abg in the top right-hand corner4 #caf4 ,from a to b--that is to say from the roots of the hair in front to the top of the head--ought to be equal to c d2--that is from the bottom of the nose to the meeting of the lips in the middle of the mouth4 ,from the inner corner of the eye m to the top of the head a is as far as from m down to the chin s4 s c f b are all at equal distances from each other4 ,footnote3 ,the drawing in silver-point on bluish tinted paper--,pl4 ,x--which belongs to this chapter has been partly drawn over in ink by ,leonardo himself4 #cag4 ,from the top of the head to the bottom of the chin is #a_/i1 and from the roots of the hair to the chin is #a_/i of the distance from the roots of the hair to the ground4 ,the greatest width of the face is equal to the space between the mouth and the roots of the hair and is #a_/ab of the whole height4 ,from the top of the ear to the top of the head is equal to the distance from the bottom of the chin to the lachrymatory duct of the eye2 and also equal to the distance from the angle of the chin to that of the jaw2 that is the #a_/af of the whole4 ,the small cartilage which projects over the opening of the ear towards the nose is half-way between the nape and the eyebrow2 the thickness of the neck in profile is equal to the space between the chin and the eyes1 and to the space between the chin and the jaw1 and it is #a_/ah of the height of the man4 #cah4 a b1 c d1 e f1 g h1 i k are equal to each other in size excepting that d f is accidental4 ,footnote3 ,see ,pl4 ,,xi4 ,proportions of the head seen in front 7#cai-cba74 #cai4 a n o f are equal to the mouth4 a c and a f are equal to the space between one eye and the other4 n m o f q r are equal to half the width of the eye lids1 that is from the inner lachrymatory corner of the eye to its outer corner2 and in like manner the division between the chin and the mouth2 and in the same way the narrowest part of the nose between the eyes4 ,and these spaces1 each in itself1 is the #aith part of the head1 n o is equal to the length of the eye or of the space between the eyes4 m c is #a_/c of n m measuring from the outer corner of the eyelids to the letter c4 b s will be equal to the width of the nostril4 ,footnote3 ,see ,pl4 ,,xii4 #cbj4 ,the distance between the centres of the pupils of the eyes is #a_/c of the face4 ,the space between the outer corners of the eyes1 that is where the eye ends in the eye socket which contains it1 thus the outer corners1 is half the face4 ,the greatest width of the face at the line of the eyes is equal to the distance from the roots of the hair in front to the parting of the lips4 ,footnote3 ,there are1 with this section1 two sketches of eyes1 not reproduced here4 #cba4 ,the nose will make a double square2 that is the width of the nose at the nostrils goes twice into the length from the tip of the nose to the eyebrows4 ,and1 in the same way1 in profile the distance from the extreme side of the nostril where it joins the cheek to the tip of the nose is equal to the width of the nose in front from one nostril to the other4 ,if you divide the whole length of the nose--that is from the tip to the insertion of the eyebrows1 into #d equal parts1 you will find that one of these parts extends from the tip of the nostrils to the base of the nose1 and the upper division lies between the inner corner of the eye and the insertion of the eyebrows2 and the two middle parts together are equal to the length of the eye from the inner to the outer corner4 ,footnote3 ,the two bottom sketches on ,pl4 ,,vii1 ,no4 #d face the six lines of this section1--,with regard to the proportions of the head in profile see ,no4 #cab4 #cbb4 ,the great toe is the sixth part of the foot1 taking the measure in profile1 on the inside of the foot1 from where this toe springs from the ball of the sole of the foot to its tip a b2 and it is equal to the distance from the mouth to the bottom of the chin4 ,if you draw the foot in profile from the outside1 make the little toe begin at three quarters of the length of the foot1 and you will find the same distance from the insertion of this toe as to the farthest prominence of the great toe4 #cbc4 ,for each man respectively the distance between a b is equal to c d4 #cbd4 ,relative proportion of the hand and foot4 ,the foot is as much longer than the hand as the thickness of the arm at the wrist where it is thinnest seen facing4 ,again1 you will find that the foot is as much longer than the hand as the space between the inner angle of the little toe to the last projection of the big toe1 if you measure along the length of the foot4 ,the palm of the hand without the fingers goes twice into the length of the foot without the toes4 ,if you hold your hand with the fingers straight out and close together you will find it to be of the same width as the widest part of the foot1 that is where it is joined onto the toes4 ,and if you measure from the prominence of the inner ancle to the end of the great toe you will find this measure to be as long as the whole hand4 ,from the top angle of the foot to the insertion of the toes is equal to the hand from wrist joint to the tip of the thumb4 ,the smallest width of the hand is equal to the smallest width of the foot between its joint into the leg and the insertion of the toes4 ,the width of the heel at the lower part is equal to that of the arm where it joins the hand2 and also to the leg where it is thinnest when viewed in front4 ,the length of the longest toe1 from its first division from the great toe to its tip is the fourth of the foot from the centre of the ancle bone to the tip1 and it is equal to the width of the mouth4 ,the distance between the mouth and the chin is equal to that of the knuckles and of the three middle fingers and to the length of their first joints if the hand is spread1 and equal to the distance from the joint of the thumb to the outset of the nails1 that is the fourth part of the hand and of the face4 ,the space between the extreme poles inside and outside the foot called the ancle or ancle bone a b is equal to the space between the mouth and the inner corner of the eye4 #cbe4 ,the foot1 from where it is attached to the leg1 to the tip of the great toe is as long as the space between the upper part of the chin and the roots of the hair a b2 and equal to five sixths of the face4 #cbf4 a d is a head's length1 c b is a head's length4 ,the four smaller toes are all equally thick from the nail at the top to the bottom1 and are #a_/ac of the foot4 ,footnote3 ,see ,pl4 ,,xiv1 ,no4 #a1 a drawing of a foot with the text in three lines below it4 #cbg4 ,the whole length of the foot will lie between the elbow and the wrist and between the elbow and the inner angle of the arm towards the breast when the arm is folded4 ,the foot is as long as the whole head of a man1 that is from under the chin to the topmost part of the head,footnote #b3 nel modo che qui i figurato4 ,see ,pl4 ,,vii1 ,no4 #d1 the upper figure4 ,the text breaks off at the end of line #b and the text given under ,no4 #cba follows below4 ,it may be here remarked that the second sketch on ,w4 ,p4 #caa has in the original no explanatory text4 in the way here figured4 ,proportions of the leg 7#cbh-cca74 #cbh4 ,the greatest thickness of the calf of the leg is at a third of its height a b1 and is a twentieth part thicker than the greatest thickness of the foot4 a c is half of the head1 and equal to d b and to the insertion of the five toes e f4 d k diminishes one sixth in the leg g h4 g h is #a_/c of the head2 m n increases one sixth from a e and is #g_/ab of the head1 o p is #a_/aj less than d k and is #f_/ag of the head4 a is at half the distance between b q1 and is #a_/d of the man4 r is half way between s and b,footnote #aa3 b is here and later on measured on the right side of the foot as seen by the spectator44 ,the concavity of the knee outside r is higher than that inside a4 ,the half of the whole height of the leg from the foot r1 is half way between the prominence s and the ground b4 v is half way between t and b4 ,the thickness of the thigh seen in front is equal to the greatest width of the face1 that is #b_/c of the length from the chin to the top of the head2 z r is #e_/f of #g to v2 m n is equal to #g v and is #a_/d of r b1 x y goes #c times into r b1 and into r s4 ,footnote #bb-ce3 ,the sketch illustrating these lines is on ,pl4 ,,xiii1 ,no4 #b4 ,footnote #bb3 a b entra in c f #f e #f in c n4 ,accurate measurement however obliges us to read #g for #f4 a b goes six times into c f and six times into c n and is equal to g h2 i k l m goes #d times into d f1 and #d times into d n and is #c_/g of the foot2 p q r s goes #c times into d f1 and #c times into b n2 ,footnote3 #be4 y is not to be found on the diagram and x occurs twice2 this makes the passage very obscure4 x y is #a_/h of x f and is equal to n q4 #c #g is #a_/i of n f2 #d #e is #a_/aj of n f ,footnote3 #bb-bg4 ,compare with this lines #ah-bd of ,no4 #cca1 and the sketch of a leg in profile ,pl4 ,,xv44 ,i want to know how much a man increases in height by standing on tip-toe and how much p g diminishes by stooping2 and how much it increases at n q likewise in bending the foot4 ,footnote #cd3 e f #d dal cazo4 ,by reading i for e the sense of this passage is made clear4 e f is four times in the distance between the genitals and the sole of the foot2 ,footnote #ce3 #b is not to be found in the sketch which renders the passage obscure4 ,the two last lines are plainly legible in the facsimile4 #c #g is six times from #c to #b and is equal to g h and i k4 ,footnote3 ,the drawing of a leg seen in front ,pl4 ,,xiii1 ,no4 #a belongs to the text from lines #c-ba4 ,the measurements in this section should be compared with the text ,no4 #cca1 lines #a-ac1 and the sketch of a leg seen in front on ,pl4 ,,xv4 #cbi4 ,the length of the foot from the end of the toes to the heel goes twice into that from the heel to the knee1 that is where the leg bone fibula joins the thigh bone femur4 #ccj4 a n b are equal2 c n d are equal2 n c makes two feet2 n d makes #b feet4 ,footnote3 ,see the lower sketch1 ,pl4 ,,xiv1 ,no4 #a4 #cca4 m n o are equal4 ,the narrowest width of the leg seen in front goes #h times from the sole of the foot to the joint of the knee1 and is the same width as the arm1 seen in front at the wrist1 and as the longest measure of the ear1 and as the three chief divisions into which we divide the face2 and this measurement goes #d times from the wrist joint of the hand to the point of the elbow4 #ad ,the foot is as long as the space from the knee between a and b2 and the patella of the knee is as long as the leg between r and s4 #ah ,the least thickness of the leg in profile goes #f times from the sole of the foot to the knee joint and is the same width as the space between the outer corner of the eye and the opening of the ear1 and as the thickest part of the arm seen in profile and between the inner corner of the eye and the insertion of the hair4 a b c d are all relatively of equal length1 c d goes twice from the sole of the foot to the centre of the knee and the same from the knee to the hip4 #bh;a b c are equal2 a to b is #b feet--that is to say measuring from the heel to the tip of the great toe4 ,footnote3 ,see ,pl4 ,,xv4 ,the text of lines #b-ag is to the left of the front view of the leg1 to which it refers4 ,lines #ah-bg are in the middle column and refer to the leg seen in profile and turned to the left1 on the right hand side of the writing4 ,lines #bj-cj are above1 to the left and apply to the sketch below them4 ,some farther remarks on the proportion of the leg will be found in ,no4 #ccf1 lines #f1 #g4 ,on the central point of the whole body4 #ccb4 ,in kneeling down a man will lose the fourth part of his height4 ,when a man kneels down with his hands folded on his breast the navel will mark half his height and likewise the points of the elbows4 ,half the height of a man who sits--that is from the seat to the top of the head--will be where the arms fold below the breast1 and below the shoulders4 ,the seated portion--that is from the seat to the top of the head--will be more than half the man's whole height by the length of the scrotum4 ,footnote3 ,see ,pl4 ,,viii1 ,no4 #b4 ,the relative proportions of the torso and of the whole figure4 #ccc4 ,the cubit is one fourth of the height of a man and is equal to the greatest width of the shoulders4 ,from the joint of one shoulder to the other is two faces and is equal to the distance from the top of the breast to the navel4 ,footnote #i3 dalla detta somita4 ,it would seem more accurate to read here dal detto ombilico4 ,from this point to the genitals is a face's length4 ,footnote3 ,compare with this the sketches on the other page of the same leaf4 ,pl4 ,,viii1 ,no4 #b4 ,the relative proportions of the head and of the torso4 #ccd4 ,from the roots of the hair to the top of the breast a b is the sixth part of the height of a man and this measure is equal4 ,from the outside part of one shoulder to the other is the same distance as from the top of the breast to the navel and this measure goes four times from the sole of the foot to the lower end of the nose4 ,the thickness of the arm where it springs from the shoulder in front goes #f times into the space between the two outside edges of the shoulders and #c times into the face1 and four times into the length of the foot and three into the hand1 inside or outside4 ,footnote3 ,the three sketches ,pl4 ,,xiv1 ,no4 #b belong to this text4 ,the relative proportions of the torso and of the leg 7#cce4 #ccf74 #cce4 a b c are equal to each other and to the space from the armpit of the shoulder to the genitals and to the distance from the tip of the fingers of the hand to the joint of the arm1 and to the half of the breast2 and you must know that c b is the third part of the height of a man from the shoulders to the ground2 d e f are equal to each other and equal to the greatest width of the shoulders4 ,footnote3 ,see ,pl4 ,,xvi1 ,no4 #a4 #ccf4 --,top of the chin--hip--the insertion of the middle finger4 ,the end of the calf of the leg on the inside of the thigh4--,the end of the swelling of the shin bone of the leg4 #f ,the smallest thickness of the leg goes #c times into the thigh seen in front4 ,footnote3 ,see ,pl4 ,,xvii1 ,no4 #b1 middle sketch4 ,the relative proportions of the torso and of the foot4 #ccg4 ,the torso a b in its thinnest part measures a foot2 and from a to b is #b feet1 which makes two squares to the seat--its thinnest part goes #c times into the length1 thus making #c squares4 ,footnote3 ,see ,pl1 ,,vii1 ,no4 #b1 the lower sketch4 ,the proportions of the whole figure 7#cch-cda74 #cch4 ,a man when he lies down is reduced to #a_/i of his height4 #cci4 ,the opening of the ear1 the joint of the shoulder1 that of the hip and the ancle are in perpendicular lines2 a n is equal to m o4 ,footnote3 ,see ,pl4 ,,xvi1 ,no4 #b1 the upper sketch4 #cdj4 ,from the chin to the roots of the hair is #a_/aj of the whole figure4 ,from the joint of the palm of the hand to the tip of the longest finger is #a_/aj4 ,from the chin to the top of the head #a_/h2 and from the pit of the stomach to the top of the breast is #a_/f1 and from the pit below the breast bone to the top of the head #a_/d4 ,from the chin to the nostrils #a_/c ,part of the face1 the same from the nostrils to the brow and from the brow to the roots of the hair1 and the foot is #a_/f1 the elbow #a_/d1 the width of the shoulders #a_/d4 #cda4 ,the width of the shoulders is #a_/d of the whole4 ,from the joint of the shoulder to the hand is #a_/c1 from the parting of the lips to below the shoulder-blade is one foot4 ,the greatest thickness of a man from the breast to the spine is one #hth of his height and is equal to the space between the bottom of the chin and the top of the head4 ,the greatest width is at the shoulders and goes #d4 ,the torso from the front and back4 #cdb4 ,the width of a man under the arms is the same as at the hips4 ,a man's width across the hips is equal to the distance from the top of the hip to the bottom of the buttock1 when a man stands equally balanced on both feet2 and there is the same distance from the top of the hip to the armpit4 ,the waist1 or narrower part above the hips will be half way between the arm pits and the bottom of the buttock4 ,footnote3 ,the lower sketch ,pl4 ,,xvi1 ,no4 #b1 is drawn by the side of line #a4 ,vitruvius' scheme of proportions4 #cdc4 ,vitruvius1 the architect1 says in his work on architecture that the measurements of the human body are distributed by ,nature as follows3 that is that #d fingers make #a palm1 and #d palms make #a foot1 #f palms make #a cubit2 #d cubits make a man's height4 ,and #d cubits make one pace and #bd palms make a man2 and these measures he used in his buildings4 ,if you open your legs so much as to decrease your height #a_/ad and spread and raise your arms till your middle fingers touch the level of the top of your head you must know that the centre of the outspread limbs will be in the navel and the space between the legs will be an equilateral triangle4 ,the length of a man's outspread arms is equal to his height4 ,from the roots of the hair to the bottom of the chin is the tenth of a man's height2 from the bottom of the chin to the top of his head is one eighth of his height2 from the top of the breast to the top of his head will be one sixth of a man4 ,from the top of the breast to the roots of the hair will be the seventh part of the whole man4 ,from the nipples to the top of the head will be the fourth part of a man4 ,the greatest width of the shoulders contains in itself the fourth part of the man4 ,from the elbow to the tip of the hand will be the fifth part of a man2 and from the elbow to the angle of the armpit will be the eighth part of the man4 ,the whole hand will be the tenth part of the man2 the beginning of the genitals marks the middle of the man4 ,the foot is the seventh part of the man4 ,from the sole of the foot to below the knee will be the fourth part of the man4 ,from below the knee to the beginning of the genitals will be the fourth part of the man4 ,the distance from the bottom of the chin to the nose and from the roots of the hair to the eyebrows is1 in each case the same1 and like the ear1 a third of the face4 ,footnote3 ,see ,pl4 ,,xviii4 ,the original leaf is #ba centimetres wide and #cc #a_/b long4 ,at the ends of the scale below the figure are written the words diti 7fingers7 and palmi 7palms74 ,the passage quoted from ,vitruvius is ,book ,,iii1 ,cap4 #a1 and ,leonardo's drawing is given in the editions of ,vitruvius by ,,fra ,,giocondo 7,venezia #aeaa1 fol41 ,firenze #aeac1 #hvo47 and by ,,cesariano 7,como #aeba74 ,the arm and head4 #cdd4 ,from b to a is one head1 as well as from c to a and this happens when the elbow forms a right angle4 ,footnote3 ,see ,pl4 ,,xli1 ,no4 #a4 ,proportions of the arm 7#cde-cdi74 #cde4 ,from the tip of the longest finger of the hand to the shoulder joint is four hands or1 if you will1 four faces4 a b c are equal and each interval is #b heads4 ,footnote3 ,lines #a-c are given on ,pl4 ,,xv below the front view of the leg2 lines #d and #e are below again1 on the left side4 ,the lettering refers to the bent arm near the text4 #cdf4 ,the hand from the longest finger to the wrist joint goes #d times from the tip of the longest finger to the shoulder joint4 #cdg4 a b c are equal to each other and to the foot and to the space between the nipple and the navel d e will be the third part of the whole man4 f g is the fourth part of a man and is equal to g h and measures a cubit4 ,footnote3 ,see ,pl4 ,,xix1 ,no4 #a4 #a4 mamolino 7bambino1 little child7 may mean here the navel4 #cdh4 a b goes #d times into a c and #i into a m4 ,the greatest thickness of the arm between the elbow and the hand goes #f times into a m and is equal to r f4 ,the greatest thickness of the arm between the shoulder and the elbow goes #d times into c m1 and is equal to h n g4 ,the smallest thickness of the arm above the elbow x y is not the base of a square1 but is equal to half the space h #c which is found between the inner joint of the arm and the wrist joint4 #aa,the width of the wrist goes #ab times into the whole arm2 that is from the tip of the fingers to the shoulder joint2 that is #c times into the hand and #i into the arm4 ,the arm when bent is #d heads4 ,the arm from the shoulder to the elbow in bending increases in length1 that is in the length from the shoulder to the elbow1 and this increase is equal to the thickness of the arm at the wrist when seen in profile4 ,and the space between the bottom of the chin and the parting of the lips1 is equal to the thickness of the #b middle fingers1 and to the width of the mouth and to the space between the roots of the hair on the forehead and the top of the head ,footnote3 ,queste cose4 ,this passage seems to have been written on purpose to rectify the foregoing lines4 ,the error is explained by the accompanying sketch of the bones of the arm44 ,all these distances are equal to each other1 but they are not equal to the above-mentioned increase in the arm4 ,the arm between the elbow and wrist never increases by being bent or extended4 ,the arm1 from the shoulder to the inner joint when extended4 ,when the arm is extended1 p n is equal to n a4 ,and when it is bent n a diminishes #a_/f of its length and p n does the same4 ,the outer elbow joint increases #a_/g when bent2 and thus by being bent it increases to the length of #b heads4 ,and on the inner side1 by bending1 it is found that whereas the arm from where it joins the side to the wrist1 was #b heads and a half1 in bending it loses the half head and measures only two3 one from the shoulder joint to the end by the elbow1 and the other to the hand4 ,the arm when folded will measure #b faces up to the shoulder from the elbow and #b from the elbow to the insertion of the four fingers on the palm of the hand4 ,the length from the base of the fingers to the elbow never alters in any position of the arm4 ,if the arm is extended it decreases by #a_/c of the length between b and h2 and if--being extended--it is bent1 it will increase the half of o e4 ,footnote #ei-fa3 ,the figure sketched in the margin is however drawn to different proportions4 ,the length from the shoulder to the elbow is the same as from the base of the thumb1 inside1 to the elbow a b c4 ,footnote #fb-fd3 ,the arm sketch on the margin of the ,,ms4 is identically the same as that given below on ,pl4 ,,xx which may therefore be referred to in this place4 ,in line #fb we read therefore z c for m n4 ,the smallest thickness of the arm in profile z c goes #f times between the knuckles of the hand and the dimple of the elbow when extended and #ad times in the whole arm and #db in the whole man #fd4 ,the greatest thickness of the arm in profile is equal to the greatest thickness of the arm in front2 but the first is placed at a third of the arm from the shoulder joint to the elbow and the other at a third from the elbow towards the hand4 ,footnote3 ,compare ,pl4 ,,xvii4 ,lines #a-aj and #aa-ae are written in two columns below the extended arm1 and at the tips of the fingers we find the words3 fine d'unghie 7ends of the nails74 ,part of the text--lines #bb to #be--;is visible by the side of the sketches on ,pl4 ,,xxxv1 ,no4 #a4 #cdi4 ,from the top of the shoulder to the point of the elbow is as far as from that point to the joints of the four fingers with the palm of the hand1 and each is #b faces4 #e;a e is equal to the palm of the hand1 r f and o g are equal to half a head and each goes #d times into a b and b c4 ,from c to m is #a_/b a head2 m n is #a_/c of a head and goes #f times into c b and into b a2 a b loses #a_/g of its length when the arm is extended2 c b never alters2 o will always be the middle point between a and s4 y l is the fleshy part of the arm and measures one head2 and when the arm is bent this shrinks #b_/e of its length2 o a in bending loses #a_/f and so does o r4 a b is #a_/g of r c4 f s will be #a_/h of r c1 and each of those #b measurements is the largest of the arm2 k h is the thinnest part between the shoulder and the elbow and it is #a_/h of the whole arm r c2 o p is #a_/e of r l2 c z goes #ac times into r c4 ,footnote3 ,see ,pl4 ,,xx where the text is also seen from lines #e-bc4 ,the movement of the arm 7#cej-ced74 #cej4 ,in the innermost bend of the joints of every limb the reliefs are converted into a hollow1 and likewise every hollow of the innermost bends becomes a convexity when the limb is straightened to the utmost4 ,and in this very great mistakes are often made by those who have insufficient knowledge and trust to their own invention and do not have recourse to the imitation of nature2 and these variations occur more in the middle of the sides than in front1 and more at the back than at the sides4 #cea4 ,when the arm is bent at an angle at the elbow1 it will produce some angle2 the more acute the angle is1 the more will the muscles within the bend be shortened2 while the muscles outside will become of greater length than before4 ,as is shown in the example2 d c e will shrink considerably2 and b n will be much extended4 ,footnote3 ,see ,pl4 ,,xix1 ,no4 #b4 #ceb4 ,,of ,,painting4 ,the arm1 as it turns1 thrusts back its shoulder towards the middle of the back4 #cec4 ,the principal movements of the hand are #aj2 that is forwards1 backwards1 to right and to left1 in a circular motion1 up or down1 to close and to open1 and to spread the fingers or to press them together4 #ced4 ,,of ,,the ,,motions ,,of ,,the ,,fingers4 ,the movements of the fingers principally consist in extending and bending them4 ,this extension and bending vary in manner2 that is1 sometimes they bend altogether at the first joint2 sometimes they bend1 or extend1 half way1 at the #bnd joint2 and sometimes they bend in their whole length and in all the three joints at once4 ,if the #b first joints are hindered from bending1 then the #crd joint can be bent with greater ease than before2 it can never bend of itself1 if the other joints are free1 unless all three joints are bent4 ,besides all these movements there are #d other principal motions of which #b are up and down1 the two others from side to side2 and each of these is effected by a single tendon4 ,from these there follow an infinite number of other movements always effected by two tendons2 one tendon ceasing to act1 the other takes up the movement4 ,the tendons are made thick inside the fingers and thin outside2 and the tendons inside are attached to every joint but outside they are not4 ,footnote #bf3 ,this head line has1 in the original1 no text to follow4 ,of the strength and effect of the #c tendons inside the fingers at the #c joints4 ,the movement of the torso 7#cee-cfa74 #cee4 ,observe the altered position of the shoulder in all the movements of the arm1 going up and down1 inwards and outwards1 to the back and to the front1 and also in circular movements and any others4 ,and do the same with reference to the neck1 hands and feet and the breast above the lips c4 #cef4 ,three are the principal muscles of the shoulder1 that is b c d1 and two are the lateral muscles which move it forward and backward1 that is a o2 a moves it forward1 and o pulls it back2 and bed raises it2 a b c moves it upwards and forwards1 and c d o upwards and backwards4 ,its own weight almost suffices to move it downwards4 ,the muscle d acts with the muscle c when the arm moves forward2 and in moving backward the muscle b acts with the muscle c4 ,footnote3 ,see ,pl4 ,,xxi4 ,in the original the lettering has been written in ink upon the red chalk drawing and the outlines of the figures have in most places been inked over4 #ceg4 ,,of ,,the ,,loins1 ,,when ,,bent4 ,the loins or backbone being bent4 ,the breasts are are always lower than the shoulderblades of the back4 ,if the breast bone is arched the breasts are higher than the shoulderblades4 ,if the loins are upright the breast will always be found at the same level as the shoulderblades4 ,footnote3 ,see ,pl4 ,,xxii1 ,no4 #a4 #ceh4 a b the tendon and ankle in raising the heel approach each other by a finger's breadth2 in lowering it they separate by a finger's breadth4 ,footnote3 ,see ,pl4 ,,xxii1 ,no4 #b4 ,compare this facsimile and text with ,pl4 ,,iii1 ,no4 #b1 and p4 #aeb of ,,manzi',s edition4 ,also with ,no4 #bgd of ,,ludwig',s edition of the ,vatican ,copy4 #cei4 ,just so much as the part d a of the nude figure decreases in this position so much does the opposite part increase2 that is3 in proportion as the length of the part d a diminishes the normal size so does the opposite upper part increase beyond its normal size4 ,the navel does not change its position to the male organ2 and this shrinking arises because when a figure stands on one foot1 that foot becomes the centre of gravity of the superimposed weight4 ,this being so1 the middle between the shoulders is thrust above it out of it perpendicular line1 and this line1 which forms the central line of the external parts of the body1 becomes bent at its upper extremity so as to be above the foot which supports the body2 and the transverse lines are forced into such angles that their ends are lower on the side which is supported4 ,as is shown at a b c4 ,footnote3 ,see ,pl4 ,,xxii1 ,no4 #c4 #cfj4 ,,of ,,painting4 ,note in the motions and attitudes of figures how the limbs vary1 and their feeling1 for the shoulderblades in the motions of the arms and shoulders vary the line of the back bone very much4 ,and you will find all the causes of this in my book of ,anatomy4 #cfa4 ,,of ,,change ,,of ,,attitude4 ,the pit of the throat is over the feet1 and by throwing one arm forward the pit of the throat is thrown off that foot4 ,and if the leg is thrown forward the pit of the throat is thrown forward2 and4 so it varies in every attitude4 #cfb4 ,,of ,,painting4 ,indicate which are the muscles1 and which the tendons1 which become prominent or retreat in the different movements of each limb2 or which do neither but are passive4 ,and remember that these indications of action are of the first importance and necessity in any painter or sculptor who professes to be a master c4 ,and indicate the same in a child1 and from birth to decrepitude at every stage of its life2 as infancy1 childhood1 boyhood1 youth c4 ,and in each express the alterations in the limbs and joints1 which swell and which grow thinner4 #cfc4 ,o ,anatomical ,painter6 beware lest the too strong indication of the bones1 sinews and muscles1 be the cause of your becoming wooden in your painting by your wish to make your nude figures display all their feeling4 ,therefore1 in endeavouring to remedy this1 look in what manner the muscles clothe or cover their bones in old or lean persons2 and besides this1 observe the rule as to how these same muscles fill up the spaces of the surface that extend between them1 which are the muscles which never lose their prominence in any amount of fatness2 and which too are the muscles of which the attachments are lost to sight in the very least plumpness4 ,and in many cases several muscles look like one single muscle in the increase of fat2 and in many cases1 in growing lean or old1 one single muscle divides into several muscles4 ,and in this treatise1 each in its place1 all their peculiarities will be explained--and particularly as to the spaces between the joints of each limb c4 ,again1 do not fail to observe the variations in the forms of the above mentioned muscles1 round and about the joints of the limbs of any animal1 as caused by the diversity of the motions of each limb2 for on some side of those joints the prominence of these muscles is wholly lost in the increase or diminution of the flesh of which these muscles are composed1 c4 ,footnote3 ,,de ,,rossi remarks on this chapter1 in the ,roman edition of the ,trattato1 p4 #ejd3 ,non in questo luogo solo1 ma in altri ancora osserver il lettore1 che ,lionardo va fungendo quelli che fanno abuso della loro dottrina anatomica1 e sicuramente con ci ha in mira il suo rivale ,bonarroti1 che di anatomia facea tanta pompa4 ,note1 that ,leonardo wrote this passage in ,rome1 probably under the immediate impression of ,,michaelangelo',s paintings in the ,sistine ,chapel and of ,,raphael',s ,isaiah in ,sant' ,agostino4 #cfd4 ,,of ,,the ,,different ,,measurements ,,of ,,boys ,,and ,,men4 ,there is a great difference in the length between the joints in men and boys for1 in man1 from the top of the shoulder by the neck to the elbow1 and from the elbow to the tip of the thumb and from one shoulder to the other1 is in each instance two heads1 while in a boy it is but one because ,nature constructs in us the mass which is the home of the intellect1 before forming that which contains the vital elements4 #cfe4 ,,of ,,painting4 ,which are the muscles which subdivide in old age or in youth1 when becoming lean8 ,which are the parts of the limbs of the human frame where no amount of fat makes the flesh thicker1 nor any degree of leanness ever diminishes it8 ,the thing sought for in this question will be found in all the external joints of the bones1 as the shoulder1 elbow1 wrists1 finger-joints1 hips1 knees1 ankle-bone and toes and the like2 all of which shall be told in its place4 ,the greatest thickness acquired by any limb is at the part of the muscles which is farthest from its attachments4 ,flesh never increases on those portions of the limb where the bones are near to the surface4 ,at b r d a c e f the increase or diminution of the flesh never makes any considerable difference4 ,nature has placed in front of man all those parts which feel most pain under a blow2 and these are the shin of the leg1 the forehead1 and the nose4 ,and this was done for the preservation of man1 since1 if such pain were not felt in these parts1 the number of blows to which they would be exposed must be the cause of their destruction4 ,describe why the bones of the arm and leg are double near the hand and foot respectively4 ,and where the flesh is thicker or thinner in the bending of the limbs4 #cff4 ,,of ,,painting4 ,every part of the whole must be in proportion to the whole4 ,thus1 if a man is of a stout short figure he will be the same in all his parts3 that is with short and thick arms1 wide thick hands1 with short fingers with their joints of the same character1 and so on with the rest4 ,i would have the same thing understood as applying to all animals and plants2 in diminishing1 the various parts do so in due proportion to the size1 as also in enlarging4 #cfg4 ,,of ,,the ,,agreement ,,of ,,the ,,proportion ,,of ,,the ,,limbs4 ,and again1 remember to be very careful in giving your figures limbs1 that they must appear to agree with the size of the body and likewise to the age4 ,thus a youth has limbs that are not very muscular not strongly veined1 and the surface is delicate and round1 and tender in colour4 ,in man the limbs are sinewy and muscular1 while in old men the surface is wrinkled1 rugged and knotty1 and the sinews very prominent4 ,,how ,,young ,,boys ,,have ,,their ,,joints ,,just ,,the ,,reverse ,,of ,,those ,,of ,,men1 ,,as ,,to ,,size4 ,little children have all the joints slender and the portions between them are thick2 and this happens because nothing but the skin covers the joints without any other flesh and has the character of sinew1 connecting the bones like a ligature4 ,and the fat fleshiness is laid on between one joint and the next1 and between the skin and the bones4 ,but1 since the bones are thicker at the joints than between them1 as a mass grows up the flesh ceases to have that superfluity which it had1 between the skin and the bones2 whence the skin clings more closely to the bone and the limbs grow more slender4 ,but since there is nothing over the joints but the cartilaginous and sinewy skin this cannot dry up1 and1 not drying up1 cannot shrink4 ,thus1 and for this reason1 children are slender at the joints and fat between the joints2 as may be seen in the joints of the fingers1 arms1 and shoulders1 which are slender and dimpled1 while in man on the contrary all the joints of the fingers1 arms1 and legs are thick2 and wherever children have hollows men have prominences4 ,the movement of the human figure 7#cfh-cge74 #cfh4 ,of the manner of representing the #ah actions of man4 ,repose1 movement1 running1 standing1 supported1 sitting1 leaning1 kneeling1 lying down1 suspended4 ,carrying or being carried1 thrusting1 pulling1 striking1 being struck1 pressing down and lifting up4 ,as to how a figure should stand with a weight in its hand ,footnote #h3 ,the original text ends here4 ,remember4 #cfi4 ,a sitting man cannot raise himself if that part of his body which is front of his axis centre of gravity does not weigh more than that which is behind that axis or centre without using his arms4 ,a man who is mounting any slope finds that he must involuntarily throw the most weight forward1 on the higher foot1 rather than behind--that is in front of the axis and not behind it4 ,hence a man will always1 involuntarily1 throw the greater weight towards the point whither he desires to move than in any other direction4 ,the faster a man runs1 the more he leans forward towards the point he runs to and throws more weight in front of his axis than behind4 ,a man who runs down hill throws the axis onto his heels1 and one who runs up hill throws it into the points of his feet2 and a man running on level ground throws it first on his heels and then on the points of his feet4 ,this man cannot carry his own weight unless1 by drawing his body back he balances the weight in front1 in such a way as that the foot on which he stands is the centre of gravity4 ,footnote3 ,see ,pl4 ,,xxii1 ,no4 #d4 #cgj4 ,how a man proceeds to raise himself to his feet1 when he is sitting on level ground4 #cga4 ,a man when walking has his head in advance of his feet4 ,a man when walking across a long level plain first leans rather backwards and then as much forwards4 ,footnote #c-f3 ,he strides forward with the air of a man going down hill2 when weary1 on the contrary he walks like a man going up hill4 #cgb4 ,a man when running throws less weight on his legs than when standing still4 ,and in the same way a horse which is running feels less the weight of the man he carries4 ,hence many persons think it wonderful that1 in running1 the horse can rest on one single foot4 ,from this it may be stated that when a weight is in progressive motion the more rapid it is the less is the perpendicular weight towards the centre4 #cgc4 ,if a man1 in taking a jump from firm ground1 can leap #c braccia1 and when he was taking his leap it were to recede #a_/c of a braccio1 that would be taken off his former leap2 and so if it were thrust forward #a_/c of a braccio1 by how much would his leap be increased8 #cgd4 ,,of ,,drawing4 ,when a man who is running wants to neutralise the impetus that carries him on he prepares a contrary impetus which is generated by his hanging backwards4 ,this can be proved1 since1 if the impetus carries a moving body with a momentum equal to #d and the moving body wants to turn and fall back with a momentum of #d1 then one momentum neutralises the other contrary one1 and the impetus is neutralised4 ,of walking up and down 7#cge-cgi7 #cge4 ,when a man wants to stop running and check the impetus he is forced to hang back and take short quick steps4 ,footnote3 ,lines #e-ca refer to the two upper figures1 and the lower figure to the right is explained by the last part of the chapter4 ,the centre of gravity of a man who lifts one of his feet from the ground always rests on the centre of the sole of the foot he stands on4 ,a man1 in going up stairs involuntarily throws so much weight forward and on the side of the upper foot as to be a counterpoise to the lower leg1 so that the labour of this lower leg is limited to moving itself4 ,the first thing a man does in mounting steps is to relieve the leg he is about to lift of the weight of the body which was resting on that leg2 and besides this1 he gives to the opposite leg all the rest of the bulk of the whole man1 including the weight of the other leg2 he then raises the other leg and sets the foot upon the step to which he wishes to raise himself4 ,having done this he restores to the upper foot all the weight of the body and of the leg itself1 and places his hand on his thigh and throws his head forward and repeats the movement towards the point of the upper foot1 quickly lifting the heel of the lower one2 and with this impetus he lifts himself up and at the same time extends the arm which rested on his knee2 and this extension of the arm carries up the body and the head1 and so straightens the spine which was curved4 #cb ,the higher the step is which a man has to mount1 the farther forward will he place his head in advance of his upper foot1 so as to weigh more on a than on b2 this man will not be on the step m4 ,as is shown by the line g f4 ,footnote3 ,see ,pl4 ,,xxiii1 ,no4 #a4 ,the lower sketch to the left belongs to the four first lines4 #cgf4 ,i ask the weight pressure of this man at every degree of motion on these steps1 what weight he gives to b and to c4 ,footnote #h3 ,these lines are1 in the original1 written in ink ,observe the perpendicular line below the centre of gravity of the man4 ,footnote3 ,see ,pl4 ,,xxiii1 ,no4 #b4 #cgg4 ,in going up stairs if you place your hands on your knees all the labour taken by the arms is removed from the sinews at the back of the knees4 ,footnote3 ,see ,pl4 ,,xxiii1 ,no4 #c4 #cgh4 ,the sinew which guides the leg1 and which is connected with the patella of the knee1 feels it a greater labour to carry the man upwards1 in proportion as the leg is more bent2 and the muscle which acts upon the angle made by the thigh where it joins the body has less difficulty and has a less weight to lift1 because it has not the additional weight of the thigh itself4 ,and besides this it has stronger muscles1 being those which form the buttock4 #cgi4 ,a man coming down hill takes little steps1 because the weight rests upon the hinder foot1 while a man mounting takes wide steps1 because his weight rests on the foremost foot4 ,footnote3 ,see ,pl4 ,,xxiii1 ,no4 #d4 ,on the human body in action 7#chj-chh74 #chj4 ,,of ,,the ,,human ,,body ,,in ,,action4 ,when you want to represent a man as moving some weight consider what the movements are that are to be represented by different lines2 that is to say either from below upwards1 with a simple movement1 as a man does who stoops forward to take up a weight which he will lift as he straightens himself4 ,or as a man does who wants to squash something backwards1 or to force it forwards or to pull it downwards with ropes passed through pullies ,footnote #aj3 ,compare the sketch on page #aih and on #bja 7,s4 ,k4 ,m4 ,,ii4#a #hf;b744 ,and here remember that the weight of a man pulls in proportion as his centre of gravity is distant from his fulcrum1 and to this is added the force given by his legs and bent back as he raises himself4 #cha4 ,again1 a man has even a greater store of strength in his legs than he needs for his own weight2 and to see if this is true1 make a man stand on the shore-sand and then put another man on his back1 and you will see how much he will sink in4 ,then take the man from off his back and make him jump straight up as high as he can1 and you will find that the print of his feet will be made deeper by the jump than from having the man on his back4 ,hence1 here1 by #b methods it is proved that a man has double the strength he requires to support his own body4 #chb4 ,,of ,,painting4 ,if you have to draw a man who is in motion1 or lifting or pulling1 or carrying a weight equal to his own1 in what way must you set on his legs below his body8 ,footnote3 ,in the ,,ms4 this question remains unanswered4 #chc4 ,,of ,,the ,,strength ,,of ,,man4 ,a man pulling a dead weight balanced against himself cannot pull more than his own weight4 ,and if he has to raise it he will be able to raise as much more than his weight as his strength may be more than that of other men4 ,footnote #g3 ,the stroke at the end of this line finishes in the original in a sort of loop or flourish1 and a similar flourish occurs at the end of the previous passage written on the same page4 ,m4 ,,ravaisson regards these as numbers 7compare the photograph of page #cj;b in his edition of ,,ms4 ,a74 ,he remarks3 ,ce chiffre #h et1 a la fin de l'alinea precedent1 le chiffre #g sont1 dans le manuscrit1 des renvois4 ,the greatest force a man can apply1 with equal velocity and impetus1 will be when he sets his feet on one end of the balance or lever and then presses his shoulders against some stable body4 ,this will raise a weight at the other end of the balance lever1 equal to his own weight and added to that as much weight as he can carry on his shoulders4 #chd4 ,no animal can simply move by its dead weight a greater weight than the sum of its own weight outside the centre of his fulcrum4 #che4 ,a man who wants to send an arrow very far from the bow must be standing entirely on one foot and raising the other so far from the foot he stands on as to afford the requisite counterpoise to his body which is thrown on the front foot4 ,and he must not hold his arm fully extended1 and in order that he may be more able to bear the strain he must hold a piece of wood which there is in all crossbows1 extending from the hand to the breast1 and when he wishes to shoot he suddenly leaps forward at the same instant and extends his arm with the bow and releases the string4 ,and if he dexterously does every thing at once it will go a very long way4 #chf4 ,when two men are at the opposite ends of a plank that is balanced1 and if they are of equal weight1 and if one of them wants to make a leap into the air1 then his leap will be made down from his end of the plank and the man will never go up again but must remain in his place till the man at the other end dashes up the board4 ,footnote3 ,see ,pl4 ,,xxiv1 ,no4 #c4 #chg4 ,of delivering a blow to the right or left4 ,footnote3 ,four sketches on ,pl4 ,,xxiv1 ,no4 #a belong to this passage4 ,the rest of the sketches and notes on that page are of a miscellaneous nature4 #chh4 ,why an impetus is not spent at once but diminishes gradually in some one direction8 ,footnote #a3 ,the paper has been damaged at the end of line #a4 ,the impetus acquired in the line a b c d is spent in the line d e but not so completely but that some of its force remains in it and to this force is added the momentum in the line d e with the force of the motive power1 and it must follow than the impetus multiplied by the blow is greater that the simple impetus produced by the momentum d e4 ,footnote #h3 ,the sketch ,no4 #b on ,pl4 ,,xxiv stands1 in the original1 between lines #g and #h4 ,compare also the sketches on ,pl4 ,,liv4 ,a man who has to deal a great blow with his weapon prepares himself with all his force on the opposite side to that where the spot is which he is to hit2 and this is because a body as it gains in velocity gains in force against the object which impedes its motion4 ,on hair falling down in curls4 #chi4 ,observe the motion of the surface of the water which resembles that of hair1 and has two motions1 of which one goes on with the flow of the surface1 the other forms the lines of the eddies2 thus the water forms eddying whirlpools one part of which are due to the impetus of the principal current and the other to the incidental motion and return flow4 ,footnote3 ,see ,pl4 ,,xxv4 ,where also the text of this passage is given in facsimile4 ,on draperies 7#cij--cib74 #cij4 ,,of ,,the ,,nature ,,of ,,the ,,folds ,,in ,,drapery4 ,that part of a fold which is farthest from the ends where it is confined will fall most nearly in its natural form4 ,every thing by nature tends to remain at rest4 ,drapery1 being of equal density and thickness on its wrong side and on its right1 has a tendency to lie flat2 therefore when you give it a fold or plait forcing it out of its flatness note well the result of the constraint in the part where it is most confined2 and the part which is farthest from this constraint you will see relapses most into the natural state2 that is to say lies free and flowing4 ,,example4 ,footnote #ac3 a c sia4 ,in the original text b is written instead of c--an evident slip of the pen4 ,let a b c be the fold of the drapery spoken of above1 a c will be the places where this folded drapery is held fast4 ,i maintain that the part of the drapery which is farthest from the plaited ends will revert most to its natural form4 ,therefore1 b being farthest from a and c in the fold a b c it will be wider there than anywhere else4 ,footnote3 ,see ,pl4 ,,xxviii1 ,no4 #f1 and compare the drawing from ,windsor ,pl4 ,,xxx for farther illustration of what is here stated4 #cia4 ,,of ,,small ,,folds ,,in ,,draperies4 ,how figures dressed in a cloak should not show the shape so much as that the cloak looks as if it were next the flesh2 since you surely cannot wish the cloak to be next the flesh1 for you must suppose that between the flesh and the cloak there are other garments which prevent the forms of the limbs appearing distinctly through the cloak4 ,and those limbs which you allow to be seen you must make thicker so that the other garments may appear to be under the cloak4 ,but only give something of the true thickness of the limbs to a nymph ,footnote #i3 ,una nifa4 ,compare the beautiful drawing of a ,nymph1 in black chalk from the ,windsor collection1 ,pl4 ,,xxvi4 or an angel1 which are represented in thin draperies1 pressed and clinging to the limbs of the figures by the action of the wind4 #cib4 ,you ought not to give to drapery a great confusion of many folds1 but rather only introduce them where they are held by the hands or the arms2 the rest you may let fall simply where it is its nature to flow2 and do not let the nude forms be broken by too many details and interrupted folds4 ,how draperies should be drawn from nature3 that is to say if youwant to represent woollen cloth draw the folds from that2 and if it is to be silk1 or fine cloth or coarse1 or of linen or of crape1 vary the folds in each and do not represent dresses1 as many do1 from models covered with paper or thin leather which will deceive you greatly4 ,footnote3 ,the little pen and ink drawing from ,windsor 7,w4 #ajb71 given on ,pl4 ,,xxviii1 ,no4 #g1 clearly illustrates the statement made at the beginning of this passage2 the writing of the cipher #ai on the same page is in ,leonardo's hand2 the cipher #ba is certainly not4 ,,viii4 ,botany for ,painters and ,elements of ,landscape ,painting4 ,the chapters composing this portion of the work consist of observations on ,form1 ,light and ,shade in ,plants1 and particularly in ,trees summed up in certain general rules by which the author intends to guide the artist in the pictorial representation of landscape4 ,with these the first principles of a ,theory of ,landscape painting are laid down--a theory as profoundly thought out in its main lines as it is lucidly worked out in its details4 ,in reading these chapters the conviction is irresistible that such a ,botany for painters is or ought to be of similar importance in the practice of painting as the principles of the ,proportions and ,movements of the human figure i4 e4 ,anatomy for painters4 ,there can be no doubt that ,leonardo1 in laying down these rules1 did not intend to write on ,botany in the proper scientific sense--his own researches on that subject have no place here2 it need only be observed that they are easily distinguished by their character and contents from those which are here collected and arranged under the title ',botany for painters'4 ,in some cases where this division might appear doubtful1--as for instance in ,no4 #djb--the ,painter is directly addressed and enjoined to take the rule to heart as of special importance in his art4 ,the original materials are principally derived from ,,ms4 ,g1 in which we often find this subject treated on several pages in succession without any of that intermixture of other matters1 which is so frequent in ,leonardo's writings4 ,this ,,ms41 too1 is one of the latest2 when it was written1 the great painter was already more than sixty years of age1 so we can scarcely doubt that he regarded all he wrote as his final views on the subject4 ,and the same remark applies to the chapters from ,,mss4 ,e and ,m which were also written between #aeac--ae4 ,for the sake of clearness1 however1 it has been desirable to sacrifice--with few exceptions--the original order of the passages as written1 though it was with much reluctance and only after long hesitation that ,i resigned myself to this necessity4 ,nor do ,i mean to impugn the logical connection of the author's ideas in his ,,ms42 but it will be easily understood that the sequence of disconnected notes1 as they occurred to ,leonardo and were written down from time to time1 might be hardly satisfactory as a systematic arrangement of his principles4 ,the reader will find in the ,appendix an exact account of the order of the chapters in the original ,,ms4 and from the data there given can restore them at will4 ,as the materials are here arranged1 the structure of the tree as regards the growth of the branches comes first 7#cid-daa7 and then the insertion of the leaves on the stems 7#dab-dai74 ,then follow the laws of ,light and ,shade as applied1 first1 to the leaves 7#dbj-dcd71 and1 secondly1 to the whole tree and to groups of trees 7#dce-deg74 ,after the remarks on the ,light and ,shade in landscapes generally 7#deh-dfd71 we find special observations on that of views of towns and buildings 7#dfe-dfi74 ,to the theory of ,landscape ,painting belong also the passages on the effect of ,wind on ,trees 7#dgj-dgc7 and on the ,light and ,shade of ,clouds 7#dgd-dgg71 since we find in these certain comparisons with the effect of ,light and ,shade on ,trees 7e4 g43 in ,no4 #dgf1 #d4 #e2 and ,no4 #dgg1 #i4 #ab74 ,the chapters given in the ,appendix ,nos4 #dgh and #dha have hardly any connection with the subjects previously treated4 ,classification of trees4 #cic4 ,,trees4 ,small1 lofty1 straggling1 thick1 that is as to foliage1 dark1 light1 russet1 branched at the top2 some directed towards the eye1 some downwards2 with white stems2 this transparent in the air1 that not2 some standing close together1 some scattered4 ,the relative thickness of the branches to the trunk 7#cic--cif74 #cid4 ,all the branches of a tree at every stage of its height when put together are equal in thickness to the trunk below them4 ,all the branches of a water course at every stage of its course1 if they are of equal rapidity1 are equal to the body of the main stream4 #cie4 ,every year when the boughs of a plant or tree have made an end of maturing their growth1 they will have made1 when put together1 a thickness equal to that of the main stem2 and at every stage of its ramification you will find the thickness of the said main stem2 as3 i k1 g h1 e f1 c d1 a b1 will always be equal to each other2 unless the tree is pollard--if so the rule does not hold good4 ,all the branches have a direction which tends to the centre of the tree m4 ,footnote3 ,the two sketches of leafless trees one above another on the left hand side of ,pl4 ,,xxvii1 ,no4 #a1 belong to this passage4 #cif4 ,if the plant n grows to the thickness shown at m1 its branches will correspond in thickness to the junction a b in consequence of the growth inside as well as outside4 ,the branches of trees or plants have a twist wherever a minor branch is given off2 and this giving off the branch forms a fork2 this said fork occurs between two angles of which the largest will be that which is on the side of the larger branch1 and in proportion1 unless accident has spoilt it4 ,footnote3 ,the sketches illustrating this are on the right hand side of ,,pi4 ,,xxvii1 ,no4 ,i1 and the text is also given there in facsimile4 #cig4 ,there is no boss on branches which has not been produced by some branch which has failed4 ,the lower shoots on the branches of trees grow more than the upper ones and this occurs only because the sap that nourishes them1 being heavy1 tends downwards more than upwards2 and again1 because those branches which grow downwards turn away from the shade which exists towards the centre of the plant4 ,the older the branches are1 the greater is the difference between their upper and their lower shoots and in those dating from the same year or epoch4 ,footnote3 ,the sketch accompanying this in the ,,ms4 is so effaced that an exact reproduction was impossible4 #cih4 ,,of ,,the ,,scars ,,on ,,trees4 ,the scars on trees grow to a greater thickness than is required by the sap of the limb which nourishes them4 #cii4 ,the plant which gives out the smallest ramifications will preserve the straightest line in the course of its growth4 ,footnote3 ,this passage is illustrated by two partly effaced sketches4 ,one of these closely resembles the lower one given under ,no4 #djh1 the other also represents short closely set boughs on an upright trunk4 #djj4 ,,of ,,the ,,ramification4 ,the beginning of the ramification the shoot always has the central line axis of its thickness directed to the central line axis of the plant itself4 #dja4 ,in starting from the main stem the branches always form a base with a prominence as is shown at a b c d4 #djb4 ,,why1 ,,very ,,frequently1 ,,timber ,,has ,,veins ,,that ,,are ,,not ,,straight4 ,when the branches which grow the second year above the branch of the preceding year1 are not of equal thickness above the antecedent branches1 but are on one side1 then the vigour of the lower branch is diverted to nourish the one above it1 although it may be somewhat on one side4 ,but if the ramifications are equal in their growth1 the veins of the main stem will be straight parallel and equidistant at every degree of the height of the plant4 ,wherefore1 ,o ,painter6 you1 who do not know these laws6 in order to escape the blame of those who understand them1 it will be well that you should represent every thing from nature1 and not despise such study as those do who work only for money4 ,the direction of growth 7#djc-djg74 #djc4 ,,of ,,the ,,ramifications ,,of ,,plants4 ,the plants which spread very much have the angles of the spaces which divide their branches more obtuse in proportion as their point of origin is lower down2 that is nearer to the thickest and oldest portion of the tree4 ,therefore in the youngest portions of the tree the angles of ramification are more acute4 ,footnote3 ,compare the sketches on the lower portion of ,pl4 ,,xxvii1 ,no4 #b4 #djd4 ,the tips of the boughs of plants and trees1 unless they are borne down by the weight of their fruits1 turn towards the sky as much as possible4 ,the upper side of their leaves is turned towards the sky that it may receive the nourishment of the dew which falls at night4 ,the sun gives spirit and life to plants and the earth nourishes them with moisture4 #i ,with regard to this ,i made the experiment of leaving only one small root on a gourd and this ,i kept nourished with water1 and the gourd brought to perfection all the fruits it could produce1 which were about #fj gourds of the long kind1 andi set my mind diligently to consider this vitality and perceived that the dews of night were what supplied it abundantly with moisture through the insertion of its large leaves and gave nourishment to the plant and its offspring--or the seeds which its offspring had to produce--#ba4 ,the rule of the leaves produced on the last shoot of the year will be that they will grow in a contrary direction on the twin branches2 that is1 that the insertion of the leaves turns round each branch in such a way1 as that the sixth leaf above is produced over the sixth leaf below1 and the way they turn is that if one turns towards its companion to the right1 the other turns to the left1 the leaf serving as the nourishing breast for the shoot or fruit which grows the following year4 ,footnote3 ,a ,french translation of lines #i-ab was given by ,m4 ,,ravaisson in the ,gazette des ,beaux ,arts1 ,oct4 #ahgg2 his paper also contains some valuable information as to botanical science in the ancient classical writers and at the time of the ,renaissance4 #dje4 ,the lowest branches of those trees which have large leaves and heavy fruits1 such as nut-trees1 fig-trees and the like1 always droop towards the ground4 ,the branches always originate above in the axis of the leaves4 #djf4 ,the upper shoots of the lateral branches of plants lie closer to the parent branch than the lower ones4 #djg4 ,the lowest branches1 after they have formed the angle of their separation from the parent stem1 always bend downwards so as not to crowd against the other branches which follow them on the same stem and to be better able to take the air which nourishes them4 ,as is shown by the angle b a c2 the branch a c after it has made the corner of the angle a c bends downwards to c d and the lesser shoot c dries up1 being too thin4 ,the main branch always goes below1 as is shown by the branch f n m1 which does not go to f n o4 ,the forms of trees 7#djh--daa74 #djh4 ,the elm always gives a greater length to the last branches of the year's growth than to the lower ones2 and ,nature does this because the highest branches are those which have to add to the size of the tree2 and those at the bottom must get dry because they grow in the shade and their growth would be an impediment to the entrance of the solar rays and the air among the main branches of the tree4 ,the main branches of the lower part bend down more than those above1 so as to be more oblique than those upper ones1 and also because they are larger and older4 #dji4 ,in general almost all the upright portions of trees curve somewhat turning the convexity towards the ,south2 and their branches are longer and thicker and more abundant towards the ,south than towards the ,north4 ,and this occurs because the sun draws the sap towards that surface of the tree which is nearest to it4 ,and this may be observed if the sun is not screened off by other plants4 #daj4 ,the cherry-tree is of the character of the fir tree as regards its ramification placed in stages round its main stem2 and its branches spring1 #d or five or #f together opposite each other2 and the tips of the topmost shoots form a pyramid from the middle upwards2 and the walnut and oak form a hemisphere from the middle upwards4 #daa4 ,the bough of the walnut which is only hit and beaten when it has brought to perfection444 ,footnote3 ,the end of the text and the sketch in red chalk belonging to it1 are entirely effaced4 ,the insertion of the leaves 7#dab--dai74 #dab4 ,,of ,,the ,,insertion ,,of ,,the ,,branches ,,on ,,plants4 ,such as the growth of the ramification of plants is on their principal branches1 so is that of the leaves on the shoots of the same plant4 ,these leaves have ,footnote #f3 ,quattro modi 7four modes74 ,only three are described in the text1 the fourth is only suggested by a sketch4 ,this passage occurs in ,,manzi',s edition of the ,trattato1 p4 #cii1 but without the sketches and the text is mutilated in an important part4 ,the whole passage has been commented on1 from ,,manzi',s version1 in ,part ,i of the ,nuovo ,giornale ,botanico ,italiano1 by ,prof4 ,g4 ,,uzielli 7,florence #ahfi1 ,vol4 ,i74 ,he remarks as to the 'four modes'3 ,leonardo1 come si vede nelle linie sententi da solo tre esempli4 ,questa ed altre inessattezze fanno desiderare1 sia esaminato di nuovo il manoscritto ,vaticano4 ,this has since been done by ,d4 ,,knapp of ,tubingen1 and his accurate copy has been published by ,h4 ,,ludwig1 the painter4 ,the passage in question occurs in his edition as ,no4 #hcc2 and there also the drawings are wanting4 ,the space for them has been left vacant1 but in the ,vatican copy 'niente' has been written on the margin2 and in it1 as well as in ,,ludwig',s and ,,manzi',s edition1 the text is mutilated4 four modes of growing one above another4 ,the first1 which is the most general1 is that the sixth always originates over the sixth below ,footnote #h3 la sesta di sotto4 ,disposizione #b_/e o #a_/e4 ,leonardo osservo probabilmente soltanto la prima 7,u,z,i,e,l,ll742 the second is that two third ones above are over the two third ones below ,footnote #aj3 terze di sotto3 ,intende qui senza dubbio parlare di foglie decussate1 in cui il terzo verticello e nel piano del primo 7,,uzielli742 and the third way is that the third above is over the third below ,footnote #aa3 #c;a di sotto3 ,disposizione #a_/b 7,,uzielli744 ,footnote3 ,see the four sketches on the upper portion of the page reproduced as fig4 #b on ,p#a4 ,,xxvii4 #dac4 ,a ,,description ,,of ,,the ,,elm4 ,the ramification of the elm has the largest branch at the top4 ,the first and the last but one are smaller1 when the main trunk is straight4 ,the space between the insertion of one leaf to the rest is half the extreme length of the leaf or somewhat less1 for the leaves are at an interval which is about the #crd of the width of the leaf4 ,the elm has more leaves near the top of the boughs than at the base2 and the broad surface of the leaves varies little as to angle and aspect4 ,footnote3 ,see ,pl4 ,,xxvii1 ,no4 #c4 ,above the sketch and close under the number of the page is the word 'olmo' 7elm74 #dad4 ,in the walnut tree the leaves which are distributed on the shoots of this year are further apart from each other and more numerous in proportion as the branch from which this shoot springs is a young one4 ,and they are inserted more closely and less in number when the shoot that bears them springs from an old branch4 ,its fruits are borne at the ends of the shoots4 ,and its largest boughs are the lowest on the boughs they spring from4 ,and this arises from the weight of its sap which is more apt to descend than to rise1 and consequently the branches which spring from them and rise towards the sky are small and slender #bj2 and when the shoot turns towards the sky its leaves spread out from it at an angle with an equal distribution of their tips2 and if the shoot turns to the horizon the leaves lie flat2 and this arises from the fact that leaves without exception1 turn their underside to the earth #bi4 ,the shoots are smaller in proportion as they spring nearer to the base of the bough they spring from4 ,footnote3 ,see the two sketches on ,pl ,,xxvii1 ,no4 #d4 ,the second refers to the passage lines #bj-cj4 #dae4 ,,of ,,the ,,insertion ,,of ,,the ,,leaves ,,on ,,the ,,branches4 ,the thickness of a branch never diminishes within the space between one leaf and the next excepting by so much as the thickness of the bud which is above the leaf and this thickness is taken off from the branch above the node as far as the next leaf4 ,nature has so placed the leaves of the latest shoots of many plants that the sixth leaf is always above the first1 and so on in succession1 if the rule is not accidentally interfered with2 and this occurs for two useful ends in the plant3 ,first that as the shoot and the fruit of the following year spring from the bud or eye which lies above and in close contact with the insertion of the leaf in the axil1 the water which falls upon the shoot can run down to nourish the bud1 by the drop being caught in the hollow axil at the insertion of the leaf4 ,and the second advantage is1 that as these shoots develop in the following year one will not cover the next below1 since the #e come forth on five different sides2 and the sixth which is above the first is at some distance4 #daf4 ,,of ,,the ,,ramifications ,,of ,,trees ,,and ,,their ,,foliage4 ,the ramifications of any tree1 such as the elm1 are wide and slender after the manner of a hand with spread fingers1 foreshortened4 ,and these are seen in the distribution thus3 the lower portions are seen from above2 and those that are above are seen from below2 and those in the middle1 some from below and some from above4 ,the upper part is the extreme top of this ramification and the middle portion is more foreshortened than any other of those which are turned with their tips towards you4 ,and of those parts of the middle of the height of the tree1 the longest will be towards the top of the tree and will produce a ramification like the foliage of the common willow1 which grows on the banks of rivers4 ,other ramifications are spherical1 as those of such trees as put forth their shoots and leaves in the order of the sixth being placed above the first4 ,others are thin and light like the willow and others4 #dag4 ,you will see in the lower branches of the elder1 which puts forth leaves two and two placed crosswise at right angles one above another1 that if the stem rises straight up towards the sky this order never fails2 and its largest leaves are on the thickest part of the stem and the smallest on the slenderest part1 that is towards the top4 ,but1 to return to the lower branches1 ,i say that the leaves on these are placed on them crosswise like those on the upper branches2 and as1 by the law of all leaves1 they are compelled to turn their upper surface towards the sky to catch the dew at night1 it is necessary that those so placed should twist round and no longer form a cross4 ,footnote3 ,see ,pl4 ,,xxvii1 ,no4 #e4 #dah4 ,a leaf always turns its upper side towards the sky so that it may the better receive1 on all its surface1 the dew which drops gently from the atmosphere4 ,and these leaves are so distributed on the plant as that one shall cover the other as little as possible1 but shall lie alternately one above another as may be seen in the ivy which covers the walls4 ,and this alternation serves two ends2 that is1 to leave intervals by which the air and sun may penetrate between them4 ,the #bnd reason is that the drops which fall from the first leaf may fall onto the fourth or--in other trees--onto the sixth4 #dai4 ,every shoot and every fruit is produced above the insertion in the axil of its leaf which serves it as a mother1 giving it water from the rain and moisture from the dew which falls at night from above1 and often it protects them against the too great heat of the rays of the sun4 ,,light ,,on ,,branches ,,and ,,leaves 7#dbj--dbb74 #dbj4 ,that part of the body will be most illuminated which is hit by the luminous ray coming between right angles4 ,footnote3 ,see ,pl4 ,,xxviii1 ,no4 #a4 #dba4 ,young plants have more transparent leaves and a more lustrous bark than old ones2 and particularly the walnut is lighter coloured in ,may than in ,september4 #dbb4 ,,of ,,the ,,accidents ,,of ,,colouring ,,in ,,trees4 ,the accidents of colour in the foliage of trees are #d4 ,that is3 shadow1 light1 lustre reflected light and transparency4 ,,of ,,the ,,visibility ,,of ,,these ,,accidents4 ,these accidents of colour in the foliage of trees become confused at a great distance and that which has most breadth whether light or shade1 c4 will be most conspicuous4 ,the proportions of light and shade in a leaf 7#dbc-dbf74 #dbc4 ,,of ,,the ,,shadows ,,of ,a ,,leaf4 ,sometimes a leaf has three accidents of light that is3 shade1 lustre reflected light and transparency transmitted light4 ,thus1 if the light were at n as regards the leaf s1 and the eye at m1 it would see a in full light1 b in shadow and c transparent4 #dbd4 ,a leaf with a concave surface seen from the under side and up-side-down will sometimes show itself as half in shade1 and half transparent4 ,thus1 if o p is the leaf and the light m and the eye n1 this will see o in shadow because the light does not fall upon it between equal angles1 neither on the upper nor the under side1 and p is lighted on the upper side and the light is transmitted to its under side4 ,footnote3 ,see ,pl4 ,,xxviii1 ,no4 #b1 the upper sketch on the page4 ,in the original they are drawn in red chalk4 #dbe4 ,although those leaves which have a polished surface are to a great extent of the same colour on the right side and on the reverse1 it may happen that the side which is turned towards the atmosphere will have something of the colour of the atmosphere2 and it will seem to have more of this colour of the atmosphere in proportion as the eye is nearer to it and sees it more foreshortened4 ,and1 without exception the shadows show as darker on the upper side than on the lower1 from the contrast offered by the high lights which limit the shadows4 ,the under side of the leaf1 although its colour may be in itself the same as that of the upper side1 shows a still finer colour--a colour that is green verging on yellow--and this happens when the leaf is placed between #dbf4 the eye and the light which falls upon it from the opposite side4 ,and its shadows are in the same positions as those were of the opposite side4 ,therefore1 ,o ,painter6 when you do trees close at hand1 remember that if the eye is almost under the tree you will see its leaves some on the upper and some on the under side1 and the upper side will be bluer in proportion as they are seen more foreshortened1 and the same leaf sometimes shows part of the right side and part of the under side1 whence you must make it of two colours4 ,of the transparency of leaves 7#dbg-dbi74 #dbg4 ,the shadows in transparent leaves seen from the under side are the same shadows as there are on the right side of this leaf1 they will show through to the underside together with lights1 but the lustre reflected light can never show through4 #dbh4 ,when one green has another green behind it1 the lustre on the leaves and their transparent lights show more strongly than in those which are seen against the brightness of the atmosphere4 ,and if the sun illuminates the leaves without their coming between it and the eye and without the eye facing the sun1 then the reflected lights and the transparent lights are very strong4 ,it is very effective to show some branches which are low down and dark and so set off the illuminated greens which are at some distance from the dark greens seen below4 ,that part is darkest which is nearest to the eye or which is farthest from the luminous atmosphere4 #dbi4 ,never paint leaves transparent to the sun1 because they are confused2 and this is because on the transparency of one leaf will be seen the shadow of another leaf which is above it4 ,this shadow has a distinct outline and a certain depth of shade and sometimes is as much as half or a third of the leaf which is shaded2 and consequently such an arrangement is very confused and the imitation of it should be avoided4 ,the light shines least through a leaf when it falls upon it at an acute angle4 ,the gradations of shade and colour in leaves 7#dcj-dcd74 #dcj4 ,the shadows of plants are never black1 for where the atmosphere penetrates there can never be utter darkness4 #dca4 ,if the light comes from m and the eye is at n the eye will see the colour of the leaves a b all affected by the colour of m --that is of the atmosphere2 and b c will be seen from the under side as transparent1 with a beautiful green colour verging on yellow4 ,if m is the luminous body lighting up the leaf s all the eyes that see the under side of this leaf will see it of a beautiful light green1 being transparent4 ,in very many cases the positions of the leaves will be without shadow or in full light1 and their under side will be transparent and the right side lustrous reflecting light4 #dcb4 ,the willow and other similar trees1 which have their boughs lopped every #c or #d years1 put forth very straight branches1 and their shadow is about the middle where these boughs spring2 and towards the extreme ends they cast but little shade from having small leaves and few and slender branches4 ,hence the boughs which rise towards the sky will have but little shade and little relief2 and the branches which are at an angle from the horizon1 downwards1 spring from the dark part of the shadow and grow thinner by degrees up to their ends1 and these will be in strong relief1 being in gradations of light against a background of shadow4 ,that tree will have the least shadow which has the fewest branches and few leaves4 #dcc4 ,,of ,,dark ,,leaves ,,in ,,front ,,of ,,transparent ,,ones4 ,when the leaves are interposed between the light and the eye1 then that which is nearest to the eye will be the darkest1 and the most distant will be the lightest1 not being seen against the atmosphere2 and this is seen in the leaves which are away from the centre of the tree1 that is towards the light4 ,footnote3 ,see ,pl4 ,,xxviii1 ,no4 #b1 the lower sketch4 #dcd4 ,,of ,,the ,,lights ,,on ,,dark ,,leaves4 ,the lights on such leaves which are darkest1 will be most near to the colour of the atmosphere that is reflected in them4 ,and the cause of this is that the light on the illuminated portion mingles with the dark hue to compose a blue colour2 and this light is produced by the blueness of the atmosphere which is reflected in the smooth surface of these leaves and adds to the blue hue which this light usually produces when it falls on dark objects4 ,,of ,,the ,,lights ,,on ,,leaves ,,of ,a ,,yellowish ,,green4 ,but leaves of a green verging on yellow when they reflect the atmosphere do not produce a reflection verging on blue1 inasmuch as every thing which appears in a mirror takes some colour from that mirror1 hence the blue of the atmosphere being reflected in the yellow of the leaf appears green1 because blue and yellow mixed together make a very fine green colour1 therefore the lustre of light leaves verging on yellow will be greenish yellow4 ,a classification of trees according to their colours4 #dce4 ,the trees in a landscape are of various kinds of green1 inasmuch as some verge towards blackness1 as firs1 pines1 cypresses1 laurels1 box and the like4 ,some tend to yellow such as walnuts1 and pears1 vines and verdure4 ,some are both yellowish and dark as chesnuts1 holm-oak4 ,some turn red in autumn as the service-tree1 pomegranate1 vine1 and cherry2 and some are whitish as the willow1 olive1 reeds and the like4 ,trees are of various forms 444 ,the proportions of light and shade in trees 7#dcf-ddj74 #dcf4 ,,of ,a ,,generally ,,distributed ,,light ,,as ,,lighting ,,up ,,trees4 ,that part of the trees will be seen to lie in the least dark shadow which is farthest from the earth4 ,to prove it let a p be the tree1 n b c the illuminated hemisphere the sky1 the under portion of the tree faces the earth p c1 that is on the side o1 and it faces a small part of the hemisphere at c d4 ,but the highest part of the convexity a faces the greatest part of the hemisphere1 that is b c4 ,for this reason--and because it does not face the darkness of the earth--it is in fuller light4 ,but if the tree has dense foliage1 as the laurel1 arbutus1 box or holm oak1 it will be different2 because1 although a does not face the earth1 it faces the dark green of the leaves cut up by many shadows1 and this darkness is reflected onto the under sides of the leaves immediately above4 ,thus these trees have their darkest shadows nearest to the middle of the tree4 #dcg4 ,,of ,,the ,,shadows ,,of ,,verdure4 ,the shadows of verdure are always somewhat blue1 and so is every shadow of every object2 and they assume this hue more in proportion as they are remote from the eye1 and less in proportion as they are nearer4 ,the leaves which reflect the blue of the atmosphere always present themselves to the eye edgewise4 ,,of ,,the ,,illuminated ,,part ,,of ,,verdure ,,and ,,of ,,mountains4 ,the illuminated portion1 at a great distance1 will appear most nearly of its natural colour where the strongest light falls upon it4 #dch4 ,,of ,,trees ,,that ,,are ,,lighted ,,by ,,the ,,sun ,,and ,,by ,,the ,,atmosphere4 ,in trees that are illuminated both by the sun and the atmosphere and that have leaves of a dark colour1 one side will be illuminated by the atmosphere only and in consequence of this light will tend to blueness1 while on the other side they will be illuminated by the atmosphere and the sun2 and the side which the eye sees illuminated by the sun will reflect light4 #dci4 ,,of ,,depicting ,a ,,forest ,,scene4 ,the trees and plants which are most thickly branched with slender branches ought to have less dark shadow than those trees and plants which1 having broader leaves1 will cast more shadow4 #ddj4 ,,on ,,painting4 ,in the position of the eye which sees that portion of a tree illuminated which turns towards the light1 one tree will never be seen to be illuminated equally with the other4 ,to prove this1 let the eye be c which sees the two trees b d which are illuminated by the sun a2 ,i say that this eye c will not see the light in the same proportion to the shade1 in one tree as in the other4 ,because1 the tree which is nearest to the sun will display so much the stronger shadow than the more distant one1 in proportion as one tree is nearer to the rays of the sun that converge to the eye than the other2 c4 ,you see that the eye c sees nothing of the tree d but shadow1 while the same eye c sees th tree b half in light and half in shade4 ,when a tree is seen from below1 the eye sees the top of it as placed within the circle made by its boughs#bc4 ,remember1 ,o ,painter6 that the variety of depth of shade in any one particular species of tree is in proportion to the rarity or density of their branches4 ,footnote3 ,the two lower sketches on the left of ,pl ,,xxviii1 ,no4 #c1 refer to lines #ba-bc4 ,the upper sketch has apparently been effaced by ,leonardo himself4 ,the distribution of light and shade with reference to the position of the spectator 7#dda-ddc74 #dda4 ,the shadows of trees placed in a landscape do not display themselves in the same position in the trees on the right hand and those on the left2 still more so if the sun is to the right or left4 ,as is proved by the #dth which says3 ,opaque bodies placed between the light and the eye display themselves entirely in shadow2 and by the #eth3 ,the eye when placed between the opaque body and the light sees the opaque body entirely illuminated4 ,and by the #fth3 ,when the eye and the opaque body are placed between darkness and light1 it will be seen half in shadow and half in light4 ,footnote3 ,see the figure on the right hand side of ,pl4 ,,xxviii1 ,no4 #c4 ,the first five lines of the text are written below the diagram and above it are the last eight lines of the text1 given as ,no4 #dfa4 #ddb4 ,,of ,,the ,,herbs ,,of ,,the ,,field4 ,of the plants which take a shadow from the plants which spring among them1 those which are on this side in front of the shadow have the stems lighted up on a background of shadow1 and the plants on which the shadows fall have their stems dark on a light background2 that is on the background beyond the shadow4 ,,of ,,trees ,,which ,,are ,,between ,,the ,,eye ,,and ,,the ,,light4 ,of the trees which are between the eye and the light the part in front will be light2 but this light will be broken by the ramifications of transparent leaves--being seen from the under side--and lustrous leaves--being seen from the upper side2 and the background below and behind will be dark green1 being in shadow from the front portion of the said tree4 ,this occurs in trees placed above the eye4 #ddc4 ,,from ,,whence ,,to ,,depict ,a ,,landscape ,landscapes should be represented so that the trees may be half in light and half in shadow2 but it is better to do them when the sun is covered with clouds1 for then the trees are lighted by the general light of the sky1 and the general darkness of the earth4 ,and then they are darkest in certain parts in proportion as those parts are nearest to the middle of the tree and to the earth4 ,the effects of morning light 7#ddd-ddh74 #ddd4 ,,of ,,trees ,,to ,,the ,,south4 ,when the sun is in the east the trees to the ,south and to the ,north have almost as much light as shadow4 ,but a greater share of light in proportion as they lie to the ,west and a greater share of shadow in proportion as they lie to the ,east4 ,,of ,,meadows4 ,if the sun is in the ,east the verdure of the meadows and of other small plants is of a most beautiful green from being transparent to the sun2 this does not occur in the meadows to the ,west1 and in those to the ,south and ,north the grass is of a moderately brilliant green4 #dde4 ,,of ,,the #d ,,points ,,of ,,the ,,compass ,,in ,,landscapes4 ,when the sun is in the ,east all the portions of plants lighted by it are of a most lively verdure1 and this happens because the leaves lighted by the sun within the half of the horizon that is the ,eastern half1 are transparent2 and within the ,western semicircle the verdure is of a dull hue and the moist air is turbid and of the colour of grey ashes1 not being transparent like that in the ,east1 which is quite clear and all the more so in proportion as it is moister4 ,the shadows of the trees to the ,east cover a large portion of them and are darker in proportion as the foliage of the trees is thicker4 #ddf4 ,,of ,,trees ,,in ,,the ,,east4 ,when the sun is in the ,east the trees seen towards the ,east will have the light which surrounds them all round their shadows1 excepting on the side towards the earth2 unless the tree has been pruned below in the past year4 ,and the trees to the ,south and ,north will be half in shade and half in light1 and more or less in shade or in light in proportion as they are more or less to the ,east or to the ,west4 ,the position of the eye above or below varies the shadows and lights in trees1 inasmuch as the eye placed above sees the tree with the little shadow1 and the eye placed below with a great deal of shadow4 ,the colour of the green in plants varies as much as their species4 #ddg4 ,,of ,,the ,,shadows ,,in ,,trees4 ,the sun being in the ,east to the right1 the trees to the ,west or left of the eye will show in small relief and almost imperceptible gradations1 because the atmosphere which lies between the eye and those trees is very dense ,footnote #g3 per la #g;a di questo4 ,this possibly referred to something written on the seventh page of this note book marked ,g4 ,unfortunately it has been cut out and lost41 see the #gth of this--and they have no shade2 for though a shadow exists in every detail of the ramification1 it results that the images of the shade and light that reach the eye are confused and mingled together and cannot be perceived on account of their minuteness4 ,and the principal lights are in the middle of the trees1 and the shadows to wards the edges2 and their separation is shown by the shadows of the intervals between the trees2 but when the forests are thick with trees the thin edges are but little seen4 #ddh4 ,,of ,,trees ,,to ,,the ,,east4 ,when the sun is in the ,east the trees are darker towards the middle while their edges are light4 ,the effects of midday light4 #ddi4 ,,objects ,,in ,,high ,,light ,,show ,,but ,,little1 ,,but ,,between ,,light ,,and ,,shadow ,,they ,,stand ,,out ,,well4 ,to represent a landscape choose that the sun shall be at noon and look towards the ,west or ,east and then draw4 ,and if you turn towards the ,north1 every object placed on that side will have no shadow1 particularly those which are nearest to the direction of the shadow of your head4 ,and if you turn towards the ,south every object on that side will be wholly in shadow4 ,all the trees which are towards the sun and have the atmosphere for their background are dark1 and the other trees which lie against that darkness will be black very dark in the middle and lighter towards the edges4 ,the appearance of trees in the distance 7#dej4 #dea74 #dej4 ,,of ,,the ,,spaces ,,showing ,,the ,,sky ,,in ,,trees ,,themselves4 ,the spaces between the parts in the mass of trees1 and the spaces between the trees in the air1 are1 at great distances1 invisible to the eye2 for1 where it is an effort even to see the whole it is most difficult to discern the parts4--,but a confused mixture is the result1 partaking chiefly of the hue which predominates4 ,the spaces between the leaves consist of particles of illuminated air which are very much smaller than the tree and are lost sight of sooner than the tree2 but it does not therefore follow that they are not there4 ,hence1 necessarily1 a compounded effect is produced of the sky and of the shadows of the tree in shade1 which both together strike the eye which sees them4 ,,of ,,trees ,,which ,,conceal ,,these ,,spaces ,,in ,,one ,,another4 ,that part of a tree will show the fewest spaces1 behind which a large number of trees are standing between the tree and the air sky2 thus in the tree a the spaces are not concealed nor in b1 as there is no tree behind4 ,but in c only half shows the spaces filled up by the tree d1 and part of the tree d is filled up by the tree e and a little farther on all the spaces in the mass of the trees are lost1 and only that at the side remains4 #dea4 ,,of ,,trees4 ,what outlines are seen in trees at a distance against the sky which serves as their background8 ,the outlines of the ramification of trees1 where they lie against the illuminated sky1 display a form which more nearly approaches the spherical on proportion as they are remote1 and the nearer they are the less they appear in this spherical form2 as in the first tree a which1 being near to the eye1 displays the true form of its ramification2 but this shows less in b and is altogether lost in c1 where not merely the branches of the tree cannot be seen but the whole tree is distinguished with difficulty4 ,every object in shadow1 of whatever form it may be1 at a great distance appears to be spherical4 ,and this occurs because1 if it is a square body1 at a very short distance it loses its angles1 and a little farther off it loses still more of its smaller sides which remain4 ,and thus before the whole is lost to sight the parts are lost1 being smaller than the whole2 as a man1 who in such a distant position loses his legs1 arms and head before the mass of his body1 then the outlines of length are lost before those of breadth1 and where they have become equal it would be a square if the angles remained2 but as they are lost it is round4 ,footnote3 ,the sketch ,no4 #d1 ,pl4 ,,xxviii1 belongs to this passage4 ,the cast shadow of trees 7#deb4 #dec74 #deb4 ,the image of the shadow of any object of uniform breadth can never be exactly the same as that of the body which casts it4 ,footnote3 ,see ,pl4 ,,xxviii1 ,no4 #e4 ,light and shade on groups of trees 7#dec-deg74 #dec4 ,all trees seen against the sun are dark towards the middle and this shadow will be of the shape of the tree when apart from others4 ,the shadows cast by trees on which the sun shines are as dark as those of the middle of the tree4 ,the shadow cast by a tree is never less than the mass of the tree but becomes taller in proportion as the spot on which it falls1 slopes towards the centre of the world4 ,the shadow will be densest in the middle of the tree when the tree has the fewest branches4 ,footnote3 ,the three diagrams which accompany this text are placed1 in the original1 before lines #g-aa4 ,at the spots marked ,b ,leonardo wrote ,albero 7tree74 ,at ,a is the word ,sole 7sun71 at ,c ,monte 7mountain7 at ,d piano 7plain7 and at ,e cima 7summit74 ,every branch participates of the central shadow of every other branch and consequently of that of the whole tree4 ,the form of any shadow from a branch or tree is circumscribed by the light which falls from the side whence the light comes2 and this illumination gives the shape of the shadow1 and this may be of the distance of a mile from the side where the sun is4 ,if it happens that a cloud should anywhere overshadow some part of a hill the shadow of the trees there will change less than in the plains2 for these trees on the hills have their branches thicker1 because they grow less high each year than in the plains4 ,therefore as these branches are dark by nature and being so full of shade1 the shadow of the clouds cannot darken them any more2 but the open spaces between the trees1 which have no strong shadow change very much in tone and particularly those which vary from green2 that is ploughed lands or fallen mountains or barren lands or rocks4 ,where the trees are against the atmosphere they appear all the same colour--if indeed they are not very close together or very thickly covered with leaves like the fir and similar trees4 ,when you see the trees from the side from which the sun lights them1 you will see them almost all of the same tone1 and the shadows in them will be hidden by the leaves in the light1 which come between your eye and those shadows4 ,,trees ,,at ,a ,,short ,,distance4 ,footnote #bi3 ,the heading alberi vicini 7trees at a short distance7 is in the original manuscript written in the margin4 ,when the trees are situated between the sun and the eye1 beyond the shadow which spreads from their centre1 the green of their leaves will be seen transparent2 but this transparency will be broken in many places by the leaves and boughs in shadow which will come between you and them1 or1 in their upper portions1 they will be accompanied by many lights reflected from the leaves4 #ded4 ,the trees of the landscape stand out but little from each other2 because their illuminated portions come against the illuminated portions of those beyond and differ little from them in light and shade4 #dee4 ,of trees seen from below and against the light1 one beyond the other and near together4 ,the topmost part of the first will be in great part transparent and light1 and will stand out against the dark portion of the second tree4 ,and thus it will be with all in succession that are placed under the same conditions4 ,let s be the light1 and r the eye1 c d n the first tree1 a b c the second4 ,then ,i say that r1 the eye1 will see the portion c f in great part transparent and lighted by the light s which falls upon it from the opposite side1 and it will see it1 on a dark ground b c because that is the dark part and shadow of the tree a b c4 ,but if the eye is placed at t it will see o p dark on the light background n g4 ,of the transparent and shadowy parts of trees1 that which is nearest to you is the darkest4 #def4 ,that part of a tree which has shadow for background1 is all of one tone1 and wherever the trees or branches are thickest they will be darkest1 because there are no little intervals of air4 ,but where the boughs lie against a background of other boughs1 the brighter parts are seen lightest and the leaves lustrous from the sunlight falling on them4 #deg4 ,in the composition of leafy trees be careful not to repeat too often the same colour of one tree against the same colour of another behind it2 but vary it with a lighter1 or a darker1 or a stronger green4 ,on the treatment of light for landscapes 7#deh-dfd74 #deh4 ,the landscape has a finer azure tone when1 in fine weather the sun is at noon than at any other time of the day1 because the air is purified of moisture2 and looking at it under that aspect you will see the trees of a beautiful green at the outside and the shadows dark towards the middle2 and in the remoter distance the atmosphere which comes between you and them looks more beautiful when there is something dark beyond4 ,and still the azure is most beautiful4 ,the objects seen from the side on which the sun shines will not show you their shadows4 ,but1 if you are lower than the sun1 you can see what is not seen by the sun and that will be all in shade4 ,the leaves of the trees1 which come between you and the sun are of two principal colours which are a splendid lustre of green1 and the reflection of the atmosphere which lights up the objects which cannot be seen by the sun1 and the shaded portions which only face the earth1 and the darkest which are surrounded by something that is not dark4 ,the trees in the landscape which are between you and the sun are far more beautiful than those you see when you are between the sun and them2 and this is so because those which face the sun show their leaves as transparent towards the ends of their branches1 and those that are not transparent--that is at the ends--reflect the light2 and the shadows are dark because they are not concealed by any thing4 ,the trees1 when you place yourself between them and the sun1 will only display to you their light and natural colour1 which1 in itself1 is not very strong1 and besides this some reflected lights which1 being against a background which does not differ very much from themselves in tone1 are not conspicuous2 and if you are lower down than they are situated1 they may also show those portions on which the light of the sun does not fall and these will be dark4 ,in the ,wind4 ,but1 if you are on the side whence the wind blows1 you will see the trees look very much lighter than on the other sides1 and this happens because the wind turns up the under side of the leaves1 which1 in all trees1 is much whiter than the upper sides2 and1 more especially1 will they be very light indeed if the wind blows from the quarter where the sun is1 and if you have your back turned to it4 ,footnote3 ,at ,s1 in the original is the word ,sole 7sun7 and at ,n parte di nuvolo 7the side of the clouds74 #dei4 ,when the sun is covered by clouds1 objects are less conspicuous1 because there is little difference between the light and shade of the trees and of the buildings being illuminated by the brightness of the atmosphere which surrounds the objects in such a way that the shadows are few1 and these few fade away so that their outline is lost in haze4 #dfj4 ,,of ,,trees ,,and ,,lights ,,on ,,them4 ,the best method of practice in representing country scenes1 or ,i should say landscapes with their trees1 is to choose them so that the sun is covered with clouds so that the landscape receives an universal light and not the direct light of the sun1 which makes the shadows sharp and too strongly different from the lights4 #dfa4 ,,of ,,painting4 ,in landscapes which represent a scene in winter4 ,the mountains should not be shown blue1 as we see in the mountains in the summer4 ,and this is proved ,footnote #e4 #f43 ,per la #d;a di questo4 ,it is impossible to ascertain what this quotation refers to4 ,questo certainly does not mean the ,,ms4 in hand1 nor any other now known to us4 ,the same remark applies to the phrase in line #ae3 per la #b;a di questo4 in the #dth of this which says3 ,among mountains seen from a great distance those will look of the bluest colour which are in themselves the darkest2 hence1 when the trees are stripped of their leaves1 they will show a bluer tinge which will be in itself darker2 therefore1 when the trees have lost their leaves they will look of a gray colour1 while1 with their leaves1 they are green1 and in proportion as the green is darker than the grey hue the green will be of a bluer tinge than the gray4 ,also by the #bnd of this3 ,the shadows of trees covered with leaves are darker than the shadows of those trees which have lost their leaves in proportion as the trees covered with leaves are denser than those without leaves--and thus my meaning is proved4 ,the definition of the blue colour of the atmosphere explains why the landscape is bluer in the summer than in the winter4 #dfb4 ,,of ,,painting ,,in ,a ,,landscape4 ,if the slope of a hill comes between the eye and the horizon1 sloping towards the eye1 while the eye is opposite the middle of the height of this slope1 then that hill will increase in darkness throughout its length4 ,this is proved by the #gth of this which says that a tree looks darkest when it is seen from below2 the proposition is verified1 since this hill will1 on its upper half show all its trees as much from the side which is lighted by the light of the sky1 as from that which is in shade from the darkness of the earth2 whence it must result that these trees are of a medium darkness4 ,and from this middle spot towards the base of the hill1 these trees will be lighter by degrees by the converse of the #gth and by the said #gth3 ,for trees so placed1 the nearer they are to the summit of the hill the darker they necessarily become4 ,but this darkness is not in proportion to the distance1 by the #hth of this which says3 ,that object shows darkest which is seen in the clearest atmosphere2 and by the #ajth3 ,that shows darkest which stands out against a lighter background4 ,footnote3 ,the quotation in this passage again cannot be verified4 #dfc4 ,,of ,,landscapes4 ,the colours of the shadows in mountains at a great distance take a most lovely blue1 much purer than their illuminated portions4 ,and from this it follows that when the rock of a mountain is reddish the illuminated portions are violet 787 and the more they are lighted the more they display their proper colour4 #dfd4 ,a place is most luminous when it is most remote from mountains4 ,on the treatment of light for views of towns 7#dfe-dfi74 #dfe4 ,,of ,,light ,,and ,,shadow ,,in ,a ,,town4 ,when the sun is in the ,east and the eye is above the centre of a town1 the eye will see the ,southern part of the town with its roofs half in shade and half in light1 and the same towards the ,north2 the ,eastern side will be all in shadow and the ,western will be all in light4 #dff4 ,of the houses of a town1 in which the divisions between the houses may be distinguished by the light which fall on the mist at the bottom4 ,if the eye is above the houses the light seen in the space that is between one house and the next sinks by degrees into thicker mist2 and yet1 being less transparent1 it appears whiter2 and if the houses are some higher than the others1 since the true colour is always more discernible through the thinner atmosphere1 the houses will look darker in proportion as they are higher up4 ,let n o p q represent the various density of the atmosphere thick with moisture1 a being the eye1 the house b c will look lightest at the bottom1 because it is in a thicker atmosphere2 the lines c d f will appear equally light1 for although f is more distant than c1 it is raised into a thinner atmosphere1 if the houses b e are of the same height1 because they cross a brightness which is varied by mist1 but this is only because the line of the eye which starts from above ends by piercing a lower and denser atmosphere at d than at b4 ,thus the line a f is lower at f than at c2 and the house f will be seen darker at e from the line e k as far as m1 than the tops of the houses standing in front of it4 #dfg4 ,,of ,,towns ,,or ,,other ,,buildings ,,seen ,,in ,,the ,,evening ,,or ,,the ,,morning ,,through ,,the ,,mist4 ,of buildings seen at a great distance in the evening or the morning1 as in mist or dense atmosphere1 only those portions are seen in brightness which are lighted up by the sun which is near the horizon2 and those portions which are not lighted up by the sun remain almost of the same colour and medium tone as the mist4 ,,why ,,objects ,,which ,,are ,,high ,,up ,,and ,,at ,a ,,distance ,,are ,,darker ,,than ,,the ,,lower ,,ones1 ,,even ,,if ,,the ,,mist ,,is ,,uniformly ,,dense4 ,of objects standing in a mist or other dense atmosphere1 whether from vapour or smoke or distance1 those will be most visible which are the highest4 ,and among objects of equal height that will be the darkest strongest which has for background the deepest mist4 ,thus the eye h looking at a b c1 towers of equal height1 one with another1 sees c the top of the first tower at r1 at two degrees of depth in the mist2 and sees the height of the middle tower b through one single degree of mist4 ,therefore the top of the tower c appears stronger than the top of the tower b1 c4 #dfh4 ,,of ,,the ,,smoke ,,of ,a ,,town4 ,smoke is seen better and more distinctly on the ,eastern side than on the ,western when the sun is in the ,east2 and this arises from two causes2 the first is that the sun1 with its rays1 shines through the particles of the smoke and lights them up and makes them visible4 ,the second is that the roofs of the houses seen in the ,east at this time are in shadow1 because their obliquity does not allow of their being illuminated by the sun4 ,and the same thing occurs with dust2 and both one and the other look the lighter in proportion as they are denser1 and they are densest towards the middle4 #dfi4 ,,of ,,smoke ,,and ,,dust4 ,if the sun is in the ,east the smoke of cities will not be visible in the ,west1 because on that side it is not seen penetrated by the solar rays1 nor on a dark background2 since the roofs of the houses turn the same side to the eye as they turn towards the sun1 and on this light background the smoke is not very visible4 ,but dust1 under the same aspect1 will look darker than smoke being of denser material than smoke which is moist4 ,the effect of wind on trees 7#dgj-dgc74 #dgj4 ,,of ,,representing ,,wind4 ,in representing wind1 besides the bending of the boughs and the reversing of their leaves towards the quarter whence the wind comes1 you should also represent them amid clouds of fine dust mingled with the troubled air4 #dga4 ,describe landscapes with the wind1 and the water1 and the setting and rising of the sun4 ,,the ,,wind4 ,all the leaves which hung towards the earth by the bending of the shoots with their branches1 are turned up side down by the gusts of wind1 and here their perspective is reversed2 for1 if the tree is between you and the quarter of the wind1 the leaves which are towards you remain in their natural aspect1 while those on the opposite side which ought to have their points in a contrary direction have1 by being turned over1 their points turned towards you4 #dgb4 ,trees struck by the force of the wind bend to the side towards which the wind is blowing2 and the wind being past they bend in the contrary direction1 that is in reverse motion4 #dgc4 ,that portion of a tree which is farthest from the force which strikes it is the most injured by the blow because it bears most strain2 thus nature has foreseen this case by thickening them in that part where they can be most hurt2 and most in such trees as grow to great heights1 as pines and the like4 ,footnote3 ,compare the sketch drawn with a pen and washed with ,indian ink on ,pl4 ,,xl1 ,no4 #a4 ,in the ,vatican copy we find1 under a section entitled 'del fumo'1 the following remark3 ,era sotto di questo capitulo un rompimento di montagna1 per dentro delle quali roture scherzaua fiame di fuoco1 disegnate di penna et ombrate d'acquarella1 da uedere cosa mirabile et uiua 7,ed4 ,,manzi1 p4 #bce4 ,ed4 ,,ludwig1 ,vol4 ,i1 #dfj74 ,this appears to refer to the left hand portion of the drawing here given from the ,windsor collection1 and from this it must be inferred1 that the leaf as it now exists in the library of the ,queen of ,england1 was already separated from the original ,,ms4 at the time when the ,vatican copy was made4 ,light and shade on clouds 7#dgd-dgg74 #dgd4 ,describe how the clouds are formed and how they dissolve1 and what cause raises vapour4 #dge4 ,the shadows in clouds are lighter in proportion as they are nearer to the horizon4 ,footnote3 ,the drawing belonging to this was in black chalk and is totally effaced4 #dgf4 ,when clouds come between the sun and the eye all the upper edges of their round forms are light1 and towards the middle they are dark1 and this happens because towards the top these edges have the sun above them while you are below them2 and the same thing happens with the position of the branches of trees2 and again the clouds1 like the trees1 being somewhat transparent1 are lighted up in part1 and at the edges they show thinner4 ,but1 when the eye is between the cloud and the sun1 the cloud has the contrary effect to the former1 for the edges of its mass are dark and it is light towards the middle2 and this happens because you see the same side as faces the sun1 and because the edges have some transparency and reveal to the eye that portion which is hidden beyond them1 and which1 as it does not catch the sunlight like that portion turned towards it1 is necessarily somewhat darker4 ,again1 it may be that you see the details of these rounded masses from the lower side1 while the sun shines on the upper side and as they are not so situated as to reflect the light of the sun1 as in the first instance they remain dark4 ,the black clouds which are often seen higher up than those which are illuminated by the sun are shaded by other clouds1 lying between them and the sun4 ,again1 the rounded forms of the clouds that face the sun1 show their edges dark because they lie against the light background2 and to see that this is true1 you may look at the top of any cloud that is wholly light because it lies against the blue of the atmosphere1 which is darker than the cloud4 ,footnote3 ,a drawing in red chalk from the ,windsor collection 7see ,pl4 ,,xxix71 representing a landscape with storm-clouds1 may serve to illustrate this section as well as the following one4 #dgg4 ,,of ,,clouds1 ,,smoke ,,and ,,dust ,,and ,,the ,,flames ,,of ,a ,,furnace ,,or ,,of ,a ,,burning ,,kiln4 ,the clouds do not show their rounded forms excepting on the sides which face the sun2 on the others the roundness is imperceptible because they are in the shade4 ,footnote3 ,the text of this chapter is given in facsimile on ,pls4 ,,xxxvi and ,,xxxvii4 ,the two halves of the leaf form but one in the original4 ,on the margin close to lines #d and #e is the note3 rossore d'aria inverso l'orizonte--7of the redness of the atmosphere near the horizon74 ,the sketches on the lower portion of the page will be spoken of in ,no4 #ffh4 ,if the sun is in the ,east and the clouds in the ,west1 the eye placed between the sun and the clouds sees the edges of the rounded forms composing these clouds as dark1 and the portions which are surrounded by this dark edge are light4 ,and this occurs because the edges of the rounded forms of these clouds are turned towards the upper or lateral sky1 which is reflected in them4 ,both the cloud and the tree display no roundness at all on their shaded side4 ,on images reflected in water4 #dgh4 ,painters often deceive themselves1 by representing water in which they make the water reflect the objects seen by the man4 ,but the water reflects the object from one side and the man sees it from the other2 and it often happens that the painter sees an object from below1 and thus one and the same object is seen from hind part before and upside down1 because the water shows the image of the object in one way1 and the eye sees it in another4 ,of rainbows and rain 7#dgi4 #dhj74 #dgi4 ,the colours in the middle of the rainbow mingle together4 ,the bow in itself is not in the rain nor in the eye that sees it2 though it is generated by the rain1 the sun1 and the eye4 ,the rainbow is always seen by the eye that is between the rain and the body of the sun2 hence if the sun is in the ,east and the rain is in the ,west it will appear on the rain in the ,west4 #dhj4 ,when the air is condensed into rain it would produce a vacuum if the rest of the air did not prevent this by filling its place1 as it does with a violent rush2 and this is the wind which rises in the summer time1 accompanied by heavy rain4 ,of flower seeds4 #dha4 ,all the flowers which turn towards the sun perfect their seeds2 but not the others2 that is to say those which get only the reflection of the sun4 ,,ix4 ,the ,practice of ,painting4 ,it is hardly necessary to offer any excuses for the division carried out in the arrangement of the text into practical suggestions and theoretical enquiries4 ,it was evidently intended by ,leonardo himself as we conclude from incidental remarks in the ,,mss4 7for instance ,no #aaj74 ,the fact that this arrangement was never carried out either in the old ,,ms4 copies or in any edition since1 is easily accounted for by the general disorder which results from the provisional distribution of the various chapters in the old copies4 ,we have every reason to believe that the earliest copyists1 in distributing the materials collected by them1 did not in the least consider the order in which the original ,,ms4lay before them4 ,it is evident that almost all the chapters which refer to the calling and life of the painter--and which are here brought together in the first section 7,nos4 #dhb-ejh7--may be referred to two distinct periods in ,leonardo's life2 most of them can be dated as belonging to the year #adib or to #aeae4 ,at about this later time ,leonardo may have formed the project of completing his ,libro della ,pittura1 after an interval of some years1 as it would seem1 during which his interest in the subject had fallen somewhat into the background4 ,in the second section1 which treats first of the artist's studio1 the construction of a suitable window forms the object of careful investigations2 the special importance attached to this by ,leonardo is sufficiently obvious4 ,his theory of the incidence of light which was fully discussed in a former part of this work1 was to him by no means of mere abstract value1 but1 being deduced1 as he says1 from experience 7or experiment7 was required to prove its utility in practice4 ,connected with this we find suggestions for the choice of a light with practical hints as to sketching a picture and some other precepts of a practical character which must come under consideration in the course of completing the painting4 ,in all this ,i have followed the same principle of arrangement in the text as was carried out in the ,theory of ,painting1 thus the suggestions for the ,perspective of a picture1 7,nos4 #ecf-efi71 are followed by the theory of light and shade for the practical method of optics 7,nos4 #edh--eff7 and this by the practical precepts or the treatment of aerial perspective 7#efg--egj74 ,in the passage on ,portrait and ,figure ,painting the principles of painting as applied to a bust and head are separated and placed first1 since the advice to figure painters must have some connection with the principles of the treatment of composition by which they are followed4 ,but this arrangement of the text made it seem advisable not to pick out the practical precepts as to the representation of trees and landscape from the close connection in which they were originally placed--unlike the rest of the practical precepts--with the theory of this branch of the subject4 ,they must therefore be sought under the section entitled ,botany for ,painters4 ,as a supplement to the ,libro di ,pittura ,i have here added those texts which treat of the ,painter's materials1--as chalk1 drawing paper1 colours and their preparation1 of the management of oils and varnishes2 in the appendix are some notes on chemical substances4 ,possibly some of these1 if not all1 may have stood in connection with the preparation of colours4 ,it is in the very nature of things that ,leonardo's incidental indications as to colours and the like should be now-a-days extremely obscure and could only be explained by professional experts--by them even in but few instances4 ,it might therefore have seemed advisable to reproduce exactly the original text without offering any translation4 ,the rendering here given is merely an attempt to suggest what ,leonardo's meaning may have been4 ,,lomazzo tells us in his ,trattato dell'arte della ,pittura1 ,scultura ed ,architettura 7,milano #aehd1 libro ,,ii1 ,cap4 ,,xiv73 ,va discorrendo ed argomentando ,leonardo ,vinci in un suo libro letto da me 787 questi anni passati1 ch'egli scrisse di mano stanca ai prieghi di ,,ludovico ,,sforza duca di ,milano1 in determinazione di questa questione1 se e piu nobile la pittura o la scultura2 dicendo che quanto piu un'arte porta seco fatica di corpo1 e sudore1 tanto piu e vile1 e men pregiata4 ,but the existence of any book specially written for ,lodovico il ,moro on the superiority of ,painting over sculpture is perhaps mythical4 ,the various passages in praise of ,painting as compared not merely with ,sculpture but with ,poetry1 are scattered among ,,mss4 of very different dates4 ,besides1 the way1 in which the subject is discussed appears not to support the supposition1 that these texts were prepared at a special request of the ,duke4 ,i4 ,,moral ,,precepts ,,for ,,the ,,student ,,of ,,painting4 ,how to ascertain the dispositions for an artistic career4 #dhb4 ,a ,,warning ,,concerning ,,youths ,,wishing ,,to ,,be ,,painters4 ,many are they who have a taste and love for drawing1 but no talent2 and this will be discernible in boys who are not diligent and never finish their drawings with shading4 ,the course of instruction for an artist 7#dhc-dhe74 #dhc4 ,the youth should first learn perspective1 then the proportions of objects4 ,then he may copy from some good master1 to accustom himself to fine forms4 ,then from nature1 to confirm by practice the rules he has learnt4 ,then see for a time the works of various masters4 ,then get the habit of putting his art into practice and work4 ,footnote3 ,the ,vatican copy and numerous abridgements all place this chapter at the beginning of the ,trattato1 and in consequence ,,dufresne and all subsequent editors have done the same4 ,in the ,vatican copy however all the general considerations on the relation of painting to the other arts are placed first1 as introductory4 #dhd4 ,,of ,,the ,,order ,,of ,,learning ,,to ,,draw4 ,first draw from drawings by good masters done from works of art and from nature1 and not from memory2 then from plastic work1 with the guidance of the drawing done from it2 and then from good natural models and this you must put into practice4 #dhe4 ,,precepts ,,for ,,drawing4 ,the artist ought first to exercise his hand by copying drawings from the hand of a good master4 ,and having acquired that practice1 under the criticism of his master1 he should next practise drawing objects in relief of a good style1 following the rules which will presently be given4 ,the study of the antique 7#dhf4 #dhg74 #dhf4 ,,of ,,drawing4 ,which is best1 to draw from nature or from the antique8 and which is more difficult to do outlines or light and shade8 #dhg4 ,it is better to imitate copy the antique than modern work4 ,footnote #dhf1 #dhg3 ,these are the only two passages in which ,leonardo alludes to the importance of antique art in the training of an artist4 ,the question asked in ,no4 #dhf remains unanswered by him and it seems to me very doubtful whether the opinion stated in ,no4 #dhg is to be regarded as a reply to it4 ,this opinion stands in the ,,ms4 in a connection--as will be explained later on--which seems to require us to limit its application to a single special case4 ,at any rate we may suspect that when ,leonardo put the question1 he felt some hesitation as to the answer4 ,among his very numerous drawings ,i have not been able to find a single study from the antique1 though a drawing in black chalk1 at ,windsor1 of a man on horseback 7,,pi4 ,,lxxiii7 may perhaps be a reminiscence of the statue of ,marcus ,aurelius at ,rome4 ,it seems to me that the drapery in a pen and ink drawing of a bust1 also at ,windsor1 has been borrowed from an antique model 7,pl4 ,,xxx74 ,g4 ,g4 ,rossi has1 ,i believe1 correctly interpreted ,leonardo's feeling towards the antique in the following note on this passage in manzi's edition1 p4 #eja3 ,sappiamo dalla storia1 che i valorosi artisti ,toscani dell'et dell'oro dell'arte studiarono sugli antichi marmi raccolti dal ,magnifico ,,lorenzo ,,de' ,,medici4 ,pare che il ,vinci a tali monumenti non si accostasse4 ,quest' uomo sempre riconosce per maestra la natura1 e questo principio lo stringeva alla sola imitazione d essa--,compare ,no4 #aj1 #bf--bh footnote4 ,the necessity of anatomical knowledge 7#dhh4 #dhi74 #dhh4 ,,of ,,painting4 ,it is indispensable to a ,painter who would be thoroughly familiar with the limbs in all the positions and actions of which they are capable1 in the nude1 to know the anatomy of the sinews1 bones1 muscles and tendons so that1 in their various movements and exertions1 he may know which nerve or muscle is the cause of each movement and show those only as prominent and thickened1 and not the others all over the limb1 as many do who1 to seem great draughtsmen1 draw their nude figures looking like wood1 devoid of grace2 so that you would think you were looking at a sack of walnuts rather than the human form1 or a bundle of radishes rather than the muscles of figures4 #dhi4 ,,how ,,it ,,is ,,necessary ,,to ,a ,,painter ,,that ,,he ,,should ,,know ,,the ,,intrinsic ,,forms ,,structure ,,of ,,man4 ,the painter who is familiar with the nature of the sinews1 muscles1 and tendons1 will know very well1 in giving movement to a limb1 how many and which sinews cause it2 and which muscle1 by swelling1 causes the contraction of that sinew2 and which sinews1 expanded into the thinnest cartilage1 surround and support the said muscle4 ,thus he will variously and constantly demonstrate the different muscles by means of the various attitudes of his figures1 and will not do1 as many who1 in a variety of movements1 still display the very same things modelling in the arms1 back1 breast and legs4 ,and these things are not to be regarded as minor faults4 ,how to acquire practice4 #dij4 ,,of ,,study ,,and ,,the ,,order ,,of ,,study4 ,i say that first you ought to learn the limbs and their mechanism1 and having this knowledge1 their actions should come next1 according to the circumstances in which they occur in man4 ,and thirdly to compose subjects1 the studies for which should be taken from natural actions and made from time to time1 as circumstances allow2 and pay attention to them in the streets and piazze and fields1 and note them down with a brief indication of the forms2 ,footnote #e3 ,lines #e-g explained by the lower portion of the sketch ,no4 #a on ,pl4 ,,xxxi4 thus for a head make an o1 and for an arm a straight or a bent line1 and the same for the legs and the body1 ,footnote #g3 ,lines #e-g explained by the lower portion of the sketch ,no4 #a on ,pl4 ,,xxxi4 and when you return home work out these notes in a complete form4 ,the ,adversary says that to acquire practice and do a great deal of work it is better that the first period of study should be employed in drawing various compositions done on paper or on walls by divers masters1 and that in this way practice is rapidly gained1 and good methods2 to which ,i reply that the method will be good1 if it is based on works of good composition and by skilled masters4 ,but since such masters are so rare that there are but few of them to be found1 it is a surer way to go to natural objects1 than to those which are imitated from nature with great deterioration1 and so form bad methods2 for he who can go to the fountain does not go to the water-jar4 ,footnote3 ,this passage has been published by ,dr4 ,m4 ,,jordan1 ,das ,malerbuck des ,l4 da ,vinci1 p4 #hi2 his reading however varies slightly from mine4 ,industry and thoroughness the first conditions 7#dia-dic47 #dia4 ,,what ,,rules ,,should ,,be ,,given ,,to ,,boys ,,learning ,,to ,,paint4 ,we know for certain that sight is one of the most rapid actions we can perform4 ,in an instant we see an infinite number of forms1 still we only take in thoroughly one object at a time4 ,supposing that you1 ,reader1 were to glance rapidly at the whole of this written page1 you would instantly perceive that it was covered with various letters2 but you could not1 in the time1 recognise what the letters were1 nor what they were meant to tell4 ,hence you would need to see them word by word1 line by line to be able to understand the letters4 ,again1 if you wish to go to the top of a building you must go up step by step2 otherwise it will be impossible that you should reach the top4 ,thus ,i say to you1 whom nature prompts to pursue this art1 if you wish to have a sound knowledge of the forms of objects begin with the details of them1 and do not go on to the second step till you have the first well fixed in memory and in practice4 ,and if you do otherwise you will throw away your time1 or certainly greatly prolong your studies4 ,and remember to acquire diligence rather than rapidity4 #dib4 ,,how ,,that ,,diligence ,,accuracy ,,should ,,first ,,be ,,learnt ,,rather ,,than ,,rapid ,,execution4 ,if you1 who draw1 desire to study well and to good purpose1 always go slowly to work in your drawing2 and discriminate in4 the lights1 which have the highest degree of brightness1 and to what extent and likewise in the shadows1 which are those that are darker than the others and in what way they intermingle2 then their masses and the relative proportions of one to the other4 ,and note in their outlines1 which way they tend2 and which part of the lines is curved to one side or the other1 and where they are more or less conspicuous and consequently broad or fine2 and finally1 that your light and shade blend without strokes and borders but looking like smoke4 ,and when you have thus schooled your hand and your judgment by such diligence1 you will acquire rapidity before you are aware4 ,the artist's private life and choice of company 7#dic-did74 #dic4 ,,of ,,the ,,life ,,of ,,the ,,painter ,,in ,,the ,,country4 ,a painter needs such mathematics as belong to painting4 ,and the absence of all companions who are alienated from his studies2 his brain must be easily impressed by the variety of objects1 which successively come before him1 and also free from other cares ,footnote #f3 ,leonardo here seems to be speaking of his own method of work as displayed in his ,,mss4 and this passage explains1 at least in part1 the peculiarities in their arrangement44 ,and if1 when considering and defining one subject1 a second subject intervenes--as happens when an object occupies the mind1 then he must decide which of these cases is the more difficult to work out1 and follow that up until it becomes quite clear1 and then work out the explanation of the other ,footnote #aa3 ,leonardo here seems to be speaking of his own method of work as displayed in his ,,mss4 and this passage explains1 at least in part1 the peculiarities in their arrangement44 ,and above all he must keep his mind as clear as the surface of a mirror1 which assumes colours as various as those of the different objects4 ,and his companions should be like him as to their studies1 and if such cannot be found he should keep his speculations to himself alone1 so that at last he will find no more useful company than his own4 ,footnote3 ,in the title line ,leonardo had originally written del pictore filosofo 7the philosophical painter71 but he himself struck outfilosofo4 ,compare in ,no4 #cfc pictora notomista 7anatomical painter74 ,the original text is partly reproduced on ,pl4 ,,ci4 #did4 ,,of ,,the ,,life ,,of ,,the ,,painter ,,in ,,his ,,studio4 ,to the end that well-being of the body may not injure that of the mind1 the painter or draughtsman must remain solitary1 and particularly when intent on those studies and reflections which will constantly rise up before his eye1 giving materials to be well stored in the memory4 ,while you are alone you are entirely your own master and if you have one companion you are but half your own1 and the less so in proportion to the indiscretion of his behaviour4 ,and if you have many companions you will fall deeper into the same trouble4 ,if you should say3 ,i will go my own way and withdraw apart1 the better to study the forms of natural objects1 ,i tell you1 you will not be able to help often listening to their chatter4 ,and so1 since one cannot serve two masters1 you will badly fill the part of a companion1 and carry out your studies of art even worse4 ,and if you say3 ,i will withdraw so far that their words cannot reach me and they cannot disturb me1 ,i can tell you that you will be thought mad4 ,but1 you see1 you will at any rate be alone4 ,and if you must have companions ship find it in your studio4 ,this may assist you to have the advantages which arise from various speculations4 ,all other company may be highly mischievous4 ,the distribution of time for studying 7#die-dig74 #die4 ,,of ,,whether ,,it ,,is ,,better ,,to ,,draw ,,with ,,companions ,,or ,,not4 ,i say and insist that drawing in company is much better than alone1 for many reasons4 ,the first is that you would be ashamed to be seen behindhand among the students1 and such shame will lead you to careful study4 ,secondly1 a wholesome emulation will stimulate you to be among those who are more praised than yourself1 and this praise of others will spur you on4 ,another is that you can learn from the drawings of others who do better than yourself2 and if you are better than they1 you can profit by your contempt for their defects1 while the praise of others will incite you to farther merits4 ,footnote3 ,the contradiction by this passage of the foregoing chapter is only apparent4 ,it is quite clear1 from the nature of the reasoning which is here used to prove that it is more improving to work with others than to work alone1 that the studies of pupils only are under consideration here4 #dif4 ,,of ,,studying1 ,,in ,,the ,,dark1 ,,when ,,you ,,wake1 ,,or ,,in ,,bed ,,before ,,you ,,go ,,to ,,sleep4 ,i myself have proved it to be of no small use1 when in bed in the dark1 to recall in fancy the external details of forms previously studied1 or other noteworthy things conceived by subtle speculation2 and this is certainly an admirable exercise1 and useful for impressing things on the memory4 #dig4 ,,of ,,the ,,time ,,for ,,studying ,,selection ,,of ,,subjects4 ,winter evenings ought to be employed by young students in looking over the things prepared during the summer2 that is1 all the drawings from the nude done in the summer should be brought together and a choice made of the best studies of limbs and bodies among them1 to apply in practice and commit to memory4 ,,of ,,positions4 ,after this in the following summer you should select some one who is well grown and who has not been brought up in doublets1 and so may not be of stiff carriage1 and make him go through a number of agile and graceful actions2 and if his muscles do not show plainly within the outlines of his limbs that does not matter at all4 ,it is enough that you can see good attitudes and you can correct the drawing of the limbs by those you studied in the winter4 ,footnote3 ,an injunction to study in the evening occurs also in ,no4 #ebd4 ,on the productive power of minor artists 7#dih-eja74 #dih4 ,he is a poor disciple who does not excel his master4 #dii4 ,nor is the painter praiseworthy who does but one thing well1 as the nude figure1 heads1 draperies1 animals1 landscapes or other such details1 irrespective of other work2 for there can be no mind so inept1 that after devoting itself to one single thing and doing it constantly1 it should fail to do it well4 ,footnote3 ,in ,,manzi',s edition 7p4 #ejb7 the painter ,g4 ,g4 ,bossi indignantly remarks on this passage4 ,parla il ,vince in questo luogo come se tutti gli artisti avessero quella sublimita d'ingegno capace di abbracciare tutte le cose1 di cui era egli dotato ,and he then mentions the case of ,,claude ,,lorrain4 ,but he overlooks the fact that in ,leonardo's time landscape painting made no pretensions to independence but was reckoned among the details 7particulari1 lines #c1 #d74 #ejj4 ,,that ,a ,,painter ,,is ,,not ,,admirable ,,unless ,,he ,,is ,,universal4 ,some may distinctly assert that those persons are under a delusion who call that painter a good master who can do nothing well but a head or a figure4 ,certainly this is no great achievement2 after studying one single thing for a life-time who would not have attained some perfection in it8 ,but1 since we know that painting embraces and includes in itself every object produced by nature or resulting from the fortuitous actions of men1 in short1 all that the eye can see1 he seems to me but a poor master who can only do a figure well4 ,for do you not perceive how many and various actions are performed by men only2 how many different animals there are1 as well as trees1 plants1 flowers1 with many mountainous regions and plains1 springs and rivers1 cities with public and private buildings1 machines1 too1 fit for the purposes of men1 divers costumes1 decorations and arts8 ,and all these things ought to be regarded as of equal importance and value1 by the man who can be termed a good painter4 #eja4 ,,of ,,the ,,miserable ,,pretences ,,made ,,by ,,those ,,who ,,falsely ,,and ,,unworthily ,,acquire ,,the ,,name ,,of ,,painters4 ,now there is a certain race of painters who1 having studied but little1 must need take as their standard of beauty mere gold and azure1 and these1 with supreme conceit1 declare that they will not give good work for miserable payment1 and that they could do as well as any other if they were well paid4 ,but1 ye foolish folks6 cannot such artists keep some good work1 and then say3 this is a costly work and this more moderate and this is average work and show that they can work at all prices8 ,a caution against one-sided study4 #ejb4 ,,how1 ,,in ,,important ,,works1 ,a ,,man ,,should ,,not ,,trust ,,entirely ,,to ,,his ,,memory ,,without ,,condescending ,,to ,,draw ,,from ,,nature4 ,any master who should venture to boast that he could remember all the forms and effects of nature would certainly appear to me to be graced with extreme ignorance1 inasmuch as these effects are infinite and our memory is not extensive enough to retain them4 ,hence1 ,o6 painter1 beware lest the lust of gain should supplant in you the dignity of art2 for the acquisition of glory is a much greater thing than the glory of riches4 ,hence1 for these and other reasons which might be given1 first strive in drawing to represent your intention to the eye by expressive forms1 and the idea originally formed in your imagination2 then go on taking out or putting in1 until you have satisfied yourself4 ,then have living men1 draped or nude1 as you may have purposed in your work1 and take care that in dimensions and size1 as determined by perspective1 nothing is left in the work which is not in harmony with reason and the effects in nature4 ,and this will be the way to win honour in your art4 ,how to acquire universality 7#ejc-ejf74 #ejc4 ,,of ,,variety ,,in ,,the ,,figures4 ,the painter should aim at universality1 because there is a great want of self-respect in doing one thing well and another badly1 as many do who study only the rules of measure and proportion in the nude figure and do not seek after variety2 for a man may be well proportioned1 or he may be fat and short1 or tall and thin1 or medium4 ,and a painter who takes no account of these varieties always makes his figures on one pattern so that they might all be taken for brothers2 and this is a defect that demands stern reprehension4 #ejd4 ,,how ,,something ,,may ,,be ,,learnt ,,everywhere4 ,nature has beneficently provided that throughout the world you may find something to imitate4 #eje4 ,,of ,,the ,,means ,,of ,,acquiring ,,universality4 ,it is an easy matter to men to acquire universality1 for all terrestrial animals resemble each other as to their limbs1 that is in their muscles1 sinews and bones2 and they do not vary excepting in length or in thickness1 as will be shown under ,anatomy4 ,but then there are aquatic animals which are of great variety2 ,i will not try to convince the painter that there is any rule for them for they are of infinite variety1 and so is the insect tribe4 #ejf4 ,,painting4 ,the mind of the painter must resemble a mirror1 which always takes the colour of the object it reflects and is completely occupied by the images of as many objects as are in front of it4 ,therefore you must know1 ,oh ,painter6 that you cannot be a good one if you are not the universal master of representing by your art every kind of form produced by nature4 ,and this you will not know how to do if you do not see them1 and retain them in your mind4 ,hence as you go through the fields1 turn your attention to various objects1 and1 in turn look now at this thing and now at that1 collecting a store of divers facts selected and chosen from those of less value4 ,but do not do like some painters who1 when they are wearied with exercising their fancy dismiss their work from their thoughts and take exercise in walking for relaxation1 but still keep fatigue in their mind which1 though they see various objects around them1 does not apprehend them2 but1 even when they meet friends or relations and are saluted by them1 although they see and hear them1 take no more cognisance of them than if they had met so much empty air4 ,useful games and exercises 7#ejg4 #ejh74 #ejg4 ,,of ,,games ,,to ,,be ,,played ,,by ,,those ,,who ,,draw4 ,when1 ,oh draughtsmen1 you desire to find relaxation in games you should always practise such things as may be of use in your profession1 by giving your eye good practice in judging accurately of the breadth and length of objects4 ,thus1 to accustom your mind to such things1 let one of you draw a straight line at random on a wall1 and each of you1 taking a blade of grass or of straw in his hand1 try to cut it to the length that the line drawn appears to him to be1 standing at a distance of #aj braccia2 then each one may go up to the line to measure the length he has judged it to be4 ,and he who has come nearest with his measure to the length of the pattern is the best man1 and the winner1 and shall receive the prize you have settled beforehand4 ,again you should take forshortened measures3 that is take a spear1 or any other cane or reed1 and fix on a point at a certain distance2 and let each one estimate how many times he judges that its length will go into that distance4 ,again1 who will draw best a line one braccio long1 which shall be tested by a thread4 ,and such games give occasion to good practice for the eye1 which is of the first importance in painting4 #ejh4 ,a ,,way ,,of ,,developing ,,and ,,arousing ,,the ,,mind ,,to ,,various ,,inventions4 ,i cannot forbear to mention among these precepts a new device for study which1 although it may seem but trivial and almost ludicrous1 is nevertheless extremely useful in arousing the mind to various inventions4 ,and this is1 when you look at a wall spotted with stains1 or with a mixture of stones1 if you have to devise some scene1 you may discover a resemblance to various landscapes1 beautified with mountains1 rivers1 rocks1 trees1 plains1 wide valleys and hills in varied arrangement2 or again you may see battles and figures in action2 or strange faces and costumes1 and an endless variety of objects1 which you could reduce to complete and well drawn forms4 ,and these appear on such walls confusedly1 like the sound of bells in whose jangle you may find any name or word you choose to imagine4 ,,ii4 ,,the ,,artist',s ,,studio4--,,instruments ,,and ,,helps ,,for ,,the ,,application ,,of ,,perspective4--,,on ,,judging ,,of ,a ,,picture4 ,on the size of the studio4 #eji4 ,small rooms or dwellings discipline the mind1 large ones weaken it4 ,on the construction of windows 7#eaj-eab74 #eaj4 ,the larger the wall the less the light will be4 #eaa4 ,the different kinds of light afforded in cellars by various forms of windows4 ,the least useful and the coldest is the window at a4 ,the most useful1 the lightest and warmest and most open to the sky is the window at b4 ,the window at c is of medium utility4 ,footnote3 ,from a reference to the notes on the right light for painting it becomes evident that the observations made on cellar-windows have a direct bearing on the construction of the studio-window4 ,in the diagram b as well as in that under ,no4 #eaj the window-opening is reduced to a minimum1 but only1 it would seem1 in order to emphasize the advantage of walls constructed on the plan there shown4 #eab4 ,,of ,,the ,,painter',s ,,window ,,and ,,its ,,advantage4 ,the painter who works from nature should have a window1 which he can raise and lower4 ,the reason is that sometimes you will want to finish a thing you are drawing1 close to the light4 ,let a b c d be the chest on which the work may be raised or lowered1 so that the work moves up and down and not the painter4 ,and every evening you can let down the work and shut it up above so that in the evening it may be in the fashion of a chest which1 when shut up1 may serve the purpose of a bench4 ,footnote3 ,see ,pl4 ,,xxxi1 ,no4 #b4 ,in this plate the lines have unfortunately lost their sharpness1 for the accidental loss of the negative has necessitated a reproduction from a positive4 ,but having formerly published this sketch by another process1 in ,,von ,,lutzow',s ,zeitschrift fur bildende ,kunst 7,vol4 ,,xvii1 pg4 #ac7 ,i have reproduced it here in the text4 ,the sharpness of the outline in the original sketch is here preserved but it gives it from the