,transcriber's ,notes3 ,underscores 80 before and after a word or phrase indicate italics in the original text4 ,small capitals have been converted to ,,solid capitals4 ,illustrations have been moved so they do not break up paragraphs4 ,old or antiquated spellings have been preserved4 ,typographical errors have been silently corrected4 ,the table 8,,time ,,references ,,in ,,the ,,divine ,,comedy0 on pages #ceh-cff has been reformatted from horizontal to vertical in order to better fit the #gb-;column format4 ,footnotes have been separated out from the main text by the use of lines above and below1 made of hyphens4 ,illustration3 ,,dante ,,studying4 ,frontispiece ,from a fresco by ,luca ,signorelli at ,orvieto4 ,or vedi insieme l'uno e l'altro polo1 ,le stelle vaghe e lor viaggio torto2 ,e vedi 'l veder nostro quanto corte4 ,petrarch4 ,,dante ,,and ,,the ,,early ,,astronomers ,,by ,m4 ,a4 ,,orr 7,,mrs4 ,,john ,,evershed74 ,plainness and clearness without shadow of stain1 ,clearness divine6 ,ye heavens1 whose pure dark regions have no sign ,of languor1 though so calm1 and though so great ,are yet untroubled and unpassionate2 ,who1 though so noble1 share in the world's toil1 ,and though so tasked keep free from dust and soil6 99 99 99 99 99 ,you remain ,a world above man's head1 to let him see ,how boundless might his soul's horizons be1 ,how vast1 yet of what clear transparency4 ,,matthew ,,arnold4 ,london ,,gall ,,and ,,inglis1 #ca ,,henrietta ,,st41 ,w4,c4 ,and ,edinburgh4 ,,printed ,,and ,,bound ,,by ,,gall ,,and ,,inglis1 ,,newington ,,printing ,,and ,,bookbinding ,,works1 ,,edinburgh4 ,,preface4 ,an observatory on a mountain top is an ideal place in which to write on astronomy and poetry1 but it has one drawback3 the difficulty of obtaining books on special subjects4 ,my husband's criticisms and help have been invaluable1 and of books on modern astronomy there is no lack2 but many others which ,i have wished to consult ,i have been unable to procure1 and doubtless there are many more which ,i ought to have read1 but of whose existence ,i am ignorant4 ,this defect has been partly remedied1 however1 by ,mr4 ,wicksteed's great kindness in lending me a number of books on ,dante subjects4 ,i am much indebted to my sister1 ,miss ,orr1 who has helped me in preparing these sheets for the press4 ,the index is mainly her work4 ,thanks are also due to several members of the staff of this observatory3 ,mr4 ,sitarama ,aiyar made some calculations1 ,mr4 ,nagarajan ,aiyar projected the map facing page #bie1 ,mr4 ,krishna ,aiyar prepared photographs of several illustrations1 and ,mr4 ,krishnasawmy typed the greater part of the copy for press4 ,mr4 ,raymond ,beazley1 the ,trustees of the ,british ,museum1 and ,messrs ,macmillan1 have kindly allowed me to reproduce illustrations from their publications4 ,to all these ,i offer grateful thanks4 ,m4 ,a4 ,,evershed4 ,,kodaikanal ,,observatory1 ,,south ,,india4 ,october #aiac4 ,,this ,,book ,,is ,,dedicated ,,to ,,lucy4 ,,list ,,of ,,principal ,,authorities4 ,alfraganus1 ,elementa ,astronomica4 ,arabic et ,latin1 opera ,jacobi ,golii 7,amsterdam1 #affi74 ,angelitti1 ,sulla ,data del ,viaggio ,dantesco4 0 ,sull' ,anno della ,visione ,dantesca4 ,antonelli1 ,sulle ,dottrine ,astronomiche della ,divina ,commedia 7#ahfe74 ,aratus1 ,the ,phainomena4 ,translation by ,r4 ,brown4 ,aristotle1 ,four ,books on the ,heavens4 ,greek and ,german1 with notes1 by ,c4 ,prantl4 ,beazley1 ,dawn of ,modern ,geography4 ,berry1 ,history of ,astronomy4 ,blake1 ,astronomical ,myths1 based on ,flammarion's ,history of the ,heavens4 ,boffito et ,melzi ,eril1 ,almanach ,dantis ,aligherii 7#aijh74 ,brunetto ,latini1 ,li ,livres dou ,trsor4 7,chabaille1 ,paris1 #ahfc74 ,budge1 ,wallis1 ,guide to the ,babylonian and ,assyrian ,antiquities1 ,british ,museum1 #aijj4 ,cantelli1 ,la ,conoscenza dei ,tempi nel ,viaggio ,dantesco4 ,cicero1 ,de ,senectute4 0 ,somnium ,scipionis4 ,cornewall ,lewis1 ,historical ,survey of the ,astronomy of the ,ancients4 ,coulton1 ,from ,st4 ,francis to ,dante4 ,delambre1 ,histoire de l',astronomie ,ancienne4 0 ,histoire de l',astronomie du ,moyen ,age4 ,della ,valle1 ,il ,senso ,geografico-,astronomico della ,divina ,commedia 7#ahfi74 ,dreyer1 ,planetary ,systems from ,thales to ,kepler4 ,epping and ,strassmeier1 ,astronomisches aus ,babylon4 ,gardner1 ,dante's ,ten ,heavens4 ,gruppe1 ,die ,kosmischen ,systeme der ,griechen4 ,ideler1 ,ursprung und ,bedeutung der ,sternnamen4 ,imbriani1 ,studi ,danteschi4 ,king1 ,history of ,sumer and ,accad4 ,lockyer1 ,dawn of ,astronomy4 ,lubin1 ,dante e gli ,astronomi ,italiani4 ,maunder1 ,the ,oldest ,astronomy4 7,journal of the ,british ,astronomical ,association74 ,moore1 ,dante and his ,biographers4 0 ,studies in ,dante4 #c vols4 0 ,time references in the ,divina ,commedia4 ,parker1 ,mrs4 ,langloh1 ,australian ,fairy ,tales4 ,plato1 ,the ,republic4 ,translation by ,jowett4 0 ,the ,timaeus4 0 0 ,plutarch1 ,on the ,face in the ,moon4 ,translation by ,prickard4 ,pradeau1 ,key to the ,time-,allusions of ,dante4 ,rashdall1 ,universities of ,europe in the ,middle ,ages4 ,ristoro d',arezzo1 ,della ,composizione del ,mondo colle sue ,cagioni4 7,narducci1 ,milan1 #ahfd74 ,scartazzini1 ,a ,companion to ,dante1 translated by ,butler4 0 ,la ,divina ,commedia 7edizione minore1 with notes74 ,schaubach1 ,geschichte der ,griechischen ,astronomie bis auf ,eratosthenes4 ,schiaparelli1 ,i precursori di ,copernico nell' ,antichit4 0 ,i ,primord dell' ,astronomia ,babilonese4 0 ,i ,progressi dell' ,astronomia ,babilonese4 0 ,l',astronomia nell' antico ,testamento4 0 ,le ,sfere ,omocentriche di ,eudosso1 di ,callipo1 e di ,aristotile4 0 ,origine del ,sistema ,planetario ,eliocentrico presso i ,greci4 ,temple ,classics1 ,dante1 7,divine ,comedy1 ,convivio1 ,latin ,works1 with translations and notes74 ,the ,panchasiddhntik of ,varha ,mihira4 ,translated from the ,sanscrit1 and edited by ,thibaut and ,m4 ,s4 ,dvivedi4 ,toynbee1 ,paget1 ,articles on ,dante's ,obligations to ,alfraganus1 ,albertus ,magnus1 ,orosius1 and ,dante's theories regarding the markings on the ,moon 7in ,romania and ,giornale ,storico della ,letteratura ,italiana74 0 ,dante ,dictionary4 0 ,the ,life of ,dante 7,oxford ,biographies74 ,tozer1 ,an ,english ,commentary on ,dante's ,divina ,commedia4 ,wicksteed1 ,the ,early ,lives of ,dante4 ,wicksteed and ,selfe1 ,villani's ,chronicle4 ,witte1 ,dante-,forschungen4 99 99 99 99 99 ,all quotations from ,dante's works are taken from ,moore's ,tutte le ,opere di ,dante ,alighieri1 #crd edition1 ,oxford #ahid4 ,astronomical data are chiefly taken from ,young's ,manual of ,astronomy1 and the ,nautical ,almanac4 ,,contents4 ,,page ,,introduction #a ,,part ,i4 ,,astronomy ,,from ,,primitive ,,times ,,until ,,the ,,age ,,of ,,dante4 ,i4 ,,apparent ,,movements ,,of ,,the ,,heavenly ,,bodies ,,as ,,seen ,,from ,,earth #i ,,ii4 ,,the ,,beginnings ,,of ,,astronomy4 ,gnomons and clepsydras2 the constellations and the calendar2 astrology and star-worship2 early cosmogonies #be ,,iii4 ,,greek ,,astronomy3 ,,first ,,period4 ,b4,c4 #ijj to ,b4,c4 #cej #a4 ,homeric ,greece2 ,first ,notions of ,astronomy #ea #b4 ,thales and ,anaximander3 ,earth flat1 heaven a series of hemispheres #ee #c4 ,later ,flat ,earth ,systems3 the ,universe a sphere #fj #d4 ,pythagoras and his ,followers3 ,earth round1 ,earth in ,motion #ff ,,iv4 ,,greek ,,astronomy3 ,,second ,,period1 ,b4,c4 #djj to ,a4,d4 #aej #a4 ,plato3 the ,world-,soul #gi #b4 ,eudoxus3 the ,spheres #hh #c4 ,calippus3 the ,spheres of ,eudoxus improved #ic #d4 ,aristotle3 the ,philosophy of the ,spheres2 the three kinds of motion2 ,earth immoveable at the centre of the ,universe2 the elements2 the celestial movers1 and the ,first ,mover #ie #e4 ,aristarchus3 ,earth turning on her axis1 and revolving round the sun #ajg #f4 ,the ,school of ,alexandria3 instruments and methods2 ,earth's diameter measured2 the theory of ,moveable ,eccentrics #aab #g4 ,hipparchus3 8the ,father of ,astronomy20 his star catalogue2 his inventions and discoveries2 the precession of the equinoxes #abb #h4 ,ptolemy3 the ,almagest2 the system of ,epicycles and ,eccentrics2 distance and size of the moon discovered2 the stars2 astrology2 geography1 the seven climates #acd ,v4 ,,retrospect3 ,greek ,cosmogonies2 ,greek calendar #aei ,,vi4 ,,astronomy ,,under ,,imperial ,,and ,,christian ,,rome4 ,b4,c4 #df to ,a4,d4 #ajjj4 ,amateur ,astronomers2 the ,julian ,calendar2 passion for ,astrology2 the ,fathers2 the ecclesiastical ,calendar2 the ,schools2 the ,monasteries #afg ,,vii4 ,,arab ,,astronomy4 ,a4,d4 #gej to #abej4 ,schools of ,baghdad1 ,egypt1 ,spain4 ,improvements in ,mathematics and ,instruments2 ,ptolemy's values more correctly determined2 supposed discoveries of planetary distances and trepidation2 a ninth sphere added to ,ptolemy's eight #aha ,,viii4 ,,the ,,return ,,of ,,greek ,,astronomy ,,to ,,europe4 ,a4,d4 #ajjj to #acjj4 ,the ,universities2 ,arab influence2 ,greek books2 new ,european books2 the course in ,astrology in ,bologna2 ,aristotle and the ,church #aii ,,part ,,ii4 ,,the ,,astronomy ,,of ,,dante4 ,i4 ,,popular ,,astronomy ,,in ,,italy ,,in ,,dante',s ,,time4 ,the astronomy of ,dante contrasted with ,homer and ,milton4 ,general feeling for astronomy in his day2 some famous astrologers3 astronomy considered an ennobling study2 ,ptolemy's system final4 ,knowledge of average educated man4 #bji ,,ii4 ,,dante',s ,,studies4 ,dante a representative of contemporary beliefs3 his erudition2 his education2 ,brunetto ,latini's influence2 possible visits to universities of ,bologna1 ,padua1 ,paris4 #bbc ,,iii4 ,,books ,,on ,,astronomy ,,used ,,by ,,dante4 ,dante's wide reading2 his diligence and memory4 ,ptolemy his supreme authority on astronomy2 his principal text-books ,alfraganus and ,aristotle2 versions used4 ,classical ,latin authors2 ,greek2 ,arab2 ,christian #bca ,,iv4 ,,astronomy ,,in ,,dante',s ,,writings4 ,references to heavenly bodies in ,vita ,nuova1 the ,canzoniere1 ,convivio1 ,latin works and letters1 ,divine ,comedy4 ,artistic use of the facts and theories of astronomy4 #bec ,v4 ,,observational ,,astronomy #a4 ,movements of the ,moon #bfa #b4 ,movements of the ,sun #bgj #c4 ,the ,stars #bhc #d4 ,the ,galaxy #cjc #e4 ,the ,planets #cjg #f4 ,eclipses #caf #g4 ,comets and ,meteors #cah #h4 ,the ,sun's ,path in the ,sky seen from different ,parts of the ,earth #cbb #i4 ,celestial ,phenomena and ,time #cch ,,vi4 ,,dante',s ,,journey ,,through ,,the ,,three ,,realms3 ,,indications ,,of ,,time ,,and ,,direction ,,by ,,means ,,of ,,the ,,skies #a4 ,time references in the ,divine ,comedy #cec #b4 ,the ,inferno #cfg #c4 ,purgatory #cgc #d4 ,paradise #cia #e4 ,positions of ,sun1 ,moon1 and ,planets among the ,stars during ,dante's ,vision #djb #f4 ,the ,assumed ,date of the ,vision #dji ,,vii4 ,,theoretical ,,and ,,speculative ,,astronomy #a4 ,the ,spheres #dbi #b4 ,the ,spheres and the four ,elements #dda #c4 ,dimensions and ,physical ,nature of the ,universe #deg #d4 ,influence of the ,spheres on ,human ,affairs #dga #e4 ,the ,motive ,power #dhj ,,viii4 ,,medi,,val ,,and ,,modern ,,views ,,of ,,the ,,universe #dhg ,,illustrations4 ,,part ,i4 ,,fig4 ,,page ,,dante ,,studying4 ,from a fresco by ,luca ,signorelli at ,orvieto ,frontispiece #a4 ,the ,sun's ,path in the ,sky at different ,seasons #aa #b4 ,the ,moon at ,sunset1 soon after ,new1 and three days old #ad #c4 ,path of ,mars among the ,stars1 #aiji #af #d4 ,the ,star ,sphere #ai #e4 ,synodic and ,sidereal ,periods #ba ,,star ,,map #cd ,,the ,,moon-,,god ,,of ,,ur4 ,from a ,cylinder-seal in the ,british ,museum1 date about ,b4,c4 #bdjj4 ,by permission of the ,trustees of the ,british ,museum #cf #f4 ,the triple ,star-sign of the ,babylonians #cg #g1 #h1 #i4 ,the young ,moon and the ,pleiades after sunset1 as seen in ,babylon1 ,b4,c4 #ajjj #db #aj4 ,the ,scorpion4 ,from a ,babylonian boundary stone of about ,b4,c4 #aabj1 set up in the reign of ,nebuchadnezzar ,i4 ,now in the ,british ,museum #dc #aa4 ,the ,goat with ,fishes' ,scales4 ,from a ,babylonian boundary stone #dc ,,the ,,boat ,,of ,,the ,,sun ,,travelling ,,over ,,the ,,sky4 ,from an ancient ,egyptian papyrus4 ,reproduced from ,flammarion's ,astronomical ,myths #df #ab4 ,the ,universe according to ,anaximander #ei #ac4 ,the ,universe of ,leucippus #fc #ad4 ,the ,universe of ,democritus #fd #ae4 ,the ,universe of ,pythagoras #ga #af4 ,the ,system of ,philolaus3 night on ,earth #gc #ag4 do4 twelve hours later3 day on ,earth #gc #ah4 ,earth and ,sun according to ,heraclides #gd #ai4 ,the ,spheres of the ,sun in the system of ,eudoxus #ij #bj4 ,method of ,aristarchus for finding the ,distance of the ,sun #ajh #ba4 ,pekin ,observatory #aad #bb4 ,a ,pekin ,astrolabe of the thirteenth century ,a4,d4 ,from photographs taken in #ahhh and published in the ,bulletin de la ,socit belge d',astronomie #aaf #bc4 ,the ,moveable ,eccentric #aai #bd4 ,the ,movement of ,spica #abd #be4 ,the ,sun and the ,equinox #abh #bf4 ,the ,movement of the ,earth's ,axis which is the true cause of ,precession4 ,from ,young's ,manual of ,astronomy1 #aijb #aca #bg4 ,precession of the ,equinoxes #acc #bh4 ,path of ,mars1 #aiji #aci #bi4 ,the ,epicycle #aci #cj4 ,a ,planet 8retrograding0 and 8in opposition0 #adj #ca4 ,venus1 ,mercury1 and the ,sun #adb #cb4 ,the ,sun's ,deferent #ade #cc4 ,apparent ,variation in the size of the ,sun4 ,photographs taken at ,kodaikanal ,observatory1 with the spectroheliograph1 ,july #a1 #aiaa1 and ,jan4 #c1 #aiab4 ,actual size of the negative #adf #cd4 ,the ,moon's ,epicycle and ,deferent #adh #ce4 ,the ,ptolemaic ,system #aea #cf4 ,method 7erroneous7 of estimating ,planetary ,distances1 described by ,alfraganus #ahh #cg4 ,earth's ,shadow #aib ,,part ,,ii4 ,,fig4 ,,page ,a ,,medi,,val ,,astronomer4 ,from a painting by ,gerard ,dow #bjj ,,astronomy4 ,from a fresco in the ,spanish ,chapel of ,santa ,maria ,novella1 ,florence #bag #ch4 ,the ,half-,moon shape of the ,habitable ,earth 7,ristoro7 #bdg ,,climate ,,map ,,of ,,about ,a4,d4 #aaaj4 ,reproduced from ,beazley's ,dawn of ,modern ,geography #bdh #ci4 ,sun1 ,moon1 and zenith4 ,to illustrate ,par4 xxix #a-f #bfg #dj4 ,the ,zodiac and the ,months #bgf #da4 ,the ,ram on the ,ecliptic4 ,from the ,cosmi ,historia of ,robert ,flud1 ,a4,d4 #afab4 ,reproduced from ,brown's ,aratos4 #bgi ,,map ,,of ,,stars ,,visible ,,before ,,dawn ,,in ,,purgatory #bie #db4 ,ursa ,minor as a ,horn4 ,par4 xiii4 #aj #bii #dc4 ,the ,sun at the ,equinox1 seen from the poles and the equator4 ,conv4 ,,iii4 v4 #cbg #dd4 ,lunar and ,solar ,eclipses #cci ,,map ,,of ,,the ,,world ,,by ,,heinrich ,,of ,,mainz1 about ,a4,d4 #aaaj4 ,reproduced from ,beazley's ,dawn of ,modern ,geography #cdd #de4 ,the ,universe of ,dante #cee #df4 ,the ,signs of the ,zodiac at sunrise from the ,mountain of ,purgatory #cge #dg4 ,northern ,slope of the ,mountain of ,purgatory #cgg #dh4 ,dante's ,view of ,earth from the stars4 ,par4 xxii4 #cie #di4 do4 ,six hours later4 ,par4 xxvii4 #cif #ej4 ,an impossible interpretation of ,par4 xxvii4 #cii #ea4 ,the ,rising ,sun at the spring equinox4 ,par4 i4 #ci #djc #eb4 ,the ,moon's ,epicycle and ,deferent #ddi #ec4 ,comparative sizes of the ,sun and his satellites #dij ,,abbreviated ,,titles ,,of ,,books ,,used ,,in ,,the ,,text4 ,dante's ,works3-- ,inf4 ,inferno4 ,purg4 ,purgatorio4 ,par4 ,paradiso4 ,canz4 ,canzone4 ,son4 ,sonetto4 ,ball4 ,ballata4 ,ecl4 ,eclogue4 ,v4 ,n4 ,vita ,nuova4 ,conv4 ,convivio4 ,de ,mon4 ,de ,monarchia4 ,v4 ,e4 ,de ,vulgari ,eloquentia4 ,ep4 ,epistola4 ,qu4 ,qustio de ,aqua et ,terra4 ,el4 ,ast4 ,elementa ,astronomica 7,alfraganus74 ,comp4 del ,mond4 ,della ,composizione del ,mondo 7,ristoro74 ,,dante ,,and ,,the ,,early ,,astronomers4 ,,introduction4 ,in a beautiful passage of the ,convivio ,dante describes how he first began to devote himself diligently to science and philosophy4 ,when the gentle soul of ,beatrice had passed to heaven1 a great darkness fell upon him3 the streets of ,florence were to him as a deserted city1 and his life empty and purposeless4 ,it was long before he could find any comfort1 but at last he bethought himself of studying a book by ,bothius1 who when exiled1 imprisoned1 and unjustly condemned to death1 had strengthened his soul with the 8,consolations of ,philosophy40 ,this led him on to ,cicero's book 8,on ,friendship10 in which ,llius explains how he is consoled for the death of ,scipio4 ,books in those days could only be had in manuscript1 full of abbreviations1 and often also of errors1 and at first the young student found the ,latin hard to master2 but as he struggled on1 half deciphering and half divining the meaning1 the mists cleared a little1 and the weight was lifted from brain and heart4 ,with elation he discovered that obscure passages were becoming luminous1 and to the exhilarating sense of conquest was added the joy of finding1 beautifully expressed1 thoughts which had already floated in his own mind1 but dimly1 as in a dream4 ,he compares himself to one who1 seeking silver1 should light 7not without ,divine guidance7 on a treasure of gold2 for he found not only relief from his tears1 but a door into a new world of literature1 philosophy1 and science4 ,henceforth1 he tells us1 he eagerly frequented the schools of the religious orders and the discussions of the philosophers2 and how extensive and thorough was his learning we can see in his writings4 ,in them we find a reflection of thirteenth-century thought in every field of intellectual research4 ,among all his studies was one which evidently had a great attraction for him1 even in the early days of the ,vita ,nuova1 before learning had become a passion4 ,astronomy appealed to many sides of his nature4 ,the beauty of the skies stirred his imagination2 their suggestive symbolism touched his religious sense2 the harmony of the celestial movements and the accuracy with which they can be foretold delighted his instinct for order and precision4 ,he must have read1 and perhaps possessed1 some of the best text-books then available1 and he grasped with singular clearness the phenomena observed and the theories taught in his day4 ,his works are full of allusions to astronomy4 ,in the ,vita ,nuova he finds pleasure in connecting the story of his lady with the revolutions of the spheres2 in the ,convivio he teaches the elements of the science2 in the ,vision of the ,divine ,comedy he journeys through the universe as it was depicted by medival astronomers2 and throughout his works are scattered similes drawn from celestial phenomena and descriptions of 8le belle cose che porta il ciel40#a ---------------------------------------- -------------------------------- #a 8,the fair things that ,heaven holds40 ,inferno ,,xxxiv4 #acg1 #ach4 ---------------------------------------- -------------------------------- ,therefore1 for full enjoyment and understanding of ,dante's works it is necessary to have a rudimentary knowledge of astronomy4 ,many of his readers think that ,dante's astronomy is very complicated and difficult to understand4 ,what makes it seem difficult is that in this age we are generally unfamiliar with the skies4 ,we do not eat our breakfast or go to our office by the sun1 nor do we watch the stars to see when grouse-shooting begins or the summer holidays end4 ,if it is important for us to know at what hour the sun sets and lamps must be lighted1 or if we wish to see a view by moonlight1 we consult an almanac4 ,when we think at all of the movements of the heavenly bodies1 our notions are usually taken from diagrams and tables1 not from what is actually seen in the skies4 ,we only think1 for instance1 of the seasons as caused by the earth's journey round the sun1 and the tilt of her axis3 therefore1 when ,dante speaks of ,venus as a ,morning ,star veiling the ,fishes with her rays1 or the horn of the ,celestial ,goat touching the sun1 it conveys little1 although the seasons of spring and of winter are as clearly indicated as if he had spoken of the blossoming of primroses or the fall of snow4 ,when ,cacciaguida1 in the heaven of ,mars1 tells the date of his birth by counting how many times the planet had since then returned to his ,lion1 those who only think of ,mars as circling round the ,sun1 and have never traced his path among the stars1 are at a loss1 and think the method very far-fetched4 ,a short description1 and especially a little individual watching1 of the apparent movements of the heavenly bodies1 would put us in a position to realize the meaning of a large number of ,dante's astronomical descriptions and allusions1 without any knowledge of any theory4 ,others complain that the subject is dull4 ,dante's astronomy1 when interpreted only by means of notes on single passages1 is undoubtedly dull--as dull as the history of his own times learned in the same way4 ,but when either subject is studied as a whole these passages acquire a special interest2 and they in their turn give new life to the subject they illustrate4 ,other readers say that ,dante's astronomy is so entirely false and obsolete that it is not worth study4 ,this is hardly true4 ,where ,dante speaks of appearances he is remarkably accurate1 far more so than most modern artists and writers of fiction4 ,where he speaks of the heavens as he supposes them actually to exist1 he is interpreting the appearances according to the astronomical theories of his day1 with which he was very well acquainted4 ,this interpretation was not correct1 but it was an ingenious and beautiful system1 and very successful in so far as it enabled astronomers to calculate the positions of sun1 moon1 stars1 and planets for any date4 ,its main outlines can be explained in a few pages1 with the help of a couple of diagrams1 but when presented thus1 especially to those unfamiliar with the skies1 it seems very strange and artificial4 ,to appreciate it at its true worth1 we must know just what are the phenomena it was intended to explain1 and trace its gradual development out of man's first clear perception that the movements of sun1 moon1 and stars follow unchanging laws4 ,the story of this development is of enthralling interest1 and after the system had been completed by one of the greatest mathematicians the world has seen1 its later history reads like a romance4 ,though of classical ,greek origin1 it was almost wholly lost to ,europe for many centuries1 it returned at last in ,oriental dress1 and its final form was given by a devout and learned ,dominican friar4 ,it was at this time that ,dante was born1 and the scholar-poet immortalized the ,ptolemaic system of astronomy in his verse1 adding to its popularity in his own day1 and making it known to thousands of readers since1 who might otherwise scarcely have heard of it4 ,dante's astronomy1 therefore1 is of wide and deep significance4 ,to study its history is to learn a chapter in the development of the human intellect2 to see the universe with his eyes is to know how it appeared1 not only to his contemporaries but to men in many lands and many centuries4 ,the system of ,ptolemy was already a thousand years old when ,dante studied it1 and it continued to be taught long after ,copernicus had introduced a truer one2 nor has it ever been completely swept away1 for much that it taught was accurate4 ,the new astronomy has developed from the old1 and bears traces to this day1 in its phraseology1 its written symbols1 and its methods1 of the many races and ages which have contributed to its progress4 ,this book1 therefore1 is divided into two parts4 ,in the first1 ,i put before my readers the elementary facts which form the foundations upon which all astronomy is based1 the movements of sun1 moon1 stars1 and planets1 so far as they can be easily observed by the naked eye2 then follows a sketch of the attempts which were made to interpret these observations from very early days until ,dante's time4 ,unnecessary technicalities are avoided1 but we shall try to enter into the thoughts of past generations concerning the stars1 to see why they were interested1 how they worked1 what hindered and what helped them in their search for truth4 ,in the second part1 we shall examine ,dante's works1 and see how familiar he was with the movements of the skies1 and how well he understood the theories which in his time were held to explain them4 ,we shall see how astronomy was generally regarded in his day1 what books he read1 and which authors influenced him most4 ,we shall see how false is the assertion often made that in the ,middle ,ages men studied astronomy only for the sake of astrology1 and how closely the science of the stars was connected with religion and the loftiest speculations of philosophy4 ,we shall also examine in particular some difficult passages connected with astronomy which occur in ,dante's works1 but my aim is not so much to explain all the astronomical references as to put the reader in a position to attempt an explanation himself4 ,my greatest ambition is to share with others the pleasure ,i have had in learning what ,dante knew and thought about the stars1 and who were the master builders who had erected through the ages the system so vividly pictured in his immortal poem4 ,,first ,,part4 ,,the ,,story ,,of ,,astronomy ,,from ,,primitive ,,times ,,until ,,the ,,age ,,of ,,dante4 ,i4 ,,apparent ,,movements ,,of ,,the ,,heavenly ,,bodies ,,as ,,seen ,,from ,,earth4 ,the stars appear to us like points of light1 differing greatly in brightness1 and scattered very irregularly over the dome above us4 ,all are moving1 some much more quickly than others1 yet a little attention shows that they do not change their relative positions1 and therefore that all must share in one connected movement4 ,if1 for instance1 any one group be singled out1 and looked for again some hours later1 it will be evident that it has moved considerably as a whole1 yet the stars composing it have kept the same places with regard to one another4 ,careful and prolonged observations prove that to observers in the northern hemisphere one star has hardly any perceptible movement1 that those nearest to it sweep round it in small circles1 and those further away in larger and larger circles1 parts of which are hidden below the horizon4 ,all these circlings are performed in the same time1 and therefore the stars near the stationary point move more slowly in their small circles than those further away4 ,all this is precisely what we should see if the sky were a great hollow sphere1 turning about the earth on an axis which runs close to the almost stationary star--known therefore as the ,pole ,star4 ,the direction is from east to west1 and a complete revolution is made in a day and night4 ,we can plot the stars on a globe1 and draw an equator on it1 which will everywhere be at an equal distance from the poles1 and we may add other circles1 as on a terrestrial globe3 then the position of each star can be referred to these circles as towns on earth are found by latitude and longitude1 and the path of any moving body1 such as a comet1 may be traced4 ,the stars fade out when the sun rises1 but he too sweeps across the sky as though carried round by the same sphere1 and he sets like them1 in the west4 ,has he a fixed place on the sphere1 keeping always the same position relatively to the stars8 ,no1 for in the place where he has just set we do not always see the same stars4 ,night after night those which were clear in the western sky as soon as it was dark enough to see them1 grow closer to him1 till at last they are lost in his twilight beams4 ,thus the sun1 though sharing in the daily east to west movement1 has a slow movement of his own on the sky-sphere1 slipping back from west to east1 until in a year he has accomplished the whole round1 and sets again among the same stars4 ,moreover1 this peculiar movement of the sun is not a mere lagging behind the stars1 for his west to east motion is combined with a north and south motion4 ,if we note the star-groups which are just behind him when