,this e,book was produced by ,charles ,aldarondo and the ,distributed ,proofreaders team4 ,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