reversed side4 ,on the best light for painting 7#eac-ebj74 #eac4 ,which light is best for drawing from nature2 whether high or low1 or large or small1 or strong and broad1 or strong and small1 or broad and weak or small and weak8 ,footnote3 ,the question here put is unanswered in the original ,,ms4 #ead4 ,,of ,,the ,,quality ,,of ,,the ,,light4 ,a broad light high up and not too strong will render the details of objects very agreeable4 #eae4 ,,that ,,the ,,light ,,for ,,drawing ,,from ,,nature ,,should ,,be ,,high ,,up4 ,the light for drawing from nature should come from the ,north in order that it may not vary4 ,and if you have it from the ,south1 keep the window screened with cloth1 so that with the sun shining the whole day the light may not vary4 ,the height of the light should be so arranged as that every object shall cast a shadow on the ground of the same length as itself4 #eaf4 ,,the ,,kind ,,of ,,light ,,requisite ,,for ,,painting ,,light ,,and ,,shade4 ,an object will display the greatest difference of light and shade when it is seen in the strongest light1 as by sunlight1 or1 at night1 by the light of a fire4 ,but this should not be much used in painting because the works remain crude and ungraceful4 ,an object seen in a moderate light displays little difference in the light and shade2 and this is the case towards evening or when the day is cloudy1 and works then painted are tender and every kind of face becomes graceful4 ,thus1 in every thing extremes are to be avoided3 ,too much light gives crudeness2 too little prevents our seeing4 ,the medium is best4 ,,of ,,small ,,lights4 ,again1 lights cast from a small window give strong differences of light and shade1 all the more if the room lighted by it be large1 and this is not good for painting4 #eag4 ,,painting4 ,the luminous air which enters by passing through orifices in walls into dark rooms will render the place less dark in proportion as the opening cuts into the walls which surround and cover in the pavement4 #eah4 ,,of ,,the ,,quality ,,of ,,light4 ,in proportion to the number of times that a b goes into c d will it be more luminous than c d4 ,and similarly1 in proportion as the point e goes into c d will it be more luminous than c d2 and this light is useful for carvers of delicate work4 ,footnote #e3 ,for the same reason a window thus constructed would be convenient for an illuminator or a miniature painter4 ,footnote3 ,m4 ,,ravaisson in his edition of the ,paris ,,ms4 ,a remarks on this passage3 ,la figure porte les lettres f et g1 auxquelles rien ne renvoie dans l'explication2 par consequent1 cette explication est incomplete4 ,la figure semblerait1 d'ailleurs1 se rapporter a l'effet de la reflexion par un miroir concave4 ,so far as ,i can see the text is not imperfect1 nor is the sense obscure4 ,it is hardly necessary to observe that c d here indicate the wall of the room opposite to the window e and the semicircle described by f g stands for the arch of the sky2 this occurs in various diagrams1 for example under #eaa4 ,a similar semicircle1 ,pl ,,iii1 ,no4 #b 7and compare ,no4 #adi7 is expressly called 'orizonte' in writing4 #eai4 ,that the light should fall upon a picture from one window only4 ,this may be seen in the case of objects in this form4 ,if you want to represent a round ball at a certain height you must make it oval in this shape1 and stand so far off as that by foreshortening it appears round4 #ebj4 ,,of ,,selecting ,,the ,,light ,,which ,,gives ,,most ,,grace ,,to ,,faces4 ,if you should have a court yard that you can at pleasure cover with a linen awning that light will be good4 ,or when you want to take a portrait do it in dull weather1 or as evening falls1 making the sitter stand with his back to one of the walls of the court yard4 ,note in the streets1 as evening falls1 the faces of the men and women1 and when the weather is dull1 what softness and delicacy you may perceive in them4 ,hence1 ,oh ,painter6 have a court arranged with the walls tinted black and a narrow roof projecting within the walls4 ,it should be #aj braccia wide and #bj braccia long and #aj braccia high and covered with a linen awning2 or else paint a work towards evening or when it is cloudy or misty1 and this is a perfect light4 ,on various helps in preparing a picture 7#eba-ecj74 #eba4 ,to draw a nude figure from nature1 or any thing else1 hold in your hand a plumb-line to enable you to judge of the relative position of objects4 #ebb4 ,,of ,,drawing ,,an ,,object4 ,when you draw take care to set up a principal line which you must observe all throughout the object you are drawing2 every thing should bear relation to the direction of this principal line4 #ebc4 ,,of ,a ,,mode ,,of ,,drawing ,a ,,place ,,accurately4 ,have a piece of glass as large as a half sheet of royal folio paper and set thus firmly in front of your eyes that is1 between your eye and the thing you want to draw2 then place yourself at a distance of #b_/c of a braccia from the glass fixing your head with a machine in such a way that you cannot move it at all4 ,then shut or entirely cover one eye and with a brush or red chalk draw upon the glass that which you see beyond it2 then trace it on paper from the glass1 afterwards transfer it onto good paper1 and paint it if you like1 carefully attending to the arial perspective4 ,,how ,,to ,,learn ,,to ,,place ,,your ,,figures ,,correctly4 ,if you want to acquire a practice of good and correct attitudes for your figures1 make a square frame or net1 and square it out with thread2 place this between your eye and the nude model you are drawing1 and draw these same squares on the paper on which you mean to draw the figure1 but very delicately4 ,then place a pellet of wax on a spot of the net which will serve as a fixed point1 which1 whenever you look at your model1 must cover the pit of the throat2 or1 if his back is turned1 it may cover one of the vertebrae of the neck4 ,thus these threads will guide you as to each part of the body which1 in any given attitude will be found below the pit of the throat1 or the angles of the shoulders1 or the nipples1 or hips and other parts of the body2 and the transverse lines of the net will show you how much the figure is higher over the leg on which it is posed than over the other1 and the same with the hips1 and the knees and the feet4 ,but always fix the net perpendicularly so that all the divisions that you see the model divided into by the net work correspond with your drawing of the model on the net work you have sketched4 ,the squares you draw may be as much smaller than those of the net as you wish that your figure should be smaller than nature4 ,afterwards remember when drawing figures1 to use the rule of the corresponding proportions of the limbs as you have learnt it from the frame and net4 ,this should be #c braccia and a half high and #c braccia wide2 #g braccia distant from you and #a braccio from the model4 ,footnote3 ,leonardo is commonly credited with the invention of the arrangement of a plate of glass commonly known as the vertical plane4 ,professor ,e4 ,,von ,,brucke in his ,bruchstucke aus der ,theorie der bildenden ,kunste1 ,leipzig #ahgg1 pg4 #c1 writes on this contrivance4 ,unsere ,glastafel ist die sogenannte ,glastafel des ,leonardo da ,vinci1 die in ,gestalt einer ,glastafel vorgestellte ,bildflache4 #ebd4 ,a ,,method ,,of ,,drawing ,,an ,,object ,,in ,,relief ,,at ,,night4 ,place a sheet of not too transparent paper between the relievo and the light and you can draw thus very well4 ,footnote3 ,bodies thus illuminated will show on the surface of the paper how the copyist has to distribute light and shade4 #ebe4 ,if you want to represent a figure on a wall1 the wall being foreshortened1 while the figure is to appear in its proper form1 and as standing free from the wall1 you must proceed thus3 have a thin plate of iron and make a small hole in the centre2 this hole must be round4 ,set a light close to it in such a position as that it shines through the central hole1 then place any object or figure you please so close to the wall that it touches it and draw the outline of the shadow on the wall2 then fill in the shade and add the lights2 place the person who is to see it so that he looks through that same hole where at first the light was2 and you will never be able to persuade yourself that the image is not detached from the wall4 ,footnote3 uno piccolo spiracelo nel mezzo4 ,m4 ,,ravaisson1 in his edition of ,,ms4 ,a 7,paris71 p4 #eb1 reads nel muro--evidently a mistake for nel mezzo which is quite plainly written2 and he translates it fait lui une petite ouverture dans le mur1 adding in a note3 les mots 'dans le mur' paraissent etre de trop4 ,leonardo a du les ecrire par distraction ,but 'nel mezzo' is clearly legible even on the photograph facsimile given by ,ravaisson himself1 and the objection he raises disappears at once4 ,it is not always wise or safe to try to prove our author's absence of mind or inadvertence by apparent difficulties in the sense or connection of the text4 #ebf4 ,,to ,,draw ,a ,,figure ,,on ,a ,,wall #ab ,,braccia ,,high ,,which ,,shall ,,look #bd ,,braccia ,,high4 ,if you wish to draw a figure or any other object to look #bd braccia high you must do it in this way4 ,first1 on the surface m r draw half the man you wish to represent2 then the other half2 then put on the vault m n the rest of the figure spoken of above2 first set out the vertical plane on the floor of a room of the same shape as the wall with the coved part on which you are to paint your figure4 ,then1 behind it1 draw a figure set out in profile of whatever size you please1 and draw lines from it to the point f and1 as these lines cut m n on the vertical plane1 so will the figure come on the wall1 of which the vertical plane gives a likeness1 and you will have all the relative heights and prominences of the figure4 ,and the breadth or thickness which are on the upright wall m n are to be drawn in their proper form1 since1 as the wall recedes the figure will be foreshortened by itself2 but that part of the figure which goes into the cove you must foreshorten1 as if it were standing upright2 this diminution you must set out on a flat floor and there must stand the figure which is to be transferred from the vertical plane r n,footnote #ag3 che leverai dalla pariete r n4 ,the letters refer to the larger sketch1 ,no4 #c on ,pl4 ,,xxxi4 in its real size and reduce it once more on a vertical plane2 and this will be a good method ,footnote #ah3 ,leonardo here says nothing as to how the image foreshortened by perspective and thus produced on the vertical plane is to be transferred to the wall2 but from what is said in ,nos4 #ebe and #ebc we may conclude that he was familiar with the process of casting the enlarged shadow of a squaring net on the surface of a wall to guide him in drawing the figure4 ,pariete di rilieuo2 sur une parai en relief 7,,ravaisson74 ,auf einer ,schnittlinie zum ,aufrichten 7,,ludwig74 ,the explanation of this puzzling expression must be sought in ,no4 #ede1 lines #ae-ag44 ,footnote3 ,see ,pl4 ,,xxxi4 #c4 ,the second sketch1 which in the plate is incomplete1 is here reproduced and completed from the original to illustrate the text4 ,in the original the larger diagram is placed between lines #e and #f4 #a4 #b4 ,c4 ,a4 #aeg;a2 #dfc;a has the similar heading3 'del cressciere della figura'1 and the text begins3 ,se voli fare #a;a figura grande b c but here it breaks off4 ,the translation here given renders the meaning of the passage as ,i think it must be understood4 ,the ,,ms4 is perfectly legible and the construction of the sentence is simple and clear2 difficulties can only arise from the very fullness of the meaning1 particularly towards the end of the passage4 #ebg4 ,if you would to draw a cube in an angle of a wall1 first draw the object in its own proper shape and raise it onto a vertical plane until it resembles the angle in which the said object is to be represented4 #ebh4 ,why are paintings seen more correctly in a mirror than out of it8 #ebi4 ,,how ,,the ,,mirror ,,is ,,the ,,master ,,and ,,guide ,,of ,,painters4 ,when you want to see if your picture corresponds throughout with the objects you have drawn from nature1 take a mirror and look in that at the reflection of the real things1 and compare the reflected image with your picture1 and consider whether the subject of the two images duly corresponds in both1 particularly studying the mirror4 ,you should take the mirror for your guide--that is to say a flat mirror--because on its surface the objects appear in many respects as in a painting4 ,thus you see1 in a painting done on a flat surface1 objects which appear in relief1 and in the mirror--also a flat surface--they look the same4 ,the picture has one plane surface and the same with the mirror4 ,the picture is intangible1 in so far as that which appears round and prominent cannot be grasped in the hands2 and it is the same with the mirror4 ,and since you can see that the mirror1 by means of outlines1 shadows and lights1 makes objects appear in relief1 you1 who have in your colours far stronger lights and shades than those in the mirror1 can certainly1 if you compose your picture well1 make that also look like a natural scene reflected in a large mirror4 ,footnote3 ,i understand the concluding lines of this passage as follows3 ,if you draw the upper half a figure on a large sheet of paper laid out on the floor of a room 7sala be piana7 to the same scale 7con le sue vere grosseze7 as the lower half1 already drawn upon the wall 7lines #aj1 #aa7you must then reduce them on a 'pariete di rilievo1' a curved vertical plane which serves as a model to reproduce the form of the vault4 #ecj4 ,,of ,,judging ,,your ,,own ,,pictures4 ,we know very well that errors are better recognised in the works of others than in our own2 and that often1 while reproving little faults in others1 you may ignore great ones in yourself4 ,to avoid such ignorance1 in the first place make yourself a master of perspective1 then acquire perfect knowledge of the proportions of men and other animals1 and also1 study good architecture1 that is so far as concerns the forms of buildings and other objects which are on the face of the earth2 these forms are infinite1 and the better you know them the more admirable will your work be4 ,and in cases where you lack experience do not shrink from drawing them from nature4 ,but1 to carry out my promise above in the title--,i say that when you paint you should have a flat mirror and often look at your work as reflected in it1 when you will see it reversed1 and it will appear to you like some other painter's work1 so you will be better able to judge of its faults than in any other way4 ,again1 it is well that you should often leave off work and take a little relaxation1 because1 when you come back to it you are a better judge2 for sitting too close at work may greatly deceive you4 ,again1 it is good to retire to a distance because the work looks smaller and your eye takes in more of it at a glance and sees more easily the discords or disproportion in the limbs and colours of the objects4 ,on the management of works 7#eca4 #ecb74 #eca4 ,,of ,a ,,method ,,of ,,learning ,,well ,,by ,,heart4 ,when you want to know a thing you have studied in your memory proceed in this way3 ,when you have drawn the same thing so many times that you think you know it by heart1 test it by drawing it without the model2 but have the model traced on flat thin glass and lay this on the drawing you have made without the model1 and note carefully where the tracing does not coincide with your drawing1 and where you find you have gone wrong2 and bear in mind not to repeat the same mistakes4 ,then return to the model1 and draw the part in which you were wrong again and again till you have it well in your mind4 ,if you have no flat glass for tracing on1 take some very thin kidts-kin parchment1 well oiled and dried4 ,and when you have used it for one drawing you can wash it clean with a sponge and make a second4 #ecb4 ,,that ,a ,,painter ,,ought ,,to ,,be ,,curious ,,to ,,hear ,,the ,,opinions ,,of ,,every ,,one ,,on ,,his ,,work4 ,certainly while a man is painting he ought not to shrink from hearing every opinion4 ,for we know very well that a man1 though he may not be a painter1 is familiar with the forms of other men and very capable of judging whether they are hump backed1 or have one shoulder higher or lower than the other1 or too big a mouth or nose1 and other defects2 and1 as we know that men are competent to judge of the works of nature1 how much more ought we to admit that they can judge of our errors2 since you know how much a man may be deceived in his own work4 ,and if you are not conscious of this in yourself study it in others and profit by their faults4 ,therefore be curious to hear with patience the opinions of others1 consider and weigh well whether those who find fault have ground or not for blame1 and1 if so amend2 but1 if not make as though you had not heard1 or if he should be a man you esteem show him by argument the cause of his mistake4 ,on the limitations of painting 7#ecc-ece7 #ecc4 ,,how ,,in ,,small ,,objects ,,errors ,,are ,,less ,,evident ,,than ,,in ,,large ,,ones4 ,in objects of minute size the extent of error is not so perceptible as in large ones2 and the reason is that if this small object is a representation of a man or of some other animal1 from the immense diminution the details cannot be worked out by the artist with the finish that is requisite4 ,hence it is not actually complete2 and1 not being complete1 its faults cannot be determined4 ,for instance3 ,look at a man at a distance of #cjj braccia and judge attentively whether he be handsome or ugly1 or very remarkable or of ordinary appearance4 ,you will find that with the utmost effort you cannot persuade yourself to decide4 ,and the reason is that at such a distance the man is so much diminished that the character of the details cannot be determined4 ,and if you wish to see how much this man is diminished by distance hold one of your fingers at a span's distance from your eye1 and raise or lower it till the top joint touches the feet of the figure you are looking at1 and you will see an incredible reduction4 ,for this reason we often doubt as to the person of a friend at a distance4 #ecd4 ,,why ,a ,,painting ,,can ,,never ,,appear ,,detached ,,as ,,natural ,,objects ,,do4 ,painters often fall into despair of imitating nature when they see their pictures fail in that relief and vividness which objects have that are seen in a mirror2 while they allege that they have colours which for brightness or depth far exceed the strength of light and shade in the reflections in the mirror1 thus displaying their own ignorance rather than the real cause1 because they do not know it4 ,it is impossible that painted objects should appear in such relief as to resemble those reflected in the mirror1 although both are seen on a flat surface1 unless they are seen with only one eye2 and the reason is that two eyes see one object behind another as a and b see m and n4 m cannot exactly occupy the space of n because the base of the visual lines is so broad that the second body is seen beyond the first4 ,but if you close one eye1 as at s the body f will conceal r1 because the line of sight proceeds from a single point and makes its base in the first body1 whence the second1 of the same size1 can never be seen4 ,footnote3 ,this passage contains the solution of the problem proposed in ,no4 #bi1 lines #aj-ad4 ,leonardo was evidently familiar with the law of optics on which the construction of the stereoscope depends4 ,compare ,e4 ,,von ,,brucke1 ,bruchstucke aus der ,theorie der bildenden ,kunste1 pg4 #fi3 ,schon ,leonardo da ,vinci wusste1 dass ein noch so gut gemaltes ,bild nie den vollen ,eindruck der ,korperlichkeit geben kann1 wie ihn die ,natur selbst giebt4 ,er erklart dies auch in ,kap4 ,,liii und ,kap4 ,,cccxli 7ed4 ,,du ,,fresne7 des ',trattato' in sachgemasser ,weise aus dem ,sehen mit beiden ,augen4 ,chap4 #ec of ,,du ,,fresne',s edition corresponds to ,no4 #ecd of this work4 #ece4 ,,why ,,of ,,two ,,objects ,,of ,,equal ,,size ,a ,,painted ,,one ,,will ,,look ,,larger ,,than ,a ,,solid ,,one4 ,the reason of this is not so easy to demonstrate as many others4 ,still ,i will endeavour to accomplish it1 if not wholly1 at any rate in part4 ,the perspective of diminution demonstrates by reason1 that objects diminish in proportion as they are farther from the eye1 and this reasoning is confirmed by experience4 ,hence1 the lines of sight that extend between the object and the eye1 when they are directed to the surface of a painting are all intersected at uniform limits1 while those lines which are directed towards a piece of sculpture are intersected at various limits and are of various lengths4 ,the lines which are longest extend to a more remote limb than the others and therefore that limb looks smaller4 ,as there are numerous lines each longer than the others--since there are numerous parts1 each more remote than the others and these1 being farther off1 necessarily appear smaller1 and by appearing smaller it follows that their diminution makes the whole mass of the object look smaller4 ,but this does not occur in painting2 since the lines of sight all end at the same distance there can be no diminution1 hence the parts not being diminished the whole object is undiminished1 and for this reason painting does not diminish1 as a piece of sculpture does4 ,on the choice of a position 7#ecf-ecg7 #ecf4 ,,how ,,high ,,the ,,point ,,of ,,sight ,,should ,,be ,,placed4 ,the point of sight must be at the level of the eye of an ordinary man1 and the farthest limit of the plain where it touches the sky must be placed at the level of that line where the earth and sky meet2 excepting mountains1 which are independent of it4 #ecg4 ,,of ,,the ,,way ,,to ,,draw ,,figures ,,for ,,historical ,,pictures4 ,the painter must always study on the wall on which he is to picture a story the height of the position where he wishes to arrange his figures2 and when drawing his studies for them from nature he must place himself with his eye as much below the object he is drawing as1 in the picture1 it will have to be above the eye of the spectator4 ,otherwise the work will look wrong4 ,the apparent size of figures in a picture 7#ech-eci7 #ech4 ,,of ,,placing ,a ,,figure ,,in ,,the ,,foreground ,,of ,a ,,historical ,,picture4 ,you must make the foremost figure in the picture less than the size of nature in proportion to the number of braccia at which you place it from the front line1 and make the others in proportion by the above rule4 #eci4 ,,perspective4 ,you are asked1 ,o ,painter1 why the figures you draw on a small scale according to the laws of perspective do not appear--notwithstanding the demonstration of distance--as large as real ones--their height being the same as in those painted on the wall4 ,and why painted objects seen at a small distance appear larger than the real ones8 ,the right position of the artist1 when painting1 and of the spectator 7#edj-edg7 #edj4 ,,of ,,painting4 ,when you draw from nature stand at a distance of #c times the height of the object you wish to draw4 #eda4 ,,of ,,drawing ,,from ,,relief4 ,in drawing from the round the draughtsman should so place himself that the eye of the figure he is drawing is on a level with his own4 ,this should be done with any head he may have to represent from nature because1 without exception1 the figures or persons you meet in the streets have their eyes on the same level as your own2 and if you place them higher or lower you will see that your drawing will not be true4 #edb4 ,,why ,,groups ,,of ,,figures ,,one ,,above ,,another ,,are ,,to ,,be ,,avoided4 ,the universal practice which painters adopt on the walls of chapels is greatly and reasonably to be condemned4 ,inasmuch as they represent one historical subject on one level with a landscape and buildings1 and then go up a step and paint another1 varying the point of sight1 and then a third and a fourth1 in such a way as that on one wall there are #d points of sight1 which is supreme folly in such painters4 ,we know that the point of sight is opposite the eye of the spectator of the scene2 and if you would have me tell you how to represent the life of a saint divided into several pictures on one and the same wall1 ,i answer that you must set out the foreground with its point of sight on a level with the eye of the spectator of the scene1 and upon this plane represent the more important part of the story large and then1 diminishing by degrees the figures1 and the buildings on various hills and open spaces1 you can represent all the events of the history4 ,and on the remainder of the wall up to the top put trees1 large as compared with the figures1 or angels if they are appropriate to the story1 or birds or clouds or similar objects2 otherwise do not trouble yourself with it for your whole work will be wrong4 #edc4 ,a ,,picture ,,of ,,objects ,,in ,,perspective ,,will ,,look ,,more ,,lifelike ,,when ,,seen ,,from ,,the ,,point ,,from ,,which ,,the ,,objects ,,were ,,drawn4 ,if you want to represent an object near to you which is to have the effect of nature1 it is impossible that your perspective should not look wrong1 with every false relation and disagreement of proportion that can be imagined in a wretched work1 unless the spectator1 when he looks at it1 has his eye at the very distance and height and direction where the eye or the point of sight was placed in doing this perspective4 ,hence it would be necessary to make a window1 or rather a hole1 of the size of your face through which you can look at the work2 and if you do this1 beyond all doubt your work1 if it is correct as to light and shade1 will have the effect of nature2 nay you will hardly persuade yourself that those objects are painted2 otherwise do not trouble yourself about it1 unless indeed you make your view at least #bj times as far off as the greatest width or height of the objects represented1 and this will satisfy any spectator placed anywhere opposite to the picture4 ,if you want the proof briefly shown1 take a piece of wood in the form of a little column1 eight times as high as it is thick1 like a column without any plinth or capital2 then mark off on a flat wall #dj equal spaces1 equal to its width so that between them they make #dj columns resembling your little column2 you then must fix1 opposite the centre space1 and at #d braccia from the wall1 a thin strip of iron with a small round hole in the middle about as large as a big pearl4 ,close to this hole place a light touching it4 ,then place your column against each mark on the wall and draw the outline of its shadow2 afterwards shade it and look through the hole in the iron plate4 ,footnote3 ,in the original there is a wide space between lines #c and #d in which we find two sketches not belonging to the text4 ,it is unnecessary to give prominence to the points in which my reading differs from that of ,m4 ,,ravaisson or to justify myself1 since they are all of secondary importance and can also be immediately verified from the photograph facsimile in his edition4 #edd4 ,a diminished object should be seen from the same distance1 height and direction as the point of sight of your eye1 or else your knowledge will produce no good effect4 ,and if you will not1 or cannot1 act on this principle--because as the plane on which you paint is to be seen by several persons you would need several points of sight which would make it look discordant and wrong--place yourself at a distance of at least #aj times the size of the objects4 ,the lesser fault you can fall into then1 will be that of representing all the objects in the foreground of their proper size1 and on whichever side you are standing the objects thus seen will diminish themselves while the spaces between them will have no definite ratio4 ,for1 if you place yourself in the middle of a straight row of objects1 and look at several columns arranged in a line you will see1 beyond a few columns separated by intervals1 that the columns touch2 and beyond where they touch they cover each other1 till the last column projects but very little beyond the last but one4 ,thus the spaces between the columns are by degrees entirely lost4 ,so1 if your method of perspective is good1 it will produce the same effect2 this effect results from standing near the line in which the columns are placed4 ,this method is not satisfactory unless the objects seen are viewed from a small hole1 in the middle of which is your point of sight2 but if you proceed thus your work will be perfect and will deceive the beholder1 who will see the columns as they are here figured4 ,here the eye is in the middle1 at the point a and near to the columns4 ,footnote3 ,the diagram which stands above this chapter in the original with the note belonging to it3 a b e la ripruova 7a b is the proof7 has obviously no connection with the text4 ,the second sketch alone is reproduced and stands in the original between lines #bb and #bc4 #ede4 ,if you cannot arrange that those who look at your work should stand at one particular point1 when constructing your work1 stand back until your eye is at least #bj times as far off as the greatest height and width of your work4 ,this will make so little difference when the eye of the spectator moves1 that it will be hardly appreciable1 and it will look very good4 ,if the point of sight is at t you would make the figures on the circle d b e all of one size1 as each of them bears the same relation to the point t4 ,but consider the diagram given below and you will see that this is wrong1 and why ,i shall make b smaller than d e ,footnote #h3 ,the second diagram of this chapter stands in the original between lines #h and #i44 ,it is easy to understand that if #b objects equal to each other are placed side by side the one at #c braccia distance looks smaller than that placed at #b braccia4 ,this however is rather theoretical than for practice1 because you stand close by ,footnote #aa3 ,instead of 'se preso' 7sie presso7 ,m4 ,,ravaisson reads 'sempre se' which gives rise to the unmeaning rendering3 'parceque toujours 444'4 ,all the objects in the foreground1 whether large or small1 are to be drawn of their proper size1 and if you see them from a distance they will appear just as they ought1 and if you see them close they will diminish of themselves4 ,footnote #ae3 ,compare ,no4 #ebf line #ah4 ,take care that the vertical plan on which you work out the perspective of the objects seen is of the same form as the wall on which the work is to be executed4 #edf4 ,,of ,,painting4 ,the size of the figures represented ought to show you the distance they are seen from4 ,if you see a figure as large as nature you know it appears to be close to the eye4 #edg4 ,,where ,a ,,spectator ,,should ,,stand ,,to ,,look ,,at ,a ,,picture4 ,supposing a b to be the picture and d to be the light1 ,i say that if you place yourself between c and e you will not understand the picture well and particularly if it is done in oils1 or still more if it is varnished1 because it will be lustrous and somewhat of the nature of a mirror4 ,and for this reason the nearer you go towards the point c1 the less you will see1 because the rays of light falling from the window on the picture are reflected to that point4 ,but if you place yourself between e and d you will get a good view of it1 and the more so as you approach the point d1 because that spot is least exposed to these reflected rays of light4 ,,iii4 ,,the ,,practical ,,methods ,,of ,,light ,,and ,,shade ,,and ,,aerial ,,perspective4 ,gradations of light and shade4 #edh4 ,,of ,,painting3 ,,of ,,the ,,darkness ,,of ,,the ,,shadows1 ,,or ,i ,,may ,,say1 ,,the ,,brightness ,,of ,,the ,,lights4 ,although practical painters attribute to all shaded objects--trees1 fields1 hair1 beards and skin--four degrees of darkness in each colour they use3 that is to say first a dark foundation1 secondly a spot of colour somewhat resembling the form of the details1 thirdly a somewhat brighter and more defined portion1 fourthly the lights which are more conspicuous than other parts of the figure2 still to me it appears that these gradations are infinite upon a continuous surface which is in itself infinitely divisible1 and ,i prove it thus3--,footnote #g3 ,see ,pl4 ,,xxxi1 ,no4 #a2 the two upper sketches4 ,let a g be a continuous surface and let d be the light which illuminates it2 ,i say--by the #dth proposition which says that that side of an illuminated body is most highly lighted which is nearest to the source of light--that therefore g must be darker than c in proportion as the line d g is longer than the line d c1 and consequently that these gradations of light--or rather of shadow1 are not #d only1 but may be conceived of as infinite1 because c d is a continuous surface and every continuous surface is infinitely divisible2 hence the varieties in the length of lines extending between the light and the illuminated object are infinite1 and the proportion of the light will be the same as that of the length of the lines between them2 extending from the centre of the luminous body to the surface of the illuminated object4 ,on the choice of light for a picture 7#edi-eed74 #edi4 ,,how ,,the ,,painter ,,must ,,place ,,himself ,,with ,,reference ,,to ,,the ,,light1 ,,to ,,give ,,the ,,effect ,,of ,,relief4 ,let a b be the window1 m the point of light4 ,i say that on whichever side the painter places himself he will be well placed if only his eye is between the shaded and the illuminated portions of the object he is drawing2 and this place you will find by putting yourself between the point m and the division between the shadow and the light on the object to be drawn4 #eej4 ,,that ,,shadows ,,cast ,,by ,a ,,particular ,,light ,,should ,,be ,,avoided1 ,,because ,,they ,,are ,,equally ,,strong ,,at ,,the ,,ends ,,and ,,at ,,the ,,beginning4 ,the shadows cast by the sun or any other particular light have not a pleasing effect on the body to which they belong1 because the parts remain confuse1 being divided by distinct outlines of light and shade4 ,and the shadows are of equal strength at the end and at the beginning4 #eea4 ,,how ,,light ,,should ,,be ,,thrown ,,upon ,,figures4 ,the light must be arranged in accordance with the natural conditions under which you wish to represent your figures3 that is1 if you represent them in the sunshine make the shadows dark with large spaces of light1 and mark their shadows and those of all the surrounding objects strongly on the ground4 ,and if you represent them as in dull weather give little difference of light and shade1 without any shadows at their feet4 ,if you represent them as within doors1 make a strong difference between the lights and shadows1 with shadows on the ground4 ,if the window is screened and the walls white1 there will be little difference of light4 ,if it is lighted by firelight make the high lights ruddy and strong1 and the shadows dark1 and those cast on the walls and on the floor will be clearly defined and the farther they are from the body the broader and longer will they be4 ,if the light is partly from the fire and partly from the outer day1 that of day will be the stronger and that of the fire almost as red as fire itself4 ,above all see that the figures you paint are broadly lighted and from above1 that is to say all living persons that you paint2 for you will see that all the people you meet out in the street are lighted from above1 and you must know that if you saw your most intimate friend with a light on his face from below you would find it difficult to recognise him4 #eeb4 ,,of ,,helping ,,the ,,apparent ,,relief ,,of ,a ,,picture ,,by ,,giving ,,it ,,artificial ,,light ,,and ,,shade4 ,to increase relief of a picture you may place1 between your figure and the solid object on which its shadow falls1 a line of bright light1 dividing the figure from the object in shadow4 ,and on the same object you shall represent two light parts which will surround the shadow cast upon the wall by the figure placed opposite #f2 and do this frequently with the limbs which you wish should stand out somewhat from the body they belong to2 particularly when the arms cross the front of the breast show1 between the shadow cast by the arms on the breast and the shadow on the arms themselves1 a little light seeming to fall through a space between the breast and the arms2 and the more you wish the arm to look detached from the breast the broader you must make the light2 always contrive also to arrange the figures against the background in such a way as that the parts in shadow are against a light background and the illuminated portions against a dark background4 ,footnote #f3 ,compare the two diagrams under ,no4 #efe4 #eec4 ,,of ,,situation4 ,remember to note the situation of your figures2 for the light and shade will be one thing if the object is in a dark place with a particular light1 and another thing if it is in a light place with direct sunlight2 one thing in a dark place with a diffused evening light or a cloudy sky1 and another in the diffused light of the atmosphere lighted by the sun4 #eed4 ,,of ,,the ,,judgment ,,to ,,be ,,made ,,of ,a ,,painter',s ,,work4 ,first you must consider whether the figures have the relief required by their situation and the light which illuminates them2 for the shadows should not be the same at the extreme ends of the composition as in the middle1 because it is one thing when figures are surrounded by shadows and another when they have shadows only on one side4 ,those which are in the middle of the picture are surrounded by shadows1 because they are shaded by the figures which stand between them and the light4 ,and those are lighted on one side only which stand between the principal group and the light1 because where they do not look towards the light they face the group and the darkness of the group is thrown on them3 and where they do not face the group they face the brilliant light and it is their own darkness shadowing them1 which appears there4 ,in the second place observe the distribution or arrangement of figures1 and whether they are distributed appropriately to the circumstances of the story4 ,thirdly1 whether the figures are actively intent on their particular business4 #eee4 ,,of ,,the ,,treatment ,,of ,,the ,,lights4 ,first give a general shadow to the whole of that extended part which is away from the light4 ,then put in the half shadows and the strong shadows1 comparing them with each other and1 in the same way give the extended light in half tint1 afterwards adding the half lights and the high lights1 likewise comparing them together4 ,the distribution of light and shade 7#eef-eei7 #eef4 ,,of ,,shadows ,,on ,,bodies4 ,when you represent the dark shadows in bodies in light and shade1 always show the cause of the shadow1 and the same with reflections2 because the dark shadows are produced by dark objects and the reflections by objects only moderately lighted1 that is with diminished light4 ,and there is the same proportion between the highly lighted part of a body and the part lighted by a reflection as between the origin of the lights on the body and the origin of the reflections4 #eeg4 ,,of ,,lights ,,and ,,shadows4 ,i must remind you to take care that every portion of a body1 and every smallest detail which is ever so little in relief1 must be given its proper importance as to light and shade4 #eeh4 ,,of ,,the ,,way ,,to ,,make ,,the ,,shadow ,,on ,,figures ,,correspond ,,to ,,the ,,light ,,and ,,to ,,the ,,colour ,,of ,,the ,,body4 ,when you draw a figure and you wish to see whether the shadow is the proper complement to the light1 and neither redder nor yellower than is the nature of the colour you wish to represent in shade1 proceed thus4 ,cast a shadow with your finger on the illuminated portion1 and if the accidental shadow that you have made is like the natural shadow cast by your finger on your work1 well and good2 and by putting your finger nearer or farther off1 you can make darker or lighter shadows1 which you must compare with your own4 #eei4 ,,of ,,surrounding ,,bodies ,,by ,,various ,,forms ,,of ,,shadow4 ,take care that the shadows cast upon the surface of the bodies by different objects must undulate according to the various curves of the limbs which cast the shadows1 and of the objects on which they are cast4 ,the juxtaposition of light and shade 7#efj1 #efa74 #efj4 ,,on ,,painting4 ,the comparison of the various qualities of shadows and lights not infrequently seems ambiguous and confused to the painter who desires to imitate and copy the objects he sees4 ,the reason is this3 ,if you see a white drapery side by side with a black one1 that part of the white drapery which lies against the black one will certainly look much whiter than the part which lies against something whiter than itself4 ,footnote3 ,it is evident from this that so early as in #adib ,leonardo's writing in perspective was so far advanced that he could quote his own statements4--,as bearing on this subject compare what is said in ,no4 #bhj4 ,and the reason of this is shown in my book on perspective4 #efa4 ,,of ,,shadows4 ,where a shadow ends in the light1 note carefully where it is paler or deeper and where it is more or less indistinct towards the light2 and1 above all1 in painting youthful figures ,i remind you not to make the shadow end like a stone1 because flesh has a certain transparency1 as may be seen by looking at a hand held between the eye and the sun1 which shines through it ruddy and bright4 ,place the most highly coloured part between the light and shadow4 ,and to see what shadow tint is needed on the flesh1 cast a shadow on it with your finger1 and according as you wish to see it lighter or darker hold your finger nearer to or farther from your picture1 and copy that shadow4 ,on the lighting of the background 7#efb-efe74 #efb4 ,,of ,,the ,,backgrounds ,,for ,,painted ,,figures4 ,the ground which surrounds the forms of any object you paint should be darker than the high lights of those figures1 and lighter than their shadowed part3 c4 #efc4 ,,of ,,the ,,background ,,that ,,the ,,painter ,,should ,,adopt ,,in ,,his ,,works4 ,since experience shows us that all bodies are surrounded by light and shade it is necessary that you1 ,o ,painter1 should so arrange that the side which is in light shall terminate against a dark body and likewise that the shadow side shall terminate against a light body4 ,and by following this rule you will add greatly to the relief of your figures4 #efd4 ,a most important part of painting consists in the backgrounds of the objects represented2 against these backgrounds the outlines of those natural objects which are convex are always visible1 and also the forms of these bodies against the background1 even though the colours of the bodies should be the same as that of the background4 ,this is caused by the convex edges of the objects not being illuminated in the same way as1 by the same light1 the background is illuminated1 since these edges will often be lighter or darker than the background4 ,but if the edge is of the same colour as the background1 beyond a doubt it will in that part of the picture interfere with your perception of the outline1 and such a choice in a picture ought to be rejected by the judgment of good painters1 inasmuch as the purpose of the painter is to make his figures appear detached from the background2 while in the case here described the contrary occurs1 not only in the picture1 but in the objects themselves4 #efe4 ,that you ought1 when representing objects above the eye and on one side--if you wish them to look detached from the wall--to show1 between the shadow on the object and the shadow it casts a middle light1 so that the body will appear to stand away from the wall4 ,on the lighting of white objects4 #eff4 ,,how ,,white ,,bodies ,,should ,,be ,,represented4 ,if you are representing a white body let it be surrounded by ample space1 because as white has no colour of its own1 it is tinged and altered in some degree by the colour of the objects surrounding it4 ,if you see a woman dressed in white in the midst of a landscape1 that side which is towards the sun is bright in colour1 so much so that in some portions it will dazzle the eyes like the sun itself2 and the side which is towards the atmosphere1--luminous through being interwoven with the sun's rays and penetrated by them--since the atmosphere itself is blue1 that side of the woman's figure will appear steeped in blue4 ,if the surface of the ground about her be meadows and if she be standing between a field lighted up by the sun and the sun itself1 you will see every portion of those folds which are towards the meadow tinged by the reflected rays with the colour of that meadow4 ,thus the white is transmuted into the colours of the luminous and of the non-luminous objects near it4 ,the methods of aerial 7#efg--egj74 #efg4 ,,why ,,faces ,,seen ,,at ,a ,,distance ,,look ,,dark4 ,we see quite plainly that all the images of visible objects that lie before us1 whether large or small1 reach our sense by the minute aperture of the eye2 and if1 through so small a passage the image can pass of the vast extent of sky and earth1 the face of a man--being by comparison with such large images almost nothing by reason of the distance which diminishes it1--fills up so little of the eye that it is indistinguishable4 ,having1 also1 to be transmitted from the surface to the sense through a dark medium1 that is to say the crystalline lens which looks dark1 this image1 not being strong in colour becomes affected by this darkness on its passage1 and on reaching the sense it appears dark2 no other reason can in any way be assigned4 ,if the point in the eye is black1 it is because it is full of a transparent humour as clear as air and acts like a perforation in a board2 on looking into it it appears dark and the objects seen through the bright air and a dark one become confused in this darkness4 ,,why ,a ,,man ,,seen ,,at ,a ,,certain ,,distance ,,is ,,not ,,recognisable4 ,the perspective of diminution shows us that the farther away an object is the smaller it looks4 ,if you look at a man at a distance from you of an arrow's flight1 and hold the eye of a small needle close to your own eye1 you can see through it several men whose images are transmitted to the eye and will all be comprised within the size of the needle's eye2 hence1 if the man who is at the distance of an arrow's flight can send his whole image to your eye1 occupying only a small space in the needle's eye how can you expect in so small a figure to distinguish or see the nose or mouth or any detail of his person8 and1 not seeing these you cannot recognise the man1 since these features1 which he does not show1 are what give men different aspects4 #efh4 ,,the ,,reason ,,why ,,small ,,figures ,,should ,,not ,,be ,,made ,,finished4 ,i say that the reason that objects appear diminished in size is because they are remote from the eye2 this being the case it is evident that there must be a great extent of atmosphere between the eye and the objects1 and this air interferes with the distinctness of the forms of the object4 ,hence the minute details of these objects will be indistinguishable and unrecognisable4 ,therefore1 ,o ,painter1 make your smaller figures merely indicated and not highly finished1 otherwise you will produce effects the opposite to nature1 your supreme guide4 ,the object is small by reason of the great distance between it and the eye1 this great distance is filled with air1 that mass of air forms a dense body which intervenes and prevents the eye seeing the minute details of objects4 #efi4 ,whenever a figure is placed at a considerable distance you lose first the distinctness of the smallest parts2 while the larger parts are left to the last1 losing all distinctness of detail and outline2 and what remains is an oval or spherical figure with confused edges4 #egj4 ,,of ,,painting4 ,the density of a body of smoke looks white below the horizon while above the horizon it is dark1 even if the smoke is in itself of a uniform colour1 this uniformity will vary according to the variety in the ground on which it is seen4 ,,iv4 ,,of ,,portrait ,,and ,,figure ,,painting4 ,of sketching figures and portraits 7#ega-egb74 #ega4 ,,of ,,the ,,way ,,to ,,learn ,,to ,,compose ,,figures ,,in ,,groups ,,in ,,historical ,,pictures4 ,when you have well learnt perspective and have by heart the parts and forms of objects1 you must go about1 and constantly1 as you go1 observe1 note and consider the circumstances and behaviour of men in talking1 quarrelling or laughing or fighting together3 the action of the men themselves and the actions of the bystanders1 who separate them or who look on4 ,and take a note of them with slight strokes thus1 in a little book which you should always carry with you4 ,and it should be of tinted paper1 that it may not be rubbed out1 but change the old when full for a new one2 since these things should not be rubbed out but preserved with great care2 for the forms1 and positions of objects are so infinite that the memory is incapable of retaining them1 wherefore keep these sketches as your guides and masters4 ,footnote3 ,among ,leonardo's numerous note books of pocket size not one has coloured paper1 so no sketches answering to this description can be pointed out4 ,the fact that most of the notes are written in ink1 militates against the supposition that they were made in the open air4 #egb4 ,,of ,a ,,method ,,of ,,keeping ,,in ,,mind ,,the ,,form ,,of ,a ,,face4 ,if you want to acquire facility for bearing in mind the expression of a face1 first make yourself familiar with a variety of forms of several heads1 eyes1 noses1 mouths1 chins and cheeks and necks and shoulders3 ,and to put a case3 ,noses are of #aj types3 straight1 bulbous1 hollow1 prominent above or below the middle1 aquiline1 regular1 flat1 round or pointed4 ,these hold good as to profile4 ,in full face they are of #aa types2 these are equal thick in the middle1 thin in the middle1 with the tip thick and the root narrow1 or narrow at the tip and wide at the root2 with the nostrils wide or narrow1 high or low1 and the openings wide or hidden by the point2 and you will find an equal variety in the other details2 which things you must draw from nature and fix them in your mind4 ,or else1 when you have to draw a face by heart1 carry with you a little book in which you have noted such features2 and when you have cast a glance at the face of the person you wish to draw1 you can look1 in private1 which nose or mouth is most like1 or there make a little mark to recognise it again at home4 ,of grotesque faces ,i need say nothing1 because they are kept in mind without difficulty4 ,the position of the head4 #egc4 ,,how ,,you ,,should ,,set ,,to ,,work ,,to ,,draw ,a ,,head ,,of ,,which ,,all ,,the ,,parts ,,shall ,,agree ,,with ,,the ,,position ,,given ,,to ,,it4 ,to draw a head in which the features shall agree with the turn and bend of the head1 pursue this method4 ,you know that the eyes1 eyebrows1 nostrils1 corners of the mouth1 and sides of the chin1 the jaws1 cheeks1 ears and all the parts of a face are squarely and straightly set upon the face4 ,footnote3 ,compare the drawings and the text belonging to them on ,pl4 ,,ix4 7,no4 #cae71 ,pl4 ,x 7,no4 #caf71 ,pl4 ,,xl 7,no4 #cah7 and ,pl4 ,,xii4 7,no4 #cai74 ,therefore when you have sketched the face draw lines passing from one corner of the eye to the other2 and so for the placing of each feature2 and after having drawn the ends of the lines beyond the two sides of the face1 look if the spaces inside the same parallel lines on the right and on the left are equal #ab4 ,but be sure to remember to make these lines tend to the point of sight4 ,footnote3 ,see ,pl4 ,,xxxi1 ,no4 #d1 the slight sketch on the left hand side4 ,the text of this passage is written by the side of it4 ,in this sketch the lines seem intentionally incorrect and converging to the right 7compare ,i4 #ab7 instead of parallel4 ,compare too with this text the drawing in red chalk from ,windsor ,castle which is reproduced on ,pl4 ,,xl1 ,no4 #b4 ,of the light on the face 7#egd-egf74 #egd4 ,,how ,,to ,,know ,,which ,,side ,,of ,,an ,,object ,,is ,,to ,,be ,,more ,,or ,,less ,,luminous ,,than ,,the ,,other4 ,let f be the light1 the head will be the object illuminated by it and that side of the head on which the rays fall most directly will be the most highly lighted1 and those parts on which the rays fall most aslant will be less lighted4 ,the light falls as a blow might1 since a blow which falls perpendicularly falls with the greatest force1 and when it falls obliquely it is less forcible than the former in proportion to the width of the angle4 ,exempli gratia if you throw a ball at a wall of which the extremities are equally far from you the blow will fall straight1 and if you throw the ball at the wall when standing at one end of it the ball will hit it obliquely and the blow will not tell4 ,footnote3 ,see ,pl4 ,,xxxi4 ,no4 #d2 the sketch on the right hand side4 #ege4 ,,the ,,proof ,,and ,,reason ,,why ,,among ,,the ,,illuminated ,,parts ,,certain ,,portions ,,are ,,in ,,higher ,,light ,,than ,,others4 ,since it is proved that every definite light is1 or seems to be1 derived from one single point the side illuminated by it will have its highest light on the portion where the line of radiance falls perpendicularly2 as is shown above in the lines a g1 and also in a h and in l a2 and that portion of the illuminated side will be least luminous1 where the line of incidence strikes it between two more dissimilar angles1 as is seen at b c d4 ,and by this means you may also know which parts are deprived of light as is seen at m k4 ,where the angles made by the lines of incidence are most equal there will be the highest light1 and where they are most unequal it will be darkest4 ,i will make further mention of the reason of reflections4 ,footnote3 ,see ,pl4 ,,xxxii4 ,the text1 here given complete1 is on the right hand side4 ,the small circles above the beginning of lines #e and #aa as well as the circle above the text on ,pl4 ,,xxxi1 are in a paler ink and evidently added by a later hand in order to distinguish the text as belonging to the ,libro di ,pittura 7see ,prolegomena4 ,no4 #ab1 p4 #c74 ,the text on the left hand side of this page is given as ,nos4 #egg and #acg4 #egf4 ,where the shadow should be on the face4 ,general suggestions for historical pictures 7#egg-eha74 #egg4 ,when you compose a historical picture take two points1 one the point of sight1 and the other the source of light2 and make this as distant as possible4 #egh4 ,historical pictures ought not to be crowded and confused with too many figures4 #egi4 ,,precepts ,,in ,,painting4 ,let you sketches of historical pictures be swift and the working out of the limbs not be carried too far1 but limited to the position of the limbs1 which you can afterwards finish as you please and at your leisure4 ,footnote3 ,see ,pl4 ,,xxxviii1 ,no4 #b4 ,the pen and ink drawing given there as ,no4 #c may also be compared with this passage4 ,it is in the ,windsor collection where it is numbered #aja4 #ehj4 ,the sorest misfortune is when your views are in advance of your work4 #eha4 ,of composing historical pictures4 ,of not considering the limbs in the figures in historical pictures2 as many do who1 in the wish to represent the whole of a figure1 spoil their compositions4 ,and when you place one figure behind another take care to draw the whole of it so that the limbs which come in front of the nearer figures may stand out in their natural size and place4 ,how to represent the differences of age and sex 7#ehb-ehc74 #ehb4 ,how the ages of man should be depicted3 that is1 ,infancy1 ,childhood1 ,youth1 ,manhood1 ,old age1 ,decrepitude4 ,footnote3 ,no answer is here given to this question1 in the original ,,ms4 #ehc4 ,old men ought to be represented with slow and heavy movements1 their legs bent at the knees1 when they stand still1 and their feet placed parallel and apart2 bending low with the head leaning forward1 and their arms but little extended4 ,women must be represented in modest attitudes1 their legs close together1 their arms closely folded1 their heads inclined and somewhat on one side4 ,old women should be represented with eager1 swift and furious gestures1 like infernal furies2 but the action should be more violent in their arms and head than in their legs4 ,little children1 with lively and contorted movements when sitting1 and1 when standing still1 in shy and timid attitudes4 ,footnote3 bracci raccolte4 ,compare ,pl4 ,,xxxiii4 ,this drawing1 in silver point on yellowish tinted paper1 the lights heightened with white1 represents two female hands laid together in a lap4 ,above is a third finished study of a right hand1 apparently holding a veil from the head across the bosom4 ,this drawing evidently dates from before #aejj and was very probably done at ,florence1 perhaps as a preparatory study for some picture4 ,the type of hand with its slender thin forms is more like the style of the ,vierge aux ,rochers in the ,louvre than any later works--as the ,mona ,lisa for instance4 ,of representing the emotions4 #ehd4 ,,that ,a ,,figure ,,is ,,not ,,admirable ,,unless ,,it ,,expresses ,,by ,,its ,,action ,,the ,,passion ,,of ,,its ,,sentiment4 ,that figure is most admirable which by its actions best expresses the passion that animates it4 ,,how ,,an ,,angry ,,man ,,is ,,to ,,be ,,figured4 ,you must make an angry person holding someone by the hair1 wrenching his head against the ground1 and with one knee on his ribs2 his right arm and fist raised on high4 ,his hair must be thrown up1 his brow downcast and knit1 his teeth clenched and the two corners of his mouth grimly set2 his neck swelled and bent forward as he leans over his foe1 and full of furrows4 ,,how ,,to ,,represent ,a ,,man ,,in ,,despair4 ,you must show a man in despair with a knife1 having already torn open his garments1 and with one hand tearing open the wound4 ,and make him standing on his feet and his legs somewhat bent and his whole person leaning towards the earth2 his hair flying in disorder4 ,of representing imaginary animals4 #ehe4 ,,how ,,you ,,should ,,make ,,an ,,imaginary ,,animal ,,look ,,natural4 ,you know that you cannot invent animals without limbs1 each of which1 in itself1 must resemble those of some other animal4 ,hence if you wish to make an animal1 imagined by you1 appear natural--let us say a ,dragon1 take for its head that of a mastiff or hound1 with the eyes of a cat1 the ears of a porcupine1 the nose of a greyhound1 the brow of a lion1 the temples of an old cock1 the neck of a water tortoise4 ,footnote3 ,the sketch here inserted of two men on horseback fighting a dragon is the facsimile of a pen and ink drawing belonging to ,,baron ,,edmond ,,de ,,rothschild of ,paris4 ,the selection of forms4 #ehf4 ,,of ,,the ,,delusions ,,which ,,arise ,,in ,,judging ,,of ,,the ,,limbs4 ,a painter who has clumsy hands will paint similar hands in his works1 and the same will occur with any limb1 unless long study has taught him to avoid it4 ,therefore1 ,o ,painter1 look carefully what part is most ill-favoured in your own person and take particular pains to correct it in your studies4 ,for if you are coarse1 your figures will seem the same and devoid of charm2 and it is the same with any part that may be good or poor in yourself2 it will be shown in some degree in your figures4 #ehg4 ,,of ,,the ,,selection ,,of ,,beautiful ,,faces4 ,it seems to me to be no small charm in a painter when he gives his figures a pleasing air1 and this grace1 if he have it not by nature1 he may acquire by incidental study in this way3 ,look about you and take the best parts of many beautiful faces1 of which the beauty is confirmed rather by public fame than by your own judgment2 for you might be mistaken and choose faces which have some resemblance to your own4 ,for it would seem that such resemblances often please us2 and if you should be ugly1 you would select faces that were not beautiful and you would then make ugly faces1 as many painters do4 ,for often a master's work resembles himself4 ,so select beauties as ,i tell you1 and fix them in your mind4 #ehh4 ,of the limbs1 which ought to be carefully selected1 and of all the other parts with regard to painting4 #ehi4 ,when selecting figures you should choose slender ones rather than lean and wooden ones4 #eij4 ,,of ,,the ,,muscles ,,of ,,animals4 ,the hollow spaces interposed between the muscles must not be of such a character as that the skin should seem to cover two sticks laid side by side like c1 nor should they seem like two sticks somewhat remote from such contact so that the skin hangs in an empty loose curve as at f2 but it should be like i1 laid over the spongy fat that lies in the angles as the angle n m o2 which angle is formed by the contact of the ends of the muscles and as the skin cannot fold down into such an angle1 nature has filled up such angles with a small quantity of spongy and1 as ,i may say1 vesicular fat1 with minute bladders in it full of air1 which is condensed or rarefied in them according to the increase or the diminution of the substance of the muscles2 in which latter case the concavity i always has a larger curve than the muscle4 #eia4 ,,of ,,undulating ,,movements ,,and ,,equipoise ,,in ,,figures ,,and ,,other ,,animals4 ,when representing a human figure or some graceful animal1 be careful to avoid a wooden stiffness2 that is to say make them move with equipoise and balance so as not to look like a piece of wood2 but those you want to represent as strong you must not make so1 excepting in the turn of the head4 ,how to pose figures4 #eib4 ,,of ,,grace ,,in ,,the ,,limbs4 ,the limbs should be adapted to the body with grace and with reference to the effect that you wish the figure to produce4 ,and if you wish to produce a figure that shall of itself look light and graceful you must make the limbs elegant and extended1 and without too much display of the muscles2 and those few that are needed for your purpose you must indicate softly1 that is1 not very prominent and without strong shadows2 the limbs1 and particularly the arms easy2 that is1 none of the limbs should be in a straight line with the adjoining parts4 ,and if the hips1 which are the pole of a man1 are by reason of his position1 placed so1 that the right is higher than the left1 make the point of the higher shoulder in a perpendicular line above the highest prominence of the hip1 and let this right shoulder be lower than the left4 ,let the pit of the throat always be over the centre of the joint of the foot on which the man is leaning4 ,the leg which is free should have the knee lower than the other1 and near the other leg4 ,the positions of the head and arms are endless and ,i shall therefore not enlarge on any rules for them4 ,still1 let them be easy and pleasing1 with various turns and twists1 and the joints gracefully bent1 that they may not look like pieces of wood4 ,of appropriate gestures 7#eic-fjj74 #eic4 ,a picture or representation of human figures1 ought to be done in such a way as that the spectator may easily recognise1 by means of their attitudes1 the purpose in their minds4 ,thus1 if you have to represent a man of noble character in the act of speaking1 let his gestures be such as naturally accompany good words2 and1 in the same way1 if you wish to depict a man of a brutal nature1 give him fierce movements2 as with his arms flung out towards the listener1 and his head and breast thrust forward beyond his feet1 as if following the speaker's hands4 ,thus it is with a deaf and dumb person who1 when he sees two men in conversation--although he is deprived of hearing--can nevertheless understand1 from the attitudes and gestures of the speakers1 the nature of their discussion4 ,i once saw in ,florence a man who had become deaf who1 when you spoke very loud did not understand you1 but if you spoke gently and without making any sound1 understood merely from the movement of the lips4 ,now perhaps you will say that the lips of a man who speaks loudly do not move like those of one speaking softly1 and that if they were to move them alike they would be alike understood4 ,as to this argument1 ,i leave the decision to experiment2 make a man speak to you gently and note the motion of his lips4 ,footnote3 ,the first ten lines of this text have already been published1 but with a slightly different reading by ,dr4 ,m4 ,,jordan3 ,das ,malerbuch ,leonardo da ,vinci's p4 #hf4 #eid4 ,,of ,,representing ,a ,,man ,,speaking ,,to ,a ,,multitude4 ,when you wish to represent a man speaking to a number of people1 consider the matter of which he has to treat and adapt his action to the subject4 ,thus1 if he speaks persuasively1 let his action be appropriate to it4 ,if the matter in hand be to set forth an argument1 let the speaker1 with the fingers of the right hand hold one finger of the left hand1 having the two smaller ones closed2 and his face alert1 and turned towards the people with mouth a little open1 to look as though he spoke2 and if he is sitting let him appear as though about to rise1 with his head forward4 ,if you represent him standing make him leaning slightly forward with body and head towards the people4 ,these you must represent as silent and attentive1 all looking at the orator's face with gestures of admiration2 and make some old men in astonishment at the things they hear1 with the corners of their mouths pulled down and drawn in1 their cheeks full of furrows1 and their eyebrows raised1 and wrinkling the forehead where they meet4 ,again1 some sitting with their fingers clasped holding their weary knees4 ,again1 some bent old man1 with one knee crossed over the other2 on which let him hold his hand with his other elbow resting in it and the hand supporting his bearded chin4 ,footnote3 ,the sketches introduced here are a facsimile of a pen and ink drawing in the ,louvre which ,herr ,,carl ,,brun considers as studies for the ,last ,supper in the church of ,santa ,maria delle ,grazie 7see ,leonardo da ,vinci1 ,,lxi1 pp4 #ba1 #bg and #bh in ,,dohme',s ,kunst und ,kunstler1 ,leipzig1 ,seemann74 ,i shall not here enter into any discussion of this suggestion2 but as a justification for introducing the drawing in this place1 ,i may point out that some of the figures illustrate this passage as perfectly as though they had been drawn for that express purpose4 ,i have discussed the probability of a connection between this sketch and the picture of the ,last ,supper on p4 #cce4 ,the original drawing is #bg #c_/d centimetres wide by #ba high4--,the drawing in silver point on reddish paper given on ,pl4 ,,lii4 ,no4 #a--the original at ,windsor ,castle--may also serve to illustrate the subject of appropriate gestures1 treated in ,nos4 #eic and #eid4 #eie4 ,,of ,,the ,,disposition ,,of ,,limbs4 ,as regards the disposition of limbs in movement you will have to consider that when you wish to represent a man who1 by some chance1 has to turn backwards or to one side1 you must not make him move his feet and all his limbs towards the side to which he turns his head4 ,rather must you make the action proceed by degrees and through the different joints2 that is1 those of the foot1 the knee and the hip and the neck4 ,and if you set him on the right leg1 you must make the left knee bend inwards1 and let his foot be slightly raised on the outside1 and the left shoulder be somewhat lower than the right1 while the nape of the neck is in a line directly over the outer ancle of the left foot4 ,and the left shoulder will be in a perpendicular line above the toes of the right foot4 ,and always set your figures so that the side to which the head turns is not the side to which the breast faces1 since nature for our convenience has made us with a neck which bends with ease in many directions1 the eye wishing to turn to various points1 the different joints4 ,and if at any time you make a man sitting with his arms at work on something which is sideways to him1 make the upper part of his body turn upon the hips4 ,footnote3 ,compare ,pl4 ,,vii1 ,no4 #e4 ,the original drawing at ,windsor ,castle is numbered #ajd4 #eif4 ,when you draw the nude always sketch the whole figure and then finish those limbs which seem to you the best1 but make them act with the other limbs2 otherwise you will get a habit of never putting the limbs well together on the body4 ,never make the head turn the same way as the torso1 nor the arm and leg move together on the same side4 ,and if the face is turned to the right shoulder1 make all the parts lower on the left side than on the right2 and when you turn the body with the breast outwards1 if the head turns to the left side make the parts on the right side higher than those on the left4 ,footnote3 ,in the original ,,ms4 a much defaced sketch is to be seen by the side of the second part of this chapter2 its faded condition has rendered reproduction impossible4 ,in ,m4 ,,ravaisson',s facsimile the outlines of the head have probably been touched up4 ,this passage however is fitly illustrated by the drawings on ,pl4 ,,xxi4 #eig4 ,,of ,,painting4 ,of the nature of movements in man4 ,do not repeat the same gestures in the limbs of men unless you are compelled by the necessity of their action1 as is shown in a b4 ,footnote3 ,see ,pl4 ,v1 where part of the text is also reproduced4 ,the effaced figure to the extreme left has evidently been cancelled by ,leonardo himself as unsatisfactory4 #eih4 ,the motions of men must be such as suggest their dignity or their baseness4 #eii4 ,,of ,,painting4 ,make your work carry out your purpose and meaning4 ,that is when you draw a figure consider well who it is and what you wish it to be doing4 ,,of ,,painting4 ,with regard to any action which you give in a picture to an old man or to a young one1 you must make it more energetic in the young man in proportion as he is stronger than the old one2 and in the same way with a young man and an infant4 #fjj4 ,,of ,,setting ,,on ,,the ,,limbs4 ,the limbs which are used for labour must be muscular and those which are not much used you must make without muscles and softly rounded4 ,,of ,,the ,,action ,,of ,,the ,,figures4 ,represent your figures in such action as may be fitted to express what purpose is in the mind of each2 otherwise your art will not be admirable4 ,v4 ,,suggestions ,,for ,,compositions4 ,of painting battle pieces 7#fja-fjc74 #fja4 ,,of ,,the ,,way ,,of ,,representing ,a ,,battle4 ,first you must represent the smoke of artillery mingling in the air with the dust and tossed up by the movement of horses and the combatants4 ,and this mixture you must express thus3 ,the dust1 being a thing of earth1 has weight2 and although from its fineness it is easily tossed up and mingles with the air1 it nevertheless readily falls again4 ,it is the finest part that rises highest2 hence that part will be least seen and will look almost of the same colour as the air4 ,the higher the smoke mixed with the dust-laden air rises towards a certain level1 the more it will look like a dark cloud2 and it will be seen that at the top1 where the smoke is more separate from the dust1 the smoke will assume a bluish tinge and the dust will tend to its colour4 ,this mixture of air1 smoke and dust will look much lighter on the side whence the light comes than on the opposite side4 ,the more the combatants are in this turmoil the less will they be seen1 and the less contrast will there be in their lights and shadows4 ,their faces and figures and their appearance1 and the musketeers as well as those near them you must make of a glowing red4 ,and this glow will diminish in proportion as it is remote from its cause4 ,the figures which are between you and the light1 if they be at a distance1 will appear dark on a light background1 and the lower part of their legs near the ground will be least visible1 because there the dust is coarsest and densest #ai4 ,and if you introduce horses galloping outside the crowd1 make the little clouds of dust distant from each other in proportion to the strides made by the horses2 and the clouds which are furthest removed from the horses1 should be least visible2 make them high and spreading and thin1 and the nearer ones will be more conspicuous and smaller and denser #bc4 ,the air must be full of arrows in every direction1 some shooting upwards1 some falling1 some flying level4 ,the balls from the guns must have a train of smoke following their flight4 ,the figures in the foreground you must make with dust on the hair and eyebrows and on other flat places likely to retain it4 ,the conquerors you will make rushing onwards with their hair and other light things flying on the wind1 with their brows bent down1 ,footnote3 #ai--bc4 ,compare #fjh4 #eg--ge4 #fjb4 and with the opposite limbs thrust forward2 that is where a man puts forward the right foot the left arm must be advanced4 ,and if you make any one fallen1 you must show the place where he has slipped and been dragged along the dust into blood stained mire2 and in the half-liquid earth arround show the print of the tramping of men and horses who have passed that way4 ,make also a horse dragging the dead body of his master1 and leaving behind him1 in the dust and mud1 the track where the body was dragged along4 ,you must make the conquered and beaten pale1 their brows raised and knit1 and the skin above their brows furrowed with pain1 the sides of the nose with wrinkles going in an arch from the nostrils to the eyes1 and make the nostrils drawn up--which is the cause of the lines of which ,i speak--1 and the lips arched upwards and discovering the upper teeth2 and the teeth apart as with crying out and lamentation4 ,and make some one shielding his terrified eyes with one hand1 the palm towards the enemy1 while the other rests on the ground to support his half raised body4 ,others represent shouting with their mouths open1 and running away4 ,you must scatter arms of all sorts among the feet of the combatants1 as broken shields1 lances1 broken swords and other such objects4 ,and you must make the dead partly or entirely covered with dust1 which is changed into crimson mire where it has mingled with the flowing blood whose colour shows it issuing in a sinuous stream from the corpse4 ,others must be represented in the agonies of death grinding their teeth1 rolling their eyes1 with their fists clenched against their bodies and their legs contorted4 ,some might be shown disarmed and beaten down by the enemy1 turning upon the foe1 with teeth and nails1 to take an inhuman and bitter revenge4 ,you might see some riderless horse rushing among the enemy1 with his mane flying in the wind1 and doing no little mischief with his heels4 ,some maimed warrior may be seen fallen to the earth1 covering himself with his shield1 while the enemy1 bending over him1 tries to deal him a deathstroke4 ,there again might be seen a number of men fallen in a heap over a dead horse4 ,you would see some of the victors leaving the fight and issuing from the crowd1 rubbing their eyes and cheeks with both hands to clean them of the dirt made by their watering eyes smarting from the dust and smoke4 ,the reserves may be seen standing1 hopeful but cautious2 with watchful eyes1 shading them with their hands and gazing through the dense and murky confusion1 attentive to the commands of their captain4 ,the captain himself1 his staff raised1 hurries towards these auxiliaries1 pointing to the spot where they are most needed4 ,and there may be a river into which horses are galloping1 churning up the water all round them into turbulent waves of foam and water1 tossed into the air and among the legs and bodies of the horses4 ,and there must not be a level spot that is not trampled with gore4 #fjc4 ,,of ,,lighting ,,the ,,lower ,,parts ,,of ,,bodies ,,close ,,together1 ,,as ,,of ,,men ,,in ,,battle4 ,as to men and horses represented in battle1 their different parts will be dark in proportion as they are nearer to the ground on which they stand4 ,and this is proved by the sides of wells which grow darker in proportion to their depth1 the reason of which is that the deepest part of the well sees and receives a smaller amount of the luminous atmosphere than any other part4 ,and the pavement1 if it be of the same colour as the legs of these said men and horses1 will always be more lighted and at a more direct angle than the said legs c4 #fjd4 ,,of ,,the ,,way ,,to ,,represent ,a ,,night ,,scene4 ,that which is entirely bereft of light is all darkness2 given a night under these conditions and that you want to represent a night scene1--arrange that there shall be a great fire1 then the objects which are nearest to this fire will be most tinged with its colour2 for those objects which are nearest to a coloured light participate most in its nature2 as therefore you give the fire a red colour1 you must make all the objects illuminated by it ruddy2 while those which are farther from the fire are more tinted by the black hue of night4 ,the figures which are seen against the fire look dark in the glare of the firelight because that side of the objects which you see is tinged by the darkness of the night and not by the fire2 and those who stand at the side are half dark and half red2 while those who are visible beyond the edges of the flame will be fully lighted by the ruddy glow against a black background4 ,as to their gestures1 make those which are near it screen themselves with their hands and cloaks as a defence against the intense heat1 and with their faces turned away as if about to retire4 ,of those farther off represent several as raising their hands to screen their eyes1 hurt by the intolerable glare4 ,of depicting a tempest 7#fje4 #fjf74 #fje4 ,describe a wind on land and at sea4 ,describe a storm of rain4 #fjf4 ,,how ,,to ,,represent ,a ,,tempest4 ,if you wish to represent a tempest consider and arrange well its effects as seen1 when the wind1 blowing over the face of the sea and earth1 removes and carries with it such things as are not fixed to the general mass4 ,and to represent the storm accurately you must first show the clouds scattered and torn1 and flying with the wind1 accompanied by clouds of sand blown up from the sea shore1 and boughs and leaves swept along by the strength and fury of the blast and scattered with other light objects through the air4 ,trees and plants must be bent to the ground1 almost as if they would follow the course of the gale1 with their branches twisted out of their natural growth and their leaves tossed and turned about ,footnote #aa3 ,see ,pl4 ,,xl1 ,no4 #b44 ,of the men who are there some must have fallen to the ground and be entangled in their garments1 and hardly to be recognized for the dust1 while those who remain standing may be behind some tree1 with their arms round it that the wind may not tear them away2 others with their hands over their eyes for the dust1 bending to the ground with their clothes and hair streaming in the wind4 ,footnote #ae3 ,see ,pl4 ,,xxxiv1 the right hand lower sketch4 ,let the sea be rough and tempestuous and full of foam whirled among the lofty waves1 while the wind flings the lighter spray through the stormy air1 till it resembles a dense and swathing mist4 ,of the ships that are therein some should be shown with rent sails and the tatters fluttering through the air1 with ropes broken and masts split and fallen4 ,and the ship itself lying in the trough of the sea and wrecked by the fury of the waves with the men shrieking and clinging to the fragments of the vessel4 ,make the clouds driven by the impetuosity of the wind and flung against the lofty mountain tops1 and wreathed and torn like waves beating upon rocks2 the air itself terrible from the deep darkness caused by the dust and fog and heavy clouds4 ,of representing the deluge 7#fjg-fji74 #fjg4 ,,to ,,represent ,,the ,,deluge4 ,the air was darkened by the heavy rain whose oblique descent driven aslant by the rush of the winds1 flew in drifts through the air not otherwise than as we see dust1 varied only by the straight lines of the heavy drops of falling water4 ,but it was tinged with the colour of the fire kindled by the thunder-bolts by which the clouds were rent and shattered2 and whose flashes revealed the broad waters of the inundated valleys1 above which was seen the verdure of the bending tree tops4 ,neptune will be seen in the midst of the water with his trident1 and #ae let ,a,eolus with his winds be shown entangling the trees floating uprooted1 and whirling in the huge waves4 ,the horizon and the whole hemisphere were obscure1 but lurid from the flashes of the incessant lightning4 ,men and birds might be seen crowded on the tall trees which remained uncovered by the swelling waters1 originators of the mountains which surround the great abysses ,footnote #bc3 ,compare ,vol4 ,,ii4 ,no4 #igi44 #fjh4 ,,of ,,the ,,deluge ,,and ,,how ,,to ,,represent ,,it ,,in ,a ,,picture4 ,let the dark and gloomy air be seen buffeted by the rush of contrary winds and dense from the continued rain mingled with hail and bearing hither and thither an infinite number of branches torn from the trees and mixed with numberless leaves4 ,all round may be seen venerable trees1 uprooted and stripped by the fury of the winds2 and fragments of mountains1 already scoured bare by the torrents1 falling into those torrents and choking their valleys till the swollen rivers overflow and submerge the wide lowlands and their inhabitants4 ,again1 you might have seen on many of the hill-tops terrified animals of different kinds1 collected together and subdued to tameness1 in company with men and women who had fled there with their children4 ,the waters which covered the fields1 with their waves were in great part strewn with tables1 bedsteads1 boats and various other contrivances made from necessity and the fear of death1 on which were men and women with their children amid sounds of lamentation and weeping1 terrified by the fury of the winds which with their tempestuous violence rolled the waters under and over and about the bodies of the drowned4 ,nor was there any object lighter than the water which was not covered with a variety of animals which1 having come to a truce1 stood together in a frightened crowd--among them wolves1 foxes1 snakes and others--fleing from death4 ,and all the waters dashing on their shores seemed to be battling them with the blows of drowned bodies1 blows which killed those in whom any life remained #ai4 ,you might have seen assemblages of men who1 with weapons in their hands1 defended the small spots that remained to them against lions1 wolves and beasts of prey who sought safety there4 ,ah6 what dreadful noises were heard in the air rent by the fury of the thunder and the lightnings it flashed forth1 which darted from the clouds dealing ruin and striking all that opposed its course4 ,ah6 how many you might have seen closing their ears with their hands to shut out the tremendous sounds made in the darkened air by the raging of the winds mingling with the rain1 the thunders of heaven and the fury of the thunder-bolts4 ,others were not content with shutting their eyes1 but laid their hands one over the other to cover them the closer that they might not see the cruel slaughter of the human race by the wrath of ,god4 ,ah6 how many laments6 and how many in their terror flung themselves from the rocks6 ,huge branches of great oaks loaded with men were seen borne through the air by the impetuous fury of the winds4 ,how many were the boats upset1 some entire1 and some broken in pieces1 on the top of people labouring to escape with gestures and actions of grief foretelling a fearful death4 ,others1 with desperate act1 took their own lives1 hopeless of being able to endure such suffering2 and of these1 some flung themselves from lofty rocks1 others strangled themselves with their own hands1 other seized their own children and violently slew them at a blow2 some wounded and killed themselves with their own weapons2 others1 falling on their knees recommended themselves to ,god4 ,ah6 how many mothers wept over their drowned sons1 holding them upon their knees1 with arms raised spread out towards heaven and with words and various threatening gestures1 upbraiding the wrath of the gods4 ,others with clasped hands and fingers clenched gnawed them and devoured them till they bled1 crouching with their breast down on their knees in their intense and unbearable anguish4 ,herds of animals were to be seen1 such as horses1 oxen1 goats and swine already environed by the waters and left isolated on the high peaks of the mountains1 huddled together1 those in the middle climbing to the top and treading on the others1 and fighting fiercely themselves2 and many would die for lack of food4 ,already had the birds begun to settle on men and on other animals1 finding no land uncovered which was not occupied by living beings1 and already had famine1 the minister of death1 taken the lives of the greater number of the animals1 when the dead bodies1 now fermented1 where leaving the depth of the waters and were rising to the top4 ,among the buffeting waves1 where they were beating one against the other1 and1 like as balls full of air1 rebounded from the point of concussion1 these found a resting place on the bodies of the dead4 ,and above these judgements1 the air was seen covered with dark clouds1 riven by the forked flashes of the raging bolts of heaven1 lighting up on all sides the depth of the gloom4 ,the motion of the air is seen by the motion of the dust thrown up by the horse's running and this motion is as swift in again filling up the vacuum left in the air which enclosed the horse1 as he is rapid in passing away from the air4 ,perhaps it will seem to you that you may reproach me with having represented the currents made through the air by the motion of the wind notwithstanding that the wind itself is not visible in the air4 ,to this ,i must answer that it is not the motion of the wind but only the motion of the things carried along by it which is seen in the air4 ,,the ,,divisions4 ,footnote #gf3 ,these observations1 added at the bottom of the page containing the full description of the doluge seem to indicate that it was ,leonardo's intention to elaborate the subject still farther in a separate treatise4 ,darkness1 wind1 tempest at sea1 floods of water1 forests on fire1 rain1 bolts from heaven1 earthquakes and ruins of mountains1 overthrow of cities ,footnote #ha3 ,spianamenti di citta 7overthrow of cities74 ,a considerable number of drawings in black chalk1 at ,windsor1 illustrate this catastrophe4 ,most of them are much rubbed2 one of the least injured is reproduced at ,pl4 ,,xxxix4 ,compare also the pen and ink sketch ,pl4 ,,xxxvi44 ,whirlwinds which carry water spouts branches of trees1 and men through the air4 ,boughs stripped off by the winds1 mingling by the meeting of the winds1 with people upon them4 ,broken trees loaded with people4 ,ships broken to pieces1 beaten on rocks4 ,flocks of sheep4 ,hail stones1 thunderbolts1 whirlwinds4 ,people on trees which are unable to to support them2 trees and rocks1 towers and hills covered with people1 boats1 tables1 troughs1 and other means of floating4 ,hills covered with men1 women and animals2 and lightning from the clouds illuminating every thing4 ,footnote3 ,this chapter1 which1 with the next one1 is written on a loose sheet1 seems to be the passage to which one of the compilers of the ,vatican copy alluded when he wrote on the margin of fol4 #cf3 ,qua mi ricordo della mirabile discritione del ,diluuio dello autore4 ,it is scarcely necessary to point out that these chapters are among those which have never before been published4 ,the description in ,no4 #fjg may be regarded as a preliminary sketch for this one4 ,as the ,,ms4 ,g4 7in which it is to be found7 must be attributed to the period of about #aeae we may deduce from it the approximate date of the drawings on ,pl4 ,,xxxiv1 ,,xxxv1 ,nos4 #b and #c1 ,,xxxvi and ,,xxxvii1 since they obviously belong to this text4 ,the drawings ,no4 #b on ,pl4 ,,xxxv are1 in the original1 side by side with the text of ,no4 #fjh2 lines #eg to #gf are shown in the facsimile4 ,in the drawing in ,indian ink given on ,pl4 ,,xxxiv we see ,wind-gods in the sky1 corresponding to the allusion to ,aeolus in ,no4 #fjg #a4 #ae4-,plates ,,xxxvi and ,,xxxvii form one sheet in the original4 ,the texts reproduced on these ,plates have however no connection with the sketches1 excepting the sketches of clouds on the right hand side4 ,these texts are given as ,no4 #dgg4 ,the group of small figures on ,pl4 ,,xxxvii1 to the left1 seems to be intended for a 'congregatione d'uomini4' ,see ,no4 #fjh1 #a4 #ai4 #fji4 ,,description ,,of ,,the ,,deluge4 ,let there be first represented the summit of a rugged mountain with valleys surrounding its base1 and on its sides let the surface of the soil be seen to slide1 together with the small roots of the bushes1 denuding great portions of the surrounding rocks4 ,and descending ruinous from these precipices in its boisterous course1 let it dash along and lay bare the twisted and gnarled roots of large trees overthrowing their roots upwards2 and let the mountains1 as they are scoured bare1 discover the profound fissures made in them by ancient earthquakes4 ,the base of the mountains may be in great part clothed and covered with ruins of shrubs1 hurled down from the sides of their lofty peaks1 which will be mixed with mud1 roots1 boughs of trees1 with all sorts of leaves thrust in with the mud and earth and stones4 ,and into the depth of some valley may have fallen the fragments of a mountain forming a shore to the swollen waters of its river2 which1 having already burst its banks1 will rush on in monstrous waves2 and the greatest will strike upon and destroy the walls of the cities and farmhouses in the valley #ad4 ,then the ruins of the high buildings in these cities will throw up a great dust1 rising up in shape like smoke or wreathed clouds against the falling rain2 ,but the swollen waters will sweep round the pool which contains them striking in eddying whirlpools against the different obstacles1 and leaping into the air in muddy foam2 then1 falling back1 the beaten water will again be dashed into the air4 ,and the whirling waves which fly from the place of concussion1 and whose impetus moves them across other eddies going in a contrary direction1 after their recoil will be tossed up into the air but without dashing off from the surface4 ,where the water issues from the pool the spent waves will be seen spreading out towards the outlet2 and there falling or pouring through the air and gaining weight and impetus they will strike on the water below piercing it and rushing furiously to reach its depth2 from which being thrown back it returns to the surface of the lake1 carrying up the air that was submerged with it2 and this remains at the outlet in foam mingled with logs of wood and other matters lighter than water4 ,round these again are formed the beginnings of waves which increase the more in circumference as they acquire more movement2 and this movement rises less high in proportion as they acquire a broader base and thus they are less conspicuous as they die away4 ,but if these waves rebound from various objects they then return in direct opposition to the others following them1 observing the same law of increase in their curve as they have already acquired in the movement they started with4 ,the rain1 as it falls from the clouds is of the same colour as those clouds1 that is in its shaded side2 unless indeed the sun's rays should break through them2 in that case the rain will appear less dark than the clouds4 ,and if the heavy masses of ruin of large mountains or of other grand buildings fall into the vast pools of water1 a great quantity will be flung into the air and its movement will be in a contrary direction to that of the object which struck the water2 that is to say3 ,the angle of reflection will be equal to the angle of incidence4 ,of the objects carried down by the current1 those which are heaviest or rather largest in mass will keep farthest from the two opposite shores4 ,the water in the eddies revolves more swiftly in proportion as it is nearer to their centre4 ,the crests of the waves of the sea tumble to their bases falling with friction on the bubbles of their sides2 and this friction grinds the falling water into minute particles and this being converted into a dense mist1 mingles with the gale in the manner of curling smoke and wreathing clouds1 and at last it1 rises into the air and is converted into clouds4 ,but the rain which falls through the atmosphere being driven and tossed by the winds becomes rarer or denser according to the rarity or density of the winds that buffet it1 and thus there is generated in the atmosphere a moisture formed of the transparent particles of the rain which is near to the eye of the spectator4 ,the waves of the sea which break on the slope of the mountains which bound it1 will foam from the velocity with which they fall against these hills2 in rushing back they will meet the next wave as it comes and and after a loud noise return in a great flood to the sea whence they came4 ,let great numbers of inhabitants--men and animals of all kinds--be seen driven #ed by the rising of the deluge to the peaks of the mountains in the midst of the waters aforesaid4 ,the wave of the sea at ,piombino is all foaming water4 ,footnote #ee4 #ef3 ,these two lines are written below the bottom sketch on ,pl4 ,,xxxv1 #c4 ,the ,,ms4 ,leic4 being written about the year #aeaj or later1 it does not seem to me to follow that the sketches must have been made at ,piombino1 where ,leonardo was in the year #aejb and possibly returned there subsequently 7see ,vol4 ,,ii4 ,topographical notes74 ,of the water which leaps up from the spot where great masses fall on its surface4 ,of the winds of ,piombino at ,piombino4 ,eddies of wind and rain with boughs and shrubs mixed in the air4 ,emptying the boats of the rain water4 ,footnote3 ,the sketches on ,pl4 ,,xxxv #c stand by the side of lines #ad to #ed4 ,of depicting natural phenomena 7#faj4 #faa74 #faj4 ,the tremendous fury of the wind driven by the falling in of the hills on the caves within--by the falling of the hills which served as roofs to these caverns4 ,a stone flung through the air leaves on the eye which sees it the impression of its motion1 and the same effect is produced by the drops of water which fall from the clouds when it #af rains4 #ag ,a mountain falling on a town1 will fling up dust in the form of clouds2 but the colour of this dust will differ from that of the clouds4 ,where the rain is thickest let the colour of the dust be less conspicuous and where the dust is thickest let the rain be less conspicuous4 ,and where the rain is mingled with the wind and with the dust the clouds created by the rain must be more transparent than those of dust alone4 ,and when flames of fire are mingled with clouds of smoke and water very opaque and dark clouds will be formed ,footnote #bf-bh3 ,compare ,pl4 ,,xl1 #a--the drawing in ,indian ink on the left hand side1 which seems to be a reminiscence of his observations of an eruption 7see his remarks on ,mount ,etna in ,vol ,,ii744 ,and the rest of this subject will be treated in detail in the book on painting4 ,footnote3 ,see the sketches and text on ,pl4 ,,xxxviii1 ,no4 #a4 ,lines #a-af are there given on the left hand side1 #ag-cj on the right4 ,the four lines at the bottom on the right are given as ,no4 #dgb4 ,above these texts1 which are written backwards1 there are in the original sixteen lines in a larger writing from left to right1 but only half of this is here visible4 ,they treat of the physical laws of motion of air and water4 ,it does not seem to me that there is any reason for concluding that this writing from left to right is spurious4 ,compare with it the facsimile of the rough copy of ,leonardo's letter to ,ludovico il ,moro in ,vol4 ,,ii4 #faa4 ,people were to be seen eagerly embarking victuals on various kinds of hastily made barks4 ,but little of the waves were visible in those places where the dark clouds and rain were reflected4 ,but where the flashes caused by the bolts of heaven were reflected1 there were seen as many bright spots1 caused by the image of the flashes1 as there were waves to reflect them to the eye of the spectator4 ,the number of the images produced by the flash of lightning on the waves of the water were multiplied in proportion to the distance of the spectator's eye4 ,so also the number of the images was diminished in proportion as they were nearer the eye which saw them ,footnote #bb4 #bc3 ,com'e provato4 ,see ,vol4 ,,ii1 ,nos4 #hgd-hgh and #hib-ija1 as it has been proved in the definition of the luminosity of the moon1 and of our marine horizon when the sun's rays are reflected in it and the eye which receives the reflection is remote from the sea4 ,,vi4 ,,the ,,artist',s ,,materials4 ,of chalk and paper 7#fab--fag74 #fab4 ,to make points crayons for colouring dry4 ,temper with a little wax and do not dry it2 which wax you must dissolve with water3 so that when the white lead is thus tempered1 the water being distilled1 may go off in vapour and the wax may remain2 you will thus make good crayons2 but you must know that the colours must be ground with a hot stone4 #fac4 ,chalk dissolves in wine and in vinegar or in aqua fortis and can be recombined with gum4 #fad4 ,,paper ,,for ,,drawing ,,upon ,,in ,,black ,,by ,,the ,,aid ,,of ,,your ,,spittle4 ,take powdered gall nuts and vitriol1 powder them and spread them on paper like a varnish1 then write on it with a pen wetted with spittle and it will turn as black as ink4 #fae4 ,if you want to make foreshortened letters stretch the paper in a drawing frame and then draw your letters and cut them out1 and make the sunbeams pass through the holes on to another stretched paper1 and then fill up the angles that are wanting4 #faf4 ,this paper should be painted over with candle soot tempered with thin glue1 then smear the leaf thinly with white lead in oil as is done to the letters in printing1 and then print in the ordinary way4 ,thus the leaf will appear shaded in the hollows and lighted on the parts in relief2 which however comes out here just the contrary4 ,footnote3 ,this text1 which accompanies a facsimile impression of a leaf of sage1 has already been published in the ,saggio delle ,opere di ,l4 da ,vinci1 ,milano #ahgb1 p4 #aa4 ,g4 ,,govi observes on this passage3 ,forse aveva egli pensato ancora a farsi un erbario1 od almeno a riprodurre facilmente su carta le forme e i particolari delle foglie di diverse piante2 poiche 7modificando un metodo che probabilmente gli eia stato insegnato da altri1 e che piu tardi si legge ripetuto in molti ricettarii e libri di segreti71 accanto a una foglia di ,salvia impressa in nero su carta bianca1 lascio scritto3 ,questa carta 444 ,erano i primi tentativi di quella riproduzione immediata delle parti vegetali1 che poi sotto il nome d',impressione ,naturale1 fu condotta a tanta perfezione in questi ultimi tempi dal signor de ,hauer e da altri4 #fag4 ,very excellent will be a stiff white paper1 made of the usual mixture and filtered milk of an herb called calves foot2 and when this paper is prepared and damped and folded and wrapped up it may be mixed with the mixture and thus left to dry2 but if you break it before it is moistened it becomes somewhat like the thin paste called lasagne and you may then damp it and wrap it up and put it in the mixture and leave it to dry2 or again this paper may be covered with stiff transparent white and sardonio and then damped so that it may not form angles and then covered up with strong transparent size and as soon as it is firm cut it two fingers1 and leave it to dry2 again you may make stiff cardboard of sardonio and dry it and then place it between two sheets of papyrus and break it inside with a wooden mallet with a handle and then open it with care holding the lower sheet of paper flat and firm so that the broken pieces be not separated2 then have a sheet of paper covered with hot glue and apply it on the top of all these pieces and let them stick fast2 then turn it upside down and apply transparent size several times in the spaces between the pieces1 each time pouring in first some black and then some stiff white and each time leaving it to dry2 then smooth it and polish it4 ,on the preparation and use of colours 7#fah-fbg74 #fah4 ,to make a fine green take green and mix it with bitumen and you will make the shadows darker4 ,then1 for lighter shades green with yellow ochre1 and for still lighter green with yellow1 and for the high lights pure yellow2 then mix green and turmeric together and glaze every thing with it4 ,to make a fine red take cinnabar or red chalk or burnt ochre for the dark shadows and for the lighter ones red chalk and vermilion and for the lights pure vermilion and then glaze with fine lake4 ,to make good oil for painting4 ,one part of oil1 one of the first refining and one of the second4 #fai4 ,use black in the shadow1 and in the lights white1 yellow1 green1 vermilion and lake4 ,medium shadows2 take the shadow as above and mix it with the flesh tints just alluded to1 adding to it a little yellow and a little green and occasionally some lake2 for the shadows take green and lake for the middle shades4 ,footnote #fah and #fai3 ,if we may judge from the flourishes with which the writing is ornamented these passages must have been written in ,leonardo's youth4 #fbj4 ,you can make a fine ochre by the same method as you use to make white4 #fba4 ,a ,,fine ,,yellow4 ,dissolve realgar with one part of orpiment1 with aqua fortis4 ,,white4 ,put the white into an earthen pot1 and lay it no thicker than a string1 and let it stand in the sun undisturbed for #b days2 and in the morning when the sun has dried off the night dews4 #fbb4 ,to make reddish black for flesh tints take red rock crystals from ,rocca ,nova or garnets and mix them a little2 again armenian bole is good in part4 #fbc4 ,the shadow will be burnt 1terra-verte'4 #fbd4 ,,the ,,proportions ,,of ,,colours4 ,if one ounce of black mixed with one ounce of white gives a certain shade of darkness1 what shade of darkness will be produced by #b ounces of black to #a ounce of white8 #fbe4 ,remix black1 greenish yellow and at the end blue4 #fbf4 ,verdigris with aloes1 or gall or turmeric makes a fine green and so it does with saffron or burnt orpiment2 but ,i doubt whether in a short time they will not turn black4 ,ultramarine blue and glass yellow mixed together make a beautiful green for fresco1 that is wall-painting4 ,lac and verdigris make a good shadow for blue in oil painting4 #fbg4 ,grind verdigris many times coloured with lemon juice and keep it away from yellow 7874 ,of preparing the panel4 #fbh4 ,,to ,,prepare ,a ,,panel ,,for ,,painting ,,on4 ,the panel should be cypress or pear or service-tree or walnut4 ,you must coat it over with mastic and turpentine twice distilled and white or1 if you like1 lime1 and put it in a frame so that it may expand and shrink according to its moisture and dryness4 ,then give it a coat of aqua vitae in which you have dissolved arsenic or corrosive sublimate1 #b or #c times4 ,then apply boiled linseed oil in such a way as that it may penetrate every part1 and before it is cold rub it well with a cloth to dry it4 ,over this apply liquid varnish and white with a stick1 then wash it with urine when it is dry1 and dry it again4 ,then pounce and outline your drawing finely and over it lay a priming of #cj parts of verdigris with one of verdigris with two of yellow4 ,footnote3 ,m4 ,,ravaisson',s reading varies from mine in the following passages3 #a4opero allor 8 bo alloro8 ou bien de laurier4 #f4 fregalo bene con un panno4 ,he reads pane for panno and renders it4 ,frotte le bien avec un pain de facon jusqu'a ce qu'il etc4 #g4 colla stecca po laua4 ,he reads polacca avec le couteau de bois 8 polonais 84 ,the preparation of oils 7#fbi--fcd74 #fbi4 ,,oil4 ,make some oil of mustard seed2 and if you wish to make it with greater ease mix the ground seeds with linseed oil and put it all under the press4 #fcj4 ,,to ,,remove ,,the ,,smell ,,of ,,oil4 ,take the rank oil and put ten pints into a jar and make a mark on the jar at the height of the oil2 then add to it a pint of vinegar and make it boil till the oil has sunk to the level of the mark and thus you will be certain that the oil is returned to its original quantity and the vinegar will have gone off in vapour1 carrying with it the evil smell2 and ,i believe you may do the same with nut oil or any other oil that smells badly4 #fca4 ,since walnuts are enveloped in a thin rind1 which partakes of the nature of 4441 if you do not remove it when you make the oil from them1 this skin tinges the oil1 and when you work with it this skin separates from the oil and rises to the surface of the painting1 and this is what makes it change4 #fcb4 ,,to ,,restore ,,oil ,,colours ,,that ,,have ,,become ,,dry4 ,if you want to restore oil colours that have become dry keep them soaking in soft soap for a night and1 with your finger1 mix them up with the soft soap2 then pour them into a cup and wash them with water1 and in this way you can restore colours that have got dry4 ,but take care that each colour has its own vessel to itself adding the colour by degrees as you restore it and mind that they are thoroughly softened1 and when you wish to use them for tempera wash them five and six times with spring water1 and leave them to settle2 if the soft soap should be thick with any of the colours pass it through a filter4 ,footnote3 ,the same remark applies to these sections as to ,no4 #fah and #fai4 #fcc4 ,,oil4 ,mustard seed pounded with linseed oil4 #fcd4 444 outside the bowl #b fingers lower than the level of the oil1 and pass it into the neck of a bottle and let it stand and thus all the oil will separate from this milky liquid2 it will enter the bottle and be as clear as crystal2 and grind your colours with this1 and every coarse or viscid part will remain in the liquid4 ,you must know that all the oils that have been created in seads or fruits are quite clear by nature1 and the yellow colour you see in them only comes of your not knowing how to draw it out4 ,fire or heat by its nature has the power to make them acquire colour4 ,see for example the exudation or gums of trees which partake of the nature of rosin2 in a short time they harden because there is more heat in them than in oil2 and after some time they acquire a certain yellow hue tending to black4 ,but oil1 not having so much heat does not do so2 although it hardens to some extent into sediment it becomes finer4 ,the change in oil which occurs in painting proceeds from a certain fungus of the nature of a husk which exists in the skin which covers the nut1 and this being crushed along with the nuts and being of a nature much resembling oil mixes with it2 it is of so subtle a nature that it combines with all colours and then comes to the surface1 and this it is which makes them change4 ,and if you want the oil to be good and not to thicken1 put into it a little camphor melted over a slow fire and mix it well with the oil and it will never harden4 ,footnote3 ,the same remark applies to these sections as to ,no4 #fah and #fai4 ,on varnishes or powders 7#fce-fcg74 #fce4 ,,varnish ,,or ,,powder4 ,take cypress oil and distil it and have a large pitcher1 and put in the extract with so much water as may make it appear like amber1 and cover it tightly so that none may evaporate4 ,and when it is dissolved you may add in your pitcher as much of the said solution1 as shall make it liquid to your taste4 ,and you must know that amber is the gum of the cypress-tree4 ,,varnish ,,or ,,powder4 ,and since varnish powder is the resin of juniper1 if you distil juniper you can dissolve the said varnish powder in the essence1 as explained above4 #fcf4 ,,varnish ,,or ,,powder4 ,notch a juniper tree and give it water at the roots1 mix the liquor which exudes with nut-oil and you will have a perfect varnish powder1 made like amber varnish powder1 fine and of the best quality make it in ,may or ,april4 #fcg4 ,,varnish ,,or ,,powder4 ,mercury with ,jupiter and ,venus1--a paste made of these must be corrected by the mould 787 continuously1 until ,mercury separates itself entirely from ,jupiter and ,venus4 ,footnote3 ,here1 and in ,no4 #fda ,mercurio seems to mean quicksilver1 ,giove stands for iron1 ,venere for copper and ,saturno for lead4 ,on chemical materials 7#fch-fej74 #fch4 ,note how aqua vitae absorbs into itself all the colours and smells of flowers4 ,if you want to make blue put iris flowers into it and for red solanum berries 787 #fci4 ,salt may be made from human excrement burnt and calcined and made into lees1 and dried by a slow fire1 and all dung in like manner yields salt1 and these salts when distilled are very pungent4 #fdj4 ,sea water filtered through mud or clay1 leaves all its saltness in it4 ,woollen stuffs placed on board ship absorb fresh water4 ,if sea water is distilled under a retort it becomes of the first excellence and any one who has a little stove in his kitchen can1 with the same wood as he cooks with1 distil a great quantity of water if the retort is a large one4 #fda4 ,,mould7874 ,the mould 787 may be of ,venus1 or of ,jupiter and ,saturn and placed frequently in the fire4 ,and it should be worked with fine emery and the mould 787 should be of ,venus and ,jupiter impasted over 787 ,venus4 ,but first you will test ,venus and ,mercury mixed with ,jove1 and take means to cause ,mercury to disperse2 and then fold them well together so that ,venus or ,jupiter be connected as thinly as possible4 ,footnote3 ,see the note to #fcg4 #fdb4 ,nitre1 vitriol1 cinnabar1 alum1 salt ammoniac1 sublimated mercury1 rock salt1 alcali salt1 common salt1 rock alum1 alum schist 7871 arsenic1 sublimate1 realgar1 tartar1 orpiment1 verdegris4 #fdc4 ,pitch four ounces virgin wax1 four ounces incense1 two ounces oil of roses one ounce4 #fdd4 ,four ounces virgin wax1 four ounces ,greek pitch1 two ounces incense1 one ounce oil of roses1 first melt the wax and oil then the ,greek pitch then the other things in powder4 #fde4 ,very thin glass may be cut with scissors and when placed over inlaid work of bone1 gilt1 or stained of other colours you can saw it through together with the bone and then put it together and it will retain a lustre that will not be scratched nor worn away by rubbing with the hand4 #fdf4 ,,to ,,dilute ,,white ,,wine ,,and ,,make ,,it ,,purple4 ,powder gall nuts and let this stand #h days in the white wine2 and in the same way dissolve vitriol in water1 and let the water stand and settle very clear1 and the wine likewise1 each by itself1 and strain them well2 and when you dilute the white wine with the water the wine will become red4 #fdg4 ,put marcasite into aqua fortis and if it turns green1 know that it has copper in it4 ,take it out with saltpetre and soft soap4 #fdh4 ,a white horse may have the spots removed with the ,spanish haematite or with aqua fortis or with 444 ,removes the black hair on a white horse with the singeing iron4 ,force him to the ground4 #fdi4 ,,fire4 ,if you want to make a fire which will set a hall in a blaze without injury do this3 first perfume the hall with a dense smoke of incense or some other odoriferous substance3 ,it is a good trick to play4 ,or boil ten pounds of brandy to evaporate1 but see that the hall is completely closed and throw up some powdered varnish among the fumes and this powder will be supported by the smoke2 then go into the room suddenly with a lighted torch and at once it will be in a blaze4 #fej4 ,,fire4 ,take away that yellow surface which covers oranges and distill them in an alembic1 until the distillation may be said to be perfect4 ,,fire4 ,close a room tightly and have a brasier of brass or iron with fire in it and sprinkle on it two pints of aqua vitae1 a little at a time1 so that it may be converted into smoke4 ,then make some one come in with a light and suddenly you will see the room in a blaze like a flash of lightning1 and it will do no harm to any one4 ,,vii4 ,,philosophy ,,and ,,history ,,of ,,the ,,art ,,of ,,painting4 ,the relation of art and nature 7#fea4 #feb74 #fea4 ,what is fair in men1 passes away1 but not so in art4 #feb4 ,,he ,,who ,,despises ,,painting ,,loves ,,neither ,,philosophy ,,nor ,,nature4 ,if you condemn painting1 which is the only imitator of all visible works of nature1 you will certainly despise a subtle invention which brings philosophy and subtle speculation to the consideration of the nature of all forms--seas and plains1 trees1 animals1 plants and flowers--which are surrounded by shade and light4 ,and this is true knowledge and the legitimate issue of nature2 for painting is born of nature--or1 to speak more correctly1 we will say it is the grandchild of nature2 for all visible things are produced by nature1 and these her children have given birth to painting4 ,hence we may justly call it the grandchild of nature and related to ,god4 ,painting is superior to poetry 7#fec4 #fed74 #fec4 ,,that ,,painting ,,surpasses ,,all ,,human ,,works ,,by ,,the ,,subtle ,,considerations ,,belonging ,,to ,,it4 ,the eye1 which is called the window of the soul1 is the principal means by which the central sense can most completely and abundantly appreciate the infinite works of nature2 and the ear is the second1 which acquires dignity by hearing of the things the eye has seen4 ,if you1 historians1 or poets1 or mathematicians had not seen things with your eyes you could not report of them in writing4 ,and if you1 #j poet1 tell a story with your pen1 the painter with his brush can tell it more easily1 with simpler completeness and less tedious to be understood4 ,and if you call painting dumb poetry1 the painter may call poetry blind painting4 ,now which is the worse defect8 to be blind or dumb8 ,though the poet is as free as the painter in the invention of his fictions they are not so satisfactory to men as paintings2 for1 though poetry is able to describe forms1 actions and places in words1 the painter deals with the actual similitude of the forms1 in order to represent them4 ,now tell me which is the nearer to the actual man3 the name of man or the image of the man4 ,the name of man differs in different countries1 but his form is never changed but by death4 #fed4 ,and if the poet gratifies the sense by means of the ear1 the painter does so by the eye--the worthier sense2 but ,i will say no more of this but that1 if a good painter represents the fury of a battle1 and if a poet describes one1 and they are both together put before the public1 you will see where most of the spectators will stop1 to which they will pay most attention1 on which they will bestow most praise1 and which will satisfy them best4 ,undoubtedly painting being by a long way the more intelligible and beautiful1 will please most4 ,write up the name of ,god ,christ in some spot and setup ,his image opposite and you will see which will be most reverenced4 ,painting comprehends in itself all the forms of nature1 while you have nothing but words1 which are not universal as form is1 and if you have the effects of the representation1 we have the representation of the effects4 ,take a poet who describes the beauty of a lady to her lover and a painter who represents her and you will see to which nature guides the enamoured critic4 ,certainly the proof should be allowed to rest on the verdict of experience4 ,you have ranked painting among the mechanical arts but1 in truth1 if painters were as apt at praising their own works in writing as you are1 it would not lie under the stigma of so base a name4 ,if you call it mechanical because it is1 in the first place1 manual1 and that it is the hand which produces what is to be found in the imagination1 you too writers1 who set down manually with the pen what is devised in your mind4 ,and if you say it is mechanical because it is done for money1 who falls into this error--if error it can be called--more than you8 ,if you lecture in the schools do you not go to whoever pays you most8 ,do you do any work without pay8 ,still1 ,i do not say this as blaming such views1 for every form of labour looks for its reward4 ,and if a poet should say3 ,i will invent a fiction with a great purpose1 the painter can do the same1 as ,apelles painted ,calumny4 ,if you were to say that poetry is more eternal1 ,i say the works of a coppersmith are more eternal still1 for time preserves them longer than your works or ours2 nevertheless they have not much imagination #bi4 ,and a picture1 if painted on copper with enamel colours may be yet more permanent4 ,we1 by our arts may be called the grandsons of ,god4 ,if poetry deals with moral philosophy1 painting deals with natural philosophy4 ,poetry describes the action of the mind1 painting considers what the mind may effect by the motions of the body4 ,if poetry can terrify people by hideous fictions1 painting can do as much by depicting the same things in action4 ,supposing that a poet applies himself to represent beauty1 ferocity1 or a base1 a foul or a monstrous thing1 as against a painter1 he may in his ways bring forth a variety of forms2 but will the painter not satisfy more8 are there not pictures to be seen1 so like the actual things1 that they deceive men and animals8 ,painting is superior to sculpture 7#fee4 #fef74 #fee4 ,,that ,,sculpture ,,is ,,less ,,intellectual ,,than ,,painting1 ,,and ,,lacks ,,many ,,characteristics ,,of ,,nature4 ,i myself1 having exercised myself no less in sculpture than in painting and doing both one and the other in the same degree1 it seems to me that ,i can1 without invidiousness1 pronounce an opinion as to which of the two is of the greatest merit and difficulty and perfection4 ,in the first place sculpture requires a certain light1 that is from above1 a picture carries everywhere with it its own light and shade4 ,thus sculpture owes its importance to light and shade1 and the sculptor is aided in this by the nature1 of the relief which is inherent in it1 while the painter whose art expresses the accidental aspects of nature1 places his effects in the spots where nature must necessarily produce them4 ,the sculptor cannot diversify his work by the various natural colours of objects2 painting is not defective in any particular4 ,the sculptor when he uses perspective cannot make it in any way appear true2 that of the painter can appear like a hundred miles beyond the picture itself4 ,their works have no aerial perspective whatever1 they cannot represent transparent bodies1 they cannot represent luminous bodies1 nor reflected lights1 nor lustrous bodies--as mirrors and the like polished surfaces1 nor mists1 nor dark skies1 nor an infinite number of things which need not be told for fear of tedium4 ,as regards the power of resisting time1 though they have this resistance ,footnote #ai3 ,from what is here said as to painting on copper it is very evident that ,leonardo was not acquainted with the method of painting in oil on thin copper plates1 introduced by the ,flemish painters of the ,x,v,i,ith century4 ,j4 ,,lermolieff has already pointed out that in the various collections containing pictures by the great masters of the ,italian ,renaissance1 those painted on copper 7for instance the famous reading ,magdalen in the ,dresden ,gallery7 are the works of a much later date 7see ,zeitschrift fur bildende ,kunst4 ,vol4 ,x pg4 #ccc1 and3 ,werke italienischer ,master in den ,galerien von ,munchen1 ,dresden und ,berlin4 ,leipzig #ahhj1 pg4 #aeh and #aei47--;,compare ,no4 #fed1 #bi41 a picture painted on thick copper covered with white enamel on which it is painted with enamel colours and then put into the fire again and baked1 far exceeds sculpture in permanence4 ,it may be said that if a mistake is made it is not easy to remedy it2 it is but a poor argument to try to prove that a work be the nobler because oversights are irremediable2 ,i should rather say that it will be more difficult to improve the mind of the master who makes such mistakes than to repair the work he has spoilt4 #fef4 ,we know very well that a really experienced and good painter will not make such mistakes2 on the contrary1 with sound rules he will remove so little at a time that he will bring his work to a good issue4 ,again the sculptor if working in clay or wax1 can add or reduce1 and when his model is finished it can easily be cast in bronze1 and this is the last operation and is the most permanent form of sculpture4 ,inasmuch as that which is merely of marble is liable to ruin1 but not bronze4 ,hence a painting done on copper which as ,i said of painting may be added to or altered1 resembles sculpture in bronze1 which1 having first been made in wax could then be altered or added to2 and if sculpture in bronze is durable1 this work in copper and enamel is absolutely imperishable4 ,bronze is but dark and rough after all1 but this latter is covered with various and lovely colours in infinite variety1 as has been said above2 or if you will have me only speak of painting on panel1 ,i am content to pronounce between it and sculpture2 saying that painting is the more beautiful and the more imaginative and the more copious1 while sculpture is the more durable but it has nothing else4 ,sculpture shows with little labour what in painting appears a miraculous thing to do2 to make what is impalpable appear palpable1 flat objects appear in relief1 distant objects seem close4 ,in fact painting is adorned with infinite possibilities which sculpture cannot command4 ,aphorisms 7#feg-fei74 #feg4 ,,of ,,painting4 ,men and words are ready made1 and you1 ,o ,painter1 if you do not know how to make your figures move1 are like an orator who knows not how to use his words4 #feh4 ,as soon as the poet ceases to represent in words what exists in nature1 he in fact ceases to resemble the painter2 for if the poet1 leaving such representation1 proceeds to describe the flowery and flattering speech of the figure1 which he wishes to make the speaker1 he then is an orator and no longer a poet nor a painter4 ,and if he speaks of the heavens he becomes an astrologer1 and philosopher2 and a theologian1 if he discourses of nature or ,god4 ,but1 if he restricts himself to the description of objects1 he would enter the lists against the painter1 if with words he could satisfy the eye as the painter does4 #fei4 ,though you may be able to tell or write the exact description of forms1 the painter can so depict them that they will appear alive1 with the shadow and light which show the expression of a face2 which you cannot accomplish with the pen though it can be achieved by the brush4 ,on the history of painting 7#ffj4 #ffa74 #ffj4 ,,that ,,painting ,,declines ,,and ,,deteriorates ,,from ,,age ,,to ,,age1 ,,when ,,painters ,,have ,,no ,,other ,,standard ,,than ,,painting ,,already ,,done4 ,hence the painter will produce pictures of small merit if he takes for his standard the pictures of others4 ,but if he will study from natural objects he will bear good fruit2 as was seen in the painters after the ,romans who always imitated each other and so their art constantly declined from age to age4 ,after these came ,giotto the ,florentine who--not content with imitating the works of ,cimabue his master--being born in the mountains and in a solitude inhabited only by goats and such beasts1 and being guided by nature to his art1 began by drawing on the rocks the movements of the goats of which he was keeper4 ,and thus he began to draw all the animals which were to be found in the country1 and in such wise that after much study he excelled not only all the masters of his time but all those of many bygone ages4 ,afterwards this art declined again1 because everyone imitated the pictures that were already done2 thus it went on from century to century until ,tomaso1 of ,florence1 nicknamed ,masaccio1 showed by his perfect works how those who take for their standard any one but nature--the mistress of all masters--weary themselves in vain4 ,and1 ,i would say about these mathematical studies that those who only study the authorities and not the works of nature are descendants but not sons of nature the mistress of all good authors4 ,oh6 how great is the folly of those who blame those who learn from nature ,footnote #bb3 lasciando stare li autori4 ,in this observation we may detect an indirect evidence that ,leonardo regarded his knowledge of natural history as derived from his own investigations1 as well as his theories of perspective and optics4 ,compare what he says in praise of experience 7,vol ,,ii2 ,,xix741 setting aside those authorities who themselves were the disciples of nature4 #ffa4 ,that the first drawing was a simple line drawn round the shadow of a man cast by the sun on a wall4 ,the painter's scope4 #ffb4 ,the painter strives and competes with nature4 ,x4 ,studies and ,sketches for ,pictures and ,decorations4 ,an artist's manuscript notes can hardly be expected to contain any thing more than incidental references to those masterpieces of his work of which the fame1 sounded in the writings of his contemporaries1 has left a glorious echo to posterity4 ,we need not therefore be surprised to find that the texts here reproduced do not afford us such comprehensive information as we could wish4 ,on the other hand1 the sketches and studies prepared by ,leonardo for the two grandest compositions he ever executed3 ,the ,fresco of the ,last ,supper in the ,refectory of ,santa ,maria delle ,grazie at ,milan1 and the ,cartoon of the ,battle of ,anghiari1 for the ,palazzo della ,signoria at ,florence--have been preserved2 and1 though far from complete1 are so much more numerous than the manuscript notes1 that we are justified in asserting that in value and interest they amply compensate for the meagerness of the written suggestions4 ,the notes for the composition of the ,last ,supper1 which are given under nos4 #ffe and #fff occur in a ,,ms4 at ,south ,kensington1 ,,ii#b1 written in the years #adid-adie4 ,this ,,ms4 sketch was noted down not more than three or four years before the painting was executed1 which justifies the inference that at the time when it was written the painter had not made up his mind definitely even as to the general scheme of the work2 and from this we may also conclude that the drawings of apostles' heads at ,windsor1 in red chalk1 must be ascribed to a later date4 ,they are studies for the head of ,st4 ,matthew1 the fourth figure on ,christ's left hand--see ,pl4 ,,xl ,,vii1 the sketch 7in black chalk7 for the head of ,st4 ,philip1 the third figure on the left hand--see ,pl4 ,,xl ,,viii1 for ,st4 ,peter's right arm--see ,pl4 ,,xlix1 and for the expressive head of ,judas which has unfortunately somewhat suffered by subsequent restoration of outlines1--see ,pl4 ,l4 ,according to a tradition1 as unfounded as it is improbable1 ,leonardo made use of the head of ,padre ,bandelli1 the prior of the convent1 as the prototype of his ,judas2 this however has already been contradicted by ,amoretti ,memorie storiche cap4 ,,xiv4 ,the study of the head of a criminal on ,pl4 ,,li has1 it seems to me1 a better claim to be regarded as one of the preparatory sketches for the head of ,judas4 ,the ,windsor collection contains two old copies of the head of ,st4 ,simon1 the figure to the extreme left of ,christ1 both of about equal merit 7they are marked as ,nos4 #ba and #cf7--the second was reproduced on ,pl4 ,,viii of the ,grosvenor ,gallery ,publication in #ahgh4 ,there is also at ,windsor a drawing in black chalk of folded hands 7marked with the old ,no4 #bab2 ,no4 ,,lxi of the ,grosvenor ,gallery ,publication7 which ,i believe to be a copy of the hands of ,st4 ,john1 by some unknown pupil4 ,a reproduction of the excellent drawings of heads of ,apostles in the possession of ,h4 ,r4 ,h4 the ,grand ,duchess of ,weimar would have been out of my province in this work1 and1 with regard to them1 ,i must confine myself to pointing out that the difference in style does not allow of our placing the ,weimar drawings in the same category as those here reproduced4 ,the mode of grouping in the ,weimar drawings is of itself sufficient to indicate that they were not executed before the picture was painted1 but1 on the contrary1 afterwards1 and it is1 on the face of it1 incredible that so great a master should thus have copied from his own work4 ,the drawing of ,christ's head1 in the ,brera palace at ,milan was perhaps originally the work of ,leonardo's hand2 it has unfortunately been entirely retouched and re-drawn1 so that no decisive opinion can be formed as to its genuineness4 ,the red chalk drawing reproduced on ,pl4 ,,xlvi is in the ,accademia at ,venice2 it was probably made before the text1 ,nos4 #ffd and #ffe1 was written4 ,the two pen and ink sketches on ,pl4 ,,xlv seem to belong to an even earlier date2 the more finished drawing of the two1 on the right hand1 represents ,christ with only ,st4 ,john and ,judas and a third disciple whose action is precisely that described in ,no4 #fff1 ,pl4 #d4 ,it is hardly necessary to observe that the other sketches on this page and the lines of text below the circle 7containing the solution of a geometrical problem7 have no reference to the picture of the ,last ,supper4 ,with this figure of ,christ may be compared a similar pen and ink drawing reproduced on page #big below on the left hand2 the original is in the ,louvre4 ,on this page again the rest of the sketches have no direct bearing on the composition of the ,last ,supper1 not even1 as it seems to me1 the group of four men at the bottom to the right hand--who are listening to a fifth1 in their midst addressing them4 ,moreover the writing on this page 7an explanation of a disk shaped instrument7 is certainly not in the same style as we find constantly used by ,leonardo after the year #adhi4 ,it may be incidentally remarked that no sketches are known for the portrait of ,mona ,lisa1 nor do the ,,ms4 notes ever allude to it1 though according to ,vasari the master had it in hand for fully four years4 ,leonardo's cartoon for the picture of the battle of ,anghiari has shared the fate of the rival work1 ,michaelangelo's ,bathers summoned to ,battle4 ,both have been lost in some wholly inexplicable manner4 ,i cannot here enter into the remarkable history of this work2 ,i can only give an account of what has been preserved to us of ,leonardo's scheme and preparations for executing it4 ,the extent of the material in studies and drawings was till now quite unknown4 ,their publication here may give some adequate idea of the grandeur of this famous work4 ,the text given as ,no4 #ffi contains a description of the particulars of the battle1 but for the reasons given in the note to this text1 ,i must abandon the idea of taking this passage as the basis of my attempt to reconstruct the picture as the artist conceived and executed it4 ,i may here remind the reader that ,leonardo prepared the cartoon in the ,sala del ,papa of ,santa ,maria ,novella at ,florence and worked there from the end of ,october #aejc till ,february #aejd1 and then was busied with the painting in the ,sala del ,consiglio in the ,palazzo della ,signoria1 till the work was interrupted at the end of ,may #aejf4 7,see ,milanesi's note to ,vasari pp4 #dc--de ,vol4 ,,iv ed4 #ahhj47 ,vasari1 as is well known1 describes only one scene or episode of the cartoon--the ,battle for the ,standard in the foreground of the composition1 as it would seem2 and this only was ever finished as a mural decoration in the ,sala del ,consiglio4 ,this portion of the composition is familiar to all from the disfigured copy engraved by ,edelinck4 ,mariette had already very acutely observed that ,edelinck must surely have worked from a ,flemish copy of the picture4 ,there is in the ,louvre a drawing by ,rubens 7,no4 #efe7 which also represents four horsemen fighting round a standard and which agrees with ,edelinck's engraving1 but the engraving reverses the drawing4 ,an earlier ,flemish drawing1 such as may have served as the model for both ,rubens and ,edelinck1 is in the ,uffizi collection 7see ,philpots's ,photograph1 ,no4 #gcb74 ,it seems to be a work of the second half of the ,x,v,ith century1 a time when both the picture and the cartoon had already been destroyed4 ,it is apparently the production of a not very skilled hand4 ,raphael ,trichet du ,fresne1 #afea1 mentions that a small picture by ,leonardo himself of the ,battle of the ,standard was then extant in the ,tuileries2 by this he probably means the painting on panel which is now in the possession of ,madame ,timbal in ,paris1 and which has lately been engraved by ,haussoullier as a work by ,leonardo4 ,the picture1 which is very carefully painted1 seems to me however to be the work of some unknown ,florentine painter1 and probably executed within the first ten years of the ,x,v,ith century4 ,at the same time1 it would seem to be a copy not from ,leonardo's cartoon1 but from his picture in the ,palazzo della ,signoria2 at any rate this little picture1 and the small ,flemish drawing in ,florence are the oldest finished copies of this episode in the great composition of the ,battle of ,anghiari4 ,in his ,life of ,raphael1 ,vasari tells us that ,raphael copied certain works of ,leonardo's during his stay in ,florence4 ,raphael's first visit to ,florence lasted from the middle of ,october #aejd till ,july #aeje1 and he revisited it in the summer of #aejf4 ,the hasty sketch1 now in the possession of the ,university of ,oxford and reproduced on page #ccg also represents the ,battle of the ,standard and seems to have been made during his first stay1 and therefore not from the fresco but from the cartoon2 for1 on the same sheet we also find1 besides an old man's head drawn in ,leonardo's style1 some studies for the figure of ,st4 ,john the ,martyr which ,raphael used in #aeje in his great fresco in the ,church of ,san ,severo at ,perugia4 ,of ,leonardo's studies for the ,battle of ,anghiari ,i must in the first place point to five1 on three of which--,pl4 ,,lii #b1 ,pl4 ,,liii1 ,pl4 ,,lvi--we find studies for the episode of the ,standard4 ,the standard bearer1 who1 in the above named copies is seen stooping1 holding on to the staff across his shoulder1 is immediately recognisable as the left-hand figure in ,raphael's sketch1 and we find it in a similar attitude in ,leonardo's pen and ink drawing in the ,british ,museum--,pl4 ,,lii1 #b--the lower figure to the right4 ,it is not difficult to identify the same figure in two more complicated groups in the pen and ink drawings1 now in the ,accademia at ,venice--,pl4 ,,liii1 and ,pl4 ,,liv--where we also find some studies of foot soldiers fighting4 ,on the sheet in the ,british ,museum--,pl4 ,,lii1 #b--we find1 among others1 one group of three horses galloping forwards3 one horseman is thrown and protects himself with his buckler against the lance thrusts of two others on horseback1 who try to pierce him as they ride past4 ,the same action is repeated1 with some variation1 in two sketches in pen and ink on a third sheet1 in the ,accademia at ,venice1 ,pl4 ,,lv2 a coincidence which suggests the probability of such an incident having actually been represented on the cartoon4 ,we are not1 it is true1 in a position to declare with any certainty which of these three dissimilar sketches may have been the nearest to the group finally adopted in executing the cartoon4 ,with regard1 however1 to one of the groups of horsemen it is possible to determine with perfect certainty not only which arrangement was preferred1 but the position it occupied in the composition4 ,the group of horsemen on ,pl4 ,,lvii is a drawing in black chalk at ,windsor1 which is there attributed to ,leonardo1 but which appears to me to be the work of ,cesare da ,sesto1 and the ,commendatore ,giov4 ,morelli supports me in this view4 ,it can hardly be doubted that da ,sesto1 as a pupil of ,leonardo's1 made this drawing from his master's cartoon1 if we compare it with the copy made by ,raphael--here reproduced1 for just above the fighting horseman in ,raphael's copy it is possible to detect a horse which is seen from behind1 going at a slower pace1 with his tail flying out to the right and the same horse may be seen in the very same attitude carrying a dimly sketched rider1 in the foreground of ,cesare da ,sesto's drawing4 ,if a very much rubbed drawing in black chalk at ,windsor--,pl4 ,,lvi--is1 as it appears to be1 the reversed impression of an original drawing1 it is not difficult to supplement from it the portions drawn by ,cesare da ,sesto4 ,nay1 it may prove possible to reconstruct the whole of the lost cartoon from the mass of materials we now have at hand which we may regard as the nucleus of the composition4 ,a large pen and ink drawing by ,raphael in the ,dresden collection1 representing three horsemen fighting1 and another1 by ,cesare da ,sesto1 in the ,uffizi1 of light horsemen fighting are a further contribution which will help us to reconstruct it4 ,the sketch reproduced on ,pl4 ,,lv gives a suggestive example of the way in which foot-soldiers may have been introduced into the cartoon as fighting among the groups of horsemen2 and ,i may here take the opportunity of mentioning that1 for reasons which it would be out of place to enlarge upon here1 ,i believe the two genuine drawings by ,raphael's hand in his ,venetian sketch-book as it is called--one of a standard bearer marching towards the left1 and one of two foot-soldiers armed with spears and fighting with a horseman--to be undoubtedly copies from the cartoon of the ,battle of ,anghiari4 ,leonardo's two drawings1 preserved in the museum at ,buda-,pesth and reproduced on pages #cch and #cci are preliminary studies for the heads of fighting warriors4 ,the two heads drawn in black chalk 7pg4 #cch7 and the one seen in profile1 turned to the left1 drawn in red chalk 7pg4 #cci71 correspond exactly with those of two horsemen in the scene of the fight round the standard as we see them in ,madame ,timbal's picture and in the other finished copies4 ,an old copy of the last named drawing by a pupil of ,leonardo is in ,,ms4 ,c4 ,a4 #ahg;b2 #efa;b 7,see ,saggio1 ,tav4 ,,xxii74 ,leonardo used to make such finished studies of heads as those1 drawn on detached sheets1 before beginning his pictures from his drawings--compare the preparatory studies for the fresco of the ,last ,supper1 given on ,pl4 ,,xlvii and ,pl4 ,l4 ,other drawings of heads1 all characterised by the expression of vehement excitement that is appropriate to men fighting1 are to be seen at ,windsor 7,no4 #dd7 and at the ,accademia at ,venice 7,,iv1 #ac72 at the back of one of the drawings at ,buda-,pesth there is the bust of a warrior carrying a spear on his left shoulder1 holding up the left arm 7,see ,csatakepek a ,,xvi--lk ,szazadbol osszeallitotta ,pvlszky ,karoly74 ,these drawings may have been made for other portions of the cartoon1 of which no copies exist1 and thus we are unable to identify these preparatory drawings4 ,finally ,i may add that a sketch of fighting horse and foot soldiers1 formerly in the possession of ,m4 ,thiers and published by ,charles ,blanc in his ,vies des ,peintres can hardly be accepted as genuine4 ,it is not to be found1 as ,i am informed1 among the late ,president's property1 and no one appears to know where it now is4 ,an attempted reconstruction of the ,cartoon1 which is not only unsuccessful but perfectly unfounded1 is to be seen in the lithograph by ,bergeret1 published in ,charles ,blanc's ,vies des peintres and reprinted in ,the great ,artists4 ,l4 da ,vinci1 p4 #hj4 ,this misleading pasticcio may now be rejected without hesitation4 ,there are yet a few original drawings by ,leonardo which might be mentioned here as possibly belonging to the cartoon of the ,battle2 such as the pen and ink sketches on ,pl4 ,,xxi and on ,pl4 ,,xxxviii1 ,no4 #c1 but we should risk too wide a departure from the domain of ascertained fact4 ,with regard to the colours and other materials used by ,leonardo the reader may be referred to the quotations from the accounts for the picture in question given by ,milanesi in his edition of ,vasari 7,vol4 ,,iv1 p4 #dd1 note7 where we find entries of a similar character to