he sets 7or just before him when he rises71 we shall find that they form a great circle round the globe1 half of which lies north and half south of the celestial equator4 ,the ,greeks named this circle the ,zodiac1 or 8,path of the ,animals10 because the star-groups forming it were mostly called by the names of animals 7the ,ram1 ,lion1 ,fishes1 etc474 ,when the sun is in the most northerly part of the zodiac it is summer in the northern hemisphere2 when he is in the most southerly1 it is summer in the south4 7,see ,map74 ,illustration3 ,fig4 #a4 ,the ,sun's path in the sky at different seasons4 ,this north and south motion of the sun may be noted more directly in another way4 ,seen from any given place on the earth1 each star rises and sets at the same points of the horizon always1 and has the same course in the sky2 but the rising and setting points of the sun1 which on about the #bast of ,march are due east and west1 travel daily further north1 and the sun mounts daily higher in northern skies until about the #bjth of ,june2 then he returns towards the south1 passing the east and west points again about ,september #bc1 and reaches his furthest point south about ,december #ba4 7,the dates vary slightly owing to ,leap ,year74 ,the dates on which the sun reaches his furthest north and furthest south points in this yearly journey are called the 8solstices10 because his motion seems to be checked1 and he pauses or 8stands0 before reversing his direction2 the dates on which he passes the midway point are the 8equinoxes10 because at those points he is on the equator1 and makes day and night equal all over the earth4 ,the time taken by the sun to pass from one vernal 7spring7 equinox to another is #cfe days1 #e hours1 #dh minutes1 #de seconds4 ,since this slow motion along the zodiac is from west to east1 contrary to the rapid east to west motion which he shares with all the stars1 he takes a little longer to complete a daily revolution than they do2 and if we reckon a solar day as consisting of #bd hours1 a 8sidereal0 7or star7 day is equal to #bc hours1 #ef minutes1 #d seconds4 ,these are very elementary facts1 but they are the fundamental facts of astronomy1 and without recollecting and holding them clearly in mind we cannot understand ,dante's allusions1 nor see the fitness of any astronomical system1 ancient or modern4 ,to those who have only read about astronomy in books1 and have not watched the skies1 they may be puzzling1 and ,i would beg these readers to make a few simple observations for themselves1 as this will help them more than any written explanation can ever do to see the heavens with ,dante's eyes4 ,to appreciate the connected movement of the whole sky1 some bright stars near the ,pole should first be watched1 such as the ,great ,bear and ,cassiopeia1 or for those in the southern hemisphere the ,southern ,cross1 ,canopus1 ,achernar4 ,their motions should be compared with those of bright stars near the equator1 such as ,orion1 ,virgo1 or ,aquila4 ,the constellations of the zodiac should be studied1 and notes made of the seasons at which each disappears in the rays of the sun4 ,the sun's north and south movements can be easily recognized by noting at what points of the horizon he rises or sets at different times of the year2 and the different heights to which he rises in the sky are most simply observed by marking the length of the shadow of some tree or pole at midday4 ,or if some rough kind of gnomon#b be made1 even a flat piece of wood1 laid on a sunny window-sill1 with a long nail driven vertically into it1 the movement and varying length of the shadow1 from hour to hour1 and from day to day1 will make one realize vividly the diurnal and the seasonal movement of the sun4 ,this device1 in one form or another1 was probably the first astronomical instrument invented1 and by its means ancient astronomers in many lands solved important problems4 ---------------------------------------- -------------------------------- #b ,greek gnomon1 an interpreter4 ,a pole set up in order to show the length of shadow thrown by the sun4 ---------------------------------------- -------------------------------- ,it is not necessary to explain that the daily apparent movements are caused in reality by the earth's rotation on her axis1 and the yearly apparent movements by her revolution round the sun4 ,these are the book-learned facts which for the most part obscure our perception of the very things on which they are based4 ,i would ask the reader to do his best1 for the moment1 to forget them4 ,the movements of the moon among the stars are much more easily observed than those of the sun1 since we can see the stars at the same time1 and her revolution is much more rapid4 ,she also is apparently carried round with the daily east to west movement1 and she also has a west to east motion of her own1 but so fast that it takes her round the star sphere in one month1 instead of one year4 ,this revolution also takes place in the zodiac4 ,she is first visible as a fine crescent1 just following the sun1 in the west1 after he has set2 next night she is markedly further from the sun1 on her eastward course1 and is a larger crescent2 she continues increasing her distance from the sun and the size of her disc1 until1 as full moon1 she is rising in the east when the sun sets opposite her in the west1 and setting when the sun rises4 ,after this1 she begins to wane1 and1 still travelling in the same direction1 rises later and later at night1 and sets in the day2 she draws gradually nearer to the sun on the western side1 till at last1 as a fine crescent with the horns turned in the other direction 7i4e4 always away from the sun71 she appears just before the rising sun in the east4 ,then for a short time she is lost in his rays1 till she emerges as a new moon on the sunset side again4 ,illustration3 ,fig4 #b4 ,the ,moon at ,sunset4 ,the moon completes a revolution among the stars in #bg days1 #h hours2 but it takes her a little longer to come up with the sun again1 since he has meanwhile been moving in the same direction along his yearly path2 and the #8synodic' month1 or period from one new moon to the next1 is #bi days1 #ac hours4 ,as well as the moving sun and the moving moon1 there are five other bodies1 visible to the naked eye1 which move among the stars4 ,they look like stars1 but their movements would lead us rather to class them with sun and moon4 ,they also are in the zodiac1 and they also1 while carried round with the universal movement from east to west1 revolve slowly1 each in its own period1 from west to east4 ,but their motions are more complicated than those of sun and moon4 ,two1 which we call ,venus and ,mercury1 are never seen very far from the sun1 and they oscillate from side to side1 sometimes appearing before him near sunrise1 and sometimes after him at sunset4 ,mercury keeps closest to the sun1 and is not so bright1 and therefore less easy to see2 but ,venus is a brilliant object when she gradually swings out further from the sun1 remaining longer each evening after sunset in the western sky4 ,then she gradually draws back1 closer to the sun1 is lost in his rays1 and a few days after begins to appear on his other side1 as a ,morning ,star1 visible in the east before sunrise4 ,here she swings out again1 like a pendulum1 to her furthest distance west1 and then draws in again1 just as she did on the sunset side of the sun4 ,in this way1 swinging slowly from side to side of the sun1 ,mercury and ,venus make with him the circuit of the zodiac1 completing a revolution from west to east in about a year4 ,the average period of ,mercury's oscillation1 counting1 for instance1 from one ,greatest ,western ,elongation 7i4e4 furthest distance from the sun on the west7 to the next1 is #aaf days2 that of ,venus is #ehd days4 ,illustration3 ,fig4 #c4 ,the ,path of ,mars among the ,stars1 #aiji4 ,the other three 8wandering stars0--or 8planets10#c as they were named by the ancient ,greeks--,mars1 ,jupiter and ,saturn1 are also often seen as morning or evening stars near the sun1 but they do not always accompany him1 like ,venus and ,mercury4 ,they may be seen at any distance from him1 even exactly opposite1 so that they rise as he sets4 ,they keep as strictly to the zodiac1 however1 and travel in it from west to east1 in periods of approximately two1 twelve1 and thirty years respectively2 and their paths are also complicated by oscillations4 ,periodically they slacken speed1 stop1 and go back a little distance among the stars1 then they slacken1 stop1 and advance again4 ,these changes are technically called direct motion1 stations or stationary points1 and retrograde motion4 ---------------------------------------- -------------------------------- #c ,greek planetes1 a wanderer4 ,this name was originally given to ,mercury1 ,venus1 ,mars1 ,jupiter1 ,saturn1 and also to sun and moon1 for it indicated all the known heavenly bodies which changed their places among the stars4 ,in modern usage it is not applied to the sun1 but only to his satellites1 of which many more are now known4 ---------------------------------------- -------------------------------- ,it must have originally taken many years of patient watching to discover and distinguish all these planets4 ,in these days1 by means of an almanac and some knowledge of the constellations1 they may easily be found and traced4 ,mars and ,venus move quickly during part of the time they are visible1 and if sketches be made of their positions among the stars1 and their paths marked for a few weeks1 a very good idea may be gained of the motions of planets as seen in the skies4 ,once again1 it is not necessary to explain here that these movements of the planets are due partly to their revolution round the sun1 and partly to the ,earth's motion4 ,nor need we1 for our present purpose1 consider them in any detail3 all that is important to realize is the general character of the movements1 and their likeness to those of sun and moon4 ,the distances1 and therefore the sizes1 of all the heavenly bodies are completely beyond measurement1 except with instruments and refined methods2 their physical nature could only be guessed at before the discoveries of universal gravitation and spectrum analysis1 in the #agth and #aith centuries of our era4 ,all that can be observed by naked eye astronomy is difference of brightness and colour2 as for instance the contrast between ruddy ,mars and white ,jupiter2 the steadier light of all the planets as compared with stars2 and the interesting fact that the moon shines by reflected sunlight1 which is made evident by the connection between her phases and her position with regard to the sun4 ,her surface1 too1 is clearly seen to be diversified by dark markings of definite shape1 but on no other body in all the sky can we make out the least detail without a telescope4 ,the movements of the heavenly bodies1 therefore1 which still form one of the most important parts of astronomy1 were almost all that could be studied by ancient astronomers1 and gave them the only key they had to the problems of the universe4 ,to sum up3--,the chief apparent movements of the heavens1 visible to the naked eye1 are eight1 viz3-- ,the daily revolution of the entire heavens1 carrying with it every visible celestial body1 in a little less than #bd hours2 the revolutions of sun1 moon1 and five naked eye planets1 in seven different periods4 ,the first of these is from east to west1 and is by far the most rapid4 ,the axis of revolution passes through two points which we call the celestial poles1 and the motion is parallel to the celestial equator4 ,all the others are in the main from west to east1 though the progress of the planets is complicated by periodical retrograde movements4 ,all take place in the zodiac1 which is a series of constellations forming a great band round the heavens4 ,the path of the sun is a great circle through this1 called the ,ecliptic 7because eclipses can only happen when the moon is also on it72 and the paths of moon and planets are slightly and variously inclined to it4 ,thus the daily path of a star is affected only by the simple uniform movement of the entire heaven 7in reality the rotation of the ,earth7 but the daily path of a planet1 or of the sun or moon1 results from a combination of this general movement with its own peculiar movement1 which is generally in the opposite direction4 ,illustration3 ,fig4 #d4 ,the star sphere4 ,if it is difficult to conceive a body moving simultaneously in two different directions1 an earthly analogy will make it easy4 ,on a great moving platform1 such as that which encircled the ,paris ,exhibition in #aijj1 there are fixed posts etc4 which revolve exactly as the whole platform revolves and do not move about amongst themselves4 ,these are like the fixed stars on the 7apparently7 revolving sphere4 ,but human beings are free to add their own movements to that given them by the platform on which they stand4 ,one man turns his back and walks steadily and very slowly in the opposite direction1 and so he neutralizes part of the platform movement and is not carried onward quite so quickly as the stationary posts3 he is the sun4 ,a woman walks as he does1 but much more quickly1 so that she rapidly passes many posts1 although all the time she is being carried backwards with them3 she is the moon4 ,children run backwards and forwards3 they are the planets4 ,finally1 if all these people are also constantly crossing the platform slowly from right to left and back again1 their movements will be oblique to the platform movement and will imitate the north and south movements of sun1 moon1 and planets4 ,it is in this fashion that the movements of the skies present themselves to careful observers on this seemingly stationary earth2 and in the youth of the world these apparent movements were believed to be real4 ,the ancients thought that the sky was actually revolving round a steadfast earth1 while the sun and moon and certain other 8wandering stars0 had in addition various motions peculiar to themselves4 ,the table of periods which follows 7see pp4 #bb-bc7 will be found useful for occasional reference4 ,some of the terms used will be explained later4 ,illustration3 ,fig4 #e4 ,diagram illustrating ,synodic and ,sidereal ,periods4 ,the arrows show the direction of the ,moon's monthly and the ,sun's yearly revolutions in the zodiac1 as seen from ,earth4 ,when the ,moon is opposite the ,sun1 for instance in ,libra while he is in ,aries1 she is full4 ,in #bg days she returns to the same place among the stars1 and this is a ,,sidereal ,,month4 ,but the ,sun meanwhile has moved into ,taurus1 and not until the ,moon has reached ,scorpio1 opposite to him1 will she be full again1 and complete her ,,synodic ,,month 7#bi days74 ,,revolutions ,,of ,,sun1 ,,moon1 ,,and ,,planets ,,as ,,seen ,,from ,,the ,,earth4 ,days4 ,hrs4 ,mins4 ,secs4 ,tropical ,solar ,year3 period from one vernal equinox to another1 or from one summer solstice to the next1 c4 #cfe #e #dh #dee 7,our civil year is based on this74 ,sidereal ,year3 period between two successive returns of the sun to any star on his path #cfe #f #i #hi ,the difference between these two kinds of year is due to ,precession of the ,equinoxes1 vide infra1 p4 #bc4 ,days4 ,hrs4 ,mins4 ,secs4 ,solar ,day3 period between two successive passages of the sun across the meridian 7noon7 -- #bd #j #j ,sidereal ,day3 period between two successive passages of a star across the meridian -- #bc #ef #d ,the difference between these two kinds of day is due to lag of the sun behind the stars1 his daily motion westward being slightly retarded by his slow yearly motion eastward4 ,days4 ,hrs4 ,mins4 ,secs4 ,mean ,synodic ,month3 period between two full moons #bi #ab #dd #bh ,mean ,sidereal ,month3 period between two successive returns of moon to any star on her path #bg #g #dc #aae ,the difference between these two kinds of months is due to the fact that while the moon is making her revolution among the stars1 the sun is also moving slowly on in the same direction4 ,days4 ,hrs4 ,mins4 ,secs4 ,mean ,anomalistic ,month3 period between perigee and perigee 7vide infra7 #bg #ac #ah #cgd ,,planets3--,mean ,synodic ,revolution3 period between two successive conjunctions with the sun1 and mean zodiacal revolution3 period of revolution round the zodiac4 ,mean ,synodic ,revolution4 ,mean ,zodiacal ,revolution4 ,mercury #aaf ,days#d #aj ,years ,venus #ehd 0 #aj 0 ,mars #ghj 0 #ahh 0 ,jupiter #cii 0 #aahf 0 ,saturn #cdh 0 #bidf 0 ---------------------------------------- -------------------------------- #d ,fractions omitted4 ---------------------------------------- -------------------------------- ,,precession ,,of ,,equinoxes3 #ejbe seconds of arc in one year2 that is1 #cfj degrees 7a revolution among the stars of the zodiac7 in #be1hjj years nearly4 ,,ii4 ,,the ,,beginnings ,,of ,,astronomy4 ,note4 ,as these pages are passing through the press1 a letter from ,mr4 ,maunder appears in ,the ,observatory for ,august #aiac on 8,the ,origin of the ,constellations10 and this should be consulted by anyone interested in the subject4 ,mr4 ,maunder points out that ,ptolemy gives us much more precise information than ,aratus regarding the southern limits of the ancient constellations1 and that the changes which he says he ventured to make in their traditional forms are extremely insignificant4 ,mr4 ,maunder further observes that the celestial equator of ,aratus cannot give any clue to the origin of the constellations 7as ,r4 ,brown suggested71 but only to the date of the work from which ,aratus copied1 when some astronomer had drawn the equator through the constellations4 ,a slight alteration of the text1 ,mr4 ,maunder says1 would give a correct equator for the date ,b4,c4 #ajjj4 ,see also ,mr4 and ,mrs4 ,maunder's article in ,monthly ,notices of the ,royal ,astronomical ,society for ,march #aijd4 ,proctor's 8,origin of the ,constellation ,figures0 is in his book ,myths and ,marvels of ,astronomy4 ,,ii4 ,,the ,,beginnings ,,of ,,astronomy4 ,the sky appears to us like an arch1 embracing all our lives1 ,dante says4#e ,from the dawn of intelligence man must have recognized his dependence upon the all-embracing heavens1 especially the sun1 without which life would be impossible4 ,the consciousness expressed itself in many ways3 in adoration of the sky1 the sun1 moon1 and hosts of heaven2 in superstitious fear which regarded events on earth as directly controlled by the heavenly bodies2 in careful watching and recording of their movements for useful purposes4 ,thus1 long before astronomy became an exact science1 and was studied simply for its own sake1 patient observers had laid the foundations1 and were familiar with many of the movements we have been describing4 ---------------------------------------- -------------------------------- #e ,conv4 ,,iv41 xxiii4 #ef1 #eg4 ---------------------------------------- -------------------------------- ,these are of great importance to primitive man4 ,sun1 moon1 and stars are invaluable as guides1 especially at sea1 and we know that the ancient ,greek mariners used to steer their ships by observations of the ,great ,bear1 while the ,phoenicians preferred to use the ,little ,bear for this purpose4 ,but the strongest and most universal incentive to careful and prolonged study of the skies is our complete dependence upon them for the measurement of time4 ,in the earliest period of their history1 the ,jews1 the ,greeks1 and probably every other nation1 divided the day simply into morning1 noon1 and evening1 according as the sun was rising1 or apparently stationary1 or sinking1 with regard to the horizon2 and the passage of some bright stars indicated the time at night4 ,but at a very early period the first of all astronomical instruments was invented1 by which the sun's varying height can be measured3 hence the time of noon1 the dates of equinoxes and solstices1 and the length of the solar year can be determined4 ,the gnomon in its simplest form is a pole set up vertically on a smooth level surface1 on which its shadow as cast by the sun can be observed4 ,the moment of shortest shadow marks the middle of the day1 the shortest midday shadow marks the summer solstice1 the longest the winter solstice1 the equinoxes falling between4 ,the instrument also indicates the points of the compass1 for the sun is always due south in northern latitudes at midday3 hence the ,latin word meridies 7,french midi7 means south as well as midday1 and the ,meridian in astronomy is a line which passes through the north and south points and the zenith1 and is crossed by the sun at midday4 ,the gnomon was said to have been introduced into ,greece by ,anaximander about #fjj ,b4,c41 and the ,babylonians claimed to be the inventors1 but it was probably invented independently by several races4 ,the ,chinese certainly observed the length of the shadow more than two thousand years ,b4,c41 and the very interesting fact has recently come to light that a tribe in a hitherto unexplored part of ,borneo use such an instrument1 invented by themselves4 ,they set up a post about #f ft4 high1 and throw over the top a piece of string weighted at each end to show when it is vertical2 the length of the shadow cast by the post is measured with a notched stick4 ,by this means they tell the time of day2 and they also observe the sun 7presumably with the gnomon7 to know the right season for planting their rice4#f ---------------------------------------- -------------------------------- #f ,dr4 ,c4 ,hose1 in 8,travel and ,exploration10 for ,feb4 #aiaj1 quoted in 8,nature10 ,feb4 #ag1 #aiaj4 ---------------------------------------- -------------------------------- ,however rough the first gnomon may have been1 its importance can scarcely be overrated1 for it introduced measurement and calculation into observation of the sun's movements1 and it is the ancestor of our modern sextants1 transit telescopes1 and other instruments of precision4 ,it was also the beginning of the sundial4 ,the course followed by the moving end of the shadow was traced on the ground1 and divided into equal parts3 hence arose the custom which the ,greeks adopted from the ,babylonians of counting twelve hours in every day1 from sunrise to sunset1 and twelve hours in every night1 from sunset to sunrise1 regardless of the varying lengths of day and night at different seasons4 ,this is known as the system of 8temporary hours40 ,if we used it in ,england1 the twelve hours of a midsummer day would take twice as long to pass as the twelve fleeting hours of a midsummer night2 but in ,greece the inequality is much less1 and in the latitudes of ,babylonia it is never striking4 ,the skill and knowledge of the ,greeks enabled them1 later on1 to construct dials of different kinds1 which marked 8equal hours10 such as we use now2 but the system of 8temporary hours0 did not altogether die out till after the invention of pendulum clocks in the #agth century of our era4 ,clepsydras1 or water-clocks1 were also used in ,egypt and ,babylonia1 and ancient ,greece2 and there is still a large one in ,canton1 where a reservoir is placed in a tower1 and the water falling1 drop by drop1 into a receiver whose depth is marked in figures on the wall1 indicates the passing of time just as sand does in running through an hour-glass4 ,these clocks cannot have kept very good time1 however1 or they would have been more used by the ,babylonian and ,greek astronomers who took pains to ascertain the exact positions of the stars4 ,owing to the diurnal revolution of the skies1 the time at which any celestial body rises or crosses the meridian after another is an index of their distance apart1 east and west on the sphere1 and this is how it is reckoned by modern astronomers4 ,but the ancients seem to have been never able to trust their clepsydras sufficiently to use this method1 and only referred to them for approximate time4 ,the gnomon1 valuable as it is for marking the sun's daily course1 and the north and south part of his yearly motion1 is a limited instrument4 ,it cannot show his westerly motion on the sphere1 nor is it of any use for the planets4 ,to trace these motions1 and the monthly journey of the moon1 the first step is to distinguish the stars1 by grouping and naming them1 especially those which lie in the path of sun1 moon1 and planets4 ,the invention of some kind of zodiac is probably older even than the invention of the gnomon1 and also originated independently among different races4 ,the germ of the idea may be found to-day among races low in the scale of civilization4 ,the ,australian aborigines are familiar with that unique star-cluster which we call the ,pleiades1 and know that its appearances and disappearances are periodical and coincide with the seasons4 ,a ,queensland tribe1 for instance1 has a legend in which the stars figure as six sisters who have been transported to the skies1 and it is said that they sometimes appear before the sun in order to throw down icicles1 an evident allusion to the fact that the ,pleiades begin to appear just before sunrise in ,may1 the ,australian winter4 ,the natives of ,tahiti divide their year into 8,matarii i nia0 and 8,matarii i raro10 which means ,pleiades ,above and ,pleiades ,below 7i4e4 the horizon at the beginning of night74 ,sir ,norman ,lockyer has shown that the mysterious alignments of stones found at ,stonehenge1 ,carnac1 and other places1 may have been so arranged in order to show the direction1 some of the sun at his rising on certain dates1 notably the morning of the summer solstice1 and some of the ,pleiades or other striking stars1 whose rising just before the sun would enable ancient astronomers to fix the dates of important festivals4 ,such observations as these1 of which many instances might be drawn from many parts of the world1 are first steps towards studying the whole path of the sun through the stars1 and of forming a calendar with a name or number for every day in the year4 ,until the stars are known1 and a calendar fixed1 the motions of sun and moon cannot be learned in detail1 the planets can scarcely be distinguished from the stars and from one another1 and there are no settled dates from which to calculate their periods4 ,the first zodiac of which we have written record is a lunar one of #bh constellations1 which is referred to in the 8,canon of the ,emperor ,yaou10 a ,chinese emperor who began to reign in ,b4,c4 #bcef4 8,yaou commanded ,he and ,ho1 in reverend accordance with their observation of the wide heavens1 to calculate and delineate the movements and appearances of the sun1 the moon1 the stars1 and the zodiacal spaces1 and so to deliver respectfully the seasons to the people40 ,that these astronomers studied 8the movements and appearances0 of the sun by means of the gnomon as well as observations of the stars is plain from what follows1 where directions are given for determining the solstices4 ,one astronomer was commanded by the ,emperor to 8reside at ,nankeaou and arrange the transformations of the summer1 and respectfully to observe the extreme limit of the shadow4 ,the day1 he said1 is at its longest1 and the star is ,ho3 you may thus exactly determine midsummer40 ,ho 7 fire7 is the fiery red ,antares in ,scorpio4 ,the star of the winter solstice1 when 8the day is at its shortest0 was ,maou1 which is the ,pleiades4 ,directions are also given for observing the spring and autumn equinoxes1 when day and night are of medium length1 and certain other stars are to be observed4#g ---------------------------------------- -------------------------------- #g ,journal of the ,british ,astronomical ,association1 ,june #bd1 #aiji1 report of a lecture on ,chinese astronomy by ,e4 ,b4 ,knobel1 ,f4,r4,a4,s4 ---------------------------------------- -------------------------------- ,the ,hindus had also a lunar ,zodiac1 but with only #bg constellations1 and the ,arabs had their #bh 8,mansions of the ,moon40 ,these #bg or #bh asterisms were evidently suggested by the moon's sidereal period of #bg days4 ,but her synodical period1 i4e4 her revolution with regard to the sun1 in which she runs through her phases1 is much more convenient for marking a period of time for general uses1 and this month of about #cj days has been almost universally adopted by primitive peoples1 the first day being counted when the crescent new moon begins to be seen after sunset4 ,from this custom arose another1 that of counting the beginning of the day from sunset1 but in various times and places other starting-points have been chosen--sunrise1 midday1 or midnight4 ,twelve of these synodical lunar months are nearly equal to one solar year1 and this doubtless suggested the solar zodiac of twelve constellations1 each constellation marking the portion of sky passed over by the sun in a month4 ,the ,chinese 8,yellow ,path of the ,sun0 contained twelve animals1 the ,mouse1 ,cow1 ,tiger1 ,rabbit1 ,dragon1 ,serpent1 ,horse1 ,ram1 ,ape1 ,hen1 ,dog1 and ,pig4 ,these animals were widely adopted by other nations--the ,koreans and the ,japanese1 the ,mongols of ,tibet1 the ,tartars1 and the ,turks4 ,another zodiac1 however1 was destined to have an even wider popularity1 spreading1 in the course of centuries1 from ,greece to ,arabia1 ,persia1 ,india1 and ,china1 where it finally superseded the native constellations2 it crossed the ,mediterranean into ,africa1 conquered the whole of ,europe1 and is used to-day over the whole civilised world4 ,the names of these twelve zodiacal constellations are familiar to us all3-- ,english ,names4 ,latin ,names4 ,ram ,aries ,bull ,taurus ,twins ,gemini ,crab ,cancer ,lion ,leo ,virgin ,virgo ,scales ,libra ,scorpion ,scorpio ,archer ,sagittarius ,capricorn ,capricornus ,water-,bearer ,aquarius ,fishes ,pisces4 ,strange to say1 we cannot tell with any certainty where1 when1 or by whom1 this ancient series of constellations was devised and named4 ,the earliest full description which we possess is by a ,greek poet of the #dth century ,b4,c41 ,aratus4 ,a line from the prologue to his 8,phenomena0 was quoted by ,st4 ,paul in his address to the ,athenians on ,mars' ,hill4 8,from ,zeus we lead the strain1 he whom mankind ,ne'er leave unhymned2 of ,zeus all public ways1 ,all haunts of men are full1 and full the sea ,and harbours2 and of ,zeus all stand in need4 ,we are his offspring2#h and he1 mild to man1 ,gives favouring signs and rouses us to toil1 ,calling to mind life's wants2 when clods are best ,for plough and mattock1 when the time is ripe ,for planting vines and sowing seeds he tells4 ,since he himself hath fixed in heaven these signs1 ,the stars dividing2 and throughout the year ,stars he provides to indicate to men ,the seasons' course1 that all things duly grow40#i ---------------------------------------- -------------------------------- #h ,acts1 xvii4 #bh4 #i ,the ,phainomena of ,aratos1 done into ,english verse by ,robert ,brown1 lines #a-ac4 ---------------------------------------- -------------------------------- ,but ,aratus did not know who had invented the names of the star-groups which he describes4 8,some man of yore10 he supposes1 8,a nomenclature thought of and devised1 ,and forms sufficient found4 ,for men could not ,or tell or learn the separate names of all1 ,since everywhere are many1 size and tint ,of multitudes the same1 but all are drawn around4 ,so thought he good to make the stellar groups1 ,that each by other lying orderly1 ,they might display their forms4 ,and thus the stars ,at once took names and rise familiar now40#aj ---------------------------------------- -------------------------------- #aj ,ibid41 #cgc-chb4 ---------------------------------------- -------------------------------- ,it is1 to say the least1 exceedingly doubtful1 whether the naming of star-groups was so promptly carried out by one individual1 especially as ,aratus' poem includes1 besides the twelve zodiacal constellations1 thirty-six others1 which contain all the bright stars of the sky except those too far south to be seen in the temperate regions of our northern hemisphere4 ,the spaces thus left blank were afterwards filled up1 chiefly in the #agth and #ahth centuries of our era1 and the regions round the ,south ,pole are now crowded with a mixture of birds and scientific instruments2 but the names and the figures of the traditional forty-eight constellations still find undisputed places on our globes and star-maps4 ,some of these figures are very strange and suggestive4 ,we have a maiden with wings1 a centaur shooting arrows1 a flying horse1 a water-snake with a crow and a cup on its back1 a charioteer with a goat on his shoulder1 a man strangling a serpent1 another pouring water into the mouth of a fish1 and a strange beast like a goat with a fish's tail4 ,all had their meaning1 doubtless1 to their originators1 but to us they are cryptic characters1 hard to decipher4 ,among the zodiacal constellations only one is obvious1 ,libra the ,scales1 the sign in which the sun is when days and nights are perfectly balanced in length2 but this is comparatively recent1 for ,aratus and his contemporaries give in its place the ,claws of the ,scorpion1 the latter being an enormous monster extending over the space of two asterisms4 ,the figures may have been religious symbols1 or an illustration of some myth concerning the sun's yearly course1 or each of the twelve may have indicated the weather or the occupation suitable to the month it represented4 ,the ear of corn in the hand of the ,virgin1 and the juxtaposition of three watery figures in ,capricornus1 ,aquarius1 and ,pisces1 suggest the latter explanation4 ,many different ideas probably played a part in the origin of these mysterious constellation-forms4 ,the ,greeks1 and after them the ,romans1 when adopting the old constellations1 sometimes adopted also the old myths which still clung about them2 sometimes they ascribed legends to them from their own mythology4 ,thus1 the kneeling figure with his foot upon a dragon1 became and remains the hero ,hercules1 although ,aratus only describes him as a man toiling at some unknown task1 and says he is called simply the ,kneeler4 ,successive generations of astronomers altered some of the figures1 but probably only to a slight extent4#aa ---------------------------------------- -------------------------------- #aa ,ptolemy says he made a few changes1 as his predecessors had done4 7,delambre1 ,histoire de l',astronomie ,ancienne1 ii4 #bfa74 ---------------------------------------- -------------------------------- ,the poem of ,aratus enjoyed an immense popularity in classical times and throughout the ,middle ,ages1 and no doubt helped to stereotype the forms whose origin was already forgotten when he wrote4 ,he was not an astronomer1 however1 and the poem is only a popular paraphrase of a lost work by ,eudoxus4 ,this ,greek astronomer had lived a hundred years earlier1 and it is thought that he himself copied from an older source4 ,the attempt to discover this source has been the object of many ingenious conjectures1 and much research among ancient monuments and writings4 ,some of the old constellations are met with in ,isaiah and ,job1 in ,homer1 on tablets found at ,nineveh1 and an immense antiquity is sometimes claimed for them4 ,dupuis1 writing at the end of the eighteenth century1 thought he had conclusively proved that the figures of the zodiac were designed in ,egypt #ae1jjj years ago6#ab ,miss ,plunkett1 in her 8,ancient ,calendars and ,constellations0 assigns them to the seventh millenium before ,christ4 ---------------------------------------- -------------------------------- #ab ,origine de tous les cultes1 ou ,religion universelle1 by ,c4 ,f4 ,dupuis4 ---------------------------------------- -------------------------------- ,illustration3 ,,the ,,old ,,constellation ,,figures4 ,,southern ,,hemisphere4 ,illustration3 ,,northern ,,hemisphere4 ,,the ,,old ,,constellation ,,figures ,,according ,,to ,,aratus4 ,in ,ptolemy's ,catalogue ,equuleus and ,corona ,australis are added to these4 7,from ,peck's 8,constellations and ,how to ,find ,them407 ,an ingenious theory1 suggested independently by ,schwartz and ,proctor1 and developed by ,mr4 ,e4 ,w4 ,maunder1#ac is founded on an examination of the space round the ,south ,pole which was left blank by the ancient constellation designers4 ,from its extent1 ,proctor concluded that they cannot have seen further south than about #dj from the ,south ,pole1 and therefore that they must have lived in a latitude of about #dj north of the equator 7say1 central ,asia or ,asia ,minor72 from the position of its centre1 which must have been the ,pole1 he concluded that the date was about ,b4,c4 #bbjj4 ,for the centre of the circular patch seems to lie near the star ,delta ,hydri1 which was the ,south ,pole star at that time4 7,this movement of the ,pole among the stars1 due to 8precession10 will be explained later74 ,this date does not differ much from that found by ,robert ,brown1 from the position of the celestial equator among the stars1 as described by ,aratus2 he says ,b4,c4 #bjhd4ad ,schwartz gave ,b4,c4 #adjj2 ,mr4 ,maunder1 from additional considerations of the positions of various constellation figures1 says that they must all have been originally designed about ,b4,c4 #bhjj4 ---------------------------------------- -------------------------------- #ac ,journal of the ,british ,astronomical ,association1 8,the ,oldest ,astronomy10 ,july #ahih1 ,june #ahii1 ,april #aijd1 ,may #aiji2 ,the ,observatory1 ,december #ahih2 ,knowledge1 ,october #aijd2 and elsewhere4 #ad ,the ,phainomena of ,aratos1 by ,robert ,brown4 ,see also his ,eridanus1 ,river and ,constellation2 ,primitive ,constellations1 and other works4 ---------------------------------------- -------------------------------- ,unfortunately the descriptions of ,aratus are neither very precise nor consistent with one another1 and he is our oldest and our main authority for the forms and positions of the ancient constellations4#ae ,it may1 however1 be taken as practically certain that they had been designed many centuries before he wrote1 and that the ,greeks received them from the ,babylonians4 ,orion and the ,pleiades1 the ,great ,bear and ,arcturus1 and perhaps many others1 were familiarly known in the ,levant as early as the tenth century before ,christ2 and we find traces of our zodiac1 or its beginnings1 in ,babylonia at least as early as the eleventh4 ,it is always to ,egyptians and ,babylonians that the ,greeks referred as their predecessors and teachers in astronomy1 but the native constellations of ,egypt seem to have been different1 and so far as we know at present the ,babylonians began earlier and made greater progress in star-lore than any other nation before ,greece4 ,the latest results of expert investigation of astronomical tablets discovered in the ancient clay libraries of ,babylonia and ,assyria1 tend to show that astronomy was of native growth there1 and developed very slowly4#af ,star-worship and the need for a calendar led their inhabitants to observe the skies thousands of years ago2 but their early work was naturally vague and rude4 ---------------------------------------- -------------------------------- #ae ,we are not sure what limits ,aratus intended to set in the south to ,centaur and ,argo1 and notably to the ,river ,eridanus1 which used to flow beneath the ,sea-,monster 7,cetus71 joining the ,water poured out by ,aquarius4 ,it changed its bed 7like the ,euphrates1 of which it is perhaps the heavenly counterpart71 and now has left the ,sea-,monster high and dry1 while on its ancient banks a chemist's furnace and a sculptor's workshop have been set up4 ,the ,celestial ,equator of ,aratus fails to agree with the ,equator of ,b4,c4 #bjhd1 not only in passing over the head of ,orion1 instead of through his belt1 as ,brown himself points out1 but also in running through the eye of the ,bull1 instead of his 8crouching legs alone10 so this part is altogether too far north4 ,the ,equator some #abjj years later agreed better here1 and equally well elsewhere1 except in the opposite part of the sky where it was then too northerly for ,aratus1 leaving ,corvus to the south of the line4 ,much the same may be said about the tropical circles4 ,either ,aratus was careless1 or the globe from which he took his descriptions was incorrect3 in any case1 there results an uncertainty of many centuries and many degrees in date and latitude4 #af ,epping and ,strassmeier1 ,astronomisches aus ,babylon1 ,kugler's ,babylonische ,mondrechnung1 and ,babylonische ,sternkunde4 ,schiaparelli's two monographs on ,babylonian ,astronomy1 from which much of the information here given is derived1 are chiefly based on these works4 ---------------------------------------- -------------------------------- ,this star-worship and star-study seems to have been learned by the ,semitic ,babylonians1 and their descendants and rivals the ,assyrians1 from a race with whom they met and mingled in the grey dawn of history1 but whose existence was unknown to us before the middle of last century4 ,illustration3 ,the ,moon-,god of ,ur4 ,to face p4 #cf4 ,from a cylinder-seal in the ,british ,museum1 dated about ,b4,c4 #bdjj4 ,reproduced by permission of the ,trustees4 ,illustration3 ,fig4 #f4 ,the triple star-sign of the ,babylonians4 ,this people1 who belonged to a totally distinct family of nations1 and are known to us now as ,sumerians1 had settled near the mouth of the ,persian ,gulf1 when it ran further inland than it does now1 and more than five thousand years ago used a kind of writing on soft stones 7later1 on bricks7 which had obviously arisen from some form of picture writing1 and ultimately developed into cuneiform4 ,their reverence for the heavenly bodies is shown by the fact that the familiar star sign1 star sign which appears on very early ,sumerian inscriptions1 denotes their word for god or lord1 and on the monuments of ,babylonia and ,assyria we meet constantly the triple sign ,this1 we learn from the inscriptions1 stood for three great deities1 the ,moon-god1 the ,sun-god1 and the goddess of the planet ,venus4 ,our illustration shows an inscription in early ,babylonian script1 and a scene which represents the vassal of a king of ,ur 7,abraham's 8,ur of the ,chaldees07 being led into the presence of the ,moon-god4#ag ,it is believed to date from about ,b4,c4 #bdjj4 ,the ,babylonians were an intensely superstitious people1 and a large part of their omens were drawn from observations of the skies4 ,every city from this period onward had its ziggurat or great tower formed of several superimposed cubes1 usually seven in number1 diminishing in size and probably crowned by the shrine of the local deity4 ,it is not certain what purposes were served by these towers1 but the successive platforms may well have been the observatories from which the ,babylonian priests1 gazing through the clear air and over the level plains1 watched1 year after year1 and century after century1 eclipses of sun and moon1 risings and settings of stars and planets1 and all the changing pageant of the skies1 which to them were eloquent of peace and prosperity1 or of war and misfortunes in their land4 ---------------------------------------- -------------------------------- #ag ,king1 ,history of ,sumer and ,akkad1 p4 #bdf4 ---------------------------------------- -------------------------------- ,although this illusory art chiefly occupied the early ,babylonian astronomers1 they made some observations of real value1 and gradually acquired true knowledge concerning the movements of the heavenly bodies4 ,tablets a few centuries older than the ,chinese ,canon of ,yaou containing lists of the ,sumerian names of twelve months1 show that this people had established a luni-solar year4 ,fortunately for the progress of astronomy the year does not contain an exact number of months1 or even of days3 at the end of twelve lunar months1 a few more days and hours must elapse before the sun has returned to his original place among the stars1 and before the round of the seasons is completed4 ,therefore the first rough approximation had to be constantly corrected if calendar festivals were to recur at the same seasons2 and thus the priests1 who in early times were usually the calendar makers and keepers1 became gradually better and better acquainted with the movements of sun and moon1 and the appearance of star-groups4 ,it is interesting to compare the different ways in which various races have solved the problem of calendar-formation4 ,the ,chinese had a year of twelve months1 and added an intercalary month occasionally1 in such a way that the average length of the year was brought up to #cff days4 ,the written character for 8intercalary0 in both ,chinese and ,japanese is a compound of the characters for 8gate0 and 8,emperor10 because in ancient days the ,emperor used to perform the ceremonies proper to each of the twelve months in the special room of his palace dedicated to that month1 but in the intercalary month he performed them in the doorway of the palace4 ,the ,egyptians and the ,arabs seem to have given up the attempt to harmonize the two periods1 though both of these nations reckoned twelve months in their years4 ,the ,egyptians counted thirty days to each month1 and added five days more at the end of the twelfth1 so that the months can have had no connection with the moon3 the year had1 in fact1 been calculated from the position of the sun among the stars1 beginning with the morning on which ,sirius rose just before it4 ,this 8heliacal rising0 of ,sirius heralded the great event of their year1 the overflow of the ,nile4 ,the ,arab year1 on the contrary1 was purely lunar1 for it consisted of twelve months which were alternately of twenty-nine and thirty days3 they therefore corresponded pretty closely with the moon's phases1 but had no connection with the sun or the seasons4 ,the ,mahomedans still use this lunar year4 ,the new moon festivals of the ,hebrews prove that the moon was important to their calendar1 but the three chief feasts of ,first-fruits1 of ,ingathering1 and of the ,passover1 were so closely connected with the seasons that their year must have been luni-solar4 ,it consisted of twelve months1 one of which was sometimes doubled1 but how they decided when this was necessary is nowhere described in the ,old ,testament4 ,some think1 that as an offering of first-fruits was to be made on a certain day of a certain month1 the month preceding it was doubled in every year in which it was evident that the crops would not be far enough advanced for the first-fruits to be gathered so soon3 in this way no direct observations had to be made of the sun's movements1 but the year was accommodated to them by observations of the seasons4#ah ---------------------------------------- -------------------------------- #ah ,schiaparelli1 ,l' ,astronomia nell' ,antico ,testamento1 chap4 vii42 ,wellhausen1 ,history of ,israel1 chap4 iii4 ---------------------------------------- -------------------------------- ,the ,babylonian calendar is the most interesting of all1 for it was the most intimately connected with star-observation4 ,at first an extra month seems to have been added to the usual twelve1 in an irregular way1 whenever found necessary1 judging by a tablet of the great king ,hammurabi1 who united all the cities of southern ,babylonia under one rule1 and gave them the famous ,code of ,laws1 communicated to him by the ,sun-god4 ,the tablet runs as follows3-- 8,thus saith ,hammurabi3 the year having gone wrong1 let the coming month be registered by the name of ,ululu the second4 ,and instead of the payment of taxes being made on the #beth day of ,tasritsu1 let it be made on the #beth day of ,ululu the second40 ,hammurabi reigned about ,b4,c4 #bbjj4 ,a thousand years or more after this1 we find that royal decrees for correcting the calendar were never necessary1 for the astronomers had invented more than one system for keeping the year right4 ,one of these was to observe1 like the ,egyptians1 the heliacal rising of certain stars4 ,the little group of three stars in the head of the ,ram1 which we call ,alpha1 ,beta1 and ,gamma ,arietis1 was found very convenient for this purpose4 ,when it rose just before the sun in the month ,nisan1 the observers knew that all the twelve months would fall in their right seasons1 but when it remained invisible 7hidden in the morning twilight7 until the following month1 the calendar was evidently running ahead of the sun1 and that year was lengthened by adding a thirteenth month4 ,this is the meaning of the directions given on a tablet now in the ,british ,museum3-- 8,the asterism ,dilgan#ai rises heliacally in the month of ,nisan4 ,whenever this asterism remains invisible1 let its month be forgotten10 ---------------------------------------- -------------------------------- #ai ,sayce and ,bosanquet identify ,dilgan with ,capella1 not with part of ,aries1 and consider that a date of about ,b4,c4 #bjjj is indicated--7,monthly ,notices xxxix1 #ded74 ,but in any case the method of calendar formation is the same4 ---------------------------------------- -------------------------------- that is1 let it be taken over again1 as if it had not already been counted4 ,similar directions are given for some other asterisms and their corresponding months4 ,but a second method1 which was peculiar1 so far as we know1 to the ,babylonians1 was that of using the moon as a pointer to indicate the place of the sun4 ,whereas the sun's place among the stars can only be inferred1 the moon's can be plainly seen1 and her phase indicates her distance from the sun at any time4 ,a tablet of unknown date1 belonging to the last millenium before our era1 or a little earlier1 gives the following directions3-- 8,when on the first day of the month of ,nisan the asterism ,mulmul 7the ,pleiades7#bj and the ,moon are seen together1 the year will be normal4 ,when on the third day of ,nisan the asterism ,mulmul and the ,moon are together1 the year will be full0 7that is1 will contain #ac months74 ---------------------------------------- -------------------------------- #bj ,sayce and ,bosanquet understand ,capella here also4 ---------------------------------------- -------------------------------- ,each ,babylonian month began when the new moon was first visible after sunset2 if at this moment she was seen with the ,pleiades1 it is clear that the sun1 which had just set1 was not far west of the cluster2 if however1 it was not till the moon was three days old that she was seen with the ,pleiades1 she would then be some distance above the horizon at sunset3 consequently the sun was some distance west of the ,pleiades4 ,in this case he would also be west of ,dilgan1 the ,ram's ,head1 so those stars would rise after him in the morning1 and be hidden in his light3 therefore1 both the morning and the evening observation combined to show that his course was not completed1 and that the year must be lengthened by the addition of an extra month4 ,illustration3 ,fig4 #g4 ,first ,year1 normal4 ,new ,moon near the ,pleiades after sunset on the #ast of ,nisan4 ,the position of the young moon 7which always closely follows the sun7 showed that the sun was not far west of the ,pleiades2 and about #ajjj ,b4,c4 this proved that it was near the vernal equinox4 ,the sun's position is given for about half an hour after sunset1 when the ,pleiades would first be visible4 ,illustration3 ,fig4 #h4 ,second ,year1 normal4 ,new ,moon not far from ,pleiades on the #ast of ,nisan4 ,it takes the sun #cfe days to return to the same place among the stars1 but the ,babylonian year of #ab lunar months 7each of #bi or #cj days7 was #aa days short of this3 therefore on the #ast of ,nisan in this year the sun had still #aa days' march before him ere he returned to the position of ,fig4 #g4 ,this is equal to about #aa1 so the young moon was also about #aa west of her former position1 near the ,pleiades4 ,but as she travels about #ac eastward every day1 she would be near the ,pleiades on the following evening1 the #bnd of ,nisan1 so this year was also counted normal4 ,illustration3 ,fig4 #i4 ,third ,year1 8full40 ,new ,moon distant from the ,pleiades on the #ast of ,nisan4 ,the sun is now #b #aa #bb days' march1 or about #bb1 short of his first position1 and the young moon consequently about #bb west of the ,pleiades1 so she will not come up with them until the #crd ,nisan1 after travelling #b #ac #bf4 ,the year was therefore 8full10 that is an extra month of #bi days was added1 which is more than the #bb days needed to enable the sun to reach his first position by the #ast of ,nisan in the fourth year4 ,it appears1 therefore1 that the extra month must have been added once in three or four years4 ,several lists of stars and star-groups indicating the months in this way have been found1 the early lists containing only a few1 the later twelve4 ,if our zodiac originated with the ,babylonians1 there is little doubt the idea took its rise from these monthly stars1 but it is not possible1 with our present knowledge1 to say when these old astronomers first linked the isolated stars into a continuous series of twelve star-groups and connected the idea of the month with the invisible group among which the sun was known to be shining1 instead of with the stars seen east or west of him1 or in conjunction with the crescent moon4#ba ---------------------------------------- -------------------------------- #ba ,if ,taurus was originally considered the first constellation of the zodiac1 instead of ,aries1 of which there are some indications1 the change may well be explained by this change of method4 ,it does not necessarily imply that the equinox was in ,taurus when our zodiac was invented4 ,it was near ,arietis in ,b4,c4 #ajjj4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #aj4 ,the ,scorpion4 ,from a boundary stone 7now in the ,british ,museum7 set up in the reign of ,nebuchadnezzar ,i41 king of ,babylonia1 about #aajj ,b4,c4 ,illustration3 ,fig4 #aa4 ,the ,goat1 with ,fishes' ,scales4 ,from a ,babylonian boundary stone4 ,a ,scorpion with immense claws1 and a ,goat with fishes' scales appear several times on monuments at least as old as #ajjj ,b4,c4 and it is very probable1 although this fact alone would not prove it1 that they were then used as constellation figures4 ,it has been definitely proved from inscriptions that before #fjj ,b4,c4 the name of ,scorpion was applied to some stars of our present ,scorpion1 that there was a ,lion corresponding with ours1 and the principal star in that asterism1 which was called 8,the ,king0 by ,greeks and ,romans 7,basiliskos and ,regulus71 bore a name with the same meaning in ,babylonia2 the ,celestial ,bull seems to have been the group of the ,hyades1 and the ,great ,twins were the two stars ,castor and ,pollux4 ,the last two identifications seem to show how the single stars or small groups of the monthly lists were expanded into the large zodiacal constellations1 for the ,hyades cluster is in our present ,bull1 and ,castor and ,pollux are in our ,twins4 ,under the great ,assyrian kings who in the #hth and #gth centuries ,b4,c4 made ,nineveh the capital of their empire1 ,babylonian astronomy flourished exceedingly1 and it made much progress through all the political changes which followed1 until the beginning of our era4 ,the motions1 phases1 and eclipses of the moon were carefully studied and could be accurately predicted1 the positions of many stars were determined2 the zodiac was divided into twelve equal spaces1 which afterwards became #cf by sub-division 7the constellations being too unequal in size for convenience72 and finally the whole circle was marked out in #cfj degrees4 ,the movements of all the naked eye planets were well understood1 their positions being constantly compared with those of a number of standard stars1 mostly in the