those in ,leonardo's note books for the year #aeje2 ,s4 ,k4 ,m4 #ab 7see ,no4 #fcf74 ,that ,leonardo was employed in designing decorations and other preparations for high festivals1 particularly for the court of ,milan1 we learn not only from the writings of his contemporaries but from his own incidental allusions2 for instance in ,,ms4 ,c4 l#e;b 7#a71 l4 #i4 ,in the arrangement of the texts referring to this ,i have placed those first1 in which historical personages are named--,nos4 #fgj-fgd4 ,among the descriptions of ,allegorical subjects two texts lately found at ,oxford have been included1 ,nos4 #fgf and #fgg4 ,they are particularly interesting because they are accompanied by large sketches which render the meaning of the texts perfectly clear4 ,it is very intelligible that in other cases1 where there are no illustrative sketches1 the notes must necessarily remain obscure or admit of various interpretations4 ,the literature of the time affords ample evidence of the use of such allegorical representations1 particularly during the ,carnival and in ,leonardo's notes we find the ,carnival expressly mentioned--,nos4 #fhe and #gjd4 ,vasari in his ,life of ,pontormo1 particularly describes that artist's various undertakings for ,carnival festivities4 ,these very graphic descriptions appear to me to throw great light in more ways than one on the meaning of ,leonardo's various notes as to allegorical representations and also on mottoes and emblems--,nos4 #fha-gjb4 ,in passing judgment on the allegorical sketches and emblems it must not be overlooked that even as pictures they were always accompanied by explanations in words4 ,several finished drawings of allegorical compositions or figures have been preserved1 but as they have no corresponding explanation in the ,,mss4 they had no claim to be reproduced here4 ,the female figure on ,pl4 ,,xxvi may perhaps be regarded as a study for such an allegorical painting1 of which the purport would have been explained by an inscription4 ,on ,madonna pictures4 #ffc4 ,in the autumn of #adgh ,i began the two ,madonna pictures4 ,footnote3 ,photographs of this page have been published by ,,braun1 ,no4 #dci1 and ,,philpot1 ,no4 #gah4 #a4 ,incominciai4 ,we have no other information as to the two pictures of the ,madonna here spoken of4 ,as ,leonardo here tells us that he had begun two ,madonnas at the same time1 the word 'incominciai' may be understood to mean that he had begun at the same time preparatory studies for two pictures to be painted later4 ,if this is so1 the non-existence of the pictures may be explained by supposing that they were only planned and never executed4 ,i may here mention a few studies for pictures of the ,madonna which probably belong to this early time2 particularly a drawing in silver-point on bluish tinted paper at ,windsor--see ,pl4 ,,xl1 ,no4 #c--1 a drawing of which the details have almost disappeared in the original but have been rendered quite distinct in the reproduction2 secondly a slight pen and ink sketch in1 the ,codex ,,vallardi1 in the ,louvre1 fol4 #fd1 ,no4 #bcaf2 again a silver point drawing of a ,virgin and child drawn over again with the pen in the ,his de la ,salle collection also in the ,louvre1 ,no4 #aja4 7,see ,vicomte ,,both ,,de ,,tauzia1 ,notice des dessins de la collection ,his de la ,salle1 exposes au ,louvre4 ,paris #ahha1 pp4 #hj1 #ha47 ,this drawing is1 it is true1 traditionally ascribed to ,raphael1 but the author of the catalogue very justly points out its great resemblance with the sketches for ,madonnas in the ,british ,museum which are indisputably ,leonardo's4 ,some of these have been published by ,mr4 ,,henry ,,wallis in the ,art ,journal1 ,new ,ser4 ,no4 #ad1 ,feb4 #ahhb4 ,if the non-existence of the two pictures here alluded to justifies my hypothesis that only studies for such pictures are meant by the text1 it may also be supposed that the drawings were made for some comrade in ,,verrocchio',s atelier4 7,see ,,vasari1 ,sansoni's ed4 ,florence #ahhj4 ,vol4 ,,iv1 p4 #efd73 ,e perche a ,lerenzo piaceva fuor di modo la maniera di ,lionardo1 la seppe cosi bene imitare1 che niuno fu che nella pulitezza e nel finir l'opere con diligenza l'imitasse pi di lui4 ,leonardo's notes give me no opportunity of discussing the pictures executed by him in ,florence1 before he moved to ,milan4 ,so the studies for the unfinished picture of the ,adoration of the ,magi--in the ,uffizi1 ,florence--cannot be described here1 nor would any discussion about the picture in the ,louvre ,la ,vierge aux ,rochers be appropriate in the absence of all allusion to it in the ,,mss4 ,therefore1 when ,i presently add a few remarks on this painting in explanation of the ,master's drawings for it1 it will be not merely with a view to facilitate critical researches about the picture now in the ,national ,gallery1 ,london1 which by some critics has been pronounced to be a replica of the ,louvre picture1 but also because ,i take this opportunity of publishing several finished studies of the ,master's which1 even if they were not made in ,florence but later in ,milan1 must have been prior to the painting of the ,last ,supper4 ,the original picture in ,paris is at present so disfigured by dust and varnish that the current reproductions in photography actually give evidence more of the injuries to which the picture has been exposed than of the original work itself4 ,the wood-cut given on p4 #cdd1 is only intended to give a general notion of the composition4 ,it must be understood that the outline and expression of the heads1 which in the picture is obscured but not destroyed1 is here altogether missed4 ,the facsimiles which follow are from drawings which appear to me to be studies for ,la ,vierge aux ,rochers4 #a4 ,a drawing in silver point on brown toned paper of a woman's head looking to the left4 ,in the ,royal ,library at ,turin1 apparently a study from nature for the ,angel's head 7,pl4 ,,xlii74 #b4 ,a study of drapery for the left leg of the same figure1 done with the brush1 ,indian ink on greenish paper1 the lights heightened with white4 ,the original is at ,windsor1 ,no4 #bbc4 ,the reproduction ,pl4 ,,xliii is defective in the shadow on the upper part of the thigh1 which is not so deep as in the original2 it should also be observed that the folds of the drapery near the hips are somewhat altered in the finished work in the ,louvre1 while the ,london copy shows a greater resemblance to this study in that particular4 #c4 ,a study in red chalk for the bust of the ,infant ,christ--,no4 #c in the ,windsor collection 7,pl4 ,,xliv74 ,the well-known silver-point drawing on pale green paper1 in the ,louvre1 of a boy's head 7,no4 #cfc in ,,reiset1 ,notice des dessins1 ,ecoles d',italie7 seems to me to be a slightly altered copy1 either from the original picture or from this red chalk study4 #d4 ,a silver-point study on greenish paper1 for the head of ,john the ,baptist1 reproduced on p4 #cdb4 ,this was formerly in the ,codex ,vallardi and is now exhibited among the drawings in the ,louvre4 ,the lights are1 in the original1 heightened with white2 the outlines1 particularly round the head and ear1 are visibly restored4 ,there is a study of an outstretched hand--,no4 #bhh in the ,windsor collection--which was published in the ,grosvenor ,gallery ,publication1 #ahgh1 simply under the title of3 ,no4 #gb ,study of a hand1 pointing which1 on the other hand1 ,i regard as a copy by a pupil4 ,the action occurs in the kneeling angel of the ,paris picture and not in the ,london copy4 ,these four genuine studies form1 ,i believe1 a valuable substitute in the absence of any ,,ms4 notes referring to the celebrated ,paris picture4 ,bernardo di ,bandino's ,portrait4 #ffd4 ,a tan-coloured small cap1 ,a doublet of black serge1 ,a black jerkin lined ,a blue coat lined1 with fur of foxes' breasts1 and the collar of the jerkin covered with black and white stippled velvet ,bernardo di ,bandino ,baroncelli2 black hose4 ,footnote3 ,these eleven lines of text are by the side of the pen and ink drawing of a man hanged--,pl4 ,,lxii1 ,no4 #a4 ,this drawing was exhibited in #ahgi at the ,ecole des ,beaux-,arts in ,paris and the compilers of the catalogue amused themselves by giving the victim's name as follows3 ,un pendu1 vetu d'une longue robe1 les mains lies sur le dos 444 ,bernardo di ,bendino ,barontigni1 marchand de pantalons 7see ,catalogue descriptif des ,dessins de ,mailres anciens exposes a l',ecole des ,beaux ,arts1 ,paris #ahgi2 ,no4 #hc1 pp4 #i-aj74 ,now1 the criminal represented here1 is none other than ,bernardino di ,bandino ,baroncelli the murderer of ,giuliano de',medici1 whose name as a coadjutor in the conspiracy of the ,pazzi has gained a melancholy notoriety by the tragedy of the #bfth ,april #adgh4 ,bernardo was descended from an ancient family and the son of the man who1 under ,king ,ferrante1 was ,president of the ,high ,court of ,justice in ,naples4 ,his ruined fortunes1 it would seem1 induced him to join the ,pazzi2 he and ,francesco ,pazzi were entrusted with the task of murdering ,giuliano de',medici on the fixed day4 ,their victim not appearing in the cathedral at the hour when they expected him1 the two conspirators ran to the palace of the ,medici and induced him to accompany them4 ,giuliano then took his place in the chancel of the ,cathedral1 and as the officiating priest raised the ,host--the sign agreed upon--,bernardo stabbed the unsuspecting ,giuliano in the breast with a short sword2 ,giuliano stepped backwards and fell dead4 ,the attempt on ,lorenzo's life however1 by the other conspirators at the same moment1 failed of success4 ,bernardo no sooner saw that ,lorenzo tried to make his escape towards the sacristy1 than he rushed upon him1 and struck down ,francesco ,nori who endeavoured to protect ,lorenzo4 ,how ,lorenzo then took refuge behind the brazen doors of the sacristy1 and how1 as soon as ,giuliano's death was made known1 the further plans of the conspirators were defeated1 while a terrible vengeance overtook all the perpetrators and accomplices1 this is no place to tell4 ,bernardo ,bandini alone seemed to be favoured by fortune2 he hid first in the tower of the ,cathedral1 and then escaped undiscovered from ,florence4 ,poliziano1 who was with ,lorenzo in the ,cathedral1 says in his ',conjurationis ,pactianae ,commentarium'3 ,bandinus fugitans in ,tiphernatem incidit1 a quo in aciem receptus ,senas pervenit4 ,and ,gino ,capponi in summing up the reports of the numerous contemporary narrators of the event1 says3 ,bernardo ,bandini ricoverato in ,costantinopoli1 fu per ordine del ,sultano preso e consegnato a un ,antonio di ,bernardino dei ,medici1 che ,lorenzo aveva mandato apposta in ,turchia3 cos era grande la potenza di quest' uomo e grande la voglia di farne mostra e che non restasse in vita chi aveagli ucciso il fratello1 fu egli applicato appena giunto 7,storia della ,republica di ,firenze ,,ii1 #cgg1 #cgh74 ,details about the dates may be found in the ,chronichetta di ,belfredello ,strinati ,alfieri3 ,bernardo di ,bandino ,bandini sopradetto ne venne preso da ,gostantinopoti a d #ad4 ,dicembre #adgi e disaminato1 che fu al ,bargello1 fu impiccato alle finestre di detto ,bargello allato alla ,doana a d #bi4 ,dicembre ,,mcccclxxix che pochi d stette4 ,it may however be mentioned with reference to the mode of writing the name of the assassin that1 though most of his contemporaries wrote ,bernardo ,bandini1 in the ,breve ,chronicon ,caroli ,petri de ,joanninis he is called ,bernardo di ,bandini ,baroncelli2 and1 in the ,sententiae ,domini ,matthaei de ,toscana1 ,bernardus ,joannis ,bandini de ,baroncellis1 as is written on ,leonardo's drawing of him when hanged4 ,now ,,vasari1 in the life of ,andrea del ,castagno 7,vol4 ,,ii1 #fhj2 ed4 ,milanesi #ahgh71 tells us that in #adgh this painter was commissioned by order of the ,signoria to represent the members of the ,pazzi conspiracy as traitors1 on the facade of the ,palazzo del ,podest--the ,bargello4 ,this statement is obviously founded on a mistake1 for ,andrea del ,castagno was already dead in #adeg4 ,he had however been commissioned to paint ,rinaldo degli ,albizzi1 when declared a rebel and exiled in #adcd1 and his adherents1 as hanging head downwards2 and in consequence he had acquired the nickname of ,andrea degl' ,impiccati4 ,on the #bast ,july #adgh the ,council of ,eight came to the following resolution3 item servatis etc4 deliberaverunt et santiaverunt ,sandro ,botticelli pro ejus labore in pingendo proditores flor4 quadraginta largos 7see ,g4 ,,milanesi1 ,arch4 star4 ,,vi 7#ahfb7 p4 #e note47 ,as has been told1 ,giuliano de' ,medici was murdered on the #bfth ,april #adgh1 and we see by this that only three months later ,botticelli was paid for his painting of the proditores4 ,we can however hardly suppose that all the members of the conspiracy were depicted by him in fresco on the facade of the palace1 since no fewer than eighty had been condemned to death4 ,we have no means of knowing whether1 besides ,botticelli1 any other painters1 perhaps ,leonardo1 was commissioned1 when the criminals had been hanged in person out of the windows of the ,palazzo del ,podest to represent them there afterwards in effigy in memory of their disgrace4 ,nor do we know whether the assassin who had escaped may at first not have been provisionally represented as hanged in effigy4 ,now1 when we try to connect the historical facts with this drawing by ,leonardo reproduced on ,pl4 ,,lxii1 ,no4 ,i1 and the full description of the conspirator's dress and its colour on the same sheet1 there seems to be no reasonable doubt that ,bernardo ,bandini is here represented as he was actually hanged on ,december #bith1 #adgi1 after his capture at ,constantinople4 ,the dress is certainly not that in which he committed the murder4 ,a long furred coat might very well be worn at ,constantinople or at ,florence in ,december1 but hardly in ,april4 ,the doubt remains whether ,leonardo described ,bernardo's dress so fully because it struck him as remarkable1 or whether we may not rather suppose that this sketch was actually made from nature with the intention of using it as a study for a wall painting to be executed4 ,it cannot be denied that the drawing has all the appearance of having been made for this purpose4 ,be this as it may1 the sketch under discussion proves1 at any rate1 that ,leonardo was in ,florence in ,december #adgi1 and the note that accompanies it is valuable as adding one more characteristic specimen to the very small number of his ,,mss4 that can be proved to have been written between #adgj and #adhj4 ,notes on the ,last ,supper 7#ffe-ffh74 #ffe4 ,one who was drinking and has left the glass in its position and turned his head towards the speaker4 ,another1 twisting the fingers of his hands together turns with stern brows to his companion #f4 ,another with his hands spread open shows the palms1 and shrugs his shoulders up his ears making a mouth of astonishment #h4 #i ,another speaks into his neighbour's ear and he1 as he listens to him1 turns towards him to lend an ear #aj1 while he holds a knife in one hand1 and in the other the loaf half cut through by the knife4 #ac ,another who has turned1 holding a knife in his hand1 upsets with his hand a glass on the table #ad4 ,footnote #ffe1 #fff3 ,in the original ,,ms4 there is no sketch to accompany these passages1 and if we compare them with those drawings made by ,leonardo in preparation for the composition of the picture--,pl4 ,,xlv1 ,,xlvi--1 7compare also ,pl4 ,,lii1 #a and the drawings on p4 #big7 it is impossible to recognise in them a faithful interpretation of the whole of this text2 but1 if we compare these passages with the finished picture 7see p4 #ccd7 we shall see that in many places they coincide4 ,for instance1 compare ,no4 #ffe1 #a4 #f--h1 with the fourth figure on the right hand of ,christ4 ,the various actions described in lines #i--aj1 #ac--ad are to be seen in the group of ,peter1 ,john and ,judas2 in the finished picture however it is not a glass but a salt cellar that ,judas is upsetting4 #fff4 ,another lays his hand on the table and is looking4 ,another blows his mouthful4 #c ,another leans forward to see the speaker shading his eyes with his hand4 #e ,another draws back behind the one who leans forward1 and sees the speaker between the wall and the man who is leaning ,footnote3 #f4 chinato4 ,i have to express my regret for having misread this word1 written cinato in the original1 and having altered it to ciclo when ,i first published this text1 in ',the ,academy' for ,nov4 #h1 #ahgi immediately after ,i had discovered it1 and subsequently in the small biography of ,leonardo da ,vinci 7,great ,artists7 p4 #bi44 ,footnote3 ,in ,no4 #fff4 ,line ,i must refer to the furthest figure on the left2 #c1 #e and #f describe actions which are given to the group of disciples on the left hand of ,christ4 #ffg4 ,,christ4 ,count ,giovanni1 the one with the ,cardinal of ,mortaro4 ,footnote3 ,as this note is in the same small ,manuscript as the passage here immediately preceding it1 ,i may be justified in assuming that ,leonardo meant to use the features of the person here named as a suitable model for the figure of ,christ4 ,the celebrated drawing of the head of ,christ1 now hanging in the ,brera ,gallery at ,milan1 has obviously been so much restored that it is now impossible to say1 whether it was ever genuine4 ,we have only to compare it with the undoubtedly genuine drawings of heads of the disciples in ,,pi4 ,,xlvii1 ,,xlviii and ,l1 to admit that not a single line of the ,milan drawing in its present state can be by the same hand4 #ffh4 ,philip1 ,simon1 ,matthew1 ,thomas1 ,james the ,greater1 ,peter1 ,philip1 ,andrew1 ,bartholomew4 ,footnote3 ,see ,,pi4 ,,xlvi4 ,the names of the disciples are given in the order in which they are written in the original1 from right to left1 above each head4 ,the original drawing is here slightly reduced in scale2 it measures #ci centimetres in length by #bf in breadth4 #ffi4 ,on the battle of ,anghiari4 ,florentine ,neri di ,gino ,capponi ,bernardetto de' ,medici ,micheletto1 ,niccolo da ,pisa ,conte ,francesco ,pietro ,gian ,paolo ,guelfo ,orsino1 ,messer ,rinaldo degli ,albizzi ,begin with the address of ,niccolo ,piccinino to the soldiers and the banished ,florentines among whom are ,messer ,rinaldo degli ,albizzi and other ,florentines4 ,then let it be shown how he first mounted on horseback in armour2 and the whole army came after him--#dj squadrons of cavalry1 and #bjjj foot soldiers went with him4 ,very early in the morning the ,patriarch went up a hill to reconnoitre the country1 that is the hills1 fields and the valley watered by a river2 and from thence he beheld ,niccolo ,picinino coming from ,borgo ,san ,sepolcro with his people1 and with a great dust2 and perceiving them he returned to the camp of his own people and addressed them4 ,having spoken he prayed to ,god with clasped hands1 when there appeared a cloud in which ,saint ,peter appeared and spoke to the ,patriarch4--#ejj cavalry were sent forward by the ,patriarch to hinder or check the rush of the enemy4 ,in the foremost troop ,francesco the son of ,niccolo ,piccinino #bd was the first to attack the bridge which was held by the ,patriarch and the ,florentines4 ,beyond the bridge to his left he sent forward some infantry to engage ours1 who drove them back1 among whom was their captain ,micheletto #bi whose lot it was to be that day at the head of the army4 ,here1 at this bridge there is a severe struggle2 our men conquer and the enemy is repulsed4 ,here ,guido and ,astorre1 his brother1 the ,lord of ,faenza with a great number of men1 re-formed and renewed the fight1 and rushed upon the ,florentines with such force that they recovered the bridge and pushed forward as far as the tents4 ,but ,simonetto advanced with #fjj horse1 and fell upon the enemy and drove them back once more from the place1 and recaptured the bridge2 and behind him came more men with #bjjj horse soldiers4 ,and thus for a long time they fought with varying fortune4 ,but then the ,patriarch1 in order to divert the enemy1 sent forward ,niccolo da ,pisa #dd and ,napoleone ,orsino1 a beardless lad1 followed by a great multitude of men1 and then was done another great feat of arms4 ,at the same time ,niccolo ,piccinino urged forward the remnant of his men1 who once more made ours give way2 and if it had not been that the ,patriarch set himself at their head and1 by his words and deeds controlled the captains1 our soldiers would have taken to flight4 ,the ,patriarch had some artillery placed on the hill and with these he dispersed the enemy's infantry2 and the disorder was so complete that ,niccolo began to call back his son and all his men1 and they took to flight towards ,borgo4 ,and then began a great slaughter of men2 none escaped but the foremost of those who had fled or who hid themselves4 ,the battle continued until sunset1 when the ,patriarch gave his mind to recalling his men and burying the dead1 and afterwards a trophy was erected4 ,footnote3 #ffi4 ,this passage does not seem to me to be in ,leonardo's hand1 though it has hitherto been generally accepted as genuine4 ,not only is the writing unlike his1 but the spelling also is quite different4 ,i would suggest that this passage is a description of the events of the battle drawn up for the ,painter by order of the ,signoria1 perhaps by some historian commissioned by them1 to serve as a scheme or programme of the work4 ,the whole tenor of the style seems to me to argue in favour of this theory2 and besides1 it would be in no way surprising that such a document should have been preserved among ,leonardo's autographs4 ,allegorical representations referring to the duke of ,milan 7#fgj-fgc74 #fgj4 ,ermine with blood ,galeazzo1 between calm weather and a representation of a tempest4 ,footnote3 #fgj4 ,only the beginning of this text is legible2 the writing is much effaced and the sense is consequently obscure4 ,it seems to refer like the following passage to an allegorical picture4 #fga4 ,il ,moro with spectacles1 and ,envy depicted with ,false ,report and ,justice black for il ,moro4 ,labour as having a branch of vine or a screw in her hand4 #fgb4 ,il ,moro as representing ,good ,fortune1 with hair1 and robes1 and his hands in front1 and ,messer ,gualtieri taking him by the robes with a respectful air from below1 having come in from the front #e4 ,again1 ,poverty in a hideous form running behind a youth4 ,il ,moro covers him with the skirt of his robe1 and with his gilt sceptre he threatens the monster4 ,a plant with its roots in the air to represent one who is at his last2--a robe and ,favour4 ,of tricks or of magpies and of burlesque poems or of starlings4 ,those who trust themselves to live near him1 and who will be a large crowd1 these shall all die cruel deaths2 and fathers and mothers together with their families will be devoured and killed by cruel creatures4 ,footnote3 #a--aj have already been published by ,amoretti in ,memorie ,storiche cap4 ,,xii4 ,he adds this note with regard to ,gualtieri3 ,a questo ,m4 ,gualtieri come ad uomo generoso e benefico scrive il ,bellincioni un ,sonetto 7pag1 #agd7 per chiedergli un piacere2 e 'l ,tantio rendendo ragione a ,lodovico il ,moro1 perche pubblicasse le ,rime del ,bellincioni2 ci hammi imposto1 gli dice3 l'humano fidele1 prudente e sollicito executore delli tuoi comandamenti ,gualtero1 che fa in tutte le cose ove tu possi far utile1 ogni studio vi metti4 ,a somewhat mysterious and evidently allegorical composition--a pen and ink drawing--at ,windsor1 see ,,pl ,,lviii1 contains a group of figures in which perhaps the idea is worked out which is spoken of in the text1 lines #a-e4 #fgc4 ,he was blacker than a hornet1 his eyes were as red as a burning fire and he rode on a tall horse six spans across and more than #bj long with six giants tied up to his saddle-bow and one in his hand which he gnawed with his teeth4 ,and behind him came boars with tusks sticking out of their mouths1 perhaps ten spans4 ,allegorical representations 7#fgd--fgh74 #fgd4 ,above the helmet place a half globe1 which is to signify our hemisphere1 in the form of a world2 on which let there be a peacock1 richly decorated1 and with his tail spread over the group2 and every ornament belonging to the horse should be of peacock's feathers on a gold ground1 to signify the beauty which comes of the grace bestowed on him who is a good servant4 ,on the shield a large mirror to signify that he who truly desires favour must be mirrored in his virtues4 ,on the opposite side will be represented ,fortitude1 in like manner in her place with her pillar in her hand1 robed in white1 to signify 444 ,and all crowned2 and ,prudence with #c eyes4 ,the housing of the horse should be of plain cloth of gold closely sprinkled with peacock's eyes1 and this holds good for all the housings of the horse1 and the man's dress4 ,and the man's crest and his neck-chain are of peacock's feathers on golden ground4 ,on the left side will be a wheel1 the centre of which should be attached to the centre of the horse's hinder thigh piece1 and in the centre ,prudence is seen robed in red1 ,charity sitting in a fiery chariot and with a branch of laurel in her hand1 to signify the hope which comes of good service4 #ba ,messer ,antonio ,grimani of ,venice companion of ,antonio ,maria #bc4 ,footnote3 ,messer ,antonio ,gri4 ,his name thus abbreviated is1 there can be no doubt1 ,grimani4 ,antonio ,grimani was the famous ,doge who in #adii commanded the ,venetian fleet in battle against the ,turks4 ,but after the abortive conclusion of the expedition--,ludovico being the ally of the ,turks who took possession of ,friuli--1 ,grimani was driven into exile2 he went to live at ,rome with his son ,cardinal ,domenico ,grimani4 ,on being recalled to ,venice he filled the office of ,doge from #aeba to #aebc4 ,antonio ,maria probably means ,antonio ,maria ,grimani1 the ,patriarch of ,aquileia4 #fge4 ,fame should be depicted as covered all over with tongues instead of feathers1 and in the figure of a bird4 #fgf4 ,pleasure and ,pain represent as twins1 since there never is one without the other2 and as if they were united back to back1 since they are contrary to each other4 #f ,clay1 gold4 ,footnote3 #g4 oro4 fango3 gold1 clay4 ,these words stand below the allegorical figure4 ,if you take ,pleasure know that he has behind him one who will deal you ,tribulation and ,repentance4 #i ,this represents ,pleasure together with ,pain1 and show them as twins because one is never apart from the other4 ,they are back to back because they are opposed to each other2 and they exist as contraries in the same body1 because they have the same basis1 inasmuch as the origin of pleasure is labour and pain1 and the various forms of evil pleasure are the origin of pain4 ,therefore it is here represented with a reed in his right hand which is useless and without strength1 and the wounds it inflicts are poisoned4 ,in ,tuscany they are put to support beds1 to signify that it is here that vain dreams come1 and here a great part of life is consumed4 ,it is here that much precious time is wasted1 that is1 in the morning1 when the mind is composed and rested1 and the body is made fit to begin new labours2 there again many vain pleasures are enjoyed2 both by the mind in imagining impossible things1 and by the body in taking those pleasures that are often the cause of the failing of life4 ,and for these reasons the reed is held as their support4 ,footnote3 #fgf4 ,the pen and ink drawing on ,,pi4 ,,lix belongs to this passage4 ,footnote3 #h4 tribolatione4 ,in the drawing caltrops may be seen lying in the old man's right hand1 others are falling and others again are shewn on the ground4 ,similar caltrops are drawn in ,,ms4 ,tri4 p4 #ih and underneath them1 as well as on page #if the words triboli di ferro are written4 ,from the accompanying text it appears that they were intended to be scattered on the ground at the bottom of ditches to hinder the advance of the enemy4 ,count ,giulio ,porro who published a short account of the ,trivulzio ,,ms4 in the ,archivio ,storico ,lombardo1 ,anno ,,viii part ,,iv 7,dec4 #ca1 #ahha7 has this note on the passages treating of triboli3 ,e qui aggiunger che anni sono quando venne fabbricata la nuova cavallerizza presso il castello di ,milano1 ne furono trovati due che io ho veduto ed erano precisamente quali si trovano descritti e disegnati da ,leonardo in questo codice4 ,there can therefore be no doubt that this means of defence was in general use1 whether it were originally ,leonardo's invention or not4 ,the play on the word tribolatione1 as it occurs in the drawing at ,oxford1 must then have been quite intelligible4 ,footnote3 #i--bb4 ,these lines1 in the original1 are written on the left side of the page and refer to the figure shown on ,,pi4 ,,lxi4 ,next to it is placed the group of three figures given in ,,pi4 ,,lx ,no4 ,i4 ,lines #ba and #bb1 which are written under it1 are the only explanation given4 ,evil-thinking is either ,envy or ,ingratitude4 #fgg4 ,envy must be represented with a contemptuous motion of the hand towards heaven1 because if she could she would use her strength against ,god2 make her with her face covered by a mask of fair seeming2 show her as wounded in the eye by a palm branch and by an olive-branch1 and wounded in the ear by laurel and myrtle1 to signify that victory and truth are odious to her4 ,many thunderbolts should proceed from her to signify her evil speaking4 ,let her be lean and haggard because she is in perpetual torment4 ,make her heart gnawed by a swelling serpent1 and make her with a quiver with tongues serving as arrows1 because she often offends with it4 ,give her a leopard's skin1 because this creature kills the lion out of envy and by deceit4 ,give her too a vase in her hand full of flowers and scorpions and toads and other venomous creatures2 make her ride upon death1 because ,envy1 never dying1 never tires of ruling4 ,make her bridle1 and load her with divers kinds of arms because all her weapons are deadly4 ,toleration4 ,intolerable4 ,no sooner is ,virtue born than ,envy comes into the world to attack it2 and sooner will there be a body without a shadow than ,virtue without ,envy4 ,footnote3 ,the larger of the two drawings on ,,pi4 ,,lxi is explained by the first #ba lines of this passage4 ,l4 #bb and #bc1 which are written above the space between the two drawings1 do not seem to have any reference to either4 ,l4 #bd-bg are below the allegorical twin figure which they serve to explain4 #fgh4 ,when ,pluto's ,paradise is opened1 then there may be devils placed in twelve pots like openings into hell4 ,here will be ,death1 the ,furies1 ashes1 many naked children weeping2 living fires made of various colours4444 #fgi4 ,john the ,baptist ,saint ,augustin ,saint ,peter ,paul ,elisabeth ,saint ,clara4 ,bernardino ,our ,lady ,louis ,bonaventura ,anthony of ,padua4 ,saint ,francis4 ,francis1 ,anthony1 a lily and book2 ,bernardino with the monogram of ,jesus1 ,louis with #c fleur de lys on his breast and the crown at his feet1 ,bonaventura with ,seraphim1 ,saint ,clara with the tabernacle1 ,elisabeth with a ,queen's crown4 ,footnote3 #fgi4 ,the text of the first six lines is written within a square space of the same size as the copy here given4 ,the names are written in the margin following the order in which they are here printed4 ,in lines #g--ab the names of those saints are repeated of whom it seemed necessary to point out the emblems4 ,list of drawings4 #fhj4 ,a head1 full face1 of a young man with fine flowing hair1 ,many flowers drawn from nature1 ,a head1 full face1 with curly hair1 ,certain figures of ,saint ,jerome1 #f ,the measurements of a figure1 ,drawings of furnaces4 ,a head of the ,duke1 #i many designs for knots1 #d studies for the panel of ,saint ,angelo ,a small composition of ,girolamo da ,fegline1 ,a head of ,christ done with the pen1 #ac #h ,saint ,sebastians1 ,several compositions of ,angels1 ,a chalcedony1 ,a head in profile with fine hair1 ,some pitchers seen in787 perspective1 ,some machines for ships1 ,some machines for waterworks1 ,a head1 a portrait of ,atalanta raising her face2 ,the head of ,geronimo da ,fegline1 ,the head of ,gian ,francisco ,borso1 ,several throats of old women1 ,several heads of old men1 ,several nude figures1 complete1 ,several arms1 eyes1 feet1 and positions1 ,a ,madonna1 finished1 ,another1 nearly in profile1 ,head of ,our ,lady ascending into ,heaven1 ,a head of an old man with long chin1 ,a head of a gypsy girl1 ,a head with a hat on1 ,a representation of the ,passion1 a cast1 ,a head of a girl with her hair gathered in a knot1 ,a head1 with the brown hair dressed4 ,footnote3 #fhj4 ,this has already been published by ,,amoretti ,memorie storiche cap4 ,,xvi4 ,his reading varies somewhat from that here given1 e4 g4 l4 #e and #f4 ,certi ,sangirolami in su d'una figura2 and instead of ,i4 #ac4 ,un ,san ,bastiano4 ,footnote3 #fhj4 #i4 ,molti disegni di gruppi4 ,,vasari in his life of ,leonardo 7,,iv1 #ba1 ed4 ,,milanesi #ahhj7 says3 ,oltrech perse tempo fino a disegnare gruppi di corde fatti con ordine1 e che da un capo seguissi tutto il resto fino all' altro1 tanto che s'empiessi un tondo2 che se ne vede in istampa uno difficilissimo e molto bello1 e nel mezzo vi sono queste parole3 ,leonardus ,vinci ,accademia4 ,gruppi must here be understood as a technical expression for those twisted ornaments which are well known through wood cuts4 ,,amoretti mentions six different ones in the ,ambrosian ,library4 ,i am indebted to ,m4 ,,delaborde for kindly informing me that the original blocks of these are preserved in his department in the ,bibliothque ,nationale in ,paris4 ,on the cover of these volumes is a copy from one of them4 ,the size of the original is #bc #a_/b centimetres by #bf #a_/d4 ,the centre portion of another is given on p4 #cfa4 ,g4 ,govi remarks on these ornaments 7,saggio p4 #bb73 ,codesti gruppi eran probabilmente destinati a servir di modello a ferri da rilegatori per adornar le cartelle degli scolari 7874 ,fregi somigliantissimi a questi troviamo infatti impressi in oro sui cartoni di vari volumi contemporanei1 e li vediam pur figurare nelle lettere iniziali di alcune edizioni del tempo4 ,drer who copied them1 omitting the inscription1 added to the second impressions his own monogram4 ,in his diary he designates them simply as ,die sechs ,knoten 7see ,,thausing1 ,life of ,a4 ,drer ,i1 #cfb1 #cfc74 ,in ,leonardo's ,,mss4 we find here and there little sketches or suggestions for similar ornaments4 ,compare too ,g4 ,,mongeri1 ,l',arte in ,milano1 p4 #cae where an ornament of the same character is given from the old decorations of the vaulted ceiling of the ,sacristy of ,s4 ,maria delle ,grazie4 ,footnote3 #fhj1 #ag4 ,the meaning in which the word coppi1 literally pitchers1 is here used ,i am unable to determine2 but a change to copie seems to me too doubtful to be risked4 #fha4 ,stubborn rigour4 ,doomed rigour4 ,footnote3 ,see ,,pi4 ,,lxii1 ,no4 #b1 the two upper pen and ink drawings4 ,the originals1 in the ,windsor collection are slightly washed with colour4 ,the background is blue sky2 the plough and the instrument with the compass are reddish brown1 the sun is tinted yellow4 #fhb4 ,obstacles cannot crush me ,every obstacle yields to stern resolve ,he who is fixed to a star does not change his mind4 ,footnote3 ,this text is written to elucidate two sketches which were obviously the first sketches for the drawings reproduced on ,,pl ,,lxii1 ,no4 #b4 #fhc4 ,ivy is a type of longevity4 ,footnote3 ,in the original there is1 near this text1 a sketch of a coat wreathed above the waist with ivy4 #fhd4 ,truth the sun4 falsehood a mask4 innocence1 malignity4 ,fire destroys falsehood1 that is sophistry1 and restores truth1 driving out darkness4 ,fire may be represented as the destroy of all sophistry1 and as the image and demonstration of truth2 because it is light and drives out darkness which conceals all essences or subtle things4 ,footnote3 ,see ,,pi4 ,,lxiii4 ,l4 #a-h are in the middle of the page2 #a4 #i-ad to the right below2 #a4 #ae-bb below in the middle column4 ,the rest of the text is below the sketches on the left4 ,there are some other passages on this page relating to geometry4 ,,truth4 ,fire destroys all sophistry1 that is deceit2 and maintains truth alone1 that is gold4 ,truth at last cannot be hidden4 ,dissimulation is of no avail4 ,dissimulation is to no purpose before so great a judge4 ,falsehood puts on a mask4 ,nothing is hidden under the sun4 ,fire is to represent truth because it destroys all sophistry and lies2 and the mask is for lying and falsehood which conceal truth4 #fhe4 ,movement will cease before we are weary of being useful4 ,movement will fail sooner than usefulness4 ,death sooner than ,i am never weary of weariness4 being useful1 ,in serving others ,i is a motto for carnval4 cannot do enough4 ,without fatigue4 ,no labour is sufficient to tire me4 ,hands into which ducats and precious stones fall like snow2 they never become tired by serving1 but this service is only for its utility and not for our ,i am never weary own benefit4 of being useful4 ,naturally nature has so disposed me4 #fhf4 ,this shall be placed in the hand of ,ingratitude4 ,wood nourishes the fire that consumes it4 #fhg4 ,,to ,,represent ,,ingratitude4 ,when the sun appears which dispels darkness in general1 you put out the light which dispelled it for you in particular for your need and convenience4 #fhh4 ,on this side ,adam and ,eve on the other2 ,o misery of mankind1 of how many things do you make yourself the slave for money6 ,footnote3 ,see ,,pi4 ,,lxiv4 ,the figures of ,adam and ,eve in the clouds here alluded to would seem to symbolise their superiority to all earthly needs4 #fhi4 ,thus are base unions sundered4 ,footnote3 ,a much blurred sketch is on the page by this text4 ,it seems to represent an unravelled plait or tissue4 #fij4 ,constancy does not begin1 but is that which perseveres4 ,footnote3 ,a drawing in red chalk1 also rubbed1 which stands in the original in the middle of this text1 seems to me to be intended for a sword hilt1 held in a fist4 #fia4 ,love1 ,fear1 and ,esteem1-- ,write these on three stones4 ,of servants4 #fib4 ,prudence ,strength4 #fic4 ,fame alone raises herself to ,heaven1 because virtuous things are in favour with ,god4 ,disgrace should be represented upside down1 because all her deeds are contrary to ,god and tend to hell4 #fid4 ,short liberty4 #fie4 ,nothing is so much to be feared as ,evil ,report4 ,this ,evil ,report is born of life4 #fif4 ,not to disobey4 #fig4 ,a felled tree which is shooting again4 ,i am still hopeful4 ,a falcon1 ,time4 ,footnote3 ,i4 ,albero tagliato4 ,this emblem was displayed during the ,carnival at ,florence in #aeac4 ,see ,,vasari ,,vi1 #bea1 ed4 ,,milanesi #ahha4 ,but the coincidence is probably accidental4 #fih4 ,truth here makes ,falsehood torment lying tongues4 #fii4 ,such as harm is when it hurts me not1 is good which avails me not4 ,footnote3 ,see ,,pi4 ,,lx1 ,no4 #b4 ,compare this sketch with that on ,,pi4 ,,lxii1 ,no4 #b4 ,below the two lines of the text there are two more lines3 li gchi 7giunchi7 che ritg le paglucole 7pagliucole7 chelli 7che li7 anniegano4 #gjj4 ,he who offends others1 does not secure himself4 ,footnote3 ,see ,,pi4 ,,lx1 ,no4 #c4 #gja4 ,ingratitude4 ,footnote3 ,see ,,pi4 ,,lx1 ,no4 #d4 ,below the bottom sketches are the unintelligible words sta stilli4 ,for ,ingratitudo compare also ,nos4 #fhf and #fhg4 #gjb4 ,one's thoughts turn towards ,hope4 ,footnote3 #gjb4 ,by the side of this passage is a sketch of a cage with a bird sitting in it4 ,ornaments and ,decorations for feasts 7#gjc-gje74 #gjc4 ,a bird1 for a comedy4 ,footnote3 ,the biographies say so much1 and the author's notes say so little of the invention attributed to ,leonardo of making artificial birds fly through the air1 that the text here given is of exceptional interest from being accompanied by a sketch4 ,it is a very slight drawing of a bird with outspread wings1 which appears to be sliding down a stretched string4 ,leonardo's flying machines and his studies of the flight of birds will be referred to later4 #gjd4 ,a ,,dress ,,for ,,the ,,carnival4 ,to make a beautiful dress cut it in thin cloth and give it an odoriferous varnish1 made of oil of turpentine and of varnish in grain1 with a pierced stencil1 which must be wetted1 that it may not stick to the cloth2 and this stencil may be made in a pattern of knots which afterwards may be filled up with black and the ground with white millet4,footnote #g3 ,the grains of black and white millet would stick to the varnish and look like embroidery4 ,footnote3 ,ser ,giuliano1 da ,vinci the painter's brother1 had been commissioned1 with some others1 to order and to execute the garments of the ,allegorical figures for the ,carnival at ,florence in #aeae--af2 ,,vasari however is incorrect in saying of the ,florentine ,carnival of #aeac3 equelli che feciono ed ordinarono gli abiti delle figure furono ,ser ,piero da ,vinci1 padre di ,lonardo1 e ,bernardino di ,giordano1 bellissimi ingegni 7,see ,,milanesi',s ed4 ,voi4 ,,vi1 pg4 #bea47 #gje4 ,snow taken from the high peaks of mountains might be carried to hot places and let to fall at festivals in open places at summer time4 999999 ,end of ,volume #a ,the ,notebooks of ,leonardo ,da ,vinci ,volume #b ,translated by ,jean ,paul ,richter #ahhh ,,xi4 ,the notes on ,sculpture4 ,compared with the mass of manuscript treating of ,painting1 a very small number of passages bearing on the practice and methods of ,sculpture are to be found scattered through the note books2 these are here given at the beginning of this section 7,nos4 #gjf-gji74 ,there is less cause for surprise at finding that the equestrian statue of ,francesco ,sforza is only incidentally spoken of2 for1 although ,leonardo must have worked at it for a long succession of years1 it is not in the nature of the case that it could have given rise to much writing4 ,we may therefore regard it as particularly fortunate that no fewer than thirteen notes in the master's handwriting can be brought together1 which seem to throw light on the mysterious history of this famous work4 ,until now writers on ,leonardo were acquainted only with the passages numbered #gab1 #gai1 #gbj1 #gbb and #gbc4 ,in arranging these notes on sculpture ,i have given the precedence to those which treat of the casting of the monument1 not merely because they are the fullest1 but more especially with a view to reconstructing the monument1 an achievement which really almost lies within our reach by combining and comparing the whole of the materials now brought to light1 alike in notes and in sketches4 ,a good deal of the first two passages1 ,nos4 #gaj and #gaa1 which refer to this subject seems obscure and incomprehensible2 still1 they supplement each other and one contributes in no small degree to the comprehension of the other4 ,a very interesting and instructive commentary on these passages may be found in the fourth chapter of ,vasari's ,introduzione della ,scultura under the title ,come si fanno i modelli per fare di bronzo le figure grandi e picciole1 e come le forme per buttarle2 come si armino di ferri1 e come si gettino di metallo1 c4 ,among the drawings of models of the moulds for casting we find only one which seems to represent the horse in the act of galloping--,no4 #gac4 ,all the other designs show the horse as pacing quietly and as these studies of the horse are accompanied by copious notes as to the method of casting1 the question as to the position of the horse in the model finally selected1 seems to be decided by preponderating evidence4 ,il cavallo dello ,sforza--,c4 ,boito remarks very appositely in the ,saggio on page #bf1 doveva sembrare fratello al cavallo del ,colleoni4 ,e si direbbe che questo fosse figlio del cavallo del ,gattamelata1 il quale pare figlio di uno dei quattro cavalli che stavano forse sull' ,arco di ,nerone in ,roma 7now at ,venice74 ,the publication of the ,saggio also contains the reproduction of a drawing in red chalk1 representing a horse walking to the left and supported by a scaffolding1 given here on ,pl4 ,,lxxvi1 ,no4 #a4 ,it must remain uncertain whether this represents the model as it stood during the preparations for casting it1 or whether--as seems to me highly improbable--this sketch shows the model as it was exhibited in #adic on the ,piazza del ,castello in ,milan under a triumphal arch1 on the occasion of the marriage of the ,emperor ,maximilian to ,bianca ,maria ,sforza4 ,the only important point here is to prove that strong evidence seems to show that1 of the numerous studies for the equestrian statue1 only those which represent the horse pacing agree with the schemes of the final plans4 ,the second group of preparatory sketches1 representing the horse as galloping1 must therefore be considered separately1 a distinction which1 in recapitulating the history of the origin of the monument seems justified by the note given under ,no4 #gbj4 ,galeazza ,maria ,sforza was assassinated in #adgf before his scheme for erecting a monument to his father ,francesco ,sforza could be carried into effect4 ,in the following year ,ludovico il ,moro the young aspirant to the throne was exiled to ,pisa1 and only returned to ,milan in #adgi when he was ,lord 7,governatore7 of the ,state of ,milan1 in #adhj after the minister ,cecco ,simonetta had been murdered4 ,it may have been soon after this that ,ludovico il ,moro announced a competition for an equestrian statue1 and it is tolerably certain that ,antonio del ,pollajuolo took part in it1 from this passage in ,vasari's ,life of this artist3 ,e si trovo1 dopo la morte sua1 il disegno e modello che a ,lodovico ,sforza egli aveva fatto per la statua a cavallo di ,francesco ,sforza1 duca di ,milano2 il quale disegno e nel nostro ,libro1 in due modi3 in uno egli ha sotto ,verona2 nell'altro1 egli tutto armato1 e sopra un basamento pieno di battaglie1 fa saltare il cavallo addosso a un armato2 ma la cagione perche non mettesse questi disegni in opera1 non ho gia potuto sapere4 ,one of ,pollajuolo's drawings1 as here described1 has lately been discovered by ,senatore ,giovanni ,morelli in the ,munich ,pinacothek4 ,here the profile of the horseman is a portrait of ,francesco ,duke of ,milan1 and under the horse1 who is galloping to the left1 we see a warrior thrown and lying on the ground2 precisely the same idea as we find in some of ,leonardo's designs for the monument1 as on ,pl4 ,,lxvi1 ,,lxvii1 ,,lxviii1 ,,lxix and ,,lxxii ,no4 #a2 and1 as it is impossible to explain this remarkable coincidence by supposing that either artist borrowed it from the other1 we can only conclude that in the terms of the competition the subject proposed was the ,duke on a horse in full gallop1 with a fallen foe under its hoofs4 ,leonardo may have been in the competition there and then1 but the means for executing the monument do not seem to have been at once forthcoming4 ,it was not perhaps until some years later that ,leonardo in a letter to the ,duke 7,no4 #gai7 reminded him of the project for the monument4 ,then1 after he had obeyed a summons to ,milan1 the plan seems to have been so far modified1 perhaps in consequence of a remonstrance on the part of the artist1 that a pacing horse was substituted for one galloping1 and it may have been at the same time that the colossal dimensions of the statue were first decided on4 ,the designs given on ,pl4 ,,lxx1 ,,lxxi1 ,,lxxii1 #b and #c1 ,,lxxiii and ,,lxxiv and on pp4 #d and #bd1 as well as three sketches on ,pl4 ,,lxix may be studied with reference to the project in its new form1 though it is hardly possible to believe that in either of these we see the design as it was actually carried out4 ,it is probable that in ,milan ,leonardo worked less on drawings1 than in making small models of wax and clay as preparatory to his larger model4 ,among the drawings enumerated above1 one in black chalk1 ,pl4 ,,lxxiii--the upper sketch on the right hand side1 reminds us strongly of the antique statue of ,marcus ,aurelius4 ,if1 as it would seem1 ,leonardo had not until then visited ,rome1 he might easily have known this statue from drawings by his former master and friend ,verrocchio1 for ,verrocchio had been in ,rome for a long time between #adgj and #adhj4 ,in #adgc ,pope ,sixtus ,,iv had this antique equestrian statue restored and placed on a new pedestal in front of the church of ,san ,giovanni in ,luterano4 ,leonardo1 although he was painting independently as early as in #adgb is still spoken of as working in ,verrocchio's studio in #adgg4 ,two years later the ,venetian senate decided on erecting an equestrian statue to ,colleoni2 and as ,verrocchio1 to whom the work was entrusted1 did not at once move from ,florence to ,venice--where he died in #adhh before the casting was completed--but on the contrary remained in ,florence for some years1 perhaps even till #adhe1 ,leonardo probably had the opportunity of seeing all his designs for the equestrian statue at ,venice and the red chalk drawing on ,pl4 ,,lxxiv may be a reminiscence of it4 ,the pen and ink drawing on ,pl4 ,,lxxii1 ,no4 #c1 reminds us of ,donatello's statue of ,gattamelata at ,padua4 ,however it does not appear that ,leonardo was ever at ,padua before #adii1 but we may conclude that he took a special interest in this early bronze statue and the reports he could procure of it1 form an incidental remark which is to be found in ,c4 ,a4 #ade;a2 #dcb;a1 and which will be given in ,vol4 ,,ii under ,ricordi or ,memoranda4 ,among the studies--in the widest sense of the word--made in preparation statue we may include the ,anatomy of the ,horse which ,lomazzo and ,vas mention2 the most important parts of this work still exist in the ,queen's ,li ,windsor4 ,it was beyond a doubt compiled by ,leonardo when at ,milan2 only interesting records to be found among these designs are reproduced in ,nos4 #gaf;a but it must be pointed out that out of #dj sheets of studies of the movements of the belonging to that treatise1 a horse in full gallop occurs but once4 ,if we may trust the account given by ,paulus ,jovius--about l#ebg-- ,leonardo's horse was represented as vehementer incitatus et anhelatus4 ,jovius had probably seen the model exhibited at ,milan2 but1 need we1 in fact1 infer from this description that the horse was galloping8 ,compare ,vasari's description of the ,gattamelata monument at ,padua3 ,egli ,donatello vi ando ben volentieri1 e fece il cavallo di bronzo1 che e in sulla piazza di ,sant ,antonio1 nel quale si dimostra lo sbuffamento ed il fremito del cavallo1 ed il grande animo e la fierezza vivacissimamente espressa dall'arte nella figura che lo cavalca4 ,these descriptions1 it seems to me1 would only serve to mark the difference between the work of the middle ages and that of the renaissance4 ,we learn from a statement of ,sabba da ,castiglione that1 when ,milan was taken by the ,french in #adii1 the model sustained some injury2 and this informant1 who1 however is not invariably trustworthy1 adds that ,leonardo had devoted fully sixteen years to this work 7la forma del cavallo1 intorno a cui ,leonardo avea sedici anni continui consumati74 ,this often-quoted passage has given ground for an assumption1 which has no other evidence to support it1 that ,leonardo had lived in ,milan ever since #adhc4 ,but ,i believe it is nearer the truth to suppose that this author's statement alludes to the fact that about sixteen years must have past since the competition in which ,leonardo had taken part4 ,i must in these remarks confine myself strictly to the task in hand and give no more of the history of the ,sforza monument than is needed to explain the texts and drawings ,i have been able to reproduce4 ,in the first place1 with regard to the drawings1 ,i may observe that they are all1 with the following two exceptions1 in the ,queen's ,library at ,windsor ,castle2 the red chalk drawing on ,pl4 ,,lxxvi ,no4 #a is in the ,,ms4 ,c4 ,a4 7see ,no4 #gl#b7 and the fragmentary pen and ink drawing on page #d is in the ,ambrosian ,library4 ,the drawings from ,windsor on ,pl4 ,,lxvi have undergone a trifling reduction from the size of the originals4 ,there can no longer be the slightest doubt that the well-known engraving of several horsemen 7,passavant1 ,le ,peintre-,graveur1 ,vol4 ,v1 p4 #aha1 ,no4 #c7 is only a copy after original drawings by ,leonardo1 executed by some unknown engraver2 we have only to compare the engraving with the facsimiles of drawings on ,pl4 ,,lxv1 ,no4 #b1 ,pl4 ,,lxvii1 ,,lxviii and ,,lxix which1 it is quite evident1 have served as models for the engraver4 ,on ,pl4 ,,lxv ,no4 #a1 in the larger sketch to the right hand1 only the base is distinctly visible1 the figure of the horseman is effaced4 ,leonardo evidently found it unsatisfactory and therefore rubbed it out4 ,the base of the monument--the pedestal for the equestrian statue--is repeatedly sketched on a magnificent plan4 ,in the sketch just mentioned it has the character of a shrine or aedicula to contain a sarcophagus4 ,captives in chains are here represented on the entablature with their backs turned to that portion of the monument which more strictly constitutes the pedestal of the horse4 ,the lower portion of the aedicula is surrounded by columns4 ,in the pen and ink drawing ,pl4 ,,lxvi--the lower drawing on the right hand side--the sarcophagus is shown between the columns1 and above the entablature is a plinth on which the horse stands4 ,but this arrangement perhaps seemed to ,leonardo to lack solidity1 and in the little sketch on the left hand1 below1 the sarcophagus is shown as lying under an arched canopy4 ,in this the trophies and the captive warriors are detached from the angles4 ,in the first of these two sketches the place for the trophies is merely indicated by a few strokes2 in the third sketch on the left the base is altogether broader1 buttresses and pinnacles having been added so as to form three niches4 ,the black chalk drawing on ,pl4 ,,lxviii shows a base in which the angles are formed by niches with pilasters4 ,in the little sketch to the extreme left on ,pl4 ,,lxv1 ,no4 #a1 the equestrian statue serves to crown a circular temple somewhat resembling ,bramante's tempietto of ,san ,pietro in ,montario at ,rome1 while the sketch above to the right displays an arrangement faintly reminding us of the tomb of the ,scaligers in ,verona4 ,the base is thus constructed of two platforms or slabs1 the upper one considerably smaller than the lower one which is supported on flying buttresses with pinnacles4 ,on looking over the numerous studies in which the horse is not galloping but merely walking forward1 we find only one drawing for the pedestal1 and this1 to accord with the altered character of the statue1 is quieter and simpler in style 7,pl4 ,,lxxiv74 ,it rises almost vertically from the ground and is exactly as long as the pacing horse4 ,the whole base is here arranged either as an independent baldaquin or else as a projecting canopy over a recess in which the figure of the deceased ,duke is seen lying on his sarcophagus2 in the latter case it was probably intended as a tomb inside a church4 ,here1 too1 it was intended to fill the angles with trophies or captive warriors4 ,probably only ,no4 #gbd in the text refers to the work for the base of the monument4 ,if we compare the last mentioned sketch with the description of a plan for an equestrian monument to ,gian ,giacomo ,trivulzio 7,no4 #gbe7 it seems by no means impossible that this drawing is a preparatory study for the very monument concerning which the manuscript gives us detailed information4 ,we have no historical record regarding this sketch nor do the archives in the ,trivulzio ,palace give us any information4 ,the simple monument to the great general in ,san ,nazaro ,maggiore in ,milan consists merely of a sarcophagus placed in recess high on the wall of an octagonal chapel4 ,the figure of the warrior is lying on the sarcophagus1 on which his name is inscribed2 a piece of sculpture which is certainly not ,leonardo's work4 ,gian ,giacomo ,trivulzio died at ,chartres in #aeah1 only five months before ,leonardo1 and it seems to me highly improbable that this should have been the date of this sketch2 under these circumstances it would have been done under the auspices of ,francis ,i1 but the ,italian general was certainly not in favour with the ,french monarch at the time4 ,gian ,giacomo ,trivulzio was a sworn foe to ,ludovico il ,moro1 whom he strove for years to overthrow4 ,on the #fth ,september #adii he marched victorious into ,milan at the head of a ,french army4 ,in a short time1 however1 he was forced to quit ,milan again when ,ludovico il ,moro bore down upon the city with a force of ,swiss troops4 ,on the #aeth of ,april following1 after defeating ,lodovico at ,novara1 ,trivulzio once more entered ,milan as a ,conqueror1 but his hopes of becoming ,governatore of the place were soon wrecked by intrigue4 ,this victory and triumph1 historians tell us1 were signalised by acts of vengeance against the dethroned ,sforza1 and it might have been particularly flattering to him that the casting and construction of the ,sforza monument were suspended for the time4 ,it must have been at this moment--as it seems to me--that he commissioned the artist to prepare designs for his own monument1 which he probably intended should find a place in the ,cathedral or in some other church4 ,he1 the husband of ,margherita di ,nicolino ,colleoni1 would have thought that he had a claim to the same distinction and public homage as his less illustrious connection had received at the hands of the ,venetian republic4 ,it was at this very time that ,trivulzio had a medal struck with a bust portrait of himself and the following remarkable inscription on the reverse3 ,,deo ,,favente--#adii--;,,dictvs--#aj--;,,ia- -,,expvlit--,,lvdovicv--,,sf-- 7,sfortiam7 ,,dvc-- 7ducem7 ,,mli 7,mediolani7--,,noie 7nomine7--,,regis--,,francorvm--,,eodem- -,,ann --7anno7 ,,red',t 7redit7--,,lvs 7,ludovicus7--,,svperatvs ,,et ,,captvs--,,est--,,ab--,,eo4 ,in the ,library of the ,palazzo ,trivulzio there is a ,,ms4 of ,callimachus ,siculus written at the end of the ,x,vth or beginning of the ,x,v,ith century4 ,at the beginning of this ,,ms4 there is an exquisite illuminated miniature of an equestrian statue with the name of the general on the base2 it is however very doubtful whether this has any connection with ,leonardo's design4 ,nos4 #gca-gdj1 which treat of casting bronze1 have probably a very indirect bearing on the arrangements made for casting the equestrian statue of ,francesco ,sforza4 ,some portions evidently relate to the casting of cannon4 ,still1 in our researches about ,leonardo's work on the monument1 we may refer to them as giving us some clue to the process of bronze casting at that period4 ,some practical hints 7#gjf-gji74 #g,o#f4 ,,of ,a ,,statue4 ,if you wish to make a figure in marble1 first make one of clay1 and when you have finished it1 let it dry and place it in a case which should be large enough1 after the figure is taken out of it1 to receive also the marble1 from which you intend to reveal the figure in imitation of the one in clay4 ,after you have put the clay figure into this said case1 have little rods which will exactly slip in to the holes in it1 and thrust them so far in at each hole that each white rod may touch the figure in different parts of it4 ,and colour the portion of the rod that remains outside black1 and mark each rod and each hole with a countersign so that each may fit into its place4 ,then take the clay figure out of this case and put in your piece of marble1 taking off so much of the marble that all your rods may be hidden in the holes as far as their marks2 and to be the better able to do this1 make the case so that it can be lifted up2 but the bottom of it will always remain under the marble and in this way it can be lifted with tools with great ease4 #gjg4 ,some have erred in teaching sculptors to measure the limbs of their figures with threads as if they thought that these limbs were equally round in every part where these threads were wound about them4 #gjh4 ,,measurement ,,and ,,division ,,of ,a ,,statue4 ,divide the head into #ab degrees1 and each degree divide into #ab points1 and each point into #ab minutes1 and the minutes into minims and the minims into semi minims4 ,degree--point--minute--minim4 #gji4 ,sculptured figures which appear in motion1 will1 in their standing position1 actually look as if they were falling forward4 ,footnote3 figure di rilievo4 ,leonardo applies this term exclusively to wholly detached figures1 especially to those standing free4 ,this note apparently refers to some particular case1 though we have no knowledge of what that may have been4 ,if we suppose it to refer to the first model of the equestrian statue of ,francesco ,sforza 7see the introduction to the notes on ,sculpture7 this observation may be regarded as one of his arguments for abandoning the first scheme of the ,sforza ,monument1 in which the horse was to be galloping 7see page #b74 ,it is also in favour of this theory that the note is written in a manuscript volume already completed in #adib4 ,leonardo's opinions as to the shortcomings of plastic works when compared with paintings are given under ,no4 #fee and #fef4 ,notes on the casting of the ,sforza monument 7#gaj-gae74 #gaj4 ,three braces which bind the mould4 ,if you want to make simple casts quickly1 make them in a box of river sand wetted with vinegar4 ,when you shall have made the mould upon the horse you must make the thickness of the metal in clay4 ,observe in alloying how many hours are wanted for each hundredweight4 ,in casting each one keep the furnace and its fire well stopped up4 ,let the inside of all the moulds be wetted with linseed oil or oil of turpentine1 and then take a handful of powdered borax and ,greek pitch with aqua vitae1 and pitch the mould over outside so that being under ground the damp may not damage it8 ,to manage the large mould make a model of the small mould1 make a small room in proportion4 ,make the vents in the mould while it is on the horse4 ,hold the hoofs in the tongs1 and cast them with fish glue4 ,weigh the parts of the mould and the quantity of metal it will take to fill them1 and give so much to the furnace that it may afford to each part its amount of metal2 and this you may know by weighing the clay of each part of the mould to which the quantity in the furnace must correspond4 ,and this is done in order that the furnace for the legs when filled may not have to furnish metal from the legs to help out the head1 which would be impossible4 ,cast at the same casting as the horse the little door ,footnote3 ,the importance of the notes included under this number is not diminished by the fact that they have been lightly crossed out with red chalk4 ,possibly they were the first scheme for some fuller observations which no longer exist2 or perhaps they were crossed out when ,leonardo found himself obliged to give up the idea of casting the equestrian statue4 ,in the original the first two sketches are above l4 #a1 and the third below l4 #i4 #gaa4 ,,the ,,mould ,,for ,,the ,,horse4 ,make the horse on legs of iron1 strong and well set on a good foundation2 then grease it and cover it with a coating1 leaving each coat to dry thoroughly layer by layer2 and this will thicken it by the breadth of three fingers4 ,now fix and bind it with iron as may be necessary4 ,moreover take off the mould and then make the thickness4 ,then fill the mould by degrees and make it good throughout2 encircle and bind it with its irons and bake it inside where it has to touch the bronze4 ,,of ,,making ,,the ,,mould ,,in ,,pieces4 ,draw upon the horse1 when finished1 all the pieces of the mould with which you wish to cover the horse1 and in laying on the clay cut it in every piece1 so that when the mould is finished you can take it off1 and then recompose it in its former position with its joins1 by the countersigns4 ,the square blocks a b will be between the cover and the core1 that is in the hollow where the melted bronze is to be2 and these square blocks of bronze will support the intervals between the mould and the cover at an equal distance1 and for this reason these squares are of great importance4 ,the clay should be mixed with sand4 ,take wax1 to return what is not used and to pay for what is used4 ,dry it in layers4 ,make the outside mould of plaster1 to save time in drying and the expense in wood2 and with this plaster enclose the irons props both outside and inside to a thickness of two fingers2 make terra cotta4 ,and this mould can be made in one day2 half a boat load of plaster will serve you4 ,good4 ,dam it up again with glue and clay1 or white of egg1 and bricks and rubbish4 ,footnote3 ,see ,pl4 ,,lxxv4 ,the figure #dj1 close to the sketch in the middle of the page between lines #af and #ag has been added by a collector's hand4 ,in the original1 below line #ba1 a square piece of the page has been cut out about #i centimetres by #g and a blank piece has been gummed into the place4 ,lines #bb-bd are written on the margin4 l4 #bg and #bh are close to the second marginal sketch4 l4 #db is a note written above the third marginal sketch and on the back of this sheet is the text given as ,no4 #fdb4 ,compare also ,no4 #hjb4 #gab4 ,all the heads of the large nails4 ,footnote3 ,see ,pl4 ,,lxxvi1 ,no4 i4 ,this drawing has already been published in the ,saggio delle ,opere di ,l4 da ,vinci4 ,milano #ahgb1 ,pl4 ,,xxiv1 ,no4 i4 ,but1 for various reasons ,i cannot regard the editor's suggestions as satisfactory4 ,he says3 ,veggonsi le armature di legname colle quali forse venne sostenuto il modello1 quando per le nozze di ,bianca ,maria ,sforza con ,massimiliano imperatore1 esso fu collocato sotto un arco trionfale davanti al ,castello4 #gac4 ,these bindings go inside4 #gad4 ,salt may be made from human excrements1 burnt and calcined1 made into lees and dried slowly at a fire1 and all the excrements produce salt in a similar way and these salts when distilled1 are very strong4 ,footnote3 ,,vasari repeatedly states1 in the fourth chapter of his ,introduzione della ,scultura1 that in preparing to cast bronze statues horse-dung was frequently used by sculptors4 ,if1 notwithstanding this1 it remains doubtful whether ,i am justified in having introduced here this text of but little interest1 no such doubt can be attached to the sketch which accompanies it4 #gae4 ,,method ,,of ,,founding ,,again4 ,this may be done when the furnace is made ,footnote3 this note is written below the sketches4 strong and bruised4 ,models for the horse of the ,sforza monument 7#gaf-gah74 #gl#f4 ,messer ,galeazzo's big genet #gag4 ,messer ,galeazzo's ,sicilian horse4 ,footnote3 ,these notes are by the side of a drawing of a horse with figured measurements4 #gah4 ,measurement of the ,sicilian horse the leg from behind1 seen in front1 lifted and extended4 ,footnote3 ,there is no sketch belonging to this passage4 ,galeazze here probably means ,galeazze di ,san ,severino1 the famous captain who married ,bianca the daughter of ,ludovico il ,moro4 ,occasional references to the ,sforza monument 7#gai-gbd74 #gai4 ,again1 the bronze horse may be taken in hand1 which is to be to the immortal glory and eternal honour of the happy memory of the prince your father1 and of the illustrious house of ,sforza4 ,footnote3 ,the letter from which this passage is here extracted will be found complete in section ,,xxi4 7see the explanation of it1 on page #b74 #gbj4 ,on the #bcrd of ,april #adij ,i began this book1 and recommenced the horse4 #gba4 ,there is to be seen1 in the mountains of ,parma and ,piacenza1 a multitude of shells and corals full of holes1 still sticking to the rocks1 and when ,i was at work on the great horse for ,milan1 a large sackful of them1 which were found thereabout1 was brought to me into my workshop1 by certain peasants4 #gbb4 ,believe me1 ,leonardo the ,florentine1 who has to do the equestrian bronze statue of the ,duke ,francesco that he does not need to care about it1 because he has work for all his life time1 and1 being so great a work1 ,i doubt whether he can ever finish it4 ,footnote3 ,this passage is quoted from a letter to a committee at ,piacenza for whom ,leonardo seems to have undertaken to execute some work4 ,the letter is given entire in section ,,xxl2 in it ,leonardo remonstrates as to some unreasonable demands4 #gbc4 ,of the horse ,i will say nothing because ,i know the times4 ,footnote3 ,this passage occurs in a rough copy of a letter to ,ludovico il ,moro1 without date 7see below among the letters74 #gbd4 ,during ten years the works on the marbles have been going on ,i will not wait for my payment beyond the time1 when my works are finished4 ,footnote3 ,this possibly refers to the works for the pedestal of the equestrian statue concerning which we have no farther information in the ,,mss4 ,see p4 #f4 ,the project of the ,trivulzio monument4 #gbe4 ,,the ,,monument ,,to ,,messer ,,giovanni ,,jacomo ,,da ,,trevulzo4 #b ,cost of the making and materials for the horse #e4 ,footnote3 ,in the original1 lines #b-e1 #ab-ad1 #cc-ce1 are written on the margin4 ,this passage has been recently published by ,g4 ,govi in ,vol4 ,v1 ,ser4 #c;a1 of ,transunti1 ,reale ,accademia dei ,linea1 sed4 del #e ,giugno1 #ahha1 with the following introductory note3 ,desidero intanto che siano stampati questi pochi frammenti perche so che sono stati trascritti ultimamente1 e verranno messi in luce tra poco fuori d',italia4 ,li ripubblichi pure chi vuole1 ma si sappia almeno che anche tra noi si conoscevano1 e s'eran raccolti da anni per comporne1 quando che fosse1 una edizione ordinata degli scritti di ,leonardo4 ,the learned editor has left out line #bb and has written #c pie for #h piedi in line #be4 ,there are other deviations of less importance from the original4 ,a courser1 as large as life1 with the rider requires for the cost of the metal1 duc4 #ejj4 ,and for cost of the iron work which is inside the model1 and charcoal1 and wood1 and the pit to cast it in1 and for binding the mould1 and including the furnace where it is to be cast 444 duc4 #bjj4 ,to make the model in clay and then in wax444444444 duc4 #dcb4 ,to the labourers for polishing it when it is cast4 4444444 duc4 #dej4 in all4 4 duc4 #aehb4 #ab ,cost of the marble of the monument #ad4 ,cost of the marble according to the drawing4 ,the piece of marble under the horse which is #d braccia long1 #b braccia and #b inches wide and #i inches thick #eh hundredweight1 at #d ,lire and #aj ,soldi per hundredweight44 duc4 #eh4 ,and for #ac braccia and #f inches of cornice1 #g in4 wide and #d in4 thick1 #bd hundredweight4444444 duc4 #bd4 ,and for the frieze and architrave1 which is #d br4 and #f in4 long1 #b br4 wide and #f in4 thick1 #bi hundredweight41 duc4 #bj4 ,and for the capitals made of metal1 which are #h1 #e inches in4 square and #b in4 thick1 at the price of #ae ducats each1 will come to444444 duc4 #abb4 ,and for #h columns of #b br4 #g in41 #d #a_/b in4 thick1 #bj hundredweight duc4 #bj4 ,and for #h bases which are #e #a_/b in4 square and #b in4 high #e hund'44 duc4 #e4 ,and for the slab of the tombstone #d br4 io in4 long1 #b br4 #d #a_/b in4 wide #cf hundredweight4444444 duc4 #cf4 ,and for #h pedestal feet each #h br4 long and #f #a_/b in4 wide and #f #a_/b in4 thick1 #bj hundredweight come to444 duc4 #bj4 ,and for the cornice below which is #d br4 and #aj in4 long1 and #b br4 and #e in4 wide1 and #d in4 thick1 #cb hund'44 duc4 #cb4 ,and for the stone of which the figure of the deceased is to be made which is #c br4 and #h in4 long1 and #a br4 and #f in4 wide1 and #i in4 thick1 #cj hund'44 duc4 #cj4 ,and for the stone on which the figure lies which is #c br4 and #d in4 long and #a br4 and #b in41 wide and #d #a_/b in4 thick duc4 #af4 ,and for the squares of marble placed between the pedestals which are #h and are #i br4 long and #i in4 wide1 and #c in4 thick1 #h hundredweight 4 4 4 duc4 #h4 in all4 4 duc4 #chi4 #cc;,cost of the work in marble#ce4 ,round the base on which the horse stands there are #h figures at #be ducats each 444444444444 duc4 #bjj4 ,and on the same base there are #h festoons with some other ornaments1 and of these there are #d at the price of #ae ducats each1 and #d at the price of #h ducats each 4444444 duc4 #ib4 ,and for squaring the stones duc4 #f4 ,again1 for the large cornice which goes below the base on which the horse stands1 which is #ac br4 and #f in41 at #b due4 per br4 444444 duc4 #bg4 ,and for #ab br4 of frieze at #e due4 per br4 44444444444 duc4 #fj4 ,and for #ab br4 of architrave at #a #a_/b duc4 per br4 4444444 duc4 #ah4 ,and for #c rosettes which will be the soffit of the monument1 at #bj ducats each 4444444444 duc4 #fj4 ,and for #h fluted columns at #h ducats each 444444444 duc4 #fd4 ,and for #h bases at #a ducat each1 duc4 #h4 ,and for #h pedestals1 of which #d are at #aj duc4 each1 which go above the angles2 and #d at #f duc4 each 44 duc4 #fd4 ,and for squaring and carving the moulding of the pedestals at #b duc4 each1 and there are #h 4444 duc4 #af4 ,and for #f square blocks with figures and trophies1 at #be duc4 each 44 duc4 #aej4 ,and for carving the moulding of the stone under the figure of the deceased 4444444444 duc4 #dj4 ,for the statue of the deceased1 to do it well 4444444444 duc4 #ajj4 ,for #f harpies with candelabra1 at #be ducats each 444444444 duc4 #aej4 ,for squaring the stone on which the statue lies1 and carving the moulding 444444444444 duc4 #bj4 in all 44 duc4 #ajge4 ,the sum total of every thing added together amount to 444444 duc4 #cjdf4 #gbf4 ,,mint ,,at ,,rome4 ,it can also be made without a spring4 ,but the screw above must always be joined to the part of the movable sheath3 ,margin note3 ,the mint of ,rome4 ,footnote3 ,see ,pl4 ,,lxxvi4 ,this passage is taken from a note book which can be proved to have been used in ,rome4 ,all coins which do not have the rim complete1 are not to be accepted as good2 and to secure the perfection of their rim it is requisite that1 in the first place1 all the coins should be a perfect circle2 and to do this a coin must before all be made perfect in weight1 and size1 and thickness4 ,therefore have several plates of metal made of the same size and thickness1 all drawn through the same gauge so as to come out in strips4 ,and out of #bd these strips you will stamp the coins1 quite round1 as sieves are made for sorting chestnuts #bg2 and these coins can then be stamped in the way indicated above2 c4 #ca ,the hollow of the die must be uniformly wider than the lower1 but imperceptibly #ce4 ,this cuts the coins perfectly round and of the exact thickness1 and weight2 and saves the man who cuts and weighs1 and the man who makes the coins round4 ,hence it passes only through the hands of the gauger and of the stamper1 and the coins are very superior4 ,footnote3 ,see ,pl4 ,,lxxvi ,no4 #b4 ,the text of lines #ca-ce stands parallel #a4 #bd-bg4 ,farther evidence of ,leonardo's occupations and engagements at ,rome under ,pope ,leo ,x4 may be gathered from some rough copies of letters which will be found in this volume4 ,hitherto nothing has been known of his work in ,rome beyond some doubtful1 and perhaps mythical1 statements in ,vasari4 #gbg4 ,,powder ,,for ,,medals4 ,the incombustible growth of soot on wicks reduced to powder1 burnt tin and all the metals1 alum1 isinglass1 smoke from a brass forge1 each ingredient to be moistened1 with aqua vitae or malmsey or strong malt vinegar1 white wine or distilled extract of turpentine1 or oil2 but there should be little moisture1 and cast in moulds4 ,margin note3 ,on the coining of medals 7#gbg4 #gbh74 ,footnote3 ,the meaning of scagliuolo in this passage is doubtful4 #gbh4 ,,of ,,taking ,,casts ,,of ,,medals4 ,a paste of emery mixed with aqua vitae1 or iron filings with vinegar1 or ashes of walnut leaves1 or ashes of straw very finely powdered4 ,footnote3 ,the meaning of scagliuolo in this passage is doubtful4 ,the diameter is given in the lead enclosed2 it is beaten with a hammer and several times extended2 the lead is folded and kept wrapped up in parchment so that the powder may not be spilt2 then melt the lead1 and the powder will be on the top of the melted lead1 which must then be rubbed between two plates of steel till it is thoroughly pulverised2 then wash it with aqua fortis1 and the blackness of the iron will be dissolved leaving the powder clean4 ,emery in large grains may be broken by putting it on a cloth many times doubled1 and hit it sideways with the hammer1 when it will break up2 then mix it little by little and it can be founded with ease2 but if you hold it on the anvil you will never break it1 when it is large4 ,any one who grinds smalt should do it on plates of tempered steel with a cone shaped grinder2 then put it in aqua fortis1 which melts away the steel that may have been worked up and mixed with the smalt1 and which makes it black2 it then remains purified and clean2 and if you grind it on porphyry the porphyry will work up and mix with the smalt and spoil it1 and aqua fortis will never remove it because it cannot dissolve the porphyry4 ,if you want a fine blue colour dissolve the smalt made with tartar1 and then remove the salt4 ,vitrified brass makes a fine red4 #gbi4 ,,stucco4 ,place stucco over the prominence of the44444 which may be composed of ,venus and ,mercury1 and lay it well over that prominence of the thickness of the side of a knife1 made with the ruler and cover this with the bell of a still1 and you will have again the moisture with which you applied the paste4 ,the rest you may dry ,margin note3 ,on stucco 7#gbi4 #gcj74 ,footnote3 ,in this passage a few words have been written in a sort of cipher--that is to say backwards2 as in l4 #c erenev for ,venere1 l4 #d oirucrem for ,mercurio1 l4 #ab il orreve co ecarob for il everro 787 co borace4 ,the meaning of the word before di giesso in l4 #a is unknown2 and the sense1 in which sagoma is used here and in other passages is obscure4-- ,venere and ,mercurio may mean 'marble' and 'lime'1 of which stucco is composed4 #ab4 ,the meaning of orreve is unknown4 well2 afterwards fire it1 and beat it or burnish it with a good burnisher1 and make it thick towards the side4 ,,stucco4 ,powder 444 with borax and water to a paste1 and make stucco of it1 and then heat it so that it may dry1 and then varnish it1 with fire1 so that it shines well4 #gcj4 ,,stucco ,,for ,,moulding4 ,take of butter #f parts1 of wax #b parts1 and as much fine flour as when put with these #b things melted1 will make them as firm as wax or modelling clay4 ,,glue4 ,take mastic1 distilled turpentine and white lead4 ,on bronze casting generally 7#gca-gdj74 #gca4 ,,to ,,cast4 ,tartar burnt and powdered with plaster and cast cause the plaster to hold together when it is mixed up again2 and then it will dissolve in water4 #gcb4 ,,to ,,cast ,,bronze ,,in ,,plaster4 ,take to every #b cups of plaster #a of ox-horns burnt1 mix them together and make your cast with it4 #gcc4 ,when you want to take a cast in wax1 burn the scum with a candle1 and the cast will come out without bubbles4 #gcd4 #b ounces of plaster to a pound of metal2-- walnut1 which makes it like the curve4 ,footnote3 ,the second part of this is quite obscure4 #gce4 ,dried earth #af pounds1 #ajj pounds of metal wet clay #bj1--of wet #ajj1-;half1- which increases #d ,ibs4 of water1--#a of wax1 #a ,ib4 of metal1 a little less1-the scrapings of linen with earth1 measure for measure4 ,footnote3 ,the translation is given literally1 but the meaning is quite obscure4 #gcf4 ,such as the mould is1 so will the cast be4 #gcg4 ,,how ,,casts ,,ought ,,to ,,be ,,polished4 ,make a bunch of iron wire as thick as thread1 and scrub them with this and water2 hold a bowl underneath that it may not make a mud below4 ,,how ,,to ,,remove ,,the ,,rough ,,edges ,,from ,,bronze4 ,make an iron rod1 after the manner of a large chisel1 and with this rub over those seams on the bronze which remain on the casts of the guns1 and which are caused by the joins in the mould2 but make the tool heavy enough1 and let the strokes be long and broad4 ,,to ,,facilitate ,,melting4 ,first alloy part of the metal in the crucible1 then put it in the furnace1 and this being in a molten state will assist in beginning to melt the copper4 ,,to ,,prevent ,,the ,,copper ,,cooling ,,in ,,the ,,furnace4 ,when the copper cools in the furnace1 be ready1 as soon as you perceive it1 to cut it with a long stick while it is still in a paste2 or if it is quite cold cut it as lead is cut with broad and large chisels4 ,,if ,,you ,,have ,,to ,,make ,a ,,large ,,cast4 ,if you have to make a cast of a hundred thousand pounds do it with two furnaces and with #bjjj pounds in each1 or as much as #cjjj pounds at most4 #gch4 ,,how ,,to ,,proceed ,,to ,,break ,a ,,large ,,mass ,,of ,,bronze4 ,if you want to break up a large mass of bronze1 first suspend it1 and then make round it a wall on the four sides1 like a trough of bricks1 and make a great fire therein4 ,when it is quite red hot give it a blow with a heavy weight raised above it1 and with great force4 #gci4 ,,to ,,combine ,,lead ,,with ,,other ,,metal4 ,if you wish for economy in combining lead with the metal in order to lessen the amount of tin which is necessary in the metal1 first alloy the lead with the tin and then add the molten copper4 ,how ,,to ,,melt ,,metal ,,in ,a ,,furnace4 ,the furnace should be between four well founded pillars4 ,,of ,,the ,,thickness ,,of ,,the ,,coating4 ,the coating should not be more than two fingers thick1 it should be laid on in four thicknesses over fine clay and then well fixed1 and it should be fired only on the inside and then carefully covered with ashes and cow's dung4 ,,of ,,the ,,thickness ,,of ,,the ,,gun4 ,the gun being made to carry #fjj ,ibs4 of ball and more1 by this rule you will take the measure of the diameter of the ball and divide it into #f parts and one of these parts will be its thickness at the muzzle2 but at the breech it must always be half4 ,and if the ball is to be #gjj lbs41 #a_/gth of the diameter of the ball must be its thickness in front2 and if the ball is to be #hjj1 the eighth of its diameter in front2 and if #ijj1 #a_/hth and #a_/b #c_/af1 and if #ajjj1 #a_/ith4 ,,of ,,the ,,length ,,of ,,the ,,body ,,of ,,the ,,gun4 ,if you want it to throw a ball of stone1 make the length of the gun to be #f1 or as much as #g diameters of the ball2 and if the ball is to be of iron make it as much as #ab balls1 and if the ball is to be of lead1 make it as much as #ah balls4 ,i mean when the gun is to have the mouth fitted to receive #fjj lbs4 of stone ball1 and more4 ,,of ,,the ,,thickness ,,of ,,small ,,guns4 ,the thickness at the muzzle of small guns should be from a half to one third of the diameter of the ball1 and the length from #cj to #cf balls4 #gdj4 ,,of ,,luting ,,the ,,furnace ,,within4 ,the furnace must be luted before you put the metal in it1 with earth from ,valenza1 and over that with ashes4 ,footnote #a4 #b43 ,terra di ,valenza4--,valenza is north of ,alessandria on the ,po4 ,,of ,,restoring ,,the ,,metal ,,when ,,it ,,is ,,becoming ,,cool4 ,when you see that the bronze is congealing take some willow-wood cut in small chips and make up the fire with it4 ,,the ,,cause ,,of ,,its ,,curdling4 ,i say that the cause of this congealing often proceeds from too much fire1 or from ill-dried wood4 ,,to ,,know ,,the ,,condition ,,of ,,the ,,fire4 ,you may know when the fire is good and fit for your purpose by a clear flame1 and if you see the tips of the flames dull and ending in much smoke do not trust it1 and particularly when the flux metal is almost fluid4 ,,of ,,alloying ,,the ,,metal4 ,metal for guns must invariably be made with #f or even #h per cent1 that is #f of tin to one hundred of copper1 for the less you put in1 the stronger will the gun be4 ,,when ,,the ,,tin ,,should ,,be ,,added ,,to ,,the ,,copper4 ,the tin should be put in with the copper when the copper is reduced to a fluid4 ,,how ,,to ,,hasten ,,the ,,melting4 ,you can hasten the melting when #b_/c;ds of the copper is fluid2 you can then1 with a stick of chestnut-wood1 repeatedly stir what of copper remains entire amidst what is melted4 ,introductory ,observations on the ,architectural ,designs 7,,xii71 and ,writings on ,architecture 7,,xiii74 ,until now very little has been known regarding ,leonardo's labours in the domain of ,architecture4 ,no building is known to have been planned and executed by him1 though by some contemporary writers incidental allusion is made to his occupying himself with architecture1 and his famous letter to ,lodovico il ,moro1--which has long been a well-known document1--in which he offers his service as an architect to that prince1 tends to confirm the belief that he was something more than an amateur of the art4 ,this hypothesis has lately been confirmed by the publication of certain documents1 preserved at ,milan1 showing that ,leonardo was not only employed in preparing plans but that he took an active part1 with much credit1 as member of a commission on public buildings2 his name remains linked with the history of the building of the ,cathedral at ,pavia and that of the ,cathedral at ,milan4 ,leonardo's writings on ,architecture are dispersed among a large number of ,,mss41 and it would be scarcely possible to master their contents without the opportunity of arranging1 sorting and comparing the whole mass of materials1 so as to have some comprehensive idea of the whole4 ,the sketches1 when isolated and considered by themselves1 might appear to be of but little value2 it is not till we understand their general purport1 from comparing them with each other1 that we can form any just estimate of their true worth4 ,leonardo seems to have had a project for writing a complete and separate treatise on ,architecture1 such as his predecessors and contemporaries had composed--,leon ,battista ,alberti1 ,filarete1 ,francesco di ,giorgio and perhaps also ,bramante4 ,but1 on the other hand1 it cannot be denied that possibly no such scheme was connected with the isolated notes and researches1 treating on special questions1 which are given in this work2 that he was merely working at problems in which1 for some reason or other he took a special interest4 ,a great number of important buildings were constructed in ,lombardy during the period between #adgb and #adii1 and among them there are several by unknown architects1 of so high an artistic merit1 that it is certainly not improbable that either ,bramante or ,leonardo da ,vinci may have been1 directly or indirectly1 concerned in their erection4 ,having been engaged1 for now nearly twenty years1 in a thorough study of ,bramante's life and labours1 ,i have taken a particular interest in detecting the distinguishing marks of his style as compared with ,leonardo's4 ,in #ahfi ,i made researches about the architectural drawings of the latter in the ,codex ,atlanticus at ,milan1 for the purpose of finding out1 if possible the original plans and sketches of the churches of ,santa ,maria delle ,grazie at ,milan1 and of the ,cathedral at ,pavia1 which buildings have been supposed to be the work both of ,bramante and of ,leonardo4 ,since #ahgf ,i have repeatedly examined ,leonardo's architectural studies in the collection of his manuscripts in the ,institut de ,france1 and some of these ,i have already given to the public in my work on ,les ,projets ,primitifs pour la ,basilique de ,st4 ,pierre de ,rome1 ,p#a4 #dc4 ,in #ahgi ,i had the opportunity of examining the manuscript in the ,palazzo ,trivulzio at ,milan1 and in #ahhj ,dr ,richter showed me in ,london the manuscripts in the possession of ,lord ,ashburnham1 and those in the ,british ,museum4 ,i have thus had opportunities of seeing most of ,leonardo's architectural drawings in the original1 but of the manuscripts tliemselves ,i have deciphered only the notes which accompany the sketches4 ,it is to ,dr ,richter's exertions that we owe the collected texts on ,architecture which are now published1 and while he has undertaken to be responsible for the correct reading of the original texts1 he has also made it his task to extract the whole of the materials from the various ,,mss4 ,it has been my task to arrange and elucidate the texts under the heads which have been adopted in this work4 ,,ms4 ,b4 at ,paris and the ,codex ,atlanticus at ,milan are the chief sources of our knowledge of ,leonardo as an architect1 and ,i have recently subjected these to a thorough re-investigation expressly with a view to this work4 ,a complete reproduction of all ,leonardo's architectural sketches has not1 indeed1 been possible1 but as far as the necessarily restricted limits of the work have allowed1 the utmost completeness has been aimed at1 and no efforts have been spared to include every thing that can contribute to a knowledge of ,leonardo's style4 ,it would have been very interesting1 if it had been possible1 to give some general account at least of ,leonardo's work and studies in engineering1 fortification1 canal-making and the like1 and it is only on mature reflection that we have reluctantly abandoned this idea4 ,leonardo's occupations in these departments have by no means so close a relation to literary work1 in the strict sense of the word as we are fairly justified in attributing to his numerous notes on ,architecture4 ,leonardo's architectural studies fall naturally under two heads3 ,i4 ,those drawings and sketches1 often accompanied by short remarks and explanations1 which may be regarded as designs for buildings or monuments intended to be built4 ,with these there are occasionally explanatory texts4 ,,ii4 ,theoretical investigations and treatises4 ,a special interest attaches to these because they discuss a variety of questions which are of practical importance to this day4 ,leonardo's theory as to the origin and progress of cracks in buildings is perhaps to be considered as unique in its way in the literature of ,architecture4 ,,henry ,,de ,,geymuller ,,xii4 ,architectural ,designs4 ,i4 ,plans for towns4 ,a4 ,sketches for laying out a new town with a double system of high- level and low-level road-ways4 ,pl4 ,,lxxvii1 ,no4 #a 7,,ms4 ,b1 #ae;b74 ,a general view of a town1 with the roads outside it sloping up to the high-level ways within4 ,pl4 ,,lxxvii1 ,no4 #c 7,,ms4 ,b1 #af;b4 see ,no4 #gda2 and ,,ms4 ,b4 #ae;b1 see ,no4 #gdb7 gives a partial view of the town1 with its streets and houses1 with explanatory references4 ,pl4 ,,lxxvii1 ,no4 #b 7,,ms4 ,b1 #ae;b2 see ,no4 #gdc74 ,view of a double staircaise with two opposite flights of steps4 ,pl4 ,,lxxviii1 ,nos4 #b and #c 7,,ms4 ,b1 #cg;a74 ,sketches illustrating the connection of the two levels of roads by means of steps4 ,the lower galleries are lighted by openings in the upper roadway4 ,b4 ,notes on removing houses 7,,ms4 ,br4 ,m41 #bgj;b1 see ,no4 #gdd74 #gda4 ,the roads m are #f braccia higher than the roads p s1 and each road must be #bj braccia wide and have #a_/b braccio slope from the sides towards the middle2 and in the middle let there be at every braccio an opening1 one braccio long and one finger wide1 where the rain water may run off into hollows made on the same level as p s4 ,and on each side at the extremity of the width of the said road let there be an arcade1 #f braccia broad1 on columns2 and understand that he who would go through the whole place by the high level streets can use them for this purpose1 and he who would go by the low level can do the same4 ,by the high streets no vehicles and similar objects should circulate1 but they are exclusively for the use of gentlemen4 ,the carts and burdens for the use and convenience of the inhabitants have to go by the low ones4 ,one house must turn its back to the other1 leaving the lower streets between them4 ,provisions1 such as wood1 wine and such things are carried in by the doors n1 and privies1 stables and other fetid matter must be emptied away underground4 ,from one arch to the next #gdb4 must be #cjj braccia1 each street receiving its light through the openings of the upper streets1 and at each arch must be a winding stair on a circular plan because the corners of square ones are always fouled2 they must be wide1 and at the first vault there must be a door entering into public privies and the said stairs lead from the upper to the lower streets and the high level streets begin outside the city gates and slope up till at these gates they have attained the height of #f braccia4 ,let such a city be built near the sea or a large river in order that the dirt of the city may be carried off by the water4 #gdc4 ,the construction of the stairs3 ,the stairs c d go down to f g1 and in the same way f g goes down to h k4 #gdd4 ,,on ,,moving ,,houses4 ,let the houses be moved and arranged in order2 and this will be done with facility because such houses are at first made in pieces on the open places1 and can then be fitted together with their timbers in the site where they are to be permanent4 #i ,let the men of the country or the village partly inhabit the new houses when the court is absent #ab4 ,footnote3 ,on the same page we find notes referring to ,romolontino and ,villafranca with a sketch-map of the course of the ,sodro and the 7,lo7cra 7both are given in the text farther on74 ,there can hardly be a doubt that the last sentence of the passage given above1 refers to the court of ,francis ,i4 ,king of ,france4--,l4#i-ac are written inside the larger sketch1 which1 in the original1 is on the right hand side of the page by the side of lines #a-h4 ,the three smaller sketches are below4 ,j4 ,p4 ,r4 ,,ii4 ,plans for canals and streets in a town4 ,pl4 ,,lxxix1 #a4 and #b1 7,,ms4 ,b1 #cg;b1 see ,no4 #gde1 and ,,ms4 ,b4 #cf;a1 see ,no4 #gdf74 ,a ,plan for streets and canals inside a town1 by which the cellars of the houses are made accessible in boats4 ,the third text given under ,no4 #gdg refers to works executed by ,leonardo in ,france4 #gde4 ,the front a m will give light to the rooms2 a e will be #f braccia--a b #h braccia --b e #cj braccia1 in order that the rooms under the porticoes may be lighted2 c d f is the place where the boats come to the houses to be unloaded4 ,in order to render this arrangement practicable1 and in order that the inundation of the rivers may not penetrate into the cellars1 it is necessary to chose an appropriate situation1 such as a spot near a river which can be diverted into canals in which the level of the water will not vary either by inundations or drought4 ,the construction is shown below2 and make choice of a fine river1 which the rains do not render muddy1 such as the ,ticino1 the ,adda and many others4 ,footnote #ab3 ,tesino1 ,adda e molti altri1 i4e4 rivers coming from the mountains and flowing through lakes4 ,the construction to oblige the waters to keep constantly at the same level will be a sort of dock1 as shown below1 situated at the entrance of the town2 or better still1 some way within1 in order that the enemy may not destroy it #ad4 ,footnote3 ,l4 #a-d are on the left hand side and within the sketch given on ,pl4 ,,lxxix1 ,no4 ,i4 ,then follows after line #ad1 the drawing of a sluicegate--conca--of which the use is explained in the text below it4 ,on the page #ch;a1 which comes next in the original ,,ms4 is the sketch of an oval plan of a town over which is written modo di canali per la citta and through the longer axis of it canale magior is written with ,tesino on the prolongation of the canal4 ,j4 ,p4 ,r4 #gdf4 ,let the width of the streets be equal to the average height of the houses4 #gdg4 ,the main underground channel does not receive turbid water1 but that water runs in the ditches outside the town with four mills at the entrance and four at the outlet2 and this may be done by damming the water above ,romorantin4 #aa,there should be fountains made in each piazza#ac4 ,footnote3 ,in the original this text comes immediately after the passage given as ,no4 #gdd4 ,the remainder of the writing on the same page refers to the construction of canals and is given later1 in the ,topographical ,notes4 ,lines #a-aa are written to the right of the plan lines #aa-ac underneath it4 ,j4 ,p4 ,r4 ,footnote #aj3 ,romolontino is ,romorantin1 ,south of ,orleans in ,france4 ,,iii4 ,castles and ,villas4 ,a4 ,castles4 ,pl4 ,,lxxx1 ,no4 #a 7,p4 ,v4 fol4 #ci;b2 ,no4 d'ordre #bbhb74 ,the fortified place here represented is said by ,vallardi to be the castello at ,milan1 but without any satisfactory reason4 ,the high tower behind the rivellino ravelin--seems to be intended as a watch-tower4 ,pl4 ,,lxxx1 ,no4 #b 7,,ms4 ,b1 #bc;b74 ,a similarly constructed tower probably intended for the same use4 ,pl4 ,,lxxx1 ,no4 #c 7,,ms4 ,b74 ,sketches for corner towers with steps for a citadel4 ,pl4 ,,lxxx1 ,no4 #d 7,w4 ,,xvi74 ,a cupola crowning a corner tower2 an interesting example of decorative fortification4 ,in this reproduction of the original pen and ink drawing it appears reversed4 ,b4 ,projects for ,palaces4 ,pl4 ,,lxxxi1 ,no4 #b 7,,ms4 ,c4 ,a1 #ge;b2 #bba;a1 see ,no4 #gdh74 ,project for a royal residence at ,amboise in ,france4 ,pl4 ,,lxxxii1 ,no4 #a 7,c4 ,a #cjh;a2 #ici;a74 ,a plan for a somewhat extensive residence1 and various details2 but there is no text to elucidate it2 in courts are written the three names3 ,sam cosi giova 7,st4 ,mark7 7,cosmo7 7,john71 arch mo nino ,c4 ,plans for small castles or ,villas4 ,the three following sketches greatly resemble each other4 ,pl4 ,,lxxxii1 ,no4 #b 7,,ms4 ,k#c #cf;b2 see ,no4 #gdi74 ,pl4 ,,lxxxii1 ,no4 #c 7,,ms4 ,b #fj;a2 ,see ,no4 #gej74 ,pl4 ,,lxxxiii 7,w4 ,,xvii74 ,the text on this sheet refers to ,cyprus 7see ,topographical ,notes ,no4 #aajc71 but seems to have no direct connection with the sketches inserted between4 ,pl4 ,,lxxxviii1 ,nos4 #f and #g 7,,ms4 ,b1 #ab;a2 see ,no4 #gea74 ,a section of a circular pavilion with the plan of a similar building by the side of it4 ,these two drawings have a special historical interest because the text written below mentions the ,duke and ,duchess of ,milan4 ,the sketch of a villa on a terrace at the end of a garden occurs in ,c4 ,a4 #aej2 and in ,c4 ,a4 #gg;b2 #bbe;b is another sketch of a villa somewhat resembling the ,belvedere of ,pope ,innocent ,,viii1 at ,rome4 ,in ,c4 ,a4 #fb;b2 #aic;b there is a ,loggia4 ,pl4 ,,lxxxii1 ,no4 #d 7,c4 ,a4 #chg;a2 #aaih;a7 is a tower-shaped ,loggia above a fountain4 ,the machinery is very ingeniously screened from view4 #gdh4 ,the ,palace of the prince must have a piazza in front of it4 ,houses intended for dancing or any kind of jumping or any other movements with a multitude of people1 must be on the ground- floor2 for ,i have already witnessed the destruction of some1 causing death to many persons1 and above all let every wall1 be it ever so thin1 rest on the ground or on arches with a good foundation4 ,let the mezzanines of the dwellings be divided by walls made of very thin bricks1 and without wood on account of fire4 ,let all the privies have ventilation by shafts in the thickness of the walls1 so as to exhale by the roofs4 ,the mezzanines should be vaulted1 and the vaults will be stronger in proportion as they are of small size4 ,the ties of oak must be enclosed in the walls in order to be protected from fire4 ,footnote3 ,the remarks accompanying the plan reproduced on ,pl4 ,,lxxxi1 ,no4 #b are as follows3 ,above1 to the left3 in a angholo stia la guardia de la sstalla 7in the angle a may be the keeper of the stable74 ,below are the words strada dabosa 7road to ,amboise71 parallel with this fossa br #dj 7the moat #dj braccia7 fixing the width of the moat4 ,in the large court surrounded by a portico in terre ,no4--,largha br4#hj e lugha br #abj4 ,to the right of the castle is a large basin for aquatic sports with the words ,giostre colle nave cioe li giostra li stieno sopra le na 7,jousting in boats that is the men are to be in boats74 ,j4 ,p4 ,r4 ,the privies must be numerous and going one into the other in order that the stench may not penetrate into the dwellings41 and all their doors must shut off themselves with counterpoises4 ,the main division of the facade of this palace is into two portions2 that is to say the width of the court-yard must be half the whole facade2 the #bnd 444 #gdi4 #cj braccia wide on each side2 the lower entrance leads into a hall #aj braccia wide and #cj braccia long with #d recesses each with a chimney4 ,footnote3 ,on each side of the castle1 ,pl4 ,,lxxxii4 ,no4 #b there are drawings of details1 to the left ,camino a chimney1 to the right the central lantern1 sketched in red #h lati i4e4 an octagon4 #gej4 ,the firststorey or terrace must be entirely solid4 #gea4 ,the pavilion in the garden of the ,duchess of ,milan4 ,the plan of the pavilion which is in the middle of the labyrinth of the ,duke of ,milan4 ,footnote3 ,this passage was first published by ,,amoretti in ,memorie ,storiche ,cap4 ,x3 ,una sua opera da riportarsi a quest' anno fu il bagno fatto per la duchessa ,beatrice nel parco o giardino del ,castello4 ,lionardo non solo ne disegno il piccolo edifizio a foggia di padiglione1 nel cod4 segnato ,q4 #c1 dandone anche separatamente la pianta2 ma sotto vi scrisse3 ,padiglione del giardino della duchessa2 e sotto la pianta3 ,fondamento del padiglione ch'e nel mezzo del labirinto del duca di ,milano2 nessuna data e presso il padiglione1 disegnato nella pagina #ab1 ma poco sopra fra molti circoli intrecciati vedesi #aj ,luglio #adib e nella pagina #b presso ad alcuni disegni di legumi qualcheduno ha letto ,settembre #adhb in vece di #adib1 come dovea scriverevi1 e probabilmente scrisse ,lionardo4 ,the original text however hardly bears the interpretation put upon it by ,,amoretti4 ,he is mistaken as to the mark on the ,,ms4 as well as in his statements as to the date1 for the ,,ms4 in question has no date2 the date he gives occurs1 on the contrary1 in another note-book4 ,finally1 it appears to me quite an open question whether ,leonardo was the architect who carried out the construction of the dome-like ,pavilion here shown in section1 or of the ground plan of the ,pavilion drawn by the side of it4 ,must we1 in fact1 suppose that il duca di ,milano here mentioned was1 as has been generally assumed1 ,ludovico il ,moro8 ,he did not hold this title from the ,emperor before #adid2 till that date he was only called ,governatore and ,leonardo in speaking of him1 mentions him generally as il ,moro even after #adid4 ,on ,january #ah1 #adia1 he married ,beatrice d',este the daughter of ,ercole ,i1 ,duke of ,ferrara4 ,she died on the #bnd ,january #adig1 and for the reasons ,i have given it seems improbable that it should be this princess who is here spoken of as the ,duchessa di ,milano4 ,from the style of the handwriting it appears to me to be beyond all doubt that the ,,ms4 ,b1 from which this passage is taken1 is older than the dated ,,mss4 of #adib and #adic4 ,in that case the ,duke of ,milan here mentioned would be ,gian ,galeazzo 7#adfi-adid7 and the ,duchess would be his wife ,isabella of ,aragon1 to whom he was married on the second ,february #adhi4 ,j4 ,p4 ,r4 #geb4 ,the earth that is dug out from the cellars must be raised on one side so high as to make a terrace garden as high as the level of the hall2 but between the earth of the terrace and the wall of the house1 leave an interval in order that the damp may not spoil the principal walls4 ,,iv4 ,ecclesiastical ,architecture4 ,a4 ,general ,observations4 #gec4 ,a building should always be detached on all sides so that its form may be seen4 ,footnote3 ,the original text is reproduced on ,pl4 ,,xcii1 ,no4 #a to the left hand at the bottom4 #ged4 ,here there cannot and ought not to be any campanile2 on the contrary it must stand apart like that of the ,cathedral and of ,san ,giovanni at ,florence1 and of the ,cathedral at ,pisa1 where the campanile is quite detached as well as the dome4 ,thus each can display its own perfection4 ,if however you wish to join it to the church1 make the lantern serve for the campanile as in the church at ,chiaravalle4 ,footnote3 ,this text is written by the side of the plan given on ,pl4 ,,xci4 ,no4 #b4 ,footnote #ab3 ,the ,abbey of ,chiaravalle1 a few miles from ,milan1 has a central tower on the intersection of the cross in the style of that of the ,certosa of ,pavia1 but the style is mediaeval 7,a4 ,d4 #accj74 ,leonardo seems here to mean1 that in a building1 in which the circular form is strongly conspicuous1 the campanile must either be separated1 or rise from the centre of the building and therefore take the form of a lantern4 #gee4 ,it never looks well to see the roofs of a church2 they should rather be flat and the water should run off by gutters made in the frieze4 ,footnote3 ,this text is to the left of the domed church reproduced on ,pl4 ,,lxxxvii1 ,no4 #b4 ,b4 ,the theory of ,dome ,architecture4 ,this subject has been more extensively treated by ,leonardo in drawings than in writing4 ,still we may fairly assume that it was his purpose1 ultimately to embody the results of his investigation in a ,trattato delle ,cupole4 ,the amount of materials is remarkably extensive4 ,,ms4 ,b is particularly rich in plans and elevations of churches with one or more domes--from the simplest form to the most complicated that can be imagined4 ,considering the evident connexion between a great number of these sketches1 as well as the impossibility of seeing in them designs or preparatory sketches for any building intended to be erected1 the conclusion is obvious that they were not designed for any particular monument1 but were theoretical and ideal researches1 made in order to obtain a clear understanding of the laws which must govern the construction of a great central dome1 with smaller ones grouped round it2 and with or without the addition of spires1 so that each of these parts by itself and in its juxtaposition to the other parts should produce the grandest possible effect4 ,in these sketches ,leonardo seems to have exhausted every imaginable combination4 ,footnote #a3 ,in ,,ms4 ,b1 #cb;b 7see ,pl4 ,c ,,iii1 ,no4 #b7 we find eight geometrical patterns1 each drawn in a square2 and in ,,ms4 ,c4,a41 fol4 #hg to #ih form a whole series of patterns done with the same intention4 ,the results of some of these problems are perhaps not quite satisfactory2 still they cannot be considered to give evidence of a want of taste or of any other defect in ,leonardo s architectural capacity4 ,they were no doubt intended exclusively for his own instruction1 and1 before all1 as it seems1 to illustrate the features or consequences resulting from a given principle4 ,i have already1 in another place1 ,footnote #a3 ,les ,projets ,primitifs pour la ,basilique de ,st4 ,pierre de ,rome1 par ,bramante1 ,raphael etc41,vol4 ,i1 p4 #b4 pointed out the law of construction for buildings crowned by a large dome3 namely1 that such a dome1 to produce the greatest effect possible1 should rise either from the centre of a ,greek cross1 or from the centre of a structure of which the plan has some symmetrical affinity to a circle1 this circle being at the same time the centre of the whole plan of the building4 ,leonardo's sketches show that he was fully aware1 as was to be expected1 of this truth4 ,few of them exhibit the form of a ,latin cross1 and when this is met with1 it generally gives evidence of the determination to assign as prominent a part as possible to the dome in the general effect of the building4 ,while it is evident1 on the one hand1 that the greater number of these domes had no particular purpose1 not being designed for execution1 on the other hand several reasons may be found for ,leonardo's perseverance in his studies of the subject4 ,besides the theoretical interest of the question for ,leonardo and his ,trattato and besides the taste for domes prevailing at that time1 it seems likely that the intended erection of some building of the first importance like the ,duomos of ,pavia and ,como1 the church of ,sta4 ,maria delle ,grazie at ,milan1 and the construction of a ,dome or central ,tower 7,tiburio7 on the cathedral of ,milan1 may have stimulated ,leonardo to undertake a general and thorough investigation of the subject2 whilst ,leonardo's intercourse with ,bramante for ten years or more1 can hardly have remained without influence in this matter4 ,in fact now that some of this great ,architect's studies for ,s4 ,peter's at ,rome have at last become known1 he must be considered henceforth as the greatest master of ,dome-,architecture that ever existed4 ,his influence1 direct or indirect even on a genius like ,leonardo seems the more likely1 since ,leonardo's sketches reveal a style most similar to that of ,bramante1 whose name indeed1 occurs twice in ,leonardo's manuscript notes4 ,it must not be forgotten that ,leonardo was a ,florentine2 the characteristic form of the two principal domes of ,florence1 ,sta4 ,maria del ,fiore and the ,battisterio1 constantly appear as leading features in his sketches4 ,the church of ,san ,lorenzo at ,milan1 was at that time still intact4 ,the dome is to this day one of the most wonderful cupolas ever constructed1 and with its two smaller domes might well attract the attention and study of a never resting genius such as ,leonardo4 ,a whole class of these sketches betray in fact the direct influence of the church of ,s4 ,lorenzo1 and this also seems to have suggested the plan of ,bramante's dome of ,st4 ,peter's at ,rome4 ,in the following pages the various sketches for the construction of domes have been classified and discussed from a general point of view4 ,on two sheets3 ,pl4 ,,lxxxiv 7,c4,a4 #ced;b2 #aah;a7 and ,pl4 ,,lxxxv1 ,nos4 #a-aa 7,ash4 ,,ii1 #f;b7 we see various dissimilar types1 grouped together2 thus these two sheets may be regarded as a sort of nomenclature of the different types1 on which we shall now have to treat4 #a4 ,churches formed on the plan of a ,greek cross4 ,group ,i4 ,domes rising from a circular base4 ,the simplest type of central building is a circular edifice4 ,pl4 ,,lxxxiv1 ,no4 #i4 ,plan of a circular building surrounded by a colonnade4 ,pl4 ,,lxxxiv1 ,no4 #h4 ,elevation of the former1 with a conical roof4 ,pl4 ,,xc4 ,no4 #e4 ,a dodecagon1 as most nearly approaching the circle4 ,pl4 ,,lxxxvi1 ,no4 #a1 #b1 #c4 ,four round chapels are added at the extremities of the two principal axes2--compare this plan with fig4 #a on p4 #dd and fig4 #c on p4 #dg 7,w4 ,p4 #e;b7 where the outer wall is octagonal4 ,group ,,ii4 ,domes rising from a square base4 ,the plan is a square surrounded by a colonnade1 and the dome seems to be octagonal4 ,pl4 ,,lxxxiv4 ,the square plan below the circular building ,no4 #h1 and its elevation to the left1 above the plan3 here the ground-plan is square1 the upper storey octagonal4 ,a further development of this type is shown in two sketches ,c4 ,a4 #c;a 7not reproduced here71 and in ,pl4 ,,lxxxvi1 ,no4 #e 7which possibly belongs to ,no4 #g on ,pl4 ,,lxxxiv74 ,pl1 ,,lxxxv1 ,no4 #d1 and p4 #de1 ,fig4 #c1 a ,greek cross1 repeated p4 #de1 ,fig4 #c1 is another development of the square central plan4 ,the remainder of these studies show two different systems2 in the first the dome rises from a square plan1--in the second from an octagonal base4 ,group ,,iii4 ,domes rising from a square base and four pillars4 ,footnote #a3 ,the ancient chapel ,san ,satiro1 via del ,falcone1 ,milan1 is a specimen of this type4 a7 ,first type4 ,a ,dome resting on four pillars in the centre of a square edifice1 with an apse in the middle1 of each of the four sides4 ,we have eleven variations of this type4 aa7 ,pl4 ,,lxxxviii1 ,no4 #c4 bb7 ,pl4 ,,lxxx1 ,no4 #e4 cc7 ,pl4 ,,lxxxv1 ,nos4 #b1 #c1 #e4 dd7 ,pl4 ,,lxxxiv1 ,no4 #a and #d beneath4 ee7 ,pl4 ,,lxxxv1 ,nos4 #a1 #g1 #aj1 #aa4 b7 ,second type4 ,this consists in adding aisles to the whole plan of the first type2 columns are placed between the apses and the aisles2 the plan thus obtained is very nearly identical with that of ,s4 ,lorenzo at ,milan4 ,fig4 #a on p4 #ef4 7,,ms4 ,b1 #ge;a7 shows the result of this treatment adapted to a peculiar purpose about which we shall have to say a few words later on4 ,pl4 ,,xcv1 ,no4 #a1 shows the same plan but with the addition of a short nave4 ,this plan seems to have been suggested by the general arrangement of ,s4 ,sepolcro at ,milan4 ,,ms4 ,b4 #eg;b 7see the sketch reproduced on p4#ea74 ,by adding towers in the four outer angles to the last named plan1 we obtain a plan which bears the general features of ,bramante's plans for ,s4 ,peter's at ,rome4 ,footnote #b3 ,see ,les projets primitifs etc41 ,pl4 #i-ab4 7,see p4 #ea ,fig4 #a47 ,group ,,iv4 ,domes rising from an octagonal base4 ,this system1 developed according to two different schemes1 has given rise to two classes with many varieties4 ,in a7 ,on each side of the octagon chapels of equal form are added4 ,in b7 ,the chapels are dissimilar2 those which terminate the principal axes being different in form from those which are added on the diagonal sides of the octagon4 a4 ,first ,class4 ,the ,chapel degli ,angeli1 at ,florence1 built only to a height of about #bj feet by ,brunellesco1 may be considered as the prototype of this group2 and1 indeed it probably suggested it4 ,the fact that we see in ,,ms4 ,b4 #aa;b 7,pl4 ,,xciv1 ,no4 #c7 by the side of ,brunellesco's plan for the ,basilica of ,sto4 ,spirito at ,florence1 a plan almost identical with that of the ,capella degli ,angeli1 confirms this supposition4 ,only two small differences1 or we may say improvements1 have been introduced by ,leonardo4 ,firstly the back of the chapels contains a third niche1 and each angle of the ,octagon a folded pilaster like those in ,bramante's ,sagrestia di ,s4 ,m4 presso ,san ,satiro at ,milan1 instead of an interval between the two pilasters as seen in the ,battistero at ,florence and in the ,sacristy of ,sto4 ,spirito in the same town and also in the above named chapel by ,brunellesco4 ,the first set of sketches which come under consideration have at first sight the appearance of mere geometrical studies4 ,they seem to have been suggested by the plan given on page #dd ,fig4 #b 7,,ms4 ,b1 #ee;a7 in the centre of which is written ,santa ,maria in perticha da ,pavia1 at the place marked ,a on the reproduction4 a7 7,,ms4 ,b1 #cd;b1 page #dd ,fig4 #c74 ,in the middle of each side a column is added1 and in the axes of the intercolumnar spaces a second row of columns forms an aisle round the octagon4 ,these are placed at the intersection of a system of semicircles1 of which the sixteen columns on the sides of the octagon are the centres4 b7 ,the preceding diagram is completed and becomes more monumental in style in the sketch next to it 7,,ms4 ,b1 #ce;a1 see p4 #de ,fig4 #a74 ,an outer aisle is added by circles1 having for radius the distance between the columns in the middle sides of the octagon4 c7 7,,ms4 ,b4 #if;b1 see p4 #de ,fig4 #b74 ,octagon with an aisle round it2 the angles of both are formed by columns4 ,the outer sides are formed by #h niches forming chapels4 ,the exterior is likewise octagonal1 with the angles corresponding to the centre of each of the interior chapels4 ,pl4 ,,xcii1 ,no4 #b 7,,ms4 ,b4 #if;b74 ,detail and modification of the preceding plan--half columns against piers--an arrangement by which the chapels of the aisle have the same width of opening as the inner arches between the half columns4 ,underneath this sketch the following note occurs3 questo vole - avere #ab facce - co #ab tabernaculi - come - a - b4 7,this will have twelve sides with twelve tabernacles as a b47 ,in the remaining sketches of this class the octagon is not formed by columns at the angles4 ,the simplest type shows a niche in the middle of each side and is repeated on several sheets1 viz3 ,,ms4 ,b #c2 ,,ms4 ,c4,a4 #ced;b 7see ,pl4 ,,lxxxiv1 ,no4 #aa7 and ,,ms4 ,ash ,,ii #f;b2 7see ,pl4 ,,lxxxv1 ,no4 #i and the elevations ,no4 #h2 ,pl4 ,,xcii1 ,no4 #c2 ,,ms4 ,b4 #d;b not reproduced here and ,pl4 ,,lxxxiv1 ,no4 #b74 ,pl4 ,,xcii1 #c 7,,ms4 ,b1 #ef;b7 corresponds to a plan like the one in ,,ms4 ,b #ce;a1 in which the niches would be visible outside or1 as in the following sketch1 with the addition of a niche in the middle of each chapel4 ,pl4 ,,xc1 ,no4 #f4 ,the niches themselves are surrounded by smaller niches 7see also ,no4 #a on the same plate74 ,octagon expanded on each side4 ,a4 by a square chapel3 ,,ms4 ,b4 #cd;b 7not reproduced here74 ,b4 by a square with #c niches3 ,,ms4 ,b4 #aa;b 7see ,pl4 ,,xciv1 ,no4 #c74 ,c4 by octagonal chapels3 a7 ,,ms4 ,b1 #ba;a2 ,pl4 ,,lxxxviii1 ,no4 #d4 b7 ,no4 #b on the same plate4 ,underneath there is the remark3 quest'e come le #h cappele ano a essere facte 7this is how the eight chapels are to be executed74 c7 ,pl4 ,,lxxxviii1 ,no4 #e4 ,elevation to the plans on the same sheet1 it is accompanied by the note3 ciasscuno de' #i tiburi no'uole - passare l'alteza - di - #b - quadri 7neither of the #i domes must exceed the height of two squares74 d7 ,pl4 ,,lxxxviii1 ,no4 #a4 ,inside of the same octagon4 ,,ms4 ,b1 #cj;a1 and #cd;b2 these are three repetitions of parts of the same plan with very slight variations4 ,d4 by a circular chapel3 ,,ms4 ,b1 #ah;a 7see ,fig4 #a on page #dg7 gives the plan of this arrangement in which the exterior is square on the ground floor with only four of the chapels projecting1 as is explained in the next sketch4 ,pl4 ,,lxxxix1 ,,ms4 ,b1 #ag;b4 ,elevation to the preceding plan sketched on the opposite side of the sheet1 and also marked ,a4 ,it is accompanied by the following remark1 indicating the theoretical character of these studies3 questo - edifitio - anchora - starebbe - bene affarlo dalla linja - a - b - c - d - insu4 7,this edifice would also produce a good effect if only the part above the lines a b1 c d1 were executed74 ,pl4 ,,lxxxiv1 ,no4 #aa4 ,the exterior has the form of an octagon1 but the chapels project partly beyond it4 ,on the left side of the sketch they appear larger than on the right side4 ,pl4 ,,xc1 ,no4 #a1 7,,ms4 ,b1 #be;b72 ,repetition of ,pl4 ,,lxxxiv1 ,no4 #aa4 ,pl4 ,,xc1 ,no4 #b4 ,elevation to the plan ,no4 #a1 and also to ,no4 #f of the same sheet4 ,e4 ,by chapels formed by four niches3 ,pl4 ,,lxxxiv1 ,no4 #g 7the circular plan on the left below7 shows this arrangement in which the central dome has become circular inside and might therefore be classed after this group4 ,footnote #a3 ,this plan and some others of this class remind us of the plan of the ,mausoleum of ,augustus as it is represented for instance by ,durand4 ,see ,cab4 des ,estampes1 ,bibliotheque ,nationale1 ,paris1 ,topographie de ,rome1 ,v1 #f1 #hb4 ,the sketch on the right hand side gives most likely the elevation for the last named plan4 ,f4 ,by chapels of still richer combinations1 which necessitate an octagon of larger dimensions3 ,pl4 ,,xci1 ,no4 #b 7,,ms4 ,ash4 #aa4 #h;b7 ,footnote #b3 ,the note accompanying this plan is given under ,no4 #ged42 on this plan the chapels themselves appear to be central buildings formed like the first type of the third group4 ,pl4 ,,lxxxviii1 ,no4 #c4 ,pl4 ,,xci1 ,no4 #b above2 the exterior of the preceding figure1 particularly interesting on account of the alternation of apses and niches1 the latter containing statues of a gigantic size1 in proportion to the dimension of the niches4 b4 ,second ,class4 ,composite plans of this class are generally obtained by combining two types of the first class--the one worked out on the principal axes1 the other on the diagonal ones4 ,,ms4 ,b4 #bb shows an elementary combination1 without any additions on the diagonal axes1 but with the dimensions of the squares on the two principal axes exceeding those of the sides of the octagon4 ,in the drawing ,w4 ,p4 #e;b 7see page #dd ,fig4 #a7 the exterior only of the edifice is octagonal1 the interior being formed by a circular colonnade2 round chapels are placed against the four sides of the principal axes4 ,the elevation1 drawn on the same sheet 7see page #dg ,fig4 #c71 shows the whole arrangement which is closely related with the one on ,pl4 ,,lxxxvi ,no4 #a1 #b4 ,,ms4 ,b4 #ba;a shows3 a7 four sides with rectangular chapels crowned by pediments ,pl4 ,,lxxxvii ,no4 #c 7plan and elevation72 b7 four sides with square chapels crowned by octagonal domes4 ,pl4 ,,lxxxvii ,no4 #d2 the plan underneath4 ,,ms4 ,b4 #ah;a shows a variation obtained by replacing the round chapels in the principal axes of the sketch ,,ms4 ,b4 l#h;a by square ones1 with an apse4 ,leonardo repeated both ideas for better comparison side by side1 see page #dg4 ,fig4 #b4 ,pl4 ,,lxxxix 7,,ms4 ,b4 #ag;b74 ,elevation for the preceding figure4 ,the comparison of the drawing marked ,m with the plan on page #dg ,fig4 #b1 bearing the same mark1 and of the elevation on ,pl4 ,,lxxxix below 7marked ,a7 with the corresponding plan on page #dg is highly instructive1 as illustrating the spirit in which ,leonardo pursued these studies4 ,pl4 ,,lxxxiv ,no4 #ab shows the design ,pl4 ,,lxxxvii ,no4 #c combined with apses1 with the addition of round chapels on the diagonal sides4 ,pl4 ,,lxxxiv ,no4 #ac is a variation of the preceding sketch4 ,pl4 ,,xc ,no4 #c4 ,,ms4 ,b4 #be;b4 ,the round chapels of the preceding sketch are replaced by octagonal chapels1 above which rise campaniles4 ,pl4 ,,xc ,no4 #d is the elevation for the preceding plan4 ,pl4 ,,xcii ,no4 #a4 7,,ms4 ,b4 #ci;b472 the plan below4 ,on the principal as well as on the diagonal axes are diagonal chapels1 but the latter are separated from the dome by semicircular recesses4 ,the communication between these eight chapels forms a square aisle round the central dome4 ,above this figure is the elevation1 showing four campaniles on the angles4 ,footnote #a3 ,the note accompanying this drawing is reproduced under ,no4 #gec4 ,pl4 ,,lxxxiv ,no4 #c4 ,on the principal axes are square chapels with three niches2 on the diagonals octagonal chapels with niches4 ,cod4 ,atl4 #cdj;b gives a somewhat similar arrangement4 ,,ms4 ,b4 #cj4 ,the principal development is thrown on the diagonal axes by square chapels with three niches2 on the principal axes are inner recesses communicating with outer ones4 ,the plan ,pl4 ,,xciii ,no4 #b 7,,ms4 ,b4 #bb7 differs from this only in so far as the outer semicircles have become circular chapels1 projecting from the external square as apses2 one of them serves as the entrance by a semicircular portico4 ,the elevation is drawn on the left side of the plan4 ,,ms4 ,b4 #ai4 ,a further development of ,,ms4 ,b4 #ah1 by employing for the four principal chapels the type ,pl4 ,,lxxxviii ,no4 #c1 as we have already seen in ,pl4 ,,xci ,no4 #b2 the exterior presents two varieties4 a7 ,the outer contour follows the inner4 ,footnote #b3 ,these chapels are here sketched in two different sizes2 it is the smaller type which is thus formed4 b7 ,it is semicircular4 ,pl4 ,,lxxxvii ,no4 #b 7,,ms4 ,b4 #ah;b7 ,elevation to the first variation ,,ms4 ,b4 #ai4 ,if we were not certain that this sketch was by ,leonardo1 we might feel tempted to take it as a study by ,bramante for ,st4 ,peter's at ,rome4 ,footnote #c3 ,see ,les projets primitifs ,pl4 #dc4 ,,ms4 ,p4 ,v4 #ci;b4 ,in the principal axes the chapels of ,,ms4 ,b4 #ai1 and semicircular niches on the diagonals4 ,the exterior of the whole edifice is also an octagon1 concealing the form of the interior chapels1 but with its angles on their axes4 ,group ,v4 ,suggested by ,san ,lorenzo at ,milan4 ,in ,,ms4 ,c4 ,a4 #bff ,i,ib1 #hl#b;b there is a plan almost identical with that of ,san ,lorenzo4 ,the diagonal sides of the irregular octagon are not indicated4 ,if it could be proved that the arches which1 in the actual church1 exist on these sides in the first story1 were added in #aegd by ,martimo ,bassi1 then this plan and the following section would be still nearer the original state of ,san ,lorenzo than at present4 ,a reproduction of this slightly sketched plan has not been possible4 ,it may however be understood from ,pl4 ,,lxxxviii ,no4 #c1 by suppressing the four pillars corresponding to the apses4 ,pl4 ,,lxxxvii ,no4 #a shows the section in elevation corresponding with the above-named plan4 ,the recessed chapels are decorated with large shells in the halfdomes like the arrangement in ,san ,lorenzo1 but with proportions like those of ,bramante's ,sacristy of ,santa ,maria presso ,s4 ,satiro4 ,,ms4 ,c4 ,a4 #bff2 a sheet containing three views of exteriors of ,domes4 ,on the same sheet there is a plan similar to the one above-named but with uninterrupted aisles and with the addition of round chapels in the axes 7compare ,pl4 ,,xcvii ,no4 #c and page #dd ,fig4 #a71 perhaps a reminiscence of the two chapels annexed to ,san ,lorenzo4--,leonardo has here sketched the way of transforming this plan into a ,latin cross by means of a nave with side aisles4 ,pl4 ,,xci ,no4 #a4 ,plan showing a type deprived of aisles and comprised in a square building which is surrounded by a portico4 ,it is accompanied by the following text3 #gef4 ,this edifice is inhabited accessible below and above1 like ,san ,sepolcro1 and it is the same above as below1 except that the upper story has the dome c d2 and the ,footnote3 ,the church of ,san ,sepolcro at ,milan1 founded in #ajcj and repeatedly rebuilt after the middle of the ,x,v,ith century1 still stands over the crypt of the original structure4 lower has the dome a b1 and when you enter into the crypt1 you descend #aj steps1 and when you mount into the upper you ascend #bj steps1 which1 with #a_/c braccio for each1 make #aj braccia1 and this is the height between one floor of the church and the other4 ,above the plan on the same sheet is a view of the exterior4 ,by the aid of these two figures and the description1 sections of the edifice may easily be reconstructed4 ,but the section drawn on the left side of the building seems not to be in keeping with the same plan1 notwithstanding the explanatory note written underneath it3 dentro il difitio di sopra 7interior of the edifice above7,footnote #a3 ,the small inner dome corresponds to a b on the plan--it rises from the lower church into the upper-- above1 and larger1 rises the dome c d4 ,the aisles above and below thus correspond 7e di sopra come di sotto1 salvoche etc474 ,the only difference is1 that in the section ,leonardo has not taken the trouble to make the form octagonal1 but has merely sketched circular lines in perspective4 ,j4 ,p4 ,r44 ,before leaving this group1 it is well to remark that the germ of it seems already indicated by the diagonal lines in the plans ,pl4 ,,lxxxv ,no4 #aa and ,no4 #g4 ,we shall find another application of the same type to the ,latin cross in ,pl4 ,,xcvii ,no4 #c4 #b4 ,churches formed on the plan of a ,latin cross4 ,we find among ,leonardo's studies several sketches for churches on the plan of the ,latin cross2 we shall begin by describing them1 and shall add a few observations4 ,a4 ,studies after existing ,monuments4 ,pl4 ,,xciv ,no4 #b4 7,,ms4 ,b4 #aa;b47 ,plan of ,santo ,spirito at ,florence1 a basilica built after the designs of ,brunellesco4--,leonardo has added the indication of a portico in front1 either his own invention or the reproduction of a now lost design4 ,pl4 ,,xcv ,no4 #b4 ,plan accompanied by the words3 ,a e santo sepolcro di milano di sopra7,a is the upper church of ,s4 ,sepolcro at ,milan72 although since ,leonardo's time considerably spoilt1 it is still the same in plan4 ,the second plan with its note3 ,b e la sua parte socto tera 7,b is its subterranean part the crypt7 still corresponds with the present state of this part of the church as ,i have ascertained by visiting the crypt with this plan4 ,excepting the addition of a few insignificant walls1 the state of this interesting part of the church still conforms to ,leonardo's sketch2 but in the ,vestibolo the two columns near the entrance of the winding stairs are absent4 ,b4 ,designs or ,studies4 ,,pl4 ,,xcv ,no4 #a4 ,plan of a church evidently suggested by that of ,san ,sepolcro at ,milan4 ,the central part has been added to on the principle of the second type of ,group ,,iii4 ,leonardo has placed the coro 7choir7 in the centre4 ,pl4 ,,xcvi ,no4 #b4 ,in the plan the dome1 as regards its interior1 belongs to the ,first ,class of ,group ,,iv1 and may be grouped with the one in ,,ms4 ,b4 #ce;a4 ,the nave seems to be a development of the type represented in ,pl4 ,,xcv ,no4 #b1 ,b4 by adding towers and two lateral porticos,footnote #a3 ,already published in ,les projets primitifs ,pl4 ,,xliii44 ,on the left is a view of the exterior of the preceding plan4 ,it is accompanied by the following note3 #geg4 ,this building is inhabited below and above2 the way up is by the campaniles1 and in going up one has to use the platform1 where the drums of the four domes are1 and this platform has a parapet in front1 and none of these domes communicate with the church1 but they are quite separate4 ,pl4 ,,xcvi ,no4 #a 7,,ms4 ,c4 ,a4 #af;b2 #fe;a74 ,perspective view of a church seen from behind2 this recalls the ,duomo at ,florence1 but with two campaniles,footnote #b3 ,already published in the ,saggio ,pl4 ,,ix44 ,pl4 ,,xcvii ,no4 #c 7,,ms4 ,b4 #eb;a74 ,the central part is a development of ,s4 ,lorenzo at ,milan1 such as was executed at the ,duomo of ,pavia4 ,there is sufficient analogy between the building actually executed and this sketch to suggest a direct connection between them4 ,leonardo accompanied ,francesco di ,giorgio,footnote #c3 ,see ,,malaspina1 il ,duomo di ,pavia4 ,documents4 when the latter was consulted on ,june #bast1 #adij as to this church2 the fact that the only word accompanying the plan is3 sagrestia1 seems to confirm our supposition1 for the sacristies were added only in #adib1 i4 e4 four years after the beginning of the ,cathedral1 which at that time was most likely still sufficiently unfinished to be capable of receiving the form of the present sketch4 ,pl4 ,,xcvii ,no4 #b shows the exterior of this design4 ,below is the note3 edifitio al proposito del fodameto figurato di socto 7edifice proper for the ground plan figured below74 ,here we may also mention the plan of a ,latin cross drawn in ,,ms4 ,c4 ,a4 fol4 #bff 7see p4 #ej74 ,pl4 ,,xciv ,no4 #a 7,,ms4 ,l4 #ae;b74 ,external side view of ,brunellesco's ,florentine basilica ,san ,lorenzo1 seen from the ,north4 ,pl4 ,,xciv ,no4 #d 7,v4 ,a4 ,v1 #a74 ,principal front of a nave1 most likely of a church on the plan of a ,latin cross4 ,we notice here not only the principal features which were employed afterwards in ,alberti's front of ,s4 ,maria ,novella1 but even details of a more advanced style1 such as we are accustomed to meet with only after the year #aebj4 ,in the background of ,leonardo's unfinished picture of ,st4 ,jerome 7,vatican ,gallery7 a somewhat similar church front is indicated 7see the accompanying sketch74 ,illustration with caption3 ,the view of the front of a temple1 apparently a dome in the centre of four corinthian porticos bearing pediments 7published by ,amoretti ,tav4 ,,ii4 ,b as being by ,leonardo71 is taken from a drawing1 now at the ,ambrosian ,gallery4 ,we cannot consider this to be by the hand of the master4 ,c4 ,studies for a form of a ,church most proper for preaching4 ,the problem as to what form of church might answer the requirements of acoustics seems to have engaged ,leonardo's very particular attention4 ,the designation of teatro given to some of these sketches1 clearly shows which plan seemed to him most favourable for hearing the preacher's voice4 ,pl4 ,,xcvii1 ,no4 #a 7,,ms4 ,b1 #eb74 ,rectangular edifice divided into three naves with an apse on either side1 terminated by a semicircular theatre with rising seats1 as in antique buildings4 ,the pulpit is in the centre4 ,leonardo has written on the left side of the sketch3 teatro da predicare 7,theatre for preaching74 ,,ms4 ,b1 #ee;a 7see page #ef1 ,fig4 #a74 ,a domed church after the type of ,pl4 ,,xcv1 ,no4 #a1 shows four theatres occupying the apses and facing the square coro 7choir71 which is in the centre between the four pillars of the dome4,footnote #a3 ,the note teatro de predicar1 on the right side is1 ,i believe1 in the handwriting of ,pompeo ,leoni4 ,j4 ,p4 ,r4 ,the rising arrangement of the seats is shown in the sketch above4 ,at the place marked ,b ,leonardo wrote teatri per uldire messa 7rows of seats to hear mass71 at ,t teatri1 and at ,c coro 7choir74 ,in ,,ms4 ,c4,a4 #bfj1 are slight sketches of two plans for rectangular choirs and two elevations of the altar and pulpit which seem to be in connection with these plans4 ,in ,,ms4 ,ash ,,ii1 #h;a 7see p4 #ef and #eg4 ,fig4 #b and #c74 ,locho dove si predica 7,place for preaching74 ,a most singular plan for a building4 ,the interior is a portion of a sphere1 the centre of which is the summit of a column destined to serve as the preacher's pulpit4 ,the inside is somewhat like a modern theatre1 whilst the exterior and the galleries and stairs recall the ancient amphitheatres4 ,illustration with caption3 ,page #eg1 ,fig4 #d4 ,a plan accompanying the two preceding drawings4 ,if this gives the complete form ,leonardo intended for the edifice1 it would have comprised only about two thirds of the circle4 ,leonardo wrote in the centre fondamento1 a word he often employed for plans1 and on the left side of the view of the exterior3 locho dove si predicha 7a place for preaching in74 ,d4 ,design for a ,mausoleum4 ,pl4 ,,xcviii 7,p4 ,v41 #ahb4 ,no4 d'ordre #bchf74 ,in the midst of a hilly landscape rises an artificial mountain in the form of a gigantic cone1 crowned by an imposing temple4 ,at two thirds of the height a terrace is cut out with six doorways forming entrances to galleries1 each leading to three sepulchral halls1 so constructed as to contain about five hundred funeral urns1 disposed in the customary antique style4 ,from two opposite sides steps ascend to the terrace in a single flight and beyond it to the temple above4 ,a large circular opening1 like that in the ,pantheon1 is in the dome above what may be the altar1 or perhaps the central monument on the level of the terrace below4 ,the section of a gallery given in the sketch to the right below shows the roof to be constructed on the principle of superimposed horizontal layers1 projecting one beyond the other1 and each furnished with a sort of heel1 which appears to be undercut1 so as to give the appearance of a beam from within4 ,granite alone would be adequate to the dimensions here given to the key stone1 as the thickness of the layers can hardly be considered to be less than a foot4 ,in taking this as the basis of our calculation for the dimensions of the whole construction1 the width of the chamber would be about #be feet but1 judging from the number of urns it contains--and there is no reason to suppose that these urns were larger than usual--it would seem to be no more than about #h or #aj feet4 ,the construction of the vaults resembles those in the galleries of some etruscan tumuli1 for instance the ,regulini ,galeassi tomb at ,cervetri 7lately discovered7 and also that of the chamber and passages of the pyramid of ,cheops and of the treasury of ,atreus at ,mycenae4 ,the upper cone displays not only analogies with the monuments mentioned in the note1 but also with ,etruscan tumuli1 such as the ,cocumella tomb at ,vulci1 and the ,regulini ,galeassi tomb,footnote #a3 ,see ,,fersguson1 ,handbook of ,architecture1 ,i1 #bia44 ,the whole scheme is one of the most magnificent in the history of ,architecture4 ,it would be difficult to decide as to whether any monument he had seen suggested this idea to ,leonardo1 but it is worth while to enquire1 if any monument1 or group of monuments of an earlier date may be supposed to have done so4,footnote #b3 ,there are1 in ,algiers1 two ,monuments1 commonly called ,le ,madracen and ,le tombeau de la ,chretienne1 which somewhat resemble ,leonardo's design4 ,they are known to have served as the ,mausolea of the ,kings of ,mauritania4 ,pomponius ,mela1 the geographer of the time of the ,emperor ,claudius1 describes them as having been ,monumentum commune regiae gentis4 ,see ,le ,madracen1 ,rapport fait par ,m4 le ,grand ,rabbin ,,ab4 ,,cahen1 ,constantine #ahgc--,memoire sur les fouilles executees au ,madras'en 44 par le ,colonel ,,brunon1 ,constantine l#hgc4--;,deux ,mausolees ,africains1 le ,madracen et le tombeau de la ,chretienne par ,m4 ,j4 ,,de ,,lauriere1 ,tours l#hgd4--,le tombeau de la ,chretienne1 ,mausolee des rois ,mauritaniens par ,m4 ,,berbrugger1 ,alger #ahfg4--;,i am indebted to ,m4 ,,le ,,blanc1 of the ,institut1 and ,m4 ,,lud1 ,,lalanne1 ,bibliothecaire of the ,institut for having first pointed out to me the resemblance between these monuments2 while ,m4 ,,ant4 ,,heron ,,de ,vl,l,l,e,f,o,s,s,e of the ,louvre was kind enough to place the abovementioned rare works at my disposal4 ,leonardo's observations on the coast of ,africa are given later in this work4 ,the ,herodium near ,bethlehem in ,palestine 7,jebel el ,fureidis1 the ,frank ,mountain7 was1 according to the latest researches1 constructed on a very similar plan4 ,see ,der ,frankenberg1 von ,baurath ,c4 ,,schick in ,jerusalem1 ,zeitschrift des ,deutschen ,palastina-,vereins1 ,leipzag #ahhj1 ,vol4 ,,iii1 pages #hh-ii and ,plates ,,iv and ,v4 ,j4 ,p4 ,r4 ,e4 ,studies for the ,central ,tower1 or ,tiburio of ,milan ,cathedral4 ,towards the end of the fifteenth century the ,fabbricceria del ,duomo had to settle on the choice of a model for the crowning and central part of this vast building4 ,we learn from a notice published by ,g4 ,l4 ,calvi ,footnote3 ,g4 ,l4 ,,calvi1 ,notizie sulla vita e sulle opere dei principali architetti scultori e pittori che fiorirono in ,milano1 ,part ,,iii1 #bj4 ,see also3 ,h4 ,,de ,,geymuller1 ,les projets primitifs etc4 ,i1 #cg and #aaf-aai4--,the ,fabbricceria of the ,duomo has lately begun the publication of the archives1 which may possibly tell us more about the part taken by ,leonardo1 than has hitherto been known4 that among the artists who presented models in the year #adhh were3 ,bramante1 ,pietro da ,gorgonzola1 ,luca ,paperio 7,fancelli71 and ,leonardo da ,vinci4-- ,several sketches by ,leonardo refer to this important project3 ,pl4 ,,xcix1 ,no4 #b 7,,ms4 ,s4 ,k4 ,,iii1 ,no4 #cf;a7 a small plan of the whole edifice4--,the projecting chapels in the middle of the transept are wanting here4 ,the nave appears to be shortened and seems to be approached by an inner vestibolo4-- ,pl4 ,c1 ,no4 #b 7,tr4 #ba74 ,plan of the octagon tower1 giving the disposition of the buttresses2 starting from the eight pillars adjoining the four principal piers and intended to support the eight angles of the ,tiburio4 ,these buttresses correspond exactly with those described by ,bramante as existing in the model presented by ,omodeo4 ,footnote3 ,bramante's opinion was first published by ,g4 ,m,o,n,g,e,rl1 ,arch4 stor4 ,lomb4 ,v1 fasc4 #c and afterwards by me in the publication mentioned in the preceding note4 ,pl4 ,c1 #c 7,,ms4 ,tr4 #af74 ,two plans showing different arrangements of the buttresses1 which seem to be formed partly by the intersection of a system of pointed arches such as that seen in 9999 ,pl4 ,c1 ,no4 #e 7,,ms4 ,b1 #bg;a7 destined to give a broader base to the drum4 ,the text underneath is given under ,no4 #ghh4 ,,ms4 ,b1 #c--three slight sketches of plans in connexion with the preceding ones4 ,pl4 ,,xcix1 ,no4#a 7,,ms4 ,tr4 #ae7 contains several small sketches of sections and exterior views of the ,dome2 some of them show buttress-walls shaped as inverted arches4 ,respecting these ,leonardo notes3 #geh4 ,l'arco rivescio e migliore per fare spalla che l'ordinario1 perche il rovescio trova sotto se muro resistete alla sua debolezza1 e l'ordinario no trova nel suo debole se non aria ,the inverted arch is better for giving a shoulder than the ordinary one1 because the former finds below it a wall resisting its weakness1 whilst the latter finds in its weak part nothing but air4 ,footnote3 ,three slight sketches of sections on the same leaf--above those reproduced here--are more closely connected with the large drawing in the centre of ,pl4 ,c1 ,no4 #d 7,m4,s1 ,tr4 #da7 which shows a section of a very elevated dome1 with double vaults1 connected by ribs and buttresses ingeniously disposed1 so as to bring the weight of the lantern to bear on the base of the dome4 ,a sketch underneath it shows a round pillar on which is indicated which part of its summit is to bear the weight3 il pilastro sara charicho in 4 a 4 b4 7,the column will bear the weight at a b47 ,another note is above on the right side3 ,larcho regiera tanto sotto asse chome di sopra se 7,the arch supports as much below it i4 e4 a hanging weight as above it74 ,pl4 ,c1 ,no4 #a 7,c4 ,a4 #cjc;a74 ,larger sketch of half section of the ,dome1 with a very complicated system of arches1 and a double vault4 ,each stone is shaped so as to be knit or dovetailed to its neighbours4 ,thus the inside of the ,dome cannot be seen from below4 ,,ms4 ,c4 ,a4 #cjc;b4 ,a repetition of the preceding sketch with very slight modifications4 ,figs4 #a4 and ,fig4 #b4 two sketeches of the dome ,,ms4 ,tr4 #i 7see ,fig4 #a and #b74 ,section of the ,dome with reverted buttresses between the windows1 above which iron anchors or chains seem to be intended4 ,below is the sketch of the outside4 ,,pi4 ,,xcix1 ,no4 #c 7,c4 ,a41 #bfb;a7 four sketches of the exterior of the ,dome4 ,c4 ,a4 #ab4 ,section1 showing the points of rupture of a gothic vault1 in evident connection with the sketches described above4 ,it deserves to be noticed how easily and apparently without effort1 ,leonardo manages to combine gothic details and structure with the more modern shape of the ,dome4 ,the following notes are on the same leaf1 oni cosa poderosa1 and oni cosa poderosa desidera de7scendere72 farther below1 several multiplications most likely intended to calculate the weight of some parts of the ,dome1 thus #af x #dg #gbj2 #gbj x #hjj #agfjjj1 next to which is written3 peso del pilastro di #i teste 7weight of the pillar #i diameters high74 ,below3 #agfjjj x #h #adjhjjj2 and below3 ,semjlio e se ce #hj 787 il peso del tiburio 7six millions six hundred 787 #hj the weight of the ,dome74 ,bossi hazarded the theory that ,leonardo might have been the architect who built the church of ,sta4 ,maria delle ,grazie1 but there is no evidence to support this1 either in documents or in the materials supplied by ,leonardos manuscripts and drawings4 ,the sketch given at the side shows the arrangement of the second and third socle on the apses of the choir of that church2 and it is remarkable that those sketches1 in ,,ms4 ,s4 ,k4 ,m4 ,,ii#b1 #b;a and ,ib1 occur with the passage given in ,volume ,i as ,no4 #ffe and #fff referring to the composition of the ,last ,supper in the ,refectory of that church4 ,f4 ,the ,project for lifting up the ,battistero of ,florence and setting it on a basement4 ,among the very few details ,vasari gives as to the architectural studies of ,leonardo1 we read3 ,and among these models and designs there was one by way of which he showed several times to many ingenious citizens who then governed ,florence1 his readiness to lift up without ruining it1 the church of ,san ,giovanni in ,florence 7the ,battistero1 opposite the ,duomo7 in order to place under it the missing basement with steps2 he supported his assertions with reasons so persuasive1 that while he spoke the undertaking seemed feasable1 although every one of his hearers1 when he had departed1 could see by himself the impossibility of so vast an undertaking4 ,footnote3 ,this latter statement of ,vasari's must be considered to be exaggerated4 ,i may refer here to some data given by ,,libri1 ,histoire des sciences mathematiques en ,italie 7,,ii1 #baf1 #bag73 ,on a cru dans ces derniers temps faire un miracle en mecanique en effectuant ce transport1 et cependant des l'annee #adee1 ,gaspard ,nadi et ,aristote de ,fioravantio avaient transporte1 a une distance considerable1 la tour de la ,magione de ,bologne1 avec ses fondements1 qui avait presque quatre-vingts pieds de haut4 ,le continuateur de la chronique de ,pugliola dit que le trajet fut de #ce pieds et que durant le transport auquel le chroniqueur affirme avoir assiste1 il arriva un accident grave qui fit pencher de trois pieds la tour pendant qu'elle etait suspendue1 mais que cet accident fut promptement repare 7,muratori1 ,scriptores rer4 ital4 ,tom4 ,,xviii1 col4 #gag1 #gah74 ,alidosi a rapporte une note ou ,nadi rend compte de ce transport avec une rare simplicite4 ,d'apres cette note1 on voit que les operations de ce genre n'etaient pas nouvelles4 ,celle-ci ne couta que #aej livres 7monnaie d'alors7 y compris le cadeau que le ,legat fit aux deux mecaniciens4 ,dans la meme annee1 ,aristote redressa le clocher de ,cento1 qui penchait de plus de cinq pieds 7,alidosi1 instruttione p4 #ahh-- ,muratori1 ,scriptores rer4 ital41 tom4 ,,xxiii1 col4 #hhh4--;,bossii1 chronica ,mediol41 #adib1 in-fol4 ad ann4 #adee74 ,on ne concoit pas comment les historiens des beaux-arts ont pu negliger de tels hommes4 ,j4 ,p4 ,r4 ,in the ,,ms4 ,c4 ,a4 fol4 #bic1 there are two sketches which possibly might have a bearing on this bold enterprise4 ,we find there a plan of a circular or polygonal edifice surrounded by semicircular arches in an oblique position4 ,these may be taken for the foundation of the steps and of the new platform4 ,in the perspective elevation the same edifice1 forming a polygon1 is shown as lifted up and resting on a circle of inverted arches which rest on an other circle of arches in the ordinary position1 but so placed that the inverted arches above rest on the spandrels of the lower range4 ,what seems to confirm the supposition that the lifting up of a building is here in question1 is the indication of engines for winding up1 such as jacks1 and a rack and wheel4 ,as the lifting apparatus represented on this sheet does not seem particularly applicable to an undertaking of such magnitude1 we may consider it to be a first sketch or scheme for the engines to be used4 ,g4 ,description of an unknown ,temple4 #gei4 ,twelve flights of steps led up to the great temple1 which was eight hundred braccia in circumference and built on an octagonal plan4 ,at the eight corners were eight large plinths1 one braccia and a half high1 and three wide1 and six long at the bottom1 with an angle in the middle2 on these were eight great pillars1 standing on the plinths as a foundation1 and twenty four braccia high4 ,and on the top of these were eight capitals three braccia long and six wide1 above which were the architrave frieze and cornice1 four braccia and a half high1 and this was carried on in a straight line from one pillar to the next and so1 continuing for eight hundred braccia1 surrounded the whole temple1 from pillar to pillar4 ,to support this entablature there were ten large columns of the same height as the pillars1 three braccia thick above their bases which were one braccia and a half high4 ,the ascent to this temple was by twelve flights of steps1 and the temple was on the twelfth1 of an octagonal form1 and at each angle rose a large pillar2 and between the pillars were placed ten columns of the same height as the pillars1 rising at once from the pavement to a height of twenty eight braccia and a half2 and at this height the architrave1 frieze and cornice were placed which surrounded the temple having a length of eight hundred braccia4 ,at the same height1 and within the temple at the same level1 and all round the centre of the temple at a distance of #bd braccia farther in1 are pillars corresponding to the eight pillars in the angles1 and columns corresponding to those placed in the outer spaces4 ,these rise to the same height as the former ones1 and over these the continuous architrave returns towards the outer row of pillars and columns4 ,footnote3 ,either this description is incomplete1 or1 as seems to me highly probable1 it refers to some ruin4 ,the enormous dimensions forbid our supposing this to be any temple in ,italy or ,greece4 ,syria was the native land of colossal octagonal buildings1 in the early centuries ,a4 ,d4 ,the ,temple of ,baalbek1 and others are even larger than that here described4 ,j4 ,p4 ,r4 ,v4 ,palace architecture4 ,but a small number of ,leonardo's drawings refer to the architecture of palaces1 and our knowledge is small as to what style ,leonardo might have adopted for such buildings4 ,pl4 ,,cii ,no4 #a 7,w4 ,,xviii74 ,a small portion of a facade of a palace in two stories1 somewhat resembling ,alberti's ,palazzo ,rucellai4--,compare with this ,bramante's painted front of the ,casa ,silvestri1 and a painting by ,montorfano in ,san ,pietro in ,gessate at ,milan1 third chapel on the left hand side and also with ,bramante's palaces at ,rome4 ,the pilasters with arabesques1 the rustica between them1 and the figures over the window may be painted or in sgraffito4 ,the original is drawn in red chalk4 ,pl4 ,,lxxxi ,no4 #a 7,,ms4 ,tr4 #db74 ,sketch of a palace with battlements and decorations1 most likely graffiti2 the details remind us of those in the ,castello at ,vigevano4 ,footnote #a3 ,count ,,giulio ,,porro1 in his valuable contribution to the ,archivio ,storico ,lombardo1 ,anno ,,viii1 ,fasc4 ,,iv 7#ca ,dec4 #ahha73 ,leonardo da ,vinci1 ,libro di ,annotazioni e ,memorie1 refers to this in the following note3 ,alla pag4 #da vi e uno schizzo di volta ed accanto scrisse3 'il pilastro sara charicho in su #f' e potrebbe darsi che si riferisse alla cupola della chiesa delle ,grazie tanto piu che a pag4 #db vi e un disegno che rassomiglia assai al basamento che oggi si vede nella parte esterna del coro di quella chiesa4 ,this may however be doubted4 ,the drawing1 here referred to1 on page #da of the same manuscript1 is reproduced on ,pl4 ,c ,no4 #d and described on page #fa as being a study for the cupola of the ,duomo of ,milan4 ,j4 ,p4 ,r4 ,,ms4 ,mz4 #j1 contains a design for a palace or house with a loggia in the middle of the first story1 over which rises an attic with a ,pediment reproduced on page #fg4 ,the details drawn close by on the left seem to indicate an arrangement of coupled columns against the wall of a first story4 ,pl4 ,,lxxxv ,no4 #ad 7,,ms4 ,s4 ,k4 ,m4 ,ill #gi;a7 contains a very slight sketch in red chalk1 which most probably is intended to represent the facade of a palace4 ,inside is the short note #g he #g 7#g and #g74 ,,ms4 ,j#b #h;a 7see pages #fh ,fig4 #a and #b7 contains a view of an unknown palace4 ,its plan is indicated at the side4 ,in ,,ms4 ,br4 ,m4 #abf;a7see ,fig4 #c on page #fh7 there is a sketch of a house1 on which ,leonardo notes2 casa con tre terrazi 7house with three terraces74 ,pl4 ,,cx1 ,no4 #d 7,,ms4 ,l4 #cf;b7 represents the front of a fortified building drawn at ,cesena in #aejb 7see ,no4 #ajdj74 ,here we may also mention the singular building in the allegorical composition represented on ,pl4 ,,lviii in ,vol4 ,i4 ,in front of it appears the head of a sphinx or of a dragon which seems to be carrying the palace away4 ,the following texts refer to the construction of palaces and other buildings destined for private use3 #gfj4 ,in the courtyard the walls must be half the height of its width1 that is if the court be #dj braccia1 the house must be #bj high as regards the walls of the said courtyard2 and this courtyard must be half as wide as the whole front4 ,footnote3 ,see ,pl4 ,,ci1 no4 #a1 and compare the dimensions here given1 with ,no4 #gdh lines #bf-bi2 and the drawing belonging to it ,pl4 ,,lxxxi1 no4 #b4 ,on the dispositions of a stable4 #gfa4 ,,for ,,making ,a ,,clean ,,stable4 ,the manner in which one must arrange a stable4 ,you must first divide its width in #c parts1 its depth matters not2 and let these #c divisions be equal and #f braccia broad for each part and #aj high1 and the middle part shall be for the use of the stablemasters2 the #b side ones for the horses1 each of which must be #f braccia in width and #f in length1 and be half a braccio higher at the head than behind4 ,let the manger be at #b braccia from the ground1 to the bottom of the rack1 #c braccia1 and the top of it #d braccia4 ,now1 in order to attain to what ,i promise1 that is to make this place1 contrary to the general custom1 clean and neat3 as to the upper part of the stable1 i4 e4 where the hay is1 that part must have at its outer end a window #f braccia high and #f broad1 through which by simple means the hay is brought up to the loft1 as is shown by the machine ,e2 and let this be erected in a place #f braccia wide1 and as long as the stable1 as seen at k p4 ,the other two parts1 which are on either side of this1 are again divided2 those nearest to the hay-loft are #d braccia1 p s1 and only for the use and circulation of the servants belonging to the stable2 the other two which reach to the outer walls are #b braccia1 as seen at s k1 and these are made for the purpose of giving hay to the mangers1 by means of funnels1 narrow at the top and wide over the manger1 in order that the hay should not choke them4 ,they must be well plastered and clean and are represented at #d f s4 ,as to the giving the horses water1 the troughs must be of stone and above them cisterns of water4 ,the mangers may be opened as boxes are uncovered by raising the lids4 ,footnote3 ,see ,pl4 ,,lxxviii1 ,no4#a4 ,decorations for feasts4 #gfb4 ,,the ,,way ,,to ,,construct ,a ,,frame-,,work ,,for ,,decorating ,,buildings4 ,the way in which the poles ought to be placed for tying bunches of juniper on to them4 ,these poles must lie close to the framework of the vaulting and tie the bunches on with osier withes1 so as to clip them even afterwards with shears4 ,let the distance from one circle to another be half a braccia2 and the juniper sprigs must lie top downwards1 beginning from below4 ,round this column tie four poles to which willows about as thick as a finger must be nailed and then begin from the bottom and work upwards with bunches of juniper sprigs1 the tops downwards1 that is upside down4 ,footnote3 ,see ,pl4 ,,cii1 ,no4 #c4 ,the words here given as the title line1 lines #a--d1 are the last in the original ,,ms4--,lines #e--af are written under fig4 #d4 #gfc4 ,the water should be allowed to fall from the whole circle a b4 ,footnote3 ,other drawings of fountains are given on ,pl4 ,,ci 7,w4 ,,xx72 the original is a pen and ink drawing on blue paper2 on ,pl4 ,,ciii 7,,ms4 ,b47 and ,pl4 ,,lxxxii4 ,,vi4 ,studies of architectural details4 ,several of ,leonardo's drawings of architectural details prove that1 like other great masters of that period1 he had devoted his attention to the study of the proportion of such details4 ,as every organic being in nature has its law of construction and growth1 these masters endeavoured1 each in his way1 to discover and prove a law of proportion in architecture4 ,the following notes in ,leonardo's manuscripts refer to this subject4 ,,ms4 ,s4 ,k4 ,m4 ,ill1 #dg;b 7see ,fig4 #a74 ,a diagram1 indicating the rules as given by ,vitruvius and by ,leon ,battista ,alberti for the proportions of the ,attic base of a column4 ,,ms4 ,s4 ,k4 ,m4 ,ill #ee;a 7see ,fig4 #b74 ,diagram showing the same rules4 #gfd4 ,b toro superiore 4 4 4 4 4 toro superiore #b;,b nestroli 4 4 4 4 4 4 astragali quadre #c;,b orbiculo 4 4 4 4 4 4 4 4 troclea #d;,b nestroli 4 4 4 4 4 4 astragali quadre #e;,b toro iferiore 4 4 4 4 4 4 toro iferiore #f;,b latastro 4 4 4 4 4 4 4 4 plintho ,footnote3 ,no explanation can be offered of the meaning of the letter ,b1 which precedes each name4 ,it may be meant for basa 7base74 ,perhaps it refers to some author on architecture or an architect 7,bramante87 who employed the designations1 thus marked for the mouldings4 #c4 troclea4 ,philander3 ,trochlea sive trochalia aut rechanum4 #f4 ,laterculus or latastrum is the ,latin name for ,plinthus 7pi lambda ,xiv7 but ,vitruvius adopted this ,greek name and latastro seems to have been little in use4 ,it is to be found besides the text given above1 as far as ,i am aware1 only two drawings of the ,uffizi ,collection1 where in one instance1 it indicates the abacus of a ,doric capital4 #gfe4 ,,steps ,,of ,,urrbino4 ,the plinth must be as broad as the thickness of the wall against which the plinth is built4 ,footnote3 ,see ,pl4 ,,cx ,no4 #c4 ,the hasty sketch on the right hand side illustrates the unsatisfactory effect produced when the plinth is narrower than the wall4 #gff4 ,the ancient architects 444444 beginning with the ,egyptians 787 who1 as ,diodorus ,siculus writes1 were the first to build and construct large cities and castles1 public and private buildings of fine form1 large and well proportioned 44444 ,the column1 which has its thickness at the third part 4444 ,the one which would be thinnest in the middle1 would break 4442 the one which is of equal thickness and of equal strength1 is better for the edifice4 ,the second best as to the usefulness will be the one whose greatest thickness is where it joins with the base4 ,footnote3 ,see ,pl4 ,,ciii1 ,no4 #c1 where the sketches belonging to lines #aj--af are reproduced1 but reversed4 ,the sketch of columns1 here reproduced by a wood cut1 stands in the original close to lines #e--h4 ,the capital must be formed in this way4 ,divide its thickness at the top into #h2 at the foot make it #e_/g1 and let it be #e_/g high and you will have a square2 afterwards divide the height into #h parts as you did for the column1 and then take #a_/h for the echinus and another eighth for the thickness of the abacus on the top of the capital4 ,the horns of the abacus of the capital have to project beyond the greatest width of the bell #b_/g1 i4 e4 sevenths of the top of the bell1 so #a_/g falls to the projection of each horn4 ,the truncated part of the horns must be as broad as it is high4 ,i leave the rest1 that is the ornaments1 to the taste of the sculptors4 ,but to return to the columns and in order to prove the reason of their strength or weakness according to their shape1 ,i say that when the lines starting from the summit of the column and ending at its base and their direction and length 4441 their distance apart or width may be equal2 ,i say that this column 444 #gfg4 ,the cylinder of a body columnar in shape and its two opposite ends are two circles enclosed between parallel lines1 and through the centre of the cylinder is a straight line1 ending at the centre of these circles1 and called by the ancients the axis4 ,footnote3 ,leonardo wrote these lines on the margin of a page of the ,trattato di ,francesco di ,giorgio1 where there are several drawings of columns1 as well as a head drawn in profile inside an outline sketch of a capital4 #gfh4 a b is #a_/c of n m2 m o is #a_/f of r o4 ,the ovolo projects #a_/f of r o2 s #g #a_/e of r o1 a b is divided into #i #a_/b2 the abacus is #c_/i the ovolo #d_/i1 the bead-moulding and the fillet #b_/i and #a_/b4 ,footnote3 ,see ,pl4 ,,lxxxv1 ,no4 #af4 ,in the original the drawing and writing are both in red chalk4 ,pl4 ,,lxxxv ,no4 #f 7,,ms4 ,ash4 ,,ii #f;b7 contains a small sketch of a capital with the following note1 written in three lines3 ,i chorni del capitelo deono essere la quarta parte d'uno quadro 7,the horns of a capital must measure the fourth part of a square74 ,,ms4 ,s4 ,k4 ,m4 ,,iii #gb;b contains two sketches of ornamentations of windows4 ,in ,,ms4 ,c4 ,a4 #cjh;a2 #ich;a 7see ,pl4 ,,lxxxii ,no4 #a7 there are several sketches of columns4 ,one of the two columns on the right is similar to those employed by ,bramante at the ,canonica di ,s4 ,ambrogio4 ,the same columns appear in the sketch underneath the plan of a castle4 ,there they appear coupled1 and in two stories one above the other4 ,the archivolls which seem to spring out of the columns1 are shaped like twisted cords1 meant perhaps to be twisted branches4 ,the walls between the columns seem to be formed out of blocks of wood1 the pedestals are ornamented with a reticulated pattern4 ,from all this we may suppose that ,leonardo here had in mind either some festive decoration1 or perhaps a pavilion for some hunting place or park4 ,the sketch of columns marked #ce gives an example of columns shaped like candelabra1 a form often employed at that time1 particularly in ,milan1 and the surrounding districts for instance in the ,cortile di ,casa ,castiglione now ,silvestre1 in the cathedral of ,como1 at ,porta della ,rana c4 #gfi4 ,,concerning ,,architraves ,,of ,,one ,,or ,,several ,,pieces4 ,an architrave of several pieces is stronger than that of one single piece1 if those pieces are placed with their length in the direction of the centre of the world4 ,this is proved because stones have their grain or fibre generated in the contrary direction i4 e4 in the direction of the opposite horizons of the hemisphere1 and this is contrary to fibres of the plants which have 444 ,footnote3 ,the text is incomplete in the original4 ,the ,proportions of the stories of a building are indicated by a sketch in ,,ms4 ,s4 ,k4 ,m4 ,,ii#b #aa;b 7see ,pl4 ,,lxxxv ,no4 #ae74 ,the measures are written on the left side1 as follows3 br #a #a_/b--f #c_/d--;br #a_/ab--b br--#i e #a_/b--a #a_/b--;br #e--o #i--o #c brbraccia2 ooncie4 ,pl4 ,,lxxxv ,no4 #ac 7,,ms4 ,b4 #fb;a7 and ,pl4 ,,xciii ,no4 #a4 7,,ms4 ,b4 #ae;a7 give a few examples of arches supported on piers4 ,,xiii4 ,theoretical writings on ,architecture4 ,leonardo's original writings on the theory of ,architecture have come down to us only in a fragmentary state2 still1 there seems to be no doubt that he himself did not complete them4 ,it would seem that ,leonardo entertained the idea of writing a large and connected book on ,architecture2 and it is quite evident that the materials we possess1 which can be proved to have been written at different periods1 were noted down with a more or less definite aim and purpose4 ,they might all be collected under the one title3 ,studies on the ,strength of ,materials4 ,among them the investigations on the subject of fissures in walls are particularly thorough1 and very fully reported2 these passages are also especially interesting1 because ,leonardo was certainly the first writer on architecture who ever treated the subject at all4 ,here1 as in all other cases ,leonardo carefully avoids all abstract argument4 ,his data are not derived from the principles of algebra1 but from the laws of mechanics1 and his method throughout is strictly experimental4 ,though the conclusions drawn from his investigations may not have that precision which we are accustomed to find in ,leonardo's scientific labours1 their interest is not lessened4 ,they prove at any rate his deep sagacity and wonderfully clear mind4 ,no one perhaps1 who has studied these questions since ,leonardo1 has combined with a scientific mind anything like the artistic delicacy of perception which gives interest and lucidity to his observations4 ,i do not assert that the arrangement here adopted for the passages in question is that originally intended by ,leonardo2 but their distribution into five groups was suggested by the titles1 or headings1 which ,leonardo himself prefixed to most of these notes4 ,some of the longer sections perhaps should not1 to be in strict agreement with this division1 have been reproduced in their entirety in the place where they occur4 ,but the comparatively small amount of the materials we possess will render them1 even so1 sufficiently intelligible to the reader2 it did not therefore seem necessary or desirable to subdivide the passages merely for the sake of strict classification4 ,the small number of chapters given under the fifth class1 treating on the centre of gravity in roof-beams1 bears no proportion to the number of drawings and studies which refer to the same subject4 ,only a small selection of these are reproduced in this work since the majority have no explanatory text4 ,i4 ,,on ,,fissures ,,in ,,walls4 #ggj4 ,first write the treatise on the causes of the giving way of walls and then1 separately1 treat of the remedies4 ,parallel fissures constantly occur in buildings which are erected on a hill side1 when the hill is composed of stratified rocks with an oblique stratification1 because water and other moisture often penetrates these oblique seams carrying in greasy and slippery soil2 and as the strata are not continuous down to the bottom of the valley1 the rocks slide in the direction of the slope1 and the motion does not cease till they have reached the bottom of the valley1 carrying with them1 as though in a boat1 that portion of the building which is separated by them from the rest4 ,the remedy for this is always to build thick piers under the wall which is slipping1 with arches from one to another1 and with a good scarp and let the piers have a firm foundation in the strata so that they may not break away from them4 ,in order to find the solid part of these strata1 it is necessary to make a shaft at the foot of the wall of great depth through the strata2 and in this shaft1 on the side from which the hill slopes1 smooth and flatten a space one palm wide from the top to the bottom2 and after some time this smooth portion made on the side of the shaft1 will show plainly which part of the hill is moving4 ,footnote3 ,see ,pl4 ,,civ4 #gga4 ,the cracks in walls will never be parallel unless the part of the wall that separates from the remainder does not slip down4 ,,what ,,is ,,the ,,law ,,by ,,which ,,buildings ,,have ,,stability4 ,the stability of buildings is the result of the contrary law to the two former cases4 ,that is to say that the walls must be all built up equally1 and by degrees1 to equal heights all round the building1 and the whole thickness at once1 whatever kind of walls they may be4 ,and although a thin wall dries more quickly than a thick one it will not necessarily give way under the added weight day by day and thus1 #af although a thin wall dries more quickly than a thick one1 it will not give way under the weight which the latter may acquire from day to day4 ,because if double the amount of it dries in one day1 one of double the thickness will dry in two days or thereabouts2 thus the small addition of weight will be balanced by the smaller difference of time #ah4 ,the adversary says that a which projects1 slips down4 ,and here the adversary says that r slips and not c4 ,,how ,,to ,,prognosticate ,,the ,,causes ,,of ,,cracks ,,in ,,any ,,sort ,,of ,,wall4 ,the part of the wall which does not slip is that in which the obliquity projects and overhangs the portion which has parted from it and slipped down4 ,,on ,,the ,,situation ,,of ,,foundations ,,and ,,in ,,what ,,places ,,they ,,are ,a ,,cause ,,of ,,ruin4 ,when the crevice in the wall is wider at the top than at the bottom1 it is a manifest sign1 that the cause of the fissure in the wall is remote from the perpendicular line through the crevice4 ,footnote3 ,lines #a-e refer to ,pl4 ,,cv1 ,no4 #b4 ,line #i alle due anteciedete1 see on the same page4 ,lines #af-ah4 ,the translation of this is doubtful1 and the meaning in any case very obscure4 ,lines #ai-bc are on the right hand margin close to the two sketches on ,pl4 ,,cii1 ,no4 #c4 #ggb4 ,,of ,,cracks ,,in ,,walls1 ,,which ,,are ,,wide ,,at ,,the ,,bottom ,,and ,,narrow ,,at ,,the ,,top ,,and ,,of ,,their ,,causes4 ,that wall which does not dry uniformly in an equal time1 always cracks4 ,a wall though of equal thickness will not dry with equal quickness if it is not everywhere in contact with the same medium4 ,thus1 if one side of a wall were in contact with a damp slope and the other were in contact with the air1 then this latter side would remain of the same size as before2 that side which dries in the air will shrink or diminish and the side which is kept damp will not dry4 ,and the dry portion will break away readily from the damp portion because the damp part not shrinking in the same proportion does not cohere and follow the movement of the part which dries continuously4 ,,of ,,arched ,,cracks1 ,,wide ,,at ,,the ,,top1 ,,and ,,narrow ,,below4 ,arched cracks1 wide at the top and narrow below are found in walled-up doors1 which shrink more in their height than in their breadth1 and in proportion as their height is greater than their width1 and as the joints of the mortar are more numerous in the height than in the width4 ,the crack diminishes less in r o than in m n1 in proportion as there is less material between r and o than between n and m4 ,any crack made in a concave wall is wide below and narrow at the top2 and this originates1 as is here shown at b c d1 in the side figure4 #a4 ,that which gets wet increases in proportion to the moisture it imbibes4 #b4 ,and a wet object shrinks1 while drying1 in proportion to the amount of moisture which evaporates from it4 ,footnote3 ,the text of this passage is reproduced in facsimile on ,pl4 ,,cvi to the left4 ,l4 #cf-dj are written inside the sketch ,no4 #b4 ,l4 #da-df are partly written over the sketch ,no4 #c to which they refer4 #ggc4 ,,of ,,the ,,causes ,,of ,,fissures ,,in ,,the ,,walls ,,of ,,public ,,and ,,private ,,buildings4 ,the walls give way in cracks1 some of which are more or less vertical and others are oblique4 ,the cracks which are in a vertical direction are caused by the joining of new walls1 with old walls1 whether straight or with indentations fitting on to those of the old wall2 for1 as these indentations cannot bear the too great weight of the wall added on to them1 it is inevitable that they should break1 and give way to the settling of the new wall1 which will shrink one braccia in every ten1 more or less1 according to the greater or smaller quantity of mortar used between the stones of the masonry1 and whether this mortar is more or less liquid4 ,and observe1 that the walls should always be built first and then faced with the stones intended to face them4 ,for1 if you do not proceed thus1 since the wall settles more than the stone facing1 the projections left on the sides of the wall must inevitably give way2 because the stones used for facing the wall being larger than those over which they are laid1 they will necessarily have less mortar laid between the joints1 and consequently they settle less2 and this cannot happen if the facing is added after the wall is dry4 a b the new wall1 c the old wall1 which has already settled2 and the part a b settles afterwards1 although a1 being founded on c1 the old wall1 cannot possibly break1 having a stable foundation on the old wall4 ,but only the remainder b of the new wall will break away1 because it is built from top to bottom of the building2 and the remainder of the new wall will overhang the gap above the wall that has sunk4 #ggd4 ,a new tower founded partly on old masonry4 #gge4 ,,of ,,stones ,,which ,,disjoin ,,themselves ,,from ,,their ,,mortar4 ,stones laid in regular courses from bottom to top and built up with an equal quantity of mortar settle equally throughout1 when the moisture that made the mortar soft evaporates4 ,by what is said above it is proved that the small extent of the new wall between ,a and n will settle but little1 in proportion to the extent of the same wall between c and d4 ,the proportion will in fact be that of the thinness of the mortar in relation to the number of courses or to the quantity of mortar laid between the stones above the different levels of the old wall4 ,footnote3 ,see ,pl4 ,,cv1 ,no4 #a4 ,the top of the tower is wanting in this reproduction1 and with it the letter n which1 in the original1 stands above the letter ,a over the top of the tower1 while c stands perpendicularly over d4 #ggf4 ,this wall will break under the arch e f1 because the seven whole square bricks are not sufficient to sustain the spring of the arch placed on them4 ,and these seven bricks will give way in their middle exactly as appears in a b4 ,the reason is1 that the brick a has above it only the weight a k1 whilst the last brick under the arch has above it the weight c d x a4 c d seems to press on the arch towards the abutment at the point p but the weight p o opposes resistence to it1 whence the whole pressure is transmitted to the root of the arch4 ,therefore the foot of the arch acts like #g #f1 which is more than double of x z4 ,,ii4 ,,on ,,fissures ,,in ,,niches4 #ggg4 ,,on ,,fissures ,,in ,,niches4 ,an arch constructed on a semicircle and bearing weights on the two opposite thirds of its curve will give way at five points of the curve4 ,to prove this let the weights be at n m which will break the arch a1 b1 f4 ,i say that1 by the foregoing1 as the extremities c and a are equally pressed upon by the thrust n1 it follows1 by the #eth1 that the arch will give way at the point which is furthest from the two forces acting on them and that is the middle e4 ,the same is to be understood of the opposite curve1 d g b2 hence the weights n m must sink1 but they cannot sink by the #gth1 without coming closer together1 and they cannot come together unless the extremities of the arch between them come closer1 and if these draw together the crown of the arch must break2 and thus the arch will give way in two places as was at first said c4 ,i ask1 given a weight at a what counteracts it in the direction n f and by what weight must the weight at f be counteracted4 #ggh4 ,,on ,,the ,,shrinking ,,of ,,damp ,,bodies ,,of ,,different ,,thickness ,,and ,,width4 ,the window a is the cause of the crack at b2 and this crack is increased by the pressure of n and m which sink or penetrate into the soil in which foundations are built more than the lighter portion at b4 ,besides1 the old foundation under b has already settled1 and this the piers n and m have not yet done4 ,hence the part b does not settle down perpendicularly2 on the contrary1 it is thrown outwards obliquely1 and it cannot on the contrary be thrown inwards1 because a portion like this1 separated from the main wall1 is larger outside than inside and the main wall1 where it is broken1 is of the same shape and is also larger outside than inside2 therefore1 if this separate portion were to fall inwards the larger would have to pass through the smaller--which is impossible4 ,hence it is evident that the portion of the semicircular wall when disunited from the main wall will be thrust outwards1 and not inwards as the adversary says4 ,when a dome or a half-dome is crushed from above by an excess of weight the vault will give way1 forming a crack which diminishes towards the top and is wide below1 narrow on the inner side and wide outside2 as is the case with the outer husk of a pomegranate1 divided into many parts lengthwise2 for the more it is pressed in the direction of its length1 that part of the joints will open most1 which is most distant from the cause of the pressure2 and for that reason the arches of the vaults of any apse should never be more loaded than the arches of the principal building4 ,because that which weighs most1 presses most on the parts below1 and they sink into the foundations2 but this cannot happen to lighter structures like the said apses4 ,footnote3 ,the figure on ,pl4 ,,cv1 ,no4 #d belongs to the first paragraph of this passage1 lines #a-ad2 fig4 #e is sketched by the side of lines l#e--;and following4 ,the sketch below of a pomegranate refers to line #bb4 ,the drawing fig4 #f is1 in the original1 over line #cg and fig4 #g over line #ed4 ,which of these two cubes will shrink the more uniformly3 the cube ,a resting on the pavement1 or the cube b suspended in the air1 when both cubes are equal in weight and bulk1 and of clay mixed with equal quantities of water8 ,the cube placed on the pavement diminishes more in height than in breadth1 which the cube above1 hanging in the air1 cannot do4 ,thus it is proved4 ,the cube shown above is better shown here below4 ,the final result of the two cylinders of damp clay that is a and b will be the pyramidal figures below c and d4 ,this is proved thus3 ,the cylinder a resting on block of stone being made of clay mixed with a great deal of water will sink by its weight1 which presses on its base1 and in proportion as it settles and spreads all the parts will be somewhat nearer to the base because that is charged with the whole weight4 ,,iii4 ,,on ,,the ,,nature ,,of ,,the ,,arch4 #ggi4 ,,what ,,is ,,an ,,arch8 ,the arch is nothing else than a force originated by two weaknesses1 for the arch in buildings is composed of two segments of a circle1 each of which being very weak in itself tends to fall2 but as each opposes this tendency in the other1 the two weaknesses combine to form one strength4 ,,of ,,the ,,kind ,,of ,,pressure ,,in ,,arches4 ,as the arch is a composite force it remains in equilibrium because the thrust is equal from both sides2 and if one of the segments weighs more than the other the stability is lost1 because the greater pressure will outweigh the lesser4 ,,of ,,distributing ,,the ,,pressure ,,above ,,an ,,arch4 ,next to giving the segments of the circle equal weight it is necessary to load them equally1 or you will fall into the same defect as before4 ,,where ,,an ,,arch ,,breaks4 ,an arch breaks at the part which lies below half way from the centre4 ,,second ,,rupture ,,of ,,the ,,arch4 ,if the excess of weight be placed in the middle of the arch at the point a1 that weight tends to fall towards b1 and the arch breaks at #b_/c of its height at c e2 and g e is as many times stronger than e a1 as m o goes into m n4 ,,on ,,another ,,cause ,,of ,,ruin4 ,the arch will likewise give way under a transversal thrust1 for when the charge is not thrown directly on the foot of the arch1 the arch lasts but a short time4 #ghj4 ,,on ,,the ,,strength ,,of ,,the ,,arch4 ,the way to give stability to the arch is to fill the spandrils with good masonry up to the level of its summit4 ,,on ,,the ,,loading ,,of ,,round ,,arches4 ,,on ,,the ,,proper ,,manner ,,of ,,loading ,,the ,,pointed ,,arch4 ,,on ,,the ,,evil ,,effects ,,of ,,loading ,,the ,,pointed ,,arch ,,directly ,,above ,,its ,,crown4 ,,on ,,the ,,damage ,,done ,,to ,,the ,,pointed ,,arch ,,by ,,throwing ,,the ,,pressure ,,on ,,the ,,flanks4 ,an arch of small curve is safe in itself1 but if it be heavily charged1 it is necessary to strengthen the flanks well4 ,an arch of a very large curve is weak in itself1 and stronger if it be charged1 and will do little harm to its abutments1 and its places of giving way are o p4 ,footnote3 ,inside the large figure on the righi is the note3 ,da pesare la forza dell' archo4 #gha4 ,,on ,,the ,,remedy ,,for ,,earthquakes4 ,the arch which throws its pressure perpendicularly on the abutments will fulfil its function whatever be its direction1 upside down1 sideways or upright4 ,the arch will not break if the chord of the outer arch does not touch the inner arch4 ,this is manifest by experience1 because whenever the chord a o n of the outer arch n r a approaches the inner arch x b y the arch will be weak1 and it will be weaker in proportion as the inner arch passes beyond that chord4 ,when an arch is loaded only on one side the thrust will press on the top of the other side and be transmitted to the spring of the arch on that side2 and it will break at a point half way between its two extremes1 where it is farthest from the chord4 #ghb4 ,a continuous body which has been forcibly bent into an arch1 thrusts in the direction of the straight line1 which it tends to recover4 #ghc4 ,in an arch judiciously weighted the thrust is oblique1 so that the triangle c n b has no weight upon it4 #ghd4 ,i here ask what weight will be needed to counterpoise and resist the tendency of each of these arches to give way8 ,footnote3 ,the two lower sketches are taken from the ,,ms4 ,s4 ,k4 ,m4 ,,iii1 #aj;a2 they have there no explanatory text4 #ghe4 ,,on ,,the ,,strength ,,of ,,the ,,arch ,,in ,,architecture4 ,the stability of the arch built by an architect resides in the tie and in the flanks4 ,,on ,,the ,,position ,,of ,,the ,,tie ,,in ,,the ,,above ,,named ,,arch4 ,the position of the tie is of the same importance at the beginning of the arch and at the top of the perpendicular pier on which it rests4 ,this is proved by the #bnd of supports which says3 that part of a support has least resistance which is farthest from its solid attachment2 hence1 as the top of the pier is farthest from the middle of its true foundation and the same being the case at the opposite extremities of the arch which are the points farthest from the middle1 which is really its upper attachment1 we have concluded that the tie a b requires to be in such a position as that its opposite ends are between the four above-mentioned extremes4 ,the adversary says that this arch must be more than half a circle1 and that then it will not need a tie1 because then the ends will not thrust outwards but inwards1 as is seen in the excess at a c1 b d4 ,to this it must be answered that this would be a very poor device1 for three reasons4 ,the first refers to the strength of the arch1 since it is proved that the circular parallel being composed of two semicircles will only break where these semicircles cross each other1 as is seen in the figure n m2 besides this it follows that there is a wider space between the extremes of the semicircle than between the plane of the walls2 the third reason is that the weight placed to counterbalance the strength of the arch diminishes in proportion as the piers of the arch are wider than the space between the piers4 ,fourthly in proportion as the parts at c a b d turn outwards1 the piers are weaker to support the arch above them4 ,the #eth is that all the material and weight of the arch which are in excess of the semicircle are useless and indeed mischievous2 and here it is to be noted that the weight placed above the arch will be more likely to break the arch at a b1 where the curve of the excess begins that is added to the semicircle1 than if the pier were straight up to its junction with the semicircle spring of the arch4 ,,an ,,arch ,,loaded ,,over ,,the ,,crown ,,will ,,give ,,way ,,at ,,the ,,left ,,hand ,,and ,,right ,,hand ,,quarters4 ,this is proved by the #gth of this which says3 ,the opposite ends of the support are equally pressed upon by the weight suspended to them2 hence the weight shown at f is felt at b c1 that is half at each extremity2 and by the third which says3 in a support of equal strength throughout that portion will give way soonest which is farthest from its attachment2 whence it follows that d being equally distant from f1 e 44444 ,if the centering of the arch does not settle as the arch settles1 the mortar1 as it dries1 will shrink and detach itself from the bricks between which it was laid to keep them together2 and as it thus leaves them disjoined the vault will remain loosely built1 and the rains will soon destroy it4 #ghf4 ,,on ,,the ,,strength ,,and ,,nature ,,of ,,arches1 ,,and ,,where ,,they ,,are ,,strong ,,or ,,weak2 ,,and ,,the ,,same ,,as ,,to ,,columns4 ,that part of the arch which is nearer to the horizontal offers least resistance to the weight placed on it4 ,when the triangle a z n1 by settling1 drives backwards the #b_/c of each #a_/b circle that is a s and in the same way z m1 the reason is that a is perpendicularly over b and so likewise z is above f4 ,either half of an arch1 if overweighted1 will break at #b_/c of its height1 the point which corresponds to the perpendicular line above the middle of its bases1 as is seen at a b2 and this happens because the weight tends to fall past the point r4--,and if1 against its nature it should tend to fall towards the point s the arch n s would break precisely in its middle4 ,if the arch n s were of a single piece of timber1 if the weight placed at n should tend to fall in the line n m1 the arch would break in the middle of the arch e m1 otherwise it will break at one third from the top at the point a because from a to n the arch is nearer to the horizontal than from a to o and from o to s1 in proportion as p t is greater than t n1 a o will be stronger than a n and likewise in proportion as s o is stronger than o a1 r p will be greater than p t4 ,the arch which is doubled to four times of its thickness will bear four times the weight that the single arch could carry1 and more in proportion as the diameter of its thickness goes a smaller number of times into its length4 ,that is to say that if the thickness of the single arch goes ten times into its length1 the thickness of the doubled arch will go five times into its length4 ,hence as the thickness of the double arch goes only half as many times into its length as that of the single arch does1 it is reasonable that it should carry half as much more weight as it would have to carry if it were in direct proportion to the single arch4 ,hence as this double arch has #d times the thickness of the single arch1 it would seem that it ought to bear #d times the weight2 but by the above rule it is shown that it will bear exactly #h times as much4 ,,that ,,pier1 ,,which is ,,charged ,,most ,,unequally1 ,,will ,,soonest ,,give ,,way4 ,the column c b1 being charged with an equal weight1 on each side will be most durable1 and the other two outward columns require on the part outside of their centre as much pressure as there is inside of their centre1 that is1 from the centre of the column1 towards the middle of the arch4 ,arches which depend on chains for their support will not be very durable4 ,,that ,,arch ,,will ,,be ,,of ,,longer ,,duration ,,which ,,has ,a ,,good ,,abutment ,,opposed ,,to ,,its ,,thrust4 ,the arch itself tends to fall4 ,if the arch be #cj braccia and the interval between the walls which carry it be #bj1 we know that #cj cannot pass through the #bj unless #bj becomes likewise #cj4 ,hence the arch being crushed by the excess of weight1 and the walls offering insufficient resistance1 part1 and afford room between them1 for the fall of the arch4 ,but if you do not wish to strengthen the arch with an iron tie you must give it such abutments as can resist the thrust2 and you can do this thus3 fill up the spandrels m n with stones1 and direct the lines of the joints between them to the centre of the circle of the arch1 and the reason why this makes the arch durable is this4 ,we know very well that if the arch is loaded with an excess of weight above its quarter as a b1 the wall f g will be thrust outwards because the arch would yield in that direction2 if the other quarter b c were loaded1 the wall f g would be thrust inwards1 if it were not for the line of stones x y which resists this4 #ghg4 ,,plan4 ,here it is shown how the arches made in the side of the octagon thrust the piers of the angles outwards1 as is shown by the line h c and by the line t d which thrust out the pier m2 that is they tend to force it away from the centre of such an octagon4 #ghh4 ,an ,experiment to show that a weight placed on an arch does not discharge itself entirely on its columns2 on the contrary the greater the weight placed on the arches1 the less the arch transmits the weight to the columns4 ,the experiment is the following4 ,let a man be placed on a steel yard in the middle of the shaft of a well1 then let him spread out his hands and feet between the walls of the well1 and you will see him weigh much less on the steel yard2 give him a weight on the shoulders1 you will see by experiment1 that the greater the weight you give him the greater effort he will make in spreading his arms and legs1 and in pressing against the wall and the less weight will be thrown on the steel yard4 ,,iv4 ,,on ,,foundations1 ,,the ,,nature ,,of ,,the ,,ground ,,and ,,supports4 #ghi4 ,the first and most important thing is stability4 ,as to the foundations of the component parts of temples and other public buildings1 the depths of the foundations must bear the same proportions to each other as the weight of material which is to be placed upon them4 ,every part of the depth of earth in a given space is composed of layers1 and each layer is composed of heavier or lighter materials1 the lowest being the heaviest4 ,and this can be proved1 because these layers have been formed by the sediment from water carried down to the sea1 by the current of rivers which flow into it4 ,the heaviest part of this sediment was that which was first thrown down1 and so on by degrees2 and this is the action of water when it becomes stagnant1 having first brought down the mud whence it first flowed4 ,and such layers of soil are seen in the banks of rivers1 where their constant flow has cut through them and divided one slope from the other to a great depth2 where in gravelly strata the waters have run off1 the materials have1 in consequence1 dried and been converted into hard stone1 and this happened most in what was the finest mud2 whence we conclude that every portion of the surface of the earth was once at the centre of the earth1 and viceversa c4 #gij4 ,the heaviest part of the foundations of buildings settles most1 and leaves the lighter part above it separated from it4 ,and the soil which is most pressed1 if it be porous yields most4 ,you should always make the foundations project equally beyond the weight of the walls and piers1 as shown at m a b4 ,if you do as many do1 that is to say if you make a foundation of equal width from the bottom up to the surface of the ground1 and charge it above with unequal weights1 as shown at b e and at e o1 at the part of the foundation at b e1 the pier of the angle will weigh most and thrust its foundation downwards1 which the wall at e o will not do2 since it does not cover the whole of its foundation1 and therefore thrusts less heavily and settles less4 ,hence1 the pier b e in settling cracks and parts from the wall e o4 ,this may be seen in most buildings which are cracked round the piers4 #gia4 ,the window a is well placed under the window c1 and the window b is badly placed under the pier d1 because this latter is without support and foundation2 mind therefore never to make a break under the piers between the windows4 #gib4 ,,of ,,the ,,supports4 ,a pillar of which the thickness is increased will gain more than its due strength1 in direct proportion to what its loses in relative height4 ,,example4 ,if a pillar should be nine times as high as it is broad--that is to say1 if it is one braccio thick1 according to rule it should be nine braccia high--then1 if you place #ajj such pillars together in a mass this will be ten braccia broad and #i high2 and if the first pillar could carry #ajjjj pounds the second being only about as high as it is wide1 and thus lacking #h parts of its proper length1 it1 that is to say1 each pillar thus united1 will bear eight times more than when disconnected2 that is to say1 that if at first it would carry ten thousand pounds1 it would now carry #ij thousand4 ,v4 ,,on ,,the ,,resistance ,,of ,,beams4 #gic4 ,that angle will offer the greatest resistance which is most acute1 and the most obtuse will be the weakest4 ,footnote3 ,the three smaller sketches accompany the text in the original1 but the larger one is not directly connected with it4 ,it is to be found on fol4 #hi;a of the same ,manuscript and there we read in a note1 written underneath1 coverchio della perdicha del castello 7roof of the flagstaff of the castle71--,compare also ,pl4 ,,xciii1 ,no4 #a4 #gid4 ,if the beams and the weight o are #ajj pounds1 how much weight will be wanted at ae to resist such a weight1 that it may not fall down8 #gie4 ,,on ,,the ,,length ,,of ,,beams4 ,that beam which is more than #bj times as long as its greatest thickness will be of brief duration and will break in half2 and remember1 that the part built into the wall should be steeped in hot pitch and filleted with oak boards likewise so steeped4 ,each beam must pass through its walls and be secured beyond the walls with sufficient chaining1 because in consequence of earthquakes the beams are often seen to come out of the walls and bring down the walls and floors2 whilst if they are chained they will hold the walls strongly together and the walls will hold the floors4 ,again ,i remind you never to put plaster over timber4 ,since by expansion and shrinking of the timber produced by damp and dryness such floors often crack1 and once cracked their divisions gradually produce dust and an ugly effect4 ,again remember not to lay a floor on beams supported on arches2 for1 in time the floor which is made on beams settles somewhat in the middle while that part of the floor which rests on the arches remains in its place2 hence1 floors laid over two kinds of supports look1 in time1 as if they were made in hills ,footnote3 #ai ,m4 ,,ravaisson1 in his edition of ,,ms4 ,a gives a very different rendering of this passage translating it thus3 ,les planchers qui sont soutenus par deux differentes natures de supports paraissent avec le temps faits en voute a cholli4 ,remarks on the style of ,leonardo's architecture4 ,a few remarks may here be added on the style of ,leonardo's architectural studies4 ,however incomplete1 however small in scale1 they allow us to establish a certain number of facts and probabilities1 well worthy of consideration4 ,when ,leonardo began his studies the great name of ,brunellesco was still the inspiration of all ,florence1 and we cannot doubt that ,leonardo was open to it1 since we find among his sketches the plan of the church of ,santo ,spirito,footnote #a3 ,see ,pl4 ,,xciv1 ,no4 #b4 ,then only in course of erection after the designs of ,brunellesco1 though he was already dead2 finished in #adha4 and a lateral view of ,san ,lorenzo 7,pl4 ,,xciv ,no4 #a71 a plan almost identical with the chapel ,degli ,angeli1 only begun by him 7,pl4 ,,xciv1 ,no4 #c7 while among ,leonardo's designs for domes several clearly betray the influence of ,brunellesco's ,cupola and the lantern of ,santa ,maria del ,fiore,footnote #b3 ,a small sketch of the tower of the ,palazzo della ,signoria 7,,ms4 ,c4,a4 #cji7 proves that he also studied mediaeval monuments4 ,the beginning of the second period of modern ,italian architecture falls during the first twenty years of ,leonardo's life4 ,however the new impetus given by ,leon ,battista ,alberti either was not generally understood by his contemporaries1 or those who appreciated it1 had no opportunity of showing that they did so4 ,it was only when taken up by ,bramante and developed by him to the highest rank of modern architecture that this new influence was generally felt4 ,now the peculiar feature of ,leonardo's sketches is that1 like the works of ,bramante1 they appear to be the development and continuation of ,alberti's4 ,but a question here occurs which is difficult to answer4 ,did ,leonardo1 till he quitted ,florence1 follow the direction given by the dominant school of ,brunellesco1 which would then have given rise to his ,first manner1 or had he1 even before he left ,florence1 felt ,alberti's influence--either through his works 7,palazzo ,ruccellai1 and the front of ,santa ,maria ,novella7 or through personal intercourse8 ,or was it not till he went to ,milan that ,alberti's work began to impress him through ,bramante1 who probably had known ,alberti at ,mantua about #adgj and who not only carried out ,alberti's views and ideas1 but1 by his designs for ,st4 ,peter's at ,rome1 proved himself the greatest of modern architects4 ,when ,leonardo went to ,milan ,bramante had already been living there for many years4 ,one of his earliest works in ,milan was the church of ,santa ,maria presso ,san ,satiro1 ,via del ,falcone,footnote #a3 ,evidence of this ,i intend to give later on in a ,life of ,bramante1 which ,i have in preparation44 ,now we find among ,leonardos studies of ,cupolas on ,plates ,,lxxxiv and ,,lxxxv and in ,pl4 ,,lxxx several sketches which seem to me to have been suggested by ,bramante's dome of this church4 ,the ,,mss4 ,b and ,ash4 ,,ii contain the plans of ,s4 ,sepolcro1 the pavilion in the garden of the duke of ,milan1 and two churches1 evidently inspired by the church of ,san ,lorenzo at ,milan4 ,,ms4 ,b4 contains besides two notes relating to ,pavia1 one of them a design for the sacristy of the ,cathedral at ,pavia1 which cannot be supposed to be dated later than #adib1 and it has probably some relation to ,leonardo's call to ,pavia ,june #ba1 #adij;,footnote #b3 ,the sketch of the plan of ,brunellesco's church of ,santo ,spirito at ,florence1 which occurs in the same ,manuscript1 may have been done from memory44 ,these and other considerations justify us in concluding1 that ,leonardo made his studies of cupolas at ,milan1 probably between the years #adhg and #adib in anticipation of the erection of one of the grandest churches of ,italy1 the ,cathedral of ,pavia4 ,this may explain the decidedly ,lombardo-,bramantesque tendency in the style of these studies1 among which only a few remind us of the forms of the cupolas of ,s4 ,maria del ,fiore and of the ,baptistery of ,florence4 ,thus1 although when compared with ,bramante's work1 several of these sketches plainly reveal that master's influence1 we find1 among the sketches of domes1 some1 which show already ,bramante's classic style1 of which the ,tempietto of ,san ,pietro in ,montorio1 his first building executed at ,rome1 is the foremost example,footnote #c3 ,it may be mentioned here1 that in #adid ,bramante made a similar design for the lantern of the ,cupola of the ,church of ,santa ,maria delle ,grazie44 ,on ,plate ,,lxxxiv is a sketch of the plan of a similar circular building2 and the ,mausoleum on ,pl4 ,,xcviii1 no less than one of the pedestals for the statue of ,francesco ,sforza 7,pl4 ,,lxv71 is of the same type4 ,the drawings ,pl4 ,,lxxxiv ,no4 #b1 ,pl4 ,,lxxxvi ,no4 #a and #b and the ground flour 7flour sic but should be floor 87 of the building in the drawing ,pl4 ,,xci ,no4 #b1 with the interesting decoration by gigantic statues in large niches1 are also1 ,i believe1 more in the style ,bramante adopted at ,rome1 than in the ,lombard style4 ,are we to conclude from this that ,leonardo on his part influenced ,bramante in the sense of simplifying his style and rendering it more congenial to antique art8 ,the answer to this important question seems at first difficult to give1 for we are here in presence of ,bramante1 the greatest of modern architects1 and with ,leonardo1 the man comparable with no other4 ,we have no knowledge of any buildings erected by ,leonardo1 and unless we admit personal intercourse--which seems probable1 but of which there is no proof--1 it would be difficult to understand how ,leonardo could have affected ,bramante's style4 ,the converse is more easily to be admitted1 since ,bramante1 as we have proved elsewhere1 drew and built simultaneously in different manners1 and though in ,lombardy there is no building by him in his classic style1 the use of brick for building1 in that part of ,italy1 may easily account for it4 ,bramante's name is incidentally mentioned in ,leonardo's manuscripts in two passages 7,nos4 #adad and #addh74 ,on each occasion it is only a slight passing allusion1 and the nature of the context gives us no due information as to any close connection between the two artists4 ,it might be supposed1 on the ground of ,leonardo's relations with the ,east given in sections ,,xvii and ,,xxi of this volume1 that some evidence of oriental influence might be detected in his architectural drawings4 ,i do not however think that any such traces can be pointed out with certainty unless perhaps the drawing for a ,mausoleum1 ,pl4 ,,xc ,,viii4 ,among several studies for the construction of cupolas above a ,greek cross there are some in which the forms are decidedly monotonous4 ,these1 it is clear1 were not designed as models of taste2 they must be regarded as the results of certain investigations into the laws of proportion1 harmony and contrast4 ,the designs for churches1 on the plan of a ,latin cross are evidently intended to depart as little as possible from the form of a ,greek cross2 and they also show a preference for a nave surrounded with outer porticos4 ,the architectural forms preferred by ,leonardo are pilasters coupled 7,pl4 ,,lxxxii ,no4 #a2 or grouped 7,pl4 ,,lxxx ,no4 #e and ,,xciv ,no4 #d71 often combined with niches4 ,we often meet with orders superposed1 one in each story1 or two small orders on one story1 in combination with one great order 7,pl4 ,,xcvi ,no4 #b74 ,the drum 7tamburo7 of these cupolas is generally octagonal1 as in the cathedral of ,florence1 and with similar round windows in its sides4 ,in ,pl4 ,,lxxxvii ,no4 #b it is circular like the model actually carried out by ,michael ,angelo at ,st4 ,peter's4 ,the cupola itself is either hidden under a pyramidal roof1 as in the ,baptistery of ,florence1 ,san ,lorenzo of ,milan and most of the ,lombard churches 7,pl4 ,,xci ,no4 #a and ,pl4 ,,xcii ,no4 #a72 but it more generally suggests the curve of ,sta ,maria del ,fiore 7,pl4 ,,lxxxviii ,no4 #e2 ,pl4 ,,xc ,no4 #b2 ,pl4 ,,lxxxix1 ,m2 ,pl ,,xc ,no4 #d1 ,pl4 ,,xcvi ,no4 #b74 ,in other cases 7,pl4 ,,lxxx ,no4 #d2 ,pl4 ,,lxxxix2 ,pl4 ,,xc ,no4 #b7 it shows the sides of the octagon crowned by semicircular pediments1 as in ,brunellesco's lantern of the ,cathedral and in the model for the ,cathedral of ,pavia4 ,finally1 in some sketches the cupola is either semicircular1 or as in ,pl4 ,,lxxxvii ,no4 #b1 shows the beautiful line1 adopted sixty years later by ,michael ,angelo for the existing dome of ,st4 ,peter's4 ,it is worth noticing that for all these domes ,leonardo is not satisfied to decorate the exterior merely with ascending ribs or mouldings1 but employs also a system of horizontal parallels to complete the architectural system4 ,not the least interesting are the designs for the tiburio 7cupola7 of the ,milan ,cathedral4 ,they show some of the forms1 just mentioned1 adapted to the peculiar gothic style of that monument4 ,the few examples of interiors of churches recall the style employed in ,lombardy by ,bramante1 for instance in ,s4 ,maria di ,canepanuova at ,pavia1 or by ,dolcebuono in the ,monastero ,maggiore at ,milan 7see ,pl4 ,,ci ,no4 #a ,c4 ,a4 #aha;b2 #edf;b2 ,pl4 ,,lxxxiv ,no4 #aj74 ,the few indications concerning palaces seem to prove that ,leonardo followed ,alberti's example of decorating the walls with pilasters and a flat rustica1 either in stone or by graffitti 7,pl4 ,,cii ,no4 #a and ,pl4 ,,lxxxv ,no4 #ad74 ,by pointing out the analogies between ,leonardo's architecture and that of other masters we in no way pretend to depreciate his individual and original inventive power4 ,these are at all events beyond dispute4 ,the project for the ,mausoleum 7,pl4 ,,xcviii7 would alone suffice to rank him among the greatest architects who ever lived4 ,the peculiar shape of the tower 7,pl4 ,,lxxx71 of the churches for preaching 7,pl4 ,,xcvii ,no4 #a and pages #ef and #eg1 ,fig4 #a-d71 his curious plan for a city with high and low level streets 7,pl4 ,,lxxvii and ,,lxxviii ,no4 #b and ,no4 #c71 his ,loggia with fountains 7,pl4 ,,lxxxii ,no4 #d7 reveal an originality1 a power and facility of invention for almost any given problem1 which are quite wonderful4 ,in addition to all these qualities he propably stood alone in his day in one department of architectural study1--his investigations1 namely1 as to the resistance of vaults1 foundations1 walls and arches4 ,as an application of these studies the plan of a semicircular vault 7,pl4 ,,ciii ,no4 #b7 may be mentioned here1 disposed so as to produce no thrust on the columns on which it rests3 volta i botte e non ispignie ifori le colone4 ,above the geometrical patterns on the same sheet1 close to a circle inscribed in a square is the note3 la ragio d'una volta cioe il terzo del diamitro della sua 444 del tedesco in domo4 ,there are few data by which to judge of ,leonardo's style in the treatment of detail4 ,on ,pl4 ,,lxxxv ,no4 #aj and ,pl4 ,,ciii ,no4 #c1 we find some details of pillars2 on ,pl4 ,,ci ,no4 #c slender pillars designed for a fountain and on ,pl4 ,,ciii ,no4 #a ,,ms4 ,b1 is a pen and ink drawing of a vase which also seems intended for a fountain4 ,three handles seem to have been intended to connect the upper parts with the base4 ,there can be no doubt that ,leonardo1 like ,bramante1 but unlike ,michael ,angelo1 brought infinite delicacy of motive and execution to bear on the details of his work4 ,,xiv4 ,anatomy1 ,zoology and ,physiology4 ,leonardo's eminent place in the history of medicine1 as a pioneer in the sciences of ,anatomy and ,physiology1 will never be appreciated till it is possible to publish the mass of manuscripts in which he largely treated of these two branches of learning4 ,in the present work ,i must necessarily limit myself to giving the reader a general view of these labours1 by publishing his introductory notes to the various books on anatomical subjects4 ,i have added some extracts1 and such observations as are scattered incidentally through these treatises1 as serving to throw a light on ,leonardo's scientific attitude1 besides having an interest for a wider circle than that of specialists only4 ,,vasari expressly mentions ,leonardo's anatomical studies1 having had occasion to examine the manuscript books which refer to them4 ,according to him ,leonardo studied ,anatomy in the companionship of ,marc ,antonio della ,torre aiutato e scambievolmente aiutando4--,this learned ,anatomist taught the science in the universities first of ,padua and then of ,pavia1 and at ,pavia he and ,leonardo may have worked and studied together4 ,we have no clue to any exact dates1 but in the year #aejf ,marc ,antonio della ,torre seems to have not yet left ,padua4 ,he was scarcely thirty years old when he died in #aeab1 and his writings on anatomy have not only never been published1 but no manuscript copy of them is known to exist4 ,this is not the place to enlarge on the connection between ,leonardo and ,marc ,antonio della ,torre4 ,i may however observe that ,i have not been able to discover in ,leonardo's manuscripts on anatomy any mention of his younger contemporary4 ,the few quotations which occur from writers on medicine--either of antiquity or of the middle ages are printed in ,section ,,xxii4 ,here and there in the manuscripts mention is made of an anonymous adversary 7avversario7 whose views are opposed and refuted by ,leonardo1 but there is no ground for supposing that ,marc ,antonio della ,torre should have been this adversary4 ,only a very small selection from the mass of anatomical drawings left by ,leonardo have been published here in facsimile1 but to form any adequate idea of their scientific merit they should be compared with the coarse and inadequate figures given in the published books of the early part of the ,,xvi4 century4 ,william ,hunter1 the great surgeon--a competent judge--who had an opportunity in the time of ,george ,,iii4 of seeing the originals in the ,king's ,library1 has thus recorded his opinion3 ,i expected to see little more than such designs in ,anatomy as might be useful to a painter in his own profession4 ,but ,i saw1 and indeed with astonishment1 that ,leonardo had been a general and deep student4 ,when ,i consider what pains he has taken upon every part of the body1 the superiority of his universal genius1 his particular excellence in mechanics and hydraulics1 and the attention with which such a man would examine and see objects which he has to draw1 ,i am fully persuaded that ,leonardo was the best ,anatomist1 at that time1 in the world 444 ,leonardo was certainly the first man1 we know of1 who introduced the practice of making anatomical drawings 7,two introductory letters4 ,london #aghd1 pages #cg and #ci74 ,the illustrious ,german ,naturalist ,johan ,friedrich ,blumenback esteemed them no less highly2 he was one of the privileged few who1 after ,hunter1 had the chance of seeing these ,manuscripts4 ,he writes3 ,der ,scharfblick dieses grossen ,forschers und ,darstellers der ,natur hat schon auf ,dinge geachtet1 die noch ,jahrhunderte nachher unbemerkt geblieben sind 7see ,blumenbach's medicinische ,bibliothek1 ,vol4 #c1 ,st4 #d1 #agie4 page #gbh74 ,these opinions were founded on the drawings alone4 ,up to the present day hardly anything has been made known of the text1 and1 for the reasons ,i have given1 it is my intention to reproduce here no more than a selection of extracts which ,i have made from the originals at ,windsor ,castle and elsewhere4 ,in the ,bibliography of the ,manuscripts1 at the end of this volume a short review is given of the valuable contents of these ,anatomical note books which are at present almost all in the possession of her ,majesty the ,queen of ,england4 ,it is1 ,i believe1 possible to assign the date with approximate accuracy to almost all the fragments1 and ,i am thus led to conclude that the greater part of ,leonardo's anatomical investigations were carried out after the death of della ,torre4 ,merely in reading the introductory notes to his various books on ,anatomy which are here printed it is impossible to resist the impression that the ,master's anatomical studies bear to a very great extent the stamp of originality and independent thought4 ,i4 ,,anatomy4 #gif4 ,a general introduction ,i wish to work miracles2--it may be that ,i shall possess less than other men of more peaceful lives1 or than those who want to grow rich in a day4 ,i may live for a long time in great poverty1 as always happens1 and to all eternity will happen1 to alchemists1 the would-be creators of gold and silver1 and to engineers who would have dead water stir itself into life and perpetual motion1 and to those supreme fools1 the necromancer and the enchanter4 ,footnote #bc3 ,the following seems to be directed against students of painting and young artists rather than against medical men and anatomists4 ,and you1 who say that it would be better to watch an anatomist at work than to see these drawings1 you would be right1 if it were possible to observe all the things which are demonstrated in such drawings in a single figure1 in which you1 with all your cleverness1 will not see nor obtain knowledge of more than some few veins1 to obtain a true and perfect knowledge of which ,i have dissected more than ten human bodies1 destroying all the other members1 and removing the very minutest particles of the flesh by which these veins are surrounded1 without causing them to bleed1 excepting the insensible bleeding of the capillary veins2 and as one single body would not last so long1 since it was necessary to proceed with several bodies by degrees1 until ,i came to an end and had a complete knowledge2 this ,i repeated twice1 to learn the differences #ei4 ,footnote3 ,lines #a-ei and #fj-hi are written in two parallel columns4 ,when we here find ,leonardo putting himself in the same category as the ,alchemists and ,necromancers1 whom he elsewhere mocks at so bitterly1 it is evidently meant ironically4 ,in the same way ,leonardo1 in the introduction to the ,books on ,perspective sets himself with transparent satire on a level with other writers on the subject4 ,and if you should have a love for such things you might be prevented by loathing1 and if that did not prevent you1 you might be deterred by the fear of living in the night hours in the company of those corpses1 quartered and flayed and horrible to see4 ,and if this did not prevent you1 perhaps you might not be able to draw so well as is necessary for such a demonstration2 or1 if you had the skill in drawing1 it might not be combined with knowledge of perspective2 and if it were so1 you might not understand the methods of geometrical demonstration and the method of the calculation of forces and of the strength of the muscles2 patience also may be wanting1 so that you lack perseverance4 ,as to whether all these things were found in me or not ,footnote #hd3 ,leonardo frequently1 and perhaps habitually1 wrote in note books of a very small size and only moderately thick2 in most of those which have been preserved undivided1 each contains less than fifty leaves4 ,thus a considerable number of such volumes must have gone to make up a volume of the bulk of the ',codex ,atlanticus' which now contains nearly #abjj detached leaves4 ,in the passage under consideration1 which was evidently written at a late period of his life1 ,leonardo speaks of his ,manuscript note-books as numbering #ab,o2 but we should hardly be justified in concluding from this passage that the greater part of his ,manuscripts were now missing 7see ,prolegomena1 ,vol4 ,i1 pp4 #e-g741 the hundred and twenty books composed by me will give verdict ,yes or ,no4 ,in these ,i have been hindered neither by avarice nor negligence1 but simply by want of time4 ,farewell #hi4 ,plans and suggestions for the arrangement of materials 7#gig-hjb74 #gig4 ,,of ,,the ,,order ,,of ,,the ,,book4 ,this work must begin with the conception of man1 and describe the nature of the womb and how the foetus lives in it1 up to what stage it resides there1 and in what way it quickens into life and feeds4 ,also its growth and what interval there is between one stage of growth and another4 ,what it is that forces it out from the body of the mother1 and for what reasons it sometimes comes out of the mother's womb before the due time4 ,then ,i will describe which are the members1 which1 after the boy is born1 grow more than the others1 and determine the proportions of a boy of one year4 ,then describe the fully grown man and woman1 with their proportions1 and the nature of their complexions1 colour1 and physiognomy4 ,then how they are composed of veins1 tendons1 muscles and bones4 ,this ,i shall do at the end of the book4 ,then1 in four drawings1 represent four universal conditions of men4 ,that is1 ,mirth1 with various acts of laughter1 and describe the cause of laughter4 ,weeping in various aspects with its causes4 ,contention1 with various acts of killing2 flight1 fear1 ferocity1 boldness1 murder and every thing pertaining to such cases4 ,then represent ,labour1 with pulling1 thrusting1 carrying1 stopping1 supporting and such like things4 ,further ,i would describe attitudes and movements4 ,then perspective1 concerning the functions and effects of the eye2 and of hearing--here ,i will speak of music--1 and treat of the other senses4 ,and then describe the nature of the senses4 ,this mechanism of man we will demonstrate in 444 figures2 of which the three first will show the ramification of the bones2 that is3 first one to show their height and position and shape3 the second will be seen in profile and will show the depth of the whole and of the parts1 and their position4 ,the third figure will be a demonstration of the bones of the backparts4 ,then ,i will make three other figures from the same point of view1 with the bones sawn across1 in which will be shown their thickness and hollowness4 ,three other figures of the bones complete1 and of the nerves which rise from the nape of the neck1 and in what limbs they ramify4 ,and three others of the bones and veins1 and where they ramify4 ,then three figures with the muscles and three with the skin1 and their proper proportions2 and three of woman1 to illustrate the womb and the menstrual veins which go to the breasts4 ,footnote3 ,the meaning of the word nervo varies in different passages1 being sometimes used for muscolo 7muscle74 #gih4 ,,the ,,order ,,of ,,the ,,book4 ,this depicting of mine of the human body will be as clear to you as if you had the natural man before you2 and the reason is that if you wish thoroughly to know the parts of man1 anatomically1 you--or your eye--require to see it from different aspects1 considering it from below and from above and from its sides1 turning it about and seeking the origin of each member2 and in this way the natural anatomy is sufficient for your comprehension4 ,but you must understand that this amount of knowledge will not continue to satisfy you2 seeing the very great confusion that must result from the combination of tissues1 with veins1 arteries1 nerves1 sinews1 muscles1 bones1 and blood which1 of itself1 tinges every part the same colour4 ,and the veins1 which discharge this blood1 are not discerned by reason of their smallness4 ,moreover integrity of the tissues1 in the process of the investigating the parts within them1 is inevitably destroyed1 and their transparent substance being tinged with blood does not allow you to recognise the parts covered by them1 from the similarity of their blood-stained hue2 and you cannot know everything of the one without confusing and destroying the other4 ,hence1 some further anatomy drawings become necessary4 ,of which you want three to give full knowledge of the veins and arteries1 everything else being destroyed with the greatest care4 ,and three others to display the tissues2 and three for the sinews and muscles and ligaments2 and three for the bones and cartilages2 and three for the anatomy of the bones1 which have to be sawn to show which are hollow and which are not1 which have marrow and which are spongy1 and which are thick from the outside inwards1 and which are thin4 ,and some are extremely thin in some parts and thick in others1 and in some parts hollow or filled up with bone1 or full of marrow1 or spongy4 ,and all these conditions are sometimes found in one and the same bone1 and in some bones none of them4 ,and three you must have for the woman1 in which there is much that is mysterious by reason of the womb and the foetus4 ,therefore by my drawings every part will be known to you1 and all by means of demonstrations from three different points of view of each part2 for when you have seen a limb from the front1 with any muscles1 sinews1 or veins which take their rise from the opposite side1 the same limb will be shown to you in a side view or from behind1 exactly as if you had that same limb in your hand and were turning it from side to side until you had acquired a full comprehension of all you wished to know4 ,in the same way there will be put before you three or four demonstrations of each limb1 from various points of view1 so that you will be left with a true and complete knowledge of all you wish to learn of the human figure,footnote #ce3 ,compare ,pl4 ,,cvii4 ,the original drawing at ,windsor is #bh #a_/b ,x #ai #a_/b centimetres4 ,the upper figures are slightly washed with ,indian ink4 ,on the back of this drawing is the text ,no4 #aadj44 ,thus1 in twelve entire figures1 you will have set before you the cosmography of this lesser world on the same plan as1 before me1 was adopted by ,ptolemy in his cosmography2 and so ,i will afterwards divide them into limbs as he divided the whole world into provinces2 then ,i will speak of the function of each part in every direction1 putting before your eyes a description of the whole form and substance of man1 as regards his movements from place to place1 by means of his different parts4 ,and thus1 if it please our great ,author1 ,i may demonstrate the nature of men1 and their customs in the way ,i describe his figure4 ,and remember that the anatomy of the nerves will not give the position of their ramifications1 nor show you which muscles they branch into1 by means of bodies dissected in running water or in lime water2 though indeed their origin and starting point may be seen without such water as well as with it4 ,but their ramifications1 when under running water1 cling and unite--just like flat or hemp carded for spinning--all into a skein1 in a way which makes it impossible to trace in which muscles or by what ramification the nerves are distributed among those muscles4 #gii4 ,,the ,,arrangement ,,of ,,anatomy ,first draw the bones1 let us say1 of the arm1 and put in the motor muscle from the shoulder to the elbow with all its lines4 ,then proceed in the same way from the elbow to the wrist4 ,then from the wrist to the hand and from the hand to the fingers4 ,and in the arm you will put the motors of the fingers which open1 and these you will show separately in their demonstration4 ,in the second demonstration you will clothe these muscles with the secondary motors of the fingers and so proceed by degrees to avoid confusion4 ,but first lay on the bones those muscles which lie close to the said bones1 without confusion of other muscles2 and with these you may put the nerves and veins which supply their nourishment1 after having first drawn the tree of veins and nerves over the simple bones4 #hjj4 ,begin the anatomy at the head and finish at the sole of the foot4 #hja4 #c men complete1 #c with bones and nerves1 #c with the bones only4 ,here we have #ab demonstrations of entire figures4 #hjb4 ,when you have finished building up the man1 you will make the statue with all its superficial measurements4 ,footnote3 ,cresciere l'omo4 ,the meaning of this expression appears to be different here and in the passage ,c4,a4 #aeg;a1 #dfh;a 7see ,no4 #ebf1 ,note #a4 #b74 ,here it can hardly mean anything else than modelling1 since the sculptor forms the figure by degrees1 by adding wet clay and the figure consequently increases or grows4 ,tu farai la statua would then mean1 you must work out the figure in marble4 ,if this interpretation is the correct one1 this passage would have no right to find a place in the series on anatomical studies4 ,i may say that it was originally inserted in this connection under the impression that di cresciere should be read descrivere4 ,plans for the representation of muscles by drawings 7#hjc-hji74 #hjc4 ,you must show all the motions of the bones with their joints to follow the demonstration of the first three figures of the bones1 and this should be done in the first book4 #hjd4 ,remember that to be certain of the point of origin of any muscle1 you must pull the sinew from which the muscle springs in such a way as to see that muscle move1 and where it is attached to the ligaments of the bones4 ,,note4 ,you will never get any thing but confusion in demonstrating the muscles and their positions1 origin1 and termination1 unless you first make a demonstration of thin muscles after the manner of linen threads2 and thus you can represent them1 one over another as nature has placed them2 and thus1 too1 you can name them according to the limb they serve2 for instance the motor of the point of the great toe1 of its middle bone1 of its first bone1 c4 ,and when you have the knowledge you will draw1 by the side of this1 the true form and size and position of each muscle4 ,but remember to give the threads which explain the situation of the muscles in the position which corresponds to the central line of each muscle2 and so these threads will demonstrate the form of the leg and their distance in a plain and clear manner4 ,i have removed the skin from a man who was so shrunk by illness that the muscles were worn down and remained in a state like thin membrane1 in such a way that the sinews instead of merging in muscles ended in wide membrane2 and where the bones were covered by the skin they had very little over their natural size4 ,footnote3 ,the photograph ,no4 #da of ,grosvenor ,gallery ,publications3 a drawing of the muscles of the foot1 includes a complete facsimile of the text of this passage4 #hje4 ,which nerve causes the motion of the eye so that the motion of one eye moves the other8 ,of frowning the brows1 of raising the brows1 of lowering the brows1--of closing the eyes1 of opening the eyes1--of raising the nostrils1 of opening the lips1 with the teeth shut1 of pouting with the lips1 of smiling1 of astonishment4-- ,describe the beginning of man when it is caused in the womb and why an eight months child does not live4 ,what sneezing is4 ,what yawning is4 ,falling sickness1 spasms1 paralysis1 shivering with cold1 sweating1 fatigue1 hunger1 sleepiness1 thirst1 lust4 ,of the nerve which is the cause of movement from the shoulder to the elbow1 of the movement from the elbow to the hand1 from the joint of the hand to the springing of the fingers4 ,from the springing of the fingers to the middle joints1 and from the middle joints to the last4 ,of the nerve which causes the movement of the thigh1 and from the knee to the foot1 and from the joint of the foot to the toes1 and then to the middle of the toes and of the rotary motion of the leg4 #hjf4 ,,anatomy4 ,which nerves or sinews of the hand are those which close and part the fingers and toes latteraly8 #hjg4 ,remove by degrees all the parts of the front of a man in making your dissection1 till you come to the bones4 ,description of the parts of the bust and of their motions4 #hjh4 ,give the anatomy of the leg up to the hip1 in all views and in every action and in every state2 veins1 arteries1 nerves1 sinews and muscles1 skin and bones2 then the bones in sections to show the thickness of the bones4 ,footnote3 ,a straightened leg in profile is sketched by the side of this text4 ,on corpulency and leanness 7#hji-haa74 #hji4 ,make the rule and give the measurement of each muscle1 and give the reasons of all their functions1 and in which way they work and what makes them work c4 #d ,first draw the spine of the back2 then clothe it by degrees1 one after the other1 with each of its muscles and put in the nerves and arteries and veins to each muscle by itself2 and besides these note the vertebrae to which they are attached2 which of the intestines come in contact with them2 and which bones and other organs c4 ,the most prominent parts of lean people are most prominent in the muscular1 and equally so in fat persons4 ,but concerning the difference in the forms of the muscles in fat persons as compared with muscular persons1 it shall be described below4 ,footnote3 ,the two drawings given on ,pl4 ,,cviii no4 #a come between lines #c and #d4 ,a good and very early copy of this drawing without the written text exists in the collection of drawings belonging to ,christ's ,college ,oxford1 where it is attributed to ,leonardo4 #haj4 ,describe which muscles disappear in growing fat1 and which become visible in growing lean4 ,and observe that that part which on the surface of a fat person is most concave1 when he grows lean becomes more prominent4 ,where the muscles separate one from another you must give profiles and where they coalesce 444 #haa4 ,,of ,,the ,,human ,,figure4 ,which is the part in man1 which1 as he grows fatter1 never gains flesh8 ,or what part which as a man grows lean never falls away with a too perceptible diminution8 ,and among the parts which grow fat which is that which grows fattest8 ,among those which grow lean which is that which grows leanest8 ,in very strong men which are the muscles which are thickest and most prominent8 ,in your anatomy you must represent all the stages of the limbs from man's creation to his death1 and then till the death of the bone2 and which part of him is first decayed and which is preserved the longest4 ,and in the same way of extreme leanness and extreme fatness4 ,the divisions of the head 7#hab4 #hac74 #hab4 ,,anatomy4 ,there are eleven elementary tissues3-- ,cartilage1 bones1 nerves1 veins1 arteries1 fascia1 ligament and sinews1 skin1 muscle and fat4 ,,of ,,the ,,head4 ,the divisions of the head are #aj1 viz4 #e external and #e internal1 the external are the hair1 skin1 muscle1 fascia and the skull2 the internal are the dura mater1 the pia mater1 which enclose the brain4 ,the pia mater and the dura mater come again underneath and enclose the brain2 then the rete mirabile1 and the occipital bone1 which supports the brain from which the nerves spring4 #hac4 a4 hair n4 skin c4 muscle m4 fascia o4 skull i4e4 bone b4 dura mater d4 pia mater f4 brain r4 pia mater1 below t4 dura mater l4 rete mirablile s4 the occipitul bone4 ,footnote3 ,see ,pl4 ,,cviii1 ,no4 #c4 ,physiological problems 7#had4 #hae74 #had4 ,of the cause of breathing1 of the cause of the motion of the heart1 of the cause of vomiting1 of the cause of the descent of food from the stomach1 of the cause of emptying the intestines4 ,of the cause of the movement of the superfluous matter through the intestines4 ,of the cause of swallowing1 of the cause of coughing1 of the cause of yawning1 of the cause of sneezing1 of the cause of limbs getting asleep4 ,of the cause of losing sensibility in any limb4 ,of the cause of tickling4 ,of the cause of lust and other appetites of the body1 of the cause of urine and also of all the natural excretions of the body4 ,footnote3 ,by the side of this text stands the pen and ink drawing reproduced on ,pl4 ,,cviii1 ,no4 #d2 a skull with indications of the veins in the fleshy covering4 #hae4 ,the tears come from the heart and not from the brain4 ,define all the parts1 of which the body is composed1 beginning with the skin with its outer cuticle which is often chapped by the influence of the sun4 ,,ii4 ,,zoology ,,and ,,comparative ,,anatomy4 ,the divisions of the animal kingdom 7#haf4 #hag74 #haf4 ,man4 ,the description of man1 which includes that of such creatures as are of almost the same species1 as ,apes1 ,monkeys and the like1 which are many1 ,the ,lion and its kindred1 as ,panthers4 ,footnote #c3 ,leonza--wild cat8 ,secondo alcuni1 lo stesso che ,leonessa2 e secondo altri con piu certezza1 lo stesso che ,pantera ,,fanfani1 ,vocabolario page #heh4 ,wildcats 787 ,tigers1 ,leopards1 ,wolfs1 ,lynxes1 ,spanish cats1 common cats and the like4 ,the ,horse and its kindred1 as ,mule1 ,ass and the like1 with incisor teeth above and below4 ,the ,bull and its allies with horns and without upper incisors as the ,buffalo1 ,stag ,fallow ,deer1 ,wild ,goat1 ,swine1 ,goat1 wild ,goats ,muskdeers1 ,chamois1 ,giraffe4 #hag4 ,describe the various forms of the intestines of the human species1 of apes and such like4 ,then1 in what way the leonine species differ1 and then the bovine1 and finally birds2 and arrange this description after the manner of a disquisition4 ,miscellaneous notes on the study of ,zoology 7#hah-hba74 #hah4 ,procure the placenta of a calf when it is born and observe the form of the cotyledons1 if their cotyledons are male or female4 #hai4 ,describe the tongue of the woodpecker and the jaw of the crocodile4 #hbj4 ,of the flight of the #dth kind of butterflies that consume winged ants4 ,of the three principal positions of the wings of birds in downward flight4 ,footnote3 ,a passing allusion is all ,i can here permit myself to ,leonardo's elaborate researches into the flight of birds4 ,compare the observations on this subject in the ,introduction to section ,,xviii and in the ,bibliography of ,manuscripts at the end of the work4 #hba4 ,of the way in which the tail of a fish acts in propelling the fish2 as in the eel1 snake and leech4 ,footnote3 ,a sketch of a fish1 swimming upwards is in the original1 inserted above this text4--,compare ,no4 #aaad4 ,comparative study of the structure of bones and of the action of muscles 7#hbb-hbf74 #hbb4 ,,of ,,the ,,palm ,,of ,,the ,,hand4 ,then ,i will discourse of the hands of each animal to show in what they vary2 as in the bear1 which has the ligatures of the sinews of the toes joined above the instep4 #hbc4 ,a second demonstration inserted between anatomy and the treatise on the living being4 ,you will represent here for a comparison1 the legs of a frog1 which have a great resemblance to the legs of man1 both in the bones and in the muscles4 ,then1 in continuation1 the hind legs of the hare1 which are very muscular1 with strong active muscles1 because they are not encumbered with fat4 ,footnote3 ,this text is written by the side of a drawing in black chalk of a nude male figure1 but there is no connection between the sketch and the text4 #hbd4 ,here ,i make a note to demonstrate the difference there is between man and the horse and in the same way with other animals4 ,and first ,i will begin with the bones1 and then will go on to all the muscles which spring from the bones without tendons and end in them in the same way1 and then go on to those which start with a single tendon at one end4 ,footnote3 ,see ,pl4 ,,cviii1 ,no4 #b4 #hbe4 ,note on the bendings of joints and in what way the flesh grows upon them in their flexions or extensions2 and of this most important study write a separate treatise3 in the description of the movements of animals with four feet2 among which is man1 who likewise in his infancy crawls on all fours4 #hbf4 ,,of ,,the ,,way ,,of ,,walking ,,in ,,man4 ,the walking of man is always after the universal manner of walking in animals with #d legs1 inasmuch as just as they move their feet crosswise after the manner of a horse in trotting1 so man moves his #d limbs crosswise2 that is1 if he puts forward his right foot in walking he puts forward1 with it1 his left arm and vice versa1 invariably4 ,,iii4 ,,physiology4 ,comparative study of the organs of sense in men and animals4 #hbg4 ,i have found that in the composition of the human body as compared with the bodies of animals the organs of sense are duller and coarser4 ,thus it is composed of less ingenious instruments1 and of spaces less capacious for receiving the faculties of sense4 ,i have seen in the ,lion tribe that the sense of smell is connected with part of the substance of the brain which comes down the nostrils1 which form a spacious receptacle for the sense of smell1 which enters by a great number of cartilaginous vesicles with several passages leading up to where the brain1 as before said1 comes down4 ,the eyes in the ,lion tribe have a large part of the head for their sockets and the optic nerves communicate at once with the brain2 but the contrary is to be seen in man1 for the sockets of the eyes are but a small part of the head1 and the optic nerves are very fine and long and weak1 and by the weakness of their action we see by day but badly at night1 while these animals can see as well at night as by day4 ,the proof that they can see is that they prowl for prey at night and sleep by day1 as nocturnal birds do also4 ,advantages in the structure of the eye in certain animals 7#hbh-hca74 #hbh4 ,every object we see will appear larger at midnight than at midday1 and larger in the morning than at midday4 ,this happens because the pupil of the eye is much smaller at midday than at any other time4 ,in proportion as the eye or the pupil of the owl is larger in proportion to the animal than that of man1 so much the more light can it see at night than man can2 hence at midday it can see nothing if its pupil does not diminish2 and1 in the same way1 at night things look larger to it than by day4 #hbi4 ,,of ,,the ,,eyes ,,in ,,animals4 ,the eyes of all animals have their pupils adapted to dilate and diminish of their own accord in proportion to the greater or less light of the sun or other luminary4 ,but in birds the variation is much greater2 and particularly in nocturnal birds1 such as horned owls1 and in the eyes of one species of owl2 in these the pupil dilates in such away as to occupy nearly the whole eye1 or diminishes to the size of a grain of millet1 and always preserves the circular form4 ,but in the ,lion tribe1 as panthers1 pards1 ounces1 tigers1 lynxes1 ,spanish cats and other similar animals the pupil diminishes from the perfect circle to the figure of a pointed oval such as is shown in the margin4 ,but man having a weaker sight than any other animal is less hurt by a very strong light and his pupil increases but little in dark places2 but in the eyes of these nocturnal animals1 the horned owl--a bird which is the largest of all nocturnal birds--the power of vision increases so much that in the faintest nocturnal light 7which we call darkness7 it sees with much more distinctness than we do in the splendour of noon day1 at which time these birds remain hidden in dark holes2 or if indeed they are compelled to come out into the open air lighted up by the sun1 they contract their pupils so much that their power of sight diminishes together with the quantity of light admitted4 ,study the anatomy of various eyes and see which are the muscles which open and close the said pupils of the eyes of animals4 ,footnote3 ,compare ,no4 #bd1 lines #h and fol4 #hcj4 a b n is the membrane which closes the eye from below1 upwards1 with an opaque film1 c n b encloses the eye in front and behind with a transparent membrane4 ,it closes from below1 upwards1 because it the eye comes downwards4 ,when the eye of a bird closes with its two lids1 the first to close is the nictitating membrane which closes from the lacrymal duct over to the outer corner of the eye2 and the outer lid closes from below upwards1 and these two intersecting motions begin first from the lacrymatory duct1 because we have already seen that in front and below birds are protected and use only the upper portion of the eye from fear of birds of prey which come down from above and behind2 and they uncover first the membrane from the outer corner1 because if the enemy comes from behind1 they have the power of escaping to the front2 and again the muscle called the nictitating membrane is transparent1 because1 if the eye had not such a screen1 they could not keep it open against the wind which strikes against the eye in the rush of their rapid flight4 ,and the pupil of the eye dilates and contracts as it sees a less or greater light1 that is to say intense brilliancy4 #hca4 ,if at night your eye is placed between the light and the eye of a cat1 it will see the eye look like fire4 ,remarks on the organs of speech 7#hcb4 #hcc74 #hcb4 a e i o u ba be bi bo bu ca ce ci co cu da de di do du fa fe fi fo fu ga ge gi go gu la le li lo lu ma me mi mo mu na ne ni no nu pa pe pi po pu qa qe qi qo qu ra re ri ro ru sa se si so su ta te ti to tu ,the tongue is found to have #bd muscles which correspond to the six muscles which compose the portion of the tongue which moves in the mouth4 ,and when a o u are spoken with a clear and rapid pronunciation1 it is necessary1 in order to pronounce continuously1 without any pause between1 that the opening of the lips should close by degrees2 that is1 they are wide apart in saying a1 closer in saying o1 and much closer still to pronounce u4 ,it may be shown how all the vowels are pronounced with the farthest portion of the false palate which is above the epiglottis4 #hcc4 ,if you draw in breath by the nose and send it out by the mouth you will hear the sound made by the division that is the membrane in ,footnote #e3 ,the text here breaks off4444 ,on the conditions of sight 7#hcd4 #hce74 #hcd4 ,,of ,,the ,,nature ,,of ,,sight4 ,i say that sight is exercised by all animals1 by the medium of light2 and if any one adduces1 as against this1 the sight of nocturnal animals1 ,i must say that this in the same way is subject to the very same natural laws4 ,for it will easily be understood that the senses which receive the images of things do not project from themselves any visual virtue ,footnote #d3 ,compare ,no4 #fh44 ,on the contrary the atmospheric medium which exists between the object and the sense incorporates in itself the figure of things1 and by its contact with the sense transmits the object to it4 ,if the object--whether by sound or by odour--presents its spiritual force to the ear or the nose1 then light is not required and does not act4 ,the forms of objects do not send their images into the air if they are not illuminated #h2 and the eye being thus constituted cannot receive that from the air1 which the air does not possess1 although it touches its surface4 ,if you choose to say that there are many animals that prey at night1 ,i answer that when the little light which suffices the nature of their eyes is wanting1 they direct themselves by their strong sense of hearing and of smell1 which are not impeded by the darkness1 and in which they are very far superior to man4 ,if you make a cat leap1 by daylight1 among a quantity of jars and crocks you will see them remain unbroken1 but if you do the same at night1 many will be broken4 ,night birds do not fly about unless the moon shines full or in part2 rather do they feed between sun-down and the total darkness of the night4 ,footnote #h3 ,see ,no4 #eh-fg4 ,no body can be apprehended without light and shade1 and light and shade are caused by light4 #hce4 ,,why ,,men ,,advanced ,,in ,,age ,,see ,,better ,,at ,a ,,distance4 ,sight is better from a distance than near in those men who are advancing in age1 because the same object transmits a smaller impression of itself to the eye when it is distant than when it is near4 ,the seat of the common sense4 #hcf4 ,the ,common ,sense1 is that which judges of things offered to it by the other senses4 ,the ancient speculators have concluded that that part of man which constitutes his judgment is caused by a central organ to which the other five senses refer everything by means of impressibility2 and to this centre they have given the name ,common ,sense4 ,and they say that this ,sense is situated in the centre of the head between ,sensation and ,memory4 ,and this name of ,common ,sense is given to it solely because it is the common judge of all the other five senses i4e4 ,seeing1 ,hearing1 ,touch1 ,taste and ,smell4 ,this ,common ,sense is acted upon by means of ,sensation which is placed as a medium between it and the senses4 ,sensation is acted upon by means of the images of things presented to it by the external instruments1 that is to say the senses which are the medium between external things and ,sensation4 ,in the same way the senses are acted upon by objects4 ,surrounding things transmit their images to the senses and the senses transfer them to the ,sensation4 ,sensation sends them to the ,common ,sense1 and by it they are stamped upon the memory and are there more or less retained according to the importance or force of the impression4 ,that sense is most rapid in its function which is nearest to the sensitive medium and the eye1 being the highest is the chief of the others4 ,of this then only we will speak1 and the others we will leave in order not to make our matter too long4 ,experience tells us that the eye apprehends ten different natures of things1 that is3 ,light and ,darkness1 one being the cause of the perception of the nine others1 and the other its absence3-- ,colour and substance1 form and place1 distance and nearness1 motion and stillness ,footnote #ae3 ,compare ,no4 #bc44 ,on the origin of the soul4 #hcg4 ,though human ingenuity may make various inventions which1 by the help of various machines answering the same end1 it will never devise any inventions more beautiful1 nor more simple1 nor more to the purpose than ,nature does2 because in her inventions nothing is wanting1 and nothing is superfluous1 and she needs no counterpoise when she makes limbs proper for motion in the bodies of animals4 ,but she puts into them the soul of the body1 which forms them that is the soul of the mother which first constructs in the womb the form of the man and in due time awakens the soul that is to inhabit it4 ,and this at first lies dormant and under the tutelage of the soul of the mother1 who nourishes and vivifies it by the umbilical vein1 with all its spiritual parts1 and this happens because this umbilicus is joined to the placenta and the cotyledons1 by which the child is attached to the mother4 ,and these are the reason why a wish1 a strong craving or a fright or any other mental suffering in the mother1 has more influence on the child than on the mother2 for there are many cases when the child loses its life from them1 c4 ,this discourse is not in its place here1 but will be wanted for the one on the composition of animated bodies--and the rest of the definition of the soul ,i leave to the imaginations of friars1 those fathers of the people who know all secrets by inspiration4 ,footnote #eg3 lettere incoronate4 ,by this term ,leonardo probably understands not the ,bible only1 but the works of the early ,fathers1 and all the books recognised as sacred by the ,roman ,church4 ,i leave alone the sacred books2 for they are supreme truth4 ,on the relations of the soul to the organs of sense4 #hch4 ,,how ,,the ,,five ,,senses ,,are ,,the ,,ministers ,,of ,,the ,,soul4 ,the soul seems to reside in the judgment1 and the judgment would seem to be seated in that part where all the senses meet2 and this is called the ,common ,sense and is not all-pervading throughout the body1 as many have thought4 ,rather is it entirely in one part4 ,because1 if it were all-pervading and the same in every part1 there would have been no need to make the instruments of the senses meet in one centre and in one single spot2 on the contrary it would have sufficed that the eye should fulfil the function of its sensation on its surface only1 and not transmit the image of the things seen1 to the sense1 by means of the optic nerves1 so that the soul--for the reason given above-- may perceive it in the surface of the eye4 ,in the same way as to the sense of hearing1 it would have sufficed if the voice had merely sounded in the porous cavity of the indurated portion of the temporal bone which lies within the ear1 without making any farther transit from this bone to the common sense1 where the voice confers with and discourses to the common judgment4 ,the sense of smell1 again1 is compelled by necessity to refer itself to that same judgment4 ,feeling passes through the perforated cords and is conveyed to this common sense4 ,these cords diverge with infinite ramifications into the skin which encloses the members of the body and the viscera4 ,the perforated cords convey volition and sensation to the subordinate limbs4 ,these cords and the nerves direct the motions of the muscles and sinews1 between which they are placed2 these obey1 and this obedience takes effect by reducing their thickness2 for in swelling1 their length is reduced1 and the nerves shrink which are interwoven among the particles of the limbs2 being extended to the tips of the fingers1 they transmit to the sense the object which they touch4 ,the nerves with their muscles obey the tendons as soldiers obey the officers1 and the tendons obey the ,common central ,sense as the officers obey the general4 #bg ,thus the joint of the bones obeys the nerve1 and the nerve the muscle1 and the muscle the tendon and the tendon the ,common ,sense4 ,and the ,common ,sense is the seat of the soul #bh1 and memory is its ammunition1 and the impressibility is its referendary since the sense waits on the soul and not the soul on the sense4 ,and where the sense that ministers to the soul is not at the service of the soul1 all the functions of that sense are also wanting in that man's life1 as is seen in those born mute and blind4 ,footnote3 ,the peculiar use of the words nervo1 muscolo1 corda1 senso comune1 which are here literally rendered by nerve1 muscle cord or tendon and ,common ,sense may be understood from lines #bg and #bh4 ,on involuntary muscular action4 #hci4 ,,how ,,the ,,nerves ,,sometimes ,,act ,,of ,,themselves ,,without ,,any ,,commands ,,from ,,the ,,other ,,functions ,,of ,,the ,,soul4 ,this is most plainly seen2 for you will see palsied and shivering persons move1 and their trembling limbs1 as their head and hands1 quake without leave from their soul and their soul with all its power cannot prevent their members from trembling4 ,the same thing happens in falling sickness1 or in parts that have been cut off1 as in the tails of lizards4 ,the idea or imagination is the helm and guiding-rein of the senses1 because the thing conceived of moves the sense4 ,pre-imagining1 is imagining the things that are to be4 ,post-imagining1 is imagining the things that are past4 ,miscellaneous physiological observations 7#hdj-hdb74 #hdj4 ,there are four ,powers3 memory and intellect1 desire and covetousness4 ,the two first are mental and the others sensual4 ,the three senses3 sight1 hearing and smell cannot well be prevented2 touch and taste not at all4 ,smell is connected with taste in dogs and other gluttonous animals4 #hda4 ,i reveal to men the origin of the first1 or perhaps second cause of their existence4 #hdb4 ,lust is the cause of generation4 ,appetite is the support of life4 ,fear or timidity is the prolongation of life and preservation of its instruments4 ,the laws of nutrition and the support of life 7#hdc-hdh74 #hdc4 ,,how ,,the ,,body ,,of ,,animals ,,is ,,constantly ,,dying ,,and ,,being ,,renewed4 ,the body of any thing whatever that takes nourishment constantly dies and is constantly renewed2 because nourishment can only enter into places where the former nourishment has expired1 and if it has expired it no longer has life4 ,and if you do not supply nourishment equal to the nourishment which is gone1 life will fail in vigour1 and if you take away this nourishment1 the life is entirely destroyed4 ,but if you restore as much is destroyed day by day1 then as much of the life is renewed as is consumed1 just as the flame of the candle is fed by the nourishment afforded by the liquid of this candle1 which flame continually with a rapid supply restores to it from below as much as is consumed in dying above3 and from a brilliant light is converted in dying into murky smoke2 and this death is continuous1 as the smoke is continuous2 and the continuance of the smoke is equal to the continuance of the nourishment1 and in the same instant all the flame is dead and all regenerated1 simultaneously with the movement of its own nourishment4 #hdd4 ,king of the animals--as thou hast described him--,i should rather say king of the beasts1 thou being the greatest--because thou hast spared slaying them1 in order that they may give thee their children for the benefit of the gullet1 of which thou hast attempted to make a sepulchre for all animals2 and ,i would say still more1 if it were allowed me to speak the entire truth #e4 ,but we do not go outside human matters in telling of one supreme wickedness1 which does not happen among the animals of the earth1 inasmuch as among them are found none who eat their own kind1 unless through want of sense 7few indeed among them1 and those being mothers1 as with men1 albeit they be not many in number72 and this happens only among the rapacious animals1 as with the leonine species1 and leopards1 panthers lynxes1 cats and the like1 who sometimes eat their children2 but thou1 besides thy children devourest father1 mother1 brothers and friends2 nor is this enough for thee1 but thou goest to the chase on the islands of others1 taking other men and these half-naked1 the 444 and the 444 thou fattenest1 and chasest them down thy own throat#ah2 now does not nature produce enough simples1 for thee to satisfy thyself8 and if thou art not content with simples1 canst thou not by the mixture of them make infinite compounds1 as ,platina wrote,footnote #ba3 ,come scrisse il ,platina 7,bartolomeo ,sacchi1 a famous humanist74 ,the ,italian edition of his treatise ,de arte coquinaria1 was published under the title ,de la honestra voluptate1 e valetudine1 ,venezia #adhg41 and other authors on feeding8 ,footnote3 ,we are led to believe that ,leonardo himself was a vegetarian from the following interesting passage in the first of ,andrea ,corsali's letters to ,giuliano de',medici3 ,alcuni gentili chiamati ,guzzarati non si cibano di cosa1 alcuna che tenga sangue1 ne fra essi loro consentono che si noccia ad alcuna cosa animata1 come il nostro ,leonardo da ,vinci4 #e-ah4 ,amerigo ,vespucci1 with whom ,leonardo was personally acquainted1 writes in his second letter to ,pietro ,soderini1 about the inhabitants of the ,canary ,islands after having stayed there in #aejc3 ,hanno una scelerata liberta di viuere2 444 si cibano di carne humana1 di maniera che il padre magia il figliuolo1 et all'incontro il figliuolo il padre secondo che a caso e per sorte auiene4 ,io viddi un certo huomo sceleratissimo che si vantaua1 et si teneua a non piccola gloria di hauer mangiato piu di trecento huomini4 ,viddi anche vna certa citta1 nella quale io dimorai forse ventisette giorni1 doue le carni humane1 hauendole salate1 eran appicate alli traui1 si come noi alli traui di cucina appicchiamo le carni di cinghali secche al sole o al fumo1 et massimamente salsiccie1 et altre simil cose3 anzi si marauigliauano gradem ete che noi non magiaissimo della carne de nemici1 le quali dicono muouere appetito1 et essere di marauiglioso sapore1 et le lodano come cibi soaui et delicati 7,lettere due di ,amerigo ,vespucci ,fiorentino drizzate al magnifico ,pietro ,soderini1 ,gonfaloniere della eccelsa ,republica di ,firenze2 various editions74 #hde4 ,our life is made by the death of others4 ,in dead matter insensible life remains1 which1 reunited to the stomachs of living beings1 resumes life1 both sensual and intellectual4 #hdf4 ,here nature appears with many animals to have been rather a cruel stepmother than a mother1 and with others not a stepmother1 but a most tender mother4 #hdg4 ,man and animals are really the passage and the conduit of food1 the sepulchre of animals and resting place of the dead1 one causing the death of the other1 making themselves the covering for the corruption of other dead bodies4 ,on the circulation of the blood 7#hdh-hej74 #hdh4 ,death in old men1 when not from fever1 is caused by the veins which go from the spleen to the valve of the liver1 and which thicken so much in the walls that they become closed up and leave no passage for the blood that nourishes it4 #f,the incessant current of the blood through the veins makes these veins thicken and become callous1 so that at last they close up and prevent the passage of the blood4 #hdi4 ,the waters return with constant motion from the lowest depths of the sea to the utmost height of the mountains1 not obeying the nature of heavier bodies2 and in this they resemble the blood of animated beings which always moves from the sea of the heart and flows towards the top of the head2 and here it may burst a vein1 as may be seen when a vein bursts in the nose2 all the blood rises from below to the level of the burst vein4 ,when the water rushes out from the burst vein in the earth1 it obeys the law of other bodies that are heavier than the air since it always seeks low places4 ,footnote3 ,from this passage it is quite plain that ,leonardo had not merely a general suspicion of the circulation of the blood but a very clear conception of it4 ,leonardo's studies on the muscles of the heart are to be found in the ,,ms4 ,w4 ,an4 ,,iii4 but no information about them has hitherto been made public4 ,the limits of my plan in this work exclude all purely anatomical writings1 therefore only a very brief excerpt from this note book can be given here4 ,,william ,,harvey 7born #aegh and ,professor of ,anatomy at ,cambridge from #afae7 is always considered to have been the discoverer of the circulation of the blood4 ,he studied medicine at ,padua in #aeih1 and in #afbh brought out his memorable and important work3 ,de motu cordis et sanguinis4 #hej4 ,that the blood which returns when the heart opens again is not the same as that which closes the valves of the heart4 ,some notes on medicine 7#hea-hee74 #hea4 ,make them give you the definition and remedies for the case 444 and you will see that men are selected to be doctors for diseases they do not know4 #heb4 ,a remedy for scratches taught me by the ,herald to the ,king of ,france4 #d ounces of virgin wax1 #d ounces of colophony1 #b ounces of incense4 ,keep each thing separate2 and melt the wax1 and then put in the incense and then the colophony1 make a mixture of it and put it on the sore place4 #hec4 ,medicine is the restoration of discordant elements2 sickness is the discord of the elements infused into the living body4 #hed4 ,those who are annoyed by sickness at sea should drink extract of wormwood4 #hee4 ,to keep in health1 this rule is wise3 ,eat only when you want and relish food4 ,chew thoroughly that it may do you good4 ,have it well cooked1 unspiced and undisguised4 ,he who takes medicine is ill advised4 ,footnote3 ,this appears to be a sketch for a poem4 #hef4 ,i teach you to preserve your health2 and in this you will succed better in proportion as you shun physicians1 because their medicines are the work of alchemists4 ,footnote3 ,this passage is written on the back of the drawing ,pl4 ,,cviii4 ,compare also ,no4 #aahd4 ,,xv4 ,astronomy4 ,ever since the publication by ,venturi in #agig and ,libri in #ahdj of some few passages of ,leonardo's astronomical notes1 scientific astronomers have frequently expressed the opinion1 that they must have been based on very important discoveries1 and that the great painter also deserved a conspicuous place in the history of this science4 ,in the passages here printed1 a connected view is given of his astronomical studies as they lie scattered through the manuscripts1 which have come down to us4 ,unlike his other purely scientific labours1 ,leonardo devotes here a good deal of attention to the opinions of the ancients1 though he does not follow the practice universal in his day of relying on them as authorities2 he only quotes them1 as we shall see1 in order to refute their arguments4 ,his researches throughout have the stamp of independent thought4 ,there is nothing in these writings to lead us to suppose that they were merely an epitome of the general learning common to the astronomers of the period4 ,as early as in the ,x,i,vth century there were chairs of astronomy in the universities of ,padua and ,bologna1 but so late as during the entire ,x,v,ith century ,astronomy and ,astrology were still closely allied4 ,it is impossible now to decide whether ,leonardo1 when living in ,florence1 became acquainted in his youth with the doctrines of ,paolo ,toscanelli the great astronomer and mathematician 7died #adhb71 of whose influence and teaching but little is now known1 beyond the fact that he advised and encouraged ,columbus to carry out his project of sailing round the world4 ,his name is nowhere mentioned by ,leonardo1 and from the dates of the manuscripts from which the texts on astronomy are taken1 it seems highly probable that ,leonardo devoted his attention to astronomical studies less in his youth than in his later years4 ,it was evidently his purpose to treat of ,astronomy in a connected form and in a separate work 7see the beginning of ,nos4 #hff and #hib2 compare also ,no4 #aafg74 ,it is quite in accordance with his general scientific thoroughness that he should propose to write a special treatise on ,optics as an introduction to ,astronomy 7see ,nos4 #hfg and #hgg74 ,some of the chapters belonging to this ,section bear the title ,prospettiva 7see ,nos4 #hfi and #hgj71 this being the term universally applied at the time to ,optics as well as ,perspective 7see ,vol4 ,i1 p4 #aj1 note to ,no4 #ac1 l4 #aj74 ,at the beginning of the ,x,v,ith century the ,ptolemaic theory of the universe was still universally accepted as the true one1 and ,leonardo conceives of the earth as fixed1 with the moon and sun revolving round it1 as they are represented in the diagram to ,no4 #hig4 ,he does not go into any theory of the motions of the planets2 with regard to these and the fixed stars he only investigates the phenomena of their luminosity4 ,the spherical form of the earth he takes for granted as an axiom from the first1 and he anticipates ,newton by pointing out the universality of ,gravitation not merely in the earth1 but even in the moon4 ,although his acute research into the nature of the moon's light and the spots on the moon did not bring to light many results of lasting importance beyond making it evident that they were a refutation of the errors of his contemporaries1 they contain various explanations of facts which modern science need not modify in any essential point1 and discoveries which history has hitherto assigned to a very much later date4 ,the ingenious theory by which he tries to explain the nature of what is known as earth shine1 the reflection of the sun's rays by the earth towards the moon1 saying that it is a peculiar refraction1 originating in the innumerable curved surfaces of the waves of the sea may be regarded as absurd2 but it must not be forgotten that he had no means of detecting the fundamental error on which he based it1 namely3 the assumption that the moon was at a relatively short distance from the earth4 ,so long as the motion of the earth round the sun remained unknown1 it was of course impossible to form any estimate of the moon's distance from the earth by a calculation of its parallax4 ,before the discovery of the telescope accurate astronomical observations were only possible to a very limited extent4 ,it would appear however from certain passages in the notes here printed for the first time1 that ,leonardo was in a position to study the spots in the moon more closely than he could have done with the unaided eye4 ,so far as can be gathered from the mysterious language in which the description of his instrument is wrapped1 he made use of magnifying glasses2 these do not however seem to have been constructed like a telescope--telescopes were first made about #afjj4 ,as ,,libri pointed out 7,histoire des ,sciences mathematiques ,,iii1 #aja7 ,fracastoro of ,verona 7#adgc-aeec7 succeeded in magnifying the moon's face by an arrangement of lenses 7compare ,no4 #iaj1 note71 and this gives probability to ,leonardo's invention at a not much earlier date4 ,i4 ,,the ,,earth ,,as ,a ,,planet4 ,the earth's place in the universe 7#heg4 #heh74 #heg4 ,the equator1 the line of the horizon1 the ecliptic1 the meridian3 ,these lines are those which in all their parts are equidistant from the centre of the globe4 #heh4 ,the earth is not in the centre of the ,sun's orbit nor at the centre of the universe1 but in the centre of its companion elements1 and united with them4 ,and any one standing on the moon1 when it and the sun are both beneath us1 would see this our earth and the element of water upon it just as we see the moon1 and the earth would light it as it lights us4 ,the fundamental laws of the solar system 7#hei-hfd74 #hei4 ,force arises from dearth or abundance2 it is the child of physical motion1 and the grand-child of spiritual motion1 and the mother and origin of gravity4 ,gravity is limited to the elements of water and earth2 but this force is unlimited1 and by it infinite worlds might be moved if instruments could be made by which the force could be generated4 ,force1 with physical motion1 and gravity1 with resistance are the four external powers on which all actions of mortals depend4 ,force has its origin in spiritual motion2 and this motion1 flowing through the limbs of sentient animals1 enlarges their muscles4 ,being enlarged by this current the muscles are shrunk in length and contract the tendons which are connected with them1 and this is the cause of the force of the limbs in man4 ,the quality and quantity of the force of a man are able to give birth to other forces1 which will be proportionally greater as the motions produced by them last longer4 ,footnote3 ,only part of this passage belongs1 strictly speaking1 to this section4 ,the principle laid down in the second paragraph is more directly connected with the notes given in the preceding section on ,physiology4 #hfj4 ,why does not the weight o remain in its place8 ,it does not remain because it has no resistance4 ,where will it move to8 ,it will move towards the centre of gravity4 ,and why by no other line8 ,because a weight which has no support falls by the shortest road to the lowest point which is the centre of the world4 ,and why does the weight know how to find it by so short a line8 ,because it is not independant and does not move about in various directions4 ,footnote3 ,this text and the sketch belonging to it1 are reproduced on ,pl4 ,,cxxi4 #hfa4 ,let the earth turn on which side it may the surface of the waters will never move from its spherical form1 but will always remain equidistant from the centre of the globe4 ,granting that the earth might be removed from the centre of the globe1 what would happen to the water8 ,it would remain in a sphere round that centre equally thick1 but the sphere would have a smaller diameter than when it enclosed the earth4 ,footnote3 ,compare ,no4 #hif1 lines #dh-fd2 and ,no4 #icf4 #hfb4 ,supposing the earth at our antipodes which supports the ocean were to rise and stand uncovered1 far out of the sea1 but remaining almost level1 by what means afterwards1 in the course of time1 would mountains and vallies be formed8 ,and the rocks with their various strata8 #hfc4 ,each man is always in the middle of the surface of the earth and under the zenith of his own hemisphere1 and over the centre of the earth4 #hfd4 ,mem43 ,that ,i must first show the distance of the sun from the earth2 and1 by means of a ray passing through a small hole into a dark chamber1 detect its real size2 and besides this1 by means of the aqueous sphere calculate the size of the globe 444 ,here it will be shown1 that when the sun is in the meridian of our hemisphere ,footnote #aj3 ,antipodi orientali cogli occidentali4 ,the word ,antipodes does not here bear its literal sense1 but--as we may infer from the simultaneous reference to inhabitants of the ,north and ,south-- is used as meaning men living at a distance of #ij degrees from the zenith of the rational horizon of each observer41 the antipodes to the ,east and to the ,west1 alike1 and at the same time1 see the sun mirrored in their waters2 and the same is equally true of the arctic and antarctic poles1 if indeed they are inhabited4 ,how to prove that the earth is a planet 7#hfe-hfg74 #hfe4 ,that the earth is a star4 #hff4 ,in your discourse you must prove that the earth is a star much like the moon1 and the glory of our universe2 and then you must treat of the size of various stars1 according to the authors4 #hfg4 ,,the ,,method ,,of ,,proving ,,that ,,the ,,earth ,,is ,a ,,star4 ,first describe the eye2 then show how the twinkling of a star is really in the eye and why one star should twinkle more than another1 and how the rays from the stars originate in the eye2 and add1 that if the twinkling of the stars were really in the stars --as it seems to be--that this twinkling appears to be an extension as great as the diameter of the body of the star2 therefore1 the star being larger than the earth1 this motion effected in an instant would be a rapid doubling of the size of the star4 ,then prove that the surface of the air where it lies contiguous to fire1 and the surface of the fire where it ends are those into which the solar rays penetrate1 and transmit the images of the heavenly bodies1 large when they rise1 and small1 when they are on the meridian4 ,let a be the earth and n d m the surface of the air in contact with the sphere of fire2 h f g is the orbit of the moon or1 if you please1 of the sun2 then ,i say that when the sun appears on the horizon g1 its rays are seen passing through the surface of the air at a slanting angle1 that is o m2 this is not the case at d k4 ,and so it passes through a greater mass of air2 all of e m is a denser atmosphere4 #hfh4 ,beyond the sun and us there is darkness and so the air appears blue4 ,footnote3 ,compare ,vol4 ,i1 ,no4 #cja4 #hfi4 ,,perspective4 ,it is possible to find means by which the eye shall not see remote objects as much diminished as in natural perspective1 which diminishes them by reason of the convexity of the eye which necessarily intersects1 at its surface1 the pyramid of every image conveyed to the eye at a right angle on its spherical surface4 ,but by the method ,i here teach in the margin #i these pyramids are intersected at right angles close to the surface of the pupil4 ,the convex pupil of the eye can take in the whole of our hemisphere1 while this will show only a single star2 but where many small stars transmit their images to the surface of the pupil those stars are extremely small2 here only one star is seen but it will be large4 ,and so the moon will be seen larger and its spots of a more defined form ,footnote #bj and fol43 ,telescopes were not in use till a century later4 ,compare ,no4 #iaj and page #acf44 ,you must place close to the eye a glass filled with the water of which mention is made in number #d of ,book #aac ,on natural substances ,footnote #bc3 libro #aac4 ,this is perhaps the number of a book in some library catalogue4 ,but it may refer1 on the other hand1 to one of the #abj ,books mentioned in ,no4 #gif4 l4 #hd42 for this water makes objects which are enclosed in balls of crystalline glass appear free from the glass4 ,,of ,,the ,,eye4 ,among the smaller objects presented to the pupil of the eye1 that which is closest to it1 will be least appreciable to the eye4 ,and at the same time1 the experiments here made with the power of sight1 show that it is not reduced to speck if the c4 #cb;,footnote #cb3 ,compare with this the passage in ,vol4 ,i1 ,no4 #eb1 written about twenty years earlier44 ,read in the margin4 #cd,those objects are seen largest which come to the eye at the largest angles4 ,but the images of the objects conveyed to the pupil of the eye are distributed to the pupil exactly as they are distributed in the air3 and the proof of this is in what follows2 that when we look at the starry sky1 without gazing more fixedly at one star than another1 the sky appears all strewn with stars2 and their proportions to the eye are the same as in the sky and likewise the spaces between them #fa4 ,footnote3 #i4 #cb4 in margine3 lines #cd-fa are1 in the original1 written on the margin and above them is the diagram to which ,leonardo seems to refer here4 #hgj4 ,,perspective4 ,among objects moved from the eye at equal distance1 that undergoes least diminution which at first was most remote4 ,when various objects are removed at equal distances farther from their original position1 that which was at first the farthest from the eye will diminish least4 ,and the proportion of the diminution will be in proportion to the relative distance of the objects from the eye before they were removed4 ,that is to say in the object t and the object e the proportion of their distances from the eye a is quintuple4 ,i remove each from its place and set it farther from the eye by one of the #e parts into which the proposition is divided4 ,hence it happens that the nearest to the eye has doubled the distance and according to the last proposition but one of this1 is diminished by the half of its whole size2 and the body e1 by the same motion1 is diminished #a_/e of its whole size4 ,therefore1 by that same last proposition but one1 that which is said in this last proposition is true2 and this ,i say of the motions of the celestial bodies which are more distant by #cejj miles when setting than when overhead1 and yet do not increase or diminish in any sensible degree4 #hga4 a b is the aperture through which the sun passes1 and if you could measure the size of the solar rays at n m1 you could accurately trace the real lines of the convergence of the solar rays1 the mirror being at a b1 and then show the reflected rays at equal angles to n m2 but1 as you want to have them at n m1 take them at the4 inner side of the aperture at cd1 where they maybe measured at the spot where the solar rays fall4 ,then place your mirror at the distance a b1 making the rays d b1 c a fall and then be reflected at equal angles towards c d2 and this is the best method1 but you must use this mirror always in the same month1 and the same day1 and hour and instant1 and this will be better than at no fixed time because when the sun is at a certain distance it produces a certain pyramid of rays4 #hgb4 a1 the side of the body in light and shade b1 faces the whole portion of the hemisphere bed e f1 and does not face any part of the darkness of the earth4 ,and the same occurs at the point o2 therefore the space a o is throughout of one and the same brightness1 and s faces only four degrees of the hemisphere d e f g h1 and also the whole of the earth s h1 which will render it darker2 and how much must be demonstrated by calculation4 ,footnote3 ,this passage1 which has perhaps a doubtful right to its place in this connection1 stands in the ,manuscript between those given in ,vol4 ,i as ,no4 #aag and ,no4 #dbg4 #hgc4 ,,the ,,reason ,,of ,,the ,,increased ,,size ,,of ,,the ,,sun ,,in ,,the ,,west4 ,some mathematicians explain that the sun looks larger as it sets1 because the eye always sees it through a denser atmosphere1 alleging that objects seen through mist or through water appear larger4 ,to these ,i reply3 ,no2 because objects seen through a mist are similar in colour to those at a distance2 but not being similarly diminished they appear larger4 ,again1 nothing increases in size in smooth water2 and the proof of this may be seen by throwing a light on a board placed half under water4 ,but the reason why the sun looks larger is that every luminous body appears larger in proportion as it is more remote4 ,footnote3 ,lines #e and #f are thus rendered by ,m4 ,,ravaisson in his edition of ,,ms4 ,a4 ,de meme1 aucune chose ne croit dans l'eau plane1 et tu en feras l'experience en calquant un ais sous l'eau4--,compare the diagrams in ,vol4 ,i1 p4 #aad4 ,on the luminosity of the ,earth in the universal space 7#hgd-hgh74 #hgd4 ,in my book ,i propose to show1 how the ocean and the other seas must1 by means of the sun1 make our world shine with the appearance of a moon1 and to the remoter worlds it looks like a star2 and this ,i shall prove4 ,show1 first that every light at a distance from the eye throws out rays which appear to increase the size of the luminous body2 and from this it follows that #b 444,footnote #aj3 ,here the text breaks off2 lines #aa and fol4 are written in the margin44 #aa,the moon is cold and moist4 ,water is cold and moist4 ,thus our seas must appear to the moon as the moon does to us4 #hge4 ,the waves in water magnify the image of an object reflected in it4 ,let a be the sun1 and n m the ruffled water1 b the image of the sun when the water is smooth4 ,let f be the eye which sees the image in all the waves included within the base of the triangle c e f4 ,now the sun reflected in the unruffled surface occupied the space c d1 while in the ruffled surface it covers all the watery space c e 7as is proved in the #dth of my ,perspective7 ,footnote #i3 ,nel quarto della mia prospettiva4 ,if this reference is to the diagrams accompanying the text--as is usual with ,leonardo--and not to some particular work1 the largest of the diagrams here given must be meant4 ,it is the lowest and actually the fifth1 but he would have called it the fourth1 for the text here given is preceded on the same page of the manuscript by a passage on whirlpools1 with the diagram belonging to it also reproduced here4 ,the words della mia prospettiva may therefore indicate that the diagram to the preceding chapter treating on a heterogeneal subject is to be excluded4 ,it is a further difficulty that this diagram belongs properly to lines #i-aj and not to the preceding sentence4 ,the reflection of the sun in water is also discussed in the ,theoretical part of the ,book on ,painting2 see ,vol4 ,i1 ,no4 #bjf1 #bjg4 and it will cover more of the water in proportion as the reflected image is remote from the eye #aj4 ,footnote3 ,in the original sketch1 inside the circle in the first diagram1 is written ,sole 7sun71 and to the right of it luna 7moon74 ,thus either of these heavenly bodies may be supposed to fill that space4 ,within the lower circle is written simulacro 7image74 ,in the two next diagrams at the spot here marked ,l the word ,luna is written1 and in the last sole is written in the top circle at a4 ,the image of the sun will be more brightly shown in small waves than in large ones--and this is because the reflections or images of the sun are more numerous in the small waves than in large ones1 and the more numerous reflections of its radiance give a larger light than the fewer4 ,waves which intersect like the scales of a fir cone reflect the image of the sun with the greatest splendour2 and this is the case because the images are as many as the ridges of the waves on which the sun shines1 and the shadows between these waves are small and not very dark2 and the radiance of so many reflections together becomes united in the image which is transmitted to the eye1 so that these shadows are imperceptible4 ,that reflection of the sun will cover most space on the surface of the water which is most remote from the eye which sees it4 ,let a be the sun1 p q the reflection of the sun2 a b is the surface of the water1 in which the sun is mirrored1 and r the eye which sees this reflection on the surface of the water occupying the space o m4 c is the eye at a greater distance from the surface of the water and also from the reflection2 hence this reflection covers a larger space of water1 by the distance between n and o4 #hgf4 ,it is impossible that the side of a spherical mirror1 illuminated by the sun1 should reflect its radiance unless this mirror were undulating or filled with bubbles4 ,you see here the sun which lights up the moon1 a spherical mirror1 and all of its surface1 which faces the sun is rendered radiant4 ,whence it may be concluded that what shines in the moon is water like that of our seas1 and in waves as that is2 and that portion which does not shine consists of islands and terra firma4 ,this diagram1 of several spherical bodies interposed between the eye and the sun1 is given to show that1 just as the reflection of the sun is seen in each of these bodies1 in the same way that image may be seen in each curve of the waves of the sea2 and as in these many spheres many reflections of the sun are seen1 so in many waves there are many images1 each of which at a great distance is much magnified to the eye4 ,and1 as this happens with each wave1 the spaces interposed between the waves are concealed2 and1 for this reason1 it looks as though the many suns mirrored in the many waves were but one continuous sun2 and the shadows11 mixed up with the luminous images1 render this radiance less brilliant than that of the sun mirrored in these waves4 ,footnote3 ,in the original1 at letter ,a in the diagram ,sole 7the sun7 is written1 and at o occhio 7the eye74 #hgg4 ,this will have before it the treatise on light and shade4 ,the edges in the moon will be most strongly lighted and reflect most light1 because1 there1 nothing will be visible but the tops of the waves of the water ,footnote #e3 ,i have thought it unnecessary to reproduce the detailed explanation of the theory of reflection on waves contained in the passage which follows this44 #hgh4 ,the sun will appear larger in moving water or on waves than in still water2 an example is the light reflected on the strings of a monochord4 ,,ii4 ,,the ,,sun4 ,the question of the true and of the apparent size of the sun 7#hgi-hhd74 #hgi4 ,,in ,,praise ,,of ,,the ,,sun4 ,if you look at the stars1 cutting off the rays 7as may be done by looking through a very small hole made with the extreme point of a very fine needle1 placed so as almost to touch the eye71 you will see those stars so minute that it would seem as though nothing could be smaller2 it is in fact their great distance which is the reason of their diminution1 for many of them are very many times larger than the star which is the earth with water4 ,now reflect what this our star must look like at such a distance1 and then consider how many stars might be added--both in longitude and latitude--between those stars which are scattered over the darkened sky4 ,but ,i cannot forbear to condemn many of the ancients1 who said that the sun was no larger than it appears2 among these was ,epicurus1 and ,i believe that he founded his reason on the effects of a light placed in our atmosphere equidistant from the centre of the earth4 ,any one looking at it never sees it diminished in size at whatever distance2 and the rea- ,footnote #hgi-hhb3 ,what ,leonardo says of ,epicurus-- who according to ,,lewis1 ,the ,astronomy of the ancients1 and ,,madler1 ,geschichte der ,himmelskunde1 did not devote much attention to the study of celestial phenomena--1 he probably derived from ,book ,x of ,diogenes ,laertius1 whose ,vitae ,philosophorum was not printed in ,greek till #aecc1 but the ,latin translation appeared in #adge4 #hhj4 sons of its size and power ,i shall reserve for ,book #d4 ,but ,i wonder greatly that ,socrates ,footnote #b3 ,socrates2 ,i have little light to throw on this reference4 ,plato's ,socrates himself declares on more than one occasion that in his youth he had turned his mind to the study of celestial phenomena 7,,metewpa7 but not in his later years 7see ,g4 ,c4 ,,lewis1 ,the ,astronomy of the ancients1 page #aji2 ,,madler1 ,geschichte der ,himmelskunde1 page #da74 ,here and there in ,plato's writings we find incidental notes on the sun and other heavenly bodies4 ,leonardo may very well have known of these1 since the ,latin version by ,ficinus was printed as early as #adia2 indeed an undated edition exists which may very likely have appeared between #adhj--ij4 ,there is but one passage in ,plato1 ,epinomis 7p4 #ihc7 where he speaks of the physical properties of the sun and says that it is larger than the earth4 ,aristotle who goes very fully into the subject says the same4 ,a complete edition of ,aristotele's works was first printed in ,venice #adie-ih1 but a ,latin version of the ,books ,de ,coelo et ,mundo and ,de ,physica had been printed in ,venice as early as in #adhc 7,h4 ,,muller-,,strubing74 should have depreciated that solar body1 saying that it was of the nature of incandescent