zodiac2 and after watching and recording these for a number of years the astronomers were able to calculate where each planet would be found at future dates4 ,tables have been found on clay tablets of the #bnd century ,b4,c4 predicting the heliacal risings and settings1 and the stations and retrogressions etc41 with considerable accuracy4 ,when astronomy had reached this stage of accurate prediction1 it was no longer in its infancy1 but was fairly on its way to become a true science4#bb ---------------------------------------- -------------------------------- #bb ,a ,babylonian treatise on astronomy recently published by the trustees of the ,british ,museum supports ,kugler's view that truly scientific methods were not adopted before the sixth century ,b4,c4 ,this treatise formed the subject of a lecture given by ,mr ,l4 ,w4 ,king before the ,society of ,biblical ,archology on ,feb4 #ai1 #aiac4 ---------------------------------------- -------------------------------- ,nevertheless1 the astronomy of the ,babylonians1 advanced as it was1 seems never to have progressed beyond the empirical stage4 ,with them1 there seems to have been no desire to group the facts they so patiently and skilfully collected into a system1 and form a theory to explain them4 ,and this must be said of other ancient nations also4 ,the ,egyptians made careful observations1 especially of the heliacal risings of different stars1 by means of which they determined the length of the year1 as we have already mentioned1 and oriented their temples and pyramids4 ,they worshipped the sun in all his aspects1 and their astrology so much resembles the ,babylonian that it is believed to have been derived from it4 ,the ,babylonians seem to have been more interested in the planets than any other nation of antiquity1 but they were known also in other countries4 ,the ,chinese recorded comets1 and all races were greatly interested in eclipses1 which they were able to predict with some accuracy1 having discovered that they occur in cycles4 ,yet we find no more rational attempt to explain these phenomena than the ,hindu legend of a great dragon that attacks the sun1 or the ,egyptian story of a sow that swallows the moon2 and their cosmogonies can only be regarded as poetical descriptions or survivals of early childlike notions of the universe4 ,the ,hindu world resting on the back of an elephant1 and that on a tortoise1 is no doubt but an allegory4 ,the ,egyptians pictured the earth as a great parallelogram1 long from north to south but narrow from east to west1 like their own land1 with the sky over it1 upheld by huge pillars or lofty mountains4 ,the stars were set in this domed lid of the world1 but sun1 moon1 and planets were floating each in its own boat on a great celestial river which ran just below the summits of the mountains1 and whose course was hidden towards the north4 ,the bark of the sun came nearer to ,egypt in the summer1 because at that time the celestial river overflowed its usual bank1 like the ,nile4 ,the red ,doshiri was said to sail backwards1 referring no doubt to the retrograde movement of ,mars4 ,in ,eridu1 one of the oldest cities of southern ,babylonia1 on the ,persian ,gulf1 the great abyss of the ocean was looked upon as the origin of all things1 and it was believed that it encircled the earth like a great river4 ,later on1 we find the world described as a great mountain1 resting on the watery deep1 and under the mountain is the abode of the dead4 ,it is entered from the west1 which surely was suggested by the setting of the heavenly bodies in the west4 ,the vaulted sky above the earth has divisions3 the rim of the lowest part rests upon the supporting watery deep2 above it are the upper waters 7the source of rain72 and above this again is the dwelling-place of the celestials4 ,the sun issues forth each morning from a door in the upper heaven1 or from the mount of sunrise1 and enters another heavenly door1 or the sunset mountain1 at night4 ,the similarity to these ,babylonian ideas of the ,hebrew 8firmament10 the 8waters above the firmament10 and the 8of the great deep10 in the book of ,genesis1#bc and ,ezekiel's 8,sheol0 in 8the nether parts of the earth10#bd has often been noted4 ---------------------------------------- -------------------------------- #bc ,gen4 i4 #f1 #g2 vii4 #aa4 #bd ,ezek4 xxxii4 #ah1 #bd4 ---------------------------------------- -------------------------------- ,illustration3 ,the ,boat of the ,sun travelling over the sky4 ,to face p4 #df4 ,from an ancient ,egyptian papyrus4 ,the recumbent figure covered with leaves symbolizes the earth2 the figure leaning over ,earth1 covered with stars1 is the sky2 the boat of the rising sun and of the setting sun floats over it4 ,the central figure represents ,maon1 the ,divine ,intelligence which preserves the order of the universe4 7,reproduced from ,flammarion's #8,astronomical ,myths1' by permission of ,messrs4 ,macmillan ,co47 ,to sum up3-- ,if we include as astronomy any observation of the heavenly bodies which leads to a recognition of order and periodicity in their movements and a power of forecasting their positions1 then every race and age has had its astronomers1 rough though their methods may be at first4 ,with growing civilization more refined methods are used2 the gnomon is invented for studying the movements of the sun2 the changing positions of moon and planets are noted by means of certain stars2 finally1 all the visible stars are grouped into constellations1 and it is recognized that a great band of star-groups crosses the sky1 which forms the pathway alike of sun1 moon1 and planets2 the length of the month and of the year are determined more or less accurately1 and when an unvarying calendar has been formed1 the celestial cycles can be better recorded and studied4 ,but in all this there is as yet no scientific motive properly so called1 no curiosity regarding the phenomena for the simple pleasure of knowing and understanding them1 no attempt to group them into a system or to explain their underlying causes4 ,the primitive idea that the heavenly bodies exist for the convenience of earth-dwellers is illustrated by the ,egyptian hieroglyph for night1 glyph which consists of the sign for sky glyph combined with a star suspended like a lamp2 the other idea that they are mysterious divinities is shown by the ,babylonian star-sign for a god or king1 glyph4 ,the ancients found that the stars were of great use1 especially for measuring periods of time2 they recognised also in them a marvellous order and regularity1 of which they dreamed that they found an echo on earth1 and endeavoured to divine the future by watching the skies4 ,can we doubt that they were also attracted by the beauty that calls all men through all ages to lift their eyes and look upward8 ,,hymn ,,to ,,the ,,setting ,,sun4 ,sung by the ,priests of ,babylon4 ,sun-god1 in the midst of heaven1 ,at thy setting ,may the latch of the glorious heavens ,speak thee peace4 ,may heaven's door to thee be gracious1 ,may the ,director1 thy beloved messenger1 direct thee4 ,lord of ,e-bara1 may the road of thy path be prosperous1 ,sun-god1 cause thy highway to prosper1 ,going the everlasting road to thy rest4 ,sun-god1 thou art he who is judge of the land1 ,causing her decisions to be prosperous4 ,from a lecture by ,t4 ,g4 ,,pinches4 7,nature1 ,dec4 #ca1 #ahia74 ,,iii4 ,,greek ,,astronomy4 ,,first ,,period4 ,b4,c4 #ijj ,,to ,b4,c4 #cej4 8,great men6 elevated above the common standard of human nature by discovering the laws which celestial occurrences obey1 and by freeing the wretched mind of man from the fears which eclipses inspired6 ,hail to you and to your genius1 interpreters of heaven1 worthy recipients of the laws of the universe1 authors of the principles which connect gods and men60 ,,pliny 7,apostrophe to ,thales and ,hipparchus47 #a4 ,,homeric ,,greece4 ,to turn from the astronomy of ,egypt and ,assyria to the astronomy of the ,greeks is like coming to a sudden bend in a river which has flowed through level country for many miles in a slow majestic course1 and finding beyond the bend a series of rapids and waterfalls4 ,instead of patient age-long accumulation of observations1 instead of a mystical adoration of stars1 supposed to be beyond man's power to understand1 we find that the ,greek's first instinct is to inquire into the meaning and the origin of what he saw1 even before he had taken time to investigate4 ,behind the varied splendours of earth and skies which fascinated his bodily eyes1 his intellect divined laws and forces which held the whole together in a wonderful harmony4 ,then1 as fresh facts1 or a fresh point of view1 thrust itself upon him1 a new explanation must be attempted1 and thus many complete systems of the universe were evolved4 ,not the name only1 the idea of ,cosmos was ,greek4 ,sidenote3 ,homer c4 #ijj ,b4,c4 ,sidenote3 ,hesiod c4 #hjj ,b4,c4 ,the first ideas of astronomy among the ,greeks were as primitive as those of any other race in its early stages4 ,they evidently had no conception of the sky as a sphere1 or of the revolution of the stars as a whole1 round fixed poles1 though they watched the motions of certain bright star-groups1 and called them by the names that we use now 7however these names may have reached them71 as we see in ,homer and ,hesiod4 ,ulysses1 guiding his raft cunningly by night1 keeps on his left the ,bear1 also called the ,wain1 which turns round in her place and keeps watch on ,orion1 and never bathes in ocean2 he watches also the ,pleiades and the 8slow-setting ,ploughman0 7,botes7--an apt description1 as anyone may see who watches ,arcturus1 the brightest star of ,botes1 when low on the western horizon4 ,being a northern star1 its motion seems very slow1 and makes so small an angle with the horizon that for a long time ,arcturus glides above it before finally dropping below2 whereas the ,pleiades1 or any other stars near the equator1 move very quickly and almost at right angles to the horizon1 and so drop below it quite suddenly4 ,it is ,ulysses also who warns his companion1 when they are setting out to spy upon the ,trojan camp1 that two watches of the night are already past1 8for the stars have gone forward40 ,the stars also announced the seasons1 for ,hesiod says that the time of harvest is indicated by the heliacal rising of the ,pleiades1 and when ,orion with ,sirius stands in mid-heaven1 and ,arcturus rises in morning twilight1 it is time for the vintage4 ,homer and ,hesiod both mention ,venus1 as a morning star 8the brightest of all the stars1 which comes to herald the light of dawn10 and also as an evening star1 apparently without recognizing that it was the same star2 as they do not mention any other planet we do not know if the others were known to the ancient ,greeks4 ,the first appearance of the new moon's slender crescent was watched for from hill-tops1 and celebrated by sacrifices1 and this--as with other ancient nations--fixed the first day of their month4 ,sidenote3 ,mimnermus c4 #ehj ,b4,c4 ,day seems to have been divided into three parts1 morning1 midday1 and evening1 according as the sun was rising1 or nearly stationary1 or sinking4 ,the sun was thought to rest upon and slide over the solid dome of the sky1 otherwise perhaps it would have fallen to the ground2 and at night it was supposed to go behind ,mount ,atlas1 and then to travel behind high northern mountains to its rising place in the east4 ,this primitive explanation of its movements is so poetically described by an early poet1 ,mimnermus1 that ,i cannot resist a quotation1 though the lines can hardly be regarded as an astronomical fragment4 ,they may be freely rendered thus3-- ,endlessly toiling ,helios speeds4 ,no rest for him or for his steeds ,when ,dawn has climbed the height4 ,soon as he lays his weary head ,upon the golden wingd bed ,made by ,hephaestos' might1 ,it bears him sleeping o'er the seas1 ,far from the fair ,hesperides1 ,through realms of darkest night2 ,till in the ,ethiopian land ,he sees his horses ready stand2 ,and when the child of light1 ,the rosy-fingered1 early-born1 ,has ushered in another morn1 ,he mounts his chariot bright4 ,the earth1 as pictured on the shield of ,achilles1 was flat and round1 just as it appears from a height1 and of course ,greece was the centre1 just as ,egypt was the centre of the ,egyptian1 and ,babylon the centre of the ,babylonian cosmogonies4 ,it was a small earth3 a few countries lay round the ,middle ,sea1 and further to the south was the land of the ,ethiopians where the ,sun passes overhead and burns the inhabitants black2 there was another sea to the north1 over which the ,argonauts sailed1 and in the extreme east was the ,lake of the ,sun1 out of which he rose every morning4 ,this was a great gulf of the ,river ,oceanus which encircled the whole earth4 ,its sources were in the furthest west1 just beyond the ,pillars of ,hercules1 and thence it flowed north1 east1 and south1 finally returning into itself4 ,a branch from near the source1 called the ,styx1 flowed down into the underground world of ,hades1 the abode of the dead1 and beneath this again was ,tartarus1 where were imprisoned the ,titans who had fought against ,jove4 ,above the flat earth the blue dome of heaven was spread like a tent1 and across it travelled 8,the never-wearied ,sun1 the ,moon exactly round1 ,and all those stars with which the ample brows of heaven are crowned40 ,what a compact little universe1 and how important a part of it was man6 ,but as thought developed1 the universe expanded4 #b4 ,,thales ,,and ,,anaximander4 ,sidenote3 ,b4,c4 #ehe4 ,sidenote3 ,thales c4 #fjj ,b4,c4 ,in the sixth year of the war of the ,lydians against ,cyaxares1 king of the ,medes1 just when a battle was about to begin1 day was suddenly changed into night by an eclipse of the sun1 and ,herodotus adds3 ,thales had told the ,ionians of this before1 and in what year it would happen4 ,this does not necessarily imply any accurate understanding of eclipses on the part of the ,ionian philosopher4 ,he had visited ,egypt1 and may have learned from the priest-astronomers there that eclipses recur in cycles and so can be predicted4 ,but ,thales was not content with cycles4 ,he wanted to know1 not only that eclipses would happen at such and such times1 but how they happened4 ,perhaps from reports of ,babylonian observations1 perhaps from questions put to ,egyptian astronomers1 he learned that solar eclipses only happen when the moon is new and in the ecliptic1 that is1 in the same part of the sky as the sun1 and that the black body then seen on the sun has always a rounded edge4 ,these no doubt were the arguments on which he founded his assertion that solar eclipses are caused by the moon passing in front of the sun2 and he further added that this shows the moon to be of an 8earthy0 nature1 that is1 not made of fire or any substance either luminous or transparent1 but of opaque matter1 probably having weight and substance1 and not altogether unlike what we know on earth4 ,he is said to have stated also that the moon receives her light from the sun1 a conclusion which would follow from a little attention and thought bestowed on her phases4 ,besides his speculations regarding the moon1 ,thales took pains to note the sun's movements as accurately as possible1 by means of gnomons1 with a view to discover the exact length of the solar year1 and it was he who advised the ,greeks to adopt the ,phoenician method of directing their course at sea by the ,little ,bear instead of the ,great ,bear1 which appears to have been the constellation used in ,homeric times4 ,thales imagined that ,ocean did not merely encircle ,earth1 but that the whole ,earth1 which was a thin flat disc1 floated upon the ,ocean4 ,this zealous observer must have had something of the absent-mindedness of his great successor1 ,newton2 for it is told of him that while star-gazing he fell into a well6 ,sidenote3 ,b4,c4 #faa-ede4 ,anaximander ,it is evident that the moon's passing in front of the sun implies a lesser distance from us1 and it must have been this which suggested her place in the scheme of ,anaximander4 ,this scheme is rather difficult to understand1 from the allusions and quotations of later writers1 for we have no original writing by ,anaximander2 but we can gather enough to show that already in the sixth century ,b4,c4 the ,greek philosophers were asking themselves what was the explanation of the movements and appearances of the heavenly bodies1 how they were supported in the sky1 what force moved them1 how large and how distant they were1 and what they were made of4 ,anaximander asserted boldly that sun and moon were larger than the whole earth3 he thought the sun might be #bg and the moon #ai times as large4 ,how he reached this conclusion it is impossible to say4 ,the ,egyptians had already tried to measure the apparent size of the sun as compared with the circumference of the sky1 by noting how long it took to set from the moment the lower rim touched the horizon to the moment when the whole disc disappeared3 this1 divided by the #bd hours taken by the sun to traverse the #cfj degrees of the sky1 gave the sun's size in degrees 7it is about half a degree71 and had they been able to find the actual distance of the sun from the earth1 they could have deduced its actual size1 but this they had no means of determining4 ,there are two possible ways of seeing that the moon is smaller than the sun1 although they usually appear to us the same size4 ,anaximander may have seen or heard of an 8annular0 eclipse1 in which the moon is rather more distant from us than at a total eclipse1 and therefore her dark body just fails to cover the whole sun1 and a bright ring of light surrounds her4 ,more probably he realized what was implied in ,thales' explanation of solar eclipses1 and concluded that the moon must be smaller than the sun1 because she looks no larger although she is nearer to us4 ,his scheme is the first of which we have any knowledge in which the movements of the heavenly bodies are explained by supposing them not all in one sky together1 but placed in a series of heavens1 one above the other3 hence it is of peculiar interest to the ,dante student1 for in it we trace the first attempt towards the theory of the ,revolving ,spheres4 ,it is true that the ,babylonians and ,hebrews divided their heaven into three parts1 one above the other1 but this was only to divide the place of atmospheric phenomena from the dwelling-place of the gods1 and sun1 moon1 planets and stars all moved in the same heaven4 ,here1 in the universe of ,anaximander1 we find one heaven1 the lowest1 for air1 rain1 etc41 another for all the stars1 a higher heaven for the moon1 a yet higher for the sun1 and above all the region of fire1 the brightest1 lightest element1 whose nature it was to ascend and which therefore is outside all1 as it was the nature of earth to descend and therefore to be at the bottom4 ,probably either in or above the heaven of celestial fire was the heaven of the gods1 for1 as ,aristotle remarks1 all our ancestors1 indeed all who believe in gods at all1 whether ,greek or of any other race1 place the dwelling-place of the gods above in high heaven1 as the unchanging1 unmoving region of eternity4#be ---------------------------------------- -------------------------------- #be ,de ,clo ,i4 #c1 and ,,ii4 #a4 ---------------------------------------- -------------------------------- ,unfortunately we do not know what would be of great interest1 whether ,anaximander also provided separate heavens for the planets1 or found a home for them in the heaven of the stars4 ,perhaps he hardly knew of their existence1 or said with ,aratus who wrote nearly #hjj years later3-- 8,of these ,i dare not speak with certainty1 ,as of the fixed stars' orbits40 ,the successive heavens were in layers1 as it were1 one above the other1 8like the bark enclosing a tree10 but they were transparent and invisible4 ,the heavens themselves were not in motion1 carrying the stars1 sun1 and moon2 ,anaximander had an ingenious mechanical scheme of wheels or rings to carry them inside their respective heavens1 which doubtless was clear to himself1 though unfortunately it is not at all clear to us4 ,some writers have maintained that these heavens were spheres1 but for several reasons it is difficult to believe this1 and probably the sky was still to ,anaximander1 as to the ,homeric ,greeks1 a slightly flattened hemisphere1#bf only divided into these layers1 and instead of ending at the horizon it continued a little below1 to allow of the passage of the heavenly bodies between setting and rising4 ,perhaps it was for this reason that he gave the earth a greater thickness than the disc of ,thales1 comparing it to a short thick pillar1 three times as broad as high1 the top of which only was inhabited4 ,his ,cosmos1 then1 would be something like the diagram1 with regard to the disposition 7though not the relative sizes7 of ,earth and the heavenly bodies4 ---------------------------------------- -------------------------------- #bf ,but see note1 pp4 #ge1 #gf4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #ab4 ,the ,universe according to ,anaximander4 ,somewhat timidly the barriers have been thrust back4 ,the earth goes a little deeper into the dark unknown1 the sky is wider and higher1 the heavenly bodies are much larger and more distant and go under ,earth's surface2 but they are cautiously upheld by solid domes1 and worked by wheels4 ,earth is still the floor of the ,world1 and ,heaven--now a series of heavens--the vaulted roof above4 #c4 ,,later ,,flat ,,earth ,,systems4 ,it is interesting to see how long this timidity persisted among the ,greek philosophers1 especially of the ,ionian school1 in spite of the fact that other schools had advanced much bolder ideas1 as we shall presently see4 ,quite a number of universes were constructed somewhat after the pattern of ,anaximander's1 with ,earth as floor of the world2 but some placed the stars beyond moon and sun1 some definitely included the planets1 though they do not seem to have explained their motions2 and there were various ways of supporting the flat earth1 and of supporting and moving the heavenly bodies4 ,sidenote3 ,anaximenes c4 #eej ,b4,c4 ,sidenote3 ,empedocles c4 #dej ,b4,c4 ,sidenote3 ,anaxagoras died #dbh ,b4,c4 ,anaximenes1 a follower of ,anaximander1 having doubtless pondered the fact that very heavy bodies can float in water if only they are the right shape1 and that ,earth itself was supposed by ,thales to be floating on the ,ocean1 suggested that the moon is so broad a disc that she floats in the ether1 8like a leaf10 and of course the same would apply to the sun4 ,two later philosophers1 ,empedocles and ,anaxagoras1 held that a great whirlwind swept continually round the ,earth1 which both kept the heavenly bodies from falling down upon it and drove them across the sky4 ,equally diverse were the opinions as to the nature and composition of the heavenly bodies4 ,most philosophers of this age believed that they were of pure fire1 or else that they were vessels containing fire1 which was extinguished1 or in one way or another became invisible to us1 during eclipses and when they set4 ,others held1 as we have seen with ,thales1 that they were of an earthy nature2 and ,anaxagoras1 seeing a meteorite which had fallen from the sky during the daytime1 thought he actually held a piece of the sun in his hands1 and concluded that the sun was an enormous mass of iron1 8much greater than ,peloponnesus10 and shone because it was red-hot4 ,but the popular idea still was that the sun was a god1 or the chariot driven by a god across the sky1 and ,anaxagoras was banished from ,athens for his impious words4#bg ,the markings on the face of the moon were thought to prove that she was of mixed composition3 she was made of air mingled with only a little fire1 or earth mingled with fire2 but according to ,democritus the markings were shadows of mountains on her surface1 and ,anaxagoras is reported to have said that the moon was inhabited1 and the markings were 8plains and valleys40 ---------------------------------------- -------------------------------- #bg ,his life was saved by his illustrious pupil1 ,pericles1 of whom the story is told that on one occasion1 just as his army was embarking for an expedition1 the sun was eclipsed1 and his pilot was terrified4 ,pericles snatched off his cloak1 and held it so as to hide himself from the man's eyes4 8,is that terrible8 is that an evil omen80 he cried4 8,then do not fear the disappearance of the sun1 for it is just the same1 only the thing that hides it is larger than my cloak40 ---------------------------------------- -------------------------------- ,anaxagoras suggested that the stars were fragments torn off the circumference of the earth by the encircling whirlwind1 and that they glowed with the heat caused by friction1 though they were too distant for us to feel this heat1 being far beyond the sun4 ,the ,milky ,way was a source of speculation3 some said it was the former path of the sun1 and still burning from his heat1 but ,democritus explained it as caused by the shining of innumerable stars1 too faint and close together to be distinguished separately4 ,the doctrines of the different philosophers as to origin and first stages of the universe do not concern us here1 but we must mention that of ,empedocles1 as his views are directly referred to by ,dante4 ,this philosopher was the first to assert that everything consists of the four elements1 earth1 air1 water1 and fire1 pure or in combination2 and the combinations he supposed to be brought about by two forces1 one attractive1 the other repulsive1 which he named ,love and ,discord4 ,of these1 one alternately predominates at different ages of the world1 and thus its history is divided into periods of different character4 ,a great step forward was taken when it was realized that the sky is not a hemisphere1 ending at the horizon1 or even extending a little way below1 but that it surrounds ,earth in every direction1 like a sphere4 ,this idea probably originated with the ,pythagoreans1 or it may have occurred independently to several thinkers1 when the diurnal motion of the heavens was better observed1 and geometrical conceptions understood and applied4 ,now it became no longer necessary to extinguish and rekindle the stars1 nor to send the sun round swimming on ,river ,ocean behind northern mountains1 or creeping through strange underground regions1 through the night4 ,it was clearly recognized that the visible course of each heavenly body was part of a circle1 the whole of which we could see if we could only travel fast enough and go to the underside of the earth4 ,illustration3 ,fig4 #ac4 ,the ,universe of ,leucippus4 ,sidenote3 ,leucippus c4 #dej ,b4,c4 ,sidenote3 ,democritus c4 #dcj ,b4,c4 ,but this was just what never could be done1 for outside the schools of the ,greeks in ,italy 7,pythagorean and ,eleatic71 ,earth still had an uninhabitable underside4 ,distinguished men like ,leucippus and ,democritus sought to combine the belief in an all-surrounding spherical heaven with a flat supported earth which might still give them a solid floor beneath their feet4 ,leucippus made the earth a hemisphere1 with a hemisphere of air above1 the whole surrounded by the supporting crystal sphere which held the moon4 ,above this came the planets1 then the sun1 and probably the stars were outside this4 ,his disciple1 ,democritus1 on the other hand1 retained the disc-like earth1 raised a little at the rim1 to secure its contents1 and made it divide the sphere of air into two parts1 so that it rested upon air1 and air was also in the sky above4 ,the underside of the disc was not inhabited1 no doubt because no one could stand upside down4 ,his order of the successive heavens is not quite the same as that of ,leucippus1 as he puts the moon and the ,morning ,star