stone1 and the one who opposed him as to that error was not far wrong4 ,but ,i only wish ,i had words to serve me to blame those who are fain to extol the worship of men more than that of the sun2 for in the whole universe there is nowhere to be seen a body of greater magnitude and power than the sun4 ,its light gives light to all the celestial bodies which are distributed throughout the universe2 and from it descends all vital force1 for the heat that is in living beings comes from the soul vital spark2 and there is no other centre of heat and light in the universe as will be shown in ,book #d2 and certainly those who have chosen to worship men as gods--as ,jove1 ,saturn1 ,mars and the like--have fallen into the gravest error1 seeing that even if a man were as large as our earth1 he would look no bigger than a little star which appears but as a speck in the universe2 and seeing again that these men are mortal1 and putrid and corrupt in their sepulchres4 ,marcellus ,footnote #bc3 ,i have no means of identifying ,marcello who is named in the margin4 ,it may be ,nonius ,marcellus1 an obscure ,roman ,grammarian of uncertain date 7between the ,i,ind and ,vth centuries ,a4 ,c47 the author of the treatise ,de compendiosa doctrina per litteras ad filium in which he treats de rebus omnibus et quibusdam aliis4 ,this was much read in the middle ages4 ,the editto princeps is dated #adgj 7,h4 ,,muller-,,strubing74 and many others praise the sun4 #hha4 ,epicurus perhaps saw the shadows cast by columns on the walls in front of them equal in diameter to the columns from which the shadows were cast2 and the breadth of the shadows being parallel from beginning to end1 he thought he might infer that the sun also was directly opposite to this parallel and that consequently its breadth was not greater than that of the column2 not perceiving that the diminution in the shadow was insensibly slight by reason of the remoteness of the sun4 ,if the sun were smaller than the earth1 the stars on a great portion of our hemisphere would have no light1 which is evidence against ,epicurus who says the sun is only as large as it appears4 ,footnote3 ,in the original the writing is across the diagram4 #hhb4 ,epicurus says the sun is the size it looks4 ,hence as it looks about a foot across we must consider that to be its size2 it would follow that when the moon eclipses the sun1 the sun ought not to appear the larger1 as it does4 ,then1 the moon being smaller than the sun1 the moon must be less than a foot1 and consequently when our world eclipses the moon1 it must be less than a foot by a finger's breadth2 inasmuch as if the sun is a foot across1 and our earth casts a conical shadow on the moon1 it is inevitable that the luminous cause of the cone of shadow must be larger than the opaque body which casts the cone of shadow4 #hhc4 ,to measure how many times the diameter of the sun will go into its course in #bd hours4 ,make a circle and place it to face the south1 after the manner of a sundial1 and place a rod in the middle in such a way as that its length points to the centre of this circle1 and mark the shadow cast in the sunshine by this rod on the circumference of the circle1 and this shadow will be--let us say-- as broad as from a to n4 ,now measure how many times this shadow will go into this circumference of a circle1 and that will give you the number of times that the solar body will go into its orbit in #bd hours4 ,thus you may see whether ,epicurus was right in saying that the sun was only as large as it looked2 for1 as the apparent diameter of the sun is about a foot1 and as that sun would go a thousand times into the length of its course in #bd hours1 it would have gone a thousand feet1 that is #cjj braccia1 which is the sixth of a mile4 ,whence it would follow that the course of the sun during the day would be the sixth part of a mile and that this venerable snail1 the sun will have travelled #be braccia an hour4 #hhd4 ,posidonius composed books on the size of the sun4 ,footnote3 ,poseidonius of ,apamea1 commonly called the ,rhodian1 because he taught in ,rhodes1 was a ,stoic philosopher1 a contemporary and friend of ,cicero's1 and the author of numerous works on natural science1 among them4 ,strabo quotes no doubt from one of his works1 when he says that ,poseidonius explained how it was that the sun looked larger when it was rising or setting than during the rest of its course 7,,iii1 p4 #ace74 ,kleomedes1 a later ,greek ,naturalist also mentions this observation of ,poseidonius' without naming the title of his work2 however1 as ,kleomedes' ,cyclia ,theorica was not printed till #aece1 ,leonardo must have derived his quotation from ,strabo4 ,he probably wrote this note in #aejh1 and as the original ,greek was first printed in ,venice in #aeaf1 we must suppose him to quote here from the translation by ,guarinus ,veronensis1 which was printed as early as #adga1 also at ,venice 7,h4 ,,muller-,,strubing74 ,of the nature of ,sunlight4 #hhe4 ,,of ,,the ,,proof ,,that ,,the ,,sun ,,is ,,hot ,,by ,,nature ,,and ,,not ,,by ,,virtue4 ,of the nature of ,sunlight4 ,that the heat of the sun resides in its nature and not in its virtue or mode of action is abundantly proved by the radiance of the solar body on which the human eye cannot dwell and besides this no less manifestly by the rays reflected from a concave mirror1 which--when they strike the eye with such splendour that the eye cannot bear them--have a brilliancy equal to the sun in its own place4 ,and that this is true ,i prove by the fact that if the mirror has its concavity formed exactly as is requisite for the collecting and reflecting of these rays1 no created being could endure the heat that strikes from the reflected rays of such a mirror4 ,and if you argue that the mirror itself is cold and yet send forth hot rays1 ,i should reply that those rays come really from the sun and that it is the ray of the concave mirror after having passed through the window4 ,considerations as to the size of the sun 7#hhf-hia74 #hhf4 ,the sun does not move4 ,footnote3 ,this sentence occurs incidentally among mathematical notes1 and is written in unusually large letters4 #hhg4 ,,proof ,,that ,,the ,,nearer ,,you ,,are ,,to ,,the ,,source ,,of ,,the ,,solar ,,rays1 ,,the ,,larger ,,will ,,the ,,reflection ,,of ,,the ,,sun ,,from ,,the ,,sea ,,appear ,,to ,,you4 ,footnote3 ,lines #d and fol4 ,compare ,vol4 ,i1 ,nos4 #acj1 #aca4 ,if it is from the centre that the sun employs its radiance to intensify the power of its whole mass1 it is evident that the farther its rays extend1 the more widely they will be divided2 and this being so1 you1 whose eye is near the water that mirrors the sun1 see but a small portion of the rays of the sun strike the surface of the water1 and reflecting the form of the sun4 ,but if you were near to the sun--as would be the case when the sun is on the meridian and the sea to the westward--you would see the sun1 mirrored in the sea1 of a very great size2 because1 as you are nearer to the sun1 your eye taking in the rays nearer to the point of radiation takes more of them in1 and a great splendour is the result4 ,and in this way it can be proved that the moon must have seas which reflect the sun1 and that the parts which do not shine are land4 #hhh4 ,take the measure of the sun at the solstice in mid-,june4 #hhi4 ,,why ,,the ,,sun ,,appears ,,larger ,,when ,,setting ,,than ,,at ,,noon1 ,,when ,,it ,,is ,,near ,,to ,,us4 ,every object seen through a curved medium seems to be of larger size than it is4 ,footnote3 ,at ,a is written sole 7the sun71 at ,b terra 7the earth74 #hij4 ,because the eye is small it can only see the image of the sun as of a small size4 ,if the eye were as large as the sun it would see the image of the sun in water of the same size as the real body of the sun1 so long as the water is smooth4 #hia4 ,a ,,method ,,of ,,seeing ,,the ,,sun ,,eclipsed ,,without ,,pain ,,to ,,the ,,eye4 ,take a piece of paper and pierce holes in it with a needle1 and look at the sun through these holes4 ,,iii4 ,,the ,,moon4 ,on the luminousity of the moon 7#hib-ija74 #hib4 ,,of ,,the ,,moon4 ,as ,i propose to treat of the nature of the moon1 it is necessary that first ,i should describe the perspective of mirrors1 whether plane1 concave or convex2 and first what is meant by a luminous ray1 and how it is refracted by various kinds of media2 then1 when a reflected ray is most powerful1 whether when the angle of incidence is acute1 right1 or obtuse1 or from a convex1 a plane1 or a concave surface2 or from an opaque or a transparent body4 ,besides this1 how it is that the solar rays which fall on the waves of the sea1 are seen by the eye of the same width at the angle nearest to the eye1 as at the highest line of the waves on the horizon2 but notwithstanding this the solar rays reflected from the waves of the sea assume the pyramidal form and consequently1 at each degree of distance increase proportionally in size1 although to our sight1 they appear as parallel4 #ast4 ,nothing that has very little weight is opaque4 #b;dly4 ,nothing that is excessively weighty can remain beneath that which is heavier4 #c;dly4 ,as to whether the moon is situated in the centre of its elements or not4 ,and1 if it has no proper place of its own1 like the earth1 in the midst of its elements1 why does it not fall to the centre of our elements8 ,footnote #bf3 ,the problem here propounded by ,leonardo was not satisfactorily answered till ,newton in #afhb formulated the law of universal attraction and gravitation4 ,compare ,no4 #ijb1 lines #e-ae4 ,and1 if the moon is not in the centre of its own elements and yet does not fall1 it must then be lighter than any other element4 ,and1 if the moon is lighter than the other elements why is it opaque and not transparent8 ,when objects of various sizes1 being placed at various distances1 look of equal size1 there must be the same relative proportion in the distances as in the magnitudes of the objects4 ,footnote3 ,in the diagram ,leonardo wrote sole at the place marked ,a4 #hic4 ,,of ,,the ,,moon ,,and ,,whether ,,it ,,is ,,polished ,,and ,,spherical4 ,the image of the sun in the moon is powerfully luminous1 and is only on a small portion of its surface4 ,and the proof may be seen by taking a ball of burnished gold and placing it in the dark with a light at some distance from it2 and then1 although it will illuminate about half of the ball1 the eye will perceive its reflection only in a small part of its surface1 and all the rest of the surface reflects the darkness which surrounds it2 so that it is only in that spot that the image of the light is seen1 and all the rest remains invisible1 the eye being at a distance from the ball4 ,the same thing would happen on the surface of the moon if it were polished1 lustrous and opaque1 like all bodies with a reflecting surface4 ,show how1 if you were standing on the moon or on a star1 our earth would seem to reflect the sun as the moon does4 ,and show that the image of the sun in the sea cannot appear one and undivided1 as it appears in a perfectly plane mirror4 #hid4 ,how shadows are lost at great distances1 as is shown by the shadow side of the moon which is never seen4 ,footnote3 ,compare also ,vol4 ,i1 ,nos4 #age-agi4 #hie4 ,either the moon has intrinsic luminosity or not4 ,if it has1 why does it not shine without the aid of the sun8 ,but if it has not any light in itself it must of necessity be a spherical mirror2 and if it is a mirror1 is it not proved in ,perspective that the image of a luminous object will never be equal to the extent of surface of the reflecting body that it illuminates8 ,and if it be thus ,footnote #ac3 ,at ,a1 in the diagram1 ,leonardo wrote sole 7the sun71 and at ,b luna o noi terra 7the moon or our earth74 ,compare also the text of ,no4 #hgf41 as is here shown at r s in the figure1 whence comes so great an extent of radiance as that of the full moon as we see it1 at the fifteenth day of the moon8 #hif4 ,,of ,,the ,,moon4 ,the moon has no light in itself2 but so much of it as faces the sun is illuminated1 and of that illumined portion we see so much as faces the earth4 ,and the moon's night receives just as much light as is lent it by our waters as they reflect the image of the sun1 which is mirrored in all those waters which are on the side towards the sun4 ,the outside or surface of the waters forming the seas of the moon and of the seas of our globe is always ruffled little or much1 or more or less--and this roughness causes an extension of the numberless images of the sun which are repeated in the ridges and hollows1 the sides and fronts of the innumerable waves2 that is to say in as many different spots on each wave as our eyes find different positions to view them from4 ,this could not happen1 if the aqueous sphere which covers a great part of the moon were uniformly spherical1 for then the images of the sun would be one to each spectator1 and its reflections would be separate and independent and its radiance would always appear circular2 as is plainly to be seen in the gilt balls placed on the tops of high buildings4 ,but if those gilt balls were rugged or composed of several little balls1 like mulberries1 which are a black fruit composed of minute round globules1 then each portion of these little balls1 when seen in the sun1 would display to the eye the lustre resulting from the reflection of the sun1 and thus1 in one and the same body many tiny suns would be seen2 and these often combine at a long distance and appear as one4 ,the lustre of the new moon is brighter and stronger1 than when the moon is full2 and the reason of this is that the angle of incidence is more obtuse in the new than in the full moon1 in which the angles of incidence and reflection are highly acute4 ,the waves of the moon therefore mirror the sun in the hollows of the waves as well as on the ridges1 and the sides remain in shadow4 ,but at the sides of the moon the hollows of the waves do not catch the sunlight1 but only their crests2 and thus the images are fewer and more mixed up with the shadows in the hollows2 and this intermingling of the shaded and illuminated spots comes to the eye with a mitigated splendour1 so that the edges will be darker1 because the curves of the sides of the waves are insufficient to reflect to the eye the rays that fall upon them4 ,now the new moon naturally reflects the solar rays more directly towards the eye from the crests of the waves than from any other part1 as is shown by the form of the moon1 whose rays a strike the waves b and are reflected in the line b d1 the eye being situated at d4 ,this cannot happen at the full moon1 when the solar rays1 being in the west1 fall on the extreme waters of the moon to the ,east from n to m1 and are not reflected to the eye in the ,west1 but are thrown back eastwards1 with but slight deflection from the straight course of the solar ray2 and thus the angle of incidence is very wide indeed4 ,the moon is an opaque and solid body and if1 on the contrary1 it were transparent1 it would not receive the light of the sun4 ,the yellow or yolk of an egg remains in the middle of the albumen1 without moving on either side2 now it is either lighter or heavier than this albumen1 or equal to it2 if it is lighter1 it ought to rise above all the albumen and stop in contact with the shell of the egg2 and if it is heavier1 it ought to sink1 and if it is equal1 it might just as well be at one of the ends1 as in the middle or below #ed4 ,footnote #dh-fd3 ,compare ,no4 #hfa4 ,the innumerable images of the solar rays reflected from the innumerable waves of the sea1 as they fall upon those waves1 are what cause us to see the very broad and continuous radiance on the surface of the sea4 #hig4 ,that the sun could not be mirrored in the body of the moon1 which is a convex mirror1 in such a way as that so much of its surface as is illuminated by the sun1 should reflect the sun unless the moon had a surface adapted to reflect it--in waves and ridges1 like the surface of the sea when its surface is moved by the wind4 ,footnote3 ,in the original diagrams sole is written at the place marked ,a2 luna at ,c1 and terra at the two spots marked ,b4 ,the waves in water multiply the image of the object reflected in it4 ,these waves reflect light1 each by its own line1 as the surface of the fir cone does ,footnote #ad3 ,see the diagram p4 #ade4 ,these are #b figures one different from the other2 one with undulating water and the other with smooth water4 ,it is impossible that at any distance the image of the sun cast on the surface of a spherical body should occupy the half of the sphere4 ,here you must prove that the earth produces all the same effects with regard to the moon1 as the moon with regard to the earth4 ,the moon1 with its reflected light1 does not shine like the sun1 because the light of the moon is not a continuous reflection of that of the sun on its whole surface1 but only on the crests and hollows of the waves of its waters2 and thus the sun being confusedly reflected1 from the admixture of the shadows that lie between the lustrous waves1 its light is not pure and clear as the sun is4 ,footnote #ch3 ,this refers to the small diagram placed between ,b and ,b4--4 ,the earth between the moon on the fifteenth day and the sun4 ,footnote #ci3 ,see the diagram below the one referred to in the preceding note4 ,here the sun is in the ,east and the moon on the fifteenth day in the ,west4 ,footnote #dj4da3 ,refers to the diagram below the others4 ,the moon on the fifteenth day between the earth and the sun4 #da;,here it is the moon which has the sun to the ,west and the earth to the ,east4 #hih4 ,,what ,,sort ,,of ,,thing ,,the ,,moon ,,is4 ,the moon is not of itself luminous1 but is highly fitted to assimilate the character of light after the manner of a mirror1 or of water1 or of any other reflecting body2 and it grows larger in the ,east and in the ,west1 like the sun and the other planets4 ,and the reason is that every luminous body looks larger in proportion as it is remote4 ,it is easy to understand that every planet and star is farther from us when in the ,west than when it is overhead1 by about #cejj miles1 as is proved on the margin ,footnote #g3 refers to the first diagram4--,a sole 7the sun71 ,b terra 7the earth71 ,c luna 7the moon741 and if you see the sun or moon mirrored in the water near to you1 it looks to you of the same size in the water as in the sky4 ,but if you recede to the distance of a mile1 it will look #ajj times larger2 and if you see the sun reflected in the sea at sunset1 its image would look to you more than #aj miles long2 because that reflected image extends over more than #aj miles of sea4 ,and if you could stand where the moon is1 the sun would look to you1 as if it were reflected from all the sea that it illuminates by day2 and the land amid the water would appear just like the dark spots that are on the moon1 which1 when looked at from our earth1 appears to men the same as our earth would appear to any men who might dwell in the moon4 ,footnote3 ,this text has already been published by ,,libri3 ,histoire des ,sciences1 ,,iii1 pp4 #bbd1 #bbe4 ,,of ,,the ,,nature ,,of ,,the ,,moon4 ,when the moon is entirely lighted up to our sight1 we see its full daylight2 and at that time1 owing to the reflection of the solar rays which fall on it and are thrown off towards us1 its ocean casts off less moisture towards us2 and the less light it gives the more injurious it is4 #hii4 ,,of ,,the ,,moon4 ,i say that as the moon has no light in itself and yet is luminous1 it is inevitable but that its light is caused by some other body4 #ijj4 ,,of ,,the ,,moon4 ,all my opponent's arguments to say that there is no water in the moon4 ,footnote3 ,the objections are very minutely noted down in the manuscript1 but they hardly seem to have a place here4 #ija4 ,answer to ,maestro ,andrea da ,imola1 who said that the solar rays reflected from a convex mirror are mingled and lost at a short distance2 whereby it is altogether denied that the luminous side of the moon is of the nature of a mirror1 and that consequently the light is not produced by the innumerable multitude of the waves of that sea1 which ,i declared to be the portion of the moon which is illuminated by the solar rays4 ,let o p be the body of the sun1 c n s the moon1 and b the eye which1 above the base c n of the cathetus c n m1 sees the body of the sun reflected at equal angles c n2 and the same again on moving the eye from b to a4 ,footnote3 ,the large diagram on the margin of page #afa belongs to this chapter4 ,explanation of the lumen cinereum in the moon4 #ijb4 ,,of ,,the ,,moon4 ,no solid body is less heavy than the atmosphere4 ,footnote3 #a4 ,on the margin are the words tola romantina1 tola--ferro stagnato 7tinned iron72 romantina is some special kind of sheet-iron no longer known by that name4 ,having proved that the part of the moon that shines consists of water1 which mirrors the body of the sun and reflects the radiance it receives from it2 and that1 if these waters were devoid of waves1 it would appear small1 but of a radiance almost like the sun2 --#e ,it must now be shown whether the moon is a heavy or a light body3 for1 if it were a heavy body--admitting that at every grade of distance from the earth greater levity must prevail1 so that water is lighter than the earth1 and air than water1 and fire than air and so on successively--it would seem that if the moon had density as it really has1 it would have weight1 and having weight1 that it could not be sustained in the space where it is1 and consequently that it would fall towards the centre of the universe and become united to the earth2 or if not the moon itself1 at least its waters would fall away and be lost from it1 and descend towards the centre1 leaving the moon without any and so devoid of lustre4 ,but as this does not happen1 as might in reason be expected1 it is a manifest sign that the moon is surrounded by its own elements3 that is to say water1 air and fire2 and thus is1 of itself and by itself1 suspended in that part of space1 as our earth with its element is in this part of space2 and that heavy bodies act in the midst of its elements just as other heavy bodies do in ours ,footnote #ae3 ,this passage would certainly seem to establish ,leonardo's claim to be regarded as the original discoverer of the cause of the ashy colour of the new moon 7lumen cinereum74 ,his observations however1 having hitherto remained unknown to astronomers1 ,moestlin and ,kepler have been credited with the discoveries which they made independently a century later4 ,some disconnected notes treat of the same subject in ,,ms4 ,c4 ,a4 #bci;b2 #gah;b and #gai;b2 ,perche la luna cinta della parte alluminata dal sole in ponente1 tra maggior splendore in mezzo a tal cerchio1 che quando essa eclissava il sole4 ,questo accade perche nell' eclissare il sole ella ombrava il nostro oceano1 il qual caso non accade essendo in ponente1 quando il sole alluma esso oceano4 ,the editors of the ,saggio who first published this passage 7page #ab7 add another short one about the seasons in the moon which ,i confess not to have seen in the original manuscript3 ,la luna ha ogni mese un verno e una state1 e ha maggiori freddi e maggiori caldi1 e i suoi equinozii son piu freddi de' nostri4 ,when the eye is in the ,east and sees the moon in the ,west near to the setting sun1 it sees it with its shaded portion surrounded by luminous portions2 and the lateral and upper portion of this light is derived from the sun1 and the lower portion from the ocean in the ,west1 which receives the solar rays and reflects them on the lower waters of the moon1 and indeed affords the part of the moon that is in shadow as much radiance as the moon gives the earth at midnight4 ,therefore it is not totally dark1 and hence some have believed that the moon must in parts have a light of its own besides that which is given it by the sun2 and this light is due1 as has been said1 to the above- mentioned cause1--that our seas are illuminated by the sun4 ,again1 it might be said that the circle of radiance shown by the moon when it and the sun are both in the ,west is wholly borrowed from the sun1 when it1 and the sun1 and the eye are situated as is shown above4 ,footnote #bc4 #bd3 ,the larger of the two diagrams reproduced above stands between these two lines1 and the smaller one is sketched in the margin4 ,at the spot marked ,a ,leonardo wrote corpo solare 7solar body7 in the larger diagram and ,sole 7sun7 in the smaller one4 ,at ,c luna 7moon7 is written and at ,b terra 7the earth74 ,some might say that the air surrounding the moon as an element1 catches the light of the sun as our atmosphere does1 and that it is this which completes the luminous circle on the body of the moon4 ,some have thought that the moon has a light of its own1 but this opinion is false1 because they have founded it on that dim light seen between the hornes of the new moon1 which looks dark where it is close to the bright part1 while against the darkness of the background it looks so light that many have taken it to be a ring of new radiance completing the circle where the tips of the horns illuminated by the sun cease to shine ,footnote #cd3 ,see ,pl4 ,,cviii1 ,no4 #e44 ,and this difference of background arises from the fact that the portion of that background which is conterminous with the bright part of the moon1 by comparison with that brightness looks darker than it is2 while at the upper part1 where a portion of the luminous circle is to be seen of uniform width1 the result is that the moon1 being brighter there than the medium or background on which it is seen by comparison with that darkness it looks more luminous at that edge than it is4 ,and that brightness at such a time itself is derived from our ocean and other inland-seas4 ,these are1 at that time1 illuminated by the sun which is already setting in such a way as that the sea then fulfils the same function to the dark side of the moon as the moon at its fifteenth day does to us when the sun is set4 ,and the small amount of light which the dark side of the moon receives bears the same proportion to the light of that side which is illuminated1 as that444 ,footnote #db3 ,here the text breaks off2 lines #dc-eb are written on the margin44 ,if you want to see how much brighter the shaded portion of the moon is than the background on which it is seen1 conceal the luminous portion of the moon with your hand or with some other more distant object4 ,on the spots in the moon 7#ijc-ijg74 #ijc4 ,,the ,,spots ,,on ,,the ,,moon4 ,some have said that vapours rise from the moon1 after the manner of clouds and are interposed between the moon and our eyes4 ,but1 if this were the case1 these spots would never be permanent1 either as to position or form2 and1 seeing the moon from various aspects1 even if these spots did not move they would change in form1 as objects do which are seen from different sides4 #ijd4 ,,of ,,the ,,spots ,,on ,,the ,,moon4 ,others say that the moon is composed of more or less transparent parts2 as though one part were something like alabaster and others like crystal or glass4 ,it would follow from this that the sun casting its rays on the less transparent portions1 the light would remain on the surface1 and so the denser part would be illuminated1 and the transparent portions would display the shadow of their darker depths2 and this is their account of the structure and nature of the moon4 ,and this opinion has found favour with many philosophers1 and particularly with ,aristotle1 and yet it is a false view--for1 in the various phases and frequent changes of the moon and sun to our eyes1 we should see these spots vary1 at one time looking dark and at another light3 they would be dark when the sun is in the ,west and the moon in the middle of the sky2 for then the transparent hollows would be in shadow as far as the tops of the edges of those transparent hollows1 because the sun could not then fling his rays into the mouth of the hollows1 which however1 at full moon1 would be seen in bright light1 at which time the moon is in the ,east and faces the sun in the ,west2 then the sun would illuminate even the lowest depths of these transparent places and thus1 as there would be no shadows cast1 the moon at these times would not show us the spots in question2 and so it would be1 now more and now less1 according to the changes in the position of the sun to the moon1 and of the moon to our eyes1 as ,i have said above4 #ije4 ,,of ,,the ,,spots ,,on ,,the ,,moon4 ,it has been asserted1 that the spots on the moon result from the moon being of varying thinness or density2 but if this were so1 when there is an eclipse of the moon the solar rays would pierce through the portions which were thin as is alleged ,footnote #c-e3 ,eclissi4 ,this word1 as it seems to me1 here means eclipses of the sun2 and the sense of the passage1 as ,i understand it1 is that by the foregoing hypothesis the moon1 when it comes between the sun and the earth must appear as if pierced1--we may say like a sieve44 ,but as we do not see this effect the opinion must be false4 ,others say that the surface of the moon is smooth and polished and that1 like a mirror1 it reflects in itself the image of our earth4 ,this view is also false1 inasmuch as the land1 where it is not covered with water1 presents various aspects and forms4 ,hence when the moon is in the ,east it would reflect different spots from those it would show when it is above us or in the ,west2 now the spots on the moon1 as they are seen at full moon1 never vary in the course of its motion over our hemisphere4 ,a second reason is that an object reflected in a convex body takes up but a small portion of that body1 as is proved in perspective ,footnote #ah3 come e provato4 ,this alludes to the accompanying diagram44 ,the third reason is that when the moon is full1 it only faces half the hemisphere of the illuminated earth1 on which only the ocean and other waters reflect bright light1 while the land makes spots on that brightness2 thus half of our earth would be seen girt round with the brightness of the sea lighted up by the sun1 and in the moon this reflection would be the smallest part of that moon4 ,fourthly1 a radiant body cannot be reflected from another equally radiant2 therefore the sea1 since it borrows its brightness from the sun1--as the moon does--1 could not cause the earth to be reflected in it1 nor indeed could the body of the sun be seen reflected in it1 nor indeed any star opposite to it4 #ijf4 ,if you keep the details of the spots of the moon under observation you will often find great variation in them1 and this ,i myself have proved by drawing them4 ,and this is caused by the clouds that rise from the waters in the moon1 which come between the sun and those waters1 and by their shadow deprive these waters of the sun's rays4 ,thus those waters remain dark1 not being able to reflect the solar body4 #ijg4 ,how the spots on the moon must have varied from what they formerly were1 by reason of the course of its waters4 ,on the moon's halo4 #ijh4 ,,of ,,halos ,,round ,,the ,,moon4 ,i have found1 that the circles which at night seem to surround the moon1 of various sizes1 and degrees of density are caused by various gradations in the densities of the vapours which exist at different altitudes between the moon and our eyes4 ,and of these halos the largest and least red is caused by the lowest of these vapours2 the second1 smaller one1 is higher up1 and looks redder because it is seen through two vapours4 ,and so on1 as they are higher they will appear smaller and redder1 because1 between the eye and them1 there is thicker vapour4 ,whence it is proved that where they are seen to be reddest1 the vapours are most dense4 ,on instruments for observing the moon 7#iji4 #iaj74 #iji4 ,if you want to prove why the moon appears larger than it is1 when it reaches the horizon2 take a lens which is highly convex on one surface and concave on the opposite1 and place the concave side next the eye1 and look at the object beyond the convex surface2 by this means you will have produced an exact imitation of the atmosphere included beneath the sphere of fire and outside that of water2 for this atmosphere is concave on the side next the earth1 and convex towards the fire4 #iaj4 ,construct glasses to see the moon magnified4 ,footnote3 ,see the ,introduction1 p4 #acf1 ,fracastoro says in his work ,homocentres3 ,per dua specilla ocularla si quis perspiciat1 alteri altero superposito1 majora multo et propinquiora videbit omnia4--,quin imo quaedam specilla ocularia fiunt tantae densitatis1 ut si per ea quis aut lunam1 aut aliud siderum spectet1 adeo propinqua illa iudicet1 ut ne turres ipsas excedant 7sect4 ,,ii c4 #h and sect4 ,,iii1 c4 #bc74 9999999999999999 #iaa - #iab ,,missing 999999 when the sun is seen through the boughs of trees bare of their leaves1 at some distance the branches do not conceal any portion of the sun from our eye4 ,the same thing happens with the above mentioned planets which1 though they have no light of their own1 do not--as has been said--conceal any part of the sun from our eye #ah4 ,,second ,,argument4 ,some say that the stars appear most brilliant at night in proportion as they are higher up2 and that if they had no light of their own1 the shadow of the earth which comes between them and the sun1 would darken them1 since they would not face nor be faced by the solar body4 ,but those persons have not considered that the conical shadow of the earth cannot reach many of the stars2 and even as to those it does reach1 the cone is so much diminished that it covers very little of the star's mass1 and all the rest is illuminated by the sun4 #iac4 ,why the planets appear larger in the ,east than they do overhead1 whereas the contrary should be the case1 as they are #cejj miles nearer to us when in mid sky than when on the horizon4 ,all the degrees of the elements1 through which the images of the celestial bodies pass to reach the eye1 are equal curves and the angles by which the central line of those images passes through them1 are unequal angles ,footnote #ac3 inequali1 here and elsewhere does not mean unequal in the sense of not being equal to each other1 but angles which are not right angles42 and the distance is greater1 as is shown by the excess of a b beyond a d2 and the enlargement of these celestial bodies on the horizon is shown by the #ith of the #gth4 ,observations on the stars4 #iad4 ,to see the real nature of the planets open the covering and note at the base ,footnote #d3 basa4 ,this probably alludes to some instrument1 perhaps the ,camera obscura4 one single planet1 and the reflected movement of this base will show the nature of the said planet2 but arrange that the base may face only one at the time4 ,on history of astronomy4 #iae4 ,cicero says in his book ,de ,divinatione that ,astrology has been practised five hundred seventy thousand years before the ,trojan war4 #egjjj4 ,footnote3 ,the statement that ,,cicero1 ,de ,divin4 ascribes the discovery of astrology to a period #egjjj years before the ,trojan war ,i believe to be quite erroneous4 ,according to ,,ernesti1 ,clavis ,ciceroniana1 ,,ch4 ,g4 ,,schulz 7,lexic4 ,cicer47 and the edition of ,de ,divin4 by ,,giese the word ,astrologia occurs only twice in ,,cicero3 ,de ,divin4 ,,ii1 #db4 ,ad ,chaldaeorum monstra veniamus1 de quibus ,eudoxus1 ,platonis auditor1 in astrologia judicio doctissimorum hominum facile princeps1 sic opinatur 7id quod scriptum reliquit73 ,chaldaeis in praedictione et in notatione cujusque vitae ex natali die minime esse credendum4 ,he then quotes the condemnatory verdict of other philosophers as to the teaching of the ,chaldaeans but says nothing as to the antiquity and origin of astronomy4 ,,cicero further notes ,de oratore ,i1 #af that ,aratus was ignarus astrologiae but that is all4 ,so far as ,i know the word occurs nowhere else in ,,cicero2 and the word ,astronomia he does not seem to have used at all4 7,h4 ,,muller-,,strubing47 ,of time and its divisions 7#iaf-iah74 #iaf4 ,although time is included in the class of ,continuous ,quantities1 being indivisible and immaterial1 it does not come entirely under the head of ,geometry1 which represents its divisions by means of figures and bodies of infinite variety1 such as are seen to be continuous in their visible and material properties4 ,but only with its first principles does it agree1 that is with the ,point and the ,line2 the point may be compared to an instant of time1 and the line may be likened to the length of a certain quantity of time1 and just as a line begins and terminates in a point1 so such a space of time4 begins and terminates in an instant4 ,and whereas a line is infinitely divisible1 the divisibility of a space of time is of the same nature2 and as the divisions of the line may bear a certain proportion to each other1 so may the divisions of time4 ,footnote3 ,this passage is repeated word for word on page #aij;b of the same manuscript and this is accounted for by the text in ,vol4 ,i1 ,no4 #d4 ,compare also ,no4 #abaf4 #iag4 ,describe the nature of ,time as distinguished from the ,geometrical definitions4 #iah4 ,divide an hour into #cjjj parts1 and this you can do with a clock by making the pendulum lighter or heavier4 ,,xvi4 ,physical ,geography4 ,leonardo's researches as to the structure of the earth and sea were made at a time1 when the extended voyages of the ,spaniards and ,portuguese had also excited a special interest in geographical questions in ,italy1 and particularly in ,tuscany4 ,still1 it need scarcely surprise us to find that in deeper questions1 as to the structure of the globe1 the primitive state of the earth's surface1 and the like1 he was far in advance of his time4 ,the number of passages which treat of such matters is relatively considerable2 like almost all ,leonardo's scientific notes they deal partly with theoretical and partly with practical questions4 ,some of his theoretical views of the motion of water were collected in a copied manuscript volume by an early transcriber1 but without any acknowledgment of the source whence they were derived4 ,this copy is now in the ,library of the ,barberini palace at ,rome and was published under the title3 ,de moto e misura dell'acqua1 by ,,francesco ,,cardinali1 ,bologna #ahbh4 ,in this work the texts are arranged under the following titles3 ,libr4 ,i4 ,della spera dell'acqua2 ,libr4 ,,ii4 ,del moto dell'acqua2 ,libr4 ,,iii4 ,dell'onda dell'acqua2 ,libr4 ,,iv4 ,dei retrosi d'acqua2 ,libr4 ,v4 ,dell'acqua cadente2 ,libr4 ,,vi4 ,delle rotture fatte dall'acqua2 ,libr4 ,,vii ,delle cose portate dall'acqua2 ,libr4 ,,viii4 ,dell'oncia dell'acqua e delle canne2 ,libr4 ,,ix4 ,de molini e d'altri ordigni d'acqua4 ,the large number of isolated observations scattered through the manuscripts1 accounts for our so frequently finding notes of new schemes for the arrangement of those relating to water and its motions1 particularly in the ,codex ,atlanticus3 ,i have printed several of these plans as an introduction to the ,physical ,geography1 and ,i have actually arranged the texts in accordance with the clue afforded by one of them which is undoubtedly one of the latest notes referring to the subject 7,no4 #ibj74 ,the text given as ,no4 #icj which is also taken from a late note-book of ,leonardo's1 served as a basis for the arrangement of the first of the seven books--or sections--1 bearing the title3 ,of the ,nature of ,water 7,dell'acque in se74 ,as ,i have not made it any part of this undertaking to print the passages which refer to purely physical principles1 it has also been necessary to exclude those practical researches which1 in accordance with indications given in #ibj1 ought to come in as ,books #ac1 #ad and #ae4 ,i can only incidentally mention here that ,leonardo--as it seems to me1 especially in his youth--devoted a great deal of attention to the construction of mills4 ,this is proved by a number of drawings of very careful and minute execution1 which are to be found in the ,codex ,atlanticus4 ,nor was it possible to include his considerations on the regulation of rivers1 the making of canals and so forth 7,no4 #ibj1 ,books #aj1 #aa and #ab72 but those passages in which the structure of a canal is directly connected with notices of particular places will be found duly inserted under section ,,xvii 7,topographical notes74 ,in ,vol4 ,i1 ,no4 #e the text refers to canal-making in general4 ,on one point only can the collection of passages included under the general heading of ,physical ,geography claim to be complete4 ,when comparing and sorting the materials for this work ,i took particular care not to exclude or omit any text in which a geographical name was mentioned even incidentally1 since in all such researches the chief interest1 as it appeared to me1 attached to the question whether these acute observations on the various local characteristics of mountains1 rivers or seas1 had been made by ,leonardo himself1 and on the spot4 ,it is self-evident that the few general and somewhat superficial observations on the ,rhine and the ,danube1 on ,england and ,flanders1 must have been obtained from maps or from some informants1 and in the case of ,flanders ,leonardo himself acknowledges this 7see ,no4 #ajjh74 ,but that most of the other and more exact observations were made1 on the spot1 by ,leonardo himself1 may be safely assumed from their method and the style in which he writes of them2 and we should bear it in mind that in all investigations1 of whatever kind1 experience is always spoken of as the only basis on which he relies4 ,incidentally1 as in ,no4 #ihd1 he thinks it necessary to allude to the total absence of all recorded observations4 ,i4 ,,introduction4 ,schemes for the arrangement of the materials 7#iai-ibh74 #iai4 ,these books contain in the beginning3 ,of the nature of water itself in its motions2 the others treat of the effects of its currents1 which change the world in its centre and its shape4 #ibj4 ,,divisions ,,of ,,the ,,book4 ,book #a of water in itself4 ,book #b of the sea4 ,book #c of subterranean rivers4 ,book #d of rivers4 ,book #e of the nature of the abyss4 ,book #f of the obstacles4 ,book #g of gravels4 ,book #h of the surface of water4 ,book #i of the things placed therein4 ,book #aj of the repairing of rivers4 ,book #aa of conduits4 ,book #ab of canals4 ,book #ac of machines turned by water4 ,book #ad of raising water4 ,book #ae of matters worn away by water4 #iba4 ,first you shall make a book treating of places occupied by fresh waters1 and the second by salt waters1 and the third1 how by the disappearance of these1 our parts of the world were made lighter and in consequence more remote from the centre of the world4 #ibb4 ,first write of all water1 in each of its motions2 then describe all its bottoms and their various materials1 always referring to the propositions concerning the said waters2 and let the order be good1 for otherwise the work will be confused4 ,describe all the forms taken by water from its greatest to its smallest wave1 and their causes4 #ibc4 ,book #i1 of accidental risings of water4 #ibd4 ,,the ,,order ,,of ,,the ,,book4 ,place at the beginning what a river can effect4 #ibe4 ,a book of driving back armies by the force of a flood made by releasing waters4 ,a book showing how the waters safely bring down timber cut in the mountains4 ,a book of boats driven against the impetus of rivers4 ,a book of raising large bridges higher4 ,simply by the swelling of the waters4 ,a book of guarding against the impetus of rivers so that towns may not be damaged by them4 #ibf4 ,a book of the ordering of rivers so as to preserve their banks4 ,a book of the mountains1 which would stand forth and become land1 if our hemisphere were to be uncovered by the water4 ,a book of the earth carried down by the waters to fill up the great abyss of the seas4 ,a book of the ways in which a tempest may of itself clear out filled up sea-ports4 ,a book of the shores of rivers and of their permanency4 ,a book of how to deal with rivers1 so that they may keep their bottom scoured by their own flow near the cities they pass4 ,a book of how to make or to repair the foundations for bridges over the rivers4 ,a book of the repairs which ought to be made in walls and banks of rivers where the water strikes them4 ,a book of the formation of hills of sand or gravel at great depths in water4 #ibg4 ,water gives the first impetus to its motion4 ,a book of the levelling of waters by various means1 ,a book of diverting rivers from places where they do mischief4 ,a book of guiding rivers which occupy too much ground4 ,a book of parting rivers into several branches and making them fordable4 ,a book of the waters which with various currents pass through seas4 ,a book of deepening the beds of rivers by means of currents of water4 ,a book of controlling rivers so that the little beginnings of mischief1 caused by them1 may not increase4 ,a book of the various movements of waters passing through channels of different forms4 ,a book of preventing small rivers from diverting the larger one into which their waters run4 ,a book of the lowest level which can be found in the current of the surface of rivers4 ,a book of the origin of rivers which flow from the high tops of mountains4 ,a book of the various motions of waters in their rivers4 #ibh4 #a ,of inequality in the concavity of a ship4 ,footnote #a3 ,the first line of this passage was added subsequently1 evidently as a correction of the following line4 #a ,a book of the inequality in the curve of the sides of ships4 #a ,a book of the inequality in the position of the tiller4 #a ,a book of the inequality in the keel of ships4 #b ,a book of various forms of apertures by which water flows out4 #c ,a book of water contained in vessels with air1 and of its movements4 #d ,a book of the motion of water through a syphon4 ,footnote #g3 cicognole1 see ,no4 #iff1 #aa1 #ag4 #e ,a book of the meetings and union of waters coming from different directions4 #f ,a book of the various forms of the banks through which rivers pass4 #g ,a book of the various forms of shoals formed under the sluices of rivers4 #h ,a book of the windings and meanderings of the currents of rivers4 #i ,a book of the various places whence the waters of rivers are derived4 #aj ,a book of the configuration of the shores of rivers and of their permanency4 #aa ,a book of the perpendicular fall of water on various objects4 #ab ,abook of the course of water when it is impeded in various places4 #ab ,a book of the various forms of the obstacles which impede the course of waters4 #ac ,a book of the concavity and globosity formed round various objects at the bottom4 #ad ,abook of conducting navigable canals above or beneath the rivers which intersect them4 #ae ,a book of the soils which absorb water in canals and of repairing them4 #af ,abook of creating currents for rivers1 which quit their beds1 and for rivers choked with soil4 ,general introduction4 #ibi4 ,,the ,,beginning ,,of ,,the ,,treatise ,,on ,,water4 ,by the ancients man has been called the world in miniature2 and certainly this name is well bestowed1 because1 inasmuch as man is composed of earth1 water1 air and fire1 his body resembles that of the earth2 and as man has in him bones the supports and framework of his flesh1 the world has its rocks the supports of the earth2 as man has in him a pool of blood in which the lungs rise and fall in breathing1 so the body of the earth has its ocean tide which likewise rises and falls every six hours1 as if the world breathed2 as in that pool of blood veins have their origin1 which ramify all over the human body1 so likewise the ocean sea fills the body of the earth with infinite springs of water4 ,the body of the earth lacks sinews and this is1 because the sinews are made expressely for movements and1 the world being perpetually stable1 no movement takes place1 and no movement taking place1 muscles are not necessary4 --,but in all other points they are much alike4 ,i4 ,,of ,,the ,,nature ,,of ,,water4 ,the arrangement of ,book ,i4 #icj4 ,,the ,,order ,,of ,,the ,,first ,,book ,,on ,,water4 ,define first what is meant by height and depth2 also how the elements are situated one inside another4 ,then1 what is meant by solid weight and by liquid weight2 but first what weight and lightness are in themselves4 ,then describe why water moves1 and why its motion ceases2 then why it becomes slower or more rapid2 besides this1 how it always falls1 being in contact with the air but lower than the air4 ,and how water rises in the air by means of the heat of the sun1 and then falls again in rain2 again1 why water springs forth from the tops of mountains2 and if the water of any spring higher than the ocean can pour forth water higher than the surface of that ocean4 ,and how all the water that returns to the ocean is higher than the sphere of waters4 ,and how the waters of the equatorial seas are higher than the waters of the ,north1 and higher beneath the body of the sun than in any part of the equatorial circle2 for experiment shows that under the heat of a burning brand the water near the brand boils1 and the water surrounding this ebullition always sinks with a circular eddy4 ,and how the waters of the ,north are lower than the other seas1 and more so as they become colder1 until they are converted into ice4 ,definitions 7#ica4 #icb74 #ica4 ,,of ,,what ,,is ,,water4 ,among the four elements water is the second both in weight and in instability4 #icb4 ,,the ,,beginning ,,of ,,the ,,book ,,on ,,water4 ,sea is the name given to that water which is wide and deep1 in which the waters have not much motion4 ,footnote3 ,only the beginning of this passage is here given1 the remainder consists of definitions which have no direct bearing on the subject4 ,of the surface of the water in relation to the globe 7#icc-icf74 #icc4 ,the centres of the sphere of water are two1 one universal and common to all water1 the other particular4 ,the universal one is that which is common to all waters not in motion1 which exist in great quantities4 ,as canals1 ditches1 ponds1 fountains1 wells1 dead rivers1 lakes1 stagnant pools and seas1 which1 although they are at various levels1 have each in itself the limits of their superficies equally distant from the centre of the earth1 such as lakes placed at the tops of high mountains2 as the lake near ,pietra ,pana and the lake of the ,sybil near ,norcia2 and all the lakes that give rise to great rivers1 as the ,ticino from ,lago ,maggiore1 the ,adda from the lake of ,como1 the ,mincio from the lake of ,garda1 the ,rhine from the lakes of ,constance and of ,chur1 and from the lake of ,lucerne1 like the ,tigris which passes through ,asia ,minor carrying with it the waters of three lakes1 one above the other at different heights of which the highest is ,munace1 the middle one ,pallas1 and the lowest ,triton2 the ,nile again flows from three very high lakes in ,ethiopia4 ,footnote #e3 ,pietra ,pana1 a mountain near ,florence4 ,if for ,norcia1 we may read ,norchia1 the remains of the ,etruscan city near ,viterbo1 there can be no doubt that by ',lago della ,sibilla'--a name not known elsewhere1 so far as ,i can learn--,leonardo meant ,lago di ,vico 7,lacus ,ciminus1 ,aen4 #g74 #icd4 ,,of ,,the ,,centre ,,of ,,the ,,ocean4 ,the centre of the sphere of waters is the true centre of the globe of our world1 which is composed of water and earth1 having the shape of a sphere4 ,but1 if you want to find the centre of the element of the earth1 this is placed at a point equidistant from the surface of the ocean1 and not equidistant from the surface of the earth2 for it is evident that this globe of earth has nowhere any perfect rotundity1 excepting in places where the sea is1 or marshes or other still waters4 ,and every part of the earth that rises above the water is farther from the centre4 #ice4 ,,of ,,the ,,sea ,,which ,,changes ,,the ,,weight ,,of ,,the ,,earth4 ,the shells1 oysters1 and other similar animals1 which originate in sea-mud1 bear witness to the changes of the earth round the centre of our elements4 ,this is proved thus3 ,great rivers always run turbid1 being coloured by the earth1 which is stirred by the friction of their waters at the bottom and on their shores2 and this wearing disturbs the face of the strata made by the layers of shells1 which lie on the surface of the marine mud1 and which were produced there when the salt waters covered them2 and these strata were covered over again from time to time1 with mud of various thickness1 or carried down to the sea by the rivers and floods of more or less extent2 and thus these layers of mud became raised to such a height1 that they came up from the bottom to the air4 ,at the present time these bottoms are so high that they form hills or high mountains1 and the rivers1 which wear away the sides of these mountains1 uncover the strata of these shells1 and thus the softened side of the earth continually rises and the antipodes sink closer to the centre of the earth1 and the ancient bottoms of the seas have become mountain ridges4 #icf4 ,let the earth make whatever changes it may in its weight1 the surface of the sphere of waters can never vary in its equal distance from the centre of the world4 ,of the proportion of the mass of water to that of the earth 7#icg4 #ich74 #icg4 ,,whether ,,the ,,earth ,,is ,,less ,,than ,,the ,,water4 ,some assert that it is true that the earth1 which is not covered by water is much less than that covered by water4 ,but considering the size of #gjjj miles in diameter which is that of this earth1 we may conclude the water to be of small depth4 #ich4 ,,of ,,the ,,earth4 ,the great elevations of the peaks of the mountains above the sphere of the water may have resulted from this that3 a very large portion of the earth which was filled with water that is to say the vast cavern inside the earth may have fallen in a vast part of its vault towards the centre of the earth1 being pierced by means of the course of the springs which continually wear away the place where they pass4 ,sinking in of countries like the ,dead ,sea in ,syria1 that is ,sodom and ,gomorrah4 ,it is of necessity that there should be more water than land1 and the visible portion of the sea does not show this2 so that there must be a great deal of water inside the earth1 besides that which rises into the lower air and which flows through rivers and springs4 ,footnote3 ,the small sketch below on the left1 is placed in the original close to the text referring to the ,dead ,sea4 ,the theory of ,plato4 #ici4 ,,the ,,figures ,,of ,,the ,,elements4 ,of the figures of the elements2 and first as against those who deny the opinions of ,plato1 and who say that if the elements include one another in the forms attributed to them by ,plato they would cause a vacuum one within the other4 ,i say it is not true1 and ,i here prove it1 but first ,i desire to propound some conclusions4 ,it is not necessary that the elements which include each other should be of corresponding magnitude in all the parts1 of that which includes and of that which is included4 ,we see that the sphere of the waters varies conspicuously in mass from the surface to the bottom1 and that1 far from investing the earth when that was in the form of a cube that is of #h angles as ,plato will have it1 that it invests the earth which has innumerable angles of rock covered by the water and various prominences and concavities1 and yet no vacuum is generated between the earth and water2 again1 the air invests the sphere of waters together with the mountains and valleys1 which rise above that sphere1 and no vacuum remains between the earth and the air1 so that any one who says a vacuum is generated1 speaks foolishly4 ,but to ,plato ,i would reply that the surface of the figures which according to him the elements would have1 could not exist4 ,that the flow of rivers proves the slope of the land4 #idj4 ,,proves ,,how ,,the ,,earth ,,is ,,not ,,globular ,,and ,,not ,,being ,,globular ,,cannot ,,have ,a ,,common ,,centre4 ,we see the ,nile come from ,southern regions and traverse various provinces1 running towards the ,north for a distance of #cjjj miles and flow into the ,mediterranean by the shores of ,egypt2 and if we will give to this a fall of ten braccia a mile1 as is usually allowed to the course of rivers in general1 we shall find that the ,nile must have its mouth ten miles lower than its source4 ,again1 we see the ,rhine1 the ,rhone and the ,danube starting from the ,german parts1 almost the centre of ,europe1 and having a course one to the ,east1 the other to the ,north1 and the last to ,southern seas4 ,and if you consider all this you will see that the plains of ,europe in their aggregate are much higher than the high peaks of the maritime mountains2 think then how much their tops must be above the sea shores4 ,theory of the elevation of water within the mountains4 #ida4 ,,of ,,the ,,heat ,,that ,,is ,,in ,,the ,,world4 ,where there is life there is heat1 and where vital heat is1 there is movement of vapour4 ,this is proved1 inasmuch as we see that the element of fire by its heat always draws to itself damp vapours and thick mists as opaque clouds1 which it raises from seas as well as lakes and rivers and damp valleys2 and these being drawn by degrees as far as the cold region1 the first portion stops1 because heat and moisture cannot exist with cold and dryness2 and where the first portion stops the rest settle1 and thus one portion after another being added1 thick and dark clouds are formed4 ,they are often wafted about and borne by the winds from one region to another1 where by their density they become so heavy that they fall in thick rain2 and if the heat of the sun is added to the power of the element of fire1 the clouds are drawn up higher still and find a greater degree of cold1 in which they form ice and fall in storms of hail4 ,now the same heat which holds up so great a weight of water as is seen to rain from the clouds1 draws them from below upwards1 from the foot of the mountains1 and leads and holds them within the summits of the mountains1 and these1 finding some fissure1 issue continuously and cause rivers4 ,the relative height of the surface of the sea to that of the land 7#idb-ide74 #idb4 ,,of ,,the ,,sea1 ,,which ,,to ,,many ,,fools ,,appears ,,to ,,be ,,higher ,,than ,,the ,,earth ,,which ,,forms ,,its ,,shore4 b d is a plain through which a river flows to the sea2 this plain ends at the sea1 and since in fact the dry land that is uncovered is not perfectly level--for1 if it were1 the river would have no motion--as the river does move1 this place is a slope rather than a plain2 hence this plain d b so ends where the sphere of water begins that if it were extended in a continuous line to b a it would go down beneath the sea1 whence it follows that the sea a c b looks higher than the dry land4 ,obviously no portions of dry land left uncovered by water can ever be lower than the surface of the watery sphere4 #idc4 ,,of ,,certain ,,persons ,,who ,,say ,,the ,,waters ,,were ,,higher ,,than ,,the ,,dry ,,land4 ,certainly ,i wonder not a little at the common opinion which is contrary to truth1 but held by the universal consent of the judgment of men4 ,and this is that all are agreed that the surface of the sea is higher than the highest peaks of the mountains2 and they allege many vain and childish reasons1 against which ,i will allege only one simple and short reason2 ,we see plainly that if we could remove the shores of the sea1 it would invest the whole earth and make it a perfect sphere4 ,now1 consider how much earth would be carried away to enable the waves of the sea to cover the world2 therefore that which would be carried away must be higher than the sea-shore4 #idd4 ,,the ,,opinion ,,of ,,some ,,persons ,,who ,,say ,,that ,,the ,,water ,,of ,,some ,,seas ,,is ,,higher ,,than ,,the ,,highest ,,summits ,,of ,,mountains2 ,,and ,,nevertheless ,,the ,,water ,,was ,,forced ,,up ,,to ,,these ,,summits4 ,water would not move from place to place if it were not that it seeks the lowest level and by a natural consequence it never can return to a height like that of the place where it first on issuing from the mountain came to light4 ,and that portion of the sea which1 in your vain imagining1 you say was so high that it flowed over the summits of the high mountains1 for so many centuries would be swallowed up and poured out again through the issue from these mountains4 ,you can well imagine that all the time that ,tigris and ,euphrates #ide4 have flowed from the summits of the mountains of ,armenia1 it must be believed that all the water of the ocean has passed very many times through these mouths4 ,and do you not believe that the ,nile must have sent more water into the sea than at present exists of all the element of water8 ,undoubtedly1 yes4 ,and if all this water had fallen away from this body of the earth1 this terrestrial machine would long since have been without water4 ,whence we may conclude that the water goes from the rivers to the sea1 and from the sea to the rivers1 thus constantly circulating and returning1 and that all the sea and the rivers have passed through the mouth of the ,nile an infinite number of times ,footnote3 ,moti ,armeni1 ,ermini in the original1 in ,m4 ,,ravaisson',s transcript monti ernini le loro ruine84 ,he renders this ,le ,tigre et l',euphrate se sont deverses par les sommets des montagnes avec leurs eaux destructives8 on pent cro're c4 ,leonardo always writes ,ermini1 ,erminia1 for ,armeni1 ,armenia 7,arabic3 ,irminiah74 ,m4 ,,ravaisson also deviates from the original in his translation of the following passage3 ,or tu ne crois pas que le ,nil ait mis plus d'eau dans la mer qu'il n'y en a a present dans tout l'element de l'eau4 ,il est certain que si cette eau etait tombee c4 ,,ii4 ,,on ,,the ,,ocean4 ,refutation of ,pliny's theory as to the saltness of the sea 7#idf4 #idg74 #idf4 ,,why ,,water ,,is ,,salt4 ,pliny says in his second book1 chapter #ajc1 that the water of the sea is salt because the heat of the sun dries up the moisture and drinks it up2 and this gives to the wide stretching sea the savour of salt4 ,but this cannot be admitted1 because if the saltness of the sea were caused by the heat of the sun1 there can be no doubt that lakes1 pools and marshes would be so much the more salt1 as their waters have less motion and are of less depth2 but experience shows us1 on the contrary1 that these lakes have their waters quite free from salt4 ,again it is stated by ,pliny in the same chapter that this saltness might originate1 because all the sweet and subtle portions which the heat attracts easily being taken away1 the more bitter and coarser part will remain1 and thus the water on the surface is fresher than at the bottom ,footnote #bb3 ,compare ,no4 #idh42 but this is contradicted by the same reason given above1 which is1 that the same thing would happen in marshes and other waters1 which are dried up by the heat4 ,again1 it has been said that the saltness of the sea is the sweat of the earth2 to this it may be answered that all the springs of water which penetrate through the earth1 would then be salt4 ,but the conclusion is1 that the saltness of the sea must proceed from the many springs of water which1 as they penetrate into the earth1 find mines of salt and these they dissolve in part1 and carry with them to the ocean and the other seas1 whence the clouds1 the begetters of rivers1 never carry it up4 ,and the sea would be salter in our times than ever it was at any time2 and if the adversary were to say that in infinite time the sea would dry up or congeal into salt1 to this ,i answer that this salt is restored to the earth by the setting free of that part of the earth which rises out of the sea with the salt it has acquired1 and the rivers return it to the earth under the sea4 ,footnote3 ,see ,,pliny1 ,hist4 ,nat4 ,,ii1 ,,ciii ,c4 ,itaque ,solis ardore siccatur liquor3 et hoc esse masculum sidus accepimus1 torrens cuncta sorbensque4 7cp4 ,,civ47 ,sic mari late patenti saporem incoqui salis1 aut quia exhausto inde dulci tenuique1 quod facillime trahat vis ignea1 omne asperius crassiusque linquatur3 ideo summa aequorum aqua dulciorem profundam2 hanc esse veriorem causam1 quam quod mare terrae sudor sit aeternus3 aut quia plurimum ex arido misceatur illi vapore3 aut quia terrae natura sicut medicatas aquas inficiat 444 7cp4 ,,cv73 altissimum mare ,,xv4 stadiorum ,fabianus tradit4 ,alii n ,ponto coadverso ,coraxorum gentis 7vocant ,b ,ponti7 trecentis fere a continenti stadiis immensam altitudinem maris tradunt1 vadis nunquam repertis4 7cp4 ,,cvi ,,ciii7 ,mirabilius id faciunt aquae dulces1 juxta mare1 ut fistulis emicantes4 ,nam nec aquarum natura a miraculis cessat4 ,dulces mari invehuntur1 leviores haud dubie4 ,ideo et marinae1 quarum natura gravior1 magis invecta sustinent4 ,quaedam vero et dulces inter se supermeant alias4 #idg4 ,for the third and last reason we will say that salt is in all created things2 and this we learn from water passed over the ashes and cinders of burnt things2 and the urine of every animal1 and the superfluities issuing from their bodies1 and the earth into which all things are converted by corruption4 ,but1--to put it better1--given that the world is everlasting1 it must be admitted that its population will also be eternal2 hence the human species has eternally been and would be consumers of salt2 and if all the mass of the earth were to be turned into salt1 it would not suffice for all human food ,footnote #bg3 ,that is1 on the supposition that salt1 once consumed1 disappears for ever42 whence we are forced to admit1 either that the species of salt must be everlasting like the world1 or that it dies and is born again like the men who devour it4 ,but as experience teaches us that it does not die1 as is evident by fire1 which does not consume it1 and by water which becomes salt in proportion to the quantity dissolved in it1--and when it is evaporated the salt always remains in the original quantity--it must pass through the bodies of men either in the urine or the sweat or other excretions where it is found again2 and as much salt is thus got rid of as is carried every year into towns2 therefore salt is dug in places where there is urine4-- ,sea hogs and sea winds are salt4 ,we will say that the rains which penetrate the earth are what is under the foundations of cities with their inhabitants1 and are what restore through the internal passages of the earth the saltness taken from the sea2 and that the change in the place of the sea1 which has been over all the mountains1 caused it to be left there in the mines found in those mountains1 c4 ,the characteristics of sea water 7#idh4 #idi74 #idh4 ,the waters of the salt sea are fresh at the greatest depths4 #idi4 ,,that ,,the ,,ocean ,,does ,,not ,,penetrate ,,under ,,the ,,earth4 ,the ocean does not penetrate under the earth1 and this we learn from the many and various springs of fresh water which1 in many parts of the ocean make their way up from the bottom to the surface4 ,the same thing is farther proved by wells dug beyond the distance of a mile from the said ocean1 which fill with fresh water2 and this happens because the fresh water is lighter than salt water and consequently more penetrating4 ,which weighs most1 water when frozen or when not frozen8 ,,fresh ,,water ,,penetrates ,,more ,,against ,,salt ,,water ,,than ,,salt ,,water ,,against ,,fresh ,,water4 ,that fresh water penetrates more against salt water1 than salt water against fresh is proved by a thin cloth dry and old1 hanging with the two opposite ends equally low in the two different waters1 the surfaces of which are at an equal level2 and it will then be seen how much higher the fresh water will rise in this piece of linen than the salt2 by so much is the fresh lighter than the salt4 ,on the formation of ,gulfs 7#iej4 #iea74 #iej4 ,all inland seas and the gulfs of those seas1 are made by rivers which flow into the sea4 #iea4 ,,here ,,the ,,reason ,,is ,,given ,,of ,,the ,,effects ,,produced ,,by ,,the ,,waters ,,in ,,the ,,above ,,mentioned ,,place4 ,all the lakes and all the gulfs of the sea and all inland seas are due to rivers which distribute their waters into them1 and from impediments in their downfall into the ,mediterranean --which divides ,africa from ,europe and ,europe from ,asia by means of the ,nile and the ,don which pour their waters into it4 ,it is asked what impediment is great enough to stop the course of the waters which do not reach the ocean4 ,on the encroachments of the sea on the land and vice versa 7#ieb-ied74 #ieb4 ,,of ,,waves4 ,a wave of the sea always breaks in front of its base1 and that portion of the crest will then be lowest which before was highest4 ,footnote3 ,the page of ,,francesco ,,di ,,giorgio',s ,trattato1 on which ,leonardo has written this remark1 contains some notes on the construction of dams1 harbours c4 #iec4 ,that the shores of the sea constantly acquire more soil towards the middle of the sea2 that the rocks and promontories of the sea are constantly being ruined and worn away2 that the ,mediterranean seas will in time discover their bottom to the air1 and all that will be left will be the channel of the greatest river that enters it2 and this will run to the ocean and pour its waters into that with those of all the rivers that are its tributaries4 #ied4 ,how the river ,po1 in a short time might dry up the ,adriatic sea in the same way as it has dried up a large part of ,lombardy4 ,the ebb and flow of the tide 7#iee-ifj74 #iee4 ,where there is a larger quantity of water1 there is a greater flow and ebb1 but the contrary in narrow waters4 ,look whether the sea is at its greatest flow when the moon is half way over our hemisphere on the meridian4 #ief4 ,whether the flow and ebb are caused by the moon or the sun1 or are the breathing of this terrestrial machine4 ,that the flow and ebb are different in different countries and seas4 ,footnote3 #a4 ,allusion may here be made to the mythological explanation of the ebb and flow given in the ,edda4 ,utgardloki says to ,thor 7,gylfaginning #dh73 ,when thou wert drinking out of the horn1 and it seemed to thee that it was slow in emptying a wonder befell1 which ,i should not have believed possible3 the other end of the horn lay in the sea1 which thou sawest not2 but when thou shalt go to the sea1 thou shalt see how much thou hast drunk out of it4 ,and that men now call the ebb tide4 ,several passages in various manuscripts treat of the ebb and flow4 ,in collecting them ,i have been guided by the rule only to transcribe those which named some particular spot4 #ieg4 ,book #i of the meeting of rivers and their flow and ebb4 ,the cause is the same in the sea1 where it is caused by the straits of ,gibraltar4 ,and again it is caused by whirlpools4 #ieh4 ,,of ,,the ,,flow ,,and ,,ebb4 ,all seas have their flow and ebb in the same period1 but they seem to vary because the days do not begin at the same time throughout the universe2 in such wise as that when it is midday in our hemisphere1 it is midnight in the opposite hemisphere2 and at the ,eastern boundary of the two hemispheres the night begins which follows on the day1 and at the ,western boundary of these hemispheres begins the day1 which follows the night from the opposite side4 ,hence it is to be inferred that the above mentioned swelling and diminution in the height of the seas1 although they take place in one and the same space of time1 are seen to vary from the above mentioned causes4 ,the waters are then withdrawn into the fissures which start from the depths of the sea and which ramify inside the body of the earth1 corresponding to the sources of rivers1 which are constantly taking from the bottom of the sea the water which has flowed into it4 ,a sea of water is incessantly being drawn off from the surface of the sea4 ,and if you should think that the moon1 rising at the ,eastern end of the ,mediterranean sea must there begin to attract to herself the waters of the sea1 it would follow that we must at once see the effect of it at the ,eastern end of that sea4 ,again1 as the ,mediterranean sea is about the eighth part of the circumference of the aqueous sphere1 being #cjjj miles long1 while the flow and ebb only occur #d times in #bd hours1 these results would not agree with the time of #bd hours1 unless this ,mediterranean sea were six thousand miles in length2 because if such a superabundance of water had to pass through the straits of ,gibraltar in running behind the moon1 the rush of the water through that strait would be so great1 and would rise to such a height1 that beyond the straits it would for many miles rush so violently into the ocean as to cause floods and tremendous seething1 so that it would be impossible to pass through4 ,this agitated ocean would afterwards return the waters it had received with equal fury to the place they had come from1 so that no one ever could pass through those straits4 ,now experience shows that at every hour they are passed in safety1 but when the wind sets in the same direction as the current1 the strong ebb increases ,footnote #bc3 ,in attempting to get out of the ,mediterranean1 vessels are sometimes detained for a considerable time2 not merely by the causes mentioned by ,leonardo but by the constant current flowing eastwards through the middle of the straits of ,gibraltar44 ,the sea does not raise the water that has issued from the straits1 but it checks them and this retards the tide2 then it makes up with furious haste for the time it has lost until the end of the ebb movement4 #iei4 ,that the flow and ebb are not general2 for on the shore at ,genoa there is none1 at ,venice two braccia1 between ,england and ,flanders #ah braccia4 ,that in the straits of ,sicily the current is very strong because all the waters from the rivers that flow into the ,adriatic pass there4 ,footnote3 ,a few more recent data may be given here to facilitate comparison4 ,in the ,adriatic the tide rises #b and #a_/b feet1 at ,terracina #a #a_/d4 ,in the ,english channel between ,calais and ,kent it rises from #ah to #bj feet4 ,in the straits of ,messina it rises no more than #b #a_/b feet1 and that only in stormy weather1 but the current is all the stronger4 ,when ,leonardo accounts for this by the southward flow of all the ,italian rivers along the coasts1 the explanation is at least based on a correct observation2 namely that a steady current flows southwards along the coast of ,calabria and another northwards1 along the shores of ,sicily2 he seems to infer1 from the direction of the fust1 that the tide in the ,adriatic is caused by it4 #ifj4 ,in the ,west1 near to ,flanders1 the sea rises and decreases every #f hours about #bj braccia1 and #bb when the moon is in its favour2 but #bj braccia is the general rule1 and this rule1 as it is evident1 cannot have the moon for its cause4 ,this variation in the increase and decrease of the sea every #f hours may arise from the damming up of the waters1 which are poured into the ,mediterranean by the quantity of rivers from ,africa1 ,asia and ,europe1 which flow into that sea1 and the waters which are given to it by those rivers2 it pours them to the ocean through the straits of ,gibraltar1 between ,abila and ,calpe ,footnote #e3 ,abila1 ,lat4 ,abyla1 ,gr4 1 now ,sierra ,ximiera near ,ceuta2 ,calpe1 ,lat4 ,calpe4 ,gr41 now ,gibraltar4 ,leonardo here uses the ancient names of the rocks1 which were known as the ,pillars of ,hercules44 ,that ocean extends to the island of ,england and others farther ,north1 and it becomes dammed up and kept high in various gulfs4 ,these1 being seas of which the surface is remote from the centre of the earth1 have acquired a weight1 which as it is greater than the force of the incoming waters which cause it1 gives this water an impetus in the contrary direction to that in which it came and it is borne back to meet the waters coming out of the straits2 and this it does most against the straits of ,gibraltar2 these1 so long as this goes on1 remain dammed up and all the water which is poured out meanwhile by the aforementioned rivers1 is pent up in the ,mediterranean2 and this might be assigned as the cause of its flow and ebb1 as is shown in the #bast of the #dth of my theory4 ,,iii4 ,,subterranean ,,water ,,courses4 ,theory of the circulation of the waters 7#ifa4 #ifb74 #ifa4 ,very large rivers flow under ground4 #ifb4 ,this is meant to represent the earth cut through in the middle1 showing the depths of the sea and of the earth2 the waters start from the bottom of the seas1 and ramifying through the earth they rise to the summits of the mountains1 flowing back by the rivers and returning to the sea4 ,observations in support of the hypothesis 7#ifc-ifi74 #ifc4 ,the waters circulate with constant motion from the utmost depths of the sea to the highest summits of the mountains1 not obeying the nature of heavy matter2 and in this case it acts as does the blood of animals which is always moving from the sea of the heart and flows to the top of their heads2 and here it is that veins burst--as one may see when a vein bursts in the nose1 that all the blood from below rises to the level of the burst vein4 ,when the water rushes out of a burst vein in the earth it obeys the nature of other things heavier than the air1 whence it always seeks the lowest places4 #g ,these waters traverse the body of the earth with infinite ramifications4 ,footnote3 ,the greater part of this passage has been given as ,no4 #hdi in the section on ,anatomy4 #ifd4 ,the same cause which stirs the humours in every species of animal body and by which every injury is repaired1 also moves the waters from the utmost depth of the sea to the greatest heights4 #ife4 ,it is the property of water that it constitutes the vital human of this arid earth2 and the cause which moves it through its ramified veins1 against the natural course of heavy matters1 is the same property which moves the humours in every species of animal body4 ,but that which crowns our wonder in contemplating it is1 that it rises from the utmost depths of the sea to the highest tops of the mountains1 and flowing from the opened veins returns to the low seas2 then once more1 and with extreme swiftness1 it mounts again and returns by the same descent1 thus rising from the inside to the outside1 and going round from the lowest to the highest1 from whence it rushes down in a natural course4 ,thus by these two movements combined in a constant circulation1 it travels through the veins of the earth4 #iff4 ,,whether ,,water ,,rises ,,from ,,the ,,sea ,,to ,,the ,,tops ,,of ,,mountains4 ,the water of the ocean cannot make its way from the bases to the tops of the mountains which bound it1 but only so much rises as the dryness of the mountain attracts4 ,and if1 on the contrary1 the rain1 which penetrates from the summit of the mountain to the base1 which is the boundary of the sea1 descends and softens the slope opposite to the said mountain and constantly draws the water1 like a syphon ,footnote #aa3 ,cicognola1 ,syphon4 ,see ,vol4 ,i1 ,pl4 ,,xxiv1 ,no4 #a4 which pours through its longest side1 it must be this which draws up the water of the sea2 thus if s n were the surface of the sea1 and the rain descends from the top of the mountain a to n on one side1 and on the other sides it descends from a to m1 without a doubt this would occur after the manner of distilling through felt1 or as happens through the tubes called syphons ,footnote #ag3 ,cicognola1 ,syphon4 ,see ,vol4 ,i1 ,pl4 ,,xxiv1 ,no4 #a44 ,and at all times the water which has softened the mountain1 by the great rain which runs down the two opposite sides1 would constantly attract the rain a n1 on its longest side together with the water from the sea1 if that side of the mountain a m were longer than the other a n2 but this cannot be1 because no part of the earth which is not submerged by the ocean can be lower than that ocean4 #ifg4 ,,of ,,springs ,,of ,,water ,,on ,,the ,,tops ,,of ,,mountains4 ,it is quite evident that the whole surface of the ocean--when there is no storm--is at an equal distance from the centre of the earth1 and that the tops of the mountains are farther from this centre in proportion as they rise above the surface of that sea2 therefore if the body of the earth were not like that of man1 it would be impossible that the waters of the sea--being so much lower than the mountains--could by their nature rise up to the summits of these mountains4 ,hence it is to be believed that the same cause which keeps the blood at the top of the head in man keeps the water at the summits of the mountains4 ,footnote3 ,this conception of the rising of the blood1 which has given rise to the comparison1 was recognised as erroneous by ,leonardo himself at a later period4 ,it must be remembered that the ,,ms4 ,a1 from which these passages are taken1 was written about twenty years earlier than the ,,ms4 ,leic4 7,nos4 #ifc and #hdi7 and twenty-five years before the ,,ms4 ,w4 ,an4 ,,iv4 ,there is1 in the original a sketch with ,no4 #ifh which is not reproduced4 ,it represents a hill of the same shape as that shown at ,no4 #ihb4 ,there are veins1 or branched streams1 on the side of the hill1 like those on the skull ,pl4 ,,cviii1 ,no4 #d #ifh4 ,,in ,,confirmation ,,of ,,why ,,the ,,water ,,goes ,,to ,,the ,,tops ,,of ,,mountains4 ,i say that just as the natural heat of the blood in the veins keeps it in the head of man1--for when the man is dead the cold blood sinks to the lower parts--and when the sun is hot on the head of a man the blood increases and rises so much1 with other humours1 that by pressure in the veins pains in the head are often caused2 in the same way veins ramify through the body of the earth1 and by the natural heat which is distributed throughout the containing body1 the water is raised through the veins to the tops of mountains4 ,and this water1 which passes through a closed conduit inside the body of the mountain like a dead thing1 cannot come forth from its low place unless it is warmed by the vital heat of the spring time4 ,again1 the heat of the element of fire and1 by day1 the heat of the sun1 have power to draw forth the moisture of the low parts of the mountains and to draw them up1 in the same way as it draws the clouds and collects their moisture from the bed of the sea4 #ifi4 ,that many springs of salt water are found at great distances from the sea2 this might happen because such springs pass through some mine of salt1 like that in ,hungary where salt is hewn out of vast caverns1 just as stone is hewn4 ,footnote3 ,the great mine of ,wieliczka in ,galicia1 out of which a million cwt4 of rock-salt are annually dug out1 extends for #cjjj metres from ,west to ,east1 and #aaej metres from ,north to ,south4 ,,iv4 ,,of ,,rivers4 ,on the way in which the sources of rivers are fed4 #igj4 ,,of ,,the ,,origin ,,of ,,rivers4 ,the body of the earth1 like the bodies of animals1 is intersected with ramifications of waters which are all in connection and are constituted to give nutriment and life to the earth and to its creatures4 ,these come from the depth of the sea and1 after many revolutions1 have to return to it by the rivers created by the bursting of these springs2 and if you chose to say that the rains of the winter or the melting of the snows in summer were the cause of the birth of rivers1 ,i could mention the rivers which originate in the torrid countries of ,africa1 where it never rains--and still less snows--because the intense heat always melts into air all the clouds which are borne thither by the winds4 ,and if you chose to say that such rivers1 as increase in ,july and ,august1 come from the snows which melt in ,may and ,june from the sun's approach to the snows on the mountains of ,scythia ,footnote #i3 ,scythia means here1 as in ,ancient ,geography1 the whole of the ,northern part of ,asia as far as ,india41 and that such meltings come down into certain valleys and form lakes1 into which they enter by springs and subterranean caves to issue forth again at the sources of the ,nile1 this is false2 because ,scythia is lower than the sources of the ,nile1 and1 besides1 ,scythia is only #djj miles from the ,black sea and the sources of the ,nile are #cjjj miles distant from the sea of ,egypt into which its waters flow4 ,the tide in estuaries4 #iga4 ,book #i1 of the meeting of rivers and of their ebb and flow4 ,the cause is the same in the sea1 where it is caused by the straits of ,gibraltar2 and again it is caused by whirlpools4 #c ,if two rivers meet together to form a straight line1 and then below two right angles take their course together1 the flow and ebb will happen now in one river and now in the other above their confluence1 and principally if the outlet for their united volume is no swifter than when they were separate4 ,here occur #d instances4 ,footnote3 ,the first two lines of this passage have already been given as ,no4 #ieg4 ,in the margin1 near line #c of this passage1 the text given as ,no4 #iai is written4 ,on the alterations1 caused in the courses of rivers by their confluence 7#igb-igd74 #igb4 ,when a smaller river pours its waters into a larger one1 and that larger one flows from the opposite direction1 the course of the smaller river will bend up against the approach of the larger river2 and this happens because1 when the larger river fills up all its bed with water1 it makes an eddy in front of the mouth of the other river1 and so carries the water poured in by the smaller river with its own4 ,when the smaller river pours its waters into the larger one1 which runs across the current at the mouth of the smaller river1 its waters will bend with the downward movement of the larger river4 ,footnote3 ,in the original sketches the word ,arno is written at the spot here marked ,a1 at ,r4 ,rifredi1 and at ,m4 ,mugnone4 #igc4 ,when the fulness of rivers is diminished1 then the acute angles formed at the junction of their branches become shorter at the sides and wider at the point2 like the current a n and the current d n1 which unite in n when the river is at its greatest fulness4 ,i say1 that when it is in this condition if1 before the fullest time1 d n was lower than a n1 at the time of fulness d n will be full of sand and mud4 ,when the water d n falls1 it will carry away the mud and remain with a lower bottom1 and the channel a n finding itself the higher1 will fling its waters into the lower1 d n1 and will wash away all the point of the sand-spit b n c1 and thus the angle a c d will remain larger than the angle a n d and the sides shorter1 as ,i said before4 ,footnote3 ,above the first sketch we find1 in the original1 this note3 ,sopra il pote rubaconte alla torricella2 and by the second1 which represents a pier of a bridge1 ,sotto l'ospedal del ceppo4 #igd4 ,,water4 ,,of ,,the ,,movement ,,of ,a ,,sudden ,,rush ,,made ,,by ,a ,,river ,,in ,,its ,,bed ,,previously ,,dry4 ,in proportion as the current of the water given forth by the draining of the lake is slow or rapid in the dry river bed1 so will this river be wider or narrower1 or shallower or deeper in one place than another1 according to this proposition3 the flow and ebb of the sea which enters the ,mediterranean from the ocean1 and of the rivers which meet and struggle with it1 will raise their waters more or less in proportion as the sea is wider or narrower4 ,footnote3 ,in the margin is a sketch of a river which winds so as to form islands4 ,whirlpools4 #ige4 ,whirlpools1 that is to say caverns2 that is to say places left by precipitated waters4 ,on the alterations in the channels of rivers4 #igf4 ,,of ,,the ,,vibration ,,of ,,the ,,earth4 ,the subterranean channels of waters1 like those which exist between the air and the earth1 are those which unceasingly wear away and deepen the beds of their currents4 ,the origin of the sand in rivers 7#igg4 #igh74 #igg4 ,a river that flows from mountains deposits a great quantity of large stones in its bed1 which still have some of their angles and sides1 and in the course of its flow it carries down smaller stones with the angles more worn2 that is to say the large stones become smaller4 ,and farther on it deposits coarse gravel and then smaller1 and as it proceeds this becomes coarse sand and then finer1 and going on thus the water1 turbid with sand and gravel1 joins the sea2 and the sand settles on the sea-shores1 being cast up by the salt waves2 and there results the sand of so fine a nature as to seem almost like water1 and it will not stop on the shores of the sea but returns by reason of its lightness1 because it was originally formed of rotten leaves and other very light things4 ,still1 being almost--as was said--of the nature of water itself1 it afterwards1 when the weather is calm1 settles and becomes solid at the bottom of the sea1 where by its fineness it becomes compact and by its smoothness resists the waves which glide over it2 and in this shells are found2 and this is white earth1 fit for pottery4 #igh4 ,all the torrents of water flowing from the mountains to the sea carry with them the stones from the hills to the sea1 and by the influx of the sea-water towards the mountains2 these stones were thrown back towards the mountains1 and as the waters rose and retired1 the stones were tossed about by it and in rolling1 their angles hit together2 then as the parts1 which least resisted the blows1 were worn off1 the stones ceased to be angular and became round in form1 as may be seen on the banks of the ,elsa4 ,and those remained larger which were less removed from their native spot2 and they became smaller1 the farther they were carried from that place1 so that in the process they were converted into small pebbles and then into sand and at last into mud4 ,after the sea had receded from the mountains the brine left by the sea with other humours of the earth made a concretion of these pebbles and this sand1 so that the pebbles were converted into rock and the sand into tufa4 ,and of this we see an example in the ,adda where it issues from the mountains of ,como and in the ,ticino1 the ,adige and the ,oglio coming from the ,german ,alps1 and in the ,arno at ,monte ,albano ,footnote #ac3 ,at the foot of ,monte ,albano lies ,vinci1 the birth place of ,leonardo4 ,opposite1 on the other bank of the ,arno1 is ,monte ,lupo41 near ,monte ,lupo and ,capraia where the rocks1 which are very large1 are all of conglomerated pebbles of various kinds and colours4 ,v4 ,,on ,,mountains4 ,the formation of mountains 7#igi-ihc74 #igi4 ,mountains are made by the currents of rivers4 ,mountains are destroyed by the currents of rivers4 ,footnote3 ,compare #ghi4 #ihj4 ,that the ,northern bases of some ,alps are not yet petrified4 ,and this is plainly to be seen where the rivers1 which cut through them1 flow towards the ,north2 where they cut through the strata in the living stone in the higher parts of the mountains2 and1 where they join the plains1 these strata are all of potter's clay2 as is to be seen in the valley of ,lamona where the river ,lamona1 as it issues from the ,appenines1 does these things on its banks4 ,that the rivers have all cut and divided the mountains of the great ,alps one from the other4 ,this is visible in the order of the stratified rocks1 because from the summits of the banks1 down to the river the correspondence of the strata in the rocks is visible on either side of the river4 ,that the stratified stones of the mountains are all layers of clay1 deposited one above the other by the various floods of the rivers4 ,that the different size of the strata is caused by the difference in the floods--that is to say greater or lesser floods4 #iha4 ,the summits of mountains for a long time rise constantly4 ,the opposite sides of the mountains always approach each other below2 the depths of the valleys which are above the sphere of the waters are in the course of time constantly getting nearer to the centre of the world4 ,in an equal period1 the valleys sink much more than the mountains rise4 ,the bases of the mountains always come closer together4 ,in proportion as the valleys become deeper1 the more quickly are their sides worn away4 #ihb4 ,in every concavity at the summit of the mountains we shall always find the divisions of the strata in the rocks4 #ihc4 ,,of ,,the ,,sea ,,which ,,encircles ,,the ,,earth4 ,i find that of old1 the state of the earth was that its plains were all covered up and hidden by salt water4 ,footnote3 ,this passage has already been published by ,dr4 ,m4 ,,jordan3 ,das ,malerbuch des ,l4 da ,vinci1 ,leipzig #ahgc1 p4 #hf4 ,however1 his reading of the text differs from mine4 ,the authorities for the study of the structure of the earth4 #ihd4 ,since things are much more ancient than letters1 it is no marvel if1 in our day1 no records exist of these seas having covered so many countries2 and if1 moreover1 some records had existed1 war and conflagrations1 the deluge of waters1 the changes of languages and of laws have consumed every thing ancient4 ,but sufficient for us is the testimony of things created in the salt waters1 and found again in high mountains far from the seas4 ,,vi4 ,,geological ,,problems4 #ihe4 ,in this work you have first to prove that the shells at a thousand braccia of elevation were not carried there by the deluge1 because they are seen to be all at one level1 and many mountains are seen to be above that level2 and to inquire whether the deluge was caused by rain or by the swelling of the sea2 and then you must show how1 neither by rain nor by swelling of the rivers1 nor by the overflow of this sea1 could the shells--being heavy objects--be floated up the mountains by the sea1 nor have carried there by the rivers against the course of their waters4 ,doubts about the deluge4 #ihf4 ,a ,,doubtful ,,point4 ,here a doubt arises1 and that is3 whether the deluge1 which happened at the time of ,noah1 was universal or not4 ,and it would seem not1 for the reasons now to be given3 ,we have it in the ,bible that this deluge lasted #dj days and #dj nights of incessant and universal rain1 and that this rain rose to ten cubits above the highest mountains in the world4 ,and if it had been that the rain was universal1 it would have covered our globe which is spherical in form4 ,and this spherical surface is equally distant in every part1 from the centre of its sphere2 hence the sphere of the waters being under the same conditions1 it is impossible that the water upon it should move1 because water1 in itself1 does not move unless it falls2 therefore how could the waters of such a deluge depart1 if it is proved that it has no motion8 and if it departed how could it move unless it went upwards8 ,here1 then1 natural reasons are wanting2 hence to remove this doubt it is necessary to call in a miracle to aid us1 or else to say that all this water was evaporated by the heat of the sun4 ,footnote3 ,the passages1 here given from the ,,ms4 ,leic41 have hitherto remained unknown4 ,some preliminary notes on the subject are to be found in ,,ms4 ,f #hoa and #hob2 but as compared with the fuller treatment here given1 they are1 it seems to me1 of secondary interest4 ,they contain nothing that is not repeated here more clearly and fully4 ,,libri1 ,histoire des ,sciences mathematiques ,,iii1 pages #bah--bba1 has printed the text of ,f #hj;a and #hj;b1 therefore it seemed desirable to give my reasons for not inserting it in this work4 ,that marine shells could not go up the mountains4 #ihg4 ,,of ,,the ,,deluge ,,and ,,of ,,marine ,,shells4 ,if you were to say that the shells which are to be seen within the confines of ,italy now1 in our days1 far from the sea and at such heights1 had been brought there by the deluge which left them there1 ,i should answer that if you believe that this deluge rose #g cubits above the highest mountains-- as he who measured it has written--these shells1 which always live near the sea-shore1 should have been left on the mountains2 and not such a little way from the foot of the mountains2 nor all at one level1 nor in layers upon layers4 ,and if you were to say that these shells are desirous of remaining near to the margin of the sea1 and that1 as it rose in height1 the shells quitted their first home1 and followed the increase of the waters up to their highest level2 to this ,i answer1 that the cockle is an animal of not more rapid movement than the snail is out of water1 or even somewhat slower2 because it does not swim1 on the contrary it makes a furrow in the sand by means of its sides1 and in this furrow it will travel each day from #c to #d braccia2 therefore this creature1 with so slow a motion1 could not have travelled from the ,adriatic sea as far as ,monferrato in ,lombardy ,footnote3 ,monferrato di ,lombardia4 ,the range of hills of ,monferrato is in ,piedmont1 and ,casale di ,monferrato belonged1 in ,leonardo's time1 to the ,marchese di ,mantova41 which is #bej miles distance1 in #dj days2 which he has said who took account of the time4 ,and if you say that the waves carried them there1 by their gravity they could not move1 excepting at the bottom4 ,and if you will not grant me this1 confess at least that they would have to stay at the summits of the highest mountains1 in the lakes which are enclosed among the mountains1 like the lakes of ,lario1 or of ,como and il ,maggiore ,footnote3 ,lago di ,lario4 ,lacus ,larius was the name given by the ,romans to the lake of ,como4 ,it is evident that it is here a slip of the pen since the the words in the ,,ms4 are3 ,come ,lago di ,lario o'l ,magare e di ,como1 ,in the ,,ms4 after line #af we come upon a digression treating of the weight of water2 this has here been omitted4 ,it is #aa lines long4 and of ,fiesole1 and of ,perugia1 and others4 ,and if you should say that the shells were carried by the waves1 being empty and dead1 ,i say that where the dead went they were not far removed from the living2 for in these mountains living ones are found1 which are recognisable by the shells being in pairs2 and they are in a layer where there are no dead ones2 and a little higher up they are found1 where they were thrown by the waves1 all the dead ones with their shells separated1 near to where the rivers fell into the sea1 to a great depth2 like the ,arno which fell from the ,gonfolina near to ,monte ,lupo ,footnote3 ,monte ,lupo1 compare #igj1 #ac2 it is between ,empoli and ,florence41 where it left a deposit of gravel which may still be seen1 and which has agglomerated2 and of stones of various districts1 natures1 and colours and hardness1 making one single conglomerate4 ,and a little beyond the sandstone conglomerate a tufa has been formed1 where it turned towards ,castel ,florentino2 farther on1 the mud was deposited in which the shells lived1 and which rose in layers according to the levels at which the turbid ,arno flowed into that sea4 ,and from time to time the bottom of the sea was raised1 depositing these shells in layers1 as may be seen in the cutting at ,colle ,gonzoli1 laid open by the ,arno which is wearing away the base of it2 in which cutting the said layers of shells are very plainly to be seen in clay of a bluish colour1 and various marine objects are found there4 ,and if the earth of our hemisphere is indeed raised by so much higher than it used to be1 it must have become by so much lighter by the waters which it lost through the rift between ,gibraltar and ,ceuta2 and all the more the higher it rose1 because the weight of the waters which were thus lost would be added to the earth in the other hemisphere4 ,and if the shells had been carried by the muddy deluge they would have been mixed up1 and separated from each other amidst the mud1 and not in regular steps and layers-- as we see them now in our time4 ,the marine shells were not produced away from the sea4 #ihh4 ,as to those who say that shells existed for a long time and were born at a distance from the sea1 from the nature of the place and of the cycles1 which can influence a place to produce such creatures--to them it may be answered3 such an influence could not place the animals all on one line1 except those of the same sort and age2 and not the old with the young1 nor some with an operculum and others without their operculum1 nor some broken and others whole1 nor some filled with sea-sand and large and small fragments of other shells inside the whole shells which remained open2 nor the claws of crabs without the rest of their bodies2 nor the shells of other species stuck on to them like animals which have moved about on them2 since the traces of their track still remain1 on the outside1 after the manner of worms in the wood which they ate into4 ,nor would there be found among them the bones and teeth of fish which some call arrows and others serpents' tongues1 nor would so many ,footnote3 ,i4 ,scilla argued against this hypothesis1 which was still accepted in his days2 see3 ,la vana ,speculazione1 ,napoli #afgj4 portions of various animals be found all together if they had not been thrown on the sea shore4 ,and the deluge cannot have carried them there1 because things that are heavier than water do not float on the water4 ,but these things could not be at so great a height if they had not been carried there by the water1 such a thing being impossible from their weight4 ,in places where the valleys have not been filled with salt sea water shells are never to be seen2 as is plainly visible in the great valley of the ,arno above ,gonfolina2 a rock formerly united to ,monte ,albano1 in the form of a very high bank which kept the river pent up1 in such a way that before it could flow into the sea1 which was afterwards at its foot1 it formed two great lakes2 of which the first was where we now see the city of ,florence together with ,prato and ,pistoia1 and ,monte ,albano4 ,it followed the rest of its bank as far as where ,serravalle now stands4 ,from the ,val d',arno upwards1 as far as ,arezzo1 another lake was formed1 which discharged its waters into the former lake4 ,it was closed at about the spot where now we see ,girone1 and occupied the whole of that valley above for a distance of #dj miles in length4 ,this valley received on its bottom all the soil brought down by the turbid waters4 ,and this is still to be seen at the foot of ,prato ,magno2 it there lies very high where the rivers have not worn it away4 ,across this land are to be seen the deep cuts of the rivers that have passed there1 falling from the great mountain of ,prato ,magno2 in these cuts there are no vestiges of any shells or of marine soil4 ,this lake was joined with that of ,perugia ,footnote3 ,see ,,pi4 ,,cxiii4 ,a great quantity of shells are to be seen where the rivers flow into the sea1 because on such shores the waters are not so salt owing to the admixture of the fresh water1 which is poured into it4 ,evidence of this is to be seen where1 of old1 the ,appenines poured their rivers into the ,adriatic sea2 for there in most places great quantities of shells are to be found1 among the mountains1 together with bluish marine clay2 and all the rocks which are torn off in such places are full of shells4 ,the same may be observed to have been done by the ,arno when it fell from the rock of ,gonfolina into the sea1 which was not so very far below2 for at that time it was higher than the top of ,san ,miniato al ,tedesco1 since at the highest summit of this the shores may be seen full of shells and oysters within its flanks4 ,the shells did not extend towards ,val di ,nievole1 because the fresh waters of the ,arno did not extend so far4 ,that the shells were not carried away from the sea by the deluge1 because the waters which came from the earth although they drew the sea towards the earth1 were those which struck its depths2 because the water which goes down from the earth1 has a stronger current than that of the sea1 and in consequence is more powerful1 and it enters beneath the sea water and stirs the depths and carries with it all sorts of movable objects which are to be found in the earth1 such as the above-mentioned shells and other similar things4 ,and in proportion as the water which comes from the land is muddier than sea water it is stronger and heavier than this2 therefore ,i see no way of getting the said shells so far in land1 unless they had been born there4 ,if you were to tell me that the river ,loire ,footnote3 ,leonardo has written ,era instead of ,loera or ,loira--perhaps under the mistaken idea that ,lo was an article41which traverses ,france covers when the sea rises more than eighty miles of country1 because it is a district of vast plains1 and the sea rises about #bj braccia1 and shells are found in this plain at the distance of #hj miles from the sea2 here ,i answer that the flow and ebb in our ,mediterranean ,sea does not vary so much2 for at ,genoa it does not rise at all1 and at ,venice but little1 and very little in ,africa2 and where it varies little it covers but little of the country4 ,the course of the water of a river always rises higher in a place where the current is impeded2 it behaves as it does where it is reduced in width to pass under the arches of a bridge4 ,further researches 7#ihi-iia74 #ihi4 ,a ,,confutation ,,of ,,those ,,who ,,say ,,that ,,shells ,,may ,,have ,,been ,,carried ,,to ,a ,,distance ,,of ,,many ,,days' ,,journey ,,from ,,the ,,sea ,,by ,,the ,,deluge1 ,,which ,,was ,,so ,,high ,,as ,,to ,,be ,,above ,,those ,,heights4 ,i say that the deluge could not carry objects1 native to the sea1 up to the mountains1 unless the sea had already increased so as to create inundations as high up as those places2 and this increase could not have occurred because it would cause a vacuum2 and if you were to say that the air would rush in there1 we have already concluded that what is heavy cannot remain above what is light1 whence of necessity we must conclude that this deluge was caused by rain water1 so that all these waters ran to the sea1 and the sea did not run up the mountains2 and as they ran to the sea1 they thrust the shells from the shore of the sea and did not draw them to wards themselves4 ,and if you were then to say that the sea1 raised by the rain water1 had carried these shells to such a height1 we have already said that things heavier than water cannot rise upon it1 but remain at the bottom of it1 and do not move unless by the impact of the waves4 ,and if you were to say that the waves had carried them to such high spots1 we have proved that the waves in a great depth move in a contrary direction at the bottom to the motion at the top1 and this is shown by the turbidity of the sea from the earth washed down near its shores4 ,anything which is lighter than the water moves with the waves1 and is left on the highest level of the highest margin of the waves4 ,anything which is heavier than the water moves1 suspended in it1 between the surface and the bottom2 and from these two conclusions1 which will be amply proved in their place1 we infer that the waves of the surface cannot convey shells1 since they are heavier than water4 ,if the deluge had to carry shells three hundred and four hundred miles from the sea1 it would have carried them mixed with various other natural objects heaped together2 and we see at such distances oysters all together1 and sea-snails1 and cuttlefish1 and all the other shells which congregate together1 all to be found together and dead2 and the solitary shells are found wide apart from each other1 as we may see them on sea-shores every day4 ,and if we find oysters of very large shells joined together and among them very many which still have the covering attached1 indicating that they were left here by the sea1 and still living when the strait of ,gibraltar was cut through2 there are to be seen1 in the mountains of ,parma and ,piacenza1 a multitude of shells and corals1 full of holes1 and still sticking to the rocks there4 ,when ,i was making the great horse for ,milan1 a large sack full was brought to me in my workshop by certain peasants2 these were found in that place and among them were many preserved in their first freshness4 ,under ground1 and under the foundations of buildings1 timbers are found of wrought beams and already black4 ,such were found in my time in those diggings at ,castel ,fiorentino4 ,and these had been in that deep place before the sand carried by the ,arno into the sea1 then covering the plain1 had heen raised to such a height2 and before the plains of ,casentino had been so much lowered1 by the earth being constantly carried down from them4 ,footnote3 ,these lines are written in the margin4 ,and if you were to say that these shells were created1 and were continually being created in such places by the nature of the spot1 and of the heavens which might have some influence there1 such an opinion cannot exist in a brain of much reason2 because here are the years of their growth1 numbered on their shells1 and there are large and small ones to be seen which could not have grown without food1 and could not have fed without motion--and here they could not move ,footnote3 ,these lines are written in the margin4 #iij4 ,that in the drifts1 among one and another1 there are still to be found the traces of the worms which crawled upon them when they were not yet dry4 ,and all marine clays still contain shells1 and the shells are petrified together with the clay4 ,from their firmness and unity some persons will have it that these animals were carried up to places remote from the sea by the deluge4 ,another sect of ignorant persons declare that ,nature or ,heaven created them in these places by celestial influences1 as if in these places we did not also find the bones of fishes which have taken a long time to grow2 and as if1 we could not count1 in the shells of cockles and snails1 the years and months of their life1 as we do in the horns of bulls and oxen1 and in the branches of plants that have never been cut in any part4 ,besides1 having proved by these signs the length of their lives1 it is evident1 and it must be admitted1 that these animals could not live without moving to fetch their food2 and we find in them no instrument for penetrating the earth or the rock where we find them enclosed4 ,but how could we find in a large snail shell the fragments and portions of many other sorts of shells1 of various sorts1 if they had not been thrown there1 when dead1 by the waves of the sea like the other light objects which it throws on the earth8 ,why do we find so many fragments and whole shells between layer and layer of stone1 if this had not formerly been covered on the shore by a layer of earth thrown up by the sea1 and which was afterwards petrified8 ,and if the deluge before mentioned had carried them to these parts of the sea1 you might find these shells at the boundary of one drift but not at the boundary between many drifts4 ,we must also account for the winters of the years during which the sea multiplied the drifts of sand and mud brought down by the neighbouring rivers1 by washing down the shores2 and if you chose to say that there were several deluges to produce these rifts and the shells among them1 you would also have to affirm that such a deluge took place every year4 ,again1 among the fragments of these shells1 it must be presumed that in those places there were sea coasts1 where all the shells were thrown up1 broken1 and divided1 and never in pairs1 since they are found alive in the sea1 with two valves1 each serving as a lid to the other2 and in the drifts of rivers and on the shores of the sea they are found in fragments4 ,and within the limits of the separate strata of rocks they are found1 few in number and in pairs like those which were left by the sea1 buried alive in the mud1 which subsequently dried up and1 in time1 was petrified4 #iia4 ,and if you choose to say that it was the deluge which carried these shells away from the sea for hundreds of miles1 this cannot have happened1 since that deluge was caused by rain2 because rain naturally forces the rivers to rush towards the sea with all the things they carry with them1 and not to bear the dead things of the sea shores to the mountains4 ,and if you choose to say that the deluge afterwards rose with its waters above the mountains1 the movement of the sea must have been so sluggish in its rise against the currents of the rivers1 that it could not have carried1 floating upon it1 things heavier than itself2 and even if it had supported them1 in its receding it would have left them strewn about1 in various spots4 ,but how are we to account for the corals which are found every day towards ,monte ,ferrato in ,lombardy1 with the holes of the worms in them1 sticking to rocks left uncovered by the currents of rivers8 ,these rocks are all covered with stocks and families of oysters1 which as we know1 never move1 but always remain with one of their halves stuck to a rock1 and the other they open to feed themselves on the animalcules that swim in the water1 which1 hoping to find good feeding ground1 become the food of these shells4 ,we do not find that the sand mixed with seaweed has been petrified1 because the weed which was mingled with it has shrunk away1 and this the ,po shows us every day in the debris of its banks4 ,other problems 7#iib-iid74 #iib4 ,why do we find the bones of great fishes and oysters and corals and various other shells and sea-snails on the high summits of mountains by the sea1 just as we find them in low seas8 #iic4 ,you now have to prove that the shells cannot have originated if not in salt water1 almost all being of that sort2 and that the shells in ,lombardy are at four levels1 and thus it is everywhere1 having been made at various times4 ,and they all occur in valleys that open towards the seas4 #iid4 ,from the two lines of shells we are forced to say that the earth indignantly submerged under the sea and so the first layer was made2 and then the deluge made the second4 ,footnote3 ,this note is in the early writing of about #adgj--adhj4 ,on the same sheet are the passages ,no4 #abag and #abai4 ,compare also ,no4 #acci4 ,all the foregoing chapters are from ,manuscripts of about #aeaj4 ,this explains the want of connection and the contradiction between this and the foregoing texts4 ,,vii4 ,,on ,,the ,,atmosphere4 ,constituents of the atmosphere4 #iie4 ,that the brightness of the air is occasioned by the water which has dissolved itself in it into imperceptible molecules4 ,these1 being lighted by the sun from the opposite side1 reflect the brightness which is visible in the air2 and the azure which is seen in it is caused by the darkness that is hidden beyond the air4 ,footnote3 ,compare ,vol4 ,i1 ,no4 #cjj4 ,on the motion of air 7#iif--iii74 #iif4 ,that the return eddies of wind at the mouth of certain valleys strike upon the waters and scoop them out in a great hollow1 whirl the water into the air in the form of a column1 and of the colour of a cloud4 ,and ,i saw this thing happen on a sand bank in the ,arno1 where the sand was hollowed out to a greater depth than the stature of a man2 and with it the gravel was whirled round and flung about for a great space2 it appeared in the air in the form of a great bell-tower2 and the top spread like the branches of a pine tree1 and then it bent at the contact of the direct wind1 which passed over from the mountains4 #iig4 ,the element of fire acts upon a wave of air in the same way as the air does on water1 or as water does on a mass of sand --that is earth2 and their motions are in the same proportions as those of the motors acting upon them4 #iih4 ,,of ,,motion4 ,i ask whether the true motion of the clouds can be known by the motion of their shadows2 and in like manner of the motion of the sun4 #iii4 ,to know better the direction of the winds4 ,footnote3 ,in connection with this text ,i may here mention a hygrometer1 drawn and probably invented by ,leonardo4 ,a facsimile of this is given in ,vol4 ,i1 p4 #big with the note3 ',modi di pesare l'arie eddi sapere quando s'a arrompere il tepo' 7,mode of weighing the air and of knowing when the weather will change72 by the sponge ,spugnea is written4 ,the globe an organism4 #ajjj4 ,nothing originates in a spot where there is no sentient1 vegetable and rational life2 feathers grow upon birds and are changed every year2 hairs grow upon animals and are changed every year1 excepting some parts1 like the hairs of the beard in lions1 cats and their like4 ,the grass grows in the fields1 and the leaves on the trees1 and every year they are1 in great part1 renewed4 ,so that we might say that the earth has a spirit of growth2 that its flesh is the soil1 its bones the arrangement and connection of the rocks of which the mountains are composed1 its cartilage the tufa1 and its blood the springs of water4 ,the pool of blood which lies round the heart is the ocean1 and its breathing1 and the increase and decrease of the blood in the pulses1 is represented in the earth by the flow and ebb of the sea2 and the heat of the spirit of the world is the fire which pervades the earth1 and the seat of the vegetative soul is in the fires1 which in many parts of the earth find vent in baths and mines of sulphur1 and in volcanoes1 as at ,mount ,aetna in ,sicily1 and in many other places4 ,footnote3 ,compare ,no4 #ibi4 ,,xvii4 ,topographical ,notes4 ,a large part of the texts published in this section might perhaps have found their proper place in connection with the foregoing chapters on ,physical ,geography4 ,but these observations on ,physical ,geography1 of whatever kind they may be1 as soon as they are localised acquire a special interest and importance and particularly as bearing on the question whether ,leonardo himself made the observations recorded at the places mentioned or merely noted the statements from hearsay4 ,in a few instances he himself tells us that he writes at second hand4 ,in some cases again1 although the style and expressions used make it seem highly probable that he has derived his information from others-- though1 as it seems to me1 these cases are not very numerous--we find1 on the other hand1 among these topographical notes a great number of observations1 about which it is extremely difficult to form a decided opinion4 ,of what the ,master's life and travels may have been throughout his sixty-seven years of life we know comparatively little2 for a long course of time1 and particularly from about #adhb to #adhf1 we do not even know with certainty that he was living in ,italy4 ,thus1 from a biographical point of view a very great interest attaches to some of the topographical notes1 and for this reason it seemed that it would add to their value to arrange them in a group by themselves4 ,leonardo's intimate knowledge with places1 some of which were certainly remote from his native home1 are of importance as contributing to decide the still open question as to the extent of ,leonardo's travels4 ,we shall find in these notes a confirmation of the view1 that the ,,mss4 in which the ,topographical ,notes occur are in only a very few instances such diaries as may have been in use during a journey4 ,these notes are mostly found in the ,,mss4 books of his later and quieter years1 and it is certainly remarkable that ,leonardo is very reticent as to the authorities from whom he quotes his facts and observations3 ,for instance1 as to the ,straits of ,gibraltar1 the ,nile1 the ,taurus ,mountains and the ,tigris and ,euphrates4 ,is it likely that he1 who declared that in all scientific research1 his own experience should be the foundation of his statements 7see ,,xix ,philosophy ,no4 #ihg--iia17 should here have made an exception to this rule without mentioning it8 ,as for instance in the discussion as to the equilibrium of the mass of water in the ,mediterranean ,sea--a subject which1 it may be observed1 had at that time attracted the interest and study of hardly any other observer4 ,the acute remarks1 in ,nos4 #ihe--iic1 on the presence of shells at the tops of mountains1 suffice to prove--as it seems to me--that it was not in his nature to allow himself to be betrayed into wide generalisations1 extending beyond the limits of his own investigations1 even by such brilliant results of personal study4 ,most of these ,topographical ,notes1 though suggesting very careful and thorough research1 do not however1 as has been said1 afford necessarily indisputable evidence that that research was ,leonardo's own4 ,but it must be granted that in more than one instance probability is in favour of this idea4 ,among the passages which treat somewhat fully of the topography of ,eastern places by far the most interesting is a description of the ,taurus ,mountains2 but as this text is written in the style of a formal report and1 in the original1 is associated with certain letters which give us the history of its origin1 ,i have thought it best not to sever it from that connection4 ,it will be found under ,no4 ,,xxi 7,letters74 ,that ,florence1 and its neighbourhood1 where ,leonardo spent his early years1 should be nowhere mentioned except in connection with the projects for canals1 which occupied his attention for some short time during the first ten years of the ,x,v,ith century1 need not surprise us4 ,the various passages relating to the construction of canals in ,tuscany1 which are put together at the beginning1 are immediately followed by those which deal with schemes for canals in ,lombardy2 and after these come notes on the city and vicinity of ,milan as well as on the lakes of ,north ,italy4 ,the notes on some towns of ,central ,italy which ,leonardo visited in #aejb1 when in the service of ,cesare ,borgia1 are reproduced here in the same order as in the note book used during these travels 7,,ms4 ,l41 ,institut de ,france74 ,these notes have but little interest in themselves excepting as suggesting his itinerary4 ,the maps of the districts drawn by ,leonardo at the time are more valuable 7see ,no4 #ajed note74 ,the names on these maps are not written from right to left1 but in the usual manner1 and we are permitted to infer that they were made in obedience to some command1 possibly for the use of ,cesare ,borgia himself2 the fact that they remained nevertheless in ,leonardo's hands is not surprising when we remember the sudden political changes and warlike events of the period4 ,there can be no doubt that these maps1 which are here published for the first time1 are original in the strictest sense of the word1 that is to say drawn from observations of the places themselves2 this is proved by the fact--among others--that we find among his manuscripts not only the finished maps themselves but the rough sketches and studies for them4 ,and it would perhaps be difficult to point out among the abundant contributions to geographical knowledge published during the ,x,v,ith century1 any maps at all approaching these in accuracy and finish4 ,the interesting map of the world1 so far as it was then known1 which is among the ,leonardo ,,mss4 at ,windsor 7published in the ',archaeologia' ,vol4 ,,xi7 cannot be attributed to the ,master1 as the ,marchese ,girolamo d',adda has sufficiently proved2 it has not therefore been reproduced here4 ,such of ,leonardo's observations on places in ,italy as were made before or after his official travels as military engineer to ,cesare ,borgia1 have been arranged in alphabetical order1 under ,nos4 #ajcd-ajed4 ,the most interesting are those which relate to the ,alps and the ,appenines1 ,nos4 #ajeg-ajfh4 ,most of the passages in which ,france is mentioned have hitherto remained unknown1 as well as those which treat of the countries bordering on the ,mediterranean1 which come at the end of this section4 ,though these may be regarded as of a more questionable importance in their bearing on the biography of the ,master than those which mention places in ,france1 it must be allowed that they are interesting as showing the prominent place which the countries of the ,east held in his geographical studies4 ,he never once alludes to the discovery of ,america4 ,i4 ,,italy4 ,canals in connection with the ,arno 7#ajja-ajjh74 #ajja4 ,,canal ,,of ,,florence4 ,sluices should be made in the valley of la ,chiana at ,arezzo1 so that when1 in the summer1 the ,arno lacks water1 the canal may not remain dry3 and let this canal be #bj braccia wide at the bottom1 and at the top #cj1 and #b braccia deep1 or #d1 so that two of these braccia may flow to the mills and the meadows1 which will benefit the country2 and ,prato1 ,pistoia and ,pisa1 as well as ,florence1 will gain two hundred thousand ducats a year1 and will lend a hand and money to this useful work2 and the ,lucchese the same1 for the lake of ,sesto will be navigable2 ,i shall direct it to ,prato and ,pistoia1 and cut through ,serravalle and make an issue into the lake2 for there will be no need of locks or supports1 which are not lasting and so will always be giving trouble in working at them and keeping them up4 ,and know that in digging this canal where it is #d braccia deep1 it will cost #d dinari the square braccio2 for twice the depth #f dinari1 if you are making #d braccia ,footnote3 ,this passage is illustrated by a slightly sketched map1 on which these places are indicated from ,west to ,east3 ,pisa1 ,luccha1 ,lago1 ,seravalle1 ,pistoja1 ,prato1 ,firenze4 and there are but #b banks2 that is to say one from the bottom of the trench to the surface of the edges of it1 and the other from these edges to the top of the ridge of earth which will be raised on the margin of the bank4 ,and if this bank were of double the depth only the first bank will be increased1 that is #d braccia increased by half the first cost2 that is to say that if at first #d dinari were paid for #b banks1 for #c it would come to #f1 at #b dinari the bank1 if the trench measured #af braccia at the bottom2 again1 if the trench were #af braccia wide and #d deep1 coming to #d lire for the work1 #d ,milan dinari the square braccio2 a trench which was #cb braccia at the bottom would come to #h dinari the square braccio4 #ajjb4 ,from the wall of the ,arno at the gate of la ,giustizia to the bank of the ,arno at ,sardigna where the walls are1 to the mills1 is #gdjj braccia1 that is #b miles and #adjj braccia and beyond the ,arno is #eejj braccia4 ,footnote3 #b4 ,giustizia4 ,by this the ,porta della ,giustizia seems to be meant2 from the ,x,vth to the ,x,v,ith centuries it was also commonly known as ,porta ,guelfa1 ,porta ,san ,francesco del ,renaio1 ,porta ,nuova1 and ,porta ,reale4 ,it was close to the ,arno opposite to the ,porta ,san ,niccolo1 which still exists4 #ajjc4 ,by guiding the ,arno above and below a treasure will be found in each acre of ground by whomsoever will4 #ajjd4 ,the wall of the old houses runs towards the gate of ,san ,nicolo4 ,footnote3 ,by the side of this text there is an indistinct sketch1 resembling that given under ,no4#igc4 ,on the bank is written the word ,casace4 ,there then follows in the original a passage of #ab lines in which the consequences of the windings of the river are discussed4 ,a larger but equally hasty diagram on the same page represents the shores of the ,arno inside ,florence as in two parallel lines4 ,four horizontal lines indicate the bridges4 ,by the side these measures are stated in figures3 ,i4 7at the ,ponte alla ,carraja73 #bcj--largho br4 #ab e #b di spoda e #ad di pile e a #d pilastri2 #b4 7at the ,ponte ,s4 ,trinita72 l#hh--largho br4 #ae e #b di spode he #bh di pilastri for delle spode e pilastri so #b2 #c4 7at the ,ponte vecchio72 pote lung br4 #aeb e largo2 #d4 7at the ,ponte alle ,grazie73 #bij ellargo #ab e #b di spode e #f di pili4 ,there is1 in ,,ms4 ,w4 ,l4 #bl#b;b1 a sketched plan of ,florence1 with the following names of gates3 ,nicholo--,saminiato--,giorgo--,ghanolin i--,porta ,san ,fredian --,prato--,faenza--,ghallo--,pinti--,giu stitia4 #ajje4 ,the ruined wall is #fdj braccia2 #acj is the wall remaining with the mill2 #cjj braccia were broken in #d years by ,bisarno4 #ajjf4 ,they do not know why the ,arno will never remain in a channel4 ,it is because the rivers which flow into it deposit earth where they enter1 and wear it away on the opposite side1 bending the river in that direction4 ,the ,arno flows for #f miles between la ,caprona and ,leghorn2 and for #ab through the marshes1 which extend #cb miles1 and #af from ,la ,caprona up the river1 which makes #dh2 by the ,arno from ,florence beyond #af miles2 to ,vico #af miles1 and the canal is #e2 from ,florence to ,fucechio it is #dj miles by the river ,arno4 #ef miles by the ,arno from ,florence to ,vico2 by the ,pistoia canal it is #dd miles4 ,thus it is #ab miles shorter by the canal than by the ,arno4 ,footnote3 ,this passage is written by the side of a map washed in ,indian ink1 of the course of the ,arno2 it is evidently a sketch for a completer map4 ,these investigations may possibly be connected with the following documents4 ,francesco ,guiducci alla ,balia di ,firenze4 ,dal ,campo contro ,pisa #bd ,luglio #aejc 7,archivio di ,stato1 ,firenze1 ,lettere alla ,balia2 published by ,j4 ,,gaye1 ,carteggio inedito d',artisti1 ,firenze #ahdj1 ,tom4 ,,ii1 p4 #fb73 ,ex ,castris1 ,franciscus ,ghuiduccius1 #bd4 ,jul4 #aejc4 ,appresso fu qui hieri con una di ,v4 ,signoria ,alexandro degli ,albizi insieme con ,leonardo da ,vinci et certi altri1 et veduto el disegno insieme con el ghovernatore1 doppo molte discussioni et dubii conclusesi che l'opera fussi molto al proposito1 o si veramente ,arno volgersi qui1 o restarvi con un canale1 che almeno vieterebbe che le colline da nemici non potrebbono essere offese2 come tucto referiranno loro a bocha ,v4 ,s4 ,and1 ,archivio di ,stato1 ,firenze1 ,libro d',entrata e ,uscita di cassa de' ,magnifici ,signori di luglio e agosto #aejc a #ea ,t43 ,andata di ,leonardo al ,campo sotto ,pisa4 ,spese extraordinarie dieno dare a di ,,xxvi di luglio ,l4 ,,lvi sol4 ,,xii per loro a ,giovanni ,piffero2 e sono per tanti1 asegnia avere spexi in vetture di sei chavalli a spese di vitto per andare chon ,lionardo da ,vinci a livellare ,arno in quello di ,pisa per levallo del lilo suo4 7,published by ,,milanesi1 ,archivio ,storico ,italiano1 ,serie ,,iii1 ,tom4 ,,xvi4 ,,vasari asserts3 7,leonardo7 fu il primo ancora1 che giovanetto discorresse sopra il fiume d',arno per metterlo in canale da ,pisa a ,fiorenza 7ed4 ,,sansoni1 ,,iv1 #bj74 ,the passage above is in some degree illustrated by the map on ,pl4 ,,cxii1 where the course of the ,arno westward from ,empoli is shown4 #ajjg4 ,the eddy made by the ,mensola1 when the ,arno is low and the ,mensola full4 ,footnote3 ,mensola is a mountain stream which falls into the ,arno about a mile and a half above ,florence4 ,a,arno1 ,i,isola1 ,m,mvgone1 ,p,pesa1 ,n,mesola4 #ajjh4 ,that the river which is to be turned from one place to another must be coaxed and not treated roughly or with violence2 and to do this a sort of floodgate should be made in the river1 and then lower down one in front of it and in like manner a third1 fourth and fifth1 so that the river may discharge itself into the channel given to it1 or that by this means it may be diverted from the place it has damaged1 as was done in ,flanders--as ,i was told by ,niccolo di ,forsore4 ,how to protect and repair the banks washed by the water1 as below the island of ,cocomeri4 ,ponte ,rubaconte 7,fig4 #a72 below the palaces ,bisticci and ,canigiani 7,fig4 #b74 ,above the flood gate of la ,giustizia 7,fig4 #c72 a b is a sand bank opposite the end of the island of the ,cocomeri in the middle of the ,arno 7,fig4 #d74 ,footnote3 ,the course of the river ,arno is also discussed in ,nos4 #ihg and #ihh4 ,canals in the ,milanese 7#ajji-ajac74 #ajji4 ,the canal of ,san ,cristofano at ,milan made ,may #crd #aeji4 ,footnote3 ,this observation is written above a washed pen and ink drawing which has been published as ,tav4 ,,vi in the 11,saggio4 ,the editors of that work explain the drawing as uno ,studio di bocche per estrazione d'acqua4 #ajaj4 ,,of ,,the ,,canal ,,of ,,martesana4 ,by making the canal of ,martesana the water of the ,adda is greatly diminished by its distribution over many districts for the irrigation of the fields4 ,a remedy for this would be to make several little channels1 since the water drunk up by the earth is of no more use to any one1 nor mischief neither1 because it is taken from no one2 and by making these channels the water which before was lost returns again and is once more serviceable and useful to men4 ,footnote3 el navilio di ,martagano is also mentioned in a note written in red chalk1 ,,ms4 ,h#b #ag;a ,leonardo has1 as it seems1 little to do with ,lodovico il ,moro's scheme to render this canal navigable4 ,the canal had been made in #adfj by ,bertonino da ,novara4 ,il ,moro issued his degree in #adic1 but ,leonardo's notes about this canal were1 with the exception of one 7,no4 #acdc71 written about sixteen years later4 #ajaa4 ,no canal which is fed by a river can be permanent if the river whence it originates is not wholly closed up1 like the canal of ,martesana which is fed by the ,ticino4 #ajab4 ,from the beginning of the canal to the mill4 ,from the beginning of the canal of ,brivio to the mill of ,travaglia is #bgid trabochi1 that is #aaagf braccia1 which is more than #c miles and two thirds2 and here the canal is #eg braccia higher than the surface of the water of the ,adda1 giving a fall of two inches in every hundred trabochi2 and at that spot we propose to take the opening of our canal4 ,footnote3 ,the following are written on the sketches3 ,at the place marked ,n3 navilio da dacquiue 7canal of running water72 at ,m3 molin del ,travaglia 7,mill of ,travaglia72 at ,r3 rochetta ssanta maria 7small rock of ,santa ,maria72 at ,a3 ,adda2 at ,l3 ,lagho di ,lecho ringorgato alli #c corni in ,adda1--,concha perpetua 7lake of ,lecco overflowing at ,tre ,corni1 in ,adda1-- a permanent sluice74 ,near the second sketch1 referring to the sluice near ,q3 qui la chatena ttalie d'u peso 7here the chain is in one piece74 ,at ,m in the lower sketch3 mol del travaglia1 nel cavare la concha il tereno ara chotrapero co cassa d'acqua4 7,mill of ,travaglia1 in digging out the sluice the soil will have as a counterpoise a vessel of water74 #ajac4 ,if it be not reported there that this is to be a public canal1 it will be necessary to pay for the land2 ,footnote #c3 il re4 ,louis ,,xii or ,francis ,i of ,france4 ,it is hardly possible to doubt that the canals here spoken of were intended to be in the ,milanese4 ,compare with this passage the rough copy of a letter by ,leonardo1 to the ,presidente dell' ,ufficio regolatore dell' acqua on ,no4 #acej4 ,see also the note to ,no4 #gde1 #a4 #ab4 and the king will pay it by remitting the taxes for a year4 ,estimates and preparatory studies for canals 7#ajad4 #ajae74 #ajad4 ,,canal4 ,the canal which may be #af braccia wide at the bottom and #bj at the top1 we may say is on the average #ah braccia wide1 and if it is #d braccia deep1 at #d dinari the square braccia2 it will only cost #ijj ducats1 to excavate by the mile1 if the square braccio is calculated in ordinary braccia2 but if the braccia are those used in measuring land1 of which every #d are equal to #d #a_/b and if by the mile we understand three thousand ordinary braccia2 turned into land braccia1 these #cjjj braccia will lack #a_/d2 there remain #bbej braccia1 which at #d dinari the braccio will amount to #fge ducats a mile4 ,at #c dinari the square braccio1 the mile will amount to #ejf #a_/d ducats so that the excavation of #cj miles of the canal will amount to #aeahg #a_/b ducats4 #ajae4 ,to make the great canal1 first make the smaller one and conduct into it the waters which by a wheel will help to fill the great one4 ,notes on buildings in ,milan 7#ajaf-ajai7 #ajaf4 ,indicate the centre of ,milan4 ,moforte--porta resa--porta nova--strada nova--navilio--porta cumana--barco--porta giovia--porta vercellina--porta sco ,anbrogio--porta ,tesinese--torre dell' ,imperatore-- porta ,lodovica--acqua4 ,footnote3 ,see ,pl4 ,,cix4 ,the original sketch is here reduced to about half its size4 ,the gates of the town are here named1 beginning at the right hand and following the curved line4 ,in the bird's eye view of ,milan below1 the cathedral is plainly recognisable in the middle2 to the right is the tower of ,san ,gottardo4 ,the square1 above the number #iadg1 is the ,lazzaretto1 which was begun in #adhh4 ,on the left the group of buildings of the ',castello' will be noticed4 ,on the sketched ,plan of ,florence 7see ,no4 #ajjd note7 ,leonardo has written on the margin the following names of gates of ,milan3 ,vercellina --,ticinese--,ludovica--,romana--,orient ale-- ,nova--,beatrice--,cumana--,compare too ,no4 #addh1 #aa4 #e1 #ab4 #ajag4 ,the moat of ,milan4 ,canal #b braccia wide4 ,the castle with the moats full4 ,the filling of the moats of the ,castle of ,milan4 #ajah4 ,,the ,,bath4 ,to heat the water for the stove of the ,duchess take four parts of cold water to three parts of hot water4 ,footnote3 ,duchessa di ,milano1 ,beatrice d',este1 wife of ,ludovico il ,moro to whom she was married1 in #adia4 ,she died in ,june #adig4 #ajai4 ,in the ,cathedral at the pulley of the nail of the cross4 ,item4 ,to place the mass v r in the444 ,footnote3 ,on this passage ,,amoretti remarks 7,memorie ,storiche chap4 ,,ix73 ,nell'anno stesso lo veggiamo formare un congegno di carucole e di corde1 con cui trasportare in piu venerabile e piu sicuro luogo1 cioe nell'ultima arcata della nave di mezzo della metropolitana1 la sacra reliquia del ,santo ,chiodo1 che ivi ancor si venera4 ,al fol4 #ae del codice segnato ,q4 ,r4 in #af1 egli ci ha lasciata di tal congegno una doppia figura1 cioe una di quattro carucole1 e una di tre colle rispettive corde1 soggiugnandovi3 in ,domo alla carucola del ,chiodo della ,croce4 ,,amoretti',s views as to the mark on the ,,ms1 and the date when it was written are1 it may be observed1 wholly unfounded4 ,the ,,ms4 ,l1 in which it occurs1 is of the year #aejb1 and it is very unlikely that ,leonardo was in ,milan at that time2 this however would not prevent the remark1 which is somewhat obscure1 from applying to the ,cathedral at ,milan4 #ajbj4 ,,of ,,the ,,force ,,of ,,the ,,vacuum ,,formed ,,in ,a ,,moment4 ,i saw1 at ,milan1 a thunderbolt fall on the tower della ,credenza on its ,northern side1 and it descended with a slow motion down that side1 and then at once parted from that tower and carried with it and tore away from that wall a space of #c braccia wide and two deep2 and this wall was #d braccia thick and was built of thin and small old bricks2 and this was dragged out by the vacuum which the flame of the thunderbolt had caused1 c4 ,footnote3 ,with reference to buildings at ,milan see also ,nos4 #gea and #gef1 and ,pl4 ,,xcv1 ,no4 #b 7explained on p4 #eb71 ,pl4 ,c 7explained on pages #fj-fb74 ,see also pages #be1 #ci and #dj4 ,remarks on natural phenomena in and near ,milan 7#ajba4 #ajbb74 #ajba4 ,i have already been to see a great variety 7of atmospheric effects74 ,and lately over ,milan towards ,lago ,maggiore ,i saw a cloud in the form of an immense mountain full of rifts of glowing light1 because the rays of the sun1 which was already close to the horizon and red1 tinged the cloud with its own hue4 ,and this cloud attracted to it all the little clouds that were near while the large one did not move from its place2 thus it retained on its summit the reflection of the sunlight till an hour and a half after sunset1 so immensely large was it2 and about two hours after sunset such a violent wind arose1 that it was really tremendous and unheard of4 ,footnote3 di arie is wanting in the original but may safely be inserted in the context1 as the formation of clouds is under discussion before this text4 #ajbb4 ,on the #ajth day of ,december at #i o'clock a4 m4 fire was set to the place4 ,on the l#hth day of ,december #aeaa at #i o'clock a4 m4 this second fire was kindled by the ,swiss at ,milan at the place called ,,dcxc4 ,footnote3 ,with these two texts1 7l4 #a--b and l4 #c--e are in the original side by side7 there are sketches of smoke wreaths in red chalk4 ,note on ,pavia4 #ajbc4 ,the chimneys of the castle of ,pavia have #f rows of openings and from each to the other is one braccio4 ,footnote3 ,other notes relating to ,pavia occur on p4 #dc and p4 #ec 7,pl4 ,,xcviii1 ,no4 #c74 ,compare ,no4 #addh1 #bf4 ,notes on the ,sforzesca near ,vigevano 7#ajbd-ajbh74 #ajbd4 ,on the #bnd day of ,february #adid4 ,at ,sforzesca ,i drew twenty five steps1 #b_/c braccia to each1 and #h braccia wide4 ,footnote3 ,see ,pl4 ,,cx1 ,no4 #b4 ,the rest of the notes on this page refer to the motion of water4 ,on the lower sketch we read3 #d br4 7four braccia7 and giara 7for ghiaja1 sand1 gravel74 #ajbe4 ,the vineyards of ,vigevano on the #bjth day of ,march #adid4 ,footnote3 ,on one side there is an effaced sketch in red chalk4 #ajbf4 ,to lock up a butteris at ,vigevano4 #ajbg4 ,again if the lowest part of the bank which lies across the current of the waters is made in deep and wide steps1 after the manner of stairs1 the waters which1 in their course usually fall perpendicularly from the top of such a place to the bottom1 and wear away the foundations of this bank can no longer descend with a blow of too great a force2 and ,i find the example of this in the stairs down which the water falls in the fields at ,sforzesca at ,vigevano over which the running water falls for a height of #ej braccia4 #ajbh4 ,stair of ,vigevano below ,la ,sforzesca1 #acj steps1 #a_/d braccio high and #a_/b braccio wide1 down which the water falls1 so as not to wear away anything at the end of its fall2 by these steps so much soil has come down that it has dried up a pool2 that is to say it has filled it up and a pool of great depth has been turned into meadows4 ,notes on the ,north ,italian lake4 7#ajbi-ajcc7 #ajbi4 ,in many places there are streams of water which swell for six hours and ebb for six hours2 and ,i1 for my part1 have seen one above the lake of ,como called ,fonte ,pliniana1 which increases and ebbs1 as ,i have said1 in such a way as to turn the stones of two mills2 and when it fails it falls so low that it is like looking at water in a deep pit4 ,footnote3 ,the fountain is known by this name to this day3 it is near ,torno1 on the ,eastern shore of ,como4 ,the waters still rise and fall with the flow and ebb of the tide as ,pliny described it 7,epist4 ,,iv1 #cj2 ,hist4 ,nat4 ,,ii1 #bjf74 #ajcj4 ,,lake ,,of ,,como4 ,,valley ,,of ,,chiavenna4 ,above the lake of ,como towards ,germany is the valley of ,chiavenna where the river ,mera flows into this lake4 ,here are barren and very high mountains1 with huge rocks4 ,among these mountains are to be found the water-birds called gulls4 ,here grow fir trees1 larches and pines4 ,deer1 wildgoats1 chamois1 and terrible bears4 ,it is impossible to climb them without using hands and feet4 ,the peasants go there at the time of the snows with great snares to make the bears fall down these rocks4 ,these mountains which very closely approach each other are parted by the river4 ,they are to the right and left for the distance of #bj miles throughout of the same nature4 ,from mile to mile there are good inns4 ,above on the said river there are waterfalls of #djj braccia in height1 which are fine to see2 and there is good living at #d soldi the reckoning4 ,this river brings down a great deal of timber4 ,,val ,,sasina4 ,val ,sasina runs down towards ,italy2 this is almost the same form and character4 ,there grow here many mappello and there are great ruins and falls of water ,footnote #ad3 ,the meaning of mappello is unknown44 ,,valley ,,of ,,introzzo4 ,this valley produces a great quantity of firs1 pines and larches2 and from here ,ambrogio ,fereri has his timber brought down2 at the head of the ,valtellina are the mountains of ,bormio1 terrible and always covered with snow2 marmots 787 are found there4 ,,bellaggio4 ,opposite the castle ,bellaggio there is the river ,latte1 which falls from a height of more than #ajj braccia from the source whence it springs1 perpendicularly1 into the lake with an inconceivable roar and noise4 ,this spring flows only in ,august and ,september4 ,,valtellina4 ,valtellina1 as it is called1 is a valley enclosed in high and terrible mountains2 it produces much strong wine1 and there is so much cattle that the natives conclude that more milk than wine grows there4 ,this is the valley through which the ,adda passes1 which first runs more than #dj miles through ,germany2 this river breeds the fish temolo which live on silver1 of which much is to be found in its sands4 ,in this country every one can sell bread and wine1 and the wine is worth at most one soldo the bottle and a pound of veal one soldo1 and salt ten dinari and butter the same and their pound is #cj ounces1 and eggs are one soldo the lot4 #ajca4 ,at ,,bormio4 ,at ,bormio are the baths2--,about eight miles above ,como is the ,pliniana1 which increases and ebbs every six hours1 and its swell supplies water for two mills2 and its ebbing makes the spring dry up2 two miles higher up there is ,nesso1 a place where a river falls with great violence into a vast rift in the mountain4 ,these excursions are to be made in the month of ,may4 ,and the largest bare rocks that are to be found in this part of the country are the mountains of ,mandello near to those of ,lecco1 and of ,gravidona towards ,bellinzona1 #cj miles from ,lecco1 and those of the valley of ,chiavenna2 but the greatest of all is that of ,mandello1 which has at its base an opening towards the lake1 which goes down #bjj steps1 and there at all times is ice and wind4 ,,in ,,val ,,sasina4 ,in ,val ,sasina1 between ,vimognio and ,introbbio1 to the right hand1 going in by the road to ,lecco1 is the river ,troggia which falls from a very high rock1 and as it falls it goes underground and the river ends there4 #c miles farther we find the buildings of the mines of copper and silver near a place called ,pra' ,santo ,pietro1 and mines of iron and curious things4 ,la ,grigna is the highest mountain there is in this part1 and it is quite bare4 ,footnote3 #ajcj and #ajca4 ,from the character of the handwriting we may conclude that these observations were made in ,leonardo's youth2 and ,i should infer from their contents1 that they were notes made in anticipation of a visit to the places here described1 and derived from some person 7unknown to us7 who had given him an account of them4 #ajcb4 ,the lake of ,pusiano flows into the lake of ,segrino ,footnote #c3 ,the statement about the lake ,segrino is incorrect2 it is situated in the ,valle ,assina1 above the lake of ,pusiano4 and of ,annone and of ,sala4 ,the lake of ,annone is #bb braccia higher at the surface of its water than the surface of the water of the lake of ,lecco1 and the lake of ,pusiano is #bj braccia higher than the lake of ,annone1 which added to the afore said #bb braccia make #db braccia and this is the greatest height of the surface of the lake of ,pusiano above the surface of the lake of ,lecco4 ,footnote3 ,this text has in the original a slight sketch to illustrate it4 #ajcc4 ,at ,santa ,maria in the ,valley of ,ravagnate ,footnote #b3 ,ravagnate 7,leonardo writes ,ravagna7 in the ,brianza is between ,oggiono and ,brivio1 ,south of the lake of ,como4 ,m4 ,ravaisson avails himself of this note to prove his hypothesis that ,leonardo paid two visits to ,france4 ,see ,gazette des ,beaux ,arts1 #ahha pag4 #ebh3 ,au recto du meme feuillet1 on lit encore une note relative a une vallee nemonti brigatia2 il me semble qu'il s'agit bien des monts de ,briancon1 le ,brigantio des anciens4 ,briancon est sur la route de ,lyon en ,italie4 ,ce fut par le mont ,viso que passerent1 en aout #aeae1 les troupes francaises qui allaient remporter la victoire de ,marignan4 ,leonard de ,vinci1 ingenieur de ,francois ,ier1 comme il l'avait ete de ,louis ,,xii1 aurait-il ete pour quelque chose dans le plan du celebre passage des ,alpes1 qui eut lieu en aout #aeae1 et a la suite duquel on le vit accompagner partout le chevaleresque vainqueur8 ,auraitil ete appele par le jeune roi1 de ,rome ou l'artiste etait alors1 des son avenement au trone8 in the mountains of ,brianza are the rods of chestnuts of #i braccia and one out of an average of #ajj will be #ad braccia4 ,at ,varallo di ,ponbia near to ,sesto on the ,ticino the quinces are white1 large and hard4 ,footnote #e3 ,varallo di ,ponbia1 about ten miles ,south of ,arona is distinct from ,varallo the chief town in the ,val di ,sesia4 ,notes on places in ,central ,italy1 visited in #aejb 7#ajcd-ajed74 #ajcd4 ,pigeon-house at ,urbino1 the #cjth day of ,july #aejb4 ,footnote3 ,an indistinct sketch is introduced with this text1 in the original1 in which the word ,scolatoro 7conduit7 is written4 #ajce4 ,made by the sea at ,piombino4 ,footnote3 ,below the sketch there are eleven lines of text referring to the motion of waves4 #ajcf4 ,acquapendente is near ,orvieto4 ,footnote3 ,acquapendente is about #aj miles ,west of ,orvieto1 and is to the right in the map on ,pl4 ,,cxiii1 near the lake of ,bolsena4 #ajcg4 ,the rock of ,cesena4 ,footnote3 ,see ,pl4 ,,xciv ,no4 #a1 the lower sketch4 ,the explanation of the upper sketch is given on p4 #bi4 #ajch4 ,siena1 a b #d braccia1 a c #aj braccia4 ,steps at the castle of ,urbino4 ,footnote3 ,see ,pl4 ,,cx ,no4 #c2 compare also ,no4 #gfe4 #ajci4 ,the bell of ,siena1 that is the manner of its movement1 and the place of the attachment of the clapper4 ,footnote3 ,the text is accompanied by an indistinct sketch4 #ajdj4 ,on ,st4 ,mary's day in the middle of ,august1 at ,cesena1 #aejb4 ,footnote3 ,see ,pl4 ,,cx1 ,no4 #d4 #ajda4 ,stairs of the palace of the ,count of ,urbino1--rough4 ,footnote3 ,the text is accompanied by a slight sketch4 #ajdb4 ,at the fair of ,san ,lorenzo at ,cesena4 #aejb4 #ajdc4 ,windows at ,cesena4 ,footnote3 ,there are four more lines of text which refer to a slightly sketched diagram4 #ajdd4 ,at ,porto ,cesenatico1 on the #fth of ,september #aejb at #i o'clock a4 m4 ,the way in which bastions ought to project beyond the walls of the towers to defend the outer talus2 so that they may not be taken by artillery4 ,footnote3 ,an indistinct sketch1 accompanies this passage4 #ajde4 ,the rock of the harbour of ,cesena is four points towards the ,south ,west from ,cesena4 #ajdf4 ,in ,romagna1 the realm of all stupidity1 vehicles with four wheels are used1 of which ,o the two in front are small and two high ones are behind2 an arrangement which is very unfavourable to the motion1 because on the fore wheels more weight is laid than on those behind1 as ,i showed in the first of the #eth on ,elements4 #ajdg4 ,thus grapes are carried at ,cesena4 ,the number of the diggers of the ditches is arranged pyramidically4 ,footnote3 ,a sketch1 representing a hook to which two bunches of grapes are hanging1 refers to these first two lines4 ,cesena is mentioned again ,fol4 #hb;a3 ,carro da ,cesena 7a cart from ,cesena74 #ajdh4 ,there might be a harmony of the different falls of water as you saw them at the fountain of ,rimini on the #hth day of ,august1 #aejb4 #ajdi4 ,the fortress at ,urbino4 ,footnote3 #ajdi4 ,in the original the text is written inside the sketch in the place here marked n4 #ajej4 ,imola1 as regards ,bologna1 is five points from the ,west1 towards the ,north ,west1 at a distance of #bj miles4 ,castel ,san ,piero is seen from ,imola at four points from the ,west towards the ,north ,west1 at a distance of #g miles4 ,faenza stands with regard to ,imola between ,east and ,south ,east at a distance of ten miles4 ,forli stands with regard to ,faenza between ,south ,east and ,east at a distance of #bj miles from ,imola and ten from ,faenza4 ,forlimpopoli lies in the same direction at #be miles from ,imola4 ,bertinoro1 as regards ,imola1 is five points from the ,east to wards the ,south ,east1 at #bg miles4 #ajea4 ,imola as regards ,bologna is five points from the ,west towards the ,north ,west at a distance of #bj miles4 ,castel ,san ,pietro lies exactly ,north ,west of ,imola1 at a distance of #g miles4 ,faenza1 as regards ,imola lies exactly half way between the ,east and ,south ,east at a distance of #aj miles2 and ,forli lies in the same direction from ,imola at a distance of #bj miles2 and ,forlimpopolo lies in the same direction from ,forli at a distance of #be miles4 ,bertinoro is seen from ,imola two points from the ,east towards the ,south ,east at a distance of #bg miles4 ,footnote3 ,leonardo inserted this passage on the margin of the circular plan1 in water colour1 of ,imola--see ,pl4 ,,cxi ,no4 #a4--;,in the original the fields surrounding the town are light green2 the moat1 which surrounds the fortifications and the windings of the river ,santerno1 are light blue4 ,the parts1 which have come out blackish close to the river are yellow ochre in the original4 ,the dark groups of houses inside the town are red4 ,at the four points of the compass drawn in the middle of the town ,leonardo has written 7from right to left73 ,mezzodi 7,south7 at the top2 to the left ,scirocho 7,south east71 levante 7,east71 ,greco 7,north ,east71 ,septantrione 7,north71 ,maesstro 7,north ,west71 ponente 7,west7 ,libecco 7,south ,west74 ,the arch in which the plan is drawn is1 in the original1 #db centimetres across4 ,at the beginning of ,october #aejb ,cesare ,borgia was shut up in ,imola by a sudden revolt of the ,condottieri1 and it was some weeks before he could release himself from this state of siege 7see ,gregorovius1 ,geschichte der ,stadt ,rom im ,mittelalter1 ,vol4 ,,vii1 ,book ,,xiii1 #e1 #e74 ,besides this incident ,imola plays no important part in the history of the time4 ,i therefore think myself fully justified in connecting this map1 which is at ,windsor1 with the siege of #aejb and with ,leonardo's engagements in the service of ,cesare ,borgia1 because a comparison of these texts1 ,nos4 #ajej and #ajea1 raise1 ,i believe1 the hypothesis to a certainty4 #ajeb4 ,from ,bonconventi to ,casa ,nova are #aj miles1 from ,casa ,nova to ,chiusi #i miles1 from ,chiusi to ,perugia1 from1 ,perugia to ,santa ,maria degli ,angeli1 and then to ,fuligno4 ,footnote3 ,most of the places here described lie within the district shown in the maps on ,pl4 ,,cxiii4 #ajec4 ,on the first of ,august #aejb1 the library at ,pesaro4 #ajed4 ,,of ,,painting4 ,on the tops and sides of hills foreshorten the shape of the ground and its divisions1 but give its proper shape to what is turned towards you4 ,footnote3 ,this passage evidently refers to the making of maps1 such as ,pl4 ,,cxii1 ,,cxiii1 and ,,cxiv4 ,there is no mention of such works1 it is true1 excepting in this one passage of ,,ms4 ,l4 ,but this can scarcely be taken as evidence against my view that ,leonardo busied himself very extensively at that time in the construction of maps2 and all the less since the foregoing chapters clearly prove that at a time so full of events ,leonardo would only now and then commit his observations to paper1 in the ,,ms4 ,l4 ,by the side of this text we find1 in the original1 a very indistinct sketch1 perhaps a plan of a position4 ,instead of this drawing ,i have here inserted a much clearer sketch of a position from the same ,,ms41 ,l4 #hb;b and #hc;a4 ,they are the only drawings of landscape1 it may be noted1 which occur at all in that ,,ms4 ,alessandria in ,piedmont 7#ajee4 #ajef74 #ajee4 ,at ,candia in ,lombardy1 near ,alessandria della ,paglia1 in making a well for ,messer ,gualtieri ,footnote #b3 ,messer ,gualtieri1 the same probably as is mentioned in ,nos4 #fgb and #acdd4 of ,candia1 the skeleton of a very large boat was found about #aj braccia underground2 and as the timber was black and fine1 it seemed good to the said ,messer ,gualtieri to have the mouth of the well lengthened in such a way as that the ends of the boat should be uncovered4 #ajef4 ,at ,alessandria della ,paglia in ,lombardy there are no stones for making lime of1 but such as are mixed up with an infinite variety of things native to the sea1 which is now more than #bjj miles away4 ,the ,alps 7#ajeg-ajfb74 #ajeg4 ,at ,monbracco1 above ,saluzzo1--a mile above the ,certosa1 at the foot of ,monte ,viso1 there is a quarry of flakey stone1 which is as white as ,carrara marble1 without a spot1 and as hard as porphyry or even harder2 of which my worthy gossip1 ,master ,benedetto the sculptor1 has promised to give me a small slab1 for the colours1 the second day of ,january #aeaa4 ,footnote3 ,saluzzo at the foot of the ,alps ,south of ,turin4 ,footnote #i4 #aj43 ,maestro ,benedetto scultore2 probably some native of ,northern ,italy acquainted with the place here described4 ,hardly the ,florentine sculptor ,benedetto da ,majano4 ,amoretti had published this passage1 and ,m4 ,ravaisson who gave a ,french translation of it in the ,gazette des ,beaux ,arts 7#ahha1 pag4 #ebh71 remarks as follows3 ,le maitre sculpteur que ,leonard appelle son compare ne serait-il pas ,benedetto da ,majano1 un de ceux qui jugerent avec lui de la place a donner au ,david de ,michel-,ange1 et de qui le ,louvre a acquis recemment un buste d'apres ,philippe ,strozzi8 ,to this it may be objected that ,benedetto da ,majano had already lain in his grave fourteen years1 in the year #aeaa1 when he is supposed to have given the promise to ,leonardo4 ,the colours may have been given to the sculptor ,benedetto and the stone may have been in payment for them4 ,from the description of the stone here given we may conclude that it is repeated from hearsay of the sculptor's account of it4 ,i do not understand how1 from this observation1 it is possible to conclude that ,leonardo was on the spot4 #ajeh4 ,that there are springs which suddenly break forth in earthquakes or other convulsions and suddenly fail2 and this happened in a mountain in ,savoy where certain forests sank in and left a very deep gap1 and about four miles from here the earth opened itself like a gulf in the mountain1 and threw out a sudden and immense flood of water which scoured the whole of a little valley of the tilled soil1 vineyards and houses1 and did the greatest mischief1 wherever it overflowed4 #ajei4 ,the river ,arve1 a quarter of a mile from ,geneva in ,savoy1 where the fair is held on midsummerday in the village of ,saint ,gervais4 ,footnote3 ,an indistinct sketch is to be seen by the text4 #ajfj4 ,and this may be seen1 as ,i saw it1 by any one going up ,monbroso ,footnote3 ,i have vainly enquired of every available authority for a solution of the mystery as to what mountain is intended by the name ,monboso 7,comp4 ,vol4 ,i ,nos4 #cjj and #cja74 ,it seems most obvious to refer it to ,monte ,rosa4 ,,rosa derived from the ,keltic ,,ros which survives in ,breton and in ,gaelic1 meaning1 in its first sense1 a mountain spur1 but which also--like ,,horn--means a very high peak2 thus ,monte ,rosa would mean literally the ,high ,peak41 a peak of the ,alps which divide ,france from ,italy4 ,the base of this mountain gives birth to the #d rivers which flow in four different directions through the whole of ,europe4 ,and no mountain has its base at so great a height as this1 which lifts itself above almost all the clouds2 and snow seldom falls there1 but only hail in the summer1 when the clouds are highest4 ,and this hail lies unmelted there1 so that if it were not for the absorption of the rising and falling clouds1 which does not happen more than twice in an age1 an enormous mass of ice would be piled up there by the layers of hail1 and in the middle of ,july ,i found it very considerable2 and ,i saw the sky above me quite dark1 and the sun as it fell on the mountain was far brighter here than in the plains below1 because a smaller extent of atmosphere lay between the summit of the mountain and the sun4 ,footnote #f3 in una eta4 ,this is perhaps a slip of the pen on ,leonardo's part and should be read estate 7summer74 ,leic4 #i;b #ajfa4 ,in the mountains of ,verona the red marble is found all mixed with cockle shells turned into stone2 some of them have been filled at the mouth with the cement which is the substance of the stone2 and in some parts they have remained separate from the mass of the rock which enclosed them1 because the outer covering of the shell had interposed and had not allowed them to unite with it2 while in other places this cement had petrified those which were old and almost stripped the outer skin4 #ajfb4 ,bridge of ,goertz-,wilbach 7874 ,footnote3 ,there is a slight sketch with this text1 ,leonardo seems to have intended to suggest1 with a few pen-strokes1 the course of the ,isonzo and of the ,wipbach in the vicinity of ,gorizia 7,goerz74 ,he himself says in another place that he had been in ,friuli 7see ,no4 #ajgg #a4 #ai74 ,the ,appenins 7#ajfc-ajfh74 #ajfc4 ,that part of the earth which was lightest remained farthest from the centre of the world2 and that part of the earth became the lightest over which the greatest quantity of water flowed4 ,and therefore that part became lightest where the greatest number of rivers flow2 like the ,alps which divide ,germany and ,france from ,italy2 whence issue the ,rhone flowing ,southwards1 and the ,rhine to the ,north4 ,the ,danube or ,tanoia towards the ,north ,east1 and the ,po to the ,east1 with innumerable rivers which join them1 and which always run turbid with the soil carried by them to the sea4 ,the shores of the sea are constantly moving towards the middle of the sea and displace it from its original position4 ,the lowest portion of the ,mediterranean will be reserved for the bed and current of the ,nile1 the largest river that flows into that sea4 ,and with it are grouped all its tributaries1 which at first fell into the sea2 as may be seen with the ,po and its tributaries1 which first fell into that sea1 which between the ,appenines and the ,german ,alps was united to the ,adriatic sea4 ,that the ,gallic ,alps are the highest part of ,europe4 #ajfd4 ,and of these ,i found some in the rocks of the high ,appenines and mostly at the rock of ,la ,vernia4 ,footnote #f3 ,sasso della ,vernia4 ,the frowning rock between the sources of the ,arno and the ,tiber1 as ,dante describes this mountain1 which is #abfi metres in height4 ,this note is written by the side of that given as ,no4 #ajbj2 but their connection does not make it clear what ,leonardo's purpose was in writing it4 #ajfe4 ,at ,parma1 at ',la ,campana' on the twenty-fifth of ,october #aead4 ,footnote #b3 ,capano1 an ,inn4 ,a note on the petrifactions1 or fossils near ,parma will be found under ,no4 #ihi4 #ajff4 ,a method for drying the marsh of ,piombino4 ,footnote3 ,there is a slight sketch with this text in the original4--,piombino is also mentioned in ,nos4 #fji1 l4 #ee-eh 7compare ,pl4 ,,xxxv1 #c1 below74 ,also in ,no4 #ajce4 #ajfg4 ,the shepherds in the ,romagna at the foot of the ,apennines make peculiar large cavities in the mountains in the form of a horn1 and on one side they fasten a horn4 ,this little horn becomes one and the same with the said cavity and thus they produce by blowing into it a very loud noise4 ,footnote3 ,as to the ,romagna see also ,no4 #ajdf4 #ajfh4 ,a spring may be seen to rise in ,sicily which at certain times of the year throws out chesnut leaves in quantities2 but in ,sicily chesnuts do not grow1 hence it is evident that that spring must issue from some abyss in ,italy and then flow beneath the sea to break forth in ,sicily4 ,footnote3 ,the chesnut tree is very common in ,sicily4 ,in writing cicilia ,leonardo meant perhaps ,cilicia4 ,,ii4 ,,france4 #ajfi4 ,,germany4 ,,france4 a4 ,austria1 a4 ,picardy4 b4 ,saxony4 b4 ,normandy4 c4 ,nuremberg4 c4 ,dauphine4 d4 ,flanders4 ,,spain4 a4 ,biscay4 b4 ,castille4 c4 ,galicia4 d4 ,portugal4 e4 ,taragona4 f4 ,granada4 ,footnote3 ,two slightly sketched maps1 one of ,europe the other of ,spain1 are at the side of these notes4 #ajgj4 ,perpignan4 ,roanne4 ,lyons4 ,paris4 ,ghent4 ,bruges4 ,holland4 ,footnote3 ,roana does not seem to mean here ,rouen in ,normandy1 but is probably ,roanne 7,rodumna7 on the upper ,loire1 ,lyonnais 7,dep4 du ,loire74 ,this town is now unimportant1 but in ,leonardo's time was still a place of some consequence4 #ajga4 ,at ,bordeaux in ,gascony the sea rises about #dj braccia before its ebb1 and the river there is filled with salt water for more than a hundred and fifty miles2 and the vessels which are repaired there rest high and dry on a high hill above the sea at low tide4 ,footnote #b3 ,this is obviously an exaggeration founded on inaccurate information4 ,half of #aej miles would be nearer the mark4 #ajgb4 ,the ,rhone issues from the lake of ,geneva and flows first to the ,west and then to the ,south1 with a course of #djj miles and pours its waters into the ,mediterranean4 #ajgc4 c d is the garden at ,blois2 a b is the conduit of ,blois1 made in ,france by ,fra ,giocondo1 b c is what is wanting in the height of that conduit1 c d is the height of the garden at ,blois1 e f is the siphon of the conduit1 b c1 e f1 f g is where the siphon discharges into the river4 ,footnote3 ,the tenor of this note 7see lines #b and #c7 seems to me to indicate that this passage was not written in ,france1 but was written from oral information4 ,we have no evidence as to when this note may have been written beyond the circumstance that ,fra ,giocondo the ,veronese ,architect left ,france not before the year #aeje4 ,the greater part of the magnificent ,chateau of ,blois has now disappeared4 ,whether this note was made for a special purpose is uncertain4 ,the original form and extent of the ,chateau is shown in ,androvet1 ,les plus excellents ,bastiments de ,france1 ,paris ,,mdcvii1 and it may be observed that there is in the middle of the garden a ,pavilion somewhat similar to that shown on ,pl4 ,,lxxxviii ,no4 #g4 ,see ,s4 ,,de ,,la ,,saussaye1 ,histoire du ,chateau de ,blois #d;eme edition ,blois et ,paris p4 #age3 ,en mariant sa fille ainee a ,francois1 comte d',angouleme1 ,louis ,,xii lui avait constitue en dot les comtes de ,blois1 d',asti1 de ,coucy1 de ,montfort1 d',etampes et de ,vertus4 ,une ordonnance de ,francois ,i4 lui laissa en #aeaf l'administration du comte de ,blois4 ,le roi fit commencer1 dans la meme annee1 les travaux de celle belle partie du chateau1 connue sous le nom d'aile de ,francois ,i1 et dont nous avons donne la description au commencement de ce livre4 ,nous trouvons en effet1 dans les archives du ,baron de ,foursanvault1 une piece qui en fixe parfaitement la date4 ,on y lit3 ,je1 ,baymon ,philippeaux1 commis par le ,roy a tenir le compte et fair le payement des bastiments1 ediffices et reparacions que le dit seigneur fait faire en son chastu de ,blois1 confesse avoir eu et receu 444 la somme de trois mille livres tournois 444 le cinquieme jour de juillet1 l'an mil cinq cent et seize4 ,p4 #bd3 ,les jardins avaient ete decores avec beaucoup de luxe par les differents possesseurs du chateau4 ,il ne reste de tous les batiments qu'ils y eleverent que ceux des officiers charges de l'administration et de la culture des jardins1 et un pavilion carre en pierre et en brique flanque de terrasses a chacun de ses angles4 ,quoique defigure par des mesures elevees sur les terrasses1 cet edifice est tris-digne d'interet par l'originalite du plan1 la decoration architecturale et le souvenir d',anne de ,bretagne qui le fit construire4 ,felibien describes the garden as follows3 ,le jardin haut etait fort bien dresse par grands compartimens de toutes sortes de figures1 avec des allees de meuriers blancs et des palissades de coudriers4 ,deux grands berceaux de charpenterie separoient toute la longueur et la largeur du jardin1 et dans les quatres angles des allees1 ou ces berceaux se croissent1 il y auoit #d cabinets1 de mesme charpenterie 444 ,il y a pas longtemps qu'il y auoit dans ce mesme jardin1 a l'endroit ou se croissent les allees du milieu1 un edifice de figure octogone1 de plus de #g thoises de diametre et de plus de neuf thoises de haut2 avec #d enfoncements en forme de niches dans les #d angles des allies4 ,ce bastiment4444 esloit de charpente mais d'un extraordinairement bien travaille4 ,on y voyait particulierement la cordiliere qui regnati tout autour en forme de cordon4 ,car la ,reyne affectait de la mettre nonseulement a ses armes et a ses chiffres mais de la faire representer en divers manieres dans tous les ouvrages qu'on lui faisait pour elle 444 le bastiment estati couvert en forme de dome qui dans son milieu avait encore un plus petit dome1 ou lanterne vitree au-dessus de laquelle estait une figure doree representant ,saint ,michel4 ,les deux domes estoient proprement couvert d'ardoise et de plomb dore par dehors2 par dedans ils esloient lambrissez d'une menuiserie tres delicate4 ,au milieu de ce ,salon il y avait un grand bassin octogone de marbre blanc1 dont toutes les faces estoient enrichies de differentes sculptures1 avec les armes et les chiffres du ,roy ,louis ,,xii et de la ,reine ,anne1 ,dans ce bassin il y en avait un autre pose sur un piedestal lequel auoit sept piedz de diametre4 ,il estait de figure ronde a godrons1 avec des masques et d'autres ornements tres scauamment taillez4 ,du milieu de ce deuxiesme bassin s'y levoit un autre petit piedestal qui portait un troisiesme bassin de trois pieds de diametre1 aussy parfaitement bien taille2 c'estoit de ce dernier bassin que jallissoit l'eau qui se rependoit en suitte dans les deux autres bassins4 ,les beaux ouvrages faits d'un marbre esgalement blanc et poli1 furent brisez par la pesanteur de tout l'edifice1 que les injures de l'air renverserent de fond en comble4 #ajgd4 ,the river ,loire at ,amboise4 ,the river is higher within the bank b d than outside that bank4 ,the island where there is a part of ,amboise4 ,this is the river that passes through ,amboise2 it passes at a b c d1 and when it has passed the bridge it turns back1 against the original current1 by the channel d e1 b f in contact with the bank which lies between the two contrary currents of the said river1 a b1 c d1 and d e1 b f4 ,it then turns down again by the channel f l1 g h1 n m1 and reunites with the river from which it was at first separated1 which passes by k n1 which makes k m1 r t4 ,but when the river is very full it flows all in one channel passing over the bank b d4 ,footnote3 ,see ,pl4 ,,cxv4 ,lines #a-g are above1 lines #h-aj in the middle of the large island and the word ,isola is written above d in the smaller island2 a is written on the margin on the bank of the river above #a4 ,i2 in the reproduction it is not visible4 ,as may be seen from the last sentence1 the observation was made after long study of the river's course1 when ,leonardo had resided for some time at1 or near1 ,amboise4 #ajge4 ,the water may be dammed up above the level of ,romorantin to such a height1 that in its fall it may be used for numerous mills4 #ajge4 ,the river at ,villefranche may be conducted to ,romorantin which may be done by the inhabitants2 and the timber of which their houses are built may be carried in boats to ,romorantin ,footnote3 ,compare ,no4 #gdd44 ,the river may be dammed up at such a height that the waters may be brought back to ,romorantin with a convenient fall4 #ajgf4 ,as to whether it is better that the water should all be raised in a single turn or in two8 ,the answer is that in one single turn the wheel could not support all the water that it can raise in two turns1 because at the half turn of the wheel it would be raising #ajj pounds and no more2 and if it had to raise the whole1 #bjj pounds in one turn1 it could not raise them unless the wheel were of double the diameter and if the diameter were doubled1 the time of its revolution would be doubled2 therefore it is better and a greater advantage in expense to make such a wheel of half the size 787 the land which it would water and would render the country fertile to supply food to the inhabitants1 and would make navigable canals for mercantile purposes4 ,the way in which the river in its flow should scour its own channel4 ,by the ninth of the third2 the more rapid it is1 the more it wears away its channel2 and1 by the converse proposition1 the slower the water the more it deposits that which renders it turbid4 ,and let the sluice be movable like the one ,i arranged in ,friuli ,footnote #ai3 ,this passage reveals to us the fact that ,leonardo had visited the country of ,friuli and that he had stayed there for some time4 ,nothing whatever was known of this previously41 where when one sluice was opened the water which passed through it dug out the bottom4 ,therefore when the rivers are flooded1 the sluices of the mills ought to be opened in order that the whole course of the river may pass through falls to each mill2 there should be many in order to give a greater impetus1 and so all the river will be scoured4 ,and below the site of each of the two mills there may be one of the said sluice falls2 one of them may be placed below each mill4 #ajgh4 ,a trabocco is four braccia1 and one mile is three thousand of the said braccia4 ,each braccio is divided into #ab inches2 and the water in the canals has a fall in every hundred trabocchi of two of these inches2 therefore #ad inches of fall are necessary in two thousand eight hundred braccia of flow in these canals2 it follows that #ae inches of fall give the required momentum to the currents of the waters in the said canals1 that is one braccio and a half in the mile4 ,and from this it may be concluded that the water taken from the river of ,ville-franche and lent to the river of ,romorantin will44444 ,where one river by reason of its low level cannot flow into the other1 it will be necessary to dam it up1 so that it may acquire a fall into the other1 which was previously the higher4 ,the eve of ,saint ,antony ,i returned from ,romorantin to ,amboise1 and the ,king went away two days before from ,romorantin4 ,from ,romorantin as far as the bridge at ,saudre it is called the ,saudre1 and from that bridge as far as ,tours it is called the ,cher4 ,i would test the level of that channel which is to lead from the ,loire to ,romorantin1 with a channel one braccio wide and one braccio deep4 ,footnote3 ,lines #f-ah are partly reproduced in the facsimile on p4 #bed1 and the whole of lines #ai-be4 ,the following names are written along the rivers on the larger sketch1 era f 7the ,loire7 scier f 7the ,cher7 three times4 ,pote ,sodro 7bridge of the ,soudre74 ,villa francha 7,villefranche7 banco 7sandbank7 ,sodro 7,soudre74 ,the circle below shows the position of ,romorantin4 ,the words 'orologio del sole' written below do not belong to the map of the rivers4 ,the following names are written by the side of the smaller sketch-map3--tors 7,tours71 ,abosa 7,amboise7 bres--for ,bles 7,blois7 mo rica 7,montrichard74 ,lione 7,lyons74 ,this map was also published in the ',saggio' 7,milano1 #ahgb7 ,pl4 ,,xxii1 and the editors remark3 ,forse la linia retta che va da ,amboise a ,romorantin segna l'andamento proposto d'un ,canale1 che poi rembra prolungarsi in giu fin dove sta scritto ,lione4 ,m4 ,ravaisson has enlarged on this idea in the ,gazette des ,beaux ,arts 7#ahha p4 #ecj73 ,les traces de ,leonard permettent d'entrevoir que le canal commencant soit aupres de ,tours1 soit aupres de ,blois et passant par ,romorantin1 avec port d'embarquement a ,villefranche1 devait1 au dela de ,bourges1 traverser l',allier au-dessous des affluents de la ,dore et de la ,sioule1 aller par ,moulins jusqu' a ,digoin2 enfin1 sur l'autre rive de la ,loire1 depasser les monts du ,charolais et rejoindre la ,saone aupres de ,macon4 ,it seems to me rash1 however1 to found so elaborate an hypothesis on these sketches of rivers4 ,the slight stroke going to ,lione is perhaps only an indication of the direction4--,with regard to the ,loire compare also ,no4 #ihh4 l4 #ch4 #ajgi4 ,,the ,,road ,,to ,,orleans ,at #a_/d from the ,south to the ,south ,east4 ,at #a_/c from the ,south to the ,south ,east4 ,at #a_/d from the ,south to the ,south ,east4 ,at #a_/e from the ,south to the ,south ,east4 ,between the ,south ,west and ,south1 to the ,east bearing to the ,south2 from the ,south towards the ,east #a_/h2 thence to the ,west1 between the ,south and ,south ,west2 at the ,south4 ,footnote3 ,the meaning is obscure2 a more important passage referring to ,france is to be found under ,no4 #gdd ,on the ,germans 7#ajhj4 #ajha74 #ajhj4 ,the way in which the ,germans closing up together cross and interweave their broad leather shields against the enemy1 stooping down and putting one of the ends on the ground while they hold the rest in their hand4 ,footnote3 ,above the text is a sketch of a few lines crossing each other and the words de ponderibus4 ,the meaning of the passage is obscure4 #ajha4 ,the ,germans are wont to annoy a garrison with the smoke of feathers1 sulphur and realgar1 and they make this smoke last #g or #h hours4 ,likewise the husks of wheat make a great and lasting smoke2 and also dry dung2 but this must be mixed with olive husks1 that is olives pressed for oil and from which the oil has been extracted4 ,footnote3 ,there is with this passage a sketch of a round tower shrouded in smoke4 ,the ,danube4 #ajhb4 ,that the valleys were formerly in great part covered by lakes the soil of which always forms the banks of rivers1--and by seas1 which afterwards1 by the persistent wearing of the rivers1 cut through the mountains and the wandering courses of the rivers carried away the other plains enclosed by the mountains2 and the cutting away of the mountains is evident from the strata in the rocks1 which correspond in their sections as made by the courses of the rivers ,footnote #d3 ,emus1 the ,balkan2 ,dardania1 now ,servia41 ,the ,haemus mountains which go along ,thrace and ,dardania and join the ,sardonius mountains which1 going on to the westward change their name from ,sardus to ,rebi1 as they come near ,dalmatia2 then turning to the ,west cross ,illyria1 now called ,sclavonia1 changing the name of ,rebi to ,albanus1 and going on still to the ,west1 they change to ,mount ,ocra in the ,north2 and to the ,south above ,istria they are named ,caruancas2 and to the ,west above ,italy they join the ,adula1 where the ,danube rises #h1 which stretches to the ,east and has a course of #aejj miles2 its shortest line is about l#jjj miles1 and the same or about the same is that branch of the ,adula mountains changed as to their name1 as before mentioned4 ,to the ,north are the ,carpathians1 closing in the breadth of the valley of the ,danube1 which1 as ,i have said extends eastward1 a length of about #ajjj miles1 and is sometimes #bjj and in some places #cjj miles wide2 and in the midst flows the ,danube1 the principal river of ,europe as to size4 ,the said ,danube runs through the middle of ,austria and ,albania and northwards through ,bavaria1 ,poland1 ,hungary1 ,wallachia and ,bosnia and then the ,danube or ,donau flows into the ,black ,sea1 which formerly extended almost to ,austria and occupied the plains through which the ,danube now courses2 and the evidence of this is in the oysters and cockle shells and scollops and bones of great fishes which are still to be found in many places on the sides of those mountains2 and this sea was formed by the filling up of the spurs of the ,adula mountains which then extended to the ,east joining the spurs of the ,taurus which extend to the ,west4 ,and near ,bithynia the waters of this ,black ,sea poured into the ,propontis ,marmora falling into the ,aegean ,sea1 that is the ,mediterranean1 where1 after a long course1 the spurs of the ,adula mountains became separated from those of the ,taurus4 ,the ,black ,sea sank lower and laid bare the valley of the ,danube with the above named countries1 and the whole of ,asia ,minor beyond the ,taurus range to the ,north1 and the plains from mount ,caucasus to the ,black ,sea to the ,west1 and the plains of the ,don this side--that is to say1 at the foot of the ,ural mountains4 ,and thus the ,black ,sea must have sunk about #ajjj braccia to uncover such vast plains4 ,footnote #h3 ,danubio1 in the original ,reno2 evidently a mistake as we may infer from come dissi l4 #aj c4 ,,iii4 ,,the ,,countries ,,of ,,the ,,western ,,end ,,of ,,the ,,mediterranean4 ,the straits of ,gibraltar 7#ajhc-ajhe74 #ajhc4 ,,why ,,the ,,sea ,,makes ,a ,,stronger ,,current ,,in ,,the ,,straits ,,of ,,spain ,,than ,,elsewhere4 ,a river of equal depth runs with greater speed in a narrow space than in a wide one1 in proportion to the difference between the wider and the narrower one4 ,this proposition is clearly proved by reason confirmed by experiment4 ,supposing that through a channel one mile wide there flows one mile in length of water2 where the river is five miles wide each of the #e square miles will require #a_/e of itself to be equal to the square mile of water required in the sea1 and where the river is #c miles wide each of these square miles will require the third of its volume to make up the amount of the square mile of the narrow part2 as is demonstrated in f g h at the mile marked n4 ,footnote3 ,in the place marked ,a in the diagram ,mare ,mediterano 7,mediterranean ,sea7 is written in the original4 ,and at ,b1 stretto di ,spugna 7straits of ,spain1 i4e4 ,gibraltar74 ,compare ,no4 #ifj4 #ajhd4 ,,why ,,the ,,current ,,of ,,gibraltar ,,is ,,always ,,greater ,,to ,,the ,,west ,,than ,,to ,,the ,,east4 ,the reason is that if you put together the mouths of the rivers which discharge into the ,mediterranean sea1 you would find the sum of water to be larger than that which this sea pours through the straits into the ocean4 ,you see ,africa discharging its rivers that run northwards into this sea1 and among them the ,nile which runs through #cjjj miles of ,africa2 there is also the ,bagrada river and the ,schelif and others4 ,footnote #e3 ,bagrada 7,leonardo writes ,bragada7 in ,tunis1 now ,medscherda2 ,mavretano1 now ,schelif4 ,likewise ,europe pours into it the ,don and the ,danube1 the ,po1 the ,rhone1 the ,arno1 and the ,tiber1 so that evidently these rivers1 with an infinite number of others of less fame1 make its great breadth and depth and current2 and the sea is not wider than #ah miles at the most westerly point of land where it divides ,europe from ,africa4 #ajhe4 ,the gulf of the ,mediterranean1 as an inland sea1 received the principal waters of ,africa1 ,asia and ,europe that flowed towards it2 and its waters came up to the foot of the mountains that surrounded it and made its shores4 ,and the summits of the ,apennines stood up out of this sea like islands1 surrounded by salt water4 ,africa again1 behind its ,atlas mountains did not expose uncovered to the sky the surface of its vast plains about #cjjj miles in length1 and ,memphis ,footnote #f3 ,mefi4 ,leonardo can only mean here the citadel of ,cairo on the ,mokattam hills4 was on the shores of this sea1 and above the plains of ,italy1 where now birds fly in flocks1 fish were wont to wander in large shoals4 #ajhf4 ,tunis4 ,the greatest ebb made anywhere by the ,mediterranean is above ,tunis1 being about two and a half braccia and at ,venice it falls two braccia4 ,in all the rest of the ,mediterranean sea the fall is little or none4 #ajhg4 ,libya4 ,describe the mountains of shifting deserts2 that is to say the formation of waves of sand borne by the wind1 and of its mountains and hills1 such as occur in ,libya4 ,examples may be seen on the wide sands of the ,po and the ,ticino1 and other large rivers4 #ajhh4 ,majorca4 ,circumfulgore is a naval machine4 ,it was an invention of the men of ,majorca4 ,footnote3 ,the machine is fully described in the ,,ms4 and shown in a sketch4 #ajhi4 ,the ,tyrrhene ,sea4 ,some at the ,tyrrhene sea employ this method2 that is to say they fastened an anchor to one end of the yard1 and to the other a cord1 of which the lower end was fastened to an anchor2 and in battle they flung this anchor on to the oars of the opponent's boat and by the use of a capstan drew it to the side2 and threw soft soap and tow1 daubed with pitch and set ablaze1 on to that side where the anchor hung2 so that in order to escape that fire1 the defenders of that ship had to fly to the opposite side2 and in doing this they aided to the attack1 because the galley was more easily drawn to the side by reason of the counterpoise4 ,footnote3 ,this text is illustrated in the original by a pen and ink sketch4 ,,iv4 ,,the ,,levant4 ,the ,levantine ,sea4 #ajij4 ,on the shores of the ,mediterranean #cjj rivers flow1 and #dj1 #bjj ports4 ,and this sea is #cjjj miles long4 ,many times has the increase of its waters1 heaped up by their backward flow and the blowing of the ,west winds1 caused the overflow of the ,nile and of the rivers which flow out through the ,black ,sea1 and have so much raised the seas that they have spread with vast floods over many countries4 ,and these floods take place at the time when the sun melts the snows on the high mountains of ,ethiopia that rise up into the cold regions of the air2 and in the same way the approach of the sun acts on the mountains of ,sarmatia in ,asia and on those in ,europe2 so that the gathering together of these three things are1 and always have been1 the cause of tremendous floods3 that is1 the return flow of the sea with the ,west wind and the melting of the snows4 ,so every river will overflow in ,syria1 in ,samaria1 in ,judea between ,sinai and the ,lebanon1 and in the rest of ,syria between the ,lebanon and the ,taurus mountains1 and in ,cilicia1 in the ,armenian mountains1 and in ,pamphilia and in ,lycia within the hills1 and in ,egypt as far as the ,atlas mountains4 ,the gulf of ,persia which was formerly a vast lake of the ,tigris and discharged into the ,indian ,sea1 has now worn away the mountains which formed its banks and laid them even with the level of the ,indian ocean4 ,and if the ,mediterranean had continued its flow through the gulf of ,arabia1 it would have done the same1 that is to say1 would have reduced the level of the ,mediterranean to that of the ,indian ,sea4 ,the ,red ,sea4 7#ajia4 #ajib74 #ajia4 ,for a long time the water of the ,mediterranean flowed out through the ,red ,sea1 which is #ajj miles wide and #aejj long1 and full of reefs2 and it has worn away the sides of ,mount ,sinai1 a fact which testifies1 not to an inundation from the ,indian sea beating on these coasts1 but to a deluge of water which carried with it all the rivers which abound round the ,mediterranean1 and besides this there is the reflux of the sea2 and then1 a cutting being made to the ,west #cjjj miles away from this place1 ,gibraltar was separated from ,ceuta1 which had been joined to it4 ,and this passage was cut very low down1 in the plains between ,gibraltar and the ocean at the foot of the mountain1 in the low part1 aided by the hollowing out of some valleys made by certain rivers1 which might have flowed here4 ,hercules ,footnote #i3 ,leonardo seems here to mention ,hercules half jestingly and only in order to suggest to the reader an allusion to the legend of the pillars of ,hercules4 came to open the sea to the westward and then the sea waters began to pour into the ,western ,ocean2 and in consequence of this great fall1 the ,red ,sea remained the higher2 whence the water1 abandoning its course here1 ever after poured away through the ,straits of ,spain4 #ajib4 ,the surface of the ,red ,sea is on a level with the ocean4 ,a mountain may have fallen and closed the mouth of the ,red ,sea and prevented the outlet of the ,mediterranean1 and the ,mediterranean ,sea thus overfilled had for outlet the passage below the mountains of ,gades2 for1 in our own times a similar thing has been seen ,footnote #f3 ,compare also ,no4 #accf1 ll4 #cj1 #ce and #cf4-- ,paolo ,giovio1 the celebrated historian 7born at ,como in #adhc7 reports that in #aeac at the foot of the ,alps1 above ,bellinzona1 on the road to ,switzerland1 a mountain fell with a very great noise1 in consequence of an earthquake1 and that the mass of rocks1 which fell on the left 7,western7 side blocked the river ,breno 7,t4 ,i p4 #bah and #cde of ,d4 ,sauvage's ,french edition1 quoted in ,,alexis ,,percy1 ,memoire des tremblements de terre de la peninsule italique2 ,academie ,royale de ,belgique4 ,t4 ,,xxii74--2 a mountain fell seven miles across a valley and closed it up and made a lake4 ,and thus most lakes have been made by mountains1 as the lake of ,garda1 the lakes of ,como and ,lugano1 and the ,lago ,maggiore4 ,the ,mediterranean fell but little on the confines of ,syria1 in consequence of the ,gaditanean passage1 but a great deal in this passage1 because before this cutting was made the ,mediterranean sea flowed to the ,south ,east1 and then the fall had to be made by its run through the ,straits of ,gades4 ,at a the water of the ,mediterranean fell into the ocean4 ,all the plains which lie between the sea and mountains were formerly covered with salt water4 ,every valley has been made by its own river2 and the proportion between valleys is the same as that between river and river4 ,the greatest river in our world is the ,mediterranean river1 which moves from the sources of the ,nile to the ,western ocean4 ,and its greatest height is in ,outer ,mauritania and it has a course of ten thousand miles before it reunites with its ocean1 the father of the waters4 ,that is #cjjj miles for the ,mediterranean1 #cjjj for the ,nile1 as far as discovered and #cjjj for the ,nile which flows to the ,east1 c4 ,footnote3 ,see ,pl4 ,,cxi #b1 a sketch of the shores of the ,mediterranean ,sea1 where lines #aa to #af may be seen4 ,the large figures #aeh are not in ,leonardo's writing4 ,the character of the writing leads us to conclude that this text was written later than the foregoing4 ,a slight sketch of the ,mediterranean is also to be found in ,,ms4 ,i'1 #dg;a4 ,the ,nile 7#ajic-ajih74 #ajic4 ,therefore we must conclude those mountains to be of the greatest height1 above which the clouds falling in snow give rise to the ,nile4 #ajid4 ,the ,egyptians1 the ,ethiopians1 and the ,arabs1 in crossing the ,nile with camels1 are accustomed to attach two bags on the sides of the camel's bodies that is skins in the form shown underneath4 ,in these four meshes of the net the camels for baggage place their feet4 ,footnote3 ,unfortunately both the sketches which accompany this passage are too much effaced to be reproduced4 ,the upper represents the two sacks joined by ropes1 as here described1 the other shows four camels with riders swimming through a river4 #ajie4 ,the ,tigris passes through ,asia ,minor and brings with it the water of three lakes1 one after the other of various elevations2 the first being ,munace and the middle ,pallas and the lowest ,triton4 ,and the ,nile again springs from three very high lakes in ,ethiopia1 and runs northwards towards the sea of ,egypt with a course of #djjj miles1 and by the shortest and straightest line it is #cjjj miles4 ,it is said that it issues from the ,mountains of the ,moon1 and has various unknown sources4 ,the said lakes are about #djjj braccia above the surface of the sphere of water1 that is #a mile and #a_/c1 giving to the ,nile a fall of #a braccia in every mile4 ,footnote #e3 ,incogniti principio4 ,the affluents of the lakes are probably here intended4 ,compare1 as to the ,nile1 ,nos4 #igj1 #ajfc and #ajhd4 #ajif4 ,very many times the ,nile and other very large rivers have poured out their whole element of water and restored it to the sea4 #ajig4 ,why does the inundation of the ,nile occur in the summer1 coming from torrid countries8 #ajih4 ,it is not denied that the ,nile is constantly muddy in entering the ,egyptian sea and that its turbidity is caused by soil that this river is continually bringing from the places it passes2 which soil never returns in the sea which receives it1 unless it throws it on its shores4 ,you see the sandy desert beyond ,mount ,atlas where formerly it was covered with salt water4 ,customs of ,asiatic ,nations 7#ajii4 #aajj74 #ajii4 ,the ,assyrians and the people of ,euboea accustom their horses to carry sacks which they can at pleasure fill with air1 and which in case of need they carry instead of the girth of the saddle above and at the side1 and they are well covered with plates of cuir bouilli1 in order that they may not be perforated by flights of arrows4 ,thus they have not on their minds their security in flight1 when the victory is uncertain2 a horse thus equipped enables four or five men to cross over at need4 #aajj4 ,,small ,,boats4 ,the small boats used by the ,assyrians were made of thin laths of willow plaited over rods also of willow1 and bent into the form of a boat4 ,they were daubed with fine mud soaked with oil or with turpentine1 and reduced to a kind of mud which resisted the water and because pine would split2 and always remained fresh2 and they covered this sort of boats with the skins of oxen in safely crossing the river ,sicuris of ,spain1 as is reported by ,lucant2 ,footnote #g3 ,see ,lucan's ,pharsalia ,,iv1 #acj3 ,utque habuit ripas ,sicoris camposque reliquit1 ,primum cana salix madefacto vimine parvam ,texitur in puppim1 calsoque inducto juvenco ,vectoris patiens tumidum supernatat amnem4 ,sic ,venetus stagnante ,pado1 fusoque ,britannus ,navigat oceano1 sic cum tenet omnia ,nilus1 ,conseritur bibula ,memphitis cymbo papyro4 ,his ratibus transjecta manus festinat utrimque ,succisam cavare nemus ,the ,spaniards1 the ,scythians and the ,arabs1 when they want to make a bridge in haste1 fix hurdlework made of willows on bags of ox-hide1 and so cross in safety4 ,rhodes 7#aaja4 #aajb74 #aaja4 ,in fourteen hundred and eighty nine there was an earthquake in the sea of ,atalia near ,rhodes1 which opened the sea--that is its bottom--and into this opening such a torrent of water poured that for more than three hours the bottom of the sea was uncovered by reason of the water which was lost in it1 and then it closed to the former level4 ,footnote3 ,nello ottanto #i4 ,it is scarcely likely that ,leonardo should here mean #hi ,,ad4 ,dr4 ,h4 ,,muller- ,,strubing writes to me as follows on this subject3 ,with reference to ,rhodes ,ross says 7,reise auf den ,griechischen ,inseln1 ,,iii #gj ff4 #ahdj71 that ancient history affords instances of severe earthquakes at ,rhodes1 among others one in the second year of the #achth ,olympiad#bgj ,b4 ,c42 a remarkably violent one under ,antoninus ,pius 7,a4 ,d4 #ach-afa7 and again under ,constantine and later4 ,but ,leonardo expressly speaks of an earthquake nel mar di ,atalia presso a ,rodi1 which is singular4 ,the town of ,attalia1 founded by ,attalus1 which is what he no doubt means1 was in ,pamphylia and more than #aej ,english miles ,east of ,rhodes in a straight line4 ,leake and most other geographers identify it with the present town of ,adalia4 ,attalia is rarely mentioned by the ancients1 indeed only by ,strabo and ,pliny and no earthquake is spoken of4 ,i think therefore you are justified in assuming that ,leonardo means #adhi4 ,in the elaborate catalogue of earthquakes in the ,east by ,sciale ,dshelal eddin ,sayouthy 7an unpublished ,arabic ,,ms4 in the possession of ,prof4 ,,schefer1 7,membre de l',institut1 ,paris7 mention is made of a terrible earthquake in the year #hfg of the ,mohamedan ,era corresponding to the year #adhi1 and it is there stated that a hundred persons were killed by it in the fortress of ,kerak4 ,there are three places of this name4 ,kerak on the sea of ,tiberias1 ,kerak near ,tahle on the ,libanon1 which ,i visited in the summer of l#hgf--;but neither of these is the place alluded to4 ,possibly it may be the strongly fortified town of ,kerak,kir ,moab1 to the ,west of the ,dead ,sea4 ,there is no notice about this in ,,alexis ,,percy1 ,memoire sur les tremblements de terres ressentis dans la peninsule turco- hellenique et en ,syrie 7,memoires couronnes et memoires des savants etrangers1 ,academie ,royale de ,belgique1 ,tome ,,xxiii74 #aajb4 ,rhodes has in it #ejjj houses4 ,cyprus 7#aajc4 #aajd74 #aajc4 ,,site ,,for ,a ,,temple ,,of ,,venus4 ,you must make steps on four sides1 by which to mount to a meadow formed by nature at the top of a rock which may be hollowed out and supported in front by pilasters and open underneath in a large portico1 ,footnote3 ,see ,pl4 ,,lxxxiii4 ,compare also p4 #cc of this ,vol4 ,the standing male figure at the side is evidently suggested by ,michael ,angelo's ,david4 ,on the same place a slight sketch of horses seems to have been drawn first2 there is no reason for assuming that the text and this sketch1 which have no connection with each other1 are of the same date4 ,sito di ,venere4 ,by this heading ,leonardo appears to mean ,cyprus1 which was always considered by the ancients to be the home and birth place of ,aphrodite 7,kirpic in ,homer74 in which the water may fall into various vases of granite1 porphyryand serpentine1 within semi-circular recesses2 and the water may overflow from these4 ,and round this portico towards the ,north there should be a lake with a little island in the midst of which should be a thick and shady wood2 the waters at the top of the pilasters should pour into vases at their base1 from whence they should flow in little channels4 ,starting from the shore of ,cilicia towards the ,south you discover the beauties of the island of ,cyprus4 ,the ,caspian ,sea 7#aaje4 #aajf74 #aajd4 ,from the shore of the ,southern coast of ,cilicia may be seen to the ,south the beautiful island of ,cyprus1 which was the realm of the goddess ,venus1 and many navigators being attracted by her beauty1 had their ships and rigging broken amidst the reefs1 surrounded by the whirling waters4 ,here the beauty of delightful hills tempts wandering mariners to refresh themselves amidst their flowery verdure1 where the winds are tempered and fill the island and the surrounding seas with fragrant odours4 ,ah6 how many a ship has here been sunk4 ,ah6 how many a vessel broken on these rocks4 ,here might be seen barks without number1 some wrecked and half covered by the sand2 others showing the poop and another the prow1 here a keel and there the ribs2 and it seems like a day of judgment when there should be a resurrection of dead ships1 so great is the number of them covering all the ,northern shore2 and while the ,north gale makes various and fearful noises there4 #aaje4 ,write to ,bartolomeo the ,turk as to the flow and ebb of the ,black sea1 and whether he is aware if there be such a flow and ebb in the ,hyrcanean or ,caspian sea4 ,footnote3 ,the handwriting of this note points to a late date4 #aajf4 ,,why ,,water ,,is ,,found ,,at ,,the ,,top ,,of ,,mountains4 ,from the straits of ,gibraltar to the ,don is #cejj miles1 that is one mile and #a_/f1 giving a fall of one braccio in a mile to any water that moves gently4 ,the ,caspian sea is a great deal higher2 and none of the mountains of ,europe rise a mile above the surface of our seas2 therefore it might be said that the water which is on the summits of our mountains might come from the height of those seas1 and of the rivers which flow into them1 and which are still higher4 ,the sea of ,azov4 #aajg4 ,hence it follows that the sea of ,azov is the highest part of the ,mediterranean sea1 being at a distance of #cejj miles from the ,straits of ,gibraltar1 as is shown by the map for navigation2 and it has #cejj braccia of descent1 that is1 one mile and #a_/f2 therefore it is higher than any mountains which exist in the ,west4 ,footnote3 ,the passage before this1 in the original1 treats of the exit of the waters from ,lakes in general4 ,the ,dardanelles4 #aajh4 ,in the ,bosphorus the ,black ,sea flows always into the ,egean sea1 and the ,egean sea never flows into it4 ,and this is because the ,caspian1 which is #djj miles to the ,east1 with the rivers which pour into it1 always flows through subterranean caves into this sea of ,pontus2 and the ,don does the same as well as the ,danube1 so that the waters of ,pontus are always higher than those of the ,egean2 for the higher always fall towards the lower1 and never the lower towards the higher4 ,constantinople4 #aaji4 ,the bridge of ,pera at ,constantinople1 #dj braccia wide1 #gj braccia high above the water1 #fjj braccia long2 that is #djj over the sea and #bjj on the land1 thus making its own abutments4 ,footnote3 ,see ,pl4 ,,cx ,no4 #a4 ,in #adec by order of ,sultan ,mohamed ,,ii4 the ,golden ,horn was crossed by a pontoon bridge laid on barrels 7see ,joh4 ,dukas' ,history of the ,byzantine ,empire ,,xxxviii p4 #bgi74 --,the biographers of ,michelangelo1 ,vasari as well as ,condivi1 relate that at the time when ,michelangelo suddenly left ,rome1 in #aejf1 he entertained some intention of going to ,constantinople1 there to serve the ,sultan1 who sought to engage him1 by means of certain ,franciscan ,monks1 for the purpose of constructing a bridge to connect ,constantinople with ,pera4 ,see ,,vasari1 ,vite 7ed4 ,sansoni ,,vii1 #afh73 ,michelangelo1 veduto questa furia del papa1 dubitando di lui1 ebbe1 secondo che si dice1 voglia di andarsene in ,gostantinopoli a servire il ,turco1 per mezzo di certi frati di ,san ,francesco1 che desiderava averlo per fare un ponte che passassi da ,gostantinopoli a ,pera4 ,and ,,condivi1 ,vita di ,m4 ,buonaroti chap4 #cj2 ,michelangelo allora vedendosi condotto a questo1 temendo dell'ira del papa1 penso d'andarsene in ,levante2 massimamente essendo stato dal ,turco ricercato con grandissime promesse per mezzo di certi frati di ,san ,francesco1 per volersene servire in fare un ponte da ,costantinopoli a ,pera ed in altri affari4 ,leonardo's plan for this bridge was made in #aejb4 ,we may therefore conclude that at about that time the ,sultan ,bajazet ,,ii4 had either announced a competition in this matter1 or that through his agents ,leonardo had first been called upon to carry out the scheme4 ,the ,euphrates4 #aaaj4 ,if the river will turn to the rift farther on it will never return to its bed1 as the ,euphrates does1 and this may do at ,bologna the one who is disappointed for his rivers4 ,centrae ,asia4 #aaaa4 ,mounts ,caucasus1 ,comedorum1 and ,paropemisidae are joined together between ,bactria and ,india1 and give birth to the river ,oxus which takes its rise in these mountains and flows #ejj miles towards the ,north and as many towards the ,west1 and discharges its waters into the ,caspian sea2 and is accompanied by the ,oxus1 ,dargados1 ,arthamis1 ,xariaspes1 ,dargamaim1 ,ocus and ,margus1 all very large rivers4 ,from the opposite side towards the ,south rises the great river ,indus which sends its waters for #fjj miles ,southwards and receives as tributaries in this course the rivers ,xaradrus1 ,hyphasis1 ,vadris1 ,vandabal ,bislaspus to the ,east1 ,suastes and ,coe to the ,west1 uniting with these rivers1 and with their waters it flows #hjj miles to the ,west2 then1 turning back by the ,arbiti mountains makes an elbow and turns ,southwards1 where after a course of about #ajj miles it finds the ,indian ,sea1 in which it pours itself by seven branches4 ,on the side of the same mountains rises the great ,ganges1 which river flows ,southwards for #ejj miles and to the ,southwest a thousand 444 and ,sarabas1 ,diarnuna1 ,soas and ,scilo1 ,condranunda are its tributaries4 ,it flows into the ,indian sea by many mouths4 ,on the natives of hot countries4 #aaab4 ,men born in hot countries love the night because it refreshes them and have a horror of light because it burns them2 and therefore they are of the colour of night1 that is black4 ,and in cold countries it is just the contrary4 ,footnote3 ,the sketch here inserted is in ,,ms4 ,h#c #ee;b4 ,,xviii4 ,naval ,warfare4--,mechanical ,appliances4--,music4 ,such theoretical questions1 as have been laid before the reader in ,sections ,,xvi and ,,xvii1 though they were the chief subjects of ,leonardo's studies of the sea1 did not exclusively claim his attention4 ,a few passages have been collected at the beginning of this section1 which prove that he had turned his mind to the practical problems of navigation1 and more especially of naval warfare4 ,what we know for certain of his life gives us no data1 it is true1 as to when or where these matters came under his consideration2 but the fact remains certain both from these notes in his manuscripts1 and from the well known letter to ,ludovico il ,moro 7,no4 #acdj71 in which he expressly states that he is as capable as any man1 in this very department4 ,the numerous notes as to the laws and rationale of the flight of birds1 are scattered through several note-books4 ,an account of these is given in the ,bibliography of the manuscripts at the end of this work4 ,it seems probable that the idea which led him to these investigations was his desire to construct a flying or aerial machine for man4 ,at the same time it must be admitted that the notes on the two subjects are quite unconnected in the manuscripts1 and that those on the flight of birds are by far the most numerous and extensive4 ,the two most important passages that treat of the construction of a flying machine are those already published as ,tav4 ,,xvi1 ,no4 #a and ,tav4 ,,xviii in the ,saggio delle opere di ,leonardo da ,vinci 7,milan #ahgb74 ,the passages--,nos4 #aabj-aabe--;here printed for the first time and hitherto unknown--refer to the same subject and1 with the exception of one already published in the ,saggio-- ,no4 #aabf--they are1 so far as ,i know1 the only notes1 among the numerous observations on the flight of birds1 in which the phenomena are incidentally and expressly connected with the idea of a flying machine4 ,the notes on machines of war1 the construction of fortifications1 and similar matters which fall within the department of the ,engineer1 have not been included in this work1 for the reasons given on page #bf of this ,vol4 ,an exception has been made in favour of the passages ,nos4 #aabg and #aabh1 because they have a more general interest1 as bearing on the important question3 whence the ,master derived his knowledge of these matters4 ,though it would be rash to assert that ,leonardo was the first to introduce the science of mining into ,italy1 it may be confidently said that he is one of the earliest writers who can be proved to have known and understood it2 while1 on the other hand1 it is almost beyond doubt that in the ,east at that time1 the whole science of besieging towns and mining in particular1 was far more advanced than in ,europe4 ,this gives a peculiar value to the expressions used in ,no4 #aabg4 ,i have been unable to find in the manuscripts any passage whatever which throws any light on ,leonardo's great reputation as a musician4 ,nothing therein illustrates ,,vasarps well-known statement3 ,avvenne che morto ,giovan ,galeazze duca di ,milano1 e creato ,lodovico ,sforza nel grado medesimo anno #adid1 fu condotto a ,milano con gran riputazione ,lionardo al duca1 il quale molto si dilettava del suono della lira1 perche sonasse2 e ,lionardo porto quello strumento ch'egli aveva di sua mano fabbricato d'argento gran parte1 in forma d'un teschio di cavallo1 cosa bizzarra e nuova1 acciocche l'armonia fosse con maggior tuba e piu sonora di voce2 laonde supero tutti i musici che quivi erano concorsi a sonare4 ,the only notes on musical matters are those given as ,nos4 #aabi and #aacj1 which explain certain arrangements in instruments4 ,the ship's logs of ,vitruvius1 of ,alberti and of ,leonardo #aaac4 ,,on ,,movements2--,,to ,,know ,,how ,,much ,a ,,ship ,,advances ,,in ,,an ,,hour4 ,the ancients used various devices to ascertain the distance gone by a ship each hour1 among which ,vitruvius ,footnote #f3 ,see ,,vitruvius1 ,de ,architectura lib4 ,x4 ,c4 #ad 7p4 #bfd in the edition of ,rose and ,muller- ,strubing74 ,the ,german edition published at ,bale in #aedc has1 on fol4 #eif1 an illustration of the contrivance1 as described by ,vitruvius4 gives one in his work on ,architecture which is just as fallacious as all the others2 and this is a mill wheel which touches the waves of the sea at one end and in each complete revolution describes a straight line which represents the circumference of the wheel extended to a straightness4 ,but this invention is of no worth excepting on the smooth and motionless surface of lakes4 ,but if the water moves together with the ship at an equal rate1 then the wheel remains motionless2 and if the motion of the water is more or less rapid than that of the ship1 then neither has the wheel the same motion as the ship so that this invention is of but little use4 ,there is another method tried by experiment with a known distance between one island and another2 and this is done by a board or under the pressure of wind which strikes on it with more or less swiftness4 ,this is in ,battista ,alberti ,footnote #be3 ,,leon ,,battista ,,alberti1 ,de ,architectura lib4 ,v41 c4 #ab treats 'de le navi e parti loro'1 but there is no reference to the machine1 mentioned by ,leonardo4 ,alberti says here3 ,noi abbiamo trattato lungamente in altro luogo de' modi de le navi1 ma in questo luogo ne abbiamo detto quel tanto che si bisogna4 ,to this the following note is added in the most recent ,italian edition3 ,questo libro e tuttora inedito e porta il titolo1 secondo ,gesnero di ',liber navis'44 ,battista ,alberti's method which is made by experiment on a known distance between one island and another4 ,but such an invention does not succeed excepting on a ship like the one on which the experiment was made1 and it must be of the same burden and have the same sails1 and the sails in the same places1 and the size of the waves must be the same4 ,but my method will serve for any ship1 whether with oars or sails2 and whether it be small or large1 broad or long1 or high or low1 it always serves ,footnote #eb3 ,leonardo does not reveal the method invented by him44 ,methods of staying and moving in water #aaad4 ,how an army ought to cross rivers by swimming with air-bags 444 ,how fishes swim ,footnote #b3 ,compare ,no4 #hba42 of the way in which they jump out of the water1 as may be seen with dolphins2 and it seems a wonderful thing to make a leap from a thing which does not resist but slips away4 ,of the swimming of animals of a long form1 such as eels and the like4 ,of the mode of swimming against currents and in the rapid falls of rivers4 ,of the mode of swimming of fishes of a round form4 ,how it is that animals which have not long hind quartres cannot swim4 ,how it is that all other animals which have feet with toes1 know by nature how to swim1 excepting man4 ,in what way man ought to learn to swim4 ,of the way in which man may rest on the water4 ,how man may protect himself against whirlpools or eddies in the water1 which drag him down4 ,how a man dragged to the bottom must seek the reflux which will throw him up from the depths4 ,how he ought to move his arms4 ,how to swim on his back4 ,how he can and how he cannot stay under water unless he can hold his breath #ac4 ,how by means of a certain machine many people may stay some time under water4 ,how and why ,i do not describe my method of remaining under water1 or how long ,i can stay without eating2 and ,i do not publish nor divulge these by reason of the evil nature of men who would use them as means of destruction at the bottom of the sea1 by sending ships to the bottom1 and sinking them together with the men in them4 ,and although ,i will impart others1 there is no danger in them2 because the mouth of the tube1 by which you breathe1 is above the water supported on bags or corks #ai4 ,footnote3 ,l4 #ac-ai will also be found in ,vol4 ,i ,no4 #a4 ,on naval warfare 7#aaae4 #aaaf74 #aaae4 ,supposing in a battle between ships and galleys that the ships are victorious by reason of the high of heir tops1 you must haul the yard up almost to the top of the mast1 and at the extremity of the yard1 that is the end which is turned towards the enemy1 have a small cage fastened1 wrapped up below and all round in a great mattress full of cotton so that it may not be injured by the bombs2 then1 with the capstan1 haul down the opposite end of this yard and the top on the opposite side will go up so high1 that it will be far above the round-top of the ship1 and you will easily drive out the men that are in it4 ,but it is necessary that the men who are in the galley should go to the opposite side of it so as to afford a counterpoise to the weight of the men placed inside the cage on the yard4 #aaaf4 ,if you want to build an armada for the sea employ these ships to ram in the enemy's ships4 ,that is1 make ships #ajj feet long and #h feet wide1 but arranged so that the left hand rowers may have their oars to the right side of the ship1 and the right hand ones to the left side1 as is shown at ,m1 so that the leverage of the oars may be longer4 ,and the said ship may be one foot and a half thick1 that is made with cross beams within and without1 with planks in contrary directions4 ,and this ship must have attached to it1 a foot below the water1 an iron-shod spike of about the weight and size of an anvil2 and this1 by force of oars may1 after it has given the first blow1 be drawn back1 and driven forward again with fury give a second blow1 and then a third1 and so many as to destroy the other ship4 ,the use of swimming belts4 #aaag4 ,a ,,method ,,of ,,escaping ,,in ,a ,,tempest ,,and ,,shipwreck ,,at ,,sea4 ,have a coat made of leather1 which must be double across the breast1 that is having a hem on each side of about a finger breadth4 ,thus it will be double from the waist to the knee2 and the leather must be quite air-tight4 ,when you want to leap into the sea1 blow out the skirt of your coat through the double hems of the breast2 and jump into the sea1 and allow yourself to be carried by the waves2 when you see no shore near1 give your attention to the sea you are in1 and always keep in your mouth the air-tube which leads down into the coat2 and if now and again you require to take a breath of fresh air1 and the foam prevents you1 you may draw a breath of the air within the coat4 ,footnote3 ,,amoretti1 ,memorie ,storiche1 ,tav4 ,,ii4 ,b4 ,fig4 #e1 gives the same figure1 somewhat altered4 #f4 ,la canna dell' aria4 ,compare ,vol4 ,i4 ,no4 ,i4 ,note ,on the gravity of water4 #aaah4 ,if the weight of the sea bears on its bottom1 a man1 lying on that bottom and having l#jjj braccia of water on his back1 would have enough to crush him4 ,diving apparatus and ,skating 7#aaai-aaba74 #aaai4 ,of walking under water4 ,method of walking on water4 ,footnote3 ,the two sketches belonging to this passage are given by ,,amoretti1 ,memorie ,storiche4 ,tav4 ,,ii1 ,fig4 #c and #d4 #aabj4 ,just as on a frozen river a man may run without moving his feet1 so a car might be made that would slide by itself4 ,footnote3 ,the drawings of carts by the side of this text have no direct connection with the problem as stated in words4--,compare ,no4 #addh1 l4 #ag4 #aaba4 ,a definition as to why a man who slides on ice does not fall4 ,footnote3 ,an indistinct sketch accompanies the passage1 in the original4 ,on ,flying machines 7#aabb-aabf74 #aabb4 ,man when flying must stand free from the waist upwards so as to be able to balance himself as he does in a boat so that the centre of gravity in himself and in the machine may counterbalance each other1 and be shifted as necessity demands for the changes of its centre of resistance4 #aabc4 ,remember that your flying machine must imitate no other than the bat1 because the web is what by its union gives the armour1 or strength to the wings4 ,if you imitate the wings of feathered birds1 you will find a much stronger structure1 because they are pervious2 that is1 their feathers are separate and the air passes through them4 ,but the bat is aided by the web that connects the whole and is not pervious4 #aabd4 ,,to ,,escape ,,the ,,peril ,,of ,,destruction4 ,destruction to such a machine may occur in two ways2 of which the first is the breaking of the machine4 ,the second would be when the machine should turn on its edge or nearly on its edge1 because it ought always to descend in a highly oblique direction1 and almost exactly balanced on its centre4 ,as regards the first--the breaking of the machine--1 that may be prevented by making it as strong as possible2 and in whichever direction it may tend to turn over1 one centre must be very far from the other2 that is1 in a machine #cj braccia long the centres must be #d braccia one from the other4 ,footnote3 ,compare ,no4 #adbh4 #aabe4 ,bags by which a man falling from a height of #f braccia may avoid hurting himself1 by a fall whether into water or on the ground2 and these bags1 strung together like a rosary1 are to be fixed on one's back4 #aabf4 ,an object offers as much resistance to the air as the air does to the object4 ,you may see that the beating of its wings against the air supports a heavy eagle in the highest and rarest atmosphere1 close to the sphere of elemental fire4 ,again you may see the air in motion over the sea1 fill the swelling sails and drive heavily laden ships4 ,from these instances1 and the reasons given1 a man with wings large enough and duly connected might learn to overcome the resistance of the air1 and by conquering it1 succeed in subjugating it and rising above it4 ,footnote3 ,a parachute is here sketched1 with an explanatory remark4 ,it is reproduced on ,tav4 ,,xvi in the ,saggio1 and in3 ,leonardo da ,vinci als ,ingenieur etc41 ,ein ,beitrag zur ,geschichte der ,technik und der induktiven ,wissenschaften1 von ,dr4 ,hermann ,grothe1 ,berlin #ahgd1 p4 #ej4 ,of mining4 #aabg4 ,if you want to know where a mine runs1 place a drum over all the places where you suspect that it is being made1 and upon this drum put a couple of dice1 and when you are over the spot where they are mining1 the dice will jump a little on the drum at every blow which is given underground in the mining4 ,there are persons who1 having the convenience of a river or a lake in their lands1 have made1 close to the place where they suspect that a mine is being made1 a great reservoir of water1 and have countermined the enemy1 and having found them1 have turned the water upon them and destroyed a great number in the mine4 ,of ,greek fire4 #aabh4 ,,greek ,,fire4 ,take charcoal of willow1 and saltpetre1 and sulphuric acid1 and sulphur1 and pitch1 with frankincense and camphor1 and ,ethiopian wool1 and boil them all together4 ,this fire is so ready to burn that it clings to the timbers even under water4 ,and add to this composition liquid varnish1 and bituminous oil1 and turpentine and strong vinegar1 and mix all together and dry it in the sun1 or in an oven when the bread is taken out2 and then stick it round hempen or other tow1 moulding it into a round form1 and studding it all over with very sharp nails4 ,you must leave in this ball an opening to serve as a fusee1 and cover it with rosin and sulphur4 ,again1 this fire1 stuck at the top of a long plank which has one braccio length of the end pointed with iron that it may not be burnt by the said fire1 is good for avoiding and keeping off the ships1 so as not to be overwhelmed by their onset4 ,again throw vessels of glass full of pitch on to the enemy's ships when the men in them are intent on the battle2 and then by throwing similar burning balls upon them you have it in your power to burn all their ships4 ,footnote3 ,venturi has given another short text about the ,greek fire in a ,french translation 7,essai ,section ,,xiv74 ,he adds that the original text is to be found in ,,ms4 ,b4 #cj 7874 ,libri speaks of it in a note as follows 7,histoire des sciences mathematiques en ,italie ,vol4 ,,ii p4 #abi73 ,la composition du feu gregeois est une des chases qui ont ete les plus cherchees et qui sont encore les plus douteuses4 ,on dit qu'il fut invente au septieme siecle de l'ere chretienne par l'architecte ,callinique 7,constantini ,porphyrogenetae opera1 ,lugd4 ,batav4 #afag1-- in-#hvo2 p4 #agb1 de admin1 imper4 exp4 #dh71 et il se trouve souvent mentionne par les ,historiens ,byzantins4 ,tantot on le langait avec des machines1 comme on lancerait une banche1 tantot on le soufflait avec de longs tubes1 comme on soufflerait un gaz ou un liquide enflamme 7,annae ,comnenae ,alexias1 p4 #cce1 lib4 ,,xi4--,aeliani et ,leonis1 imperatoris tactica1 ,lugd4-,bat4 #afac1 in-#d4 part4 #b a1 p4 #cbb1 ,leonis tact4 cap4 l#i4--;,joinville1 histoire du ,saint ,louis collect4 ,petitot tom4 ,,ii1 p4 #bce74 ,les ecrivains contemporains disent que l'eau ne pouvait pas eteindre ce feu1 mais qu'avec du vinaigre et du sable on y parvenait4 ,suivant quelques historiens le feu gregeois etait compose de soufre et de resine4 ,marcus ,graecus 7,liber ignium1 ,paris1 #ahjd1 in-#dj7 donne plusieurs manieres de le faire qui ne sont pas tres intelligibles1 mais parmi lesquelles on trouve la composition de la poudre a canon4 ,leonard de ,vinci 7,,mss4 de ,leonard de ,vinci1 vol4 ,b4 f4 #cj17 dit qu'on le faisait avec du charbon de saule1 du salpetre1 de l'eau de vie1 de la resine1 du soufre1 de la poix et du camphre4 ,mais il est probable que nous ne savons pas qu'elle etait sa composition1 surtout a cause du secret qu'en faisaient les ,grecs4 ,en effet1 l'empereur ,constantin ,porphyrogenete recommende a son fils de ne jamais en donner aux ,barbares1 et de leur repondre1 s'ils en demandaient1 qu'il avait ete apporti du ciel par un ange et que le secret en avait ete confie aux ,chretiens 7,constantini ,porphyrogennetae opera1 p4 #bf-bg1 de admin4 imper41 cap4 #ab74 ,of ,music 7#aabi4 #aacj74 #aabi4 ,a drum with cogs working by wheels with springs #b4 ,footnote3 ,this chapter consists of explanations of the sketches shown on ,pl4 ,,cxxi4 ,lines #a and #b of the text are to be seen at the top at the left hand side of the first sketch of a drum4 ,lines #c-e refer to the sketch immediately below this4 ,line #f is written as the side of the seventh sketch1 and lines #g and #h at the side of the eighth4 ,lines #i-af are at the bottom in the middle4 ,the remainder of the text is at the side of the drawing at the bottom4 ,a square drum of which the parchment may be drawn tight or slackened by the lever a b #e4 ,a drum for harmony #f4 #g ,a clapper for harmony2 that is1 three clappers together4 #i ,just as one and the same drum makes a deep or acute sound according as the parchments are more or less tightened1 so these parchments variously tightened on one and the same drum will make various sounds #af4 ,keys narrow and close together2 7bicchi7 far apart2 these will be right for the trumpet shown above4 a must enter in the place of the ordinary keys which have the 444 in the openings of a flute4 #aacj4 ,tymbals to be played like the monochord1 or the soft flute4 #f ,here there is to be a cylinder of cane after the manner of clappers with a musical round called a ,canon1 which is sung in four parts2 each singer singing the whole round4 ,therefore ,i here make a wheel with #d teeth so that each tooth takes by itself the part of a singer4 ,footnote3 ,in the original there are some more sketches1 to which the text1 from line #f1 refers4 ,they are studies for a contrivance exactly like the cylinder in our musical boxes4 #aaca4 ,of decorations4 ,white and sky-blue cloths1 woven in checks to make a decoration4 ,cloths with the threads drawn at a b c d e f g h i k1 to go round the decoration4 ,,xix4 ,philosophical ,maxims4 ,morals4 ,polemics and ,speculations4 ,vasari indulges in severe strictures on ,leonardo's religious views4 ,he speaks1 among other things1 of his capricci nel filosofar delle cose naturali and says on this point3 ,per il che fece nell'animo un concetto si eretico che e' non si accostava a qualsi voglia religione1 stimando per avventura assai piu lo esser filosofo che cristiano 7see the first edition of ',le ,vite'74 ,but this accusation on the part of a writer in the days of the ,inquisition is not a very serious one--and the less so1 since1 throughout the manuscripts1 we find nothing to support it4 ,under the heading of ,philosophical ,maxims ,i have collected all the passages which can give us a clear comprehension of ,leonardo's ideas of the world at large4 ,it is scarcely necessary to observe that there is absolutely nothing in them to lead to the inference that he was an atheist4 ,his views of nature and its laws are no doubt very unlike those of his contemporaries1 and have a much closer affinity to those which find general acceptance at the present day4 ,on the other hand1 it is obvious from ,leonardo's will 7see ,no4 #aeff7 that1 in the year before his death1 he had professed to adhere to the fundamental doctrines of the ,roman ,catholic faith1 and this evidently from his own personal desire and impulse4 ,the incredible and demonstrably fictitious legend of ,leonardo's death in the arms of ,francis the ,first1 is given1 with others1 by ,vasari and further embellished by this odious comment3 ,mostrava tuttavia quanto avea offeso ,dio e gli uomini del mondo1 non avendo operato nell'arte come si conveniva4 ,this last accusation1 it may be remarked1 is above all evidence of the superficial character of the information which ,vasari was in a position to give about ,leonardo4 ,it seems to imply that ,leonardo was disdainful of diligent labour4 ,with regard to the second1 referring to ,leonardo's morality and dealings with his fellow men1 ,vasari himself nullifies it by asserting the very contrary in several passages4 ,a further refutation may be found in the following sentence from the letter in which ,melsi1 the young ,milanese nobleman1 announces the ,master's death to ,leonardo's brothers3 ,credo siate certificati della morte di ,maestro ,lionardo fratello vostro1 e mio quanto optimo padre1 per la cui morte sarebbe impossibile che io potesse esprimere il dolore che io ho preso2 e in mentre che queste mia membra si sosterranno insieme1 io possedero una perpetua infelicita1 e meritamente perche sviscerato et ardentissimo amore mi portava giornalmente4 ,e dolto ad ognuno la perdita di tal uomo1 quale non e piu in podesta della natura1 ecc4 ,it is true that1 in ,april #adgf1 we find the names of ,leonardo and ,verrocchio entered in the ,libro degli ,uffiziali di notte e de' ,monasteri as breaking the laws2 but we immediately after find the note ,absoluti cum condizione ut retamburentur 7,tamburini was the name given to the warrant cases of the night police74 ,the acquittal therefore did not exclude the possibility of a repetition of the charge4 ,it was in fact repeated1 two months later1 and on this occasion the ,master and his pupil were again fully acquitted4 ,verrocchio was at this time forty and ,leonardo four-and-twenty4 ,the documents referring to this affair are in the ,state ,archives of ,florence2 they have been withheld from publication1 but it seemed to me desirable to give the reader this brief account of the leading facts of the story1 as the vague hints of it1 which have recently been made public1 may have given to the incident an aspect which it had not in reality1 and which it does not deserve4 ,the passages here classed under the head ,morals reveal ,leonardo to us as a man whose life and conduct were unfailingly governed by lofty principles and aims4 ,he could scarcely have recorded his stern reprobation and unmeasured contempt for men who do nothing useful and strive only for riches1 if his own life and ambitions had been such as they have so often been misrepresented4 ,at a period like that1 when superstition still exercised unlimited dominion over the minds not merely of the illiterate crowd1 but of the cultivated and learned classes1 it was very natural that ,leonardo's views as to ,alchemy1 ,ghosts1 ,magicians1 and the like should be met with stern reprobation whenever and wherever he may have expressed them2 this accounts for the argumentative tone of all his utterances on such subjects which ,i have collected in ,subdivision ,,iii of this section4 ,to these ,i have added some passages which throw light on ,leonardo's personal views on the ,universe4 ,they are1 without exception1 characterised by a broad spirit of naturalism of which the principles are more strictly applied in his essays on ,astronomy1 and still more on ,physical ,geography4 ,to avoid repetition1 only such notes on ,philosophy1 ,morals and ,polemics1 have been included in this section as occur as independent texts in the original ,,mss4 ,several moral reflections have already been given in ,vol4 ,i1 in section ,allegorical representations1 ,mottoes and ,emblems4 ,others will be found in the following section4 ,nos4 #i to #ab1 ,vol4 ,i1 are also passages of an argumentative character4 ,it did not seem requisite to repeat here these and similar passages1 since their direct connection with the context is far closer in places where they have appeared already1 than it would be here4 ,i4 ,,philosophical ,,maxims4 ,prayers to ,god 7#aacb4 #aacc74 #aacb4 ,i obey ,thee ,lord1 first for the love ,i ought1 in all reason to bear ,thee2 secondly for that ,thou canst shorten or prolong the lives of men4 #aacc4 ,a ,,prayer4 ,thou1 ,o ,god1 dost sell us all good things at the price of labour4 ,the powers of ,nature 7#aacd-aaci74 #aacd4 ,o admirable impartiality of ,thine1 ,thou first ,mover2 ,thou hast not permitted that any force should fail of the order or quality of its necessary results4 #aace4 ,necessity is the mistress and guide of nature4 ,necessity is the theme and the inventress1 the eternal curb and law of nature4 #aacf4 ,in many cases one and the same thing is attracted by two strong forces1 namely ,necessity and ,potency4 ,water falls in rain2 the earth absorbs it from the necessity for moisture2 and the sun evaporates it1 not from necessity1 but by its power4 #aacg4 ,weight1 force and casual impulse1 together with resistance1 are the four external powers in which all the visible actions of mortals have their being and their end4 #aach4 ,our body is dependant on heaven and heaven on the ,spirit4 #aaci4 ,the motive power is the cause of all life4 ,psychology 7#aadj-aadg74 #aadj4 ,and you1 ,o ,man1 who will discern in this work of mine the wonderful works of ,nature1 if you think it would be a criminal thing to destroy it1 reflect how much more criminal it is to take the life of a man2 and if this1 his external form1 appears to thee marvellously constructed1 remember that it is nothing as compared with the soul that dwells in that structure2 for that indeed1 be it what it may1 is a thing divine4 ,leave it then to dwell in ,his work at ,his good will and pleasure1 and let not your rage or malice destroy a life--for indeed1 he who does not value it1 does not himself deserve it ,footnote #ai3 ,in ,,ms4 ,,ii #ae;a is the note3 chi no stima la vita1 non la merita44 ,footnote3 ,this text is on the back of the drawings reproduced on ,pl4 ,,cvii4 ,compare ,no4 #gih1 #ce note on p4 #aaa3 ,compare also ,no4 #hcg and #hch4 #aada4 ,the soul can never be corrupted with the corruption of the body11 but is in the body as it were the air which causes the sound of the organ1 where when a pipe bursts1 the wind would cease to have any good effect4 ,footnote3 ,compare ,no4 #hde4 #aadb4 ,the part always has a tendency to reunite with its whole in order to escape from its imperfection4 ,the spirit desires to remain with its body1 because1 without the organic instruments of that body1 it can neither act1 nor feel anything4 #aadc4 ,if any one wishes to see how the soul dwells in its body1 let him observe how this body uses its daily habitation2 that is to say1 if this is devoid of order and confused1 the body will be kept in disorder and confusion by its soul4 #aadd4 ,why does the eye see a thing more clearly in dreams than with the imagination being awake8 #aade4 ,the senses are of the earth2 ,reason1 stands apart in contemplation4 ,footnote3 ,compare ,no4 #hdb4 #aadf4 ,every action needs to be prompted by a motive4 ,to know and to will are two operations of the human mind4 ,discerning1 judging1 deliberating are acts of the human mind4 #aadg4 ,all our knowledge has its origin in our preceptions4 ,science1 its principles and rules 7#aadh--aafa7 #aadh4 ,science is the observation of things possible1 whether present or past2 prescience is the knowledge of things which may come to pass1 though but slowly4 #aadi4 ,experience1 the interpreter between formative nature and the human race1 teaches how that nature acts among mortals2 and being constrained by necessity cannot act otherwise than as reason1 which is its helm1 requires her to act4 #aaej4 ,wisdom is the daughter of experience4 #aaea4 ,nature is full of infinite causes that have never occured in experience4 #aaeb4 ,truth was the only daughter of ,time4 #aaec4 ,experience never errs2 it is only your judgments that err by promising themselves effects such as are not caused by your experiments4 ,experience does not err2 only your judgments err by expecting from her what is not in her power4 ,men wrongly complain of ,experience2 with great abuse they accuse her of leading them astray but they set ,experience aside1 turning from it with complaints as to our ignorance causing us to be carried away by vain and foolish desires to promise ourselves1 in her name1 things that are not in her power2 saying that she is fallacious4 ,men are unjust in complaining of innocent ,experience1 constantly accusing her of error and of false evidence4 #aaed4 ,instrumental or mechanical science is of all the noblest and the most useful1 seeing that by means of this all animated bodies that have movement perform all their actions2 and these movements are based on the centre of gravity which is placed in the middle dividing unequal weights1 and it has dearth and wealth of muscles and also lever and counterlever4 #aaee4 ,,of ,,mechanics4 ,mechanics are the ,paradise of mathematical science1 because here we come to the fruits of mathematics4 ,footnote3 ,compare ,no4 #ffj1 #aa4 #ai--bb 7,vol4 ,i41 p4 #ccb74 #aaef4 ,every instrument requires to be made by experience4 #aaeg4 ,the man who blames the supreme certainty of mathematics feeds on confusion1 and can never silence the contradictions of sophistical sciences which lead to an eternal quackery4 #aaeh4 ,there is no certainty in sciences where one of the mathematical sciences cannot be applied1 or which are not in relation with these mathematics4 99999999 ,,text ,,beyond ,,this ,,point ,,still ,,needs ,,some ,,cleanup 99999999 #aaei4 ,any one who in discussion relies upon authority uses1 not his understanding1 but rather his memory4 ,good culture is born of a good disposition2 and since the cause is more to be praised than the effect1 ,i will rather praise a good disposition without culture1 than good culture without the disposition4 #aafj4 ,science is the captain1 and practice the soldiers4 #aafa4 ,,of ,,the ,,errors ,,of ,,those ,,who ,,depend ,,on ,,practice ,,without ,,science4 ,those who fall in love with practice without science are like a sailor who enters a ship without a helm or a compass1 and who never can be certain whither he is going4 ,,ii4 ,,morals4 ,what is life8 7#aafb4 #aafc74 #aafb4 ,now you see that the hope and the desire of returning home and to one's former state is like the moth to the light1 and that the man who with constant longing awaits with joy each new spring time1 each new summer1 each new month and new year--deeming that the things he longs for are ever too late in coming--does not perceive that he is longing for his own destruction4 ,but this desire is the very quintessence1 the spirit of the elements1 which finding itself imprisoned with the soul is ever longing to return from the human body to its giver4 ,and you must know that this same longing is that quintessence1 inseparable from nature1 and that man is the image of the world4 #aafc4 ,o ,time6 consumer of all things2 ,o envious age6 thou dost destroy all things and devour all things with the relentless teeth of years1 little by little in a slow death4 ,helen1 when she looked in her mirror1 seeing the withered wrinkles made in her face by old age1 wept and wondered why she had twice been carried away4 ,o ,time6 consumer of all things1 and ,o envious age6 by which all things are all devoured4 ,death4 #aafd4 ,every evil leaves behind a grief in our memory1 except the supreme evil1 that is death1 which destroys this memory together with life4 ,how to spend life 7#aafe-aagj74 #aafe4 #j sleepers6 what a thing is slumber6 ,sleep resembles death4 ,ah1 why then dost thou not work in such wise as that after death thou mayst retain a resemblance to perfect life1 when1 during life1 thou art in sleep so like to the hapless dead8 ,footnote3 ,compare ,no4 #fgf1 ,vol4 ,i4 p4 #cec4 #aaff4 ,one pushes down the other4 ,by these square-blocks are meant the life and the studies of men4 #aafg4 ,the knowledge of past times and of the places on the earth is both an ornament and nutriment to the human mind4 #aafh4 ,to lie is so vile1 that even if it were in speaking well of godly things it would take off something from ,god's grace2 and ,truth is so excellent1 that if it praises but small things they become noble4 ,beyond a doubt truth bears the same relation to falsehood as light to darkness2 and this truth is in itself so excellent that1 even when it dwells on humble and lowly matters1 it is still infinitely above uncertainty and lies1 disguised in high and lofty discourses2 because in our minds1 even if lying should be their fifth element1 this does not prevent that the truth of things is the chief nutriment of superior intellects1 though not of wandering wits4 ,but you who live in dreams are better pleased by the sophistical reasons and frauds of wits in great and uncertain things1 than by those reasons which are certain and natural and not so far above us4 #aafi4 ,avoid studies of which the result dies with the worker4 #aagj4 ,men are in error when they lament the flight of time1 accusing it of being too swift1 and not perceiving that it is sufficient as it passes2 but good memory1 with which nature has endowed us1 causes things long past to seem present4 #aaga4 ,learning acquired in youth arrests the evil of old age2 and if you understand that old age has wisdom for its food1 you will so conduct yourself in youth that your old age will not lack for nourishment4 #aagb4 ,the acquisition of any knowledge is always of use to the intellect1 because it may thus drive out useless things and retain the good4 ,for nothing can be loved or hated unless it is first known4 #aagc4 ,as a day well spent procures a happy sleep1 so a life well employed procures a happy death4 #aagd4 ,the water you touch in a river is the last of that which has passed1 and the first of that which is coming4 ,thus it is with time present4 ,life if well spent1 is long4 #aage4 ,just as food eaten without caring for it is turned into loathsome nourishment1 so study without a taste for it spoils memory1 by retaining nothing which it has taken in4 #aagf4 ,just as eating against one's will is injurious to health1 so study without a liking for it spoils the memory1 and it retains nothing it takes in4 #aagg4 ,on ,mount ,etna the words freeze in your mouth and you may make ice of them4 ,footnote #b3 ,there is no clue to explain this strange sentence4 ,just as iron rusts unless it is used1 and water putrifies or1 in cold1 turns to ice1 so our intellect spoils unless it is kept in use4 ,you do ill if you praise1 and still worse if you reprove in a matter you do not understand4 ,when ,fortune comes1 seize her in front with a sure hand1 because behind she is bald4 #aagh4 ,it seems to me that men of coarse and clumsy habits and of small knowledge do not deserve such fine instruments nor so great a variety of natural mechanism as men of speculation and of great knowledge2 but merely a sack in which their food may be stowed and whence it may issue1 since they cannot be judged to be any thing else than vehicles for food2 for it seems to me they have nothing about them of the human species but the voice and the figure1 and for all the rest are much below beasts4 #aagi4 ,some there are who are nothing else than a passage for food and augmentors of excrement and fillers of privies1 because through them no other things in the world1 nor any good effects are produced1 since nothing but full privies results from them4 ,on foolishness and ignorance 7#aahj--aahb74 #aahj4 ,the greatest deception men suffer is from their own opinions4 #aaha4 ,folly is the shield of shame1 as unreadiness is that of poverty glorified4 #aahb4 ,blind ignorance misleads us thus and delights with the results of lascivious joys4 ,because it does not know the true light4 ,because it does not know what is the true light4 ,vain splendour takes from us the power of being 4444 behold6 for its vain splendour we go into the fire1 thus blind ignorance does mislead us4 ,that is1 blind ignorance so misleads us that 444 ,o6 wretched mortals1 open your eyes4 ,on riches 7#aahc--aahg74 #aahc4 ,that is not riches1 which may be lost2 virtue is our true good and the true reward of its possessor4 ,that cannot be lost2 that never deserts us1 but when life leaves us4 ,as to property and external riches1 hold them with trembling2 they often leave their possessor in contempt1 and mocked at for having lost them4 #aahd4 ,every man wishes to make money to give it to the doctors1 destroyers of life2 they then ought to be rich4 ,footnote #b3 ,compare ,no4 #hef4 ,man has much power of discourse which for the most part is vain and false2 animals have but little1 but it is useful and true1 and a small truth is better than a great lie4 #aahe4 ,he who possesses most must be most afraid of loss4 #aahf4 ,he who wishes to be rich in a day will be hanged in a year4 #aahg4 ,that man is of supreme folly who always wants for fear of wanting2 and his life flies away while he is still hoping to enjoy the good things which he has with extreme labour acquired4 ,rules of ,life 7#aahh-abjb74 #aahh4 ,if you governed your body by the rules of virtue you would not walk on all fours in this world4 ,you grow in reputation like bread in the hands of a child4 ,footnote3 ,the first sentence is obscure4 ,compare ,nos4 #hbe1 #hbf4 #aahi4 ,savage he is who saves himself4 #aaij4 ,we ought not to desire the impossible4 ,footnote3 ,the writing of this note1 which is exceedingly minute1 is reproduced in facsimile on ,pl4 ,,xli ,no4 #e above the first diagram4 #aaia4 ,ask counsel of him who rules himself well4 ,justice requires power1 insight1 and will2 and it resembles the queen-bee4 ,he who does not punish evil commands it to be done4 ,he who takes the snake by the tail will presently be bitten by it4 ,the grave will fall in upon him who digs it4 #aaib4 ,the man who does not restrain wantonness1 allies himself with beasts4 ,you can have no dominion greater or less than that over yourself4 ,he who thinks little1 errs much4 ,it is easier to contend with evil at the first than at the last4 ,no counsel is more loyal than that given on ships which are in peril3 ,he may expect loss who acts on the advice of an inexperienced youth4 #aaic4 ,where there is most feeling1 there is the greatest martyrdom2--a great martyr4 #aaid4 ,the memory of benefits is a frail defence against ingratitude4 ,reprove your friend in secret and praise him openly4 ,be not false about the past4 #aaie4 ,a ,,simile ,,for ,,patience4 ,patience serves us against insults precisely as clothes do against the cold4 ,for if you multiply your garments as the cold increases1 that cold cannot hurt you2 in the same way increase your patience under great offences1 and they cannot hurt your feelings4 #aaif4 ,to speak well of a base man is much the same as speaking ill of a good man4 #aaig4 ,envy wounds with false accusations1 that is with detraction1 a thing which scares virtue4 #aaih4 ,we are deceived by promises and time disappoints us 444 ,footnote #b3 ,the rest of this passage may be rendered in various ways1 but none of them give a satisfactory meaning4 #aaii4 ,fear arises sooner than any thing else4 #abjj4 ,just as courage imperils life1 fear protects it4 ,threats alone are the weapons of the threatened man4 ,wherever good fortune enters1 envy lays siege to the place and attacks it2 and when it departs1 sorrow and repentance remain behind4 ,he who walks straight rarely falls4 ,it is bad if you praise1 and worse if you reprove a thing1 ,i mean1 if you do not understand the matter well4 ,it is ill to praise1 and worse to reprimand in matters that you do not understand4 #abja4 ,words which do not satisfy the ear of the hearer weary him or vex him1 and the symptoms of this you will often see in such hearers in their frequent yawns2 you therefore1 who speak before men whose good will you desire1 when you see such an excess of fatigue1 abridge your speech1 or change your discourse2 and if you do otherwise1 then instead of the favour you desire1 you will get dislike and hostility4 ,and if you would see in what a man takes pleasure1 without hearing him speak1 change the subject of your discourse in talking to him1 and when you presently see him intent1 without yawning or wrinkling his brow or other actions of various kinds1 you may be certain that the matter of which you are speaking is such as is agreeable to him c4 #abjb4 ,the lover is moved by the beloved object as the senses are by sensible objects2 and they unite and become one and the same thing4 ,the work is the first thing born of this union2 if the thing loved is base the lover becomes base4 ,when the thing taken into union is perfectly adapted to that which receives it1 the result is delight and pleasure and satisfaction4 ,when that which loves is united to the thing beloved it can rest there2 when the burden is laid down it finds rest there4 ,politics 7#abjc4 #abjd74 #abjc4 ,there will be eternal fame also for the inhabitants of that town1 constructed and enlarged by him4 ,footnote3 ,these notes were possibly written in preparation for a letter4 ,the meaning is obscure4 ,all communities obey and are led by their magnates1 and these magnates ally themselves with the lords and subjugate them in two ways3 either by consanguinity1 or by fortune2 by consanguinity1 when their children are1 as it were1 hostages1 and a security and pledge of their suspected fidelity2 by property1 when you make each of these build a house or two inside your city which may yield some revenue and he shall have4442 #aj towns1 five thousand houses with thirty thousand inhabitants1 and you will disperse this great congregation of people which stand like goats one behind the other1 filling every place with fetid smells and sowing seeds of pestilence and death2 ,and the city will gain beauty worthy of its name and to you it will be useful by its revenues1 and the eternal fame of its aggrandizement4 #abjd4 ,to preserve ,nature's chiefest boon1 that is freedom1 ,i can find means of offence and defence1 when it is assailed by ambitious tyrants1 and first ,i will speak of the situation of the walls1 and also ,i shall show how communities can maintain their good and just ,lords4 ,footnote3 ,compare ,no4 #abff4 ,,iii4 ,,polemics4--,,speculation4 ,against ,speculators 7#abje4 #abjf74 #abje4 ,oh6 speculators on things1 boast not of knowing the things that nature ordinarily brings about2 but rejoice if you know the end of those things which you yourself devise4 #abjf4 ,oh6 speculators on perpetual motion how many vain projects of the like character you have created6 ,go and be the companions of the searchers for gold4 ,footnote3 ,another short passage in ,,ms4 ,i1 referring also to speculators1 is given by ,,libri 7,hist1 des ,sciences math4 ,,iii1 #bbh73 ,sicche voi speculatori non vi fidate delli autori che anno sol col immaginatione voluto farsi inter99preti tra la natura e l'omo1 ma sol di quelli che non coi cienni della natura1 ma cogli effetti delle sue esperienze anno esercitati i loro ingegni4 ,against alchemists 7#abjg4 #abjh74 #abjg4 ,the false interpreters of nature declare that quicksilver is the common seed of every metal1 not remembering that nature varies the seed according to the variety of the things she desires to produce in the world4 #abjh4 ,and many have made a trade of delusions and false miracles1 deceiving the stupid multitude4 ,against friars4 #abji4 ,pharisees--that is to say1 friars4 ,footnote3 ,compare ,no4 #hcg1 99#aa4 #ed-eg1 ,no4 #abif 7p4 #cfc and #cfd71 and ,no4 #acje 7p4 #cgj74 ,against writers of epitomes4 #abaj4 ,abbreviators do harm to knowledge and to love1 seeing that the love of any thing is the offspring of this knowledge1 the love being the more fervent in proportion as the knowledge is more certain4 ,and this certainty is born of a complete knowledge of all the parts1 which1 when combined1 compose the totality of the thing which ought to be loved4 ,of what use then is he who abridges the details of those matters of which he professes to give thorough information1 while he leaves behind the chief part of the things of which the whole is composed8 ,it is true that impatience1 the mother of stupidity1 praises brevity1 as if such persons had not life long enough to serve them to acquire a complete knowledge of one single subject1 such as the human body2 and then they want to comprehend the mind of ,god in which the universe is included1 weighing it minutely and mincing it into infinite parts1 as if they had to dissect it6 ,oh6 human stupidity1 do you not perceive that1 though you have been with yourself all your life1 you are not yet aware of the thing you possess most of1 that is of your folly8 and then1 with the crowd of sophists1 you deceive yourselves and others1 despising the mathematical sciences1 in which truth dwells and the knowledge of the things included in them4 ,and then you occupy yourself with miracles1 and write that you possess information of those things of which the human mind is incapable and which cannot be proved by any instance from nature4 ,and you fancy you have wrought miracles when you spoil a work of some speculative mind1 and do not perceive that you are falling into the same error as that of a man who strips a tree of the ornament of its branches covered with leaves mingled with the scented blossoms or fruit4444444 ,footnote #dh3 ,givstino1 ,marcus ,junianus ,justinus1 a ,roman historian of the second century1 who compiled an epitome from the general history written by ,trogus ,pompeius1 who lived in the time of ,augustus4 ,the work of the latter writer no longer exist4 as ,justinus did1 in abridging the histories written by ,trogus ,pompeius1 who had written in an ornate style all the worthy deeds of his forefathers1 full of the most admirable and ornamental passages2 and so composed a bald work worthy only of those impatient spirits1 who fancy they are losing as much time as that which they employ usefully in studying the works of nature and the deeds of men4 ,but these may remain in company of beasts2 among their associates should be dogs and other animals full of rapine and they may hunt with them after44441 and then follow helpless beasts1 which in time of great snows come near to your houses asking alms as from their master4444 ,on spirits 7#abaa--abac74 #abaa4 ,o mathematicians shed light on this error4 ,the spirit has no voice1 because where there is a voice there is a body1 and where there is a body space is occupied1 and this prevents the eye from seeing what is placed behind that space2 hence the surrounding air is filled by the body1 that is by its image4 #abab4 ,there can be no voice where there is no motion or percussion of the air2 there can be no percussion of the air where there is no instrument1 there can be no instrument without a body2 and this being so1 a spirit can have neither voice1 nor form1 nor strength4 ,and if it were to assume a body it could not penetrate nor enter where the passages are closed4 ,and if any one should say that by air1 compressed and compacted together1 a spirit may take bodies of various forms and by this means speak and move with strength--to him ,i reply that when there are neither nerves nor bones there can be no force exercised in any kind of movement made by such imaginary spirits4 ,beware of the teaching of these speculators1 because their reasoning is not confirmed by experience4 #abac4 ,of all human opinions that is to be reputed the most foolish which deals with the belief in ,necromancy1 the sister of ,alchemy1 which gives birth to simple and natural things4 ,but it is all the more worthy of reprehension than alchemy1 because it brings forth nothing but what is like itself1 that is1 lies2 this does not happen in ,alchemy which deals with simple products of nature and whose function cannot be exercised by nature itself1 because it has no organic instruments with which it can work1 as men do by means of their hands1 who have produced1 for instance1 glass c4 but this ,necromancy the flag and flying banner1 blown by the winds1 is the guide of the stupid crowd which is constantly witness to the dazzling and endless effects of this art2 and there are books full1 declaring that enchantments and spirits can work and speak without tongues and without organic instruments-- without which it is impossible to speak-- and can carry heaviest weights and raise storms and rain2 and that men can be turned into cats and wolves and other beasts1 although indeed it is those who affirm these things who first became beasts4 ,and surely if this ,necromancy did exist1 as is believed by small wits1 there is nothing on the earth that would be of so much importance alike for the detriment and service of men1 if it were true that there were in such an art a power to disturb the calm serenity of the air1 converting it into darkness and making coruscations or winds1 with terrific thunder and lightnings rushing through the darkness1 and with violent storms overthrowing high buildings and rooting up forests2 and thus to oppose armies1 crushing and annihilating them2 and1 besides these frightful storms may deprive the peasants of the reward of their labours4--,now what kind of warfare is there to hurt the enemy so much as to deprive him of the harvest8 ,what naval warfare could be compared with this8 ,i say1 the man who has power to command the winds and to make ruinous gales by which any fleet may be submerged1 --surely a man who could command such violent forces would be lord of the nations1 and no human ingenuity could resist his crushing force4 ,the hidden treasures and gems reposing in the body of the earth would all be made manifest to him4 ,no lock nor fortress1 though impregnable1 would be able to save any one against the will of the necromancer4 ,he would have himself carried through the air from ,east to ,west and through all the opposite sides of the universe4 ,but why should ,i enlarge further upon this8 ,what is there that could not be done by such a craftsman8 ,almost nothing1 except to escape death4 ,hereby ,i have explained in part the mischief and the usefulness1 contained in this art1 if it is real2 and if it is real why has it not remained among men who desire it so much1 having nothing to do with any deity8 ,for ,i know that there are numberless people who would1 to satisfy a whim1 destroy ,god and all the universe2 and if this necromancy1 being1 as it were1 so necessary to men1 has not been left among them1 it can never have existed1 nor will it ever exist according to the definition of the spirit1 which is invisible in substance2 for within the elements there are no incorporate things1 because where there is no body1 there is a vacuum2 and no vacuum can exist in the elements because it would be immediately filled up4 ,turn over4 #abad4 ,,of ,,spirits4 ,we have said1 on the other side of this page1 that the definition of a spirit is a power conjoined to a body2 because it cannot move of its own accord1 nor can it have any kind of motion in space2 and if you were to say that it moves itself1 this cannot be within the elements4 ,for1 if the spirit is an incorporeal quantity1 this quantity is called a vacuum1 and a vacuum does not exist in nature2 and granting that one were formed1 it would be immediately filled up by the rushing in of the element in which the vacuum had been generated4 ,therefore1 from the definition of weight1 which is this--,gravity is an accidental power1 created by one element being drawn to or suspended in another--it follows that an element1 not weighing anything compared with itself1 has weight in the element above it and lighter than it2 as we see that the parts of water have no gravity or levity compared with other water1 but if you draw it up into the air1 then it would acquire weight1 and if you were to draw the air beneath the water then the water which remains above this air would acquire weight1 which weight could not sustain itself by itself1 whence collapse is inevitable4 ,and this happens in water2 wherever the vacuum may be in this water it will fall in2 and this would happen with a spirit amid the elements1 where it would continuously generate a vacuum in whatever element it might find itself1 whence it would be inevitable that it should be constantly flying towards the sky until it had quitted these elements4 ,,as ,,to ,,whether ,a ,,spirit ,,has ,a ,,body ,,amid ,,the ,,elements4 ,we have proved that a spirit cannot exist of itself amid the elements without a body1 nor can it move of itself by voluntary motion unless it be to rise upwards4 ,but now we will say how such a spirit taking an aerial body would be inevitably melt into air2 because if it remained united1 it would be separated and fall to form a vacuum1 as is said above2 therefore it is inevitable1 if it is to be able to remain suspended in the air1 that it should absorb a certain quantity of air2 and if it were mingled with the air1 two difficulties arise2 that is to say3 ,it must rarefy that portion of the air with which it mingles2 and for this cause the rarefied air must fly up of itself and will not remain among the air that is heavier than itself2 and besides this the subtle spiritual essence disunites itself1 and its nature is modified1 by which that nature loses some of its first virtue4 ,added to these there is a third difficulty1 and this is that such a body formed of air assumed by the spirits is exposed to the penetrating winds1 which are incessantly sundering and dispersing the united portions of the air1 revolving and whirling amidst the rest of the atmosphere2 therefore the spirit which is infused in this #abae4 air would be dismembered or rent and broken up with the rending of the air into which it was incorporated4 ,,as ,,to ,,whether ,,the ,,spirit1 ,,having ,,taken ,,this ,,body ,,of ,,air1 ,,can ,,move ,,of ,,itself ,,or ,,not4 ,it is impossible that the spirit infused into a certain quantity of air1 should move this air2 and this is proved by the above passage where it is said3 the spirit rarefies that portion of the air in which it incorporates itself2 therefore this air will rise high above the other air and there will be a motion of the air caused by its lightness and not by a voluntary movement of the spirit1 and if this air is encountered by the wind1 according to the #crd of this1 the air will be moved by the wind and not by the spirit incorporated in it4 ,,as ,,to ,,whether ,,the ,,spirit ,,can ,,speak ,,or ,,not4 ,in order to prove whether the spirit can speak or not1 it is necessary in the first place to define what a voice is and how it is generated2 and we will say that the voice is1 as it were1 the movement of air in friction against a dense body1 or a dense body in friction against the air1--which is the same thing4 ,and this friction of the dense and the rare condenses the rare and causes resistance2 again1 the rare1 when in swift motion1 and the rare in slow motion condense each other when they come in contact and make a noise and very great uproar2 and the sound or murmur made by the rare moving through the rare with only moderate swiftness1 like a great flame generating noises in the air2 and the tremendous uproar made by the rare mingling with the rare1 and when that air which is both swift and rare rushes into that which is itself rare and in motion1 it is like the flame of fire which issues from a big gun and striking against the air2 and again when a flame issues from the cloud1 there is a concussion in the air as the bolt is generated4 ,therefore we may say that the spirit cannot produce a voice without movement of the air1 and air in it there is none1 nor can it emit what it has not2 and if desires to move that air in which it is incorporated1 it is necessary that the spirit should multiply itself1 and that cannot multiply which has no quantity4 ,and in the #dth place it is said that no rare body can move1 if it has not a stable spot1 whence it may take its motion2 much more is it so when an element has to move within its own element1 which does not move of itself1 excepting by uniform evaporation at the centre of the thing evaporated2 as occurs in a sponge squeezed in the hand held under water2 the water escapes in every direction with equal movement through the openings between the fingers of the hand in which it is squeezed4 ,as to whether the spirit has an articulate voice1 and whether the spirit can be heard1 and what hearing is1 and seeing2 the wave of the voice passes through the air as the images of objects pass to the eye4 ,nonentity4 #abaf4 ,every quantity is intellectually conceivable as infinitely divisible4 ,amid the vastness of the things among which we live1 the existence of nothingness holds the first place2 its function extends over all things that have no existence1 and its essence1 as regards time1 lies precisely between the past and the future1 and has nothing in the present4 ,this nothingness has the part equal to the whole1 and the whole to the part1 the divisible to the indivisible2 and the product of the sum is the same whether we divide or multiply1 and in addition as in subtraction2 as is proved by arithmeticians by their tenth figure which represents zero2 and its power has not extension among the things of ,nature4 ,what is called ,nothingness is to be found only in time and in speech4 ,in time it stands between the past and future and has no existence in the present2 and thus in speech it is one of the things of which we say3 ,they are not1 or they are impossible4 ,with regard to time1 nothingness lies between the past and the future1 and has nothing to do with the present1 and as to its nature it is to be classed among things impossible3 hence1 from what has been said1 it has no existence2 because where there is nothing there would necessarily be a vacuum4 ,footnote3 ,compare ,no4 #iaf4 ,reflections on ,nature 7#abag-abai74 #abag4 ,,example ,,of ,,the ,,lightning ,,in ,,clouds4 ,o mighty and once living instrument of formative nature4 ,incapable of availing thyself of thy vast strength thou hast to abandon a life of stillness and to obey the law which ,god and time gave to procreative nature4 ,ah6 how many a time the shoals of terrified dolphins and the huge tunny-fish were seen to flee before thy cruel fury1 to escape2 whilst thy fulminations raised in the sea a sudden tempest with buffeting and submersion of ships in the great waves2 and filling the uncovered shores with the terrified and desperate fishes which fled from thee1 and left by the sea1 remained in spots where they became the abundant prey of the people in the neighbourhood4 ,footnote3 ,the character of the handwriting points to an early period of ,leonardo's life4 ,it has become very indistinct1 and is at present exceedingly difficult to decipher4 ,some passages remain doubtful4 ,o time1 swift robber of all created things1 how many kings1 how many nations hast thou undone1 and how many changes of states and of various events have happened since the wondrous forms of this fish perished here in this cavernous and winding recess4 ,now destroyed by time thou liest patiently in this confined space with bones stripped and bare2 serving as a support and prop for the superimposed mountain4 ,footnote3 ,compare ,no4 #acci1 written on the same sheet4 #abah4 ,the watery element was left enclosed between the raised banks of the rivers1 and the sea was seen between the uplifted earth and the surrounding air which has to envelope and enclose the complicated machine of the earth1 and whose mass1 standing between the water and the element of fire1 remained much restricted and deprived of its indispensable moisture2 the rivers will be deprived of their waters1 the fruitful earth will put forth no more her light verdure2 the fields will no more be decked with waving corn2 all the animals1 finding no fresh grass for pasture1 will die and food will then be lacking to the lions and wolves and other beasts of prey1 and to men who after many efforts will be compelled to abandon their life1 and the human race will die out4 ,in this way the fertile and fruitful earth will remain deserted1 arid and sterile from the water being shut up in its interior1 and from the activity of nature it will continue a little time to increase until the cold and subtle air being gone1 it will be forced to end with the element of fire2 and then its surface will be left burnt up to cinder and this will be the end of all terrestrial nature4 ,footnote3 ,compare ,no4 #acci1 written on the same sheet4 #abai4 ,why did nature not ordain that one animal should not live by the death of another8 ,nature1 being inconstant and taking pleasure in creating and making constantly new lives and forms1 because she knows that her terrestrial materials become thereby augmented1 is more ready and more swift in her creating1 than time in his destruction2 and so she has ordained that many animals shall be food for others4 ,nay1 this not satisfying her desire1 to the same end she frequently sends forth certain poisonous and pestilential vapours upon the vast increase and congregation of animals2 and most of all upon men1 who increase vastly because other animals do not feed upon them2 and1 the causes being removed1 the effects would not follow4 ,this earth therefore seeks to lose its life1 desiring only continual reproduction2 and as1 by the argument you bring forward and demonstrate1 like effects always follow like causes1 animals are the image of the world4 ,,xx4 ,humorous ,writings4 ,just as ,michaelangelo's occasional poems reflect his private life as well as the general disposition of his mind1 we may find in the writings collected in this section1 the transcript of ,leonardo's fanciful nature1 and we should probably not be far wrong in assuming1 that he himself had recited these fables in the company of his friends or at the court festivals of princes and patrons4 ,era tanto piacevole nella conversazione-- so relates ,vasari--che tirava a se gli animi delle genti4 ,and ,paulus ,jovius says in his short biography of the artist3 ,fuit ingenio valde comi1 nitido1 liberali1 vultu autem longe venustissimo1 et cum elegantiae omnis deliciarumque maxime theatralium mirificus inventor ac arbiter esset1 ad lyramque scito caneret1 cunctis per omnem aetatem principibus mire placuit4 ,there can be no doubt that the fables are the original offspring of ,leonardo's brain1 and not borrowed from any foreign source2 indeed the schemes and plans for the composition of fables collected in division ,v seem to afford an external proof of this1 if the fables themselves did not render it self-evident4 ,several of them-- for instance ,no4 l#bgi--;are so strikingly characteristic of ,leonardo's views of natural science that we cannot do them justice till we are acquainted with his theories on such subjects2 and this is equally true of the ',prophecies'4 ,i have prefixed to these quaint writings the ',studies on the life and habits of animals' which are singular from their peculiar aphoristic style1 and ,i have transcribed them in exactly the order in which they are written in ,,ms4 ,h4 ,this is one of the very rare instances in which one subject is treated in a consecutive series of notes1 all in one ,,ms41 and ,leonardo has also departed from his ordinary habits1 by occasionally not completing the text on the page it is begun4 ,these brief notes of a somewhat mysterious bearing have been placed here1 simply because they may possibly have been intended to serve as hints for fables or allegories4 ,they can scarcely be regarded as preparatory for a natural history1 rather they would seem to be extracts4 ,on the one hand the names of some of the animals seem to prove that ,leonardo could not here be recording observations of his own2 on the other hand the notes on their habits and life appear to me to dwell precisely on what must have interested him most--so far as it is possible to form any complete estimate of his nature and tastes4 ,in ,no4 #abic lines #a-aj1 we have a sketch of a scheme for grouping the ,prophecies4 ,i have not however availed myself of it as a clue to their arrangement here because1 in the first place1 the texts are not so numerous as to render the suggested classification useful to the reader1 and1 also1 because in reading the long series1 as they occur in the original1 we may follow the author's mind2 and here and there it is not difficult to see how one theme suggested another4 ,i have however regarded ,leonardo's scheme for the classification of the ,prophecies as available for that of the ,fables and ,jests1 and have adhered to it as far as possible4 ,among the humourous writings ,i might perhaps have included the ',rebusses'1 of which there are several in the collection of ,leonardo's drawings at ,windsor2 it seems to me not likely that many or all of them could be solved at the present day and the ,,mss4 throw no light on them4 ,nor should ,i be justified if ,i intended to include in the literary works the well-known caricatures of human faces attributed to ,leonardo-- of which1 however1 it may be incidentally observed1 the greater number are in my opinion undoubtedly spurious4 ,two only have necessarily been given owing to their presence in text1 which it was desired to reproduce3 ,vol4 ,i page #cbf1 and ,pl4 ,,cxxii4 ,it can scarcely be doubted that some satirical intention is conveyed by the drawing on ,pl4 ,,lxiv 7text ,no4 #fhh74 ,my reason for not presenting ,leonardo to the reader as a poet is the fact that the maxims and morals in verse which have been ascribed to him1 are not to be found in the manuscripts1 and ,prof4 ,uzielli has already proved that they cannot be by him4 ,hence it would seem that only a few short verses can be attributed to him with any certainty4 ,i4 ,,studies ,,on ,,the ,,life ,,and ,,habits ,,of ,,animals4 #abbj4 ,,the ,,love ,,of ,,virtue4 ,the gold-finch is a bird of which it is related that1 when it is carried into the presence of a sick person1 if the sick man is going to die1 the bird turns away its head and never looks at him2 but if the sick man is to be saved the bird never loses sight of him but is the cause of curing him of all his sickness4 ,like unto this is the love of virtue4 ,it never looks at any vile or base thing1 but rather clings always to pure and virtuous things and takes up its abode in a noble heart2 as the birds do in green woods on flowery branches4 ,and this ,love shows itself more in adversity than in prosperity2 as light does1 which shines most where the place is darkest4 #abba4 ,,envy4 ,we read of the kite that1 when it sees its young ones growing too big in the nest1 out of envy it pecks their sides1 and keeps them without food4 ,,cheerfulness4 ,cheerfulness is proper to the cock1 which rejoices over every little thing1 and crows with varied and lively movements4 ,,sadness4 ,sadness resembles the raven1 which1 when it sees its young ones born white1 departs in great grief1 and abandons them with doleful lamentations1 and does not feed them until it sees in them some few black feathers4 #abbb4 ,,peace4 ,we read of the beaver that when it is pursued1 knowing that it is for the virtue contained in its medicinal testicles and not being able to escape1 it stops2 and to be at peace with its pursuers1 it bites off its testicles with its sharp teeth1 and leaves them to its enemies4 ,,rage4 ,it is said of the bear that when it goes to the haunts of bees to take their honey1 the bees having begun to sting him he leaves the honey and rushes to revenge himself4 ,and as he seeks to be revenged on all those that sting him1 he is revenged on none2 in such wise that his rage is turned to madness1 and he flings himself on the ground1 vainly exasperating1 by his hands and feet1 the foes against which he is defending himself4 #abbc4 ,,gratitude4 ,the virtue of gratitude is said to be more developed in the birds called hoopoes which1 knowing the benefits of life and food1 they have received from their father and their mother1 when they see them grow old1 make a nest for them and brood over them and feed them1 and with their beaks pull out their old and shabby feathers2 and then1 with a certain herb restore their sight so that they return to a prosperous state4 ,,avarice4 ,the toad feeds on earth and always remains lean2 because it never eats enough3-- it is so afraid lest it should want for earth4 #abbd4 ,,ingratitude4 ,pigeons are a symbol of ingratitude2 for when they are old enough no longer to need to be fed1 they begin to fight with their father1 and this struggle does not end until the young one drives the father out and takes the hen and makes her his own4 ,,cruelty4 ,the basilisk is so utterly cruel that when it cannot kill animals by its baleful gaze1 it turns upon herbs and plants1 and fixing its gaze on them withers them up4 #abbe4 ,,generosity4 ,it is said of the eagle that it is never so hungry but that it will leave a part of its prey for the birds that are round it1 which1 being unable to provide their own food1 are necessarily dependent on the eagle1 since it is thus that they obtain food4 ,,discipline4 ,when the wolf goes cunningly round some stable of cattle1 and by accident puts his foot in a trap1 so that he makes a noise1 he bites his foot off to punish himself for his folly4 #abbf4 ,,flatterers ,,or ,,syrens4 ,the syren sings so sweetly that she lulls the mariners to sleep2 then she climbs upon the ships and kills the sleeping mariners4 ,,prudence4 ,the ant1 by her natural foresight provides in the summer for the winter1 killing the seeds she harvests that they may not germinate1 and on them1 in due time she feeds4 ,,folly4 ,the wild bull having a horror of a red colour1 the hunters dress up the trunk of a tree with red and the bull runs at this with great frenzy1 thus fixing his horns1 and forthwith the hunters kill him there4 #abbg4 ,,justice4 ,we may liken the virtue of ,justice to the king of the bees which orders and arranges every thing with judgment4 ,for some bees are ordered to go to the flowers1 others are ordered to labour1 others to fight with the wasps1 others to clear away all dirt1 others to accompagny99 and escort the king2 and when he is old and has no wings they carry him4 ,and if one of them fails in his duty1 he is punished without reprieve4 ,,truth4 ,although partridges steal each other's eggs1 nevertheless the young born of these eggs always return to their true mother4 #abbh4 ,,fidelity1 ,,or ,,loyalty4 ,the cranes are so faithful and loyal to their king1 that at night1 when he is sleeping1 some of them go round the field to keep watch at a distance2 others remain near1 each holding a stone in his foot1 so that if sleep should overcome them1 this stone would fall and make so much noise that they would wake up again4 ,and there are others which sleep together round the king2 and this they do every night1 changing in turn so that their king may never find them wanting4 ,,falsehood4 ,the fox when it sees a flock of herons or magpies or birds of that kind1 suddenly flings himself on the ground with his mouth open to look as he were dead2 and these birds want to peck at his tongue1 and he bites off their heads4 #abbi4 ,,lies4 ,the mole has very small eyes and it always lives under ground2 and it lives as long as it is in the dark but when it comes into the light it dies immediately1 because it becomes known2--and so it is with lies4 ,,valour4 ,the lion is never afraid1 but rather fights with a bold spirit and savage onslaught against a multitude of hunters1 always seeking to injure the first that injures him4 ,,fear ,,or ,,cowardice4 ,the hare is always frightened2 and the leaves that fall from the trees in autumn always keep him in terror and generally put him to flight4 #abcj4 ,,magnanimity4 ,the falcon never preys but on large birds2 and it will let itself die rather than feed on little ones1 or eat stinking meat4 ,,vain ,,glory4 ,as regards this vice1 we read that the peacock is more guilty of it than any other animal4 ,for it is always contemplating the beauty of its tail1 which it spreads in the form of a wheel1 and by its cries attracts to itself the gaze of the creatures that surround it4 ,and this is the last vice to be conquered4 #abca4 ,,constancy4 ,constancy may be symbolised by the phoenix which1 knowing that by nature it must be resuscitated1 has the constancy to endure the burning flames which consume it1 and then it rises anew4 ,,inconstancy4 ,the swallow may serve for ,inconstancy1 for it is always in movement1 since it cannot endure the smallest discomfort4 ,,continence4 ,the camel is the most lustful animal there is1 and will follow the female for a thousand miles4 ,but if you keep it constantly with its mother or sister it will leave them alone1 so temperate is its nature4 #abcb4 ,,incontinence4 ,the unicorn1 through its intemperance and not knowing how to control itself1 for the love it bears to fair maidens forgets its ferocity and wildness2 and laying aside all fear it will go up to a seated damsel and go to sleep in her lap1 and thus the hunters take it4 ,,humility4 ,we see the most striking example of humility in the lamb which will submit to any animal2 and when they are given for food to imprisoned lions they are as gentle to them as to their own mother1 so that very often it has been seen that the lions forbear to kill them4 #abcc4 ,,pride4 ,the falcon1 by reason of its haughtiness and pride1 is fain to lord it and rule over all the other birds of prey1 and longs to be sole and supreme2 and very often the falcon has been seen to assault the eagle1 the ,queen of birds4 ,,abstinence4 ,the wild ass1 when it goes to the well to drink1 and finds the water troubled1 is never so thirsty but that it will abstain from drinking1 and wait till the water is clear again4 ,,gluttony4 ,the vulture is so addicted to gluttony that it will go a thousand miles to eat a carrion carcase2 therefore is it that it follows armies4 #abcd4 ,,chastity4 ,the turtle-dove is never false to its mate2 and if one dies the other preserves perpetual chastity1 and never again sits on a green bough1 nor ever again drinks of clear water4 ,,unchastity4 ,the bat1 owing to unbridled lust1 observes no universal rule in pairing1 but males with males and females with females pair promiscuously1 as it may happen4 ,,moderation4 ,the ermine out of moderation never eats but once in the day2 it will rather let itself be taken by the hunters than take refuge in a dirty lair1 in order not to stain its purity4 #abce4 ,,the ,,eagle4 ,the eagle when it is old flies so high that it scorches its feathers1 and ,nature allowing that it should renew its youth1 it falls into shallow water 99,footnote #e3 ,the meaning is obscure44 ,and if its young ones cannot bear to gaze on the sun 99,footnote #f3 ,the meaning is obscure4--2 it does not feed them with any bird1 that does not wish to die4 ,animals which much fear it do not approach its nest1 although it does not hurt them4 ,it always leaves part of its prey uneaten4 ,,lumerpa1--,,fame4 ,this is found in ,asia ,major1 and shines so brightly that it absorbs its own shadow1 and when it dies it does not lose this light1 and its feathers never fall out1 but a feather pulled out shines no longer4 #abcf4 ,,the ,,pelican4 ,this bird has a great love for its young2 and when it finds them in its nest dead from a serpent's bite1 it pierces itself to the heart1 and with its blood it bathes them till they return to life4 ,,the ,,salamander4 ,this has no digestive organs1 and gets no food but from the fire1 in which it constantly renews its scaly skin4 ,the salamander1 which renews its scaly skin in the fire1--for virtue4 ,,the ,,cameleon4 ,this lives on air1 and there it is the prey of all the birds2 so in order to be safer it flies above the clouds and finds an air so rarefied that it cannot support the bird that follows it4 ,at that height nothing can go unless it has a gift from ,heaven1 and that is where the chameleon flies4 #abcg4 ,,the ,,alepo1 ,a ,,fish4 ,the fish alepo does not live out of water4 ,,the ,,ostrich4 ,this bird converts iron into nourishment1 and hatches its eggs by its gaze2--,armies under commanders4 ,,the ,,swan4 ,the swan is white without any spot1 and it sings sweetly as it dies1 its life ending with that song4 ,,the ,,stork4 ,this bird1 by drinking saltwater purges itself of distempers4 ,if the male finds his mate unfaithful1 he abandons her2 and when it grows old its young ones brood over