together1 and the rest of the planets beyond the sun4 ,illustration3 ,fig4 #ad4 ,the ,universe of ,democritus4 ,this scheme gave the universe a beautifully symmetrical form1 which must have pleased the ,greeks1 but now they were puzzled to know why the heavenly bodies did not circle symmetrically with regard to the central earth4 ,why was not the pole in their zenith and the equator on the horizon8 ,they could only guess that it must have been so at first1 and that the disc had slipped out of position1 either through some irregularity in its weight1 or in the density of the underlying air4 ,compare ,milton's-- 8,some say ,he bid ,his angels turn askance ,the poles of ,earth twice ten degrees and more1 ,from the ,sun's axle2 they with labour pushed ,oblique the centric globe40 ,paradise ,lost1 ,bk4 ,x41 #efc-eff4 ,all these theories and guesses may seem to us very crude and fanciful1 and we may compare them to the eager questionings of intelligent children1 too impatient to consider whether the answers given are satisfactory explanations or no4 ,but we must remember that all we know of the early cosmogonies is from allusions and descriptions by later writers1 who often--like ,aristotle1 for instance--only quote to condemn4 8,if each could defend his own opinion1 may be we should see that there is truth in all40 7,conv4 ,,iv4 xxi4 #be-g74 ,at least we find a keen and disinterested desire to penetrate the causes of things1 and a fertile imagination1 without which science can make no advance3 moreover there was a progress in true knowledge4 ,it was discovered that the 7apparent7 diurnal paths of sun1 moon1 and every star were circles1 although only a part of the paths could be seen2 and that1 although all were seen projected on a sphere1 their actual distances from earth were very varied4 ,it is disappointing to find no record of observations of the planets1 and from the almost random way in which they were placed in the heavens it seems that but little attention had been paid to them as yet4 ,in fact1 ,seneca tells us that ,democritus knew neither their number nor their names4 ,they were often classed with comets1 and thought to be entirely erratic1 and the ,greek mind was more attracted towards those phenomena which were seen to be orderly4 #d4 ,,pythagoras ,,and ,,his ,,followers4 ,socrates4 ,as the eyes are appointed to look up at the stars1 so are the ears to hear harmonious motions1 and these are sister sciences4 ,that is what the ,pythagoreans say1 and we1 ,glaucon1 assent to them8 ,yes1 he replied4 ,sidenote3 ,pythagoras c4 #edj ,b4,c4 ,about the same time that ,anaximander was inventing solid hemispheres and rings to hold and move the heavenly bodies round about a flat earth1 ,pythagoras was founding a school in southern ,italy which gave to the world a very different scheme4 ,one of the characteristics of his school was secrecy1 its methods were oral1 and his later followers were fond of attributing to their master everything which had gradually grown out of his teaching3 it is difficult therefore to say with certainty what he himself taught4 ,it has often been stated by modern writers that he anticipated ,copernicus1 and discovered that the earth revolves round the sun4 ,though this is a mistake1 we may venture to believe that ,pythagoras taught that the earth is a sphere1 hanging freely in space4 ,we are so familiar with this idea from childhood1 that it is difficult to imagine what a tremendous innovation it was4 ,pythagorean noviciates1 doubtless after solemn initiation and preparation1 were told3 ,this earth1 which seems to you the floor of the world1 with heaven stretched over it like a tent1 is a round globe1 with men like you living on the other side of it1 and yet they do not fall1 and earth does not fall1 for it is poised in the centre of the world1 and has no tendency to fall in one direction rather than in another4 ,earth1 itself a perfect sphere1 is in the centre of an infinitely greater sphere1 the star-set heaven2 and within this seven heavenly bodies move in perfect circles1 each at its proper distance and pace1 all needing no support and no force to drive them1 for harmony is the motive power of the ,cosmos4 ,their distances are proportional to the intervals between musical notes1 and as they circle they make heavenly music1 which we should hear did we not always hear it1 like one who lives beside a waterfall#bh4 ,there is no below1 and no above1 for above is below and below above to our antipodes3 there is but the centre1 where we live1 and ,heaven is all around4 ---------------------------------------- -------------------------------- #bh ,some late followers said that ,pythagoras1 alone amongst men1 could hear the music of the spheres4 ---------------------------------------- -------------------------------- ,how did ,pythagoras reach this great and startling truth of the round unsupported earth8 ,his school relied more on experiment and observation than the ,ionian1 and the colonizing ,greeks of ,italy had travelled4 ,they might have noticed the curvature of the sea1 and the varying height of the ,pole ,star according to latitude4 ,we know that in early days the ,greeks were struck by the remarkable fact that the brilliant star ,canopus 7second only to ,sirius in brightness71 which was invisible in ,greece1 could just be seen close to the southern horizon in ,rhodes1 and was well seen in ,egypt4 ,then the moon may have helped once more4 ,when it was understood that lunar eclipses only happen at full moon1 when we are between her and the sun1 and that they may therefore be explained by the earth's shadow falling on the moon1 then1 since the edge of that shadow is always a circle1 it is demonstrable that the body throwing that shadow can have no form but that of a ball4 ,sun and moon are obviously round3 it was guessed that they also are globes rather than discs1 and the spherical shape of all heavenly bodies was a doctrine of the later if not the earliest ,pythagoreans4 ,whatever may have been the steps which led to these two great discoveries that ,earth is a sphere1 and that the apparent path of every celestial body is a circle1 the sphere and the circle were soon accepted as the only forms suitable for celestial bodies and their orbits4 ,the founder of the school was a great mathematician1 and it is not strange that these forms should have commended themselves to his disciples4 ,the sphere1 which has its surface everywhere similar1 and its contents greater than those of any other figure with equal surface1 was the 8most perfect0 of solids2 and the circle1 which has no beginning and no end1 is alike in every part1 and presents ideas of haunting suggestiveness to the geometer1 was the 8most perfect0 of lines4 ,in the system of ,pythagoras we first find the five planets distinctly enumerated1 and playing as important parts as sun and moon4 ,number was the principle of this universe1 and the planets with sun and moon made the sacred number of seven4 ,among the ,greeks1 and through the middle ages1 all these bodies are spoken of as planets or 8wanderers10 in distinction from the 8fixed0 stars which do not appear to move amongst themselves4 ,these seven 8planets0 represented the seven notes of a musical scale1 and the star sphere made up the octave4 ,pythagoras is said to have been the first to teach that ,phosphor and ,hesperus1 the morning and the evening star1 were the same4 ,when1 however1 we ask what was the order of the planets in his scheme1 we meet with many conflicting reports1 and a serious difficulty suggests itself4 ,if the planets had really been observed with care1 it must have been seen that their motions could not be accounted for by simple circular movement4 ,the large oscillations of ,mercury and ,venus on either side of the sun would strike an observer before he thought of tracing their movements among the stars1 and noting that they made a circuit of the zodiac4 ,similarly1 the other planets are most conspicuous1 rising after sunset and remaining long visible through the night1 at the very time of their retrograde movements1 so these must have been noticed if a long enough series of observations had been made to distinguish them from one another4 ,the only solution of the difficulty seems to be that ,pythagoras1 on the journeys into ,egypt and ,babylon which he is said to have made1 learned that there exist planets to the number of five1 which move in regular periods1 and he may also have learned the length of their zodiacal periods at the same time1 or perhaps these were only known to his school much later4 ,if the order assigned to them was that which was finally and generally accepted by the ancient world1 the periods must have been known1 for this is the only possible clue to the order ,moon1 ,mercury1 ,venus1 ,sun1 ,mars1 ,jupiter1 ,saturn4 ,the planet with shortest period 7the moon1 with a month7 was naturally placed by the ,greeks nearest to earth1 with the smallest circle to traverse1 and so on outwards4 ,it is very possible1 however1 that the early ,pythagoreans1 at least1 did not venture to assert more than that there were five planets1 without assigning to them any order1 for ,aristotle tells us that their universe was divided thus3-- ,from ,earth to ,moon was the ,ouranos1 or sky1 within which exists all that is changing and corruptible4 ,cosmos1 the place of ordered movement1 was the region of ,sun1 ,moon1 and ,planets4 ,olympos1 the place of pure elements1 held the stars2 the region of ,celestial ,fire came beyond this1 and the ,apeiron1 the ,infinite ,space1 or ,infinite ,air1 from which the world draws its breath1 was outside all4 ,sidenote3 ,philolaus towards end of #eth century ,b4,c4 ,the diagram shows1 then1 the earliest form of the ,pythagorean universe4 ,but they did not remain content with this4 ,out of it grew a most interesting scheme 7referred to by ,dante71 which is usually attributed to one ,philolaus1 of whom hardly anything is known1 not even his date4 ,it seems to have struck ,philolaus as a difficulty that the seven planets1 which were circling round ,earth in the same direction but at very different distances and speeds1 and also the immense sphere of stars beyond1 were all sweeping together at the same time in an opposite direction1 and at the almost incredible pace of one revolution in a day4 ,the brilliant idea occurred to him3 ,leave the stars at rest1 let the seven planets revolve in their seven orbits1 the nearer to the centre the faster1 and let earth herself revolve fastest of all1 viz4 in twenty-four hours1 in the same direction4 ,if she keeps one face always turned towards the centre1 like the moon1 this will account quite as well for the apparent diurnal revolution of all the heavenly bodies1 and the change of day and night on the earth4 ,philolaus did not make ,earth remain stationary and simply turn on her axis1 which would have had just the same effect on the apparent motions of the heavens2 for it seemed more natural that she should revolve as did the rest4 ,the five naked eye planets are all mentioned by name in his scheme4 ,illustration3 ,fig4 #ae4 ,the ,universe of ,pythagoras4 ,was the centre1 deprived of ,earth1 to be left empty8 ,no1 the centre was the ,watch ,tower of ,zeus1 the ,hearth of the ,universe1 and here they placed the purest element1 fire4 ,it was invisible to us1 because we live on the side of the earth-sphere turned away from the centre2 and also invisible to us was another planet1 ,antichthon1 or ,counter-,earth1 for this revolved within our orbit1 and also in twenty-four hours4 ,it was added to the system1 because the addition of ,earth as a heavenly body spoiled the sacred number of seven1 but by adding ,antichthon1 and counting the star sphere as another1 the total was brought up to ten1 another sacred number4 ,the objection was made that1 if ,earth is moving in space1 this must bring about a change in the apparent sizes of sun and moon1 as ,earth is nearer or farther from them1 but the ,pythagoreans were quite ready to believe that all the heavenly bodies are so distant that this journey of ,earth makes no difference to their apparent size or brightness4 ,the planets were thought to be worlds like ours1 and inhabited2 and it was even guessed that plants and animals on the moon must be fifteen times as strong as ours1 apparently because there the average day consists of nearly fifteen of our days 7of twenty-four hours71 and the nights are equally long4 ,it was the braver of the ,pythagoreans to shake the steady earth from her centre1 and set her whirling in the depths of space1 that they realized1 as no one had done before1 how large she must be2 for ,greece and the surrounding lands1 the ,middle and the other seas1 instead of making the whole of the earth1 were now understood to be only a portion of a great globe4 ,illustration3 ,fig4 #af4 ,the ,system of ,philolaus3 night on earth4 ,only the side turned away from the centre is inhabited3 consequently the ,central ,fire and ,antichthon are invisible4 ,illustration3 ,fig4 #ag4 ,twelve hours later3 day on earth4 ,earth has made half a revolution and her outer side is now lighted by the sun1 which has only moved about half a degree forward in its yearly orbit4 ,antichthon has also made half a revolution1 therefore remains invisible4 ,here1 then1 is a conception of the ,universe widely different from ,homer's4 ,the little flat disc has become a great round ball1 a planet among planets1 swiftly moving through space2 the crystal dome that tenderly covered it like a bell-glass over some fragile flower1 has lifted1 and the vast sphere is seen1 infinitely distant1 and studded with enormous stars4 ,man himself is now a tiny creature on a great earth1 and his world but one among many1 but if he is humiliated by his insignificance1 is he not elevated by the vastness of his outlook8 ,illustration3 ,fig4 #ah4 ,earth and sun according to ,heracleides4 ,in the upper figure it is day1 in the lower1 night1 on the inhabited side of ,earth4 ,the sun is on the equator1 as at the time of equinox4 ,sidenote3 ,heracleides c4 #cgj ,b4,c4 ,but not even here did the ,greeks stop4 ,it was taking a less startling step than they had already taken1 to reach the truth that ,earth was merely rotating on her axis once in a day1 and so causing the apparent diurnal revolution of the heavens4 ,this step was taken 7it is said7 by a ,pythagorean called ,hicetas of ,syracuse1 who is quoted as saying that the earth1 8while it turns and twists itself with the greatest velocity round its axis1 produces all the same phenomena as if the heavens were moved and the earth were standing still40 ,we are told also that 8,heracleides of ,pontus and ,ecphantus the ,pythagorean let the earth move1 not progressively1 but in a turning manner like a wheel fitted with an axis1 from west to east round its own centre40 ,a brilliant guess1#bi which seems fully justified by facts1 has recently explained the personalities of these two mysterious ,pythagoreans of unknown date1 ,hicetas and ,ecphantus1 whose names have been coupled for centuries with that of ,heracleides1 as teaching the rotation of ,earth on her axis4 ,it seems that they resemble the ,shadow in ,hans ,andersen's tale1 which became a man and lived apart from the man to whom it originally owed its existence1 for it is now thought that they were speakers introduced by ,heracleides into one of his dramatic dialogues to discuss astronomy4 ---------------------------------------- -------------------------------- #bi ,see ,heath's ,aristarchus of ,samos1 pp4 #ahg-ahi and #bea1 #beb4 ,i very much regret that as ,mr4 ,heath's book was only published this year1 ,i have been unable to make use of it while writing of early ,greek astronomy4 ,i can now only advise any readers who may be interested in my brief sketch of this period to read ,mr4 ,heath's history1 where they will find the opinions of modern writers summarized and discussed1 and also the full text 7in ,english7 of the most ancient and reliable sources of information4 ,it is a great encouragement to find that my statements are in agreement with his in nearly all essential points1 but readers will mark the following important differences3-- #a4 ,anaximander's heavens are said to have been spherical1 not hemispherical1 and this seems to be clearly proved by the evidence quoted from ancient writers4 #b4 ,anaxagoras1 not ,thales1 is said to have been the first to explain correctly the cause of solar eclipses and of the moon's phases1 viz4 that the moon is an opaque body1 shining only by reflected sunlight1 and periodically hiding the sun from us when she passes in front of it4 ,mr4 ,heath regards the authorship of ,anaxagoras as conclusively proved3 readers will be able to judge of this from his quotations4 ,personally they seem to me to prove no more than that ,anaxagoras agreed with others on this point1 and was the first to express it clearly in writing4 ,it is difficult to see why ,mr4 ,heath denies that ,parmenides held the same views before ,anaxagoras3 ,parmenides' own words seem to prove it1 and his theory that the moon was composed of air and fire mingled is rather in favour of it than otherwise4 ,he surely meant that the moon was not wholly bright1 like the sun2 yet that she had some light of her own must have seemed evident from the faint illumination we see during total lunar eclipses and on the part of her surface not lighted by the sun4 7,see ,dante's views1 p4 #djb of this book47 ,the connection between her phases and her distance from the sun in the sky is so extremely obvious that ,i can hardly think the ,greeks drew no inference from it until the fifth century ,b4,c41 and ,i cannot see why we should refuse to credit ,thales with the discovery attributed to him that her light came in some way from the sun4 ,gruppe acutely observes that the reason why ,thales' pupil ,anaximander did not accept the true explanation of lunar phases and solar eclipses may have been because he felt it necessary to have a theory which would apply equally well to eclipses of the moon2 and as he believed in a flat earth he could not advocate the true explanation here4 ,this was why he invented a new theory 7viz4 that both sun and moon were fire shining through holes in hollow rings1 and that the occasional stopping up of these holes caused both lunar and solar eclipses1 and also the lunar phases74 ,but ,parmenides had learned the ,pythagorean doctrine of ,earth's spherical form1 hence he was able to accept the older theory that the moon obtains her light from the sun1 and sometimes eclipses the sun by her opaque spherical body1 for he could have added that the moon is eclipsed in like manner by the opaque spherical body of the earth4 ,heracleides1 therefore1 was the sole author of this remarkable discovery4 ,in this way ,earth was restored to her central position1 but as a rotating sphere1 and the later ,pythagoreans apparently tried to reconcile their new scheme with the old by calling ,antichthon the uninhabited hemisphere of ,earth1 and placing the central fire within the earth4 ---------------------------------------- -------------------------------- ,,iv4 ,,greek ,,astronomy4 ,,second ,,period4 ,b4,c4 #djj ,,to ,a4,d4 #aej4 8,chiamavi il cielo1 e intorno vi si gira1 ,mostrandovi le sue bellezze eterne40 #a4 ,,plato4 ,the ,ionian school of philosophy died about the middle of the fifth century ,b4,c41 and the ,pythagorean towards the end of the fourth4 ,but meanwhile a new school of astronomers was growing up4 ,the philosophers still laid down general principles1 founded on abstract reasoning1 which they believed must regulate the nature and movements of the heavenly bodies1 but astronomy began to be regarded as a branch of mathematics1 not of philosophy1 and the mathematicians1 leaving problems of ultimate causes to the philosophers1 devoted themselves to observation and calculation4 ,they carefully studied the peculiar motions of each planet1 and their chief aim was to represent these geometrically by some scheme which should include them all1 and make it possible to predict the places of the heavenly bodies in the sky for any given date4 ,one cause of this great progress in methods was no doubt the natural intellectual growth of the ,greek race1 as they discovered that their eager curiosity concerning nature could only be satisfied by patient investigation4 ,the value of observation was taught1 in the latter half of the fourth century1 by the philosophy of ,aristotle1 and a great impetus must have been given by the campaigns of ,alexander1 in which the ,greeks saw distant countries1 new climates1 strange peoples and customs4 ,sidenote3 ,callisthenes c4 #ccj ,b4,c4 ,but a potent cause of the advance in astronomy seems to have been the closer connection between ,greek astronomers and those of ,egypt and ,babylon4 ,the astronomer ,callisthenes went with ,alexander to the ,east1 and received a letter from ,aristotle praying him to send to ,athens the ,babylonian eclipse records which were centuries old2 and ,aristotle mentions1 when speaking of the motions of the planets1 that the ,babylonians and ,egyptians had furnished trustworthy information about each one of them4 ,even before this1 we find that the ,greek descriptive names of the planets were changed for names of ,greek deities which are believed to correspond with the ,babylonian gods and goddesses who presided over the planets4 ,thus ,plato speaks of 8the star sacred to ,hermes0 as well as ,stilbon the ,glitterer1 and he is the last to use commonly the name of ,phosphor for the planet which henceforth was known as ,aphrodite among the ,greeks1 and ,venus among the ,romans1 corresponding with the ,babylonian ,ishtar2 and so on with the rest4 ,instead of vague records of journeys in ,egypt or ,babylonia1 we have a definite statement that ,eudoxus1 who was the founder of the new school1 went to ,egypt about #cgh ,b4,c41 with letters from the king of ,sparta to the king of ,egypt1 and we are told that he studied the planetary motions under a priest of ,heliopolis4 ,it seems highly probable1 to say the least1 that ,eudoxus was the first ,greek to appreciate the value of those methods of observation and continuous recording of phenomena which he found among the ,egyptians1 and to understand the wonderful regularity which was hidden behind the seeming irregularities of the 8wandering stars40 ,he was also1 apparently1 the first ,greek to write a detailed description of the forty-eight ancient constellations4 ,but if ,egypt and ,babylonia gave to ,greece records of celestial phenomena1 and set the example of accurate and long-continued observations1 ,greece made the new knowledge her own1 and transformed it4 ,the legend that ,eudoxus applied his mathematical skill to the ancient monuments of the ,egyptians1 and showed them how to calculate the height of the ,great ,pyramid by measurements of its shadow1 is typical of the history of ,greek treatment of ,oriental astronomy4 ,one geometrical theory after another was invented to represent the planetary motions1 was compared with the skies1 and rejected or improved1 and meanwhile observation became much more close and accurate2 new instruments were introduced1 new methods of calculation invented1 new motions discovered which had to be accounted for2 finally1 five hundred years after ,eudoxus' visit to ,egypt1 the result of all this labour was summarized in a truly epoch-making work1 which remained the standard treatise on astronomy until the time of ,copernicus4 ,sidenote3 ,plato c4 #dbg-cdg ,b4,c4 ,eudoxus was born at ,cnidos1 in ,asia ,minor1 but at the age of twenty-three he went to ,athens1 and studied under ,plato4 ,it is said to have been ,plato who inspired the young man with the idea of devoting his brilliant mathematical powers to solving the problem of celestial motions1 and with this view he went to ,egypt4 ,the story is easy to believe when we recall the many passages in the ,dialogues in which ,plato uses the splendid imagery of the skies to illustrate his philosophic doctrines1 dwelling especially on the perfect though little understood symmetry of the celestial motions1 and it will be remembered that astronomy was one of the subjects to be learned by the rulers of his ideal state4 ,it is true that ,glaucon is gently but decidedly snubbed by ,socrates in the ,republic1 for suggesting that the study of astronomy is valuable because of its use in navigation1 husbandry1 and the arts of war4 ,this is 8vulgar praise10 but has there ever been nobler praise of astronomy than that which ,socrates himself then proceeds to give8 ,although he believes that true knowledge1 knowledge of realities1 is only to be obtained by the exercise of pure reason without the aid of sense1 he considers that the study of celestial motions is one of the best means of training the mind to reach those heights1 and he does not hesitate to say that sight was given to us in order that we might look at the skies4 ,for the embroidery of heaven1 says ,socrates1 though wrought upon a visible ground1 is the fairest and most perfect of visible things2 and it is displayed to our mortal eyes as a pattern of the eternal realities which are granted to the vision of the soul4 ,in the ,timaeus this idea is elaborately developed1 and it undoubtedly had an effect on ,plato's contemporaries1 although his direct influence on astronomy cannot be compared with that of ,aristotle4 ,the ,timaeus was widely read also in the ,middle ,ages1 during the long period when ,plato's other writings were unknown1 and it is quoted by ,dante4 ,we are often reminded of him when reading the astronomical and quasi-astronomical parts4 ,timaeus1 who is introduced to ,socrates by ,critias as 8the most of an astronomer among us1 and one who has made a special study of the nature of the ,universe10#cj describes the ,creation as he conceives it most probable that it took place4 ,he assumes a chaos to begin with1 where there is no order1 and no matter which can be distinguished by name1 but all is confused and seething with random restless motions4 ---------------------------------------- -------------------------------- #cj ,i follow the translation of ,jowett4 ---------------------------------------- -------------------------------- ,of this1 in order to produce something which should express his own goodness1#ca the ,creator formed the four elements1--earth1 water1 air1 and fire1--and of them he made a world1 which became a fair and intelligent being1 animated by a living soul4 ,he made it in the most perfect form1 that of a sphere1 polished and smooth on the outside1 8as if from a lathe40 ,the soul was placed in the centre1 and hence diffused throughout the whole bodily frame4 ,it is the cause of the harmonious motions of the stars1 and of these there are two kinds3 the motion of the ,same 7the diurnal revolution of the whole heavens7 is in the noblest direction1 simple and uniform2 the motion of the ,diverse is in the opposite direction and diagonal to the first1 and it is divided into seven parts 7the seven orbits of the planets71 which bear certain definite ratios to one another4 ---------------------------------------- -------------------------------- #ca ,compare ,par4 vii4 #fd-ff4 ---------------------------------------- -------------------------------- ,timaeus does not name the planets1 but in the ,republic ,socrates names some1 and indicates the rest by their colour or other characteristic1#cb so we know that the order which he assigns to them1 counting outwards from the central earth1 is3 ,moon1 ,sun1 ,mercury1 ,venus1 ,mars1 ,jupiter1 ,saturn4 ---------------------------------------- -------------------------------- #cb ,see his famous description of the eight spheres1 on each of which stands a siren1 singing1 while the whole system turns upon a diamond spindle1 the end of which rests upon the knees of ,necessity4 ,this book was not known in the ,middle ,ages4 ---------------------------------------- -------------------------------- ,it