it1 and feed it till it dies4 ,h4#a #ad;a #abch4 ,,the ,,grasshopper4 ,this silences the cuckoo with its song4 ,it dies in oil and revives in vinegar4 ,it sings in the greatest heats ,,the ,,bat4 ,the more light there is the blinder this creature becomes2 as those who gaze most at the sun become most dazzled4--,for ,vice1 that cannot remain where ,virtue appears4 ,,the ,,partridge4 ,this bird changes from the female into the male and forgets its former sex2 and out of envy it steals the eggs from others and hatches them1 but the young ones follow the true mother4 ,,the ,,swallow4 ,this bird gives sight to its blind young ones by means of celandine4 ,h4#a #ad;b #abci4 ,,the ,,oyster4--,,for ,,treachery4 ,this creature1 when the moon is full opens itself wide1 and when the crab looks in he throws in a piece of rock or seaweed and the oyster cannot close again1 whereby it serves for food to that crab4 ,this is what happens to him who opens his mouth to tell his secret4 ,he becomes the prey of the treacherous hearer4 ,,the ,,basilisk4--,,cruelty4 ,all snakes flie from this creature2 but the weasel attacks it by means of rue and kills it4 ,,the ,,asp4 ,this carries instantaneous death in its fangs2 and1 that it may not hear the charmer it stops its ears with its tail4 #abdj4 ,,the ,,dragon4 ,this creature entangles itself in the legs of the elephant which falls upon it1 and so both die1 and in its death it is avenged4 ,,the ,,viper4 ,she1 in pairing opens her mouth and at last clenches her teeth and kills her husband4 ,then the young ones1 growing within her body rend her open and kill their mother4 ,,the ,,scorpion4 ,saliva1 spit out when fasting will kill a scorpion4 ,this may be likened to abstinence from greediness1 which removes and heals the ills which result from that gluttony1 and opens the path of virtue4 #abda4 ,,the ,,crocodile4 ,,hypocrisy4 ,this animal catches a man and straightway kills him2 after he is dead1 it weeps for him with a lamentable voice and many tears4 ,then1 having done lamenting1 it cruelly devours him4 ,it is thus with the hypocrite1 who1 for the smallest matter1 has his face bathed with tears1 but shows the heart of a tiger and rejoices in his heart at the woes of others1 while wearing a pitiful face4 ,,the ,,toad4 ,the toad flies from the light of the sun1 and if it is held there by force it puffs itself out so much as to hide its head below and shield itself from the rays4 ,thus does the foe of clear and radiant virtue1 who can only be constrainedly brought to face it with puffed up courage4 #abdb4 ,,the ,,caterpillar4--,,for ,,virtue ,,in ,,general4 ,the caterpillar1 which by means of assiduous care is able to weave round itself a new dwelling place with marvellous artifice and fine workmanship1 comes out of it afterwards with painted and lovely wings1 with which it rises towards ,heaven4 ,,the ,,spider4 ,the spider brings forth out of herself the delicate and ingenious web1 which makes her a return by the prey it takes4 ,footnote3 ,two notes are underneath this text4 ,the first3 'nessuna chosa e da ttemere piu che lla sozza fama' is a repetition of the first line of the text given in ,vol4 ,i ,no4 #fie4 ,the second3 faticha fugga cholla fama in braccio quasi ochultata c is written in red chalk and is evidently an incomplete sentence4 #abdc4 ,,the ,,lion4 ,this animal1 with his thundering roar1 rouses his young the third day after they are born1 teaching them the use of all their dormant senses and all the wild things which are in the wood flee away4 ,this may be compared to the children of ,virtue who are roused by the sound of praise and grow up in honourable studies1 by which they are more and more elevated2 while all that is base flies at the sound1 shunning those who are virtuous4 ,again1 the lion covers over its foot tracks1 so that the way it has gone may not be known to its enemies4 ,thus it beseems a captain to conceal the secrets of his mind so that the enemy may not know his purpose4 #abdd4 ,,the ,,tarantula4 ,the bite of the tarantula fixes a man's mind on one idea2 that is on the thing he was thinking of when he was bitten4 ,,the ,,screech-,,owl ,,and ,,the ,,owl4 ,these punish those who are scoffing at them by pecking out their eyes2 for nature has so ordered it1 that they may thus be fed4 #abde4 ,,the ,,elephant4 ,the huge elephant has by nature what is rarely found in man2 that is ,honesty1 ,prudence1 ,justice1 and the ,observance of ,religion2 inasmuch as when the moon is new1 these beasts go down to the rivers1 and there1 solemnly cleansing themselves1 they bathe1 and so1 having saluted the planet1 return to the woods4 ,and when they are ill1 being laid down1 they fling up plants towards ,heaven as though they would offer sacrifice4 --,they bury their tusks when they fall out from old age4--,of these two tusks they use one to dig up roots for food2 but they save the point of the other for fighting with2 when they are taken by hunters and when worn out by fatigue1 they dig up these buried tusks and ransom themselves4 #abdf4 ,they are merciful1 and know the dangers1 and if one finds a man alone and lost1 he kindly puts him back in the road he has missed1 if he finds the footprints of the man before the man himself4 ,it dreads betrayal1 so it stops and blows1 pointing it out to the other elephants who form in a troop and go warily4 ,these beasts always go in troops1 and the oldest goes in front and the second in age remains the last1 and thus they enclose the troop4 ,out of shame they pair only at night and secretly1 nor do they then rejoin the herd but first bathe in the river4 ,the females do not fight as with other animals2 and it is so merciful that it is most unwilling by nature ever to hurt those weaker than itself4 ,and if it meets in the middle of its way a flock of sheep #abdg4 it puts them aside with its trunk1 so as not to trample them under foot2 and it never hurts any thing unless when provoked4 ,when one has fallen into a pit the others fill up the pit with branches1 earth and stones1 thus raising the bottom that he may easily get out4 ,they greatly dread the noise of swine and fly in confusion1 doing no less harm then1 with their feet1 to their own kind than to the enemy4 ,they delight in rivers and are always wandering about near them1 though on account of their great weight they cannot swim4 ,they devour stones1 and the trunks of trees are their favourite food4 ,they have a horror of rats4 ,flies delight in their smell and settle on their back1 and the beast scrapes its skin making its folds even and kills them4 #abdh4 ,when they cross rivers they send their young ones up against the stream of the water2 thus1 being set towards the fall1 they break the united current of the water so that the current does not carry them away4 ,the dragon flings itself under the elephant's body1 and with its tail it ties its legs2 with its wings and with its arms it also clings round its ribs and cuts its throat with its teeth1 and the elephant falls upon it and the dragon is burst4 ,thus1 in its death it is revenged on its foe4 ,,the ,,dragon4 ,these go in companies together1 and they twine themselves after the manner of roots1 and with their heads raised they cross lakes1 and swim to where they find better pasture2 and if they did not thus combine #abdi4 they would be drowned1 therefore they combine4 ,,the ,,serpent4 ,the serpent is a very large animal4 ,when it sees a bird in the air it draws in its breath so strongly that it draws the birds into its mouth too4 ,marcus ,regulus1 the consul of the ,roman army was attacked1 with his army1 by such an animal and almost defeated4 ,and this animal1 being killed by a catapult1 measured #abc feet1 that is #fd #a_/b braccia and its head was high above all the trees in a wood4 ,,the ,,boa787 ,this is a very large snake which entangles itself round the legs of the cow so that it cannot move and then sucks it1 in such wise that it almost dries it up4 ,in the time of ,claudius the ,emperor1 there was killed1 on the ,vatican ,hill1 #abej4 one which had inside it a boy1 entire1 that it had swallowed4 ,,the ,,macli4--,,caught ,,when ,,asleep4 ,this beast is born in ,scandinavia4 ,it has the shape of a great horse1 excepting that the great length of its neck and of its ears make a difference4 ,it feeds on grass1 going backwards1 for it has so long an upper lip that if it went forwards it would cover up the grass4 ,its legs are all in one piece2 for this reason when it wants to sleep it leans against a tree1 and the hunters1 spying out the place where it is wont to sleep1 saw the tree almost through1 and then1 when it leans against it to sleep1 in its sleep it falls1 and thus the hunters take it4 ,and every other mode of taking it is in vain1 because it is incredibly swift in running4 #abea4 ,,the ,,bison ,,which ,,does ,,injury ,,in ,,its ,,flight4 ,this beast is a native of ,paeonia and has a neck with a mane like a horse4 ,in all its other parts it is like a bull1 excepting that its horns are in a way bent inwards so that it cannot butt2 hence it has no safety but in flight1 in which it flings out its excrement to a distance of #djj braccia in its course1 and this burns like fire wherever it touches4 ,,lions1 ,,pards1 ,,panthers1 ,,tigers4 ,these keep their claws in the sheath1 and never put them out unless they are on the back of their prey or their enemy4 ,,the ,,lioness4 ,when the lioness defends her young from the hand of the hunter1 in order not to be frightened by the spears she keeps her eyes on the ground1 to the end that she may not by her flight leave her young ones prisoners4 #abeb4 ,,the ,,lion4 ,this animal1 which is so terrible1 fears nothing more than the noise of empty carts1 and likewise the crowing of cocks4 ,and it is much terrified at the sight of one1 and looks at its comb with a frightened aspect1 and is strangely alarmed when its face is covered4 ,,the ,,panther ,,in ,,africa4 ,this has the form of the lioness but it is taller on its legs and slimmer and long bodied2 and it is all white and marked with black spots after the manner of rosettes2 and all animals delight to look upon these rosettes1 and they would always be standing round it if it were not for the terror of its face2 #abec4 therefore knowing this1 it hides its face1 and the surrounding animals grow bold and come close1 the better to enjoy the sight of so much beauty2 when suddenly it seizes the nearest and at once devours it4 ,,camels4 ,the ,bactrian have two humps2 the ,arabian one only4 ,they are swift in battle and most useful to carry burdens4 ,this animal is extremely observant of rule and measure1 for it will not move if it has a greater weight than it is used to1 and if it is taken too far it does the same1 and suddenly stops and so the merchants are obliged to lodge there4 #abed4 ,,the ,,tiger4 ,this beast is a native of ,hyrcania1 and it is something like the panther from the various spots on its skin4 ,it is an animal of terrible swiftness2 the hunter when he finds its young ones carries them off hastily1 placing mirrors in the place whence he takes them1 and at once escapes on a swift horse4 ,the panther returning finds the mirrors fixed on the ground and looking into them believes it sees its young2 then scratching with its paws it discovers the cheat4 ,forthwith1 by means of the scent of its young1 it follows the hunter1 and when this hunter sees the tigress he drops one of the young ones and she takes it1 and having carried it to the den she immediately returns to the hunter and does #abee4 the same till he gets into his boat4 ,,catoblepas4 ,it is found in ,ethiopia near to the source ,nigricapo4 ,it is not a very large animal1 is sluggish in all its parts1 and its head is so large that it carries it with difficulty1 in such wise that it always droops towards the ground2 otherwise it would be a great pest to man1 for any one on whom it fixes its eyes dies immediately4 ,footnote3 ,leonardo undoubtedly derived these remarks as to the ,catoblepas from ,pliny1 ,hist4 ,nat4 ,,viii4 #ba 7al4 #cb73 ,apud ,hesperios ,aethiopas fons est ,nigris 7different readings71 ut plerique existimavere1 ,nili caput4-----,juxta hunc fera appellatur catoblepas1 modica alioquin1 ceterisque membris iners1 caput tantum praegrave aegre ferens2 alias internecio humani generis1 omnibus qui oculos ejus videre1 confestim morientibus4 ,aelian1 ,hist4 ,an4 gives a far more minute description of the creature1 but he says that it poisons beasts not by its gaze1 but by its venomous breath4 ,athenaeus #bba ,b1 mentions both4 ,if ,leonardo had known of these two passages1 he would scarcely have omitted the poisonous breath4 7,h4 ,,muller-,,strubing47 ,,the ,,basilisk4 ,this is found in the province of ,cyrenaica and is not more than #ab fingers long4 ,it has on its head a white spot after the fashion of a diadem4 ,it scares all serpents with its whistling4 ,it resembles a snake1 but does not move by wriggling but from the centre forwards to the right4 ,it is said that one #abef4 of these1 being killed with a spear by one who was on horse-back1 and its venom flowing on the spear1 not only the man but the horse also died4 ,it spoils the wheat and not only that which it touches1 but where it breathes the grass dries and the stones are split4 ,,the ,,weasel4 ,this beast finding the lair of the basilisk kills it with the smell of its urine1 and this smell1 indeed1 often kills the weasel itself4 ,,the ,,cerastes4 ,this has four movable little horns2 so1 when it wants to feed1 it hides under leaves all of its body except these little horns which1 as they move1 seem to the birds to be some small worms at play4 ,then they immediately swoop down to pick them and the ,cerastes suddenly twines round them and encircles and devours them4 #abeg4 ,,the ,,amphisboena4 ,this has two heads1 one in its proper place the other at the tail2 as if one place were not enough from which to fling its venom4 ,,the ,,iaculus4 ,this lies on trees1 and flings itself down like a dart1 and pierces through the wild beast and kills them4 ,,the ,,asp4 ,the bite of this animal cannot be cured unless by immediately cutting out the bitten part4 ,this pestilential animal has such a love for its mate that they always go in company4 ,and if1 by mishap1 one of them is killed the other1 with incredible swiftness1 follows him who has killed it2 and it is so determined and eager for vengeance that it overcomes every difficulty1 and passing by every troop it seeks to hurt none but its enemy4 ,and it will travel any distance1 and it is impossible to avoid it unless by crossing water and by very swift flight4 ,it has its eyes turned inwards1 and large ears and it hears better than it sees4 #abeh4 ,,the ,,ichneumon4 ,this animal is the mortal enemy of the asp4 ,it is a native of ,egypt and when it sees an asp near its place1 it runs at once to the bed or mud of the ,nile and with this makes itself muddy all over1 then it dries itself in the sun1 smears itself again with mud1 and thus1 drying one after the other1 it makes itself three or four coatings like a coat of mail4 ,then it attacks the asp1 and fights well with him1 so that1 taking its time it catches him in the throat and destroys him4 ,,the ,,crocodile4 ,this is found in the ,nile1 it has four feet and lives on land and in water4 ,no other terrestrial creature but this is found to have no tongue1 and it only bites by moving its upper jaw4 ,it grows to a length of forty feet and has claws and is armed with a hide that will take any blow4 ,by day it is on land and at night in the water4 ,it feeds on fishes1 and going to sleep on the bank of the ,nile with its mouth open1 a bird called #abei4 trochilus1 a very small bird1 runs at once to its mouth and hops among its teeth and goes pecking out the remains of the food1 and so inciting it with voluptuous delight tempts it to open the whole of its mouth1 and so it sleeps4 ,this being observed by the ichneumon it flings itself into its mouth and perforates its stomach and bowels1 and finally kills it4 ,,the ,,dolphin4 ,nature has given such knowledge to animals1 that besides the consciousness of their own advantages they know the disadvantages of their foes4 ,thus the dolphin understands what strength lies in a cut from the fins placed on his chine1 and how tender is the belly of the crocodile2 hence in fighting with him it thrusts at him from beneath and rips up his belly and so kills him4 ,the crocodile is a terror to those that flee1 and a base coward to those that pursue him4 #abfj4 ,,the ,,hippopotamus4 ,this beast when it feels itself over-full goes about seeking thorns1 or where there may be the remains of canes that have been split1 and it rubs against them till a vein is opened2 then when the blood has flowed as much as he needs1 he plasters himself with mud and heals the wound4 ,in form he is something like a horse with long haunches1 a twisted tail and the teeth of a wild boar1 his neck has a mane2 the skin cannot be pierced1 unless when he is bathing2 he feeds on plants in the fields and goes into them backwards so that it may seem1 as though he had come out4 ,,the ,,ibis4 ,this bird resembles a crane1 and when it feels itself ill it fills its craw with water1 and with its beak makes an injection of it4 ,,the ,,stag4 ,these creatures when they feel themselves bitten by the spider called father-long-legs1 eat crabs and free themselves of the venom4 #abfa4 ,,the ,,lizard4 ,this1 when fighting with serpents eats the sow-thistle and is free4 ,,the ,,swallow4 ,this bird gives sight to its blind young ones1 with the juice of the celandine4 ,,the ,,weasel4 ,this1 when chasing rats first eats of rue4 ,,the ,,wild ,,boar4 ,this beast cures its sickness by eating of ivy4 ,,the ,,snake4 ,this creature when it wants to renew itself casts its old skin1 beginning with the head1 and changing in one day and one night4 ,,the ,,panther4 ,this beast after its bowels have fallen out will still fight with the dogs and hunters4 #abfb4 ,,the ,,chameleon4 ,this creature always takes the colour of the thing on which it is resting1 whence it is often devoured together with the leaves on which the elephant feeds4 ,,the ,,raven4 ,when it has killed the ,chameleon it takes laurel as a purge4 #abfc4 ,moderation checks all the vices4 ,the ermine will die rather than besmirch itself4 ,,of ,,foresight4 ,the cock does not crow till it has thrice flapped its wings2 the parrot in moving among boughs never puts its feet excepting where it has first put its beak4 ,vows are not made till ,hope is dead4 ,motion tends towards the centre of gravity4 #abfd4 ,,magnanimity4 ,the falcon never seizes any but large birds and will sooner die than eat tainted meat of bad savour4 ,,ii4 ,,fables4 ,fables on animals 7#abfe-abgj74 #abfe4 ,a ,,fable4 ,an oyster being turned out together with other fish in the house of a fisherman near the sea1 he entreated a rat to take him to the sea4 ,the rat purposing to eat him bid him open2 but as he bit him the oyster squeezed his head and closed2 and the cat came and killed him4 #abff4 ,a ,,fable4 ,the thrushes rejoiced greatly at seeing a man take the owl and deprive her of liberty1 tying her feet with strong bonds4 ,but this owl was afterwards by means of bird-lime the cause of the thrushes losing not only their liberty1 but their life4 ,this is said for those countries which rejoice in seeing their governors lose their liberty1 when by that means they themselves lose all succour1 and remain in bondage in the power of their enemies1 losing their liberty and often their life4 #abfg4 ,a ,,fable4 ,a dog1 lying asleep on the fur of a sheep1 one of his fleas1 perceiving the odour of the greasy wool1 judged that this must be a land of better living1 and also more secure from the teeth and nails of the dog than where he fed on the dog2 and without farther reflection he left the dog and went into the thick wool4 ,there he began with great labour to try to pass among the roots of the hairs2 but after much sweating had to give up the task as vain1 because these hairs were so close that they almost touched each other1 and there was no space where fleas could taste the skin4 ,hence1 after much labour and fatigue1 he began to wish to return to his dog1 who however had already departed2 so he was constrained after long repentance and bitter tears1 to die of hunger4 #abfh4 ,a ,,fable4 ,the vain and wandering butterfly1 not content with being able to fly at its ease through the air1 overcome by the tempting flame of the candle1 decided to fly into it2 but its sportive impulse was the cause of a sudden fall1 for its delicate wings were burnt in the flame4 ,and the hapless butterfly having dropped1 all scorched1 at the foot of the candlestick1 after much lamentation and repentance1 dried the tears from its swimming eyes1 and raising its face exclaimed3 ,o false light6 how many must thou have miserably deceived in the past1 like me2 or if ,i must indeed see light so near1 ought ,i not to have known the sun from the false glare of dirty tallow8 ,a ,,fable4 ,the monkey1 finding a nest of small birds1 went up to it greatly delighted4 ,but they1 being already fledged1 he could only succeed in taking the smallest2 greatly delighted he took it in his hand and went to his abode2 and having begun to look at the little bird he took to kissing it1 and from excess of love he kissed it so much and turned it about and squeezed it till he killed it4 ,this is said for those who by not punishing their children let them come to mischief4 #abfi4 ,a ,,fable4 ,a rat was besieged in his little dwelling by a weasel1 which with unwearied vigilance awaited his surrender1 while watching his imminent peril through a little hole4 ,meanwhile the cat came by and suddenly seized the weasel and forthwith devoured it4 ,then the rat offered up a sacrifice to ,jove of some of his store of nuts1 humbly thanking ,his providence1 and came out of his hole to enjoy his lately lost liberty4 ,but he was instantly deprived of it1 together with his life1 by the cruel claws and teeth of the lurking cat4 #abgj4 ,a ,,fable4 ,the ant found a grain of millet4 ,the seed feeling itself taken prisoner cried out to her3 ,if you will do me the kindness to allow me accomplish my function of reproduction1 ,i will give you a hundred such as ,i am4 ,and so it was4 ,a ,spider found a bunch of grapes which for its sweetness was much resorted to by bees and divers kinds of flies4 ,it seemed to her that she had found a most convenient spot to spread her snare1 and having settled herself on it with her delicate web1 and entered into her new habitation1 there1 every day placing herself in the openings made by the spaces between the grapes1 she fell like a thief on the wretched creatures which were not aware of her4 ,but1 after a few days had passed1 the vintager came1 and cut away the bunch of grapes and put it with others1 with which it was trodden2 and thus the grapes were a snare and pitfall both for the treacherous spider and the betrayed flies4 ,an ass having gone to sleep on the ice over a deep lake1 his heat dissolved the ice and the ass awoke under water to his great grief1 and was forthwith drowned4 ,a falcon1 unable to endure with patience the disappearance of a duck1 which1 flying before him had plunged under water1 wished to follow it under water1 and having soaked his feathers had to remain in the water while the duck rising to the air mocked at the falcon as he drowned4 ,the spider wishing to take flies in her treacherous net1 was cruelly killed in it by the hornet4 ,an eagle wanting to mock at the owl was caught by the wings in bird-lime and was taken and killed by a man4 ,fables on lifeless objects 7#abga--abgd74 #abga4 ,the water finding that its element was the lordly ocean1 was seized with a desire to rise above the air1 and being encouraged by the element of fire and rising as a very subtle vapour1 it seemed as though it were really as thin as air4 ,but having risen very high1 it reached the air that was still more rare and cold1 where the fire forsook it1 and the minute particles1 being brought together1 united and became heavy2 whence its haughtiness deserting it1 it betook itself to flight and it fell from the sky1 and was drunk up by the dry earth1 where1 being imprisoned for a long time1 it did penance for its sin4 ,c4,a4 #agb;b2 #eaf;b #abgb4 ,a ,,fable4 ,the razor having one day come forth from the handle which serves as its sheath and having placed himself in the sun1 saw the sun reflected in his body1 which filled him with great pride4 ,and turning it over in his thoughts he began to say to himself3 ,and shall ,i return again to that shop from which ,i have just come8 ,certainly not2 such splendid beauty shall not1 please ,god1 be turned to such base uses4 ,what folly it would be that could lead me to shave the lathered beards of rustic peasants and perform such menial service6 ,is this body destined for such work8 ,certainly not4 ,i will hide myself in some retired spot and there pass my life in tranquil repose4 ,and having thus remained hidden for some months1 one day he came out into the air1 and issuing from his sheath1 saw himself turned to the similitude of a rusty saw while his surface no longer reflected the resplendent sun4 ,with useless repentance he vainly deplored the irreparable mischief saying to himself3 ,oh6 how far better was it to employ at the barbers my lost edge of such exquisite keenness6 ,where is that lustrous surface8 ,it has been consumed by this vexatious and unsightly rust4 ,the same thing happens to those minds which instead of exercise give themselves up to sloth4 ,they are like the razor here spoken of1 and lose the keenness of their edge1 while the rust of ignorance spoils their form4 ,a ,,fable4 ,a stone of some size recently uncovered by the water lay on a certain spot somewhat raised1 and just where a delightful grove ended by a stony road2 here it was surrounded by plants decorated by various flowers of divers colours4 ,and as it saw the great quantity of stones collected together in the roadway below1 it began to wish it could let itself fall down there1 saying to itself3 ,what have ,i to do here with these plants8 ,i want to live in the company of those1 my sisters4 ,and letting itself fall1 its rapid course ended among these longed for companions4 ,when it had been there sometime it began to find itself constantly toiling under the wheels of the carts the iron-shoed feet of horses and of travellers4 ,this one rolled it over1 that one trod upon it2 sometimes it lifted itself a little and then it was covered with mud or the dung of some animal1 and it was in vain that it looked at the spot whence it had come as a place of solitude and tranquil place4 ,thus it happens to those who choose to leave a life of solitary comtemplation1 and come to live in cities among people full of infinite evil4 #abgc4 ,some flames had already lasted in the furnace of a glass-blower1 when they saw a candle approaching in a beautiful and glittering candlestick4 ,with ardent longing they strove to reach it2 and one of them1 quitting its natural course1 writhed up to an unburnt brand on which it fed and passed at the opposite end out by a narrow chink to the candle which was near4 ,it flung itself upon it1 and with fierce jealousy and greediness it devoured it1 having reduced it almost to death1 and1 wishing to procure the prolongation of its life1 it tried to return to the furnace whence it had come4 ,but in vain1 for it was compelled to die1 the wood perishing together with the candle1 being at last converted1 with lamentation and repentance1 into foul smoke1 while leaving all its sisters in brilliant and enduring life and beauty4 #abgd4 ,a small patch of snow finding itself clinging to the top of a rock which was lying on the topmost height of a very high mountain and being left to its own imaginings1 it began to reflect in this way1 saying to itself3 ,now1 shall not ,i be thought vain and proud for having placed myself--such a small patch of snow--in so lofty a spot1 and for allowing that so large a quantity of snow as ,i have seen here around me1 should take a place lower than mine8 ,certainly my small dimensions by no means merit this elevation4 ,how easily may ,i1 in proof of my insignificance1 experience the same fate as that which the sun brought about yesterday to my companions1 who were all1 in a few hours1 destroyed by the sun4 ,and this happened from their having placed themselves higher than became them4 ,i will flee from the wrath of the sun1 and humble myself and find a place befitting my small importance4 ,thus1 flinging itself down1 it began to descend1 hurrying from its high home on to the other snow2 but the more it sought a low place the more its bulk increased1 so that when at last its course was ended on a hill1 it found itself no less in size than the hill which supported it2 and it was the last of the snow which was destroyed that summer by the sun4 ,this is said for those who1 humbling themselves1 become exalted4 ,fables on plants 7#abge-abgi74 #abge4 ,the cedar1 being desirous of producing a fine and noble fruit at its summit1 set to work to form it with all the strength of its sap4 ,but this fruit1 when grown1 was the cause of the tall and upright tree-top being bent over4 ,the peach1 being envious of the vast quantity of fruit which she saw borne on the nut-tree1 her neighbour1 determined to do the same1 and loaded herself with her own in such a way that the weight of the fruit pulled her up by the roots and broke her down to the ground4 ,the nut-tree stood always by a road side displaying the wealth of its fruit to the passers by1 and every one cast stones at it4 ,the fig-tree1 having no fruit1 no one looked at it2 then1 wishing to produce fruits that it might be praised by men1 it was bent and broken down by them4 ,the fig-tree1 standing by the side of the elm and seeing that its boughs were bare of fruit1 yet that it had the audacity to keep the ,sun from its own unripe figs with its branches1 said to it3 ,oh elm6 art thou not ashamed to stand in front of me4 ,but wait till my offspring are fully grown and you will see where you are6 ,but when her offspring were mature1 a troop of soldiers coming by fell upon the fig-tree and her figs were all torn off her1 and her boughs cut away and broken4 ,then1 when she was thus maimed in all her limbs1 the elm asked her1 saying3 ,o fig-tree6 which was best1 to be without offspring1 or to be brought by them into so miserable a plight6 #abgf4 ,the plant complains of the old and dry stick which stands by its side and of the dry stakes that surround it4 ,one keeps it upright1 the other keeps it from low company4 #abgg4 ,a ,,fable4 ,a nut1 having been carried by a crow to the top of a tall campanile and released by falling into a chink from the mortal grip of its beak1 it prayed the wall by the grace bestowed on it by ,god in allowing it to be so high and thick1 and to own such fine bells and of so noble a tone1 that it would succour it1 and that1 as it had not been able to fall under the verdurous boughs of its venerable father and lie in the fat earth covered up by his fallen leaves it would not abandon it2 because1 finding itself in the beak of the cruel crow1 it had there made a vow that if it escaped from her it would end its life in a little hole4 ,at these words the wall1 moved to compassion1 was content to shelter it in the spot where it had fallen2 and after a short time the nut began to split open and put forth roots between the rifts of the stones and push them apart1 and to throw out shoots from its hollow shell2 and1 to be brief1 these rose above the building and the twisted roots1 growing thicker1 began to thrust the walls apart1 and tear out the ancient stones from their old places4 ,then the wall too late and in vain bewailed the cause of its destruction and in a short time1 it wrought the ruin of a great part of it4 #abgh4 ,a ,,fable4 ,the privet feeling its tender boughs loaded with young fruit1 pricked by the sharp claws and beak of the insolent blackbird1 complained to the blackbird with pitious remonstrance entreating her that since she stole its delicious fruits she should not deprive it of the leaves with which it preserved them from the burning rays of the sun1 and that she should not divest it of its tender bark by scratching it with her sharp claws4 ,to which the blackbird replied with angry upbraiding3 ,o1 be silent1 uncultured shrub6 ,do you not know that ,nature made you produce these fruits for my nourishment2 do you not see that you are in the world only to serve me as food2 do you not know1 base creature1 that next winter you will be food and prey for the ,fire8 ,to which words the tree listened patiently1 and not without tears4 ,after a short time the blackbird was taken in a net and boughs were cut to make a cage1 in which to imprison her4 ,branches were cut1 among others from the pliant privet1 to serve for the small rods of the cage2 and seeing herself to be the cause of the ,blackbird's loss of liberty it rejoiced and spoke as follows3 ,o ,blackbird1 ,i am here1 and not yet burnt by fire as you said4 ,i shall see you in prison before you see me burnt4 ,a ,,fable4 ,the laurel and the myrtle seeing the pear tree cut down cried out with a loud voice3 ,o pear-tree6 whither are you going8 ,where is the pride you had when you were covered with ripe fruits8 ,now you will no longer shade us with your mass of leaves4 ,then the pear-tree replied3 ,i am going with the husbandman who has cut me down and who will take me to the workshop of a good sculptor who by his art will make me take the form of ,jove the god2 and ,i shall be dedicated in a temple and adored by men in the place of ,jove1 while you are bound always to remain maimed and stripped of your boughs1 which will be placed round me to do me honour4 ,a ,,fable4 ,the chesnut1 seeing a man upon the fig-tree1 bending its boughs down and pulling off the ripe fruits1 which he put into his open mouth destroying and crushing them with his hard teeth1 it tossed its long boughs and with a noisy rustle exclaimed3 ,o fig6 how much less are you protected by nature than ,i4 ,see how in me my sweet offspring are set in close array2 first clothed in soft wrappers over which is the hard but softly lined husk2 and not content with taking this care of me1 and having given them so strong a shelter1 on this she has placed sharp and close-set spines so that the hand of man cannot hurt me4 ,then the fig-tree and her offspring began to laugh and having laughed she said3 ,i know man to be of such ingenuity that with rods and stones and stakes flung up among your branches he will bereave you of your fruits2 and when they are fallen1 he will trample them with his feet or with stones1 so that your offspring will come out of their armour1 crushed and maimed2 while ,i am touched carefully by their hands1 and not like you with sticks and stones4 #abgi4 ,the hapless willow1 finding that she could not enjoy the pleasure of seeing her slender branches grow or attain to the height she wished1 or point to the sky1 by reason of the vine and whatever other trees that grew near1 but was always maimed and lopped and spoiled1 brought all her spirits together and gave and devoted itself entirely to imagination1 standing plunged in long meditation and seeking1 in all the world of plants1 with which of them she might ally herself and which could not need the help of her withes4 ,having stood for some time in this prolific imagination1 with a sudden flash the gourd presented itself to her thoughts and tossing all her branches with extreme delight1 it seemed to her that she had found the companion suited to her purpose1 because the gourd is more apt to bind others than to need binding2 having come to this conclusion she awaited eagerly some friendly bird who should be the mediator of her wishes4 ,presently seeing near her the magpie she said to him3 ,o gentle bird6 by the memory of the refuge which you found this morning among my branches1 when the hungry cruel1 and rapacious falcon wanted to devour you1 and by that repose which you have always found in me when your wings craved rest1 and by the pleasure you have enjoyed among my boughs1 when playing with your companions or making love--,i entreat you find the gourd and obtain from her some of her seeds1 and tell her that those that are born of them ,i will treat exactly as though they were my own flesh and blood2 and in this way use all the words you can think of1 which are of the same persuasive purport2 though1 indeed1 since you are a master of language1 ,i need not teach you4 ,and if you will do me this service ,i shall be happy to have your nest in the fork of my boughs1 and all your family without payment of any rent4 ,then the magpie1 having made and confirmed certain new stipulations with the willow1--and principally that she should never admit upon her any snake or polecat1 cocked his tail1 and put down his head1 and flung himself from the bough1 throwing his weight upon his wings2 and these1 beating the fleeting air1 now here1 now there1 bearing about inquisitively1 while his tail served as a rudder to steer him1 he came to a gourd2 then with a handsome bow and a few polite words1 he obtained the required seeds1 and carried them to the willow1 who received him with a cheerful face4 ,and when he had scraped away with his foot a small quantity of the earth near the willow1 describing a circle1 with his beak he planted the grains1 which in a short time began to grow1 and by their growth and the branches to take up all the boughs of the willow1 while their broad leaves deprived it of the beauty of the sun and sky4 ,and not content with so much evil1 the gourds next began1 by their rude hold1 to drag the ends of the tender shoots down towards the earth1 with strange twisting and distortion4 ,then1 being much annoyed1 it shook itself in vain to throw off the gourd4 ,after raving for some days in such plans vainly1 because the firm union forbade it1 seeing the wind come by it commended itself to him4 ,the wind flew hard and opened the old and hollow stem of the willow in two down to the roots1 so that it fell into two parts4 ,in vain did it bewail itself recognising that it was born to no good end4 ,,iii4 ,,jests ,,and ,,tales4 ,c4 ,a4 #aag;a2 #cfa;a #abhj4 ,a ,,jest4 ,a priest1 making the rounds of his parish on ,easter ,eve1 and sprinkling holy water in the houses as is customary1 came to a painter's room1 where he sprinkled the water on some of his pictures4 ,the painter turned round1 somewhat angered1 and asked him why this sprinkling had been bestowed on his pictures2 then said the priest1 that it was the custom and his duty to do so1 and that he was doing good2 and that he who did good might look for good in return1 and1 indeed1 for better1 since ,god had promised that every good deed that was done on earth should be rewarded a hundred-fold from above4 ,then the painter1 waiting till he went out1 went to an upper window and flung a large pail of water on the priest's back1 saying3 ,here is the reward a hundred-fold from above1 which you said would come from the good you had done me with your holy water1 by which you have damaged my pictures4 #abha4 ,when wine is drunk by a drunkard1 that wine is revenged on the drinker4 #abhb4 ,wine1 the divine juice of the grape1 finding itself in a golden and richly wrought cup1 on the table of ,mahomet1 was puffed up with pride at so much honour2 when suddenly it was struck by a contrary reflection1 saying to itself3 ,what am ,i about1 that ,i should rejoice1 and not perceive that ,i am now near to my death and shall leave my golden abode in this cup to enter into the foul and fetid caverns of the human body1 and to be transmuted from a fragrant and delicious liquor into a foul and base one4 ,nay1 and as though so much evil as this were not enough1 ,i must for a long time lie in hideous receptacles1 together with other fetid and corrupt matter1 cast out from human intestines4 ,and it cried to ,heaven1 imploring vengeance for so much insult1 and that an end might henceforth be put to such contempt2 and that1 since that country produced the finest and best grapes in the whole world1 at least they should not be turned into wine4 ,then ,jove made that wine drunk by ,mahomet to rise in spirit to his brain2 and that in so deleterious a manner that it made him mad1 and gave birth to so many follies that when he had recovered himself1 he made a law that no ,asiatic should drink wine1 and henceforth the vine and its fruit were left free4 ,as soon as wine has entered the stomach it begins to ferment and swell2 then the spirit of that man begins to abandon his body1 rising as it were skywards1 and the brain finds itself parting from the body4 ,then it begins to degrade him1 and make him rave like a madman1 and then he does irreparable evil1 killing his friends4 #abhc4 ,an artizan often going to visit a great gentleman without any definite purpose1 the gentleman asked him what he did this for4 ,the other said that he came there to have a pleasure which his lordship could not have2 since to him it was a satisfaction to see men greater than himself1 as is the way with the populace2 while the gentleman could only see men of less consequence than himself2 and so lords and great men were deprived of that pleasure4 #abhd4 ,franciscan begging ,friars are wont1 at certain times1 to keep fasts1 when they do not eat meat in their convents4 ,but on journeys1 as they live on charity1 they have license to eat whatever is set before them4 ,now a couple of these friars on their travels1 stopped at an inn1 in company with a certain merchant1 and sat down with him at the same table1 where1 from the poverty of the inn1 nothing was served to them but a small roast chicken4 ,the merchant1 seeing this to be but little even for himself1 turned to the friars and said3 ,if my memory serves me1 you do not eat any kind of flesh in your convents at this season4 ,at these words the friars were compelled by their rule to admit1 without cavil1 that this was the truth2 so the merchant had his wish1 and eat the chicken and the friars did the best they could4 ,after dinner the messmates departed1 all three together1 and after travelling some distance they came to a river of some width and depth4 ,all three being on foot--the friars by reason of their poverty1 and the other from avarice--it was necessary by the custom of company that one of the friars1 being barefoot1 should carry the merchant on his shoulders3 so having given his wooden shoes into his keeping1 he took up his man4 ,but it so happened that when the friar had got to the middle of the river1 he again remembered a rule of his order1 and stopping short1 he looked up1 like ,saint ,christopher1 to the burden on his back and said3 ,tell me1 have you any money about you8--,you know ,i have1 answered the other1 ,how do you suppose that a ,merchant like me should go about otherwise8 ,alack6 cried the friar1 our rules forbid as to carry any money on our persons1 and forthwith he dropped him into the water1 which the merchant perceived was a facetious way of being revenged on the indignity he had done them2 so1 with a smiling face1 and blushing somewhat with shame1 he peaceably endured the revenge4 #abhe4 ,a ,,jest4 ,a man wishing to prove1 by the authority of ,pythagoras1 that he had formerly been in the world1 while another would not let him finish his argument1 the first speaker said to the second3 ,it is by this token that ,i was formerly here1 ,i remember that you were a miller4 ,the other one1 feeling himself stung by these words1 agreed that it was true1 and that by the same token he remembered that the speaker had been the ass that carried the flour4 ,a ,,jest4 ,it was asked of a painter why1 since he made such beautiful figures1 which were but dead things1 his children were so ugly2 to which the painter replied that he made his pictures by day1 and his children by night4 #abhf4 ,a man saw a large sword which another one wore at his side4 ,said he ,poor fellow1 for a long time ,i have seen you tied to that weapon2 why do you not release yourself as your hands are untied1 and set yourself free8 ,to which the other replied3 ,this is none of yours1 on the contrary it is an old story4 ,the former speaker1 feeling stung1 replied3 ,i know that you are acquainted with so few things in this world1 that ,i thought anything ,i could tell you would be new to you4 #abhg4 ,a man gave up his intimacy with one of his friends because he often spoke ill of his other friends4 ,the neglected friend one day lamenting to this former friend1 after much complaining1 entreated him to say what might be the cause that had made him forget so much friendship4 ,to which he answered3 ,i will no longer be intimate with you because ,i love you1 and ,i do not choose that you1 by speaking ill of me1 your friend1 to others1 should produce in others1 as in me1 a bad impression of yourself1 by speaking evil to them of me1 your friend4 ,therefore1 being no longer intimate together1 it will seem as though we had become enemies2 and in speaking evil of me1 as is your wont1 you will not be blamed so much as if we continued intimate4 #abhh4 ,a man was arguing and boasting that he knew many and various tricks4 ,another among the bystanders said3 ,i know how to play a trick which will make whomsoever ,i like pull off his breeches4 ,the first man-- the boaster--said3 ,you won't make me pull off mine1 and ,i bet you a pair of hose on it4 ,he who proposed the game1 having accepted the offer1 produced breeches and drew them across the face of him who bet the pair of hose and won the bet #d4 ,a man said to an acquaintance3 ,your eyes are changed to a strange colour4 ,the other replied3 ,it often happens1 but you have not noticed it4 ,when does it happen8 said the former4 ,every time that my eyes see your ugly face1 from the shock of so unpleasing a sight they suddenly turn pale and change to a strange colour4 ,a man said to another3 ,your eyes are changed to a strange colour4 ,the other replied3 ,it is because my eyes behold your strange ugly face4 ,a man said that in his country were the strangest things in the world4 ,another answered3 ,you1 who were born there1 confirm this as true1 by the strangeness of your ugly face4 ,footnote3 ,the joke turns1 it appears1 on two meanings of trarre and is not easily translated4 #abhi4 ,an old man was publicly casting contempt on a young one1 and boldly showing that he did not fear him2 on which the young man replied that his advanced age served him better as a shield than either his tongue or his strength4 #abij4 ,a ,,jest4 ,a sick man finding himself in articulo mortis heard a knock at the door1 and asking one of his servants who was knocking1 the servant went out1 and answered that it was a woman calling herself ,madonna ,bona4 ,then the sick man lifting his arms to ,heaven thanked ,god with a loud voice1 and told the servants that they were to let her come in at once1 so that he might see one good woman before he died1 since in all his life he had never yet seen one4 #abia4 ,a ,,jest4 ,a man was desired to rise from bed1 because the sun was already risen4 ,to which he replied3 ,if ,i had as far to go1 and as much to do as he has1 ,i should be risen by now2 but having but a little way to go1 ,i shall not rise yet4 #abib4 ,a man1 seeing a woman ready to hold up the target for a jousting match1 exclaimed1 looking at the shield1 and considering his spear3 ,alack6 this is too small a workman for so great a business4 ,,iv4 ,,prophecies4 #abic4 ,,the ,,division ,,of ,,the ,,prophecies4 ,first1 of things relating to animals2 secondly1 of irrational creatures2 thirdly of plants2 fourthly1 of ceremonies2 fifthly1 of manners2 sixthly1 of cases or edicts or quarrels2 seventhly1 of cases that are impossible in nature paradoxes1 as1 for instance1 of those things which1 the more is taken from them1 the more they grow4 ,and reserve the great matters till the end1 and the small matters give at the beginning4 ,and first show the evils and then the punishment of philosophical things4 ,of ,ants4 ,these creatures will form many communities1 which will hide themselves and their young ones and victuals in dark caverns1 and they will feed themselves and their families in dark places for many months without any light1 artificial or natural4 ,footnote3 ,lines #a--ea are in the original written in one column1 beginning with the text of line #aa4 ,at the end of the column is the programme for the arrangement of the prophecies1 placed here at the head3 ,lines #ef--gi form a second column1 lines #hj--ig a third one 7see the reproduction of the text on the facsimile ,,pi4 ,,cxviii74 ,another suggestion for the arrangement of the prophecies is to be found among the notes #ee--eg on page #ceg4 7 ,of ,bees47 ,and many others will be deprived of their store and their food1 and will be cruelly submerged and drowned by folks devoid of reason4 ,oh ,justice of ,god6 ,why dost thou not wake and behold thy creatures thus ill used8 7 ,of ,sheep1 ,cows1 ,goats and the like47 ,endless multitudes of these will have their little children taken from them ripped open and flayed and most barbarously quartered4 7 ,of ,nuts1 and ,olives1 and ,acorns1 and ,chesnuts1 and such like4 7 ,many offspring shall be snatched by cruel thrashing from the very arms of their mothers1 and flung on the ground1 and crushed4 7 ,of ,children bound in ,bundles4 7 ,o cities of the ,sea6 ,in you ,i see your citizens--both females and males--tightly bound1 arms and legs1 with strong withes by folks who will not understand your language4 ,and you will only be able to assuage your sorrows and lost liberty by means of tearful complaints and sighing and lamentation among yourselves2 for those who will bind you will not understand you1 nor will you understand them4 7 ,of ,cats that eat ,rats47 ,in you1 ,o cities of ,africa your children will be seen quartered in their own houses by most cruel and rapacious beasts of your own country4 7 ,of ,asses that are beaten47 ,footnote #dh3 ,compare ,no4 #hde4 ,o ,nature6 ,wherefore art thou so partial2 being to some of thy children a tender and benign mother1 and to others a most cruel and pitiless stepmother8 ,i see children of thine given up to slavery to others1 without any sort of advantage1 and instead of remuneration for the good they do1 they are paid with the severest suffering1 and spend their whole life in benefitting those who ill treat them4 ,of ,men who sleep on boards of ,trees4 ,men shall sleep1 and eat1 and dwell among trees1 in the forests and open country4 ,of ,dreaming4 ,men will seem to see new destructions in the sky4 ,the flames that fall from it will seem to rise in it and to fly from it with terror4 ,they will hear every kind of animals speak in human language4 ,they will instantaneously run in person in various parts of the world1 without motion4 ,they will see the greatest splendour in the midst of darkness4 ,o6 marvel of the human race6 ,what madness has led you thus6 ,you will speak with animals of every species and they with you in human speech4 ,you will see yourself fall from great heights without any harm and torrents will accompany you1 and will mingle with their rapid course4 ,of ,christians4 ,many who hold the faith of the ,son only build temples in the name of the ,mother4 ,of ,food which has been alive4 #hd ,a great portion of bodies that have been alive will pass into the bodies of other animals2 which is as much as to say1 that the deserted tenements will pass piecemeal into the inhabited ones1 furnishing them with good things1 and carrying with them their evils4 ,that is to say the life of man is formed from things eaten1 and these carry with them that part of man which dies 4 4 4 #abid4 ,of ,funeral ,rites1 and ,processions1 and ,lights1 and ,bells1 and ,followers4 ,the greatest honours will be paid to men1 and much pomp1 without their knowledge4 ,footnote3 ,a facsimile of this text is on ,,pi4 ,,cxvi below on the right1 but the writing is larger than the other notes on the same sheet and of a somewhat different style4 ,the ink is also of a different hue1 as may be seen on the original sheet at ,milan4 999999#hd and following2 compare ,no4 #hdf4 #abie4 7,of the ,avaricious47 ,there will be many who will eagerly and with great care and solicitude follow up a thing1 which1 if they only knew its malignity1 would always terrify them4 7,of those men1 who1 the older they grow1 the more avaricious they become1 whereas1 having but little time to stay1 they should become more liberal47 ,we see those who are regarded as being most experienced and judicious1 when they least need a thing1 seek and cherish it with most avidity4 99,of the ,ditch499 ,many will be busied in taking away from a thing1 which will grow in proportion as it is diminished4 99,of a ,weight placed on a ,feather-pillow499 ,and it will be seen in many bodies that by raising the head they swell visibly2 and by laying the raised head down again1 their size will immediately be diminished4 99,of catching ,lice499 ,and many will be hunters of animals1 which1 the fewer there are the more will be taken2 and conversely1 the more there are1 the fewer will be taken4 99,of ,drawing ,water in two ,buckets with a single ,rope499 ,and many will be busily occupied1 though the more of the thing they draw up1 the more will escape at the other end4 99,of the ,tongues of ,pigs and ,calves in ,sausage-skins499 ,oh6 how foul a thing1 that we should see the tongue of one animal in the guts of another4 99,of ,sieves made of the ,hair of ,animals499 ,we shall see the food of animals pass through their skin everyway excepting through their mouths1 and penetrate from the outside downwards to the ground4 997 ,of ,lanterns4 799 ,footnote #ce3 ,lanterns were in ,italy formerly made of horn4 ,the cruel horns of powerful bulls will screen the lights of night against the wild fury of the winds4 997 ,of ,feather-beds4 799 ,flying creatures will give their very feathers to support men4 997 ,of ,animals which walk on ,trees--wearing wooden ,shoes4 799 ,the mire will be so great that men will walk on the trees of their country4 997 ,of the ,soles of ,shoes1 which are made from the ,ox4 799 ,and in many parts of the country men will be seen walking on the skins of large beasts4 997 ,of ,sailing in ,ships4 799 ,there will be great winds by reason of which things of the ,east will become things of the ,west2 and those of the ,south1 being involved in the course of the winds1 will follow them to distant lands4 997 ,of ,worshipping the ,pictures of ,saints4 799 ,men will speak to men who hear not2 having their eyes open1 they will not see2 they will speak to these1 and they will not be answered4 ,they will implore favours of those who have ears and hear not2 they will make light for the blind4 997 ,of ,sawyers4 799 ,there will be many men who will move one against another1 holding in their hands a cutting tool4 ,but these will not do each other any injury beyond tiring each other2 for1 when one pushes forward the other will draw back4 ,but woe to him who comes between them6 ,for he will end by being cut in pieces4 997 ,of ,silk-spinning4 799 ,dismal cries will be heard loud1 shrieking with anguish1 and the hoarse and smothered tones of those who will be despoiled1 and at last left naked and motionless2 and this by reason of the mover1 which makes every thing turn round4 997 ,of putting ,bread into the ,mouth of the ,oven and taking it out again4 799 ,in every city1 land1 castle and house1 men shall be seen1 who for want of food will take it out of the mouths of others1 who will not be able to resist in any way4 997 ,of tilled ,land4 799 ,the ,earth will be seen turned up side down and facing the opposite hemispheres1 uncovering the lurking holes of the fiercest animals4 997 ,of ,sowing ,seed4 799 ,then many of the men who will remain alive1 will throw the victuals they have preserved out of their houses1 a free prey to the birds and beasts of the earth1 without taking any care of them at all4 997 ,of the ,rains1 which1 by making the ,rivers muddy1 wash away the ,land4 799 ,footnote #ha3 ,compare ,no4 #ide4 ,something will fall from the sky which will transport a large part of ,africa which lies under that sky towards ,europe1 and that of ,europe towards ,africa1 and that of the ,scythian countries will meet with tremendous revolutions ,footnote #hd3 ,compare ,no4 #ide44 997 ,of ,wood that burns4 799 ,the trees and shrubs in the great forests will be converted into cinder4 997 ,of ,kilns for ,bricks and ,lime4 799 ,finally the earth will turn red from a conflagration of many days and the stones will be turned to cinders4 997 ,of boiled ,fish4 799 ,the natives of the waters will die in the boiling flood4 997 ,of the ,olives which fall from the ,olive trees1 shedding oil which makes light4 799 ,and things will fall with great force from above1 which will give us nourishment and light4 99,of ,owls and screech owls and what will happen to certain birds499 ,many will perish of dashing their heads in pieces1 and the eyes of many will jump out of their heads by reason of fearful creatures come out of the darkness4 99,of flax which works the cure of men499 ,that which was at first bound1 cast out and rent by many and various beaters will be respected and honoured1 and its precepts will be listened to with reverence and love4 99,of ,books which teach ,precepts499 ,bodies without souls will1 by their contents give us precepts by which to die well4 99,of ,flagellants499 ,men will hide themselves under the bark of trees1 and1 screaming1 they will make themselves martyrs1 by striking their own limbs4 99,of the ,handles of ,knives made of the ,horns of ,sheep499 ,we shall see the horns of certain beasts fitted to iron tools1 which will take the lives of many of their kind4 99,of ,night when no ,colour can be discerned499 ,there will come a time when no difference can be discerned between colours1 on the contrary1 everything will be black alike4 99,of ,swords and ,spears which by themselves never hurt any one499 ,one who by himself is mild enough and void of all offence will become terrible and fierce by being in bad company1 and will most cruelly take the life of many men1 and would kill many more if they were not hindered by bodies having no soul1 that have come out of caverns--that is1 breastplates of iron4 99,of ,snares and ,traps499 ,many dead things will move furiously1 and will take and bind the living1 and will ensnare them for the enemies who seek their death and destruction4 997 ,of ,metals4 799 ,that shall be brought forth out of dark and obscure caves1 which will put the whole human race in great anxiety1 peril and death4 ,to many that seek them1 after many sorrows they will give delight1 and to those who are not in their company1 death with want and misfortune4 ,this will lead to the commission of endless crimes2 this will increase and persuade bad men to assassinations1 robberies and treachery1 and by reason of it each will be suspicious of his partner4 ,this will deprive free cities of their happy condition2 this will take away the lives of many2 this will make men torment each other with many artifices deceptions and treasons4 ,o monstrous creature6 ,how much better would it be for men that every thing should return to ,hell6 ,for this the vast forests will be devastated of their trees2 for this endless animals will lose their lives4 997 ,of ,fire4 799 ,one shall be born from small beginnings which will rapidly become vast4 ,this will respect no created thing1 rather will it1 by its power1 transform almost every thing from its own nature into another4 997 ,of ,ships which sink4 799 ,huge bodies will be seen1 devoid of life1 carrying1 in fierce haste1 a multitude of men to the destruction of their lives4 997 ,of ,oxen1 which are eaten4 799 ,the masters of estates will eat their own labourers4 997 ,of beating ,beds to renew them4 799 ,men will be seen so deeply ungrateful that they will turn upon that which has harboured them1 for nothing at all2 they will so load it with blows that a great part of its inside will come out of its place1 and will be turned over and over in its body4 997 ,of ,things which are eaten and which first are killed4 799 ,those who nourish them will be killed by them and afflicted by merciless deaths4 997,of the ,reflection of ,walls of ,cities in the ,water of their ,ditches4799 ,the high walls of great cities will be seen up side down in their ditches4 997,of ,water1 which flows turbid and mixed with ,soil and ,dust2 and of ,mist1 which is mixed with the ,air2 and of ,fire which is mixed with its own1 and each with each4799 ,all the elements will be seen mixed together in a great whirling mass1 now borne towards the centre of the world1 now towards the sky2 and now furiously rushing from the ,south towards the frozen ,north1 and sometimes from the ,east towards the ,west1 and then again from this hemisphere to the other4 997,the ,world may be divided into two ,hemispheres at any ,point4799 ,all men will suddenly be transferred into opposite hemispheres4 997,the division of the ,east from the ,west may be made at any point4799 ,all living creatures will be moved from the ,east to the ,west2 and in the same way from ,north to ,south1 and vice versa4 997,of the ,motion of ,water which carries wood1 which is dead4799 ,bodies devoid of life will move by themselves and carry with them endless generations of the dead1 taking the wealth from the bystanders4 997,of ,eggs which being eaten cannot form ,chickens4799 ,oh6 how many will they be that never come to the birth6 997,of ,fishes which are eaten unborn4799 ,endless generations will be lost by the death of the pregnant4 997,of the ,lamentation on ,good ,friday4799 ,throughout ,europe there will be a lamentation of great nations over the death of one man who died in the ,east4 997,of ,dreaming4799 ,men will walk and not stir1 they will talk to those who are not present1 and hear those who do not speak4 997,of a ,man's ,shadow which moves with him4799 ,shapes and figures of men and animals will be seen following these animals and men wherever they flee4 ,and exactly as the one moves the other moves2 but what seems so wonderful is the variety of height they assume4 997,of our ,shadow cast by the ,sun1 and our ,reflection in the ,water at one and the same time4799 ,many a time will one man be seen as three and all three move together1 and often the most real one quits him4 997,of wooden ,chests which contain great ,treasures4799 ,within walnuts and trees and other plants vast treasures will be found1 which lie hidden there and well guarded4 997,of putting out the ,light when going to ,bed4799 ,many persons puffing out a breath with too much haste1 will thereby lose their sight1 and soon after all consciousness4 997,of the ,bells of ,mules1 which are close to their ,ears4799 ,in many parts of ,europe instruments of various sizes will be heard making divers harmonies1 with great labour to those who hear them most closely4 997,of ,asses4799 ,the severest labour will be repaid with hunger and thirst1 and discomfort1 and blows1 and goadings1 and curses1 and great abuse4 997,of ,soldiers on horseback4799 ,many men will be seen carried by large animals1 swift of pace1 to the loss of their lives and immediate death4 ,in the air and on earth animals will be seen of divers colours furiously carrying men to the destruction of their lives4 997,of the ,stars of ,spurs4799 ,by the aid of the stars men will be seen who will be as swift as any swift animal4 997,of a ,stick1 which is dead4799 ,the motions of a dead thing will make many living ones flee with pain and lamentation and cries4 997,of ,tinder4799 ,with a stone and with iron things will be made visible which before were not seen4 #abif4 997,of going in ,ships4799 ,we shall see the trees of the great forests of ,taurus and of ,sinai and of the ,appenines and others1 rush by means of the air1 from ,east to ,west and from ,north to ,south2 and carry1 by means of the air1 great multitudes of men4 ,oh6 how many vows6 ,oh6 how many deaths6 ,oh6 how many partings of friends and relations6 ,oh6 how many will those be who will never again see their own country nor their native land1 and who will die unburied1 with their bones strewn in various parts of the world6 997,of moving on ,all ,saints' ,day4799 ,many will forsake their own dwellings and carry with them all their belongings and will go to live in other parts4 997,of ,all ,souls' ,day4799 ,how many will they be who will bewail their deceased forefathers1 carrying lights to them4 997,of ,friars1 who spending nothing but words1 receive great gifts and bestow ,paradise4799 ,invisible money will procure the triumph of many who will spend it4 997,of ,bows made of the ,horns of ,oxen4799 ,many will there be who will die a painful death by means of the horns of cattle4 997,of writing ,letters from one ,country to another4799 ,men will speak with each other from the most remote countries1 and reply4 997,of ,hemispheres1 which are infinite2 and which are divided by an infinite number of ,lines1 so that every ,man always has one of these ,lines between his ,feet4799 ,men standing in opposite hemispheres will converse and deride each other and embrace each other1 and understand each other's language4 997,of ,priests who say ,mass4799 ,there will be many men who1 when they go to their labour will put on the richest clothes1 and these will be made after the fashion of aprons petticoats4 997,of ,friars who are ,confessors4799 ,and unhappy women will1 of their own free will1 reveal to men all their sins and shameful and most secret deeds4 997,of ,churches and the ,habitations of ,friars4799 ,many will there be who will give up work and labour and poverty of life and goods1 and will go to live among wealth in splendid buildings1 declaring that this is the way to make themselves acceptable to ,god4 997,of ,selling ,paradise4799 ,an infinite number of men will sell publicly and unhindered things of the very highest price1 without leave from the ,master of it2 while it never was theirs nor in their power2 and human justice will not prevent it4 997,of the ,dead which are carried to be buried4799 ,the simple folks will carry vast quantities of lights to light up the road for those who have entirely lost the power of sight4 997,of ,dowries for ,maidens4799 ,and whereas1 at first1 maidens could not be protected against the violence of ,men1 neither by the watchfulness of parents nor by strong walls1 the time will come when the fathers and parents of those girls will pay a large price to a man who wants to marry them1 even if they are rich1 noble and most handsome4 ,certainly this seems as though nature wished to eradicate the human race as being useless to the world1 and as spoiling all created things4 997,of the ,cruelty of ,man4799 ,animals will be seen on the earth who will always be fighting against each other with the greatest loss and frequent deaths on each side4 ,and there will be no end to their malignity2 by their strong limbs we shall see a great portion of the trees of the vast forests laid low throughout the universe2 and1 when they are filled with food the satisfaction of their desires will be to deal death and grief and labour and wars and fury to every living thing2 and from their immoderate pride they will desire to rise towards heaven1 but the too great weight of their limbs will keep them down4 ,nothing will remain on earth1 or under the earth or in the waters which will not be persecuted1 disturbed and spoiled1 and those of one country removed into another4 ,and their bodies will become the sepulture and means of transit of all they have killed4 ,o ,earth6 why dost thou not open and engulf them in the fissures of thy vast abyss and caverns1 and no longer display in the sight of heaven such a cruel and horrible monster4 #abig4 ,,prophecies4 ,there will be many which will increase in their destruction4 997,the ,ball of ,snow rolling over ,snow4799 ,there will be many who1 forgetting their existence and their name1 will lie as dead on the spoils of other dead creatures4 997,sleeping on the ,feathers of ,birds4799 ,the ,east will be seen to rush to the ,west and the ,south to the ,north in confusion round and about the universe1 with great noise and trembling or fury4 997,in the ,east wind which rushes to the ,west4799 ,the solar rays will kindle fire on the earth1 by which a thing that is under the sky will be set on fire1 and1 being reflected by some obstacle1 it will bend downwards4 997,the ,concave ,mirror kindles a ,fire1 with which we heat the oven1 and this has its foundation beneath its roof4799 ,a great part of the sea will fly towards heaven and for a long time will not return4 997,that is1 in ,clouds4799 ,there remains the motion which divides the mover from the thing moved4 ,those who give light for divine service will be destroyed4997,the ,bees which make the ,wax for ,candles799 ,dead things will come from underground and by their fierce movements will send numberless human beings out of the world4 997,iron1 which comes from under ground is dead but the ,weapons are made of it which kill so many ,men4799 ,the greatest mountains1 even those which are remote from the sea shore1 will drive the sea from its place4 997,this is by ,rivers which carry the ,earth they wash away from the ,mountains and bear it to the ,sea-shore2 and where the ,earth comes the sea must retire4799 ,the water dropped from the clouds still in motion on the flanks of mountains will lie still for a long period of time without any motion whatever2 and this will happen in many and divers lands4 997,snow1 which falls in flakes and is ,water4799 ,the great rocks of the mountains will throw out fire2 so that they will burn the timber of many vast forests1 and many beasts both wild and tame4 997,the ,flint in the ,tinder-box which makes a ,fire that consumes all the loads of ,wood of which the ,forests are despoiled and with this the flesh of ,beasts is cooked4799 ,oh6 how many great buildings will be ruined by reason of ,fire4 997,the ,fire of great ,guns4799 ,oxen will be to a great extent the cause of the destruction of cities1 and in the same way horses and buffaloes4 997,by drawing ,guns4799 #abih4 ,the ,lion tribe will be seen tearing open the earth with their clawed paws and in the caves thus made1 burying themselves together with the other animals that are beneath them4 ,animals will come forth from the earth in gloomy vesture1 which will attack the human species with astonishing assaults1 and which by their ferocious bites will make confusion of blood among those they devour4 ,again the air will be filled with a mischievous winged race which will assail men and beasts and feed upon them with much noise-- filling themselves with scarlet blood4 #abii4 ,blood will be seen issuing from the torn flesh of men1 and trickling down the surface4 ,men will have such cruel maladies that they will tear their flesh with their own nails4 997,the ,itch4799 ,plants will be seen left without leaves1 and the rivers standing still in their channels4 ,the waters of the sea will rise above the high peaks of the mountains towards heaven and fall again on to the dwellings of men4 997,that is1 in ,clouds4799 ,the largest trees of the forest will be seen carried by the fury of the winds from ,east to ,west4 997,that is across the ,sea4799 ,men will cast away their own victuals4 997,that is1 in ,sowing4799 ,i4#b #bf;a #acjj4 ,human beings will be seen who will not understand each other's speech2 that is1 a ,german with a ,turk4 ,fathers will be seen giving their daughters into the power of man and giving up all their former care in guarding them4 997,when ,girls are married4799 ,men will come out their graves turned into flying creatures2 and they will attack other men1 taking their food from their very hand or table4 997,as ,flies4799 ,many will there be who1 flaying their mother1 will tear the skin from her back4 7,husbandmen tilling the ,earth47 ,happy will they be who lend ear to the words of the ,dead4 7,who read good works and obey them47 #ajca4 ,feathers will raise men1 as they do birds1 towards heaven 7that is1 by the letters which are written with quills47 ,the works of men's hands will occasion their death4 7,swords and ,spears47 ,men out of fear will cling to the thing they most fear4 7,that is they will be miserable lest they should fall into misery47 ,things that are separate shall be united and acquire such virtue that they will restore to man his lost memory2 that is papyrus sheets which are made of separate strips and have preserved the memory of the things and acts of men4 ,the bones of the ,dead will be seen to govern the fortunes of him who moves them4 7,by ,dice47 ,cattle with their horns protect the ,flame from its death4 7,in a ,lantern ,footnote #ac3 ,see note page #ceg447 ,the ,forests will bring forth young which will be the cause of their death4 7,the handle of the hatchet47 #acjb4 ,men will deal bitter blows to that which is the cause of their life4 7,in thrashing ,grain47 ,the skins of animals will rouse men from their silence with great outcries and curses4 7,balls for playing ,games47 ,very often a thing that is itself broken is the occasion of much union4 7,that is the ,comb made of split ,cane which unites the threads of ,silk47 ,the wind passing through the skins of animals will make men dance4 7,that is the ,bag-pipe1 which makes people dance47 #acjc4 997 ,of ,walnut trees1 that are beaten4 799 ,those which have done best will be most beaten1 and their offspring taken and flayed or peeled1 and their bones broken or crushed4 997 ,of ,sculpture4 799 ,alas6 what do ,i see8 ,the ,saviour cru- cified anew4 997 ,of the ,mouth of ,man1 which is a ,sepulchre4 799 ,great noise will issue from the sepulchres of those who died evil and violent deaths4 997 ,of the ,skins of ,animals which have the sense of feeling what is in the things written4 799 ,the more you converse with skins covered with sentiments1 the more wisdom will99 you acquire4 997 ,of ,priests who bear the ,host in their body4 799 ,then almost all the tabernacles in which dwells the ,corpus ,domini1 will be plainly seen walking about of themselves on the various roads of the world4 #acjd4 ,and those who feed on grass will turn night into day 997 ,tallow4 799 ,and many creatures of land and water will go up among the stars 997 that is ,planets4799 ,the dead will be seen carrying the living 997 in ,carts and ,ships in various places4 799 ,food shall be taken out of the mouth of many 997 the oven's mouth4 799 ,and those which will have their food in their mouth will be deprived of it by the hands of others 997 the oven4 799 #acje4 997 ,of ,crucifixes which are sold4 799 ,i see ,christ sold and crucified afresh1 and his ,saints suffering ,martyrdom4 997 ,of ,physicians1 who live by sickness4 799 ,men will come into so wretched a plight that they will be glad that others will derive profit from their sufferings or from the loss of their real wealth1 that is health4 997 ,of the ,religion of ,friars1 who live by the ,saints who have been dead a great while4 799 ,those who are dead will1 after a thou- sand years be those who will give a livelihood to many who are living4 997 ,of ,stones converted into ,lime1 with which prison walls are made4 799 ,many things that have been before that time destroyed by fire will deprive many men of liberty4 ,i4#b #ai;a #acjf4 997 ,of ,children who are suckled4 799 ,many ,franciscans1 ,dominicans and ,benedictines will eat that which at other times was eaten by others1 who for some months to come will not be able to speak4 997 ,of ,cockles and ,sea ,snails which are thrown up by the sea and which rot inside their shells4 799 ,how many will there be who1 after they are dead1 will putrefy inside their own houses1 filling all the surrounding air with a fetid smell4 #acjg4 997 ,of ,mules which have on them rich burdens of silver and gold4 799 ,much treasure and great riches will be laid upon four-footed beasts1 which will convey them to divers places4 #acjh4 997 ,of the ,shadow cast by a man at night with a light4 799 ,huge figures will appear in human shape1 and the nearer you get to them1 the more will their immense size diminish4 ,footnote page #acjg3 ,it seems to me probable that this note1 which occurs in the note book used in #aejb1 when ,leonardo1 in the service of ,cesare ,borgia1 visited ,urbino1 was suggested by the famous pillage of the riches of the palace of ,guidobaldo1 whose treasures ,cesare ,borgia at once had carried to ,cesena 7see ,,gregorovius1 ,geschichte der ,stadt ,rom im ,mittelalter4 ,,xiii1 #e1 #d74 #acji4 997,of ,snakes1 carried by ,storks4799 ,serpents of great length will be seen at a great height in the air1 fighting with birds4 997,of great guns1 which come out of a pit and a mould4799 ,creatures will come from underground which with their terrific noise will stun all who are near2 and with their breath will kill men and destroy cities and castles4 #acaj4 997,of ,grain and other ,seeds4799 ,men will fling out of their houses those victuals which were intended to sustain their life4 997,of ,trees1 which nourish grafted shoots4799 ,fathers and mothers will be seen to take much more delight in their step-children then in their own children4 997,of the ,censer4799 ,some will go about in white garments with arrogant gestures threatening others with metal and fire which will do no harm at all to them4 #acaa4 997,of drying ,fodder4799 ,innumerable lives will be destroyed and innumerable vacant spaces will be made on the earth4 997,of the ,life of ,men1 who every year change their bodily substance4799 ,men1 when dead1 will pass through their own bowels4 #acab4 997,shoemakers4799 ,men will take pleasure in seeing their own work destroyed and injured4 #acac4 997,of ,kids4799 ,the time of ,herod will come again1 for the little innocent children will be taken from their nurses1 and will die of terrible wounds inflicted by cruel men4 ,v4 ,,draughts ,,and ,,schemes ,,for ,,the ,,humorous ,,writings4 ,schemes for fables1 etc4 7#acad-acbc74 #acad4 ,a ,,fable4 ,the crab standing under the rock to catch the fish which crept under it1 it came to pass that the rock fell with a ruinous downfall of stones1 and by their fall the crab was crushed4 ,,the ,,same4 ,the spider1 being among the grapes1 caught the flies which were feeding on those grapes4 ,then came the vintage1 and the spider was cut down with the grapes4 ,the vine that has grown old on an old tree falls with the ruin of that tree1 and through that bad companionship must perish with it4 ,the torrent carried so much earth and stones into its bed1 that it was then constrained to change its course4 ,the net that was wont to take the fish was seized and carried away by the rush of fish4 ,the ball of snow when1 as it rolls1 it descends from the snowy mountains1 increases in size as it falls4 ,the willow1 which by its long shoots hopes as it grows1 to outstrip every other plant1 from having associated itself with the vine which is pruned every year was always crippled4 #acae4 ,fable of the tongue bitten by the teeth4 ,the cedar puffed up with pride of its beauty1 separated itself from the trees around it and in so doing it turned away towards the wind1 which not being broken in its fury1 flung it uprooted on the earth4 ,the traveller's joy1 not content in its hedge1 began to fling its branches out over the high road1 and cling to the opposite hedge1 and for this it was broken away by the passers by4 #acaf4 ,the goldfinch gives victuals to its caged young4 ,death rather than loss of liberty4 ,footnote3 ,above this text is another note1 also referring to liberty2 see ,no4 #fid4 #acag4 997,of ,bags4799 ,goats will convey the wine to the city4 ,l4#a #ci;b #acah4 ,all those things which in winter are hidden under the snow1 will be uncovered and laid bare in summer4 997for ,falsehood1 which cannot remain hidden7994 #acai4 ,a ,,fable4 ,the lily set itself down by the shores of the ,ticino1 and the current carried away bank and the lily with it4 #acbj4 ,a ,,jest4 ,why ,hungarian ducats have a double cross on them4 #acba4 ,a ,,simile4 ,a vase of unbaked clay1 when broken1 may be remoulded1 but not a baked one4 #acbb4 ,seeing the paper all stained with the deep blackness of ink1 it he deeply regrets it2 and this proves to the paper that the words1 composed upon it were the cause of its being preserved4 #acbc4 ,the pen must necessarily have the penknife for a companion1 and it is a useful companionship1 for one is not good for much without the other4 ,schemes for prophecies 7#acbd-acbi74 #acbd4 ,the knife1 which is an artificial weapon1 deprives man of his nails1 his natural weapons4 ,the mirror conducts itself haughtily holding mirrored in itself the ,queen4 ,when she departs the mirror remains there 444 #acbe4 ,flax is dedicated to death1 and to the corruption of mortals4 ,to death1 by being used for snares and nets for birds1 animals and fish2 to corruption1 by the flaxen sheets in which the dead are wrapped when they are buried1 and who become corrupt in these winding sheets4-- ,and again1 this flax does not separate its fibre till it has begun to steep and putrefy1 and this is the flower with which garlands and decorations for funerals should be made4 #acbf4 997,of ,peasants who work in shirts7 ,shadows will come from the ,east which will blacken with great colour darkness the sky that covers ,italy4 997,of the ,barbers4799 ,all men will take refuge in ,africa4 #acbg4 ,the cloth which is held in the hand in the current of a running stream1 in the waters of which the cloth leaves all its foulness and dirt1 is meant to signify this c4 ,by the thorn with inoculated good fruit is signified those natures which of themselves were not disposed towards virtue1 but by the aid of their preceptors they have the repudation of it4 #acbh4 ,a ,,common ,,thing4 ,a wretched person will be flattered1 and these flatterers are always the deceivers1 robbers and murderers of the wretched person4 ,the image of the sun where it falls appears as a thing which covers the person who attempts to cover it4 997 ,money and ,gold4 799 ,out of cavernous pits a thing shall come forth which will make all the nations of the world toil and sweat with the greatest torments1 anxiety and labour1 that they may gain its aid4 997 ,of the ,dread of ,poverty4 799 ,the malicious and terrible monster will cause so much terror of itself in men that they will rush together1 with a rapid motion1 like madmen1 thinking they are escaping her boundless force4 997 ,of ,advice4 799 ,the man who may be most necessary to him who needs him1 will be repaid with ingratitude1 that is greatly contemned4 #acbi4 997 ,of ,bees4 799 ,they live together in communities1 they are destroyed that we may take the honey from them4 ,many and very great nations will be destroyed in their own dwellings4 #accj4 ,,why ,,dogs ,,take ,,pleasure ,,in ,,smelling ,,at ,,each ,,other4 ,this animal has a horror of the poor1 because they eat poor food1 and it loves the rich1 because they have good living and especially meat4 ,and the excrement of animals always retains some virtue of its origin as is shown by the faeces 444 ,now dogs have so keen a smell1 that they can discern by their nose the virtue remaining in these faeces1 and if they find them in the streets1 smell them and if they smell in them the virtue of meat or of other things1 they take them1 and if not1 they leave them3 ,and to return to the question1 ,i say that if by means of this smell they know that dog to be well fed1 they respect him1 because they judge that he has a powerful and rich master2 and if they discover no such smell with the virtue of meat1 they judge that dog to be of small account and to have a poor and humble master1 and therefore they bite that dog as they would his master4 #acca4 ,the circular plans of carrying earth are very useful1 inasmuch as men never stop in their work2 and it is done in many ways4 ,by one of these ways men carry the earth on their shoulders1 by another in chests and others on wheelbarrows4 ,the man who carries it on his shoulders first fills the tub on the ground1 and he loses time in hoisting it on to his shoulders4 ,he with the chests loses no time4 ,footnote3 ,the subject of this text has apparently no connection with the other texts of this section4 ,irony 7#accb74 #accb4 ,if ,petrarch was so fond of bay1 it was because it is of a good taste in sausages and with tunny2 ,i cannot put any value on their foolery4 ,footnote3 ,conte ,porro has published these lines in the ,archivio ,stor4 ,lombarda ,,viii1 ,,iv2 he reads the concluding line thus3 ,i no posso di loro gia 7sic7 co' far tesauro4--,this is known to be by a contemporary poet1 as ,senatore ,morelli informs me4 ,tricks 7#accc-acce74 #accc4 ,we are two brothers1 each of us has a brother4 ,here the way of saying it makes it appear that the two brothers have become four4 #accd4 ,,tricks ,,of ,,dividing4 ,take in each hand an equal number2 put #d from the right hand into the left2 cast away the remainder2 cast away an equal number from the left hand2 add #e1 and now you will find #ac in this left hand2 that is-,i made you put #d from the right hand into the left1 and cast away the remainder2 now your right hand has #d more2 then ,i make you throw away as many from the right as you threw away from the left2 so1 throwing from each hand a quantity of which the remainder may be equal1 you now have #d and #d1 which make #h1 and that the trick may not be detec- ted ,i made you put #e more1 which made #ac4 ,,tricks ,,of ,,dividing4 ,take any number less than #ab that you please2 then take of mine enough to make up the number #ab1 and that which remains to me is the number which you at first had2 because when ,i said1 take any number less than #ab as you please1 ,i took #ab into my hand1 and of that #ab you took such a number as made up your number of #ab2 and what you added to your number1 you took from mine2 that is1 if you had #h to go as far as to #ab1 you took of my #ab1 #d2 hence this #d transferred from me to you reduced my #ab to a remainder of #h1 and your #h became #ab2 so that my #h is equal to your #h1 before it was made #ab4 ,footnote3 ,g4 ,govi says in the ',saggio' p4 #bb3 ,si dilett99 ,leonarda1 di giuochi di prestigi e molti 787 ne descrisse1 che si leggono poi riportati dal ,paciolo nel suo libro3 de ,viribus ,quantitatis1 e che1 se non tutti1 sono certo in gran parte invenzioni del ,vinci4 #acce4 ,if you want to teach someone a subject you do not know yourself1 let him measure the length of an object unknown to you1 and he will learn the measure you did not know before2--,master ,giovanni da ,lodi4 ,,xxi4 ,letters4 ,personal ,records4 ,dated ,notes4 ,when we consider how superficial and imperfect are the accounts of ,leonardo's life written some time after his death by ,vasari and others1 any notes or letters which can throw more light on his personal circumstances cannot fail to be in the highest degree interesting4 ,the texts here given as ,nos4 #acea--acec1 set his residence in ,rome in quite a new aspect2 nay1 the picture which irresistibly dwells in our minds after reading these details of his life in the ,vatican1 forms a striking contrast to the contemporary life of ,raphael at ,rome4 ,i have placed foremost of these documents the very remarkable letters to the ,defterdar of ,syria4 ,in these ,leonardo speaks of himself as having staid among the mountains of ,armenia1 and as the biographies of the master tell nothing of any such distant journeys1 it would seem most obvious to treat this passage as fiction1 and so spare ourselves the onus of proof and discussion4 ,but on close examination no one can doubt that these documents1 with the accompanying sketches1 are the work of ,leonardo's own hand4 ,not merely is the character of the handwriting his1 but the spelling and the language are his also4 ,in one respect only does the writing betray any marked deviation from the rest of the notes1 especially those treating on scientific questions2 namely1 in these observations he seems to have taken particular pains to give the most distinct and best form of expression to all he had to say2 we find erasures and emendations in almost every line4 ,he proceeded1 as we shall see1 in the same way in the sketches for letters to ,giuliano de' ,medici1 and what can be more natural1 ,i may ask1 than to find the draft of a letter thus altered and improved when it is to contain an account of a definite subject1 and when personal interests are in the scale8 ,the finished copies as sent off are not known to exist2 if we had these instead of the rough drafts1 we might unhesitatingly have declared that some unknown ,italian engineer must have been1 at that time1 engaged in ,armenia in the service of the ,egyptian ,sultan1 and that ,leonardo had copied his documents4 ,under this hypothesis however we should have to state that this unknown writer must have been so far one in mind with ,leonardo as to use the same style of language and even the same lines of thought4 ,this explanation might--as ,i say--have been possible1 if only we had the finished letters4 ,but why should these rough drafts of letters be regarded as anything else than what they actually and obviously are8 ,if ,leonardo had been a man of our own time1 we might perhaps have attempted to account for the facts by saying that ,leonardo1 without having been in the ,east himself1 might have undertaken to write a ,romance of which the scene was laid in ,armenia1 and at the desire of his publisher had made sketches of landscape to illustrate the text4 ,i feel bound to mention this singular hypothesis as it has actually been put forward 7see ,no4 #accf note #e72 and it would certainly seem as though there were no other possible way of evading the conclusion to which these letters point1 and their bearing on the life of the master1--absurd as the alternative is4 ,but1 if1 on a question of such importance1 we are justified in suggesting theories that have no foundation in probability1 ,i could suggest another which1 as compared with that of a ,fiction by ,leonardo1 would be neither more nor less plausible2 it is1 moreover the only other hypothesis1 perhaps1 which can be devised to account for these passages1 if it were possible to prove that the interpretation that the documents themselves suggest1 must be rejected a priori2 viz may not ,leonardo have written them with the intention of mystifying those who1 after his death1 should try to decipher these manuscripts with a view to publishing them8 ,but if1 in fact1 no objection that will stand the test of criticism can be brought against the simple and direct interpretation of the words as they stand1 we are bound to regard ,leonardo's travels in the ,east as an established fact4 ,there is1 ,i believe nothing in what we know of his biography to negative such a fact1 especially as the details of his life for some few years are wholly unknown2 nor need we be at a loss for evidence which may serve to explain--at any rate to some extent--the strangeness of his undertaking such a journey4 ,we have no information as to ,leonardo's history between #adhb and #adhf2 it cannot be proved that he was either in ,milan or in ,florence4 ,on the other hand the tenor of this letter does not require us to assume a longer absence than a year or two4 ,for1 even if his appointment 7offitio7 as ,engineer in ,syria had been a permanent one1 it might have become untenable--by the death perhaps of the ,defterdar1 his patron1 or by his removal from office--1 and ,leonardo on his return home may have kept silence on the subject of an episode which probably had ended in failure and disappointment4 ,from the text of ,no4 #acgi we can hardly doubt that ,leonardo intended to make an excursion secretly from ,rome to ,naples1 although so far as has hitherto been known1 his biographers never allude to it4 ,in another place 7,no4 #ajgg7 he says that he had worked as an ,engineer in ,friuli4 ,are we to doubt this statement too1 merely because no biographer has hitherto given us any information on the matter8 ,in the geographical notes ,leonardo frequently speaks of the ,east1 and though such passages afford no direct proof of his having been there1 they show beyond a doubt that1 next to the ,nile1 the ,euphrates1 the ,tigris and the ,taurus mountains had a special interest in his eyes4 ,as a still further proof of the futility of the argument that there is nothing in his drawings to show that he had travelled in the ,east1 we find on ,pl4 ,,cxx a study of oriental heads of ,armenian type1--though of course this may have been made in ,italy4 ,if the style of these letters were less sober1 and the expressions less strictly to the point throughout1 it miglit be possible to regard them as a romantic fiction instead of a narrative of fact4 ,nay1 we have only to compare them with such obviously fanciful passages as ,no4 #aced1 ,nos4 #fgj-fgc1 and the ,fables and ,prophecies4 ,it is unnecessary to discuss the subject any further here2 such explanations as the letter needs are given in the foot notes4 ,the drafts of letters to ,lodovico il ,moro are very remarkable4 ,leonardo and this prince were certainly far less closely connected1 than has hitherto been supposed4 ,it is impossible that ,leonardo can have remained so long in the service of this prince1 because the salary was good1 as is commonly stated4 ,on the contrary1 it would seem1 that what kept him there1 in spite of his sore need of the money owed him by the prince1 was the hope of some day being able to carry out the project of casting the 'gran cavallo'4 ,drafts of ,letters and ,reports referring to ,armenia 7#accf4 #accg74 #accf4 ,,to ,,the ,,devatdar ,,of ,,syria1 ,,lieutenant ,,of ,,the ,,sacred ,,sultan ,,of ,,babylon4 99#c ,the recent disaster in our ,northern parts which ,i am certain will terrify not you alone but the whole world1 which ,footnote3 ,lines #a-eb are reproduced in facsimile on ,pl4 ,,cxvi4 #a4 ,diodario4 ,this word is not to be found in any ,italian dictionary1 and for a long time ,i vainly sought an explanation of it4 ,the youthful reminiscences of my wife afforded the desired clue4 ,the chief town of each ,turkish ,villayet1 or province --such as ,broussa1 for instance1 in ,asia ,minor1 is the residence of a ,defterdar1 who presides over the financial affairs of the province4 ,defterdar hane was1 in former times1 the name given to the ,ministry of ,finance at ,constantinople2 the ,minister of ,finance to the ,porte is now known as the ,mallie-,nazri and the ,defterdars are his subordinates4 ,a ,defterdar1 at the present day is merely the head of the finance department in each ,provincial district4 ,with regard to my suggestion that ,leonardo's ,diodario might be identical with the ,defterdar of former times1 the late ,m4 ,c4 ,,defremerie1 ,arabic ,professor1 and ,membre de l',institut de ,france wrote to me as follows3 ,votre conjecture est parfaitement fondee2 diodario est ,vequivalent de devadar ou plus exactement devatdar1 titre d'une importante dignite en ,egypt'e1 sous les ,mamlouks4 ,the word however is not of ,turkish1 but of ,perso-,arabie derivation4 ,defter written in arab899 literally ,defter 7,arabic7 meaning folio2 for dar 7,persian7 ,bookkeeper or holder is the ,english equivalent2 and the idea is that of a deputy in command4 ,during the ,mamelook supremacy over ,syria1 which corresponded in date with ,leonardo's time1 the office of ,defterdar was the third in importance in the ,state4 ,soltano di ,babilonia4 ,the name of ,babylon was commonly applied to ,cairo in the middle ages4 ,for instance ,,breidenbach1 ,itinerarium ,hierosolyma p4 #bah says3 ,at last we reached ,babylon4 ,but this is not that ,babylon which stood on the further shore of the river ,chober1 but that which is called the ,egyptian ,babylon4 ,it is close by ,cairo and the twain are but one and not two towns2 one half is called ,cairo and the other ,babylon1 whence they are called together ,cairo-,babylon2 originally the town is said to have been named ,memphis and then ,babylon1 but now it is called ,cairo4 ,compare ,no4 #ajhe1 #f4 ,egypt was governed from #achb till #aeag by the ,borgite or ,tcherkessian dynasty of the ,mamelook ,sultans4 ,one of the most famous of these1 ,sultan ,kait ,bey1 ruled from #adfh-adif during whose reign the ,gama 7or ,mosque7 of ,kait ,bey and tomb of ,kait ,bey near the ,okella ,kait ,bey were erected in ,cairo1 which preserve his name to this day4 ,under the rule of this great and wise prince many foreigners1 particularly ,italians1 found occupation in ,egypt1 as may be seen in the ',viaggio di ,josaphat ,barbaro'1 among other travellers4 ,next to ,leonardo 7so ,i learn from ,prof4 ,jac4 ,burckhardt of ,bale7 ,kait ,bey's most helpful engineer was a ,german who in about #adhg1 superintended the construction of the ,mole at ,alexandria4 ,felix ,fabri knew him and mentions him in his ,historia ,suevorum1 written in #adhh4 shall be related to you in due order1 showing first the effect and then the cause4 ,footnote #d3 ,the text here breaks off4 ,the following lines are a fresh beginning of a letter1 evidently addressed to the same person1 but1 as it would seem1 written at a later date than the previous text4 ,the numerous corrections and amendments amply prove that it is not a copy from any account of a journey by some unknown person2 but1 on the contrary1 that ,leonardo was particularly anxious to choose such words and phrases as might best express his own ideas4 ,finding myself in this part of ,armenia ,footnote #e3 ,parti d',erminia4 ,see ,no4 #ide1 note4 ,the extent of ,armenia in ,leonardo's time is only approximately known4 ,in the ,x,vth century the ,persians governed the ,eastern1 and the ,arabs the ,southern portions4 ,arabic authors--as1 for instance ,abulfeda--include ,cilicia and a part of ,cappadocia in ,armenia1 and ,greater ,armenia was the tract of that country known later as ,turcomania1 while ,armenia ,minor was the territory between ,cappadocia and the ,euphrates4 ,it was not till #aebb1 or even #aegd that the whole country came under the dominion of the ,ottoman ,turks1 in the reign of ,selim ,i4 ,the ,mamelook ,sultans of ,egypt seem to have taken a particular interest in this1 the most ,northern province of their empire1 which was even then in danger of being conquered by the ,turks4 ,in the autumn of #adgg ,sultan ,kait ,bey made a journey of inspection1 visiting ,antioch and the valleys of the ,tigris and ,euphrates with a numerous and brilliant escort4 ,this tour is briefly alluded to by ,moodshireddin p4 #efa2 and by ,,weil1 ,geschichte der ,abbasiden ,v1 p4 #ceh4 ,an anonymous member of the suite wrote a diary of the expedition in ,arabic1 which has been published by ,r4 ,v4 ,,lonzone 7',viaggio in ,palestina e ,soria di ,kaid ,ba ,,xviii sultano della ,,ii dinastia mamelucca1 fatto nel #adgg4 ,testo arabo4 ,torino #ahgh'1 without notes or commentary74 ,compare the critique on this edition1 by ,j4 ,,gildemeister in ,zeitschrift des ,deutschen ,palaestina ,vereins 7,vol4 ,ill p4 #bdf--bdi74 ,lanzone's edition seems to be no more than an abridged copy of the original4 ,i owe to ,professor ,sche'fer1 ,membre de l',institut1 the information that he is in possession of a manuscript in which the text is fuller1 and more correctly given4 ,the ,mamelook dynasty was1 as is well known1 of ,circassian origin1 and a large proportion of the ,egyptian ,army was recruited in ,circassia even so late as in the ,x,vth century4 ,that was a period of political storms in ,syria and ,asia ,minor and it is easy to suppose that the ,sultan's minister1 to whom ,leonardo addresses his report as his superior1 had a special interest in the welfare of those frontier provinces4 ,only to mention a few historical events of ,sultan ,kait ,bey's reign1 we find that in #adhh he assisted the ,circassians to resist the encroachments of ,alaeddoulet1 an ,asiatic prince who had allied himself with the ,osmanli to threaten the province2 the consequence was a war in ,cilicia by sea and land1 which broke out in the following year between the contending powers4 ,only a few years earlier the same province had been the scene of the so-called ,caramenian war in which the united ,venetian1 ,neapolitan and ,sclavonic fleets had been engaged4 7,see ,,corialano ,,cippico1 ,della guerra dei ,veneziani nell' ,asia dal #adfi--adgd4 ,venezia #agif1 p4 #ed7 and we learn incidentally that a certain ,leonardo ,boldo1 ,governor of ,scutari under ,sultan ,mahmoud1--as his name would indicate1 one of the numerous renegades of ,italian birth--played an important part in the negotiations for peace4 ,tu mi mandasti4 ,the address tu to a personage so high in office is singular and suggests personal intimacy2 ,leonardo seems to have been a favourite with the ,diodario4 ,compare lines #ed and #ee4 ,i have endeavoured to show1 and ,i believe that ,i am also in a position to prove with regard to these texts1 that they are draughts of letters actually written by ,leonardo2 at the same time ,i must not omit to mention that shortly after ,i had discovered to carry into effect with due love and care the task for which you sent me ,footnote3 #f2 and to make a beginning in a place which seemed to me to be most to our purpose1 ,i entered into 9999,is the following from previous page89999 #c4 ,il nuovo accidente accaduto1 or as ,leonardo first wrote and then erased1 e accaduto un nuovo accidente4 ,from the sequel this must refer to an earthquake1 and indeed these were frequent at that period1 particularly in ,asia ,minor1 where they caused immense mischief4 ,see ,no4 #aaja note4 the city of ,calindrafy#g1 near to our frontiers4 ,this city is situated at the base of that part of the ,taurus mountains which is divided from the ,euphrates and looks towards the peaks of the great ,mount ,taurus #h to the ,west #i4 ,these peaks are of such a height that they seem to touch the sky1 and in all the world there is no part of the earth1 higher than its summit#aj1 and the rays of these texts in the ,codex ,atlanticus and publi- shed a paper on the subject in the ,zeit- schrift fur bildende ,kunst 7,vol4 ,,xvi71 ,prof4 ,govi put forward this hypothesis to account for their origin3 ,quanto alle notizie sul monte ,tauro1 sull',armenia e sull' ,asia minore che si contengono negli altri frammenti1 esse vennero prese da qualche geografro o viaggiatore contemporaneo4 ,dall'indice imperfetto che accompagna quei frammenti1 si potrebbe dedurre che ,leonardo volesse farne un libro1 che poi non venne compiuto4 ,a ogni modo1 non e possibile di trovare in questi brani nessun indizio di un viaggio di ,leonardo in oriente1 ne della sua conversione alla religione di ,maometto1 come qualcuno pretenderebbe4 ,leonardo amava con passione gli studi geografici1 e nel suoi scritti s'incontran spesso itinerart1 indicazioni1 o descrizioni di luoghi1 schizzi di carte e abbozzi topografici di varie regioni1 non e quindi strano che egli1 abile narratore com'era1 si fosse proposto di scrivere una specie di ,romanzo in forma epistolare svolgendone ,pintreccio nell',asia ,minore1 intorno alla quale i libri d'allora1 e forse qualche viaggiatore amico suo1 gli avevano somministrato alcuni elementi piu o meno fantastici4 7,see ,transunti della ,reale ,accademia dei ,lincei ,voi4 ,v ,ser4 #c74 ,it is hardly necessary to point out that ,prof4 ,govi omits to name the sources from which ,leonardo could be supposed to have drawn his information1 and ,i may leave it to the reader to pronounce judgment on the anomaly which is involved in the hypothesis that we have here a fragment of a ,romance1 cast in the form of a correspondence4 ,at the same time1 ,i cannot but admit that the solution of the difficulties proposed by ,prof4 ,govi is1 under the circumstances1 certainly the easiest way of dealing with the question4 ,but we should then be equally justified in supposing some more of ,leonardo's letters to be fragments of such romances2 particularly those of which the addresses can no longer be named4 ,still1 as regards these drafts of letters to the ,diodario1 if we accept the ,romance theory1 as pro- posed by ,prof4 ,govi1 we are also compelled to assume that ,leonardo purposed from the first to illustrate his tale2 for it needs only a glance at the sketches on ,,pi4 ,,cxvi to ,,cxix to perceive that they are connected with the texts2 and of course the rest of ,leonardo's numerous notes on matters pertaining to the ,east1 the greater part of which are here published for the first time1 may also be some- how connected with this strange romance4 #g4 ,citta de ,calindra 7,chalindra74 ,the position of this city is so exactly determined1 between the valley of the ,euphrates and the ,taurus range that it ought to be possible to identify it4 ,but it can hardly be the same as the sea port of ,cilicia with a somewhat similar name ,celenderis1 ,kelandria1 ,celendria1 ,kilindria1 now the ,turkish ,gulnar4 ,in two ,catalonian ,portulans in the ,bibliotheque ,natio- nale in ,paris-one dating from the ,,xv'h century1 by ,wilhelm von ,soler1 the other by ,olivez de ,majorca1 in l#ehd-;,i find this place called ,calandra4 ,but ,leonardo's ,calindra must certainly have lain more to the ,north ,west1 probably somewhere in ,kurdistan4 ,the fact that the geographical position is so care- fully determined by ,leonardo seems to prove that it was a place of no great importance and little known4 ,it is singular that the words first written in #a4 #h were divisa dal lago 7,lake ,van871 altered afterwards to dall',eitfrates4 ,nostri confini1 and in #a4 #f proposito nostro4 ,these refer to the frontier and to the affairs of the ,mamelook ,sultan1 ,lines #fe and #ff throw some light on the purpose of ,leonardo's mission4 #h4 ,i corni del gra mote ,tauro4 ,compare the sketches ,,pi4 ,,cxvi-,,cxviii4 ,so long as it is im- possible to identify the situation of ,calindra it is most difficult to decide with any certainty which peak of the ,taurus is here meant2 and ,i greatly regret that ,i had no foreknowledge of this puzzling topographical question when1 in #ahgf1 ,i was pursuing archaeological enquiries in the ,provinces of ,aleppo and ,cilicia1 and had to travel for some time in view of the imposing snow-peaks of ,bulghar ,dagh and ,ala ,tepessi4 #i-aj4 ,the opinion here expressed as to the height of the mountain would be unmeaning1 unless it had been written before ,leonardo moved to ,milan1 where ,monte ,rosa is so conspicuous an the sun always fall upon it on its ,east side1 four hours before day-time1 and being of the whitest stone ,footnote ,,ii3,pietra bianchissima4 ,the ,taurus ,mountains consist in great part of limestone4 it shines resplendently and fulfils the function to these ,armenians which a bright moon-light would in the midst of the darkness2 and by its great height it outreaches the utmost level of the clouds by a space of four miles in a straight line4 ,this peak is seen in many places towards the ,west1 illuminated by the sun after its setting the third part of the night4 ,this it is1 which with you ,footnote #ad3 ,appresso di voi4 ,leonardo had at first written noi as though his meaning had1been3 ,this peak appeared to us to be a comet when you and ,i observed it in ,north ,syria 7at ,aleppo8 at ,aintas874 ,the description of the curious reflection in the evening1 resembling the ,alpine-glow is certainly not an invented fiction1 for in the next lines an explanation of the phenomenon is offered1 or at least attempted4 we formerly in calm weather had supposed to be a comet1 and appears to us in the darkness of night1 to change its form1 being sometimes divided in two or three parts1 and sometimes long and sometimes short4 ,and this is caused by the clouds on the horizon of the sky which interpose between part of this mountain and the sun1 and by cutting off some of the solar rays the light on the mountain is intercepted by various intervals of clouds1 and therefore varies in the form of its brightness4 ,,the ,,divisions ,,of ,,the ,,book ,footnote #ai3 ,the next #cc lines are evidently the contents of a connected ,report or ,book1 but not of one which he had at hand2 more probably1 indeed1 of one he purposed writing44 ,the praise and confession of the faith ,footnote #bj3 ,persuasione di fede1 of the ,christian or the ,mohammedan faith8 ,we must suppose the latter1 at the beginning of a document addressed to so high a ,mohammedan official4 ,predica probably stands as an abbreviation for predicazione 7lat4 praedicatio7 in the sense of praise or glorification2 very probably it may mean some such initial doxology as we find in ,mohammedan works4 7,comp4 #a4 #dj474 ,the sudden inundation1 to its end4 #bc ,the destruction of the city4 #bd,the death of the people and their despair4 ,the preacher's search1 his release and benevolence ,footnote #bh3 ,the phraseology of this is too general for any conjecture as to its meaning to be worth hazarding4 ,description of the cause of this fall of the mountain ,footnote #cj3 ,ruina del monte4 ,of course by an earthquake4 ,in a catalogue of earthquakes1 entitled kechf aussalssale99b an auasf ezzel-zele99h1 and written by ,djelal eddin4 ,the mischief it did4 9999,is the following from previous page's footnotes89999 object in the landscape4 #d ore inanzi seems to mean1 four hours before the sun's rays penetrate to the bottom of the valleys4 999999,i did put this footnote as #bh but not #bf because ,i cannot find reference to #bf in text999999 #bf4 #bh4 ,the phraseology of this is too general for any conjecture as to its meaning to be worth hazarding4 #cb ,fall of snow4 ,the finding of the prophet #cc4 ,his prophesy4 #ce ,the inundation of the lower portion of ,eastern ,armenia1 the draining of which was effected by the cutting through the ,taurus ,mountains4 ,how the new prophet showed ,footnote #dj3,nova profeta1 #a4 #cc1 profeta4 ,mohammed4 ,leonardo here refers to the ,koran3 ,in the name of the most merciful ,god4--,when the earth shall be shaken by an earthquake2 and the earth shall cast forth her burdens2 and a man shall say1 what aileth her8 ,on that day the earth shall declare her tidings1 for that thy ,lord will inspire her4 ,on that day men shall go forward in distinct classes1 that they may behold their works4 ,and whoever shall have wrought good of the weight of an ant1 shall behold the same4 ,and whoever shall have wrought evil of the weight of an ant1 shall behold the same4 7,the ,koran1 translated by ,g4 ,sale1 ,chapter ,,xcix1 p4 #deb74 that this destruction would happen as he had foretold4 ,description of the ,taurus ,mountains ,footnote #dc3 and the river ,euphrates4 ,why the mountain shines at the top1 from half to a third of the night1 and looks like a comet to the inhabitants of the ,west after the sunset1 and before day to those of the ,east4 ,why this comet appears of variable forms1 so that it is now round and now long1 and now again divided into two or three parts1 and now in one piece1 and when it is to be seen again4 ,,of ,,the ,,shape ,,of ,,the ,,taurus ,,mountains ,footnote 99#ec--id993 ,the facsimile of this passage is given on ,pl4 ,,cxvii44 ,i am not to be accused1 ,oh ,devatdar1 of idleness1 as your chidings seem to hint2 but your excessive love for me1 which gave rise to the benefits you have conferred on me ,footnote #ee is that which has also compelled me to the utmost painstaking in seeking out and diligently investigating the cause of so great and stupendous an effect4 ,and this could not be done without time2 now1 in order to satisfy you fully as to the cause of so great an effect1 it is requisite that ,i should explain to you the form of the place1 and then ,i will proceed to the effect1 by which ,i believe you will be amply satisfied4 999999,is the following footnote from previous page8999999 ,syouthy1 the following statement occurs3 ,in the year #hhi 7#adhd ,a4,d47 there were six shocks of earthquake at ,aleppo4 ,they were excessively violent and threw the inhabitants into consternation4 ,i owe this communication to the kindness of ,prof4 ,ch4 ,schefer1 ,membre de l',institut1 to whom this unpublished ,arabic ,,ms4 belongs4 ,the foregoing entries refer to two earthquakes in ,cairo1 in #adgf and #adha3 the following ones indicate a time at which ,leonardo was1 certainly1 living in ,milan4 999999,where does this footnote belong8999999 #cf4 ,tagliata di ,monte ,tauro4 ,the ,euphrates flows through the ,taurus range near the influx of the ,kura ,shai2 it rushes through a rift in the wildest cliffs from #bjjj to #cjjj feet high and runs on for #ij miles in #cjj falls or rapids till it reaches ,telek1 near which at a spot called ,gleikash1 or the ,hart's leap1 it measures only #ce paces across4 ,compare the map on ,pl4 ,,cxix and the explanation fo99 it on p4 #cia4 999999,where does this footnote belong8999999 #ed4 ,the foregoing sketch of a letter1 lines #e4 #ah1 appears to have remained a fragment when ,leonardo received pressing orders which caused ,footnote #ei3 ,this passage was evidently intended as an improvement on that immediately preceding it4 ,the purport of both is essentially the same1 but the first is pitched in a key of ill-disguised annoyance which is absent from the second4 ,i do not see how these two versions can be reconciled with the romance-theory held by ,prof4 ,govi4 ,do not be aggrieved1 ,o ,devatdar1 by my delay in responding to your pressing request1 for those things which you require of me are of such a nature that they cannot be well expressed without some lapse of time2 particularly because1 in order to explain the cause of so great an effect1 it is necessary to describe with accuracy the nature of the place2 and by this means ,i can afterwards easily satisfy your above-mentioned request4 ,footnote #fb3 ,this passage was evidently intended as an improvement on that immediately preceding it4 ,the purport of both is essentially the same1 but the first is pitched in a key of ill-disguised annoyance which is absent from the second4 ,i do not see how these two versions can be reconciled with the romance-theory held by ,prof4 ,govi4 ,i will pass over any description of the form of ,asia ,minor1 or as to what seas or lands form the limits of its outline and extent1 because ,i know that by your own diligence and carefulness in your studies you have not remained in ignorance of these matters 99#fe2 and ,i will go on to describe the true form of the ,taurus ,mountain which is the cause of this stupendous and harmful marvel1 and which will serve to advance us in our purpose 99#ff4 ,this ,taurus is that mountain which1 with many others is said to be the ridge of ,mount ,caucasus2 but wishing to be very clear about it1 ,i desired to speak to some of the inhabitants of the shores of the ,caspian sea1 who give evidence that this must be the true ,caucasus1 and that though their mountains bear the same name1 yet these are higher2 and to confirm this in the ,scythian tongue ,caucasus means a very high ,footnote #fh3 ,caucasus2 ,herodot 99,kaoxaais2 ,armen4 ,kaukaz4 peak1 and in fact we have no information of there being1 in the ,east or in the ,west1 any mountain so high4 ,and the proof of this is that the inhabitants of the countries to the ,west see the rays of the sun illuminating a great part of its summit for as much as a quarter of the longest night4 ,and in the same way1 in those countries which lie to the ,east4 ,,of ,,the ,,structure ,,and ,,size ,,of ,,mount ,,taurus4 ,footnote #gc3 ,the statements are of course founded on those of the 'inhabitants' spoken of in #a4 #fg4 ,the shadow of this ridge of the ,taurus is of such a height that when1 in the middle of ,june1 the ,sun is at its meridian1 its 99him to write immediately and fully on the subject mentioned in line #dc4 99#gc-ge4 ,footnote #ge3 ,the statements are of course founded on those of the 'inhabitants' spoken of in #a4 #fg4 shadow extends as far as the borders of ,sarmatia1 twelve days off2 and in the middle of ,december it extends as far as the ,hyperborean mountains1 which are at a month's journey to the ,north 99#ge4 ,and the side which faces the wind is always free from clouds and mists1 because the wind which is parted in beating on the rock1 closes again on the further side of that rock1 and in its motion carries with it the clouds from all quarters and leaves them where it strikes4 ,and it is always full of thunderbolts from the great quantity of clouds which accumulate there1 whence the rock is all riven and full of huge debris ,footnote #gg3 ,sudden storms are equally common on the heights of ,ararat4 ,it is hardly necessary to observe that ,ararat cannot be meant here4 ,its summit is formed like the crater of ,vesuvius4 ,the peaks sketched on ,pl4 ,,cxvi-,,cxviii are probably views of the same mountain1 taken from different sides4 ,near the solitary peak1 ,pl4 ,,cxviii these three names are written goba1 arnigasar1 caruda1 names most likely of different peaks4 ,pl4 ,,cxvi and ,,cxvii are in the original on a single sheet folded down the middle1 #cj centimetres high and #dc #a_/b wide4 ,on the reverse of one half of the sheet are notes on peso and bilancia 7weight and balance71 on the other are the 'prophecies' printed under ,nos4 #abic and #abid4 ,it is evident from the arrangement that these were written subsequently1 on the space which had been left blank4 ,these pages are facsimiled on ,pl4 ,,cxviii4 ,in ,pl4 ,,cxvi-,,cxviii the size is smaller than in the original2 the map of ,armenia1 ,pl4 ,,cxviii1 is on ,pl4 ,,cxix slightly enlarged4 ,on this map we find the following names1 beginning from the right hand at the top3 pariardes mo 7for ,paryadres ,mons1 ,arm4 ,parchar1 now ,barchal or ,kolai ,dagh2 ,trebizond is on its slope74 ,aquilone --,north1 ,antitaurus ,antitaurus 99 psis mo 7probably meant for ,thospitis ,lake ,van1 ,arm4 ,dgov ,vanai1 ,tospoi1 and the ,mountain range to the ,south72 ,gordis mo 7,mountains of ,gordyaea71 the birth place of the ,tigris2 ,oriente --,east2 ,tigris1 and then1 to the left1 ,eufrates4 ,then1 above to the left ,argeo mo 7now ,erdshigas1 an extinct volcano1 #abjjj feet high72 ,celeno mo 7no doubt ,sultan ,dagh in ,pisidia74 ,celeno is the ,greek town of 99,ke,aouvat-- see ,arian ,i1 #bi1 ,i--now the ruins of ,dineir72 oriente --,east2 africo libezco 7for libeccio--,south ,west74 ,in the middle of the ,euphrates river on this small map we see a shaded portion surrounded by mountains1 perhaps to indicate the inundation mentioned in l4 #ce4 ,the affluent to the ,euphrates shown as coming with many windings from the high land of ',argeo' on the ,west1 is the ,tochma ,su1 which joins the main river at ,malatie4 ,i have not been able to discover any map of ,armenia of the ,x,vth or ,x,v,ith century in which the course of the ,euphrates is laid down with any thing like the correctness displayed in this sketch4 ,the best ,i have seen is the ,catalonian ,portulan of ,olivez de ,majorca1 executed in #aehd1 and it is far behind ,leonardo's44 ,this mountain1 at its base1 is inhabited by a very rich population and is full of most beautiful springs and rivers1 and is fertile and abounding in all good produce1 particularly in those parts which face to the ,south4 ,but after mounting about three miles we begin to find forests of great fir trees1 and beech and other similar trees2 after this1 for a space of three more miles1 there are meadows and vast pastures2 and all the rest1 as far as the beginning of the ,taurus1 is eternal snows which never disappear at any time1 and extend to a height of about fourteen miles in all4 ,from this beginning of the ,taurus up to the height of a mile the clouds never pass away2 thus we have fifteen miles1 that is1 a height of about five miles in a straight line2 and the summit of the peaks of the ,taurus are as much1 or about that4 ,there1 half way up1 we begin to find a scorching air and never feel a breath of wind2 but nothing can live long there2 there nothing is brought forth save a few birds of prey which breed in the high fissures of ,taurus and descend below the clouds to seek their prey4 ,above the wooded hills all is bare rock1 that is1 from the clouds upwards2 and the rock is the purest white4 ,and it is impossible to walk to the high summit on account of the rough and perilous ascent4 #accg4 ,having often made you1 by my letters1 acquainted with the things which have happened1 ,i think ,i ought not to be silent as to the events of the last few days1 which--#b444 ,having several times-- ,having many times rejoiced with you by letters over your prosperous fortunes1 ,i know now that1 as a friend you will be sad with me over the miserable state in which ,i find myself2 and this is1 that during the last few days ,i have been in so much trouble1 fear1 peril and loss1 besides the miseries of the people here1 that we have been envious of the dead2 and certainly ,i do not believe that since the elements by their separation reduced the vast chaos to order1 they have ever combined their force and fury to do so much mischief to man4 ,as far as regards us here1 what we have seen and gone through is such that ,i could not imagine that things could ever rise to such an amount of mischief1 as we experienced in the space of ten hours4 ,in the first place we were assailed and attacked by the violence and fury of the winds 99#aj2 to this was added the falling of great mountains of snow which filled up all this valley1 thus destroying a great part of our city ,footnote #aa3 ,della nostra citta 7,leonardo first wrote di questa citta74 ,from this we may infer that he had at some time lived in the place in question wherever it might be44 ,and not content with this the tempest sent a sudden flood of water to submerge all the low part of this city 99#ab2 added to which there came a sudden rain1 or rather a ruinous torrent and flood of water1 sand1 mud1 and stones1 entangled with roots1 and stems and fragments of various trees2 and every kind of thing flying through the air fell upon us2 finally a great fire broke out1 not brought by the wind1 but carried as it would seem1 by ten thousand devils1 which completely burnt up all this neighbourhood and it has not yet ceased4 ,and those few who remain unhurt are in such dejection and such terror that they hardly have courage to speak to each other1 as if they were stunned4 ,having abandoned all our business1 we stay here together in the ruins of some churches1 men and women mingled together1 small and great ,footnote #ag3 ,certe ruine di chiese4 ,either of ,armenian churches or of ,mosques1 which it was not unusual to speak of as churches4 ,maschi e femmini insieme unite1 implies an infringement of the usually strict rule of the separation of the sexes41 just like herds of goats4 ,the neighbours out of pity succoured us with victuals1 and they had previously been our enemies4 ,and if ,footnote #ah3 ,i vicini1 nostri nimici4 ,the town must then have stood quite close to the frontier of the country4 ,compare #accf4 ,l4 #g4 vicini ai nostri confini4 ,dr4 ,m4 ,,jordan has already published lines #d-ac 7see ,das ,malerbuch1 ,leipzig1 #ahgc1 p4 #ij3--;his reading differs from mine7 under the title of ,description of a landscape near ,lake ,como4 ,we do in fact find1 among other loose sheets in the ,codex ,atlanticus1 certain texts referring to valleys of the ,alps 7see ,nos4 #ajcj1 #ajca and note p4 #bcg7 and in the arrangement of the loose sheets1 of which the ,codex ,atlanticus has been formed1 these happen to be placed close to this text4 ,the compiler stuck both on the same folio sheet2 and if this is not the reason for ,dr4 ,,jordan',s choosing such a title 7,description c47 ,i cannot imagine what it can have been4 ,it is1 at any rate1 a merely hypothetical statement4 ,the designation of the population of the country round a city as the enemy 7nemici7 is hardly appropriate to ,italy in the time of ,leonardo4 it had not been for certain people who succoured us with victuals1 all would have died of hunger4 ,now you see the state we are in4 ,and all these evils are as nothing compared with those which are promised to us shortly4 ,i know that as a friend you will grieve for my misfortunes1 as ,i1 in former letters have shown my joy at your prosperity 444 ,footnote3 #accg4 ,on comparing this commencement of a letter l4 #a-b with that in l4 #c and #d of ,no4 #accf it is quite evident that both refer to the same event4 7,compare also ,no4 #accg l4 #aj-l#b and #ag with ,no4 #accf l4 #bc1 #bd and #cb47 ,but the text ,no4 #accf1 including the fragment l4 #c-d1 was obviously written later than the draft here reproduced4 ,the ,diodario is not directly addressed--the person addressed indeed is not known--and it seems to me highly probable that it was written to some other patron and friend whose name and position are not mentioned4 ,notes about events observed abroad 7#acch-acci74 #acch4 ,,book #dc4 ,,of ,,the ,,movement ,,of ,,air ,,enclosed ,,in ,,water4 ,i have seen motions of the air so furious that they have carried1 mixed up in their course1 the largest trees of the forest and whole roofs of great palaces1 and ,i have seen the same fury bore a hole with a whirling movement digging out a gravel pit1 and carrying gravel1 sand and water more than half a mile through the air4 ,footnote3 ,the first sixteen lines of this passage which treat of the subject as indicated on the title line have no place in this connexion and have been omitted4 99,footnote #b3 ,ho veduto movimenti c4 ,nothing of the kind happened in ,italy during ,leonardo's lifetime1 and it is therefore extremely probable that this refers to the natural phenomena which are so fully described in the foregoing passage4 7,compare too1 ,no4 #ajba47 ,there can be no doubt that the descriptions of the ,deluge in the ,libro di ,pittura 7,vol4 ,i1 ,no4 #fjg-faa71 and that of the fall of a mountain ,no4 #faj1 l4 #ag-cj were written from the vivid impressions derived from personal experience4 ,compare also ,pl4 ,,xxxiv-,,xl4 #acci4 ,like a whirling wind which rushes down a sandy and hollow valley1 and which1 in its hasty course1 drives to its centre every thing that opposes its furious course 444 ,no otherwise does the ,northern blast whirl round in its tempestuous progress 444 9999,footnote3 ,it may be inferred from the character of the writing1 which is in the style of the note in facsimile ,vol4 ,i1 p4 #big1 that this passage was written between #adgj and #adhj4 ,as the figure #f at the end of the text indicates1 it was continued on another page1 but ,i have searched in vain for it4 ,the reverse of this leaf is coloured red for drawing in silver point1 but has not been used for that purpose but for writing on1 and at about the same date4 ,the passages are given as ,nos4 #abag1 #abah1 #abai1 #aafb and ,no4 #iid 7see note page #bah74 ,the text given above is obviously not a fragment of a letter1 but a record of some personal experience4 ,no4 #acgi also seems to refer to ,leonardo's journeys in ,southern ,italy4 ,nor does the tempestuous sea bellow so loud1 when the ,northern blast dashes it1 with its foaming waves between ,scylla and ,charybdis2 nor ,stromboli1 nor ,mount ,etna1 when their sulphurous flames1 having been forcibly confined1 rend1 and burst open the mountain1 fulminating stones and earth through the air together with the flames they vomit4 ,nor when the inflamed caverns of ,mount ,etna 9999,footnote #ac3 ,mongibello is a name commonly given in ,sicily to ,mount ,etna 7from ,djebel1 ,arab4mountain74 ,fr4 ,,ferrara1 ,descrizione dell' ,etna con la storia delle 99eruzioni 7,palermo1 #ahah1 p4 #hh7 tells us1 on the authority of the ,cronaca del ,monastero ,benedettino di ,licordia of an eruption of the ,volcano with a great flow of lava on ,sept4 #ba1 #addg4 ,the next records of the mountain are from the years #aecc and #aecf4 ,a4 ,percy neither does mention any eruptions of ,etna during the years to which this note must probably refer ,memoire des tremblements de terre de la peninsule italique1 ,vol4 ,,xxii des ,memoires couronnees et ,memoires des savants etrangers4 ,academie ,royal de ,belgique74 ,a literal interpretation of the passage would not1 however1 indicate an allusion to any great eruption2 particularly in the connection with ,stromboli1 where the periodical outbreaks in very short intervals are very striking to any observer1 especially at night time1 when passing the island on the way from ,naples to ,messina41 rejecting the ill-restained element vomit it forth1 back to its own region1 driving furiously before it every obstacle that comes in the way of its impetuous rage 444 ,unable to resist my eager desire and wanting to see the great 444 of the various and strange shapes made by formative nature1 and having wandered some distance among gloomy rocks1 ,i came to the entrance of a great cavern1 in front of which ,i stood some time1 astonished and unaware of such a thing4 ,bending my back into an arch ,i rested my left hand on my knee and held my right hand over my down-cast and contracted eye brows3 often bending first one way and then the other1 to see whether ,i could discover anything inside1 and this being forbidden by the deep darkness within1 and after having remained there some time1 two contrary emotions arose in me1 fear and desire--fear of the threatening dark cavern1 desire to see whether there were any marvellous thing within it 444 ,drafts of ,letters to ,lodovico il ,moro 7#acdj-acde74 #acdj4 ,most illustrious ,lord1 ,having now sufficiently considered the specimens of all those who proclaim themselves skilled contrivers of instruments of war1 and that the invention and operation of the said instruments are nothing different to those in common use3 ,i shall endeavour1 without prejudice to any one else1 to explain myself to your ,excellency showing your ,lordship my secrets1 and then offering them to your best pleasure and approbation to work with effect at opportune moments as well as all those things which1 in part1 shall be briefly noted below4 ,footnote3 ,the numerous corrections1 the alterations in the figures 7l4 #ah7 and the absence of any signature prove that this is merely the rough draft of a letter to ,lodovico il ,moro4 ,it is one of the very few manuscripts which are written from left to right--see the facsimile of the beginning as here reproduced4 ,this is probably the final sketch of a document the clean of which copy was written in the usual manner4 ,leonardo no doubt very rarely wrote so1 and this is probably the reason of the conspicuous dissimilarity in the handwriting1 when he did4 7,compare ,pl4 ,,xxxviii47 ,it is noteworthy too that here the orthography and abbreviations are also exceptional4 ,but such superficial peculiarities are not enough to stamp the document as altogether spurious4 ,it is neither a forgery nor the production of any artist but ,leonardo himself4 ,as to this point the contents leave us no doubt as to its authenticity1 particularly l4 #cb 7see ,no4 #gai1 where this passage is repeated74 ,but whether the fragment1 as we here see it1 was written from ,leonardo's dictation--a theory favoured by the orthography1 the erasures and corrections--or whether it may be a copy made for or by ,melzi or ,mazenta is comparatively unimportant4 ,there are in the ,codex ,atlanticus a few other documents not written by ,leonardo himself1 but the notes in his own hand found on the reverse pages of these leaves amply prove that they were certainly in ,leonardo's possession4 ,this mark of ownership is wanting to the text in question1 but the compilers of the ,codex ,atlanticus1 at any rate1 accepted it as a genuine document4 ,with regard to the probable date of this projected letter see ,vol4 ,,ii1 p4 #c4 #a7 ,i have a sort of extremely light and strong bridges1 adapted to be most easily carried1 and with them you may pursue1 and at any time flee from the enemy2 and others1 secure and indestructible by fire and battle1 easy and convenient to lift and place4 ,also methods of burning and destroying those of the enemy4 #b7 ,i know how1 when a place is besieged1 to take the water out of the trenches1 and make endless variety of bridges1 and covered ways and ladders1 and other machines pertaining to such expeditions4 #c7 ,item4 ,if1 by reason of the height of the banks1 or the strength of the place and its position1 it is impossible1 when besieging a place1 to avail oneself of the plan of bombardment1 ,i have methods for destroying every rock or other fortress1 even if it were founded on a rock1 c4 #d7 ,again ,i have kinds of mortars2 most convenient and easy to carry2 and with these can fling small stones almost resembling a storm2 and with the smoke of these causing great terror to the enemy1 to his great detriment and confusion4 #i7 #h99 ,and when the fight should be at sea ,i have kinds of many machines most efficient for offence and defence2 and vessels which will resist the attack of the largest guns and powder and fumes4 #e7 ,item499 ,i have means by secret and tortuous mines and ways1 made without noise to reach a designated spot1 even if it were needed to pass under a trench or a river4 #f7 ,item4 ,i will make covered chariots1 safe and unattackable which1 entering among the enemy with their artillery1 there is no body of men so great but they would break them4 ,and behind these1 infantry could follow quite unhurt and without any hindrance4 #g7 ,item4 ,in case of need ,i will make big guns1 mortars and light ordnance of fine and useful forms1 out of the common type4 #h7 ,where the operation of bombardment should fail1 ,i would contrive catapults1 mangonels1 trabocchi and other machines of marvellous efficacy and not in common use4 ,and in short1 according to the variety of cases1 ,i can contrive various and endless means of offence and defence4 #aj7 ,in time of peace ,i believe ,i can give perfect satisfaction and to the equal of any other in architecture and the composition of buildings public and private2 and in guiding water from one place to another4 ,item3 ,i can carry out sculpture in marble1 bronze or clay1 and also in painting whatever may be done1 and as well as any other1 be he whom he may4 #cb ,again1 the bronze horse may be taken in hand1 which is to be to the immortal glory and eternal honour of the prince your father of happy memory1 and of the illustrious house of ,sforza4 ,and if any one of the above-named things seem to any one to be impossible or not feasible1 ,i am most ready to make the experiment in your park1 or in whatever place may please your ,excellency--to whom ,i commend myself with the utmost humility c4 #acda4 ,to my illustrious ,lord1 ,lodovico1 ,duke of ,bari1 ,leonardo da ,vinci of ,florence-- ,leonardo4 ,footnote3 ,evidently a note of the superscription of a letter to the ,duke1 and written1 like the foregoing from left to right4 ,the manuscript containing it is of the year #adic4 ,lodovico was not proclaimed and styled ,duke of ,milan till ,september #adid4 ,the ,dukedom of ,bari belonged to the ,sforza family till #adii4 #acdb4 ,you would like to see a model which will prove useful to you and to me1 also it will be of use to those who will be the cause of our usefulness4 ,footnote3 #acdb4 #acdc4 ,these two notes occur in the same not very voluminous ,,ms4 as the former one and it is possible that they are fragments of the same letter4 ,by the ,modello1 the equestrian statue is probably meant1 particularly as the model of this statue was publicly exhibited in this very year1 #adic1 on tne occasion of the marriage of the ,emperor ,maximilian with ,bianca ,maria ,sforza4 #acdc4 ,there are here1 my ,lord1 many gentlemen who will undertake this expense among them1 if they are allowed to enjoy the use of admission to the waters1 the mills1 and the passage of vessels and when it is sold to them the price will be repaid to them by the canal of ,martesana4 #acdd4 ,i am greatly vexed to be in necessity1 but ,i still more regret that this should be the cause of the hindrance of my wish which is always disposed to obey your ,excellency4 ,perhaps your ,excellency did not give further orders to ,messer ,gualtieri1 believing that ,i had money enough4 ,i am greatly annoyed that you should have found me in necessity1 and that my having to earn my living should have hindered me 444 #ab ,it vexes me greatly that having to earn my living has forced me to interrupt the work and to attend to small matters1 instead of following up the work which your ,lordship entrusted to me4 ,but ,i hope in a short time to have earned so much that ,i may carry it out quietly to the satisfaction of your ,excellency1 to whom ,i commend myself2 and if your ,lordship thought that ,i had money1 your ,lordship was deceived4 ,i had to feed #f men for #ef months1 and have had #ej ducats4 #acde4 ,and if any other comission is given me by any 444 of the reward of my service4 ,because ,i am not able to be 444 things assigned because meanwhile they have 444 to them 444 444 which they well may settle rather than ,i 444 not my art which ,i wish to change and 444 given some clothing if ,i dare a sum 444 ,footnote3 ,the paper on which this is written is torn down the middle2 about half of each line remains4 ,my ,lord1 ,i knowing your ,excellency's mind to be occupied 444 to remind your ,lordship of my small matters and the arts put to silence that my silence might be the cause of making your ,lordship scorn 444 my life in your service4 ,i hold myself ever in readiness to obey 444 ,footnote #aa3 ,see ,no4 #gbc1 where this passage is repeated4 ,of the horse ,i will say nothing because ,i know the times are bad to your ,lordship how ,i had still to receive two years' salary of the 444 with the two skilled workmen who are constantly in my pay and at my cost that at last ,i found myself advanced the said sum about #ae lire 444 works of fame by which ,i could show to those who shall see it that ,i have been everywhere1 but ,i do not know where ,i could bestow my work more 444 ,footnote #ag3 ,see ,no4 #acdd l4 #ab4 ,i1 having been working to gain my living 444 ,i not having been informed what it is1 ,i find myself 444 ,footnote #ai3 ,in ,april1 #adih1 ,leonardo was engaged in painting the ,saletta ,nigra of the ,castello at ,milan4 7,see ,g4 ,,mongeri1 l',arte in ,milano1 #ahgb1 p4 #dag47 remember the commission to paint the rooms 444 ,i conveyed to your ,lordship only requesting you 444 ,draft of letter to be sent to ,piacenza 7#acdf4 #acdg74 #acdf4 ,magnificent ,commissioners of ,buildings ,i1 understanding that your ,magnificencies have made up your minds to make certain great works in bronze1 will remind you of certain things3 first that you should not be so hasty or so quick to give the commission1 lest by this haste it should become impossible to select a good model and a good master2 and some man of small merit may be chosen1 who by his insufficiency may cause you to 9999,footnote3 9999#acdf4 #acdg4 ,piacenza belonged to ,milan4 ,the ,lord spoken of in this letter1 is no doubt ,lodovico il ,moro4 ,one may infer from the concluding sentence 7,no4 #acdf1 l4 #cc4 #cd and ,no4 #acdg71 that ,leonardo1 who no doubt compiled this letter1 did not forward it to ,piacenza himself1 but gave it to some influential patron1 under whose name and signature a copy of it was sent to the ,commission4 be abused by your descendants1 judging that this age was but ill supplied with men of good counsel and with good masters2 seeing that other cities1 and chiefly the city of the ,florentines1 has been as it were in these very days1 endowed with beautiful and grand works in bronze2 among which are the doors of their ,baptistery4 ,and this town of ,florence1 like ,piacenza1 is a place of intercourse1 through which many foreigners pass2 who1 seeing that the works are fine and of good quality1 carry away a good impression1 and will say that that city is well filled with worthy inhabitants1 seeing the works which bear witness to their opinion2 and on the other hand1 ,i say seeing so much metal expended and so badly wrought1 it were less shame to the city if the doors had been of plain wood2 because1 the material1 costing so little1 would not seem to merit any great outlay of skill444 ,now the principal parts which are sought for in cities are their cathedrals1 and of these the first things which strike the eye are the doors1 by which one passes into these churches4 ,beware1 gentlemen of the ,commission1 lest too great speed in your determination1 and so much haste to expedite the entrusting of so great a work as that which ,i hear you have ordered1 be the