was in order to make the world like its eternal pattern that the ,creator made a 8moving image of eternity10 which we call ,time1 in the revolutions of the heavenly bodies2 and to make it visible he 8lighted a fire which we now call the sun1 in the second of these orbits1 that it might give light to the whole of heaven note that the stars shine by reflected sunlight1 as well as moon and planets1 and that the animals who were by nature fitted might participate in number3 this was the lesson they were to learn from the revolutions of the ,same and the ,like4 ,thus1 then1 and by these means1 the night and the day were created1 being the period of the one most intelligent revolution4 ,and the month was created when the moon had completed her orbit and overtaken the sun2 and the year1 when the sun had completed his own orbit4 ,the periods of the other stars the planets have not been understood by men in general1 but only by a few1 and they have no name for them1 and do not estimate their comparative length by the aid of a number1 and hence they are hardly aware that their wanderings1 which are infinite in number and admirable for their variety1 make up time4 ,and yet there is no difficulty in seeing that the perfect number of time completes the perfect year when all the eight revolutions1 having their relative degrees of swiftness1 are accomplished together1 and again meet at their original point of departure1 measured by the circle of the ,same moving equally40 ,the heavenly bodies1 according to ,timaeus1 are all divine intelligent beings4 ,in form they are perfect spheres1 like the world of which they form part1 and they are composed of fire4 ,the stars have two motions1 for each rotates on its own axis while it is carried round the centre on the rotating star sphere4 ,earth is also a sphere1 immoveable at the centre of the ,world4 ,of her ,timaeus says3 8,the earth1 which is our nurse1 encircling the pole which is extended through the universe1 he made to be the guardian and artificer of night and day40 ,this passage has given rise to the idea that ,plato believed the apparent diurnal revolution of the heavens to be caused by earth's rotation on her axis2 but the word here translated 8encircling0#cc may mean--as that does--either motion or situation round about something1 and the whole context ascribes the diurnal movement so clearly and emphatically to the heavens1 that it seems evident ,plato could only have meant that earth was guardian and artificer of day and night by virtue of her position4 ,the only strong argument in favour of the other meaning is that ,aristotle1 when speaking of ,earth as supposed by some to be central in the ,universe but moving1 quotes ,plato and the ,timaeus4 ,it might easily happen1 however1 that ,aristotle knew from other sources1 perhaps from conversation with ,plato1 that at some time the latter had inclined towards belief in ,earth's motion1 and remembering the ambiguous expression in the ,timaeus he quoted it from memory as a statement of ,plato's belief4 ---------------------------------------- -------------------------------- #cc 4 ---------------------------------------- -------------------------------- ,there is some evidence that late in life ,plato accepted the doctrine of ,philolaus that ,earth was not only in motion1 but in motion round a ,central ,fire4 ,there is a legend that he bought the books of ,philolaus at a great price1 and ,theophrastus1 a disciple of ,aristotle1 is reported by ,plutarch to have said that 8,plato when old assigned to ,earth another place1 the central and nobler place being reserved for something else more worthy of it40 ,however this may be1 he does not teach either theory in his writings4 ,his views seem to be quite the same as those of ,pythagoreans of the old school1 whom he sometimes quotes4 ,after describing the creation of the ,universe1 ,timaeus relates that the ,creator deputed the gods whom he had made 7including the stars7 to create living beings on the earth1 he himself creating directly only their immortal part1 which he made of the same essence as the ,world-,soul1 but diluted4 ,then follows the passage which came to the mind of ,dante when he met the first spirits of ,paradise in the moon4 8,and when he had framed the ,universe1 he distributed souls in equal numbers to the stars1 and assigned each soul to a star2 and having placed them as in a chariot1 he showed them the nature of the ,universe1 and the decrees of destiny appointed for them1 and told them that no one should suffer at his hands1 and that they must be sown in the vessels of the times severally adopted to them4444 ,he said that he who lived well during his appointed time on earth would return to the habitation of his star1 and there have a blessed and suitable existence40 ,if he lived ill1 he would be a woman at his second birth1 if a bad woman1 then a beast1 and as long as he continued to do ill he would 8not cease from his toils and transformations until he followed the original principle of sameness and likeness within him4444 ,when he had given all these laws to his creatures 444 he sowed some of them in the earth1 and some in the moon1 and some in the other stars which are the measures of ,time40 ,the creation of man's body and all the remainder of the ,timaeus does not concern us here1 except that when speaking of the highest use of man's faculty of sight1 we realize how near ,dante and ,plato are in their feeling for the revolving heavens3 8,god invented and gave us sight to this end1 that we might behold the courses of intelligence in the heaven1 and apply them to the courses of our own intelligence which are akin to them1 the unperturbed to the perturbed2 and that we1 learning them and being partakers of the true computations of nature1 might imitate the absolutely unerring courses of ,god and regulate our own vagaries40 #b4 ,,eudoxus4 ,sidenote3 ,eudoxus #djh ,b4,c4 to c4 #cee ,b4,c4 ,with words like these ringing in his ears1 ,eudoxus went from the ,greek philosopher to the ,egyptian priest1 and studied 8the courses of intelligence in the heaven40 ,legend says that the sacred ,egyptian ,bull licked his garment1 and the priests no doubt were encouraged by this omen to divulge their secrets to a person so highly favoured by the gods4 ,they prophesied that he would have a short but very illustrious life4 ,after a year1 or perhaps more1 spent in ,egypt1 ,eudoxus returned to his own city1 set up an observatory of his own1 received pupils1 and worked out an exceedingly ingenious and original planetary scheme4 ,he did not accept 7if he knew of them7 the risky theories of the ,pythagoreans as to ,earth's motion1 but assumed a central stable earth1 round which circled the stars and the seven planets1 according to the teaching of ,plato and the general belief among educated ,greeks of his day4 ,but ,egyptian observation and ,greek geometry enabled him to describe for the first time the complicated movements of the planets1 and to represent them by an imaginary mechanism4 ,this was a series of spheres1 or hollow balls1 fitting inside one another1 and gradually diminishing in size like the ivory boxes of a ,chinese puzzle1 or the coats of an onion4 ,their size was stupendous1 for the outer one1 which contained all the rest1 was nothing less than the sky we see1 and was encrusted all over with stars4 ,of the inner smaller spheres1 one bore1 fixed in it like a jewel set in a ring1 the sun2 and six others bore1 in the same way1 the moon and the planets1 one in each4 ,all these hollow spheres were symmetrically placed so that all centred in a single point1 and at this point was a solid sphere1 exceedingly small in comparison1 which was the earth4 ,the star sphere1 without moving from its place1 rotated round this central ,earth1 and this caused the diurnal motion that we see in the stars4 ,each planet-bearing sphere rotated also1 but the special characteristic of ,eudoxus' system is that each of these was surrounded by its own complete set of spheres1 bearing no planet1 but all attached together1 the poles of one sphere resting on the surface of the next1 and moving with different speeds1 in different directions1 and with differently inclined axes3 these motions being all communicated to the innermost sphere on which the planet was fixed1 the net result was the movement of the planet as we see it in the sky4 ,each planetary set was quite separate from the rest1 and did not interfere with their movements1 although each set was enclosed within the next larger4 ,since all the planets have a diurnal motion like the stars1 as well as their own proper motions1 each set had to be provided with a sphere which moved exactly like the great all-enclosing star sphere4 ,thus1 the sun had one sphere turning like the star sphere1 and within this was a second1 on which the sun was fixed1 which turned round in a year1 in a west to east direction4 ,the sun1 carried along by the combined motion1 travelled through the sky with the daily and yearly motions1 as we see them4 ,illustration3 ,fig4 #ai4 ,the spheres of the sun in the system of ,eudoxus4 ,the outer sphere turns on its axis ,a ,a in a day and night2 the inner on its axis a a in a year1 in the opposite direction4 ,the planetary spheres were much more difficult to arrange4 ,eudoxus used four spheres for each1 and these had in every case to be carefully adjusted to the very different periods and amplitudes of the planetary oscillations4 ,it must be confessed that the scheme failed with the difficult case of ,mars1 and was not quite satisfactory with ,venus1 but it represented remarkably well the movement--so far as then known--of ,sun and ,moon1 ,saturn1 ,jupiter1 and ,mercury4 ,it was certainly a feat for those days1 whether we consider it merely as the solution of a mathematical problem1 or as an embodiment of astronomical knowledge4 ,the periods of the planets as known to ,eudoxus1 stated in round numbers only1 are given in the following table4 ,they are taken from ,simplicius1 who describes the system of ,eudoxus1 but as in the so-called ,papyrus of ,eudoxus the synodical revolution of ,mercury is given as #aaf days1 the same as the modern value1 ,eudoxus may have had much more exact data4 ,it will be seen that his synodic period for ,mars is the only one which is totally wrong1 and the large error is difficult to explain4 ,modern ,zodiacal ,modern ,planet4 ,synodic ,period4 ,value4 ,period4#cd ,value4 ,mercury #aaj days #aaf days #a year #a4j year ,venus #ai months #ehd 0 0 #a4j 0 ,mars #h months1 #bj days #ghj 0 #b years #a4hh 0 ,jupiter #ac months #cii 0 #ab 0 #aa4hf 0 ,saturn #ac months #cgh 0 #cj 0 #bi4df 0 ---------------------------------------- -------------------------------- #cd ,the period in which a planet is seen to revolve round the zodiac1 and return to the same star1 varies greatly1 because complicated by its retrograde movements2 but if the average of a sufficient number of periods be taken1 it coincides for ,mercury and ,venus with the sidereal year2 for ,mars1 ,jupiter1 and ,saturn1 with the period in which each is actually revolving round the sun 7its 8sidereal period074 ---------------------------------------- -------------------------------- ,it is disappointing1 after the splendid hypotheses of the ,pythagoreans1 to be back again on a central stationary ,earth among mechanical contrivances for moving the heavenly bodies1 which remind us of ,anaximander's series of hemispherical heavens and heavenly wheels1 but at least the earth is spherical1 owing to the ,pythagoreans1 and the sky extends like a sphere all round1 and we shall never have a flat ,earth or a hemispherical sky again among the ,greeks4 ,we do not know whether ,eudoxus regarded his spheres as convenient mathematical abstractions only1 or whether he reasoned that the stars were evidently set in an invisible uniformly rotating sphere1 and ,plato considered this kind of movement the most suitable for all heavenly bodies2 that therefore he would try whether a series of similar spheres interacting on one another would account for the complicated motions of a planet1 and finding that they would1 taught that they must truly exist4 ,in any case the basis of his system was a detailed knowledge of planetary motions hitherto unapproached by the ,greeks1 and its chief merit was that it challenged comparison with the skies4 #c4 ,,calippus4 ,sidenote3 ,calippus c4 #ccj ,b4,c4 ,the challenge was soon taken up1 for twenty or thirty years later one of the pupils of ,eudoxus1 ,calippus of ,cyzicus1 undertook to improve the system4 ,the defects in the theories of ,mars and ,venus had evidently been discovered1 for ,calippus added another sphere to each of these1 as well as one to ,mercury1 which would be quite enough to bring the theories into better agreement with the facts4 ,with regard to the sun and moon1 ,calippus had paid special attention to their movements1 for he made an improvement in the old luni-solar cycle of ,meton1 to which we shall return later4 ,eudoxus had ignored a very important fact discovered by ,meton and ,euctemon about ,b4,c4 #dcj1 viz43 that the seasons are of unequal length1 showing that the sun takes unequal times to pass over the four arcs of his orbit lying between the four points of the vernal and autumnal equinoxes and the summer and winter solstices4 8,why10 exclaims a later writer#ce 8are there unequal numbers of days in the four seasons1 seeing that the course of the heavenly bodies must be regular1 not being swayed by human passions or affairs80 ---------------------------------------- -------------------------------- #ce ,geminus4 ---------------------------------------- -------------------------------- ,calippus considered this question very seriously1 and made a careful determination of the length of the four seasons4 ,it seems at first sight impossible to reconcile their inequality with uniform circular motion of the sun round the earth1 but he found that he could do it by adding two more spheres to the sun's set1 rotating uniformly but so arranged that their motion1 added to the others1 would result in an actual velocity in the sun itself varying just in the way required by the facts4 ,the same had to be done for the moon1 for the same reason1 so the number of spheres1 which ,eudoxus had made twenty-seven1 was brought up to thirty-four 7including the star sphere74 ,the varying velocity of the five planets had not yet been perceived4#cf ---------------------------------------- -------------------------------- #cf ,this varying velocity is due to the fact that all celestial orbits are not true circles1 but ellipses1 which was first discovered by ,kepler 7#afji ,a4,d474 ---------------------------------------- -------------------------------- #d4 ,,aristotle4 ,sidenote3 ,aristotle ,b4,c4 #chd-cbb4 ,calippus went up to ,athens about #ccj ,b4,c4 to lay his scheme before the great master1 ,aristotle1 and it had his cordial approval4 ,but ,aristotle definitely accepted the spheres as things having a concrete existence1 for he says 7,de ,clo ,,ii1 #ab7 that we must regard them as heavenly bodies like the stars and planets1 and that they are composed of the same celestial stuff4 ,he made one change1 when incorporating the system in his scheme of the ,universe4 ,he was not satisfied that each set of spheres should work quite independently of the rest1 and thought that the outermost sphere of stars ought to communicate its motion to those below 7i4e4 nearer ,earth72 and no doubt it did seem rather clumsy to have a separate sphere in every set rotating in exactly the same manner as the star sphere4 ,but how could the impulse be communicated without disturbing the other movements8 ,aristotle introduced below each set another set of 8unrolling0 spheres1 as he called them1 which successively neutralized the rotations of all spheres in that set except the one with diurnal rotation1 hence this movement alone was communicated to the set next below4 ,this seems1 however1 more clumsy than the defect it was intended to remedy4 ,aristotle was perhaps led to it by his wish to give greatest importance to the star sphere2 and if so1 he acted on the principle which he blamed in the ,pythagoreans1 of making deductions not from things as they are seen1 but as1 according to his own ideas1 they ought to be4 ,for indeed ,aristotle1 in spite of his own doctrines1 and the great impulse which he gave to truly scientific methods of observation and experiment1 could not rise altogether above the prejudices of his age1 and consequently his ,cosmos is a curious mixture of sound reasoning1 based on observation1 and of metaphysics1 the latter predominating4 ,for instance1 it is only at the end of his second book ,on the ,heavens1 after he has 8proved10 from purely metaphysical reasons1 that ,earth must necessarily be spherical and at the centre of the ,world1 that he adds in support of his assertions the fact that the curved line of ,earth's shadow seen on the moon during eclipses is always round1 that stars vary in visibility as we change our horizon1 and that astronomers say that the celestial phenomena occur as they would if ,earth were at the centre of the ,world4 ,nevertheless1 ,aristotle's teaching had so overwhelming an influence1 not only throughout this epoch1 but in the age of ,dante1 and the latter was so greatly influenced by him1 both directly and indirectly1 that it is exceedingly interesting to know his ideas about the ,cosmos4 ,we find them in the two books ,on the ,heavens1 in the ,meteorology1 the ,metaphysics1 and some other works4 ,a special treatise on ,astronomy1 to which he refers#cg1 is unfortunately not extant4 ---------------------------------------- -------------------------------- #cg ,de ,clo ,,ii4 #aj4 ---------------------------------------- -------------------------------- ,the form of the ,universe1 ,aristotle says1 must be a sphere1 because a sphere is the most perfect of solids and a solid is more perfect than a surface or a line1 because it is in three dimensions1 and three means completion1 perfection4#ch ---------------------------------------- -------------------------------- #ch ,thus1 7he adds7 time also is threefold1 for we have ,beginning1 ,middle1 and ,end4 ,therefore we apply three to ,divine things1 and also in common speech we call two 8both10 and only say 8all0 when we reach three1 following ,nature's law4 ,the ,pythagoreans say 8,the all and all things are bounded by the number three40--,de ,clo ,i4 #a4 ---------------------------------------- -------------------------------- ,the ,universe had no beginning1 and will have no end2 and this conclusion1 drawn from reasoning1 is supported by the belief which all have who believe in gods1 8whether ,greeks or not ,greeks10 that the gods1 who are immortal1 live in the highest heaven1 which is therefore also immortal2 and by the fact that no one1 throughout the ages1 so far as we know1 has ever seen any change in it4 ,but it is of finite dimensions1 for no infinitely great body could rotate in a finite time2 and it is the only universe which exists or ever can exist3 outside is neither space1 nor void1 nor time4 ,for space is that which is or may be occupied by matter1 and time is the measure of motion occurring in matter1 and no matter exists or can exist there4 ,therefore that which exists there is not in space nor is altered by time1 but lives for ever the best and the self-sufficing life 7i4e4 the purely spiritual74 ,as matter has three dimensions1 so motion is of three kinds3 viz4 7#a7 in a straight line down1 that is1 towards the centre of the ,world2 7#b7 in a straight line up1 that is1 towards the circumference2 7#c7 in a circle round the centre4 ,thus simple heavy bodies such as all kinds of earth1 have a simple motion downwards2 simple light bodies such as fire1 move upwards2 and when they reach their respective goals they remain where they are1 unless disturbed by external force--earthy things on the earth1 fiery vapours in the upper atmosphere4 ,composite bodies have composite motions1 the motion proper to the predominant substance predominating4 ,but for the heavenly bodies the only possible motion is in a circle1 where there is neither beginning nor end1 no goal and no limit1 hence this motion is eternal4 ,thus ,aristotle solved for himself the problem of the early philosophers3 how the stars in the sky remain there1 for ever circling round us1 and never falling to the ground4 ,there is no need1 he says1 to assume an ,atlas to support the sky on his shoulders1 as in the old myths1 nor a whirlwind such as ,empedocles suggested1 nor a ,soul of the ,world1 as ,plato said2 for the heavenly bodies are not heavy things like ,earth to need support1 and they are not moved by force1 but are eternally in motion from the nature of their being4 ,in the same way he disposes of the difficulty of supporting ,earth1 having first 8proved0 that because there is an ever-circling spherical ,heaven1 there must also be an ever-resting spherical central ,earth2 there must be its opposite1 the ever upward-striving ,fire2 and there must be the intermediate pairs of opposites1 ,air and ,water4 ,it is indeed1 he says1 a strange thing1 and one to set any thoughtful man thinking1 that the smallest clod of earth1 when thrown up into the air1 immediately falls down1 and presumably would never stop falling if the earth were suddenly removed from beneath it2 yet here is ,earth herself1 so large and heavy1 not falling1 but remaining steady in one place4 ,but the explanations given by philosophers are more difficult than the fact they seek to explain4 ,xenophanes of ,colophon said that the earth roots in the infinite1 which simply saved him the trouble of considering further2 others that the earth rests on water1 which is our oldest tradition1 said to be derived from ,thales2 but on what then does water rest and how can water1 which is lighter than earth1 support it8 ,do we not see that even small pieces of earth sink in water1 and larger ones still more quickly8 ,anaximenes1 ,anaxagoras1 and ,democritus said that ,earth rests on air1 through her flat shape1 as a leaf can float on the wind1 and they added that the air cannot escape because the flat earth fits close down upon it1 like a lid1 which is also the reason that it can support the earth1 because it is compressed1 and they brought forward many proofs to show that air1 when compressed and still1 can support great weights4 ,others1 like ,anaximander1 said that ,earth rests because she is in equilibrium1 for there is no reason why she should move in one direction rather than another4 ,but all earthy things 7says ,aristotle7 do not merely remain at the centre when there1 they move thither whenever displaced4 ,they are not suspended like a hair which is powerfully but uniformly stretched1 and so never breaks1 nor like a man who is equally hungry and thirsty1 and has meat and drink at equal distances from him and therefore starves4#ci ,no1 the truth is that ,earth1 and every particle of ,earth1 tends naturally towards the centre of the ,universe1 and rests when at its goal4 ,we must remember that on every part of the sphere of ,earth1 heavy bodies fall vertically to its surface1 showing that it is not to the surface in general that they fall1 but exactly to the centre1 which is also the centre of the ,universe4 ---------------------------------------- -------------------------------- #ci ,par4 iv4 #a-c4 ---------------------------------------- -------------------------------- ,of course it was no solution of the mystery1 but only moving it a step back1 to say that the stars circle because it is their nature to do so1 and heavy bodies fall to ,earth because that is their nature4 ,but the interesting point is that the ,greeks did reason about these two motions1 and compare them2 that they clearly grasped the fact that 8weight0 simply means a tendency to move1 and that the motion of falling bodies at ,earth's surface is invariably towards ,earth's centre1 accelerating as it appproaches the surface 7,de ,clo ,i4 #h74 ,it is only the fresh mind of a little child1 or of a really intelligent man1 which is forcibly struck by the mystery of everyday sights1 such as stones falling1 and stars not falling but eternally moving in the sky4 ,the force which makes bodies move towards one another we still call 8heaviness10 i4e4 gravity1 and the mystery of its ultimate nature and mode of action is still unsolved4 ,it is so weak and so often complicated by other forces that1 except in very delicate experiments or with the mind's eye1 we can only see it in action when bodies fall to the ground2 and thus ,nature guarded for centuries the secret that every tiny particle on the whole earth attracts every other1 and also the earth itself1 as surely as the earth attracts them4 ,the further grand secret concerning this force ,eudoxus had unwittingly set out to discover1 with his planetary periods learned from the ,egyptians1 and his three motions of the moon4 ,for when this study was far enough advanced1 the necessary data were at hand for ,newton1 as he pondered the mystery which had baffled ,greece2 and he was able1 from the moon's motions1 to verify his guess1 that even the heavenly bodies are in truth always falling1 falling1 towards one another1 exactly as ,aristotle's 8smallest clod of earth0 fell to the ground4 ,from the theory of the three simple motions1 it obviously follows that ,earth must be at the centre of the world1 that her particles must be arranged in a spherical form round the central point1 also the sphere must be at rest4 ,but all are not agreed about this1 says ,aristotle4 ,all who consider the ,universe finite say ,earth is at the centre2 but the philosophers in ,italy1 the so-called ,pythagoreans1 on the contrary1 say that in the centre is ,fire1 and that ,earth1 which is one of the stars1 is in motion round the centre1 and so causes day and night4 ,they also assume a ,counter-,earth1 merely from pre-conceived ideas1 not from observation of facts4 ,and some agree about the ,central ,fire1 from pre-conceived ideas1 because they think that the noblest should have the noblest place3 fire is nobler than earth1 and boundary nobler than what is bounded1 and circumference and centre are both boundaries2 therefore 7they say7 ,fire and not ,earth is at the centre4 ,moreover1 the ,pythagoreans say that the most important part of the ,universe is the best guarded1 and that the centre is such a part1 and they call it the ,watch ,tower of ,zeus4 ,to these metaphysical reasons ,aristotle replies that the centre is not a true boundary1 it is rather an end than a source1 it is the material1 the limited1 while it is the circumference which limits1 encloses1 and gives the form4 ,besides1 the centre of a thing is not necessarily the centre of its being2 as with animals the centre of their life 7meaning the heart7 is not the centre of their body4 ,so the philosophers need not disturb themselves to put ,earth out of her local centre1 but they would be wiser to examine that other centre of the ,universe 7meaning the sun71 and find out what is its nature and its place1 for it also is a point of origin1 and noble4 ,he continues 8,some also assert that though ,earth is at the centre1 it is wound and moving round the axis which is extended through the ,universe1 as is written in the ,timaeus40 ,plato's actual words in the ,timaeus will not bear this interpretation1 as we have already seen 7p4 #he74 ,it is a little surprising that ,aristotle does not mention the names of ,ecphantus the ,pythagorean and ,heracleides of ,pontus in this connection1 since the latter was his contemporary1 and perhaps the other also1 for they are mentioned together as teaching the doctrine of ,earth's rotation on her axis4#dj ,also ,aristotle seems hardly fair to either this or the ,central ,fire theory1 in that he only answers the metaphysical reasons of the ,pythagoreans1 and omits to mention that either would unify the diurnal celestial motions in a much simpler way than all his 8unrolling0 spheres4 ,if he had not especially mentioned that ,earth's motion was supposed by the ,pythagoreans to cause day and night1 we should be inclined to think that he did not understand that the period was twenty-four hours1 and that its effect would be to produce the apparent diurnal rotation of all the heavens4 ---------------------------------------- -------------------------------- #dj ,see p4 #ge1 note4 ---------------------------------------- -------------------------------- ,the passage1 however1 has been a cause of endless controversy from the earliest commentators of ,aristotle to the present day1 and such a thorny question would have been avoided altogether in this book were it not that it is actually quoted by ,dante in the ,convivio4 ,as to the size of the earth1 ,aristotle held that it was not a large sphere1 and small when compared with the stars4 ,for1 he says1 if we take quite a short journey to north or south1 our horizon changes markedly1 so that the stars above us look quite different1 and we do not see the same stars2 for some which are well seen in ,egypt and near ,cyprus are not visible at all in northern parts1 and those which in the north are always in the sky1 set when we go south4 ,and therefore1 he adds1 those who say that the regions near the ,pillars of ,hercules are connected with ,india1 so that the ocean is one1 are not saying anything altogether incredible2 and their proof is that there are elephants both in the extreme east and the extreme west4 ,he does not mean1 evidently1 that there was no sea at all between1 but only that one could quickly travel from one to the other1 always going west3 there is no immense stretch of land or sea between west ,africa and east ,india1 nor are they the extremities of a flat disc-like earth4 ,aristotle tells us1 moreover1 that the mathematicians1 who have tried to measure the circumference of the earth1 find that it is about #djj1jjj stadia4 ,this is the first time we hear of an attempt to measure the earth1 but unfortunately we do not know what stadium was used1 nor what was the method employed4 99 99 99 99 99 ,aristotle's ,cosmos is arranged as follows3-- ,upon the central spherical ,earth rests water1 and above this is air1 but these intermingle more or less1 and are not sharply divided2 in the same way1 though fire rises highest of the four elements1 there is not a distinct sphere of fire1 but the higher part of the atmosphere is chiefly composed of it4 ,it is in this upper fiery atmosphere that shooting stars are produced3 hot and dry exhalations rising from ,earth take fire there1 but are quickly consumed4 ,comets have their origin in the same place1 when large masses of vapour rise and are directly below the sun 7had the ,greeks noticed that comets' tails are always streaming away from the sun874 ,aristotle also explains that the ,milky ,way is formed from these constantly-rising vapours1 but under the influence of the stars1 for it always has the same position amongst them1 and that is where the most numerous and brightest stars congregate4 ,thus within and below the fiery atmosphere constant changes are taking place1 and all things are perishable1 but as soon as we reach the lowest of the heavenly spheres1 the moon's1 we enter another world4 ,all is changeless1 eternal1 divine4 ,motion is in circles1 space is filled with ether1 the heavenly bodies as well as their spheres are of an ethereal substance4 ,the ,pythagorean idea of music made by the spheres1 ,aristotle dismisses as very pretty but unfortunately not true4 ,for if in truth these immense spheres made a sound as they moved1 even if we could not hear it 7as they said7 we should feel it1 for even earthly thunder bursts rocks asunder6 ,and there is no reason why they should make any sound1 for nothing moves out of one place3 the spheres are simply rotating1 which is the natural movement for a sphere1 unless it rolls along1 which they are not doing4 ,if nature had wished the spheres or the stars and planets to move forward1 she would not have treated them worse than terrestrial animals1 in giving them no limbs by which they could progress6 ,the stars and planets have no motion themselves of any kind1 but are simply carried along by their rotating spheres1 as we can plainly see by the moon turning always the same face towards us3 hence they make no more noise than a ship's mast set in a ship1 or the whole ship as it glides down a river4 ,stress is laid both by ,plato and ,aristotle on this absence of any motion of translation in the heavenly bodies and their spheres2 both insist that a movement of rotation1 in which the moving body continually occupies the same place1 is the only movement existing in the heavens4 ,one wonders whether the spheres of ,eudoxus suggested or resulted from this idea4 ,aristotle does not enter into detail about the separate planetary motions1 in any extant work1 but explains as the general principle that the outermost1 the prime movement of the whole universe1 is simple1 and the most rapid1 while the inner are complex1 slower1 and in the contrary direction2 so that the planet nearest to the prime movement 7,saturn7 is longest in making his own revolution1 because most affected by it1 and the others less so in proportion to their distance4 ,he refers his readers to the mathematicians1 and quotes the ,egyptians and ,babylonians as having furnished satisfactory proofs of the relative positions of the planets1 by such observations as occultations of other planets by the moon1 which show that she is below them 7i4e4 nearer to us74 ,the passage is quoted by ,dante#da1 in which ,aristotle describes how he himself once saw an occultation of ,mars4 8,when the moon was a half sphere1 she passed beneath ,mars and he disappeared under her dark side1 but came forth again on her bright illumined side4 ,and the same kind of thing10 he adds1 8is reported to happen with the other planets also1 as those tell us who for a vast number of years have made observations1 viz4 the ,egyptians and ,babylonians40 ---------------------------------------- -------------------------------- #da ,conv4 ,,ii4 iii4 #ei-fe4 ---------------------------------------- -------------------------------- ,there is one point which is elaborately discussed in the ,de ,clo1 which seems very curious to us1 but the main point must be noted here1 since it is of some interest to the ,dante student4 ,aristotle tells us that he considers the sphere of the ,universe to have a top and a bottom1 and that the ,pole which is not seen by us 7the south7 is at the top4 ,one cannot help thinking that ,dante had this in mind when he chose the southern hemisphere for the mount of ,purgatory1 whither1 after all their mistakes and wrong-doing on this underside of the earth1 souls go to purify themselves on the upper side1 under the stars of the southern pole4 ,in his book on metaphysics1 ,aristotle gives a very brief sketch of the spheres of ,eudoxus and his own 8unrolling0 spheres2 and says that all these planetary movements prove the existence of ,essences1 eternal and immoveable themselves1 who cause these movements4 ,and it has been handed down to us in a mythical way1 from the most ancient teachers1 that these eternal ,essences are gods4 ,above all these must be a ,first ,mover1 the ,primum ,movens ,immobile1 who is one1 eternal1 and enjoys for ever the kind of existence which we only experience in our best moments4 ,upon this ,first ,mover depend the whole heaven and all nature4 #e4 ,,aristarchus4 ,with a system of revolving spheres accepted by the mathematical astronomers1 and sanctioned by the great philosopher ,aristotle1 it may be thought that we are within sight of our goal1 the system of ,greek astronomy which was to dominate the scientific world for many centuries1 including the age of ,dante4 ,but so exacting had the careful observers become that the system of ,eudoxus must be completely transformed1 by aid of two quite new hypotheses1 before it would satisfy their demands4 ,also1 about half a century after the consultation of ,calippus and ,aristotle in ,athens1 a strange new theory was propounded1 the boldest and strangest of all4 ,sidenote3 ,aristarchus c4 ,b4,c4 #bha4 ,nearly two thousand years before ,galileo was summoned before the ,inquisition1 and forced to recant upon his knees his 8most damnable heresy0 that the earth goes round the sun1 ,aristarchus of ,samos was accused of impiety by his countrymen for the same crime4 ,but he met an even sadder fate than ,galileo--neglect4 ,his daring scheme was almost ignored by his contemporaries1 and but for a casual mention by ,archimedes and by ,plutarch1 we should know nothing about it4#db ---------------------------------------- -------------------------------- #db ,it is also mentioned in a compilation of philosophers' opinions1 probably made in the fifth century ,a4,d4 by ,stobus1 who is very likely quoting ,plutarch4 ---------------------------------------- -------------------------------- ,he was1 however1 very famous as a mathematician1 and also as an observer4 ,ptolemy quotes his determination of the summer solstice of the year b4c4 #bha1 and this tells us the date at which he flourished4 ,he was renowned for a very ingenious method by which he tried to discover how much further from us the sun is than the moon4 ,when the moon is half full the angle sun-moon-earth is a right angle1 and if the angle sun-earth-moon be measured1 by pointing the astrolabe first to sun and then to moon1 the third angle1 at the sun1 may be computed1 and then the ratio sun-earth to moon-earth will be known4 ,the method is perfect theoretically1 and if the sun were comparatively near1 say about ten times the moon's distance1 it would be practicable2 but the distance is really so much greater that the angle at the sun almost vanishes1 and a very small error in estimating it causes an error equal to many millions of miles in the result4 ,it is also impossible to determine from looking at the moon the exact time when the division between light and dark is a straight line4 ,aristarchus made the angle at ,earth #hg instead of #hi #ej1 and this gave the sun a distance of about #ai times as far as the moon1 instead of #djj times1 which is the true value4 ,illustration3 ,fig4 #bj4 ,method of ,aristarchus for finding the distance of the sun4 ,the foolish fad 7as they thought it7 about ,earth's motion1 held by this otherwise great man1 is described quite clearly by the two writers above-mentioned4 ,he suggested that the stars might be immoveable1 and ,earth be turning on her axis at the same time that she moves in a circle round the sun4 ,moreover realizing all that this implies with regard to the immense distance of the stars1 he said that the circle in which ,earth revolves round the sun1 compared with the sphere of the stars1 is as the centre of a sphere compared with its circumference4 ,that is1 not only ,earth1 but ,earth's whole orbit1 shrinks to a point when compared with the infinite distance of the stars4 ,we have unfortunately absolutely no information as to the way in which ,aristarchus was led to these remarkable truths1 and can only make conjectures from what we know of his times4 ,evidently the ,central ,fire theory was a suggestive step1 and so was another theory which was afloat about this time1 and has been called the 8,egyptian system0 on the authority of ,macrobius in his commentary on ,cicero's ,dream of ,scipio4 ,no one really knows where it arose1 but it is ascribed with much probability to ,heracleides of ,pontus4 ,according to this1 the two planets ,mercury and ,venus circled round the sun1 and all three together circled round ,earth1 which still remained the centre of the ,universe and of the other celestial motions4 ,it was an idea which might have occurred to any unprejudiced observer1 since the oscillations of ,mercury and ,venus from side to side of the sun are more striking than their movements through the stars4 ,they never go far from him in the sky1 like the other planets1 and seem to belong to him4 ,further1 the clear understanding of the periodic motions of ,mars1 ,jupiter1 and ,saturn1 and the accurate observation which had been introduced by ,eudoxus1 must have revealed the fact that the loops in the orbits of these planets are connected with the apparent movement of the sun2 and the varying brightness 7especially noticeable with ,mars7 is inconsistent with the assumption of unvarying distance from ,earth4 ,the great importance of the sun1 above all the other planets1 had of course always been recognised1 and it is possible that ,aristarchus was struck by an unconscious suggestion in ,aristotle's advice to the ,pythagoreans to examine the nature and place of the sun1 8that other centre of the ,universe10 for that was also a point of origin1 and a noble one4#dc ,his own work1 too1 would lead him to attribute a commanding position to the sun1 for as it was nineteen times as distant as the moon1 it must also be nineteen times as large 7since they appear equal71 so he must have felt certain that it was a very great size1 probably much the largest of all bodies in the ,universe4 ---------------------------------------- -------------------------------- #dc ,see page #aja4 ---------------------------------------- -------------------------------- ,it was the grandest and truest of all the ,greek astronomical theories4 ,but it was not accepted1 it was hardly even discussed1 and we can scarcely be surprised at this4 ,such an improbable theory needed many more convincing proofs than ,aristarchus could bring forward4 ,observation1 calculation1 comparison of theory with facts1 this was what was needed before safe ground could be won for belief1 and in this ,eudoxus was a true pioneer4 ,but freedom of thought and courage in imagination is needed also in science1 and ,aristarchus seems to have been almost the last to possess this4 ,sidenote3 ,seleucus ,b4,c4 #afj4 ,sidenote3 ,aryabhata born ,a4,d4 #dfg4 ,a certain ,babylonian1 named ,seleucus1 who lived about ,b4,c4 #afj1 perhaps on the ,tigris1 and an ,indian astronomer1 ,aryabhata1 of the fifth century ,a4,d41 both taught that ,earth turns on her axis1 but ,aristarchus stood alone in suggesting that she also has a movement of revolution round the sun4 ,the possibility of ,earth's motion was alluded to but seldom by classical and medival writers1 and then almost always as a foolish fancy hardly worth discussion2#dd until at last ,copernicus1 hardly daring to publish his bold idea in sixteenth century ,europe1 for fear of persecution1 sought and found among the followers of ,pythagoras1 and in ,aristarchus of ,samos1 kindred spirits with his own4 ---------------------------------------- -------------------------------- #dd ,indian astronomers also refused to accept the doctrine of ,aryabhata4 ,varha ,mihira 7sixth century ,a4,d47 says3--8,others maintain that the earth revolves and not the sphere3 if that were the case1 falcons and other birds could not return from the ether to their nests40 ---------------------------------------- -------------------------------- #f4 ,,the ,,school ,,of ,,alexandria4 ,the spheres of ,eudoxus would not work4 ,the system was already overladen1 and more variations in velocity were becoming known4 ,observation shows1 too1 that the planets1 especially ,mars and ,venus1 vary greatly in brightness1 in regular periods which correspond with their movements1 and this could not be accounted for by any possible number or arrangement of spheres if all were to remain concentric to ,earth1 so that every planet remained always at a uniform distance4 ,yet ,aristotle had said that ,earth must be at the centre of the ,universe4 ,the new philosophers of the ,stoic school agreed with him1 and among mathematicians only ,aristarchus dared to disagree4 ,but they were not long at a loss4 ,the homocentric spheres#de were thrown aside1 and during the third century two new hypotheses were suggested 7beside that of ,aristarchus71 and although we do not certainly know by whom1 there is little doubt as to the place in which they originated4 ,by a strange fate1 ,egypt1 the home of astronomy many centuries before1 became the seat of the latest1 most brilliant1 and most successful astronomical school of ancient times1 and the knowledge won there in the five centuries between ,b4,c4 #cjj and ,a4,d4 #bjj spread1 following in the wake of ,alexander's conquests1 over the whole of the civilized world4 ---------------------------------------- -------------------------------- #de ,spheres all centring in one point4 ---------------------------------------- -------------------------------- ,it was a purely ,greek school1 however4 ,greece lost her independence under ,alexander1 and was finally crushed by ,rome in #adf ,b4,c41 but never was ,greek learning and culture so much honoured and sought after as in this age4 ,in ,egyptian ,alexandria1 ,greek men of science found a welcome1 and opportunities of research which did not exist in any other place in the world4 ,in the ,museum1 founded and liberally endowed by the royal ,ptolemies1 was a great library whose custodians were bidden to obtain every book that had ever been written1 and it is said that when any stranger arrived with a new book it was taken from him and copied for the ,museum1 and the copy returned to the owner4 ,within the great marble colonnaded building were lecture-halls1 and reading rooms1 and laboratories2 there were gardens for botanists and zoologists1 and observatories for astronomers4 ,these astronomers were all ,greeks1 and though now living in ,egypt they do not seem to have learned anything more from the ,egyptians4 ,perhaps the priests resented the intrusion1 and kept their secrets jealously to themselves2 perhaps ,eudoxus and his immediate followers had learned all they had to teach4 ,this seems the more probable because1 although the ,greeks of this age did use ,babylonian records of eclipses to form a lunar theory1 they complained of the insufficient accuracy of all available planetary records4 ,moreover1 they were not hindered from learning astrology3 the sacred books of the ,egyptians which taught its principles were translated into ,greek about #cjj ,b4,c42 but it was always treated by them as quite a separate branch of study4 ,their geometrical methods were entirely their own4 ,they introduced a system of notation which greatly simplified calculation#df2 their discovery of the principles of spherical trigonometry inaugurated a new era in astronomy2 and they invented a new class of astronomical instrument4 ---------------------------------------- -------------------------------- #df ,mahaffy1 ,the ,progress of ,hellenism in ,alexander's ,empire1 p4 #aai4 ---------------------------------------- -------------------------------- ,we know what these instruments were like1 and it is even possible to give an illustration2 for1 from descriptions in ,ptolemy's ,almagest1 we find that the 8well-made copper circles10 the gnomons1 and the celestial globes1 which were set up in the ,square ,portico of the ,museum1 were of the same pattern as instruments which existed in ,pekin1 in the ancient observatory on the ramparts1 until they were looted by the ,germans during the late ,chinese war4 ,the ,alexandrian instruments were not supported on their stands by beautiful bronze dragons1 but on the other hand the circles were more accurately divided1 which after all was of more importance from the astronomers' point of view4 ,fig4 #ba gives a general view of the ,pekin ,observatory1 and ,fig4 #bb one of their astrolabes dating from the #acth century ,a4,d4 ,at first glance there seems to be here absolutely nothing like our modern observatories4 ,ancient and medival astronomers had indeed no telescopes1 being ignorant of the properties of lenses3 therefore they were unable to study the features of any heavenly body except the moon1 and they had no way of finding out anything about their physical constitution2 but they had many ways of measuring their distances and motions1 and even the angular sizes of sun and moon1 and their instruments were the forerunners of our sextants1 micrometers1 and transit instruments1 our chronometers and sidereal clocks4 ,illustration3 ,,pekin ,,observatory4 ,to face p4 #aad4 ,from a photograph taken in #ahhh1 and published in the 8,bulletin de la ,socit belge d',astronomie04 ,the gnomon has been already described#dg1 and it was one of the most valuable instruments used by the ,greeks4 ,the ,pekin gnomon at the right of figure #ba was more than #dj feet in height1 and on the top had a little plate of copper which was pierced by a hole as fine as the eye of a needle3 the observations made with this were much more exact than observations of the end of the shadow1 which must always be vague1 and the ,chinese records of the sun's movements made with this instrument between #abgj and #abhj ,a4,d4 are of great value in modern research4 ,ptolemy explains that his gnomon was made accurately vertical by the use of a plumb-line1 and that one way of testing the level of the surface on which the shadow fell was to flood it with water4 ---------------------------------------- -------------------------------- #dg ,see p4 #bf4 ---------------------------------------- -------------------------------- ,clepsydras1 or water-clocks1 were used by the ,greeks1 and many kinds of sundials for telling the time by day4 ,tables were also made of the risings of bright stars which served for clocks by night4 ,the instrument in the middle of the platform is a quadrant1 and beyond this on the left is a large celestial globe1 which1 however1 only dates from the ,jesuit missionaries of the seventeenth century4 ,ptolemy says that his globe was made the colour of the night sky2 ,sirius being marked in his proper place1 all other stars were placed relatively to him1 and in their own colours as nearly as might be2 the ,galaxy was drawn1 and the figures of the constellations outlined4 ,the globe was arranged to turn on either the poles of the ecliptic or of the equator2 circles of wood represented the horizon and meridian1 and the pole could be arranged at any altitude according to the latitude of the place4#dh ---------------------------------------- -------------------------------- #dh ,almagest1 ,bk4 viii4 ---------------------------------------- -------------------------------- ,but perhaps the most interesting are the astrolabes1 and these owe their origin to the ,greeks4 ,the essential part of any instrument for determining angular distances is a divided circle and a pointer3 the pointer is directed first to one object then to another1 and the angle between them is then read off on the circle4 ,in the astrolabe1 the pointers themselves were also circles1 provided with little perforated rods for 8sights40 7,these are not visible on the instrument in ,fig4 #bb1 and have probably been broken off47 ,there were two fixed circles1 set in the plane of the ecliptic and perpendicular to it4 ,three other circles could be rotated round the poles of the ecliptic4 ,one of these was directed 7by means of the sights71 to some body whose position was already known1 another to the body whose position was to be ascertained1 and the angle between them was read off on the ecliptic circle2 on the third the angular distance north or south of the ecliptic circle could be read4 ,this last and the ecliptic circle were both divided into #cfj degrees1 and as many fractions of a degree as space and skill would allow4 ,the equinoctial astrolabe was similar1 but the fixed circle was in the plane of the equator1 instead of the ecliptic4 ,one of each of these is seen in the view of the ,pekin ,observatory4 ,but how did the old astronomers know how to find the ecliptic and the equator in the sky1 and set their circles in those planes8 ,this they did by means of the sun's motion4 ,the gnomon told them the day of the equinox 7see p4 #be71 and on that day the sun was in the equator3 therefore1 if a circle was set up so that the shadow of the upper part fell symmetrically upon the lower1 with a little line of light each side1 it must be exactly in the plane of the equator4 ,in the ,square ,porch such a circle was erected1 a large one of copper1 and when once correctly adjusted it was a standard plane1 and also showed the date of the equinoxes1 as accurately as the gnomon itself4 ,since the ecliptic is the path of the sun as seen in the sky1 it is obvious that it could be determined from a number of different observations of his position at different times of the year4 ,illustration3 ,a ,,pekin ,,astrolabe ,,of ,,the #ac,,th ,,century1 ,a4,d4 ,to face p4 #aaf ,from a photograph taken in #ahhh1 and published in the 8,bulletin de la ,socit belge d',astronomie04 ,finally1 accurate solar tables were drawn up1 showing the sun's position in the sky in degrees for different dates1 and then from these it was possible to find the places of planets and stars4 ,they could not of course be compared directly1 but the position of sun and moon were compared during the day1 when both were in the sky1 and then after dark the planets and stars were compared with the moon1 allowing for her motion among the stars in the meantime4 ,or secondly1 when the moon was eclipsed1 and therefore known to be in the ecliptic and exactly opposite the sun1 the places of stars could be found directly4 ,this very brief description will give some idea of the chief instruments and methods used1 and when we see how very rough and elementary they were1 and remember that the ,greeks had to work out their observations without algebra1 or decimal notation1 we are amazed at their results1 and their far-reaching ambitions4 ,sidenote3 ,eratosthenes ,b4,c4 #bgf-aid4 ,already in the very early days of the ,museum1 ,eratosthenes1 a celebrated geographer1 made a bold attempt to utilize observations of the sun measuring the size of the earth4 ,it was known that in ,syene 7the modern ,assuan7 on the day of the summer solstice at noon no shadows were thrown1 and the bottoms of wells could be seen3 evidently therefore the sun was in the zenith4 ,eratosthenes found that the sun's distance from the zenith in ,alexandria at noon on the same day was #g #ab1 or one-fiftieth of the circumference of the heavenly sphere1 consequently the two towns must be distant from one another 7assuming them to be nearly in the same meridian7 one fiftieth of the circumference of the earth4 ,the distance from ,alexandria to ,meroe was known1 and from ,meroe to ,syene had been paced by the king's professional pacers2 the whole was #ejjj stadia4 #ej times #ejjj #bej1jjj4 ,the figure always quoted by the ancients is however #beb1jjj4 ,if the stadium used by ,eratosthenes was the measure generally used for long distances which have been paced1 this estimate is equal to #bd1ffb miles1 only about #bjj miles less than the modern value4 ,it was partly by luck that ,eratosthenes got such a good result1 for he was evidently only working with round numbers1 and the extra #bjjj stadia seem to have been added in order to make one degree equal to exactly #gjj stadia4 ,but in any case it was a highly creditable performance4 ,sidenote3 ,euclid c4 ,b4,c4 #cjj4 ,sidenote3 ,apollonius c4 ,b4,c4 #bgj4 ,there were celebrated mathematicians and geometers at ,alexandria1 whose work was most useful to astronomy1 such as ,euclid1 and ,apollonius of ,perge4 ,the latter is specially mentioned by ,ptolemy in connection with the new theory of 8moveable eccentrics10 which was invented to account for the varying brightness of the planets1 as well as their peculiar movements4 ,fig4 #bc explains this theory4 ,let ,p ,a be a great revolving circle upon which ,mars is fixed4 7,in the hands of the ,alexandrian mathematicians the spheres almost disappear1 and they deal practically only with circles47 ,if the earth were at its centre1 as ,eudoxus demanded1 ,mars