cause that that which was intended for the honour of ,god and of men should be turned to great dishonour of your judgments1 and of your city1 which1 being a place of mark1 is the resort and gathering-place of innumerable foreigners4 ,and this dishonour would result if by your lack of diligence you were to put your trust in some vaunter1 who by his tricks or by favour shown to him here should obtain such work from you1 by which lasting and very great shame would result to him and to you4 ,thus ,i cannot help being angry when ,i consider what men those are who have conferred with you as wishing to undertake this great work without thinking of their sufficiency for it1 not to say more4 ,this one is a potter1 that one a maker of cuirasses1 this one is a bell-founder1 another a bell ringer1 and one is even a bombardier2 and among them one in his ,lordship's service1 who boasted that he was the gossip of ,messer ,ambrosio ,ferrere ,footnote #bf3 ,messer ,ambrogio ,ferrere was ,farmer of the ,customs under the ,duke4 ,piacenza at that time belonged to ,milan41 who has some power and who has made him some promises2 and if this were not enough he would mount on horseback1 and go to his ,lord and obtain such letters that you could never refuse to give him the work4 ,but consider where masters of real talent and fit for such work are brought when they have to compete with such men as these4 ,open your eyes and look carefully lest your money should be spent in buying your own disgrace4 ,i can declare to you that from that place you will procure none but average works of inferior and coarse masters4 ,there is no capable man1--#cc and you may believe me1--except ,leonardo the ,florentine1 who is making the equestrian statue in bronze of the ,duke ,francesco and who has no need to bring himself into notice1 because he has work for all his life time2 and ,i doubt1 whether being so great a work1 he will ever finish it #cd4 ,the miserable painstakers 444 with what hope may they expect a reward of their merit8 #acdg4 ,there is one whom his ,lordship invited from ,florence to do this work and who is a worthy master1 but with so very much business he will never finish it2 and you may imagine that a difference there is to be seen between a beautiful object and an ugly one4 ,quote ,pliny4 ,letter to the ,cardinal ,ippolito d' ,este4 #acdh4 ,most ,illustrious and most ,reverend ,lord4 ,the ,lord ,ippolito1 ,cardinal of ,este at ,ferrare4 ,most ,illustrious and most ,reverend ,lord4 ,i arrived from ,milan but a few days since and finding that my elder brother refuses to 9999,footnote3 ,this letter addressed to the ,cardinal ,ippolito d',este is here given from ,marchese ,g4 ,,campori',s publication3 ,nuovi documenti per la ,vita di ,leonardo da ,vinci4 ,atti e ,memorie delle ,r4 ,r4 ,deputazioni di ,storia patria per la provincie modenesi e par- menesi1 ,vol4 ,,iii4 ,it is the only text throughout this work which ,i have not myself examined and copied from the original4 ,the learned discoverer of this letter--the only letter from ,leonardo hitherto known as having been sent--adds these interesting remarks3 ,codesto ,cardinale nato ad ,ercole ,i4 nel #adgj1 arcivescovo di ,strigonia a sette anni1 poi d',agra1 aveva conseguito nel #adig la pingue ed ambita cattedra di ,milano1 la dove avra conosciuto il ,vinci1 sebbene il poco amore ch'ei professava alle arti lasci credere che le proteste di servitu di ,leonardo piu che a gratitudine per favori ricevuti e per opere a lui allogate1 accennino a speranza per un favore che si aspetta4 ,notabile e ancora in questo prezioso documento la ripetuta signatura del grande artista 'che si scrive ,vincio e ,vincius1 non da ,vinci come si tiene comunemente1 sebbene l'una e l'altra possano valere a significare cosi il casato come il paese2 restando a sapere se il nome del paese di ,vinci fosse assunto a cognome della famiglia di ,leonardo nel qual supposto piu propriamento avrebbe a chiamarsi ,leonardo ,vinci1 o ,vincio 7latinamente ,vincius7 com'egli stesso amo segnarsi in questa lettera1 e come scrissero parecchi contenporanei di lui1 il ,casio1 il ,cesariano1 ,geoffrey ,tory1 il ,gaurico1 il ,bandello1 ,raffaelle ,maffei1 il ,paciolo4 ,per ultimo non lascero d'avvertire come la lettera del ,vinci e assai ben conservata1 di nitida e larga scrittura in forma pienemente corrispondente a quella dei suoi manoscritti1 vergata all'uso comune da sinistra a destra1 anziche contrariamente come fu suo costume2 ma indubbiamente autentica e fornita della menzione e del suggello che fresca ancora conserva l'impronta di una testa di profilo da un picciolo antico cammeo4 7,compare ,no4 #acfh1 note47 carry into effect a will1 made three years ago when my father died--as also1 and no less1 because ,i would not fail in a matter ,i esteem most important--,i cannot forbear to crave of your most ,reverend ,highness a letter of recommendation and favour to ,ser ,raphaello ,hieronymo1 at present one of the illustrious members of the ,signoria before whom my cause is being argued2 and more particularly it has been laid by his ,excellency the ,gonfaloniere into the hands of the said ,ser ,raphaello1 that his ,worship may have to decide and end it before the festival of ,all ,saints4 ,and therefore1 my ,lord1 ,i entreat you1 as urgently as ,i know how and am able1 that your ,highness will write a letter to the said ,ser ,raphaello in that admirable and pressing manner which your ,highness can use1 recommending to him ,leonardo ,vincio1 your most humble servant as ,i am1 and shall always be2 requesting him and pressing him not only to do me justice but to do so with despatch2 and ,i have not the least doubt1 from many things that ,i hear1 that ,ser ,raphaello1 being most affectionately devoted to your ,highness1 the matter will issue ad votum4 ,and this ,i shall attribute to your most ,reverend ,highness' letter1 to whom ,i once more humbly commend myself4 ,et bene valeat4 ,florence ,x,v,i,i,ia #g;bris #aejg4 ,e4 ,v4 ,r4 ,d4 your humble servant ,leonardus ,vincius1 pictor4 ,draft of ,letter to the ,governor of ,milan4 #acdi4 ,i am afraid lest the small return ,i have made for the great benefits1 ,i have received from your ,excellency1 have not made you somewhat angry with me1 and that this is why to so many letters which ,i have written to your ,lordship ,i have never had an answer4 ,i now send ,salai to explain to your ,lordship that ,i am almost at an end of the litigation ,i had with my brother2 that ,i hope to find myself with you this ,easter1 and to carry with me two pictures of two ,madonnas of different sizes4 ,these were done for our most ,christian ,king1 or for whomsoever your ,lordship may please4 ,i should be very glad to know on my return thence where ,i may have to reside1 for ,i would not give any more trouble to your ,lordship4 ,also1 as ,i have worked for the most ,christian ,king1 whether my salary is to continue or not4 ,i wrote to the ,president as to that water which the king granted me1 and which ,i was not put in possession of because at that time there was a dearth in the canal by reason of the great droughts and because ,footnote3,compare ,nos4 #ajji and #ajaj4 ,leonardo has noted the payment of the pension from the king in #aeje4 its outlets were not regulated2 but he certainly promised me that when this was done ,i should be put in possession4 ,thus ,i pray your ,lordship that you will take so much trouble1 now that these outlets are regulated1 as to remind the ,president of my matter2 that is1 to give me possession of this water1 because on my return ,i hope to make there instruments and other things which will greatly please our most ,christian ,king4 ,nothing else occurs to me4 ,i am always yours to command4 ,footnote3#acdi4 ,charles d',amboise1 ,marechal de ,chaumont1 was ,governor of ,milan under ,louis ,,xii4 ,leonardo was in personal communication with him so early as in #aejc4 ,he was absent from ,milan in the autumn of #aejf and from ,october l#el#j--when he besieged ,pope ,julius ,,ii4 in ,bologna--till his death1 which took place at ,correggio1 ,february #aa1 #aeaa4 ,francesco ,vinci1 ,leonardo's uncle1 died--as ,amoretti tells us--in the winter of l#el#j-aa 7or according to ,uzielli in #aejf871 and ,leonardo remained in ,florence for business connected with his estate4 ,the letter written with reference to this affair1 ,no4 #acdh1 is undoubtedly earlier than the letters ,nos4 #acdi and #acej4 ,amoretti tells us1 ,memorie ,storiche1 ch4 ,,ii1 that the following note existed on the same leaf in ,,ms4 ,c4 ,a4 ,i have not however succeeded in finding it4 ,the passage runs thus3 ,jo sono quasi al fine del mio letizio che io o con mie fratetgli 444 ,ancora ricordo a ,v4 ,excia la facenda che o cum ,ser ,juliana mio ,fratello capo delli altri fratelli ricordandoli come se offerse di conciar le cose nostre fra noi fratelli del comune della eredita de mio ,zio1 e quelli costringa alla expeditione1 quale conteneva la lettera che lui me mando4 ,c4 ,a4 #cfd;b2 #aach;b ,drafts of ,letters to the ,superintendent of ,canals and to ,fr4 ,melzi4 #acej4 ,magnificent ,president1 ,i am sending thither ,salai1 my pupil1 who is the bearer of this1 and from him you will hear by word of mouth the cause of my444 ,magnificent ,president1 ,i444 ,magnificent ,president3--,having ofttimes remembered the proposals made many times to me by your ,excellency1 ,i take the liberty of writing to remind your ,lordship of the promise made to me at my last departure1 that is the possession of the twelve inches of water granted to me by the most ,christian ,king4 ,your ,lordship knows that ,i did not enter into possession1 because at that time when it was given to me there was a dearth of water in the canal1 as well by reason of the great drought as also because the outlets were not regulated2 but your ,excellency promised me that as soon as this was done1 ,i should have my rights4 ,afterwards hearing that the canal was complete ,i wrote several times to your ,lordship and to ,messer ,girolamo da ,cusano1who has in his keeping the deed of this gift2 and so also ,i wrote to ,corigero and never had a reply4 ,i now send thither ,salai1 my pupil1 the bearer of this1 to whom your ,lordship may tell by word of mouth all that happened in the matter about which ,i petition your ,excellency4 ,i expect to go thither this ,easter since ,i am nearly at the end of my lawsuit1 and ,i will take with me two pictures of our ,lady which ,i have begun1 and at the present time have brought them on to a very good end2 nothing else occurs to me4 ,my ,lord the love which your ,excellency has always shown me and the benefits that ,i have constantly received from you ,i have hitherto444 ,i am fearful lest the small return ,i have made for the great benefits ,i have received from your ,excellency may not have made you somewhat annoyed with me4 ,and this is why1 to many letters which ,i have written to your ,excellency ,i have never had an answer4 ,i now send to you ,salai to explain to your ,excellency that ,i am almost at the end of my litigation with my brothers1 and that ,i hope to be with you this ,easter and carry with me two pictures on which are two ,madonnas of different sizes which ,i began for the most ,christian ,king1 or for whomsoever you please4 ,i should be very glad to know where1 on my return from this place1 ,i shall have to reside1 because ,i do not wish to give more trouble to your ,lordship2 and then1 having worked for the most ,christian ,king1 whether my salary is to be continued or not4 ,i write to the ,president as to the water that the king granted me of which ,i had not been put in possession by reason of the dearth in the canal1 caused by the great drought and because its outlets were not regulated2 but he promised me certainly that as soon as the regulation was made1 ,i should be put in possession of it2 ,i therefore pray you that1 if you should meet the said ,president1 you would be good enough1 now that the outlets are regulated1 to remind the said ,president to cause me to be put in possession of that water1 since ,i understand it is in great measure in his power4 ,nothing else occurs to me2 always yours to command4 ,good day to you ,messer ,francesco4 ,why1 in ,god's name1 of all the letters ,i have written to you1 have you never answered one4 ,now wait till ,i come1 by ,god1 and ,i shall make you write so much that perhaps you will become sick of it4 ,dear ,messer ,francesco4 ,i am sending thither ,salai to learn from ,his ,magnificence the ,president to what end the regulation of the water has come since1 at my departure this regulation of the outlets of the canal had been ordered1 because ,his ,magnificence the ,president promised me that as soon as this was done ,i should be satisfied4 ,it is now some time since ,i heard that the canal was in order1 as also its outlets1 and ,i immediately wrote to the ,president and to you1 and then ,i repeated it1 and never had an answer4 ,so you will have the goodness to answer me as to that which happened1 and as ,i am not to hurry the matter1 would you take the trouble1 for the love of me1 to urge the ,president a little1 and also ,messer ,girolamo ,cusano1 to whom you will commend me and offer my duty to his ,magnificence4 99#acej4 #bh-cf4 ,draft of a letter to ,francesco ,melzi1 born l#dic--;a youth therefore of about #ag in #aeaj4 ,leonardo addresses his young friend as ,messer1 as being the son of a noble house4 ,melzi practised art under ,leonardo as a dilettante and not as a pupil1 like ,cesare da ,sesto and others 7,see ,,lermolieff1 ,die ,galerien c41 p4 #dgf74 99,drafts of a letter to ,giuliano de' ,medici 7#acea-aceb74 #acea4 ,most illustrious ,lord4 ,i greatly rejoice most ,illustrious ,lord at your444 ,i was so greatly rejoiced1 most illustrious ,lord1 by the desired restoration of your health1 that it almost had the effect that my own health recovered--,i have got through my illness--my own illness left me-- --of your ,excellency's almost restored health4 ,but ,i am extremely vexed that ,i have not been able completely to satisfy the wishes of your ,excellency1 by reason of the wickedness of that deceiver1 for whom ,i left nothing undone which could be done for him by me and by which ,i might be of use to him2 and in the first place his allowances were paid to him before the time1 which ,i believe he would willingly deny1 if ,i had not the writing signed by myself and the interpreter4 ,and ,i1 seeing that he did not work for me unless he had no work to do for others1 which he was very careful in solliciting1 invited him to dine with me1 and to work afterwards near me1 because1 besides the saving of expense1 he 99#acea4 #acec4;,footnote3 ,it is clear from the contents of this notes that they refer to ,leonardo's residence in ,rome in #aeac-aeae4 ,nor can there be any doubt that they were addressed to ,leonardo's patron at the time3 ,giuliano de' ,medici1 third son of ,lorenzo the ,magnificent and brother of ,pope ,leo ,x 7born #adgh74 ,in #aeab he became the head of the ,florentine ,republic4 ,the ,pope invited him to ,rome1 where he settled2 in #aeac he was named patrician with much splendid ceremonial4 ,the medal struck in honour of the event bears the words ,,mag4 ,,ivlian4 ,,medices4 ,leonardo too uses the style ,magnifico1 in his letter4 ,compare also ,no4 #acgg4 ,gl,n,o ,,capponi 7,storia della ,repubblica di ,firenze1 ,vol4 ,,iii1 p4 #aci7 thus describes the character of ,giuliano de' ,medici1 who died in #aeaf3 ,era il migliore della famiglia1 di vita placida1 grande spenditore1 tenendo intorno a s99e uomini ingegnosi1 ed ogni nuova cosa voleva provare4 ,see too ,,gregorovius1 ,geschichte der ,stadi ,rom1 ,,viii 7book ,,xiv4 ,,iii1 #b73 ,die ,luftschl99osser f99urstlicher ,gr99osse1 wozu ihn der ,papst hatte erheben wollen zerfielen4 ,julian war der edelste aller damaligen ,medici1 ein ,mensch von innerlicher ,richtung1 unbefriedigt durch das ,leben1 mitten im ,sonnenglanz der ,herrlichkeit ,leo's ,x4 eine dunkle ,gestalt die wie ein ,schatten vor99uberzog4 ,giuliano lived in the ,vatican1 and it may be safely inferred from ,no4 #aceb l4 #b1 and ,no4 #acec l4 #d1 that ,leonardo did the same4 ,from the following unpublished notice in the ,vatican archives1 which ,m4 ,eug4 ,m99untz1 librarian of the ,ecole des ,beaux arts1 ,paris1 has done me the favour to communicate to me1 we get a more accurate view of ,leonardo's relation to the often named ,,giorgio ,,tedesco3 ,nota delle provisione 7sic7 a da pagare per me in nome del nostro ill4 ,s4 ,bernardo ,bini e chomp99a di ,roma1 e prima della ill99ma sua chonsorte ogni mese d4 #hjj4 ,a ,l99do da ,vinci per sua provisione d4 ,,xxxiii1 e pi99u d4 ,,vii al detto per la provisione di ,giorgio tedescho1 che sono in tutto d4 #dj4 ,from this we learn1 that seven ducats formed the ,german's monthly wages1 but according to ,no4 #acec l4 #g he pretended that eight ducats had been agreed upon4 would acquire the ,italian language4 ,he always promised1 but would never do so4 ,and this ,i did also1 because that ,giovanni1 the ,german who makes the mirrors1 was there always in the workshop1 and wanted to see and to know all that was being done there and made it known outside 444 strongly criticising it2 and because he dined with those of the ,pope's guard1 and then they went out with guns killing birds among the ruins2 and this went on from after dinner till the evening2 and when ,i sent ,lorenzo to urge him to work he said that he would not have so many masters over him1 and that his work was for your ,excellency's ,wardrobe2 and thus two months passed and so it went on2 and one day finding ,gian ,niccolo of the ,wardrobe and asking whether the ,german had finished the work for your ,magnificence1 he told me this was not true1 but only that he had given him two guns to clean4 ,afterwards1 when ,i had urged him farther1 be left the workshop and began to work in his room1 and lost much time in making another pair of pincers and files and other tools with screws2 and there he worked at mills for twisting silk which he hid when any one of my people went in1 and with a thousand oaths and mutterings1 so that none of them would go there any more4 ,i was so greatly rejoiced1 most ,illustrious ,lord1 by the desired restoration of your health1 that my own illness almost left me4 ,but ,i am greatly vexed at not having been able to completely satisfy your ,excellency's wishes by reason of the wickedness of that ,german deceiver1 for whom ,i left nothing undone by which ,i could have hope to please him2 and secondly ,i invited him to lodge and board with me1 by which means ,i should constantly see the work he was doing and with greater ease correct his errors while1 besides this1 he would learn the ,italian tongue1 by means of which be could with more ease talk without an interpreter2 his moneys were always given him in advance of the time when due4 ,afterwards he wanted to have the models finished in wood1 just as they were to be in iron1 and wished to carry them away to his own country4 ,but this ,i refused him1 telling him that ,i would give him1 in drawing1 the breadth1 length1 height and form of what he had to do2 and so we remained in ill-will4 ,the next thing was that he made himself another workshop and pincers and tools in his room where he slept1 and there he worked for others2 afterwards he went to dine with the ,swiss of the guard1 where there are idle fellows1 in which he beat them all2 and most times they went two or three together with guns1 to shoot birds among the ruins1 and this went on till evening4 ,at last ,i found how this master ,giovanni the mirror-maker was he who had done it all1 for two reasons2 the first because he had said that my coming here had deprived him of the countenance and favour of your ,lordship which always444 ,the other is that he said that his iron-workers' rooms suited him for working at his mirrors1 and of this he gave proof2 for besides making him my enemy1 he made him sell all he had and leave his workshop to him1 where he works with a number of workmen making numerous mirrors to send to the fairs4 #aceb4 ,i was so greatly rejoiced1 most ,illustrious ,lord1 by the wished for recovery of your health1 that my own ills have almost left me2 and ,i say ,god be praised for it4 ,but it vexes me greatly that ,i have not been able completely to satisfy your ,excellency's wishes by reason of the wickedness of that ,german deceiver1 for whom ,i left nothing undone by which ,i could hope to please him2 and secondly ,i invited him to lodge and board with me1 by which means ,i should see constantly the work he was doing1 for which purpose ,i would have a table fixed at the foot of one of these windows1 where he could work with the file and finish the things made below2 and so ,i should constantly see the work he might do1 and it could be corrected with greater ease4 ,draft of letter written at ,rome4 #acec4 ,this other hindered me in anatomy1 blaming it before the ,pope2 and likewise at the hospital2 and he has filled 99#d this whole ,belvedere with workshops for mirrors2 and he did the same thing in ,maestro ,giorgio's room4 ,he said that he had been promised 99#g eight ducats every month1 beginning with the first day1 when he set out1 or at latest when he spoke with you2 and that you agreed4 ,seeing that he seldom stayed in the workshop1 and that he ate a great deal1 ,i sent him word that1 if he liked ,i could deal with him separately for each thing that he might make1 and would give him what we might agree to be a fair valuation4 ,he took counsel with his neighbour and gave up his room1 selling every thing1 and went to find444 ,miscellaneous ,records 7#aced4 #acee7- #aced4 ,dear ,benedetto de' ,pertarti4 ,when the proud giant fell because of the bloody and miry state of the ground it was as though a mountain had fallen so that the country shook as with an earthquake1 and terror fell on ,pluto in hell4 ,from the violence of the shock he lay as stunned on the level ground4 ,suddenly the people1 seeing him as one killed by a thunderbolt1 turned back2 like ants running wildly over the body of the fallen oak1 so these rushing over his ample limbs4444444444 them with 99#aced4;,footnote3 ,a puzzling passage1 meant1 as it would seem1 for a jest4 ,compare the description of ,giants in ,dante1 ,inf4 ,,xxi and ,,xxii4 ,perhaps ,leonardo had the ,giant ,antaeus in his mind4 ,of him the myth relates that he was a son of ,ge1 that he fed on lions2 that he hunted in ,libya and killed the inhabitants4 ,he enjoyed the peculiarity of renewing his strength whenever he fell and came in contact with his mother earth2 but that ,hercules lifted him up and so conquered and strangled him4 ,lucan gives a full account of the struggle4 ,pharsalia ,,iv1 #fag4 ,the reading of this passage1 which is very indistinctly written1 is in many places doubtful4 frequent wounds2 by which1 the giant being roused and feeling himself almost covered by the multitude1 he suddenly perceives the smarting of the stabs1 and sent forth a roar which sounded like a terrific clap of thunder2 and placing his hands on the ground he raised his terrible face3 and having lifted one hand to his head he found it full of men and rabble sticking to it like the minute creatures which not unfrequently are found there2 wherefore with a shake of his head he sends the men flying through the air just as hail does when driven by the fury of the winds4 ,many of these men were found to be dead2 stamping with his feet4 ,and clinging to his hair1 and striving to hide in it1 they behaved like sailors in a storm1 who run up the ropes to lessen the force of the wind by taking in sail4 ,news of things from the ,east4 ,be it known to you that in the month of ,june there appeared a ,giant1 who came from the ,lybian desert444 mad with rage like ants4444 struck down by the rude4 ,this great ,giant was born in ,mount ,atlas and was a hero 444 and had to fight against the ,egyptians and ,arabs1 ,medes and ,persians4 ,he lived in the sea on whales1 grampuses and ships4 ,mars fearing for his life took refuge under the444 of ,jove4 ,and at the great fall it seemed as though the whole province quaked4 #acee4 ,this spirit returns to the brain whence it had departed1 with a loud voice and with these words1 it moved444 ,and if any man though he may have wisdom or goodness 444444444 ,footnote3 ,this passage1 very difficult to decipher1 is on the reverse of a drawing at ,windsor1 ,pl4 ,,cxxii1 which possibly has some connection with it4 ,the drawing is slightly reduced in this reproduction2 the original being #be cm4 high by #ai cm4 wide4 ,o blessed and happy spirit whence comest thou8 ,well have ,i known this man1 much against my will4 ,this one is a receptacle of villainy2 he is a perfect heap of the utmost ingratitude combined with every vice4 ,but of what use is it to fatigue myself with vain words8 ,nothing is to be found in them but every form of sin 444 ,and if there should be found among them any that possesses any good1 they will not be treated differently to myself by other men2 and in fine1 ,i come to the conclusion that it is bad if they are hostile1 and worse if they are friendly4 ,miscellaneous drafts of letters and personal records 7#acef--acfh74 #acef4 ,all the ills that are or ever were1 if they could be set to work by him1 would not satisfy the desires of his iniquitous soul2 and ,i could not in any length of time describe his nature to you1 but ,i conclude444 #aceg4 ,i know one who1 having promised me much1 less than my due1 being disappointed of his presumptuous desires1 has tried to deprive me of all my friends2 and as he has found them wise and not pliable to his will1 he has menaced me that1 having found means of denouncing me1 he would deprive me of my benefactors4 ,hence ,i have informed your ,lordship of this1 to the end that this man who wishes to sow the usual scandals1 may find no soil fit for sowing the thoughts and deeds of his evil nature so that he1 trying to make your ,lordship1 the instrument of his iniquitous and maliceous nature may be disappointed of his desire4 #aceh4 ,and in this case ,i know that ,i shall make few enemies seeing that no one will believe what ,i can say of him2 for they are but ,footnote3 ,below this text we read gusstino--,giustino and in another passage on the same page ,justin is quoted 7,no4 #abaj1 #a4 #dh74 ,the two have however no real connection4 few whom his vices have disgusted1 and he only dislikes those men whose natures are contrary to those vices4 ,and many hate their fathers1 and break off friendship with those who reprove their vices2 and he will not permit any examples against them1 nor any advice4 ,if you meet with any one who is virtuous do not drive him from you2 do him honour1 so that he may not have to flee from you and be reduced to hiding in hermitages1 or caves or other solitary places to escape from your treachery2 if there is such an one among you do him honour1 for these are our ,saints upon earth2 these are they who deserve statues from us1 and images2 but remember that their images are not to be eaten by you1 as is still done in some parts of ,india ,footnote #ae3 ,in explanation of this passage ,i have received the following communication from ,dr4 ,g4 ,w4 ,,leitner of ,lahore3 ,so far as ,indian customs are known to us1 this practice spoken of by ,leonardo as 'still existing in some parts of ,india' is perfectly unknown2 and it is equally opposed to the spirit of ,hinduism1 ,mohammedanism and ,sikhism4 ,in central ,thibet the ashes of the dead1 when burnt1 are mixed with dough1 and small figures--usually of ,buddha--are stamped out of them and some are laid in the grave while others are distributed among the relations4 ,the custom spoken of by ,leonardo may have prevailed there but ,i never heard of it4 ,possibly ,leonardo refers here to customs of nations of ,america4 where1 when the images have according to them1 performed some miracle1 the priests cut them in pieces1 being of wood1 and give them to all the people of the country1 not without payment2 and each one grates his portion very fine1 and puts it upon the first food he eats2 and thus believes that by faith he has eaten his saint who then preserves him from all perils4 ,what do you think here1 ,man1 of your own species8 ,are you so wise as you believe yourselves to be8 ,are these things to be done by men8 #acei4 ,as ,i told you in past days1 you know that ,i am without any4444 ,francesco d',antonio4 ,bernardo di ,maestro ,jacopo4 #acfj4 ,tell me how the things happened4 #acfa4 j lorezo #b inbiadali #c inferri de #d;in lorezo #e;inno abuil #f in acocatu #g per la sella #h;colte di lor #iv cavallott ,i#j;el uiagg ,i,ial ,i#b;a lurez #ac;in biada #ad;inferri #ae;abuss #af;in viagg #ag;alorz ,footnote3 ,this seems to be the beginning of a letter1 but only the first words of the lines have been preserved1 the leaf being torn down the middle4 ,no translation is possible4 #acfb4 ,and so may it please our great ,author that ,i may demonstrate the nature of man and his customs1 in the way ,i describe his figure4 ,footnote3 ,a preparatory note for the passage given as ,no4 #gih1 99#aa4 #da--db4 #acfc4 ,this writing distinctly about the kite seems to be my destiny1 because among the first recollections of my infancy1 it seemed to me that1 as ,i was in my cradle1 a kite came to me and opened my mouth with its tail1 and struck me several times with its tail inside my lips4 ,footnote3 ,this note probably refers to the text ,no4 #abba4 ,c4 ,a4 #bdh;a2 #gcg;a #acfd4 ,when ,i did well1 as a boy you used to put me in prison4 ,now if ,i do it being grown up1 you will do worse to me4 #acfe4 ,tell me if anything was ever done4 #acff4 ,tell me if ever ,i did a thing which me 4444 #acfg4 ,do not reveal1 if liberty is precious to you2 my face is the prison of love4 ,footnote3,this note seems to be a quotation4 #acfh4 ,maestro ,leonardo of ,florence4 ,footnote3 ,so ,leonardo writes his name on a sheet with sundry short notes1 evidently to try a pen4 ,compare the signature with those in ,nos4 #acda1 #acdh and #acgd 7see also ,no4 #acdf1 l4 #cc74 ,the form ,lionardo does not occur in the autographs4 ,the ,portrait of the ,master in the ,royal ,library at ,turin1 which is reproduced--slightly diminished--on ,pl4 ,i1 has in the original two lines of writing underneath2 one in red chalk of two or three words is partly effaced3 lionardo it444 lm 7or lai872 the second written in pencil is as follows3 fatto da lui stesso assai vecchio4 ,in both of these the writing is very like the ,master's1 but is certainly only an imitation4 ,notes bearing ,dates 7#acfi--acgh74 #acfi4 ,the day of ,santa ,maria della ,neve of the ,snows ,august the #bnd #adgc4 ,footnote3 99,w4 ,an4 ,i4 #acfh4 #acfi4 ,this date is on a drawing of a rocky landscape4 ,see ,chronique des ,arts #ahha no4 #bc3 ,leonard de ,vinci a-t-il ete au ,righi le #e aout #adgc8 letter by ,h4 de ,geymuller4 ,the next following date in the ,,mss4 is #adgh 7see ,no4 #ffc74 #acgj4 ,on the #bnd of ,april #adhi1 book entitled ',of the human figure'4 ,footnote3 ,while the letters in the ,,ms4 notes of #adgc and #adgh are very ornate1 this note and the texts on anatomy on the same sheet 7for instance ,no4 #hje7 are in the same simple hand as we see on ,pl4 ,,cxvi and ,,cxix4 ,no #acgj is the only dated note of the years between #adhj and #adhi1 and the characters are in all essential points identical with those that we see in the latest manuscripts written in ,france 7compare the facsimiles on ,pl4 ,,cxv and p4 #bed71 so that it is hardly possible to determine exactly the date of a manuscript from the style of the handwriting1 if it does not betray the peculiarities of style as displayed in the few notes dated previous to l#dhj4--;,compare the facsimile of the manuscripts #adgi on ,pl4,,lxii1 ,no4 #b2 ,no4 #ffd1 note1 ,vol4 ,i p4 #cdf4 ,this shows already a marked simplicity as compared with the calligraphy of ,i#dgh4 ,the text ,no4 #gbj belongs to the year #adij2 ,no4 #aeaj to the year #adib2 ,no4 #adei1 ,no4 #achd and ,no4 #adfj to the year #adic2 ,no4 #adfc1 ,no4 #aeag1 ,no4 #ajbd1 #ajbe and #adfa to the year #adid2 ,nos4 #aebc and #aebd to the year #adig4 ,c4 ,a4 #ajc;a2 #cbe;a #acga4 ,on the ist of ,august #adii1 ,i wrote here of motion and of weight4 ,footnote3#acga4 ,scrissi qui4 ,leonardo does not say where2 still we may assume that it was not in ,milan4 ,amoretti writes1 ,memorie ,storiche1 chap4 ,,xix3 ,sembra pertanto che non nel #adii ma nel #aejj1 dopo il ritorno e la prigionia del duca1 sia da qui partito ,lionardo per andare a ,firenze2 ed e quindi probabile1 che i mesi di governo nuovo e incerto abbia passati coll' amico suo ,francesco ,melzi a ,vaprio1 ove meglio che altrove studiar potea la natura1 e soprattutta le acque1 e l',adda specialmente1 che gia era stato l'ogetto delle sue idrostatiche ricerche4 ,at that time ,melzi was only six years of age4 ,the next date is #aejb2 to this year belong ,no4 #ajcd1 #ajdj1 #ajdb1 #ajdh and #ajec4 ,the note ,no4 #aebe belongs to the year #aejc4 #acgb4 ,on the #ith of ,july #aejd1 ,wednesday1 at seven o'clock1 died ,ser ,piero da ,vinci1 notary at the ,palazzo del ,podest99a1 my father1 --at seven o'clock1 being eighty years old1 leaving behind ten sons and two daughters4 ,footnote3 ,this statement of ,ser ,piero's age contradicts that of the ,riassunto della portata di ,antonio da ,vinci 7,leonardo's grandfather71 who speaks of ,ser ,piero as being thirty years old in #adeg2 and that of the ,riassunto della portata di ,ser ,piero e ,francesco1 sons of ,antonia da ,vinci1 where ,ser ,piero is mentioned as being forty in #adfi4 ,these documents were published by ,g4 ,,uzielli1 ,ricerche intorno a ,l4 da ,vinci1 ,firenze1 #ahgb1 pp4 #add and #adf4 ,leonardo was1 as is well known1 a natural son4 ,his mother ',la ,catarina' was married in #adeg to ,acchattabriga di ,piero del ,vaccha da ,vinci4 ,she died in #aeai4 ,leonardo never mentions her in the ,manuscripts4 ,in the year of ,leonardo's birth ,ser ,piero married ,albiera di ,giovanni ,amadoci1 and after her death at the age of thirty eight he again married1 ,francesca1 daughter of ,ser ,giovanni ,lanfredi1 then only fifteen4 ,their children were ,leonardo's halfbrothers1 ,antonio 7b4 #adgf71 ,ser ,giuliano 7b4 #adgi71 ,lorenzo 7b4 #adhd71 a girl1 ,violante 7b4 #adhe71 and another boy ,domenico 7b4 #adhf72 ,domenico's descendants still exist as a family4 ,ser ,piero married for the third time ,lucrezia di ,guglielmo ,cortigiani by whom he had six children3 ,margherita 7b4 #adia71 ,benedetto 7b4 #adib71 ,pandolfo 7b4 #adid71 ,guglielmo 7b4 #adif71 ,bartolommeo 7b4 #adig71 and ,giovanni7 date of birth unknown74 ,pierino da ,vinci the sculptor 7about #aebj-aeed7 was the son of ,bartolommeo1 the fifth of these children4 ,the dates of their deaths are not known1 but we may infer from the above passage that they were all still living in #aeje4 #acgc4 ,on ,wednesday at seven o'clock died ,ser ,piero da ,vinci on the #ith of ,july #aejd4 ,footnote3 ,this and the previous text it may be remarked are the only mention made by ,leonardo of his father2 ,nos4 #aebf1 #aebg and ,no4 #adfc are of the year #aejd4 #acgd4 ,begun by me1 ,leonardo da ,vinci1 on the l#bth of ,july #aeje4 ,footnote3 ,thus he writes on the first page of the ,,ms4 ,the title is on the foregoing coversheet as follows3 ,libro titolato disstrafformatione coe 7cio99e7 d'un corpo nvn 7in un7 altro sanza diminuitione e acresscemento di materia4 #acge4 ,begun at ,milan on the l#bth of ,september #aejh4 ,footnote3 ,no4 #aebh and ,no4 #aebi belong to the same year4 ,the text ,vol4 ,i1 ,no4 #d belongs to the following year #aeji 7#aejh old style72 so also does ,no4 #ajji4-- ,nos4 #ajbb1 #ajeg and #adfd belong to #aeaa4 #acgf4 ,on the #ith of ,january #aeac4 ,footnote3 ,no4 #adfe belongs to the same year4 ,no4 #ajfe has the next date #aead4 #acgg4 ,the ,magnifico ,giuliano de' ,medici left ,rome on the #ith of ,january #aeae1 just at daybreak1 to take a wife in ,savoy2 and on the same day fell the death of the king of ,france4 ,footnote3 ,giuliano de ,medici1 brother to ,pope ,leo ,x42 see note to ,nos4 #acea-acec4 ,in ,february1 #aeae1 he was married to ,filiberta1 daughter of ,filippo1 ,duke of ,savoy1 and aunt to ,francis ,i1 ,louis ,,xii's successor on the throne of ,france4 ,louis ,,xii died on ,jan4 #ast1 and not on ,jan4 #ith as is here stated4-- ,this addition is written in paler ink and evidently at a later date4 #acgh4 ,on the #bdth of ,june1 ,st ,john's day1 #aeah at ,amboise1 in the palace of444 ,footnote3 ,castello del clli4 ,the meaning of this word is obscure2 it is perhaps not written at full length4 ,,xxii4 ,miscellaneous ,notes4 ,the incidental memoranda scattered here and there throughout the ,,mss4 can have been for the most part intelligible to the writer only2 in many cases their meaning and connection are all the more obscure because we are in ignorance about the persons with whom ,leonardo used to converse nor can we say what part he may have played in the various events of his time4 ,vasari and other early biographers give us a very superficial and far from accurate picture of ,leonardo's private life4 ,though his own memoranda1 referring for the most part to incidents of no permanent interest1 do not go far towards supplying this deficiency1 they are nevertheless of some importance and interest as helping us to solve the numerous mysteries in which the history of ,leonardo's long life remains involved4 ,we may at any rate assume1 from ,leonardo's having committed to paper notes on more or less trivial matters on his pupils1 on his house-keeping1 on various known and unknown personages1 and a hundred other trifies--that at the time they must have been in some way important to him4 ,i have endeavoured to make these ',miscellaneous ,notes' as complete as possible1 for in many cases an incidental memorandum will help to explain the meaning of some other note of a similar kind4 ,the first portion of these notes 7,nos4 l#cgi--l#deg71 as well as those referring to his pupils and to other artists and artificers who lived in his house 7#adeh--adfh17 are arranged in chronological order4 ,a considerable proportion of these notes belong to the period between #adij and #aejj1 when ,leonardo was living at ,milan under the patronage of ,lodovico il ,moro1 a time concerning which we have otherwise only very scanty information4 ,if ,leonardo did really--as has always been supposed1--spend also the greater part of the preceding decade in ,milan1 it seems hardly likely that we should not find a single note indicative of the fact1 or referring to any event of that period1 on the numerous loose leaves in his writing that exist4 ,leonardo's life in ,milan between #adhi and #aejj must have been comparatively uneventful4 ,the ,,mss4 and memoranda of those years seem to prove that it was a tranquil period of intellectual and artistic labour rather than of bustling court life4 ,whatever may have been the fate of the ,,mss4 and note books of the foregoing years--whether they were destroyed by ,leonardo himself or have been lost--it is certainly strange that nothing whatever exists to inform us as to his life and doings in ,milan earlier than the consecutive series of manuscripts which begin in the year #adhi4 ,there is nothing surprising in the fact that the notes regarding his pupils are few and meagre4 ,excepting for the record of money transactions only very exceptional circumstances would have prompted him to make any written observations on the persons with whom he was in daily intercourse1 among whom1 of course1 were his pupils4 ,of them all none is so frequently mentioned as ,salai1 but the character of the notes does not--as it seems to me--justify us in supposing that he was any thing more than a sort of factotum of ,leonardo's 7see #aeai1 note74 ,leonardo's quotations from books and his lists of titles supply nothing more than a hint as to his occasional literary studies or recreations4 ,it was evidently no part of his ambition to be deeply read 7see ,nrs4 #aj1 #aa1 #aaei7 and he more than once expressly states 7in various passages which will be found in the foregoing sections7 that he did not recognise the authority of the ,ancients1 on scientific questions1 which in his day was held paramount4 ,archimedes is the sole exception1 and ,leonardo frankly owns his admiration for the illustrious ,greek to whose genius his own was so much akin 7see ,no4 #adgf74 ,all his notes on various authors1 excepting those which have already been inserted in the previous section1 have been arranged alphabetically for the sake of convenience 7#adfi--aejh74 ,the passages next in order contain accounts and inventories principally of household property4 ,the publication of these--often very trivial entries--is only justifiable as proving that the wealth1 the splendid mode of life and lavish expenditure which have been attributed to ,leonardo are altogether mythical2 unless we put forward the very improbable hypothesis that these notes as to money in hand1 outlay and receipts1 refer throughout to an exceptional state of his affairs1 viz4 when he was short of money4 ,the memoranda collected at the end 7,no4 #aeje--aefe7 are1 in the original1 in the usual writing1 from left to right4 ,besides1 the style of the handwriting is at variance with what we should expect it to be1 if really ,leonardo himself had written these notes4 ,most of them are to be found in juxtaposition with undoubtedly authentic writing of his4 ,but this may be easily explained1 if we take into account the fact1 that ,leonardo frequently wrote on loose sheets4 ,he may therefore have occasionally used paper on which others had made short memoranda1 for the most part as it would seem1 for his use4 ,at the end of all ,i have given ,leonardo's will from the copy of it preserved in the ,melzi ,library4 ,it has already been printed by ,amoretti and by ,uzielli4 ,it is not known what has become of the original document4 ,memoranda before #aejj 7#acgi-l#dac74 #acgi4 ,find ,longhi and tell him that you wait for him at ,rome and will go with him to ,naples2 make you pay the donation ,footnote #b3 ,libro di ,vitolone see ,no4 #aejf note4 and take the book by ,vitolone1 and the measurements of the public buildings4 #c ,have two covered boxes made to be carried on mules1 but bed-covers will be best2 this makes three1 of which you will leave one at ,vinci4 #d ,obtain the44444444444444 from ,giovanni ,lombardo the linen draper of ,verona4 ,buy handkerchiefs and towels14444 and shoes1 #d pairs of hose1 a jerkin of444 and skins1 to make new ones2 the lake of ,alessandro4 ,footnote3 #g and fol4 ,it would seem from the text that ,leonardo intended to have instructions in painting on paper4 ,it is hardly necessary to point out that the ,art of illuminating was quite separate from that of painting4 ,sell what you cannot take with you4 ,get from ,jean de ,paris the method of painting in tempera and the way of making white ,footnote3 ,the mysterious looking words1 quite distinctly written1 in line #a3 ingol1 amor a1 ilopan a and on line #b3 enoiganod al are obviously in cipher and the solution is a simple one2 by reading them backwards we find for ingol3 logni-probably longi1 evidently the name of a person2 for amor a3 a ,roma1 for ilopan a3 a ,napoli4 ,leonardo has done the same in two passages treating on some secrets of his art ,nos4 #fda and #gbi1 the only other places in which we find this cipher employed2 we may therefore conclude that it was for the sake of secrecy that he used it4 ,there can be no doubt1 from the tenor of this passage1 that ,leonardo projected a secret excursion to ,naples4 ,nothing has hitherto been known of this journey1 but the significance of the passage will be easily understood by a reference to the following notes1 from which we may infer that ,leonardo really had at the time plans for travelling further than ,naples4 ,from lines #c1 #d and #g it is evident that he purposed1 after selling every thing that was not easily portable1 to leave a chest in the care of his relations at ,vinci4 ,his luggage was to be packed into two trunks especially adapted for transport by mules4 ,the exact meaning of many sentences in the following notes must necessarily remain obscure4 ,these brief remarks on small and irrelevant affairs and so forth are however of no historical value4 ,the notes referring to the preparations for his journey are more intelligible4 salt1 and how to make tinted paper2 sheets of paper folded up2 and his box of colours2 learn to work flesh colours in tempera1 learn to dissolve gum lac1 linseed 444 white1 of the garlic of ,piacenza2 take 'de ,ponderibus'2 take the works of ,leonardo of ,cremona4 ,remove the small furnace 444 seed of lilies and of444 ,sell the boards of the support4 ,make him who stole it1 give you the 444 learn levelling and how much soil a man can dig out in a day4 ,c4#ai;b #achj4 ,this was done by ,leone in the piazza of the castle with a chain and an arrow4 ,footnote3 ,this note must have been made in ,milan2 as we know from the date of the ,,ms4 ,b4 #ej;b #acha4 ,,names ,,of ,,engineers4 ,callias of ,rhodes1 ,epimachus the ,athenian1 ,diogenes1 a philosopher1 of ,rhodes1 ,calcedonius of ,thrace1 ,febar of ,tyre1 ,callimachus the architect1 a master of fires4 ,footnote3 ,callias1 ,architect of ,aradus1 mentioned by ,vitruvius 7,x1 #af1 #e74--;,epimachus1 of ,athens1 invented a battering-enginee for ,demetrius ,poliorketes 7,vitruvius ,x1 #af1 #d74--;,callimachus1 the inventor of the ,corinthian capital 7,vitr4 ,,iv1 ,i1 #i71 and of the method of boring marble 7,paus4 ,i1 #bf1 #g71 was also famous for his casts in bronze 7,plin4 ,,xxxiv1 #h1 #ai74 ,he invented a lamp for the temple of ,athene ,polias1 on the ,acropolis of ,athens 7,paus4 ,i1 #bf1 #g7--,the other names1 here mentioned1 cannot be identified4 ,ash4 ,,ii4 #ac;b #achb4 ,ask maestro ,lodovico for 'the conduits of water'4 ,footnote3 ,condotti d'acqua4 ,possibly a book1 a ,,ms4 or a map4 ,f#a4 ,uff4 #achc4 444 at ,pistoja1 ,fioravante di ,domenico at ,florence is my most beloved friend1 as though he were my brother4 ,footnote3 ,on the same sheet is the text ,no4 #ffc4 999999 from previous page8999999 ,,ii4 ',de ,ponderibus'4 ,a large number of ,leonardo's notes bear this superscription4 ,compare ,no4 #adcf1 #c4 ,s4,k4,m4 ,,iii4 #a;b #achd4 ,on the #afth day of ,july4 ,caterina came on #afth day of ,july1 #adic4 ,messer ,mariolo's ,morel the ,florentin1 has a big horse with a fine neck and a beautiful head4 ,the white stallion belonging to the falconer has fine hind quarters2 it is behind the ,comasina ,gate4 ,the big horse of ,cermonino1 of ,signor ,giulio4 ,footnote3 ,compare ,nos4 #aebb and #aeag4 ,caterina seems to have been his housekeeper4 ,s4,k4,m4 ,,iii4 #cj;a #ache4 ,,of ,,the ,,instrument4 ,any one who spends one ducat may take the instrument2 and he will not pay more than half a ducat as a premium to the inventor of the instrument and one grosso to the workman every year4 ,i do not want sub-officials4 ,footnote3 ,refers perhaps to the regulation of the water in the canals4 ,s4,k4,m4 ,,iii4 #ee;a #achf4 ,maestro ,giuliano da ,marliano has a fine herbal4 ,he lives opposite to ,strami the ,carpenters4 ,footnote3 ,compare ,no4 #faf1 note4 #d4 legnamiere 7milanese dialect7 legnajuolo4 ,s4,k4,m4 ,,iii4 #id;a #achg4 ,christofano da ,castiglione who lives at the ,pieta has a fine head4 ,c4,a4 #cbh;a #ihj;a #achh4 ,work of 444 of the stable of ,galeazzo2 by the road of ,brera ,footnote #d3 ,brera1 see ,no4 #addh1 ,,ii1 #ac2 benefice of ,stanghe ,footnote #e3,stanghe1 see ,no4 #aeji42 benefice of ,porta ,nuova2 benefice of ,monza2 ,indaco's mistake2 give first the benefices2 then the works2 then ingratitude1 indignity and lamentations4 ,h4#c #dg;b #achi4 ,chiliarch--captain of #ajjj4 ,prefects--captains4 ,a legion1 six thousand and sixty three men4 ,h4#b #ad;b #acij4 ,a nun lives at ,la ,colomba at ,cremona2 she works good straw plait1 and a friar of ,saint ,francis4,footnote3 ,la ,colomba is to this day the name of a small house at ,cremona1 decorated with frescoes4 ,h4#b #df;a #acia4 ,needle1--,niccolao1--thread1--,ferrando 1 -lacopo ,andrea1--canvas1--stone1--colours1 -brushes1-pallet1-sponge1-the panel of the ,duke4 ,s4,k4,m4,,ii4#b #g;a #acib4 ,messer ,gian ,domenico ,mezzabarba and ,messer ,giovanni ,franceso ,mezzabarba4 ,by the side of ,messer ,piero d',anghiera4 ,s4,k4,m4 ,,ii4#b #g;b #acic4 ,conte ,francesco ,torello4 ,s4,k4,m4 ,,ii4#b #ab;a #acid4 ,giuliano ,trombetta1--,antonio di ,ferrara1 --,oil of 4444 ,footnote3 ,near this text is the sketch of a head drawn in red chalk4 ,s4,k4,m4 ,,ii4#b #bj;a #acie4 ,paul was snatched up to heaven4 ,footnote3 ,see the facsimile of this note on ,pl4,,xxiii ,no4 #b4 ,s4,k4,m4 ,,ii4#b #bb;a #acif4 ,giuliano da ,maria1 physician1 has a steward without hands4 ,s4,k4,m4 ,,ii4#b #bg;a #acig4 ,have some ears of corn of large size sent from ,florence4 ,s4,k4,m4,,ii4#b #eb;a #acih4 ,see the bedstead at ,santa ,maria4 ,secret4 ,s4,k4,m4,,ii4#b #ec;a #acii4 ,arrigo is to have #aa gold ,ducats4 ,arrigo is to have #d gold ducats in the middle of ,august4 ,s4,k4,m4,,ii4#b #fc;a #adjj4 ,give your master the instance of a captain who does not himself win the victory1 but the soldiers do by his counsels2 and so he still deserves the reward4 ,s4,k4,m4,,ii4#b #fh;a #adja4 ,messer ,pier ,antonio4 ,s4,k4,m4,,ii4#b #fi;a #adjb4 ,oil1--yellow1--,ambrosio1--the mouth1 --the farmhouse4 ,s4,k4,m4,,ii4#b #gh;b #adjc4 ,my dear ,alessandro from ,parma1 by the hand of 444 ,s4,k4,m4,,ii4#b #gh;b #adjd4 ,giovannina1 has a fantastic face1--is at ,santa ,caterina1 at the ,hospital4,footnote3 ,compare the text on the same page3 ,no4 #ffg4 ,i4#b ,i,ia #adje4 #bd tavole make #a perch4 #d trabochi make #a tavola4 #d braccia and a half make a trabocco4 ,a perch contains #aicf square braccia1 or #aidd4 ,i4#b #gj;b #adjf4 ,the road of ,messer ,mariolo is #ac #a_/d braccia wide2 the ,house of ,evangelista is #ge4 ,it enters #g'_/b braccia in the house of ,mariolo4 ,footnote3 ,on this page and that which faces it1 ,,ms4,i#b #gla1 are two diagrams with numerous reference numbers1 evidently relating to the measurements of a street4 ,i4#b #gb;b #adjg4 ,i ask at what part of its curved motion the moving cause will leave the thing moved and moveable4 ,speak to ,pietro ,monti of these methods of throwing spears4 ,i4#b #hg;a #adjh4 ,antonio de' ,risi is at the council of ,justice4 ,i4#a #bh;a #adji4 ,paolo said that no machine that moves another 444,footnote3 ,the passage1 of which1 the beginning is here given1 deals with questions in mechanics4 ,the instances in which ,leonardo quotes the opinions of his contemporaries on scientific matters are so rare as to be worth noticing4 ,compare ,no4 #ija4 ,w4,p4#g4 #adaj4 ,caravaggio4,footnote3,caravaggio1 a village not far from the ,adda between ,milan and ,brescia1 where ,polidoro and ,michelangelo da ,caravaggio were born4 ,this note is given in facsimile on ,pl4 ,,xiii1 ,no4 ,i 7above1 to the left74 ,on ,pl4 ,,xiii1 ,no4 #b above to the right we read cerovazo4 ,w4,a4,,ii4#e;b #adaa4 ,pulleys1--nails1--rope1--mercury1--clot h1 ,monday4 ,w4,a4,,ii4#bjb;b #adab4 ,,memorandum4 ,maghino1 ,speculus of ,master ,giovanni the ,frenchman2 ,galenus on utility4 ,w4,x4 #adac4 ,near to ,cordusio is ,pier ,antonio da ,tossano and his brother ,serafino4 ,footnote3 ,this note is written between lines #bc and #bd of the text ,no4 #gaj4 ,corduso1 ,cordusio 7curia ducis7 ,cordus in the ,milanese dialect1 is the name of a ,piazza between the ,via del ,broletto and the ,piazza de' ,mercanti at ,milan44 ,in the time of il ,moro it was the centre of the town4 ,the persons here named were members of the noble ,milanese family de',fossani2 ,ambrogio da ,possano1 the con- temporary painter1 had no connection with them4 #adad4 ,l4 o' ,memoranda after #aejj 7#adad--adcd7 #adad4 ,paul of ,vannochio at ,siena 444 ,the upper chamber for the apostles4 #d ,buildings by ,bramante4 ,the governor of the castle made a prisoner4 ,footnote #f3 ,visconti4 ,chi fosse quel ,visconte non sapremmo indovinare fra tanti di questo nome4 ,arluno narra che allora atterrate furono le case de' ,viconti1 de' ,castiglioni1 de' ,sanseverini1 e de' ,botta e non e improbabile che ne fossero insultati e morti i padroni4 ,molti ,visconti annovera lo stesso ,cronista che per essersi rallegrati del ritorno del duca in ,milano furono da ,francesi arrestati1 e strascinati in--,francia come prigionieri di stato2 e fra questi ,messer ,francesco ,visconti1 e suo figliuolo ,battista4 7,,amoretti1 ,mem4 ,stor4 ,,xix474 ,visconti carried away and his son killed4 ,giovanni della ,rosa deprived of his money4 ,footnote #h3 ,borgonzio o ,brugonzio ,botta fu regolatore delle ducali entrate sotto il ,moro1 alla cui fuga la casa sua fu pur messa a sacco da' partitanti francesi4 7,,amoretti1 #a4 c47 ,borgonzio began 4442 and moreover his fortunes fled4 ,the ,duke has lost the state1 property and liberty and none of his entreprises was carried out by him4 ,footnote #a3 #d--aj ,this passage evidently refers to events in ,milan at the time of the overthrow of ,ludovico il ,moro4 ,amoretti published it in the ',memorie ,storiche' and added copious notes4 ,l4 ,ia #adae4 ,ambrosio ,petri1 ,st4 ,mark1 #d boards for the window1 #b 4441 #c the saints of chapels1 #e the ,genoese at home4 ,l4 ,ib #adaf4 ,piece of tapestry1-pair of compasses1-- ,tommaso's book1--the book of ,giovanni ,benci1--the box in the custom-house1--to cut the cloth1--the sword-belt1--to sole the boots1 --a light hat1--the cane from the ruined houses1--the debt for the table linen1 --swimming-belt1--a book of white paper for drawing1--charcoal4--,how much is a florin 4444 a leather bodice4 ,l4#b;a #adag4 ,borges ,footnote3 ,borges4 ,a ,spanish name4 shall get for you the ,archimedes from the bishop of ,padua1 and ,vitellozzo the one from ,borgo a ,san ,sepolcro ,footnote3 ,borgo a ,san ,sepolcro1 where ,luca ,paciolo1 ,leonardo's friend1 was born4 ,l4 #cj;b #adah4 ,marzocco's tablet4 ,l4 o #adai4 ,marcello lives in the house of ,giacomo da ,mengardino4 ,br4 ,m4 #bjb;b #adbj4 ,where is ,valentino8 ,footnote3 ,valentino4 ,cesare ,borgia is probably meant4 ,after being made ,archbishop of ,valence by ,alexander ,,vi he was commonly called ,valentinus or ,valentino4 ,with reference to ,leonardo's engagements by him see pp4 #bbd and #bdc1 note4--boots1--boxes in the custom-house 4441-- ,footnote3 ,carmine4 ,a church and monastery at ,florence4 the monk at the ,carmine1--squares1--,footnotes #g an #h3 ,martelli1 ,borgherini2 names of ,florentine families4 ,see ,no4 #d4 ,piero ,martelli1--#h ,salvi ,borgherini1--send back the bags1--a support for the spectacles1--,footnote #aa3 ,san ,gallo2 possibly ,giuliano da ,san ,gallo1 the ,florentine architect4 the nude study of ,san ,gallo1--the cloak4 ,porphyry1--groups1--square1--,footnote #af3 ,pandolfini1 see ,no4 #aedd note4 ,pandolfino4 #adba4 ,concave mirrors2 philosophy of ,aristotle2,footnote3,filosofia d',aristotele see ,no4 #adha note4,footnote #b3 ,avicenna 7,leonardo here writes it ,avinega7 the ,arab philosopher1 #ihj-ajcg1 for centuries the unimpeachable authority on all medical questions4 ,leonardo possibly points here to a printed edition3 ,avicennae canonum libri ,v1 latine #adgf ,patavis4 ,other editions are1 ,padua #adgi1 and ,venice #adij4 the books of ,avicenna ,italian and ,latin vocabulary2 ,messer ,ottaviano ,palavicino or his ,vitruvius ,footnote #c3 ,vitruvius4 ,see ,vol4 ,i1 ,no4 #cdc note44 bohemian knives2 ,vitruvius,footnote #f3 ,vitruvius4 ,see ,vol4 ,i1 ,no4 #cdc note42 go every ,saturday to the hot bath where you will see naked men2 ,meteora' ,footnote #g3 ,see ,no4 #addh1 #be41 ,archimedes1 on the centre of gravity ,footnote #i3 ,the works of ,archimedes were not printed during ,leonardo's life-time42 anatomy ,footnote #aj3 ,compare ,no4 #adid4 ,alessandro ,benedetto2 ,the ,dante of ,niccolo della ,croce2 ,inflate the lungs of a pig and observe whether they increase in width and in length1 or in width diminishing in length4 ,footnote #ad3 ,johannes ,marliani sua etate philosophorum et medicorum principis et ducala phisic4 primi de proportione motuum velocitate questio subtilissima incipit ex ejusdem ,marliani originali feliciter extracta1 ,m7ilano7 #adhb4 ,another work by him has the title3 ,marlianus mediolanensis4 ,questio de caliditate corporum humanorum tempore hiemis ed estatis et de antiparistasi ad celebrem philosophorum et medicorum universitatem ticinensem4 #adgd4 ,marliano1 on ,calculation1 to ,bertuccio4 ,albertus1 on heaven and earth ,footnote #ae3 ,see ,no4 #adfi1 #a4 #g41 from the monk ,bernardino4 ,horace has written on the movements of the heavens4 ,f4 #bg;b #adbb4 ,of the three regular bodies as opposed to some commentators who disparage the ,ancients1 who were the originators of grammar and the sciences and 444 ,w4 ,an4 ,,iii #bag;a 7,g7 #adbc4 ,the room in the tower of ,vaneri4 ,footnote3 ,this note is written inside the sketch of a plan of a house4 ,on the same page is the date #aeac 7see ,no4 #acgf74 #adbd4 ,the figures you will have to reserve for the last book on shadows that they may appear in the study of ,gerardo the illuminator at ,san ,marco at ,florence4 ,go to see ,melzo1 and the ,ambassador1 and ,maestro ,bernardo4 ,footnote3 ,l4 #a-c are in the original written between lines #c and #d of ,no4 #bib4 ,but the sense is not clear in this connection4 ,it is scarcely possible to devine the meaning of the following sentence4 99#b4 #c4 ,gherardo ,miniatore1 a famous illuminator1 #adde-adig1 to whom ,vasari dedicated a section of his ,lives 7,vol4 ,,ii pp4 #bcg-bdc1 ed4 ,sansoni #ahgi74 99#e4 ,bernardo1 possibly the painter ,bernardo ,zenale4 #adbe4 ,hermes the philosopher4 #adbf4 ,suisset1 viz4 calculator1--,tisber1 --,angelo ,fossobron1--,alberto4 #adbg4 ,the structure of the drawbridge shown me by ,donnino1 and why c and d thrust downwards4 ,footnote3 ,the sketch on the same page as this text represents two poles one across the other4 ,at the ends of the longest are the letter c and d4 ,the sense of the passage is not rendered any clearer4 #adbh4 ,the great bird will take its first flight2-- on the back of his great swan1--filling the universe with wonders2 filling all writings with his fame and bringing eternal glory to his birthplace4 ,footnote3 ,this seems to be a speculation about the flying machine 7compare p4 #bga74 #adbi4 ,this stratagem was used by the ,gauls against the ,romans1 and so great a mortality ensued that all ,rome was dressed in mourning4 ,footnote3 ,leonardo perhaps alludes to the ,gauls under ,brennus1 who laid his sword in the scale when the tribute was weighed4 #adcj4 ,alberto da ,imola2--,algebra1 that is1 the demonstration of the equality of one thing to another4 #adca4 ,johannes ,rubicissa e ,robbia4 #adcb4 ,ask the wife of ,biagio ,crivelli how the capon nurtures and hatches the eggs of the hen1--he being drunk4 #adcc4 ,the book on ,water to ,messer ,marco ,antonio4 ,footnote3 ,possibly ,marc-,antonio della ,torre1 see p4 #ig4 #adcd4 ,have ,avicenna's work on useful inventions translated2 spectacles with the case1 steel and fork and44441 charcoal1 boards1 and paper1 and chalk and white1 and wax24444 4444 for glass1 a saw for bones with fine teeth1 a chisel1 inkstand 44444444 three herbs1 and ,agnolo ,benedetto4 ,get a skull1 nut1--mustard4 ,boots1--gloves1 socks1 combs1 papers1 towels1 shirts14444 shoe-tapes1--44444 shoes1 penknife1 pens4 ,a skin for the chest4 ,footnote3 #d4 ,lapis4 ,compare ,condivi1 ,vita di ,michelagnolo ,buonarotti1 ,chap4 ,,xviii43 ,ma egli 7,michelangelo7 non avendo che mostrare1 prese una penna 7percioche in quel tempo il lapis non era in uso7 e con tal leggiadria gli dipinse una mano ecc4 ,the incident is of the year l#dif4--,lapis means pencil1 and chalk 7matita74 ,between lines #g and #h are the texts given as ,nos4 #hai and ,no4 #g4 ,undated memoranda 7#adce-adeg74 #adce4 ,the book of ,piero ,crescenze1--studies from the nude by ,giovanni ,ambrosio1--compasses1 --the book of ,giovanni ,giacomo4 #adcf4 ,,memorardum4 ,to make some provisions for my garden1 --,giordano1 ,de ,ponderibus,footnote #c3 ,giordano4 ,jordanus ,nemorarius1 a mathematician of the beginning of the ,x,i,i,ith century4 ,no particulars of his life are known4 ,the title of his principal work is3 ,arithmetica decem libris demonstrata1 first published at ,paris #adif4 ,in #aebc appeared at ,nuremberg3 ,liber 99,jordani ,nemorarii de ponderibus1 propositiones ,,xiii et earundem demonstrationes1 multarumque rerum rationes sane pulcherrimas complectens1 nunc in lucem editus41--the peacemaker1 the flow and ebb of the sea1--have two baggage trunks made1 look to ,beltraffio's ,footnote #f3 ,beltraffio1 see ,no4 #dfe1 note #b4 ,there are sketches by the side of lines #h and #aj4 lathe and have taken the stone1--out leave the books belonging to ,messer ,andrea the ,german1-- make scales of a long reed and weigh the substance when hot and again when cold4 ,the mirror of ,master ,luigi2 ,a b the flow and ebb of the water is shown at the mill of ,vaprio1--a cap4 #adcg4 ,giovanni ,fabre1--,lazaro del ,volpe1-- the common1--,ser ,piero4 ,footnote3 ,these names are inserted on a plan of plots of land adjoining the ,arno4 #adch4 ,lactantius1 the book of ,benozzo1 groups1 to bind the book1--a lantern1--,ser ,pecantino1--,pandolfino4--,rosso--a square1 --small knives1--carriages1--curry combs-- cup4 #adci4 ,quadrant of ,carlo ,marmocchi1--,messer ,francesco ,araldo1--,ser ,benedetto d',accie perello1--,benedetto on arithmetic1--,maestro ,paulo1 physician1--,domenico di ,michelino1-- 444444 of the ,alberti1--,messer ,giovanni ,argimboldi4 #addj4 ,colours1 formula1--,archimedes1--,marcantonio4 ,tinned iron1--pierced iron4 #adda4 ,see the shop that was formerly ,bartolommeo's1 the stationer4 ,footnote3 #f4 ,marc ,antonio1 see ,no4 #adcc4 #addb4 ,the first book is by ,michele di ,francesco ,nabini2 it treats on science4 #addc4 ,messer ,francesco1 physician of ,lucca1 with the ,cardinal ,farnese4 ,footnote3 ,alessandro ,farnese1 afterwards ,pope ,paul ,,iii was created in #adic ,cardinal di ,san ,cosimo e ,san ,damiano1 by ,alexander ,,vi4 #addd4 ,pandolfino's book ,footnote #a3 ,pandolfino1 ,agnolo1 of ,florence4 ,it is to this day doubtful whether he or ,l4 ,b4 ,alberti was the author of the famous work ',del ,governo della ,famiglia'4 ,it is the more probable that ,leonardo should have meant this work by the words il libro1 because no other book is known to have been written by ,pandolfino4 ,this being the case this allusion of ,leonardo's is an important evidence in favour of ,pandolfino's authorship 7compare ,no4 #aded1 line #c741--knives1--a pen for ruling1--to have the vest dyed1--,the library at ,st4-,mark's1--,the library at ,santo ,spirito1--,lactantius of the ,daldi ,footnote #g3 ,the works of ,lactantius were published very often in ,italy during ,leonardo's lifetime4 ,the first edition published in #adfe in monastero sublacensi was also the first book printed in ,italy41--,antonio ,covoni1--,a book by ,maestro ,paolo ,infermieri1 --,boots1 shoes and hose1--7,shell7lac1 --,an apprentice to do the models for me4 ,grammar1 by ,lorenzo de ,medici1--,giovanni del ,sodo1--,sansovino1 ,footnote #ae3 ,sansovino1 ,andrea--the sculptor2 #adfj-aebi4--;a ruler1--a very sharp knife1--,spectacles1--fractions44441 --repair4444444441--,tomaso's book1-- ,michelagnolo's little chain2 ,learn the multiplication of roots from ,maestro ,luca2--my map of the world which ,giovanni ,benci has ,footnote #be3 ,leonardo here probably alludes to the map1 not executed by him 7,see p4 #bbd71 which is with the collection of his ,,mss4 at ,windsor1 and was published in the ,archaeologia ,vol4 ,,xi 7see p4 #bbd742-,socks1--clothes from the customhouse --officier1--,red ,cordova leather1--,the map of the world1 of ,giovanni ,benci1--a print1 the districts about ,milan--,market book4 #adde4 ,in that at ,pavia the movement is more to be admired than any thing else4 ,the imitation of antique work is better than that of the modern things4 ,beauty and utility cannot exist together1 as seen in fortresses and in men4 ,the trot is almost the nature of the free horse4 ,where natural vivacity is lacking it must be supplied by art4 ,footnote3 ,quel di ,pavia4 ,pavia is possibly a clerical error for ,padua1 and if so the meaning of the passage is easily arrived at3 ,quel di ,padua would be the bronze equestrian statue of ,gattamelata1 on the ,piazza del ,santo at ,padua executed by ,donatelle in #addc 7see pp4 #b and #c74 #addf4 ,salvadore1 the matress maker1 lives on the ,piazza di ,sant' ,andrea1 you enter by the furrier's4 #addg4 ,monsignore de' ,pazzi1--,ser ,antonio ,pacini4 #addh4 ,an algebra1 which the ,marliani have1 written by their father1 ,footnote #a3 ,marliani1 an old ,milanese family1 now extinct4-- ,on the bone1 by the ,marliani1-- ,on the bone which penetrates1 ,gian ,giacomo of ,bellinzona1 to draw out the nail with facility1-- ,the measurement of ,boccalino1-- ,the measurement of ,milan and the suburbs1 ,footnote #e3 99#ba4 ,see ,pl4 ,,cix and ,no4 #ajaf4-- ,a book1 treating of ,milan and its churches which is to be had at the last stationer's on the way to ,corduso ,footnote #f3 ,corduso1 see ,no4 #adac1 note41-- ,the measurement of the ,corte ,vecchia1-- ,the measurement of the ,castle1-- ,get the master of arithmetic to show you how to square a44441-- ,get ,messer ,fazio to show you the book on proportion1-- ,get the ,friar di ,brera to show you the book 'de ,ponderibus' 99#aa1-- ,of the measurement of ,san ,lorenzo1-- ,i lent certain groups to ,fra ,filippo de ,brera1 99#ac-- ,memorandum3 to ask ,maestro ,giovannino as to the mode in which the tower of ,ferrara is walled without loopholes1-- ,ask ,maestro ,antonio how mortars are placed on bastions by day or by night1-- ,ask ,benedetto ,portinari how the people go on the ice in ,flanders1-- ,on proportions by ,alchino1 with notes by ,marliano1 from ,messer ,fazio1-- ,the measurement of the sun1 promised me by ,maestro ,giovanni1 the ,frenchman1-- ,the cross bow of ,maestro ,gianetto1-- ,the book by ,giovanni ,taverna that ,messer ,fazio1-- ,you will draw ,milan #ba1-- ,the measurement of the canal1 locks and supports1 and large boats2 and the expense1-- ,plan of ,milan ,footnote #bc3 ,fondamento is commonly used by ,leonardo to mean ground-plan4 ,see for instance p4 #ec41-- ,groups by ,bramante ,footnote #bd3 ,gruppi4 ,see ,vol4 ,i p4 #cee1 ,no4 #fjj1 note #i41-- ,the book on celestial phenomena by ,aristoteles1 in ,italian ,footnote #be3 ,meteora4 ,by this ,leonardo means no doubt the four books 994 ,he must refer here to a ,,ms4 translation1 as no ,italian translation is known to have been published 7see ,no4 #adgg note741-- ,try to get ,vitolone1 which is in the library at ,pavia ,footnote #bf3 ,vitolone see ,no4 #aejf1 note4 ,libreria di ,pavia4 ,one of the most famous of ,italian libraries4 ,after the victory of ,novara in ,april #aejj1 ,louis ,,xii had it conveyed to ,france1 'come trofeo di vittoria'6 and which treats of ,mathematics1--,he had a master learned in waterworks and get him to explain the repairs and the costs1 and a lock and a canal and a mill in the ,lombard fashion4 ,a grandson of ,gian ,angelo's1 the painter has a book on water which was his fathers4 ,paolino ,scarpellino1 called ,assiolo has great knowledge of water works4 #addi4 ,francesco d',antonio at ,florence4 #aa4 #ac4 ,footnote3 ,brera1 now ,palazzo delle ,scienze ed ,arti4 ,until #aega it was the monastery of the order of the ,umiliati and afterwards of the ,jesuits4 ,de ponderibus1 compare ,no4 #adcf1 #c4 #ab4 ,footnote3 ,sco ,lorenzo4 ,a church at ,milan1 see pp4 #ci1 #dj and #ej4 99#ac4 #bd4 ,footnote3 ,gruppi4 ,see ,vol4 ,i p4 #cee1 ,no4 #fjj1 note #i4 99#af4 ,footnote3 ,the ,portinari were one of the great merchant- families of ,florence4 #adej4 ,giuliano ,condi99#a1--,tomaso ,ridolf#a1-- ,tomaso ,paganelli1--,nicolo del,nero1--,simone ,zasti1--,nasi1--the heir of ,lionardo ,manelli1 --,guglielmo di ,ser ,martino1--,bartolomeo del ,tovaglia1--,andrea ,arrigucci1-- ,nicolo ,capponi1--,giovanni ,portinari4 ,footnote3 ,i4 ,guiliano ,gondi4 ,ser ,piero da ,vinci1 ,leonardo's father1 lived till #adhj1 in a house belonging to ,giuliano ,gondi4 ,in #adih this was pulled down to make room for the fine ,palazzo built on the ,piazza ,san ,firenze by ,giuliano di ,san ,gallo1 which still exists4 ,in the ,riassunto del ,catasto di ,ser ,piero da ,vinci1 #adhj1 ,leonardo is not mentioned2 it is evident therefore that he was living elsewhere4 ,it may be noticed incidentally that in the ,catasto di ,giuliano ,gondi of the same year the following mention is made of his four eldest sons3 ,lionardo mio figliuolo d'eta d'anni #bi1 non fa nulla1 ,giovambatista d'eta d'anni #bh in ,ghostantinopoli1 ,billichozo d'eta d'anni #bd a ,napoli1 ,simone d'eta d'anni #bc in ,ungheria4 ,he himself was a merchant of gold filigree 7facciamo lavorare una bottegha d'arte di seta 444 facciamo un pocho di trafico a ,napoli1 ,as he was #ei years old in #adhj1 he certainly would not have been alive at the time of ,leonardo's death4 ,but ,leonardo must have been on intimate terms with the family till the end of his life1 for in a letter dated ,june #a4 #aeai1 in which ,fr4 ,melzi1 writing from ,amboise1 announces ,leonardo's death to ,giuliano da ,vinci at ,florence 7see p4 #bhd71 he says at the end ,datemene risposta per i ,gondi 7see ,,uzielli1 ,ricerche1 passim74 ,most of the other names on the list are those of well-known ,florentine families4 #adea4 ,pandolfino4 #adeb4 ,vespuccio will give me a book of ,geometry4 ,footnote3 ,see ,no4 #hdd1 note1 p4 #acj4 #adec4 ,marcantonio ,colonna at ,santi ,apostoli4 ,footnote3 ,in ,july #aejf ,pope ,julius ,,ii gave ,donna ,lucrezia della ,rovere1 the daughter of his sister ,lucchina1 in marriage to the youthful ,marcantonio ,colonna1 who1 like his brothers ,prospero and ,fabrizio1 became one of the most famous ,captains of his family4 ,he gave to him ,frascati and made him a present of the palazzo he had built1 when ,cardinal1 near the church of ,santi ,apostoli which is now known as the ,palazzo ,colonna 7see ,,gregorovius1 ,gesch4 der ,stadt ,rom4 ,vol4 ,,viii1 book ,,xiv ,i1 #c4 ,and ,,coppi1 ,mem4 ,colonnesi p4 #bea74 #aded4 ,a box1 a cage1-- ,a square1 to make the bird ,footnote #b3 ,vasari states that ,leonardo invented mechanical birds which moved through the air4 ,compare ,no4 #gjc41-- ,pandolfino's book1 mortar 81-- ,small knives1 ,venieri for the 99#aded4 ,footnote3 ,much of ,no4 #addd is repeated in this memorandum4 99,pen for ruling1 stone1--star1-- ,to have the vest dyed1 ,alfieri's tazza1-- ,the ,libraries1 the book on celestial phenomena1-- ,lactantius of the go to the house of ,daldi1-- the ,pazzi1 ,book from ,maestro small box1-- ,paolo ,infermieri1-- ,boots1 shoes and small gimlet1-- hose1 ,lac1 44444441-- ,an apprentice for 444441-- models1 ,grammar of ,lo-the amount of the renzo de' ,medici1444 ,giovanni del ,sodo 44444 for4441--the broken ,sansovino1 the4444 ,piero di ,cosino ,footnote #af3 ,pier di ,cosimo the well known ,florentine painter #adfb-aeba4 ,see ,,vasari1 ,vite 7,vol4 ,,iv1 p4 #acd ed4 ,sansoni #ahhj7 about ,leonardo's influence on ,piero di ,cosimo's style of painting41 the wings1-- ,filippo and ,lorenzo ,footnote #ag3 ,filippo e ,lorenzo2 probably the painters ,filippino ,lippi and ,lorenzo di ,credi4 ,l4 di ,credi's pictures and ,vasari's history of that painter bear ample evidence to his intimate relations with ,leonardo41--,a ruler-1-- ,spectacles1--to do the44444 again1--,to- maso's book1--,michelagnolo's chain1--,the multiplication of roots1--,of the bow and strinch1--,the map of the world from ,benci1-- ,socks1--,the clothes from the custom-house officier1--,cordova leather1--,market books1 --waters of ,cronaca1--waters of ,tanaglino4441 --the caps1--,rosso's mirror2 to see him make it1--#a_/c of which ,i have #e_/f1--on the celestial phenomena1 by ,aristotle ,footnote #cf3 ,meteora4 ,see ,no4 #addh1 #be41--;boxes of ,lorenzo di ,pier ,francesco ,footnote #cg3 ,lorenzo di ,pier ,francesco and his brother ,giovanni were a lateral branch of the ,medici family and changed their name for that of ,popolani41--,maestro ,piero of the ,borgo1--,to have my book bound1--,show the book to ,serigatto1-- and get the rule of the clock ,footnote #da3 ,possibly this refers to the clock on the tower of the ,palazzo ,vecchio at ,florence4 ,in ,february #aeab it had been repaired1 and so arranged as to indicate the hours after the ,french manner 7twelve hours a4 m4 and as many p4 m4741-- ring1--nutmeg1--gum1--the square1--,giovan' ,batista at the piazza1 de' ,mozzi1--,giovanni ,benci has my book and jaspers1--brass for the spectacles4 #adee4 ,search in ,florence for444444 99#g4 #cf4 ,meteora4 ,see ,no4 #addh1 #be4 #adef4 ,bernardo da ,ponte 444 ,val di ,lugano 444 many veins for anatomical demonstration4 ,footnote3 ,this fragmentary note is written on the margin of a drawing of two legs4 #adeg4 ,paolo of ,tavechia1 to see the marks in the ,german stones4 ,footnote3 ,this note occurs on a pen and ink drawing made by ,leonardo as a sketch for the celebrated large cartoon in the possession of the ,royal ,academy of ,arts1 in ,london4 ,this cartoon is commonly supposed to be identical with that described and lauded by ,vasari1 which was exhibited in ,florence at the time and which now seems to be lost4 ,mr4 ,alfred ,marks1 of ,long ,ditton1 in his valuable paper 7read before the ,royal ,soc4 of ,literature1 ,june #bh1 #ahhb7 ,on the ,st4 ,anne of ,leonardo da ,vinci1 has adduced proof that the cartoon now in the ,royal ,academy was executed earlier at ,milan4 ,the note here given1 which is written on the sheet containing the study for the said cartoon1 has evidently no reference to the drawing on which it is written but is obviously of the same date4 ,though ,i have not any opening here for discussing this question of the cartoon1 it seemed to me important to point out that the character of the writing in this note does not confirm the opinion hitherto held that the ,royal ,academy cartoon was the one described by ,vasari1 but1 on the contrary1 supports the hypothesis put forward by ,mr4 ,marks4 ,notes on pupils 7#adeh-adfh47 #adeh4 ,giacomo came to live with me on ,st4-,mary ,magdalen's99#a day1 #adij1 aged #aj years4 ,the second day ,i had two shirts cut out for him1 a pair of hose1 and a jerkin1 and when ,i put aside some money to pay for these things he stole #d lire the money out of the purse2 and ,i could never make him confess1 though ,i was quite certain of the fact4--,thief1 liar1 obstinate1 glutton4 ,the day after1 ,i went to sup with ,giacomo ,andrea1 and the said ,giacomo supped for two and did mischief for four2 for he brake #c cruets1 spilled the wine1 and after this came to sup where ,i4444 ,item3 on the #gth day of ,september he stole a silver point of the value of #bb soldi from ,marco ,footnote #f3 ,marco1 probably ,leonardo's pupil ,marco d',oggionno2 #adgj is supposed to be the date of his birth and #aedj of his death4 ,che stava con meco4 ,we may infer from this that he left the master shortly after this1 his term of study having perhaps expired4 who was living with me1 #d lire this being of silver2 and he took it from his studio1 and when the said ,marco had searched for it a long while he found it hidden in the said ,giacomo's box #d lire4 ,footnote3 ,il di della ,maddalena4 ,july #bb4 ,item3 on the #bfth ,january following1 ,i1 being in the house of ,messer ,galeazzo da ,san ,severino ,footnote #i3 ,galeazza4 ,see ,no4 #gah note41 was arranging the festival for his jousting1 and certain footmen having undressed to try on some costumes of wild men for the said festival1 ,giacomo went to the purse of one of them which lay on the bed with other clothes1 #b lire #d ,s1 and took out such money as was in it4 ,item3 when ,i was in the same house1 ,maestro ,agostino da ,pavia gave to me a ,turkish hide to have #b lire4 a pair of short boots made of it2 this ,giacomo stole it of me within a month and sold it to a cobbler for #bj soldi1 with which money1 by his own confession1 he bought anise comfits4 ,item3 again1 on the #bnd ,april1 ,giovan ,antonio ,footnote #af3;,giovan ,antonio1 probably ,beltraffio1 #adfg to #aeaf4 having left a silver point on a drawing of his1 ,giacomo stole it1 and this was of the value of #bd soldi #a lira #d ,s4 ,the first year- ,a cloak1 #b lire1 #f shirts1 #d lire1 #c jerkins1 #f lire1 #d pairs of hose1 #g lire #h soldi1 #a lined doublet1 #e lire1 #bd pairs of shoes1 #f lire #e soldi1 ,a cap1 l lira1 laces1 #a lira4 ,footnote3 ,leonardo here gives a detailed account not only of the loss he and others incurred through ,giacomo but of the wild tricks of the youth1 and we may therefore assume that the note was not made merely as a record for his own use1 but as a report to be forwarded to the lad's father or other responsible guardian4 ,s4,k4,m4 ,,iii4 ,ia #adei4 ,on the last day but one of ,september2 ,thursday the #bgth day of ,september ,maestro ,tommaso came back and worked for himself until the last day but one of ,february4 ,on the #ahth day of ,march1 #adic1 ,giulio1 a ,german1 came to live with me1--,lucia1 ,piero1 ,leonardo4 ,on the #fth day of ,october4 #adfj4 #adic4 ,on the #ast day of ,november we settled accounts4 ,giulio had to pay #d months2 and ,maestro ,tommaso #i months2 ,maestro ,tommaso afterwards made #f candlesticks1 #aj days' work2 ,giulio some fire-tongs #ae days work4 ,then he worked for himself till the #bgth ,may1 and worked for me at a lever till the #ahth ,july2 then for himself till the #gth of ,august1 and for one day1 on the fifteenth1 for a lady4 ,then again for me at #b locks until the #bjth of ,august4 #adfa4 ,on the #bcrd day of ,august1 #ab lire from ,pulisona4 ,on the #adth of ,march #adid1 ,galeazzo came to live with me1 agreeing to pay #e lire a month for his cost paying on the l#dth day of each month4 ,his father gave me #b ,rhenish florins4 ,on the l#dth of ,july1 ,i had from ,galeazze #b ,rhenish florins4 #adfb4 ,on the l#eth day of ,september ,giulio began the lock of my studio #adid4 #adfc4 ,saturday morning the #crd of ,august #aejd ,jacopo the ,german came to live with me in the house1 and agreed with me that ,i should charge him a carlino a day4 #adfd4 #aeaa4 ,on the #bfth of ,september ,antonio broke his leg2 he must rest #dj days4 ,footnote3 ,this note refers possibly to ,beltraffio4 #adfe4 ,i left ,milan for ,rome on the #bdth day of ,september1 #aeac1 with ,giovanni 99#b1 ,francesco di ,melzi 99#c1 ,salai1 ,lorenzo and il ,fanfoia4 #adff4 ,on the #crd day of ,january4 ,benedetto carne on the #agth of ,october2 he stayed with me two months and #ac days of last year 99#d1 in which time he earned #ch lire1 #ah soldi and #h dinari2 he had of this #bf lire and #h soldi1 and there remains to be paid for the past year #ab lire #aj soldi4 ,giodatti 787 came on the #hth day of ,september1 at #d soldi a month1 and stayed with me #c months and #bd days1 and earned #ei lire #ad soldi and #h dinari2 he has had #dc lire1 #d soldi1 there remains to pay #af lire1 #aj soldi and #h dinari4 ,benedetto1 #bd grossoni4 #adfg4 ,gian ,maria #d1 ,benedetto #d1 ,gian ,pietro 99#e #c1 ,salai #c1 ,bartolomeo #c1 ,gherardo #d4 99#adfe4 #b4 ,giovan2 it is not likely that ,leonardo should have called ,giovan' ,antonio ,beltraffio at one time ,giovanni1 as in this note and another time ,antonio1 as in ,no4 #adfd while in ,no4 #adeh l4 #af we find ,giovan',antonio1 and in ,no4 #adcf1 l4#f ,beltraffio4 ,possibly the ,giovanni here spoken of is ,leonardo's less known pupil ,giovan ,pietrino 7see ,no4 #adfg1 #e74 #b4 #c4 ,francesco de' ,melzi is often mentioned1 see ,nos4 #acej4 #c4 ,salai4 ,see ,no4 #aeai note4 #d4 ,lorenzo4 ,see ,no4 #acea1 l4 #aj 7p4 #djh74 ,amoretti gives the following note in ,mem4 ,stor4 ,,xxiii3 #aeje4 ,martedi-sera a di #ad d'aprile4 ,venne ,lorenzo a stare con mecho3 disse essere d'eta d'anni #ag 44 a di #ae del detto aprile ebbi scudi #be d'oro dal chamerlingo di ,santa ,maria nuova4 ,this1 he asserts is derived from a ,,ms4 marked ,s1 in quarto4 ,this ,,ms4 seems to have vanished and left no trace behind2 ,amoretti himself had not seen it1 but copied from a selection of extracts made by ,oltrocchi before the ,leonardo ,,mss4 were conveyed to ,paris on the responsibility of the first ,french ,republic4 ,lorenzo1 by this1 must have been born in #adhg4 ,the sculptor ,lorenzetto was born in #adij4 ,amoretti has been led by the above passage to make the following absurd observations3 ,cotesto ,lorenzo1 che poi gli fu sempre compagno1 almeno sin che stette in ,italia1 sarebb' egli ,lorenzo ,lotto bergamasco8 ,sappiamo essere stato questo valente dipintore uno de' bravi scolari del ,vinci 7874 ,il ,fafoia1 perhaps a nickname4 ,cesare da ,sesto1 ,leonardo's pupil1 seems to have been in ,rome in these years1 as we learn from a drawing by him in the ,louvre4 #adff4 ,this seems to be an account for two assistants4 ,the name of the second is scarcely legible4 ,the year is not given4 ,the note is nevertheless of chronological value4 ,the first line tells us the date when the note was registered1 ,january #c;d1 and the99 ,c4,a4,f4 #bgi;a2 #hee;a #adfh4 ,salai1 #bj lire1 ,bonifacio1 #b lire1 ,bartolomeo1 #d lire1 ,arrigo ,harry1 #ae lire4 ,c4,a4 #bjg;a2 #fji;a ,quotations and notes on books and authors 7#adfi--aejh74 #adfi4 ,book on ,arithmetic ,footnote #a3 ,la nobel opera de arithmethica ne la qual se tracta tute cosse amercantia pertinente facta compilata per ,piero borgi da ,veniesia1 in-#dj4 ,in fine3 ,nela inclita cita di ,venetia a corni4 #b augusto4 #adhd4 fu imposto fine ala presente opera4 ,segn4 a--p4 quaderni4 ,v'ha pero un' altra opera simile di ,filippo ,calandro1 #adia4 ,e da consultarsi su quest' ultimo1 ,federici3 ,memorie ,trevigiane1 ,fiore di virtu3 pag4 #gc4 ,libricciuolo composto di bello stile verso il #acbj e piu volte impresso nel secolo ,,xv 7ristampato poi anche piu tardi74 ,gli accademici della ,crusca lo ammettono nella serie dei testi di lingua4 ,vedasi ,gamba1 ,razzolini1 ,panzer1 ,brunet1 ,lechi1 ecc4 7,g4 ,d',a47 ',flowers of ,virtue'1 ,pliny1 ,footnote #b3 ,historia naturale di ,c4 ,plinio ,secondo1 tradocta di lingua latina in fiorentina per ,christophoro ,laudino ,opus ,nicolai ,jansonis gallici imp4 anno salutis ,m4 ,,cccc4,,lxxvi4,venetiis in-fol4-,diogene ,laertio4 ,incomincia3 ,el libro de la vita de philosophi etc43 ,impressum ,venetiis per ,bernardinum ,celerium de ,luere1 #adhj1 in-#dj7;,g4 ,d',a474 ',lives of the ,philosophers'1 ,the ,bible1 ,footnote #c3,la ,bibia volgare historiata 7per ,nicolo di ,mallermi7 ,venecia 444 ,m4,,cccc4,,lxxi in kalende di ,augusto 7per ,vindelino de ,spira7 #b vol4 in-fol4 a #b col4 di #ej lin12 od altra ediz4 della stessa versione del ,mallermi1 ,venetia #adga1 e sempre3 ,venecia per ,gabriel de ,piero #adgg1 in-fol42 #b vol42 ,ottavio ,scotto da ,modoetia #adha1 ,venetia #adhg per ,joan ,rosso ,vercellese1 #adij ,giovanni ,ragazo di ,monteferato a instantia di ,luchanthonio di ,giunta1 ecc4--,lapidario ,teofrasto8 ,mandebille3 ,le grand lapidaire1 versioneitaliana ms48444 ,giorgio ,agricola non puo essere1 perche nato nel #adid1 forse ,alberto ,magno3 de mineralibus4 99 ,potrebbe essere una traduzione del poema latino 7,liber lapidum seu de gemmis7 di ,marbordio ,veterio di ,rennes 7morto nel ,,ii#bc da lui stesso tradotto in francese dal greco di ,evao re d',arabia celebre medico che l'aveva composto per l'imperatore ,tiberio4 ,marbodio scrisse il suo prima per ,filippo ,augusto re di ,francia4 ,vi sono anche traduzioni in prosa4 ,il lapidario o la forza e la virtu delle pietre preziose1 delle ,erbe e degli ,animali4 7,g4 ,d',a47 ',lapidary'1 ',on warfare' ,footnote #d3;,il ,vegezio8444 ,il ,frontino8144 ,il ,cornazzano8444 ,noi crediamo piuttosto il ,valturio4 ,questo libro doveva essere uno de'favoriti di ,leonardo poiche libro di scienza e d'arte nel tempo stesso4',epistles of ,filelfo'1 ,footnote3 ,the late ,marchese ,girolamo d',adda published a highly valuable and interesting disquisition on this passage under the title3 ,leonardo da ,vinci e la sua ,libreria1 note di un bibliofilo 7,milano #ahgc4 ,ed4 di soli #ge esemplari2 privately printed74 ,in the autumn of #ahhj the ,marchese d',adda showed me a considerable mass of additional notes prepared for a second edition4 ,this1 as he then intended1 was to come out after the publication of this work of mine4 ,after the much regretted death of the elder ,marchese1 his son1 the ,marchese ,gioachino d',adda was so liberal as to place these ,,ms4 materials at my disposal for the present work1 through the kind intervention of ,signor ,gustavo ,frizzoni4 ,the following passages1 with the initials ,g4 d',a4 are prints from the valuable notes in that publication1 the ,,ms4 additions ,i have marked994 ,i did not however think myself justified in reproducing here the acute and interesting observations on the contents of most of the rare books here enumerated4 99999999below must belong to previous page's footnotes999999 observations that follow refer to events of the previous month 'of last year' 7dell' anno passato74 ,leonardo cannot therefore have written thus in ,florence where the year was1 at that period1 calculated as beginning in the month of ,march 7see ,vol4 ,i1 ,no4 #d1 note #b74 ,he must then have been in ,milan4 ,what is more important is that we thus learn how to date the beginning of the year in all the notes written at ,milan4 ,this clears up ,uzielli's doubts3 ,a ,milano facevasi cominciar l'anno ab incarnatione1 cioe il #be ,marzo e a nativitate1 cioe il #be ,decembre4 ,ci sembra probabile che ,leonardo dovesse prescegliere lo stile che era in uso a ,firenze4 7,ricerche1 p4 #hd1 note47 #adfg4 #e4 ,see ,no4 #adfe1 #b4 99999999,above must belong to previous page's footnotes999999 ,the first decade1 #e ',on the preservation of health'1 ,the third decade1 #f ,ciecho d',ascoli1 ,the fourth decade1 #g ,albertus ,magnus1 ,guido1 #h ,new treatise on rhetorics1 ,piero ,crescentio1 #i ,cibaldone1 ',quadriregio'1 #aj ,a,esop1 999999 ,,ignore ,,footnotes ,,for ,,this ,,page - ,project ,manager 999999 ,donato1 ,footnote #aa3 ,donatus latine italice3 ,impressum ,venetiis impensis ,johannis ,baptistae de ,sessa anno #adii1 in-#d994-- ,el ,psalterio de ,david in lingua volgare 7da ,malermi ,venetia nel ,m4,,cccc4,,lxxvi1 in-fol4 s4 n4 7,g4 ,d',a47 ,psalms1 ,justinus1 ,footnote #ab3 ,compare ,no4 #abaj1 #dh4--,la versione di ,girolamo ,squarzafico3 ,il libro di ,justino posto diligentemente in materna lingua4 ,venetia ale spesse 7sic7 di ,johane de ,colonia ,johane ,gheretze 444 l#dgg1 in-fol4--,marsilii ,ficini1 ,theologia platonica1 sive de animarum immortalitate1 ,florentine1 per ,ant4 ,misconimum #adhb1 in-fol41 ovvero qualche versione italiana di questo stesso libro1 ms4 7,g4 ,d',a47 ',on the immortality of the soul1 ,guido ,footnote #ac3 ,forse la ,historia ,trojana ,guidonis od il manipulus di ,guido da ,monterocherii ma piu probabilmente ,guido d',arezzo il di cui libro3 ,micrologus1 seu disciplina artis musicae poteva da ,leonardo aversi ms42 di questi ne esistono in molto biblioteche1 e fu poi impresso nel #aghd dal ,gerbert4 ,molte sono le edizione dei sonetti di ,burchiello ,fiorentino1 impresse nel secolo ,,xv4 ,la prima e piu rara e recercata3 ,incominciano li sonetti1 ecc4 7per ,christoforo ,arnaldo71 in-#d99 senza numeri1 richiami o segnature1 del #adge1 e fors' anche del #adgb1 secondo ,morelli e ,dibdin1 ecc4 7,g4 ,d',a47 ,burchiello1 ',doctrinale' ,footnote #ad3 ,versione italiana det ,doctrinal de ,sapience di ,guy de ,roy1 e foris'anche l'originale in lingua francese4-- ,di ,pulci ,luigi1 benche nell' edizione3 ,florentiae #adgi in-#d99 si dica3 ,il ,driadeo composto in rima octava per ,lucio ,pulcro ,altre ediz1 del secolo ,,xv1 ,florentie ,miscomini #adha1 in-#dj991 ,firenze1 apud ,s4 ,jacob1 de ,ripoli1 #adhc1 in-#d99 e ,antoni de ,francesco1 #adhg1 in-#d99 e ,francesco di ,jacopo #adhi1;in-#d99 ed altre ancora di ,venezia e senza alcuna nota ecc4 7,g4 ,d',a47 ,driadeo1 ,morgante ,footnote #ae3 ,una delle edizioni del ,morgante impresse nel secolo ,,xv1 ecc4-- ,quale delle opere di ,francesco ,petrarca1 sarebbe malagevole l'indovinare1 ma probabilmente il ,canzoniere4 7,g4 ,d',a47 ,petrarch4 ,john de ,mandeville ,footnote #af3 ,sono i viaggi del cavaliere ,mandeville gentiluomo inglese4 ,scrisse il suo libro in lingua francese4 ,fu stampato replicatamente nel secolo ,,xv in francese1 in inglese ed in italiano 99 ed in tedesco2 del secolo ,,xv ne annoverano forse piu di #bg edizioni1 di cui ne conosciamo #h in francese1 quattro in latino1 sei in tedesco e molte altre in volgare4 7,g4 ,d',a47 ',on honest recreation' ,footnote #ag3 ,il ,platina 7,bartolomeo ,sacchi7 la versione italiana de la honesta voluptate1 valetudine 7 de li obsonnii7 ,venetia 7senza nome di tipografo7 #adhg1 piccolo in-#d99 gotico4 7,g4 ,d',a47--,compare ,no4 #hdd1 #ba4 ,manganello1 ,footnote #ah3 ,il ,manganello3 ,satira eccessivamente vivace contro le donne ad imitazione della ,sesta di ,giovenale4 ,manganello non e soltanto il titolo del libricino1 sua ben anche il nome dell'autore ch'era un milanese4 ,di questo libercolo rarissimo1 che sembra impresso a ,venezia dallo ,zoppino 7,nicolo d',aristotile detto il71 senza data1 ma dei primissimi anni del secolo ,,xvi1 e forse piu antico1 come vedremo in appresso1 non se ne conoscono fra biblioteche pubbliche e private che due soli esemplari in ,europa4 7,g4 ,d',a47 ,the ,chronicle of ,isidoro1 ,footnote #ai3 ,cronica desidero1 sembra si deggia leggere piuttosto cronico disidoro2 ed in questo caso s'intenderebbe la cronica d',isidoro tanto in voga a quel tempo ,comenza la ,cronica di ,sancto ,isidoro menore con alchune additione cavate del testo istorie de la ,bibia del libro di ,paulo ,oroso 4444 ,impresso in ,ascoli in casa del reverendo misser ,pascale 44444 per mano di ,guglielmo de ,linis de ,alamania ,m4,,cccc4,,lxxvii in-#dj99 di #aeg ff4 ,e il primo libro impresso ad ,ascoli e l'edizione principe di questa cronica in oggi assai rara4 ,non lo e meno l'edizione di ,cividal del ,friuli1 #adhj1 e quella ben anche di ,aquila1 #adhb1 sempre in-#dj4 ,vedasi ,panzer1 ,hain1 ,brunet e ,p4 ,dechamps4 7,g4 ,d',a47 ,the ,epistles of ,ovid1 ,footnote #bj3 ,le pistole di ,ovidio tradotte in prosa4 ,napoli ,sixt4 ,riessinger1 in-#dj991 oppure3 ,epistole volgarizzate #adhi1 in-#dj99 a due col4 impresse ne la cita 7sic7 di ,bressa per pre3 ,baptista de ,farfengo1 7in ottave7 o3 ,el libro dele ,epistole di ,ovidio in rima volgare per messere ,dominico de ,monticelli toschano4 ,brescia ,farfengo1 in-#d99 got4 7in rima volgare71 #adia1 ed anche la versione di ,luca ,pulci4 ,firenze1 ,mischomini1 #adha1 in-#d994 7,g4 ,d',a47 ,epistles of ,filelfo1 ,footnote #ba3 ,see l4 #d4 ,sphere1 ,footnote #bb3 ,jo3 de ,sacrobusto1 o ,goro ,dati1 o ,tolosano da ,colle di cui molteplici edizioni del secolo ,,xv4 7,g4 ,d',a47 99nello da ,streno1 #adig1 in-#d991 ecc41 o piu probabilmente3 ,aesopi vita fabula' latine cum versione italica allegoriis ,fr4 ,tuppi impressae1 ,napoli1 #adhc1 in-fol41 rara edizione ornata di belle vignette incise in legno4 ,questo ,esopo e anche libro di novelle4 ,nel ,catalogo ,cicognara abbiamo una minuta descrizione di questo rarissimo volume4 7,g4 ,d',a47 ,the ,jests of ,poggio ,footnote #bc3 ,tre edizioni delle facezie del ,poggio abbiamo in lingua italiana della fine del secolo ,,xv1 tutte senza data4 ,facetie de ,poggio fiorentino traducte de latino in vulgare ornatissimo1 in-#d991 segn4 a--e in caratteri romani2 l'altra3 ,facetie traducte de latino in vulgare1 in-#d991 caratteri gotici1 ecc4 7,g4 ,d',a47 ,chiromancy1 ,footnote #bd3 99,die ,kunst ,cyromantia etc1 in tedesco4 #bf ff4 di testo e figure il tutte eseguito su tavole di legno verso la fine del secolo ,,xv da ,giorgio ,schapff4 ,dibdin1 ,heinecken1 ,sotheby e ,chatto ne diedero una lunga descrizione2 i primi tre accompagnati da fac-simili4 ,la data #addh che si legge alla fine del titolo si riferisce al periodo della composizione del testo1 non a quello della stampa del volume benche tabellario4 ,altri molti libri di ,chiromanzia si conoscono di quel tempo e sarebbe opera vana il citarli tutti4 7,g4 ,d',a47 ,formulary of letters1 ,footnote #be3 ,miniatore ,bartolomeo4 ,formulario de epistole vulgare missive e responsive1 altri fiori de ornali parlamenti al principe ,hercule d',esti ecc4 composto ecc4 ,bologna per ,ugo di ,rugerii1 in-#d991 del secolo ,,xv1 ,altra edizione di ,venetia ,bernardino di ,novara1 #adhg e ,milano per ,joanne ,angelo ,scinzenzeler #aejj1 in-#d994 7,g4 ,d',a47 ,five books out of this list are noted by ,leonardo in another ,,ms4 7,tr4 #c73 donato1--lapidario1--plinio1 --abacho1--morgante4 #adgj4 ,nonius ,marcellus1 ,festus ,pompeius1 ,marcus ,varro4 ,footnote3 ,nonius ,marcellus and ,sextus ,pompeius ,festus were ,roman grammarians of about the fourth century ,a4 ,d4 ,early publications of the works of ,marcellus are3 ,de proprietate sermonis1 ,romae 7about #adgj71 and #adga 7place of publication unknown74 ,compendiosa doctrina1 ad filium1 de proprietate sermonum4 ,venice1 #adgf4 ,,brunet1 ,manuel du libraire 7,,iv1 p4 #ig7 notes3 ,le texte de cet ancien grammairien a ete reimprime plusieurs fois a la fin du ,x,ve siecle1 avec ceux de ,pomponius ,festus et de ,terentius ,varro4 ,la plus ancienne edition qui reunisse ces trois auteurs est celle de ,parme1 #adhj 444 ,celles de ,venise1 #adhc1 #adij1 #adih1 et de ,milan1 #aejj1 toutes in-fol11 ont peli de valeur4 #adga4 ,map of ,elephanta in ,india which ,antonello ,merciaio has from maestro ,maffeo2--there for seven years the earth rises and for seven years it sinks2--,enquire at the stationers about ,vitruvius4 #adgb4 ,see ',on ,ships' ,messer ,battista1 and ,frontinus ',on ,acqueducts' ,footnote #b3 #b4 ,vitruvius de ,arch41 et ,frontinus de ,aquedoctibus4 ,florence1 l#el#c4--,this is the earliest edition of ,frontinus4--,the note referring to this author thus suggests a solution of the problem of the date of the ,leicester ,manuscript44 ,footnote3 ,compare ,no4 #aaac1 #be4 #adgc4 ,anaxagoras3 ,every thing proceeds from every thing1 and every thing becomes every thing1 and every thing can be turned into every thing else1 because that which exists in the elements is composed of those elements4 9999,wrong text6 #adgd- ,the ,archimedes belonging to the ,bishop of ,padua4 #adge- ,archimedes gave the quadrature of a poly- gonal figure1 but not of the circle4 ,hence ,archimedes never squared any figure with curved sides4 ,he squared the circle minus the smallest portion that the intellect can conceive1 that is the smallest point visible4 #adgf4 ,if any man could have discovered the utmost powers of the cannon1 in all its various forms and have given such a secret to the ,romans1 with what rapidity would they have conquered every country and have vanquished every army1 and what reward could have been great enough for such a service6 ,archimedes indeed1 although he had greatly damaged the ,romans in the siege of ,syra- cuse1 nevertheless did not fail of being offered great rewards from these very ,romans2 and when ,syracuse was taken1 diligent search was made for ,archimedes2 and he being found dead greater lamentation was made for him by the ,senate and people of ,rome than if they had lost all their army2 and they did not fail to honour him with burial and with a statue4 ,at their head was ,marcus ,marcellus4 ,and after the second destruction of ,syracuse1 the sepulchre of ,archimedes was found again by ,cato#be1 in the ruins of a temple4 ,so ,cato had the temple restored and the sepulchre he so highly honoured4444 ,whence it is written that ,cato said that he was not so proud of any thing he had done as of having paid such honour to ,archimedes4 #adgd4 ,see ,no4 #adba1 #a4 #c1 #f and ,vol4 ,i1 ,no4 #cdc4 #adge4 ,compare ,no4 #aejd4 #adgf4 ,where ,leonardo found the statement that ,cato had found and restored the tomb of ,archi- medes1 ,i do not know4 ,it is a merit that ,cicero claims as his own 7,tusc4 ,v1 #bc7 and certainly with a full right to it4 ,none of ,archimedes' biographers -not even the diligent ,mazzucchelli1 mentions any version in which ,cato is named4 ,it is evidently a slip of the memory on ,leonardo's part4 ,besides1 according to the passage in ,cicero1 the grave was not found 'nelle mine ffun tempio'-which is highly improbable as relating to a ,greek-but in an open spot 7,h4 ,,muller-,,strobing74--,see too1 as to ,archi- medes1 ,no4 #adag4 ,leonardo says somewhere in ,,ms4 ,c4,a43 ,archi- tronito e una macchina di fino rame1 invenzlon d99 ,archi- mede 7see ',saggiol1 p4 #bj74 ,i4#b #hb;b #adgg4 ,aristotle1 ,book #c of the ,physics1 and ,albertus ,magnus1 and ,thomas ,aquinas and the others on the rebound of bodies1 in the #gth on ,physics1 on heaven and earth4 ,m4 #fb;a #adgh4 ,aristotle says that if a force can move a body a given distance in a given time1 the same force will move half the same body twice as far in the same time4 ,c4 ,a4 #bhd;b2 #hfe;b #adgi4 ,aristotle in ,book #c of the ,ethics3 ,man merits praise or blame solely in such mat- ters as lie within his option to do or not to do4 ,c4,a4 #aba;a2 #cge;a #adhj4 ,aristotle says that every body tends to maintain its nature4 ,k4#b #c;b #adha4 ,on the increase of the ,nile1 a small book by ,aristotle4 ,footnote3 ,de inundatione ,nili1 is quoted here and by others as a work of ,aristotle4 ,the ,greek original is lost1 but a ,latin version of the beginning exists 7,arist4 ,opp4 ,,iv p4 #bac ed4 ,did4 ,par474 ,in his quotations from ,aristotle ,leonardo possibly refers to one of the following editions3 ,aristotelis libri ,,iv de coelo et mundo2 de anima libri ,,iii2 libri ,,viii physi- corum2 libri de generatione et corruptione2 de sensu et sensato444 omnia latine1 interprete ,averroe1 ,venetiis #adhc 7first ,latin edition74 ,there is also a separate edition of ,liber de coelo et mundo1 dated #adgc4 ,w4,a4 ,,iv4#aea;b #adhb4 ,avicenna will have it that soul gives birth to soul as body to body1 and each member to itself4 ,footnote3 ,avicenna1 see too ,no4 #adba1 #a4 #b4 ,f4 o #adhc4 ,avicenna on liquids4 ,br4,m4 #ga;b #adhd4 ,roger ,bacon1 done in print4 ,footnote3,the earliest printed edition known to ,brunet of the works of ,roger ,bacon1 is a ,french translation1 which appeared about fourty years after ,leonardo's death4 ,c4,a4 #aci;b2 #dai;b #adhe4 ,cleomedes the philosopher4 ,footnote3 ,cleomede4 ,a ,greek mathematician of the ,i,vth century ,b4 ,c4 ,we have a ,cyclic theory of ,meteorica by him4 ,his works were not published before ,leonardo's death4 ,tr4 #d #adhf4 ,,cornelius ,,celsus4 ,the highest good is wisdom1 the chief evil is suffering in the body4 ,because1 as we are composed of two things1 that is soul and body1 of which the first is the better1 the body is the inferior2 wisdom belongs to the better part1 and the chief evil belongs to the worse part and is the worst of all4 ,as the best thing of all in the soul is wisdom1 so the worst in the body is suf- fering4 ,therefore just as bodily pain is the chief evil1 wisdom is the chief good of the soul1 that is with the wise man2 and nothing else can be compared with it4 ,footnote3 ,aulus ,cornelius ,celsus1 a ,roman physician1 known as the ,roman ,hippocrates1 probably contemporary with ,augustus4 ,only his eight ,books ',de ,medicina1 are preserved4 ,the earliest editions are3 ,cornelius ,celsus1 de medicina libr4 ,,viii41 ,milan #adha ,venice #adic and #adig4 ,tr4 #eg #adhg4 ,demetrius was wont to say that there was no difference between the speech and words of the foolish and ignorant1 and the noises and rumblings of the wind in an inflated stomach4 ,nor did he say so without reason1 for he saw no difference between the parts whence the noise issued2 whether their lower parts or their mouth1 since one and the other were of equal use and importance4 ,footnote3 ,compare ,vol4 ,i1 ,no4 #aj4 ,s4,k4,m4 ,,iii4#ic;a #adhh4 ,maestro ,stefano ,caponi1 a physician1 lives at the piscina1 and has ,euclid ,de ,ponderibus4 ,k4#b #b;a #adhi4 #eth ,book of ,euclid4 ,first definition3 a part is a quantity of less magnitude than the greater magnitude when the less is contained a certain number of times in the greater4 ,a part properly speaking is that which may be multiplied1 that is when1 being multiplied by a certain number1 it forms exactly the whole4 ,a common aggregate part 444 ,second definition4 ,a greater magnitude is said to be a multiple of a less1 when the greater is measured by the less4 ,by the first we define the lesser magnitude and by the second the greater is defined4 ,a part is spoken ,k4#b #b;b #adij4 of in relation to the whole2 and all their relations lie between these two extremes1 and are called multiples4 ,s4,k4,m4,,iii4 #af;b #adia4 ,hippocrates says that the origin of men's sperm derives from the brain1 and from the lungs and testicles of our parents1 where the final decocture is made1 and all the other limbs transmit their substance to this sperm by means of expiration1 because there are no channels through which they might come to the sperm4 ,footnote3 ,the works of ,hippocrates were printed first after ,leonardo's death4 ,ash4,,ii4 ,i,ib #adib4 ,lucretius in his third book ',de ,rerum ,natura'4 ,the hands1 nails and teeth were 7#afe7 the weapons of ancient man4 ,they also use for a standard a bunch of grass tied to a pole 7#afg74 ,footnote3 ,lucretius1 de rerum natura libri ,,vi were printed first about #adgc1 at ,verona in #adhf1 at ,brescia in #adie1 at ,venice in #aejj and in #aeae1 and at ,florence in #aeae4 ,the numbers #afe and #afg noted by ,leonardo at the end of the two passages seem to indicate pages1 but if so1 none of the editions just mentioned can here be meant1 nor do these numbers refer to the verses in the poems of ,lucretius4 ,tr4 #b #adic4 ,ammianus ,marcellinus asserts that seven hundred thousand volumes of books were burnt in the siege of ,alexandria in the time of ,julius ,cesar4 ,footnote3 ,ammiani ,marcellini historiarum libri qui extant ,,xiii1 published at ,rome in #adgd4 ,tr4 #b ,w4 ,,xxiii4 #adid4 ,mondino says that the muscles which raise the toes are in the outward side of the thigh1 and he adds that there are no muscles in the back upper side of the feet1 because nature desired to make them light1 so as to move with ease2 and if they had been fleshy they would be heavier2 and here experience shows 444 ,footnote3 ,mundini anatomia4 ,mundinus1 ,anothomia 7sic74 ,mundini praestantissimorum doctorum almi studit ticiensis 7sic7 cura diligentissime emendata4 ,impressa ,papiae per magistrum ,antonium de ,carfano #adgh1 in-fol42 ristampata3 ,bononiae ,johan4 de ,noerdlingen1 #adhb1 in-fol42 ,padova per ,mattheum ,cerdonis de ,vuindischgretz1 #adhd1 in-#dj2 ,lipsia1 #adic1 in-#dj2 ,venezia1 #adid1 in-#dj e ivi #adih1 con fig4 ,queste figure per altro non sono1 come si e preteso1 le prime che fossero introdotte in un trattato di ,notamia4 ,nel 'fasciculus ,medicinae' di ,giovanni ,ketham1 che riproduce ,f',anatomia' del ,mundinus1 impresso pure a ,venezia da ,j4 e ,g4 de ,gregoriis1 #adia1 in-fol41 contengosi intagli in legno 7si vogliono disegnati non gia incisi da ,andrea ,mantegna7 di grande dimensione1 e che furono piu volte riprodotti negli anni successivi4 ,quest' edizione del fasciculus del #adia1 sta fra nostri libri e potrebbe benissimo essere il volume d',anatomia notato da ,leonardo4 7,g4 ,d',a47 ,g4 #h;a #adie4 ,of the error of those who practice without knowledge2--,footnote #c39999where is it89999 ,see first the ',ars poetica' of ,horace ,footnote #e3 9999where is it899994 ,footnote3 ,a #c--e are written on the margin at the side of the title line of the text given1 entire as ,no4 #ai #adif4 ,the heirs of ,maestro ,giovanni ,ghiringallo have the works of ,pelacano4 #adig4 ,the catapult1 as we are told by ,nonius and ,pliny1 is a machine devised by those c4 ,footnote3 ,plinius1 see ,no4 #idf4 #adih4 ,i have found in a history of the ,spaniards that in their wars with the ,english ,archimedes of ,syracuse who at that time was living at the court of ,ecliderides1 ,king of the ,cirodastri4 ,and in maritime warfare he ordered that the ships should have tall masts1 and that on their tops there should be a spar fixed ,footnote #f3 ,compare ,no4 #aaae4 of #dj feet long and one third of a foot thick4 ,at one end of this was a small grappling iron and at the other a counterpoise2 and there was also attached #ab feet of chain2 and1 at the end of this chain1 as much rope as would reach from the chain to the base of the top1 where it was fixed with a small rope2 from this base it ran down to the bottom of the mast where a very strong spar was attached and to this was fastened the end of the rope4 ,but to go on to the use of his machine2 ,i say that below this grappling iron was a fire ,footnote #ad3 ,compare ,no4 #aabh4 which1 with tremendous noise1 threw down its rays and a shower of burning pitch2 which1 pouring down on the enemy's top1 compelled the men who were in it to abandon the top to which the grappling-iron had clung4 ,this was hooked on to the edges of the top and then suddenly the cord attached at the base of the top to support the cord which went from the grappling iron1 was cut1 giving way and drawing in the enemy's ship2 and if the anchor--was cast 444 ,footnote3 ,archimedes never visited ,spain1 and the names here mentioned cannot be explained4 ,leonardo seems to quote here from a book1 perhaps by some questionable mediaeval writer4 ,prof4 ,c4 ,justi writes to me from ,madrid1 that ,spanish savants have no knowledge of the sources from which this story may have been derived4 ,leic4 #ad;b #adii4 ,theophrastus on the ebb and flow of the tide1 and of eddies1 and on water4 ,footnote3 ,the ,greek philosophers had no opportunity to study the phenomenon of the ebb and flow of the tide and none of them wrote about it4 ,the movement of the waters in the ,euripus however was to a few of them a puzzling problem4 ,ash4 ,,ii4 ,i,ib #aejj4 ,tryphon of ,alexandria1 who spent his life at ,apollonia1 a city of ,albania 7#afc74 ,footnote3 ,tryphon of ,alexandria1 a ,greek ,grammarian of the time of ,augustus4 ,his treatise 99,tta,o,y ,aeijecu99 appeared first at ,milan in #adgf1 in ,constantin ,laskaris's ,greek ,grammar4 ,k4#c #bi;b #aeja4 ,messer ,vincenzio ,aliprando1 who lives near the ,inn of the ,bear1 has ,giacomo ,andrea's ,vitruvius4 ,l4 #ec;b #aejb4 ,vitruvius says that small models are of no avail for ascertaining the effects of large ones2 and ,i here propose to prove that this conclusion is a false one4 ,and chiefly by bringing forward the very same argument which led him to this conclusion2 that is1 by an experiment with an auger4 ,for he proves that if a man1 by a certain exertion of strength1 makes a hole of a given diameter1 and afterwards another hole of double the diameter1 this cannot be made with only double the exertion of the man's strength1 but needs much more4 ,to this it may very well be answered that an auger ,l4 #ec;a #aejc4 of double the diameter cannot be moved by double the exertion1 be- cause the superficies of a body of the same form but twice as large has four times the extent of the superficies of the smaller1 as is shown in the two figures a and n4 ,section title3 ,notes on books and authors 99 ,there are characters present in the original footnotes that have accents - ,i have placed an asterisk next to them4 #aejd4 ,,of ,,squaring ,,the ,,circle1 ,,and ,,who ,,it ,,was ,,that ,,first ,,discovered ,,it ,,by ,,accident4 ,vitruvius1 measuring miles by means of the repeated revolutions of the wheels which move vehicles1 extended over many ,stadia the lines of the circumferences of the circles of these wheels4 ,he became aware of them by the animals that moved the vehicles4 ,but he did not discern that this was a means of finding a square equal to a circle4 ,this was first done by ,archimedes of ,syracuse1 who by multiplying the second diameter of a circle by half its circumference produced a rectangular quadrilateral equal figure to the circle4 ,footnote3 ,vitruvius1 see also ,nos4 #aaac and #cdc4 #aj4 ,compare ,no4 #adge4 #aeje4 ,virgil says that a blank shield is devoid of merit because among the people of ,athens the true recognition confirmed by testimonies 444 ,footnote3 ,the end of the text cannot be deciphered4 #aejf4 ,in ,vitolone there are #hje conclusions problems in perspective4 ,footnote3 7,witelo1 ,vitellion1 ,vitellon7 ,vitellione4 99,e da vedersi su questo ottico prospettico del secolo ,,xiii ,luca ,pacioli1 ,paolo ,lomazzo1 ,leonardo da ,vinci1 ecc4 e fra i moderni il ,graesse1 il ,libri1 il ,brunet1 e le ,memorie pubblicate dal principe ,boncompagni1 e ',sur l' orthographe du nom et sur la patrie de ,witelo 7,vitellion7 note de ,maximilien ,curtze1 professeur 99a ,thorn'1 ove sono descritti i molti codici esistenti nelle biblioteche d' ,europa4 ,bernardino ,baldi nelle sue ',vite de'matematici'1 manoscritto presso il principe ,boncompagni1 ha una biografia del ,vitellione4 ,questo scritto del ,baldi reca la data #be agosto #aehh4 ,discorsero poi di lui ,federigo ,risnerio e ,giovanni di ,monteregio nella prefazione dell' ,alfagrano1 ,giovanni ,boteone1 ,girolamo ,cardano1 ',de subtilitate'1 che nota gli errori di ,vitellione4 ,visse1 secondo il ,baldi1 intorno all' anno #abfi1 ma secondo il ,reinoldo fioriva nel #abii1 avendo dedicata la sua opera ad un frate ,guglielmo di ,monteca1 che visse di que' tempi4 ,intorno ad un manoscritto dell' ottica di ,vitellione1 citato da ,luca ,pacioli v' ha un secondo esemplare del ,kurlz1 con aggiunte del principe ,boncompagni1 e le illustrazioni del cav4 ,enrico ,narducci4 ,nel ',catalogo di manoscritti' posseduti da ,d4 ,baldassare de' principi ,boncompagni1 compilato da esso ,narducci1 ,roma1 #ahfb1 sotto al n4 #ceh1 troviamo citato3 ,vitellio1 ',perspectiva'1 manoscritto del secolo ,,xiv4 ,la ',prospettiva di ,vitelleone' 7sic7 ,thuringo-poloni 99e citata due volte da ,paolo ,lomazzo nel ,trattato dell' arte della pittura4 ,vitellio o ,vitello o ,witelo4 ,il suo libro fu impresso in foglio a ,norimberga nel #aece2 la secondo edizione 99e del #aeea1 sempre di ,norimberga1 ed una terza di ,basilea1 #aegb4 7,see ,indagini ,storiche 444 sulla ,libreria--,visconteo--,sforzesca del ,castello di ,pavia 444 per cura di ,g4 ,d',a41 ,milano #ahgi4 ,p4 ,i4 ,appendice p4 #aac4 #aad74 #aejg4 ,vitolone1 at ,saint ,mark's4 ,footnote3 ,altro codice di cotesta ',prospettiva' del ,vitolone troviamo notato nel ',canone bibliographico di ,nicol99o ,v'1 conservato alla1 ,magliabecchiana1 in copia dell' originale verosimilmente inviato dal ,parentucelli a ,cosimo de' ,medici 7,magliab4 cod4 segn4 #a ,,vii1 #cj carte da #aic a #aih74 ,proviene dal ,convento di ,san ,marco e lo aveva trascritto frate ,leonardo ,scruberti fiorentino1 dell' ordine dei predicatori che fu anche bibliotecario della ,medicea pubblica in ,san ,marco 7,see ,indagini ,storiche 444 per cura di ,g4 ,d',a4 ,parte ,i1 p4 #ig74 ,k4#b #ab;b #aejh4 ,how this proposition of ,xenophon is false4 ,if you take away unequal quantities from unequal quantities1 but in the same proportion1 c4 ,footnote3 ,xenophon's works were published several times during ,leonardo's lifetime4 ,b4 #d;a ,inventories and accounts 7#aeji-aede74 #aeji4 ,on the #bhth day of ,april ,i received from the ,marchesino #ajc lire and #ab dinari4 ,footnote3 ,instead of the indication of the year there is a blank space after d'aprile4--,marchesino ,stange was one of ,lodovico il ,moro's officials4--,campare ,no4 #achh4 ,ash4 ,i4 ,ia #aeaj4 ,on the ioth day of ,july #adib in #ace ,rhenish florins #a4 #dde in dinari of #f soldi #a4 #aab ,s #af in dinari of #e #a_/b soldi #a4 #bi ,s #ac #i in gold and #c scudi l4#ec #a4 #h;,,ii in all ,s4,k4,m4,,iii4 #dg;a #aeaa4 ,on the first day of ,february1 lire #abjj4 ,s4,k4,m4,,iii4 #dg;a #aeab4 ,the hall towards the court is #abf paces long and #bg braccia wide4 #aeac ,the narrow cornice above the hall lire #cj4 ,the cornice beneath that1 being one for each picture1 lire #g1 and for the cost of blue1 gold1 white1 plaster1 indigo and glue #c lire2 time #c days4 ,the pictures below these mouldings with their pilasters1 #ab lire each4 ,i calculate the cost for smalt1 blue and gold and other colours at #a #a_/b lire4 ,the days ,i calculate at #c1 for the invention of the composition1 pilasters and other things4 #aead4 ,item for each vault #g lire outlay for blue and gold #c #a_/b time1 #d days for the windows #a #a_/b ,the cornice below the windows #af soldi per braccio item for #bd pictures of ,roman history #ad lire each ,the philosophers #aj lire the pilasters1 one ounce of blue #aj soldi for gold #ae soldi ,total #b and #a_/b lire4 #aeae4 ,the cornice above lire #cj ,the cornice below lire #g ,the compositions1 one with another lire #ac #aeaf4 ,salai1 #f lire444 #d soldi444 #aj soldi for a chain2-- ,on the l#dth of ,march ,i had #ac lire ,s4 #d2 #af lire remain4 #aeag4 ,how many braccia high is the level of the walls8-- #abc braccia ,how large is the hall8 ,how large is the garland8 #cj ducats4 ,on the #bith day of ,january1 #adid cloth for hose lire #d ,s #c lining ,s #af making ,s #h to ,salai ,s #c a jasper ring ,s #ac a sparkling stone ,s #aa to ,caterina ,s #aj to ,caterina ,s #aj ,h4#b #cc;a #aeah4 ,the wheel lire #g the tire lire #aj the shield lire #d the cushion lire #h the ends of the axle-tree lire #b bed and frame lire #cj conduit lire #aj ,s4,k4,m4,,ii4#b #d;a #aeai4 ,parsley #aj parts mint #a part thyme #a part ,vinegar 444 and a little salt two pieces of canvas for ,salai4 ,footnote3 ,this note1 of about the year #adid1 is the earliest mention of ,salai1 and the last is of the year #aeac 7see ,no4 #adfe1 #c74 ,from the various notes in the ,,mss4 he seems to have been ,leonardo's assistant and keeper only1 and scarcely himself a painter4 ,at any rate no signed or otherwise authenticated picture by him is known to exist4 ,vasari speaks somewhat doubtfully on this point4 ,s4,k4,m4 ,,ii4,i o #aebj4 ,on ,tuesday ,i bought wine for morning drinking2 on ,friday the #dth day of ,september the same4 ,footnote3 ,this note enables us to fix the date of the ,manuscript1 in which it is to be found4 ,in #adie the #dth of ,september fell on a ,friday2 the contents of the ,manuscript do not permit us to assign it to a much earlier or later date 7,compare ,no4 #aebb1 and ,note74 ,s4,k4,m4 ,,ii4,i #id;b #aeba4 ,the cistern 444 at the ,hospital1--#b ducats1--beans1-white maize1--red maize1--millet1--buckwheat1 --kidney beans1--beans1--peas4 ,s4,k4,m4 ,,ii4,i #ie;a #aebb4 ,,expenses ,,of ,,the ,,interment ,,of ,,caterina4 ,for the #c ,ibs of tapers #bg ,s ,for the bier #h ,s ,a pall over the bier #ab ,s ,for bearing and placing the cross #d ,s ,for bearing the body #h ,s ,for #d priests and #d clerks #bj ,s ,bell1 book and sponge #b ,s ,for the gravediggers #af ,s ,to the senior #h ,s ,for a license from the authorities #a ,s #ajf ,s ,the doctor #b ,s ,sugar and candles #ab ,s #abj ,s ,footnote3 ,see ,nos4 #achd and #aeag4 #aebc4 ,salai's cloak1 the #dth of ,april #adig4 #d braccia of silver cloth l4 #ae ,s #d green velvet to trim it l4 #i ,s -- binding l4-- ,s #i loops l4-- ,s #ab the making l4 #a ,s #e binding for the front l4-- ,s #e stitching here are #ac grossoni of his l4 #bf ,s #e ,salai stole the soldi4 #aebd4 ,on ,monday ,i bought #d braccia of cloth lire #ac ,s #ad #a_/b on the #agth of1 ,october #adig4 #aebe4 ,memorandum4 ,that on the #hth day of ,april #aejc1 ,i1 ,leonardo da ,vinci1 lent to ,vante1 miniature painter #d gold ducats1 in gold4 ,salai carried them to him and gave them into his own hand1 and he said he would repay within the space of #dj days4 ,memorandum4 ,that on the same day ,i paid to ,salai #c gold ducats which he said he wanted for a pair of rose-coloured hose with their trimming2 and there remain #i ducats due to him-excepting that he owes me #bj ducats1 that is #ag ,i lent him at ,milan1 and #c at ,venice4 ,memorandum4 ,that ,i gave ,salai #ba braccia of cloth to make a shirt1 at io soldi the braccio1 which ,i gave him on the #bjth day of ,april #aejc4 ,footnote3 ,with regard to ,vante or ,attavante1 the miniature painter 7not ,nanni as ,i formerly deciphered this name1 which is difficult to read2 see ,zeitschrift fur ,bild4 ,kunst1 #ahgi1 p4 #aee71 and ,vasari1 ,lives of ,frate ,giovanni da ,fiesole1 of ,bartolommeo della ,gatta1 and of ,gherardo1 miniatore4 ,he1 like ,leonardo1 was one of the committee of artists who1 in #aejc1 considered the erection and placing of ,michel ,angelo's ,david4 ,the date of his death is not known2 he was of the same age as ,leonardo4 ,further details will be found in ',notizie di ,attavante miniatore1 e di alcuni suoi lavori' 7,milanese's ed4 of ,vasari1 ,,iii1 #bca-bce74 #aebf4 ,on the morning of ,san ,peter's day1 ,june #bith1 #aejd1 ,i took io ducats1 of which ,i gave one to ,tommaso my servant to spend4 ,on ,monday morning #a florin to ,salai to spend on the house4 ,on ,thursday ,i took #a florin for my own spending4 ,wednesday evening #a florin to ,tommaso1 before supper4 ,saturday morning #a florin to ,tommaso4 ,monday morning #a florin less #aj soldi4 ,thursday to ,salai i florin less #aj soldi4 ,for a jerkin1 #a florin4 ,for a jerkin ,and a cap #b florins4 ,to the hosier1 #a florin4 ,to ,salai1 #a florin4 ,friday morning1 the #aith of ,july1 #a florin1 less #f soldi4 ,i have #g fl4 left1 and #bb in the box4 ,tuesday1 the #bcth day of ,july1 #a florin to ,tommaso4 ,monday morning1 to ,tommaso #a florin4 ,wednesday morning #a fl4 to ,tommaso4 ,thursday morning the #ast day of ,august #a fl4 to ,tommaso4 ,sunday1 the #dth of ,august1 #a florin4 ,friday1 the pth day of ,august #aejd1 ,i took #aj ducats out of the box4 #aebg4 #aejd4 ,on the #ith day of ,august1 #aejd1 ,i took #aj florins in gold99#b 4444 99#c on ,friday the #ith day of ,august fifteen grossoni that is fl4 #e ,s #e 4444 given to me #a florin in gold on the l#bth day of ,august 99#d 44444 on the #adth of ,august1 #cb grossoni to ,tommaso4 ,on the l#hth of the same #e grossoni to ,salai4 ,on the #hth of ,september #f grossoni to the workman to spend2 that is on the day of our ,lady's birth4 ,on the #afth day of ,september ,i gave #d grossoni to ,tommaso3 on a ,sunday4 ,footnote3 ,in the original1 the passage given as ,no4 #adfc is written between lines #b and #c of this text1 and it is possible that the entries in lines #c and #d refer to the payments of ,jacopo ,tedesco1 who is there mentioned4 ,the first words of these lines are very illegible4 99#g4 ,al fattore4 ,il ,fattore1 was1 as is well known1 the nick-name of ,giovanni ,franceso ,penni1 born in ,florence in #adhf1 and subsequently a pupil of ,raphael's4 ,according to ,vasari he was known by it even as a boy4 ,whether he is spoken of in this passage1 or whether the word ,fattore should be translated literally1 ,i will not undertake to decide4 ,the latter seems to me more probably right4 ,section ,title3 ,inventories and accounts4 #aebh4 ,on the day of ,october1 #aejh1 ,i had #cj scudi2 #ac ,i lent to ,salai to make up his sister's dowry1 and #ag ,i have left4 #aebi4 ,memorandum of the money ,i have had from the ,king as my salary from ,july #aejh till ,april next #aeji4 ,first #ajj scudi1 then #gj1 then #ej1 then #bj and then #bjj florins at #dh soldi the florin4 ,footnote3 ,compare ,no4 #acej and #aefa4 #aecj4 ,saturday the #bnd day of ,march ,i had from ,santa ,maria ,novella #e gold ducats1 leaving #dej4 ,of these ,i gave #b the same day to ,salai1 who had lent them to me4 ,footnote3 ,see ',conto corrente di ,leonardo da ,vinci con lo ,spedale di ,s4 ,maria ,nuova' #aejj a #aejg1 #aeac--aebj published by ,g4 ,,uzielli1 ,ricerche intorno a ,leonardo da ,vinci1 ,firenze1 #ahgb1 pp4 #afd1 #afe1 #bah and #bai4 ,the date here given by ,leonardo does not occur in either of the accounts4 #aeca4 ,thursday1 the eighth day of ,june1 ,i took #ag grossoni1 #ah soldi2 on the same ,thursday in the morning ,i gave to ,salai #bb soldi for the expenses4 #aecb4 ,to ,salai #d grossoni1 and for one braccio of velvet1 #e lire1 and #a_/b2 viz4 #aj soldi for loops of silver2 ,salai #ad soldi for binding1 the making of the cloak #be soldi4 ,footnote3 ,compare ,no4 #aebc4 #aecc4 ,i gave to ,salai #ic lire #f soldi1 of which ,i have had #fg lire and there remain #bf lire #f soldi4 #aecd4 ,to ,salai ,s #db #b dozen of laces ,s #h for papers ,s #c d #h a pair of shoes ,s #ad for velvet ,s #ad a sword and knife ,s #ba to the barber ,s #aa to ,paolo for a4444 ,s #bj ,for having his fortune told ,s #f #aece4 ,on ,friday morning1 one florin to ,salai to spend2 #c soldi received bread ,s44 d wine ,s44 d grapes ,s44 d mushrooms ,s44 d fruit ,s44 d ,footnote #f3 ,compare ,nos4 #aede1 l4 #d and #e1 with similar entries for horse's fodder4 bran ,s44 d at the barber's ,s44 d for shoes ,s44 d #aecf4 ,on ,thursday morning one florin4 #aecg4 ,on ,saint ,ambrose's day from the morning to ,thursday #cf soldi4 #aech4 ,the moneys ,i have had from ,ser ,matteo2 first #bj grassoni1 then on #ac occasions #c f4 and then #fa grassoni1 then #c1 and then #c99c2 #df soldi #ab grossoni4 #aeci4 ,for paper ,s #ah for canvas ,s #cj for paper ,s #aj d #ai ,total ,s #gc #aedj4 #bj pounds of ,german blue1 at one ducat the pound lire #hj ,s d #fj pounds of white1 ,s44 the pound lire #ae ,s d #a #a_/b pound at #dh the pound lire #f ,s d #b pounds of cinnabar at ,s #ah the pound lire #a ,s #af d #f pounds of green at ,s #ab the pound lire #c ,s #ab d #d pounds of yellow at ,s #ab the pound lire #b ,s #h d #a pound of minium at ,s #h the pound lire #j ,s #h d #d pounds of44444 at ,s #b the pound lire #j ,s #h d #f pounds of ochre at ,s #a the pound lire #j ,s #f d black444 at ,s #b the pound for #bj lire #b ,s #j d wax to make the stars #bi pounds at ,s--the pound lire #j ,s #j d #dj pounds of oil for painting at #e soldi the pound lire #aj ,s #j d ,altogether lire #abj d #ah without the gold4 #ah tin for putting on the gold #abj #ah #eh #aeda4 ,two large hatchets and one very small one1 #h brass spoons1 #d tablecloths1 #b towels1 #ae small napkins1 #b coarse napkins1 #b coarse cloths1 #b wrappers1 #c pairs of sheets1 #b pairs new and #a old4 #aedb4 ,bed #g #j ,s ring #g #j crockery #b #e gardener #a #b 44444 #b #h porters #b #a glasses #a fuel #c #f a lock #a ,section title3 ,miscellaneous ,notes4 #aedc4 ,new tin-ware #c pairs of sheets #f small bowls1 each of #d breadths1 #f bowls1 #b small sheets1 #b large dishes1 #b tablecloths and ,j_/#b1 #b dishes medium size1 #af coarse cloths1 #b small ones #h shirts1 ,old tin-ware #i napkins1 #c small bowls1 #b hand-towels4 #d bowls1 #c square stones1 #b small bowls1 #a large bowl1 #a platter1 #d candlesticks1 #a small candlestick4 #aedd4 ,hose ,s #dj straw ,s #fj wheat ,s #db wine ,s #ed bread ,s #ah meat ,s #ed eggs ,s #e salad ,s #c the ,barber ,s #b d #f horses ,s #a #aede4 ,sunday meat ,s #aj d wine ,s #ab d bran ,s #e d #d herbs ,s #aj d buttermilk ,s #d d #d melon ,s #c d bread ,s #c d #a ,monday ,s #i #h 44444 ,s #f d wine ,s #ab d bran ,s #i d #d buttermilk ,s #d d #d herbs ,s #h d ,tuesday ,s d meat ,s #j d #h wine ,s #ab d bread ,s #c d meal ,s #e d #d herbs ,s #h d ,wednesday wine ,s #e d melon ,s #b d meal ,s #e d #d vegetables ,s #h ,ash4,i4 #ah;b ,notes by unknown persons among the ,,mss4 7#aedf--aefe74 #aedf4 ,miseracione divina sacro sancte ,romane ecclesie tituli n cardinalis #bwulgariter nuncupatus venerabili religioso fratri ,johanni ,mair d',nustorf #cordinis praedicatorum provintie teutonie 787 conventus ,wiennensis capellano #d nostro commensali salutem in dno sempi- ternam ,religione zelus rite ac in ferite8 #e;honestas aliarumque laudabilium probitatis et virtutum merita quibus apud nos fide #f;digno commendationis testimonio ,magistri videlicet ordinis felicis recordacionis ,leonardi de #g,mansuetis de ,perusio sigillo suo 444 us dans tibi ad 444 opera virtutum comen7salem78 #h locum et tempus success7ores7 cujus simi- liter officium ministratus qui praedecessoris sui donum 787 #i;confirmavit et de novo dedit aliorumque plurima laudatis qui opera tua laudant #ajnos inducunt ut tibi 787 reddamus ad gratiam liberalem hinc est quod nos cupientes4 ,footnote3 ,the meaning of this document1 which is very difficult to decipher1 and is written in unintelligible ,latin1 is1 that ,leonardo di ,mansuetis recommends the ,rev4 ,mair of ,nusdorf1 chaplain at ,vienna1 to some third person2 and says also that something1 which had to be proved1 has been proved4 ,the rest of the passages on the same leaf are undoubtedly in ,leonardo's hand4 7,nos4 #dhc1 #ffa1 #eai1 #egh1 #cib1 #ehb1 #hhg and #hid47 ,w4 ,x,i,ib #aedg4 ,johannes ,antonius di ,johannes ,ambro- sius de ,bolate4 ,he who lets time pass and does not grow in virtue1 the more ,i think of it the more ,i grieve4 ,no man has it in him to be virtuous who will give up honour for gain4 ,good fortune is valueless to him who knows not toil4 ,the man becomes happy who follows ,christ4 ,there is no perfect gift without great suffering4 ,our glories and our triumphs pass away4 ,foul lust1 and dreams1 and luxury1 and sloth have banished every virtue from the world2 so that our ,nature1 wandering and perplexed1 has almost lost the old and better track4 ,henceforth it were well to rouse thyself from sleep4 ,the master said that lying in down will not bring thee to ,fame2 nor staying beneath the quilts4 ,he who1 without ,fame1 burns his life to waste1 leaves no more vestige of himself on earth than wind-blown smoke1 or the foam upon the sea4 ,footnote3 ,from the last sentence we may infer that this text is by the hand of a pupil of ,leonardo's4-- ,on the same sheet are the notes ,nos4#aage and #gae in ,leonardo's own handwriting4 ,section ,title3 ,miscellaneous notes4 #aedh4 ,on the morning of ,santo ,zanobio the #bith of ,may #aejd1 ,i had from ,lionardo ,vinci #ae gold ducats and began to spend them4 to ,mona ,margarita ,s #fb d #d to remake the ring ,s #ai d #h clothes ,s #ac good beef ,s #d eggs ,s #f debt at the bank ,s #g velvet ,s #ab wine ,s #f d #d meat ,s #d mulberries ,s #b d #d mushrooms ,s #c d #d salad ,s #a fruit ,s #a d #d candles ,s #c 4444 ,s #a flour ,s #b ,sunday #aih #h bread ,s #f wine ,s #i d #d meat ,s #g soup ,s #b fruit ,s #c d #d candles ,s #c d ,monday #ca bread ,s #f d #d meat ,s #aj d #h wine ,s #i d #d fruit ,s #d soup ,s #a d #h #cb #aedi4 ,tuesday bread ,s #f meat ,s #aa wine ,s #g fruit ,s #i soup ,s #b salad ,s #a 99,footnote for #aedh and #aedi4 ,on the same sheet is the text ,no4 #ajae in ,leonardo's own handwriting4 ,section title3 ,notes by unknown hands4 #aeej4 ,to ,monna ,margarita ,s #e to ,tomaso ,s #ad to ,monna ,margarita d #e ,s #b on the day of ,san ,zanobi left44444 after payment d #ac ,s #b d #d of ,monna ,margarita altogether d #ad ,s #e d #d #aeea4 ,on ,monday1 the l#cth of ,february1 ,i lent lire ,s #g to ,lionardo to spend1 ,friday d #g4 ,footnote3 ,this note is followed by an account very like the one given as ,no4 #aedi4 #aeeb4 ,stephano ,chigi1 ,canonico444441 servant of the honorable ,count ,grimani at ,s4 ,apostoli4 ,footnote3 ,compare ,no4 #fgd1 #ba--bc4 #aeec4 ,having become anxious4444444444 ,bernardo di ,simone1 ,silvestro di ,stefano1 ,bernardo di ,jacopo1 ,francesco di ,matteo ,bonciani1 ,antonio di ,giovanni ,ruberti1 ,antonio da ,pistoia4444 ,antonio2 ,he who has time and waits for time1 will lose his friends and his money4 #aeed4 ,reverend ,maestro1 ,domino ,giovanni1 ,i spoke to ,maestro ,zacaria as a brother about this business1 and ,i made him satisfied with the arrangement that ,i had wished2 that is1 as regards the commission that ,i had from the parties and ,i say that between us there is no need to pay money down1 as regard the pictures of the 444 ,c4,a4 #ge;a2 #bbj;a #aeee4 ,of things seen through a mist that which is nearest its farthest limit will be least visible1 and all the more so as they are more remote4 ,cod4,a4 #gg2;b #bbe;b #aeef4 ,theodoricus ,rex ,semper ,augustus4 ,c4,a4 #id;b2 #bga;b #aeeg4 ,either you say ,hesperia alone1 and it will mean ,italy1 or you add ultima1 and it will mean ,spain4 ,umbria1 part of ,tuscany4 ,footnote3 ,,amoretti1 ,mem4 ,stor4 ,,xxiv1 quotes the first three lines of this letter as by ,leonardo4 ,the cha- racter of the writing however does not favour this hypothesis1 and still less the contents4 ,i should regard it rather a rough draft of a letter by young ,melzi4 ,i have not succeeded in deciphering completely the #ac lines of this text4 ,amoretti reads at the beginning ,canonica di ,vaprio1 but ,vaprio seems to me a very doubtful reading4 ,footnote3 ,the notes in ,greek1 ,nos4 #aeeg1 #aeeh and #aefb stand in close connection with each other1 but the meaning of some words is very doubtful1 and a translation is thus rendered impossible4 ,c4,a4 #aba;b2 #cgf;b #aeeh4 9999,ilav,tcov av,t,k,x,acp,xt7uv ,suo soostai smataupov,tou2 #b;irptoo,aiaaai w avepuuo8 ',ae#gvac ,to,t8 ,qs4oi2 #hsj7oj-ai49999 ,footnote3 ,the notes in ,greek1 ,nos4 #aeeg1 #aeeh and #aefb stand in close connection with each other1 but the meaning of some words is very doubtful1 and a translation is thus rendered impossible4 ,c4,a4#acj;a2 #cig;a #aeei4 ,canonica of 444 on the #eth of ,july #aejg2 my dearly beloved mother1 sisters and cousin ,i herewith inform you that thanks to ,god ,i am 444 about the sword which ,i 444 bring it to ,maso at the piazza 444 and ,i will settle the business of ,piero so that 444 ,c4,a4 #afd;b2 #dij;b #aefj4 ,ut bene respondet ,naturae ars docta6 dedisset ,vincius1 ut tribuit cetera sic animam ,noluit ut similis magis haec foret3 altera sic est3 ,possidet illius ,maurus amans animam4 ,footnote #aefj3 ,these three epigrams on the portrait of ,lucrezia ,crivelli1 a picture by ,leonardo which must have been lost at a very early date1 seem to have been dedicated to ,leonardo by the poet4 ,leonardo used the reverse of the sheet for notes on geometry4 ,footnote3 ,the notes in ,greek1 ,nos4 #aeeg1 #aeeh and #aefb stand in close connection with each other1 but the meaning of some words is very doubtful1 and a translation is thus rendered impossible4 ,hujus quam cernis nomen ,lucretia1 ,divi ,omnia cui larga contribuere manu4 ,rara huic forma data est2 pinxit ,leonardos1 amavit ,maurus1 pictorum primus hic1 ille ducum4 ,naturam1 ac superas hac laesit imagine ,divas ,pictor3 tantum hominis posse manum haec doluit1 ,illae longa dari tam magnae tempera formae1 ,quae spatio fuerat deperitura brevi4 #aefa4 ,egidius ,romanus on the formation of the human body in the mother's womb ,footnote #a3 ,liber magistri ,egidii de pulsibus matrice conipositus 7cum commentario ,gentilis de ,fulgineo7 published in #adhd at ,padova1 in #adid and in #aead at ,venice1 and in #aeje at ,lyons44 ,footnote #b3b4 ,this text appears to be in a handwriting different from that in the note1 l4 #a4 ,here the reading is not so simple as ,,amoretti gave it1 ,mem4 ,star4 ,,xxv3 ,a ,monsieur ,lyonard ,peintre du ,roy pour ,amboyse4 ,he says too that this address is of the year #aeji1 and ,mr4 ,ravaisson remarks3 ,de cette suscription il semble qu'on peut inferer que ,leonard etait alors en ,france1 a la cour de ,louis ,,xii 444 ,pour conclure je crois qu'il n'est pas prouve que ,leonard de ,vinci n'ait pas fait un voyage de quelques mois en ,france sous ,louis ,,xii1 entre le printemps de #aeji et l'automne de #aeaj4--;,i must confess that ,i myself have not succeeded in deciphering completely this ,french writing of which two words remain to me doubtful4 ,but so much seems to be quite evident that this is not an address of a letter at all1 but a certificate or note4 ,amboisel4 #f ,i believe to be the signature of ,charles d',amboise the ,governor of ,milan4 ,if this explanation is the right one1 it can be easily explained by the contents of ,nos4 #acej and #aebi4 ,the note1 line #a1 was perhaps added later by another hand2 and ,leonardo himself wrote afterwards on the same sheet some geometrical explanations4 ,i must also point out that the statement that this sheet belongs to the year #aeji has absolutely no foundation in fact4 ,there is no clue whatever for giving a precise date to this note4 ,to ,monsieur le ,vinci1--the horses of the king's equerry4444 ,continue the payment to ,ms4 ,lyonard1 ,painter to the ,king4 #f ,amboise4 #aefb4 999999 ,don't know what to do about these ,greek characters #aefc4 ,memorandum to ,maestro ,lionardo to have 444 the state of ,florence4 #aefd4 ,to remind your ,excellency that ,ridolfo ,manini brought to ,florence a quantity of crystal besides other stones such as are 444 #aefe4 ,x,v,io99 ,c4 #f de ,ciuitate ,dei1 #b99se ,antipodes4 ,footnote3 ,a facsimile of this note1 which refers to a well known book by ,st4 ,augustin1 is given on page #bed4 #aeff4 ,leonardo's ,will4 ,be it known to all persons1 present and to come that at the court of our ,lord the ,king at ,amboise before ourselves in person1 ,messer ,leonardo da ,vinci painter to the ,king1 at present staying at the place known as ,cloux near ,amboise1 duly considering the certainty of death and the uncertainty of its time1 has acknowledged and declared in the said court and before us that he has made1 according to the tenor of these presents1 his testament and the declaration of his last will1 as follows4 ,and first he commends his soul to our ,lord1 ,almighty ,god1 and to the ,glorious ,virgin ,mary1 and to our lord ,saint ,michael1 to all the blessed ,angels and ,saints male and female in ,paradise4 ,item4 ,the said ,testator desires to be buried within the church of ,saint ,florentin at ,amboise1 and that his body shall be borne thither by the chaplains of the church4 ,item4 ,that his body may be followed from the said place to the said church of ,saint ,florentin by the collegium of the said church1 that is to say by the rector and the prior1 or by their vicars and chaplains of the church of ,saint ,denis of ,amboise1 also the lesser friars of the place1 and before his body shall be carried to the said church this ,testator desires1 that in the said church of ,saint ,florentin three grand masses shall be celebrated by the deacon and sub-deacon and that on the day when these three high masses are celebrated1 thirty low masses shall also be performed at ,saint ,gregoire4 ,item4 ,that in the said church of ,saint ,denis similar services shall be performed1 as above4 ,item4 ,that the same shall be done in the church of the said friars and lesser brethren4 ,item4 ,the aforesaid ,testator gives and bequeaths to ,messer ,francesco da ,melzo1 nobleman1 of ,milan1 in remuneration for services and favours done to him in the past1 each ,footnote3 ,see page #dbj4 and all of the books the ,testator is at present possessed of1 and the instruments and portraits appertaining to his art and calling as a painter4 ,item4 ,the same ,testator gives and bequeaths henceforth for ever to ,battista de ,vilanis his servant one half1 that is the moity1 of his garden which is outside the walls of ,milan1 and the other half of the same garden to ,salai his servant2 in which garden aforesaid ,salai has built and constructed a house which shall be and remain henceforth in all perpetuity the property of the said ,salai1 his heirs and successors2 and this is in remuneration for the good and kind services which the said de ,vilanis and ,salai1 his servants have done him in past times until now4 ,item4 ,the said ,testator gives to ,maturina his waiting woman a cloak of good black cloth lined with fur1 a44444 of cloth and two ducats paid once only2 and this likewise is in remuneration for good service rendered to him in past times by the said ,maturina4 ,item4 ,he desires that at his funeral sixty tapers shall be carried which shall be borne by sixty poor men1 to whom shall be given money for carrying them2 at the discretion of the said ,melzo1 and these tapers shall be distributed among the four above mentioned churches4 ,item4 ,the said ,testator gives to each of the said churches ten lbs4 of wax in thick tapers1 which shall be placed in the said churches to be used on the day when those said services are celebrated4 ,item4 ,that alms shall be given to the poor of the ,hotel-,dieu1 to the poor of ,saint ,lazare d',amboise and1 to that end1 there shall be given and paid to the treasurers of that same fraternity the sum and amount of seventy soldi of ,tours4 ,item4 ,the said ,testator gives and bequeaths to the said ,messer ,francesco ,melzo1 being present and agreeing1 the remainder of his pension and the sums of money which are owing to him from the past time till the day of his death by the receiver or treasurer-general ,m4 ,johan ,sapin1 and each and every sum of money that he has already received from the aforesaid ,sapin of his said pension1 and in case he should die before the said ,melzo and not otherwise2 which moneys are at present in the possession of the said ,testator in the said place called ,cloux1 as he says4 ,and he likewise gives and bequeaths to the said ,melzo all and each of his clothes which he at present possesses at the said place of ,cloux1 and all in remuneration for the good and kind services done by him in past times till now1 as well as in payment for the trouble and annoyance he may incur with regard to the execution of this present testament1 which however1 shall all be at the expense of the said ,testator4 ,and he orders and desires that the sum of four hundred scudi del ,sole1 which he has deposited in the hands of the treasurer of ,santa ,maria ,nuova in the city of ,florence1 may be given to his brothers now living in ,florence with all the interest and usufruct that may have accrued up to the present time1 and be due from the aforesaid treasurer to the aforesaid ,testator on account of the said four hundred crowns1 since they were given and consigned by the ,testator to the said treasurers4 ,item4 ,he desires and orders that the said ,messer ,francesco de ,melzo shall be and remain the sole and only executor of the said will of the said ,testator2 and that the said testament shall be executed in its full and complete meaning and according to that which is here narrated and said1 to have1 hold1 keep and observe1 the said ,messer ,leonardo da ,vinci1 constituted ,testator1 has obliged and obliges by these presents the said his heirs and successors with all his goods moveable and immoveable present and to come1 and has renounced and expressly renounces by these presents all and each of the things which to that are contrary4 ,given at the said place of ,cloux in the presence of ,magister ,spirito ,fieri vicar1 of the church of ,saint ,denis at ,amboise1 of ,m4 ,guglielmo ,croysant priest and chaplain1 of ,magister ,cipriane ,fulchin1 ,brother ,francesco de ,corion1 and of ,francesco da ,milano1 a brother of the ,convent of the ,minorites at ,amboise1 witnesses summoned and required to that end by the indictment of the said court in the presence of the aforesaid ,m4 ,francesco de ,melze who accepting and agreeing to the same has promised by his faith and his oath which he has administered to us personally and has sworn to us never to do nor say nor act in any way to the contrary4 ,and it is sealed by his request with the royal seal apposed to legal contracts at ,amboise1 and in token of good faith4 ,given on the ,x,x,i,i,ird day of ,april ,,mdxviii1 before ,easter4 ,and on the ,x,x,i,i,ird day of this month of ,april ,,mdxviii1 in the presence of ,m4 ,guglielmo ,borian1 ,royal notary in the court of the bailiwick of ,amboise1 the aforesaid ,m4 ,leonardo de ,vinci gave and bequeathed1 by his last will and testament1 as aforesaid1 to the said ,m4 ,baptista de ,vilanis1 being present and agreeing1 the right of water which the ,king ,louis ,,xii1 of pious memory lately deceased gave to this same de ,vinci1 the stream of the canal of ,santo ,cristoforo in the duchy of ,milan1 to belong to the said ,vilanis for ever in such wise and manner that the said gentleman made him this gift in the presence of ,m4 ,francesco da ,melzo1 gentleman1 of ,milan and in mine4 ,and on the aforesaid day in the said month of ,april in the said year ,,mdxviii the same ,m4 ,leonardo de ,vinci by his last will and testament gave to the aforesaid ,m4 ,baptista de ,vilanis1 being present and agreeing1 each and all of the articles of furniture and utensils of his house at present at the said place of ,cloux1 in the event of the said de ,vilanis surviving the aforesaid ,m4 ,leonardo de ,vinci1 in the presence of the said ,m4 ,francesco ,melzo and of me ,notary c4 ,borean4