must always be at the same distance1 but if we make the circle eccentric to ,earth1 by putting its centre at ,c while ,earth is at ,e1 then the distance and consequently the brightness will constantly vary1 and ,mars will be brightest when at perigee ,p 7point nearest ,earth71 and faintest when in apogee ,a 7point furthest from ,earth74#di ---------------------------------------- -------------------------------- #di ,greek peri near1 apo away from1 ge ,earth4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #bc4 ,the ,moveable ,eccentric4 ,but1 as the ,greeks had discovered1 ,mars attains his greatest brilliance at different points of the zodiac1 so ,p must be made moveable1 and it always happens when he is opposite the sun1 therefore ,p must keep pace with the sun's apparent motion in the zodiac and ,p ,e always point towards him4 ,this was accomplished by making ,p ,c ,a turn round upon the fixed point ,e1 so that for instance when the sun had moved through a quarter of his circle 7in three months7 ,p ,a had moved to ,p ,a1 and the whole eccentric had moved into the new position shown in the diagram1 its centre ,c being now at ,c4 ,in other words1 the centre of the eccentric moves round ,earth in the same time and in the same direction as the sun1 that is in one year1 and 8with the signs0 7from west to east74 ,at the same time1 ,mars is moving in an opposite direction on the eccentric1 and without entering into all the details of the problem1 we may add that the ,greek geometers found that by determining the proper relative sizes of the large and the small circle they could make the two motions neutralize one another when the planet reached its stationary points1 and the retrograde motion prevail over the direct when it retrograded4 ,a similar arrangement was made for ,jupiter and ,saturn4 ,in this very ingenious way the varying brightness as well as the varying motions of these three planets were accounted for1 without violating the principle of uniform circular motion1 and without removing ,earth from the centre of the ,universe4 ,she was also still the centre of planetary motion1 in a certain sense2 but to place the true centres of these planets' spheres outside ,earth and in the direction of the sun was a very suggestive step1 and may well have helped ,aristarchus to his bold hypothesis4 ,for he had only to put the sun1 not at some indefinite point along the line ,e ,a1 but exactly at the point ,c1 and it became the centre of motion for ,mars1 ,jupiter1 and ,saturn1 just as in the 8,egyptian theory0 it was the centre of motion for ,venus and ,mercury4 ,in this way he would arrive at the conception of the sun circling round ,earth and carrying all the planets with him1 7a theory which was held by the great astronomer ,tycho ,brah in the sixteenth century ,a4,d474 ,then a flash of insight may have revealed to him the fact that this motion of the sun is apparent only1 being but the reflection of ,earth's own motion2 for she is circling round the sun like all the other planets4 ,it is1 however1 only a guess that the ,moveable ,eccentrics played this part in the theory of ,aristarchus4 ,they did not long hold the field1 because they were not applicable to ,venus and ,mercury1 which are never seen in opposition to the sun4 ,so they were thrown aside for another system1 the ,epicycles1 which illustrates much more simply the stations and retrogressions of the planets1 and can be used for them all4 ,later on1 when more irregularities of motion were discovered1 it was found necessary to combine eccentrics and epicycles1 and by means of this joint system it became possible at last to represent completely1 and as accurately as they could be observed1 all the apparent movements of the heavens4 ,first1 however1 an immense amount of work had to be done1 and new methods devised1 both in observation and mathematics4 ,the man who contributed most1 in both ways1 to make it possible1 was ,hipparchus4 #g4 ,,hipparchus4 ,sidenote3 ,hipparchus c4 #adj ,b4,c4 ,of this great man we know scarcely anything but what can be gathered from the work he did1 and this corroborates ,ptolemy's description of him3 8,hipparchus1 lover of toil and truth 40 ,he lived about ,b4,c4 #adj1 since this is the date of the only book of his still extant1 and his work was not done in ,alexandria1 though he may have studied there in his youth1 and he used the ,museum records4 ,we count him among the ,alexandrians1 as he belongs to this era1 but he seems to have been a private astronomer1 who set up an observatory of his own in ,rhodes1 his native place4 ,here we seem to see him1 surrounded by his primitive instruments and his papyrus books1 patient1 eager1 modest1 seeking no fame and no reward but the joy of his work4 ,by day he would keep watch over the sliding shadow of his gnomon1 would write up his observations1 make long calculations1 and devise new methods in mathematics1 improve and modify his astrolabes and his clepsydras2 at night he would spend long hours with moon1 planets1 and stars1 making up for the defects and shortcomings of his instruments by the skill and care with which he applied them to measure positions in the sky4 ,nothing but the most loving and conscientious care could have raised his work to such a pitch of accuracy1 and made such rude means suffice for such splendid achievements4 ,the book we possess1 apparently an early one1 is chiefly concerned with the positions1 the risings and the settings1 of stars1 and at the end is a list of sixteen which came to the meridian at intervals of an hour3 from this list and the knowledge of spherical trigonometry which he possessed1 it would be possible to calculate the time at night to within about a minute4 ,hipparchus was able to construct a satisfactory theory of the sun and to some extent of the moon1 but he found more irregularities in the planetary motions than ,eudoxus had suspected4 ,the records of his predecessors were not accurate enough for him to construct a theory for the planets1 and he soon realized that one life-time would not be long enough to collect all the data necessary1 so1 as ,ptolemy tells us1 8,hipparchus1 who loved truth above all things10 quietly set to work to make as good and as many observations as possible1 leaving it to his successors to complete and explain them4 ,in the same spirit he undertook the laborious task1 of which ,pliny speaks with awe as a presumptuous scheme1 even for a god1 8rem etiam ,deo improbam10 of numbering the stars4 ,pliny says he was led to do this by the appearance of a ,new ,star1 which blazed out suddenly in the constellation of ,scorpio in b4c4 #acf1 just as ,nova ,persei did in ,perseus in ,february #aija4 ,he saw that even in the upper regions of the eternal heavens1 which ,aristotle had supposed absolutely changeless1 changes may occur1 and in order that even the least of these should not pass unnoticed1 he set to work to note the number1 brightness1 and position of all he could see4 ,this great catalogue of #ajhj stars1 copied by ,ptolemy in his ,almagest1 was the basis for all succeeding catalogues1 from ,spain to ,turkestan1 until quite modern times4 ,in it1 for the first time1 the places of the stars were not merely described according to their position in the constellation figures1 but were noted in degrees on the sphere1 as is done to-day4 ,sidenote3 ,timocharis c4 ,b4,c4 #bhj4 ,one day1 when comparing his notes with those of ,timocharis1 who had worked at ,alexandria about a century and a half earlier1 he found that the brilliant star ,spica1 the ,ear-of-,corn which the ,virgin carries in her hand1 had apparently moved nearer to the autumnal equinox by about #b4 7,two degrees is about four times the angular diameter of the sun74 ,of course he or ,timocharis might have made a mistake1 or ,spica might really be moving among the stars1 or she might be carried along with the rest by a slow movement of the whole star sphere4 ,apparently ,hipparchus satisfied himself that he could rely upon ,timocharis' observation1 and took pains to verify his own2 the second hypothesis could be disproved by the fact that ,spica does not change her place perceptibly among her neighbours2 and finally it became clear that her motion is part of a slow apparent movement of the whole heavens4 ,illustration3 ,fig4 #bd4 ,the movement of ,spica4 ,here was a discovery of first importance1 an unexpected reward of patient accuracy1 of which the white ,spica1 flashing down from summer skies1 may always remind us4 ,hipparchus had discovered the grand cycle which we call the 8,precession of the ,equinoxes10 and before ,spica returns to the same position in which he saw her then1 when she led him to his great discovery1 she will have been watched by generations of astronomers for another twenty-four thousand years4 ,no notice of the cycle has been found as yet among the records of any other nation1 although it seems as if the astronomers of ,babylon and ,egypt1 and other countries where observations had been carried on for many centuries1 must have been aware of it4 ,we can only imagine that at long intervals of time they found that the stars had somehow changed1 and made corrections accordingly1 but without understanding the nature of the change4 ,what ,hipparchus thought about its cause we cannot tell3 probably he left all speculations to future astronomers1 and confined himself to noting the fact4 ,the displacement of ,spica which he observed is shown in the diagram4 ,both ,timocharis and ,hipparchus evidently measured her position indirectly by comparing it with that of the moon1 which was eclipsed at the time1#ej and therefore known to be in the ecliptic and opposite the sun4 ,to find the sun's distance from the equinox was an easy matter1 since his yearly course had long been carefully studied1 and the days on which he passed the equinoxes were regularly observed with the gnomon4 ,spica1 then1 had moved eastward along an arc parallel to the ecliptic1 and since celestial latitude and longitude are referred to the ecliptic1 we may define her apparent movement in astronomical language by saying that while her latitude had remained constant1 her longitude had increased by about two degrees2 and further1 as the celestial equator is oblique to the ecliptic1 this implied that her declination 7position north or south of the equator7 had also varied4 ,the diagram shows that she had a less northerly declination than before4 ---------------------------------------- -------------------------------- #ej ,syntaxis1 book ,,vii42 ,delambre1 ,histoire de l',astronomie ,ancienne ,vol4 ,,ii4 page #bdg 7#ahag edition74 ---------------------------------------- -------------------------------- ,at this rate1 ,spica1 which was now only #f from the autumnal equinox1 would reach it in less than five hundred years1 and thereafter would lie east instead of west of it2 and that she has in fact done so1 may be seen by consulting a modern star atlas4 ,she is now #bb of longitude east of the autumnal equinox1 and nearly #aa south of the equator4 ,her south declination will continue to increase for about five thousand years1 after which she will come north again4 ,ptolemy says that ,hipparchus examined other stars1 and found that they also were increasing their longitude at what appeared to be the same rate as ,spica4 ,the yearly amount of the movement1 derived from the ,spica observations1 is within a few seconds of arc of the true value1 which is #ej seconds2 but ,hipparchus would not fix any value until it had been tested by further observation1 and merely stated that it could not be less than one degree in a century i4e4 #cf seconds per annum4 ,this is a very uncomfortable phenomenon for astronomers1 since every star is for ever changing its measured position on the celestial sphere4 ,take three stars1 one at the north pole1 another on the equator1 and a third in the southern hemisphere4 ,after some years1 the first will no longer be a pole star1 the second no longer an equatorial star1 and the third may have so far increased its south declination that it will be invisible at latitudes in our northern hemisphere where formerly it used to rise above the horizon4 ,one compensation for this inconvenience is that if we know what star was near the pole1 or which stars lay along the equator1 on any given occasion1 we can calculate the date4 ,thus it is believed that the ,great ,pyramid was built when ,alpha ,draconis was the ,pole ,star1 that is1 nearly #cjjj years ,b4,c42 and by a similar method ,mr ,maunder determines the epoch at which the ancient southern constellations were invented1 as we have already seen4 ,the greatest inconvenience1 and also the greatest historical interest1 attaches to stars like ,spica which belong to constellations of the zodiac1 for if they are not stationary with regard to the equinoxes and solstices they are not such simple guides to the length of the solar year as the ancients supposed them to be4 ,the scheme of the ,babylonians for beginning their month ,nisan when the stars of ,dilgan rose just before the sun was an excellent one for a time1 but if they had continued it for many centuries they would have found that their year was too long1 and the months were all falling in the wrong seasons4 ,this has actually happened with ,hindus and ,parsis1 who now keep their ,new ,year in the middle of our ,april1 although when their calendar was fixed1 about thirteen hundred years ago1 the years began at the spring equinox4 ,for the sun is like a runner in a circular race-course who thinks he has completed a lap when he returns opposite a group of spectators originally standing at the starting-point1 but after several laps he finds that the spectators and the goal no longer coincide2 either they1 and also all the others surrounding the course are walking away from it1 or an unseen hand has been moving the flag towards him1 and so shortening the lap4 ,it is the flag which must count1 in any case1 not the spectators1 and with the sun it is the equinox which must count1 and not the stars1 for this is the point at which he crosses the equator1 making day and night equal1 and from this we count the beginning and ending of our seasons4 ,so our year is counted from equinox to equinox1 and is twenty minutes shorter than the 8sidereal10 or star year1 of the ancient ,babylonians4 ,hipparchus1 from observations of equinoxes and solstices1 made the year #cfe days #e hours and nearly #ee minutes1 which is only #f minutes longer than the correct value4 ,illustration3 ,fig4 #be4 ,the ,sun and the ,equinox4 ,after ,hipparchus had made his discovery1 astronomers agreed upon a somewhat clumsy and very confusing device1 by which the zodiac was divided into twelve equal 8signs0 of #cj degrees1 which bear the same names as the zodiacal constellations1 but whose beginning is always reckoned from the vernal equinox4 ,these twelve 8signs of the zodiac10 therefore1 do not now agree with the twelve constellations of the zodiac1 and our present 8first point of ,aries10 which marks the vernal equinox1 is in the constellation of ,pisces4 ,what is the true cause of this strange phenomenon8 ,are the stars really all in motion1 or is it the equinox which moves8 ,the successors of ,hipparchus1 who believed that the stars were fixed on a sphere1 found no great difficulty in conceiving that this sphere had a very slow easterly motion1 round the poles of the ecliptic1 completing a revolution once in #cf1jjj years 7i4e4 one degree in century74 ,to us1 however1 it is impossible to believe that the stars1 which we have found to be at enormous and varied distances1 are all revolving at one rate1 parallel to the ecliptic4 ,the ecliptic1 to us1 is simply the plane of ,earth's own orbit1 and as she moves in it she has a very slow 8wobbling0 motion on her axis1 as well as the rapid spinning of the diurnal motion1 like the 8wobble0 of a spinning top4 ,the top has this motion because gravity is trying to pull it down from its upright position2 the earth because the sun is trying to drag her slightly protuberant equator into the plane of her orbit4 ,the resulting motion is not a revolution of the earth1 nor an apparent revolution of the star sphere round ,earth3 what really happens may be illustrated with the traditional orange and knitting needle4 ,ignoring all motions but the one we are speaking of1 let the points of the knitting needle 7,earth's axis of rotation7 trace out small circles in space1 and the equator of the orange will be seen to alter the direction of its tilt1 but without turning round 7,fig4 #bf74 ,stick a pin in the equator1 and others in north or south latitudes1 between equator and pole2 these will always remain facing you1 but while the pole makes its small circle1 the equatorial pin will be seen to move up and down1 while the tropical and temperate pins trace out ellipses4 ,these are the movements which we see reflected in the stars2 and if ,earth's diurnal rotation were suddenly to cease1 while her revolution in her orbit and the movement of 8precession0 continued1 we should see ,spica1 for instance1 sink slowly lower in the southern sky and after ages rise again northwards1 but there would be very little preceptible movement east or west4 ,the movement observed by ,hipparchus1 then1 was not a movement of ,spica and other stars1 but a movement of the equinox4 ,for the celestial equator is simply a reflection of ,earth's equator in the skies1 and as it keeps changing the direction of its tilt in the way described1 it changes the point at which it cuts the ecliptic4 ,this may best be seen by taking two rings or hoops 7two large curtain rings1 for instance71 one of which just fits inside the other4 ,tilt the inner ring1 so that half of it is above and half below the other ring1 and they touch at two points1 #a and #b 7,fig4 #bg74 ,the outer ring is the ,ecliptic1 the inner the ,equator1 and where they touch each other are the ,equinoxes4 ,now move the inner ring1 not sliding it round1 nor making any difference in the angle between the two1 but simply so that they touch at fresh points1 #a and #b4 ,in this way you may make the points of contact revolve entirely round4 ,this is what the real equinoxes are doing3 while the equator opposite the group of stars in figure #be rises and falls1 the equinox travels on1 and finally returns to the same place4 ,illustration3 ,fig4 #bf4 ,the movement of ,earth's axis1 which is the true cause of ,precession4 ,v is the vernal equinox1 at the intersection of the equator and plane of the ecliptic3 ,,apx the earth's axis1 which always preserves the same inclination 7#bc7 to the plane of the ecliptic4 ,as ,,apx slowly revolves round ,t in the direction of the arrow1 the vernal equinox is gradually shifted to ,v1 and so on4 7,from ,young's 8,manual of ,astronomy10 #aijb47 ,the phenomenon is called 8precession of the equinoxes10 because they thus move on to meet the sun in his yearly course4 ,illustration3 ,fig4 #bg4 ,precession of the equinoxes4 ,the discovery of precession is what has chiefly made ,hipparchus famous1 but the invention of the astrolabe and of spherical trigonometry1 both believed to be due to him1 his star catalogue1 and his many observations1 more accurate than any made before1 were so valuable as pioneer work that ,ptolemy justly called him the ,father of ,astronomy4 ,if ,hipparchus could visit one of our observatories to-day1 and see the clock-driven equatorials1 the transit instruments1 the beautifully divided circles read with microscopes1 and the sidereal clocks1 one wonders whether he would be more astonished at the advance on his astrolabes and clepsydras or at the homage paid to him as one in whose footsteps all astronomers are proud to tread4 #h4 ,,ptolemy4 ,claudius ,ptolemus4 ,i know that ,i am mortal and ephemeral1 but when ,i scan the multitudinous circling spirals of the stars1 no longer do ,i touch ,earth with my feet1 but sit with ,zeus himself1 and take my fill of the ambrosial food of the gods4 ,for more than two centuries after ,hipparchus very little original work was done in astronomy1 and no one seems to have had the courage to take up his unfinished task and study seriously the difficult problem of planetary motions4 ,sidenote3 ,posidonius c4 #ace ,b4,c4 to c4 #ej ,b4,c4 ,posidonius the ,stoic1 who lived for some years in ,rhodes1 made a fresh determination of the earth's circumference1 basing it not on observations of the sun1 like ,eratosthenes1 but of the star ,canopus1 which in his time was just visible at ,rhodes while in ,alexandria it rose 8a quarter of a sign0 7i4e4 #g degrees7 above the horizon4 ,by his method1 the earth was a little smaller1 7#bdj1jjj stadia instead of #bej1jjj71 but it must have been difficult to measure the distance between ,rhodes and ,alexandria over the sea1 and it is impossible to say when a star is exactly on the horizon4 ,posidonius also observed the tides in the ,mediterranean1 and showed that 8,ocean follows the movements of the heavens10 and especially of the moon1 having daily and monthly periods4 ,sidenote3 ,geminus c4 #gj ,b4,c4 ,a little later ,geminus wrote an ,introduction to ,astronomy1 which was an excellent little book as far as it went1 but although he was apparently a native of ,rhodes1 and speaks of ,hipparchus1 he seems to know nothing of his work1 for he does not quote his careful determination of the length of the year1 nor his discovery of precession4 ,sidenote3 ,cleomedes c4 #bj ,b4,c4 ,sidenote3 ,theon of ,smyrna c4 #ajj ,a4,d4 ,nor were other writers1 such as ,cleomedes and ,theon of ,smyrna1 better informed1 and they added nothing new to the advance of astronomical science4 ,sidenote3 ,ptolemy c4 #adj ,a4,d4 ,but at last a worthy successor arose at ,alexandria1 the immortal ,ptolemy1 whom ,dante met in that ,limbo of antique spirits which was almost ,elysium1 although on the brink of the ,inferno4 ,we do not know when ,ptolemy was born nor when he died1 nor where was his native town3 we only know that his first recorded observation was made in the eleventh year of the ,emperor ,hadrian1 that is ,a4,d4 #abg1 and his latest in ,a4,d4 #aej1 and that he lived and studied in ,alexandria4 ,he had splendid opportunities for carrying on the work of ,hipparchus1 for besides the use of the instruments in the ,museum ,observatory1 he had at hand all the ,museum records1 which included the writings of ,hipparchus4 ,ptolemy was not so painstaking and accurate an observer as ,hipparchus1 but he was a very able mathematician to whom it was evidently a joy to handle figures and work out problems4 ,by examining a number of observations spread over several centuries1 and combining them with his own1 he was able to accomplish the task in which so many others had failed1 and to frame a system which embraced all the celestial motions then observed4 ,the monumental summary in which he set forth this system contains a great deal of interesting information about his methods and instruments1 and about the work of ,hipparchus1 for whom he always expresses the most generous admiration4 ,the original name of his book was the 8,mathematical ,system of ,astronomy10 but his admirers having called it the 8,great ,system10 ,megiste ,syntaxis1 the ,arabs affixed their article al and gave it the name it preserves to this day1 of ,almagest4 ,it remained the standard treatise on astronomy until the ,de ,revolutionibus ,orbium ,celestium of ,copernicus appeared in #aedc4 ,the name of his book indicates the scope of ,ptolemy's work4 ,it was to represent all the observed motions of the heavenly bodies by means of a mathematical system1 so that they became amenable to calculation2 but to explain the causes of these motions was thought to lie quite outside an astronomer's province4 ,it was not for a mere observer and calculator to determine which motions were real and which apparent1 else ,ptolemy must have decided in favour of ,earth's rotation1 for he says that it would be much easier to account for celestial motions on this assumption4 ,nor was it his business to investigate the substance of the stars4 ,little did he dream that astronomers would one day solve such problems1 and uphold their conclusions in the face of all the world3 for him1 as for his contemporaries1 the decisions of the philosophers1 and especially of ,aristotle1 were final1 and his task was to describe what he saw in the light of their teaching4 ,he brings forward1 in the introduction to his book1 a few arguments against the absurd notion1 taught by some1 that ,earth is in motion1 turning on her axis or moving through space2 but all that he proves is the immense difficulty1 even to a trained mind1 of accepting these theories1 and the great authority of the philosophers who denied them on abstract principles4 ,educated ,greeks might still discuss the nature of the heavenly bodies1 as in ,plutarch's delightful dialogue ,on the ,face of the ,moon1 7written about half a century before the days of ,ptolemy71 and might ridicule the law of gravity1 laughing at the absurdity of supposing that if the middle of a man's body were at the middle of the earth1 his feet as well as his head would be 8up10 and that falling weights if they reached this point would stop short1 or oscillate to and fro4 ,yet even they all agreed that the fixed stars do most probably move 8in a circle of eternal and never-ending revolution10 and that they are of a pure and eternal substance unlike ,earth2 and for the professional astronomers of ,alexandria these axioms were assumed as the basis of all their work4 ,earth must be immoveable at the centre of the ,universe because the heavy stuff of which she is made sinks necessarily to the centre and there remains in globular form without need of support2 the heavenly bodies must be in motion1 because1 being of ethereal substance1 it is their nature to revolve eternally in circles4 ,this being granted1 we can feel nothing but admiration for the extent of ,ptolemy's knowledge1 the comprehensiveness of his scheme1 and the skill and patience with which he overcame its difficulties4 ,earth1 according to ,ptolemy1 is but a point compared with the immense surrounding sphere in which the stars are set1 and this turns always round us1 communicating its motion 7he does not inquire how7 to sun1 moon and planets1 so that day follows night1 and the heavenly bodies daily rise and set4 ,for the slow movement of precession1 which also affects all heavenly bodies1 ,ptolemy accepted the least value of ,hipparchus1 one degree in a century1 only testing it in rather a perfunctory way1 which was a great pity1 for he might have determined it much more closely after an interval of some #bej years4 ,but one man cannot do everything1 and he doubtless thought it best to spend more time on the planets1 whose intricacies had baffled ,hipparchus and gave him also a great deal of trouble4 ,he retained the great spheres which were supposed to carry them round ,earth1 inside the star sphere1 but the chief feature of his system is the use of small spheres1 which were fixed on the larger1 and therefore called 8epicycles10 while the large were known as 8deferents0 or carriers4 ,the general principle of epicycles is very simple1 as may be seen by comparing the two diagrams4 ,fig4 #bh shows the path of ,mars as we saw it among the stars of ,pisces in the year #aiji4 ,throughout ,july the planet was travelling in its usual direction1 8with the signs10 but on ,august #bbnd it came to a stop1 then turned and travelled backwards 8against the signs0 until ,october #bfth1 when it stopped again1 reversed its direction once more1 and during the rest of the year moved rapidly forward4 ,fig4 #bi shows the principle on which ,ptolemy would have explained this curious track4 ,each planet was supposed to be fixed on a small circle1 the epicycle1 and this was fixed upon a large circle1 or deferent1 upon which it travels in the direction shown by the arrow1 at a uniform speed1 returning to the same place in the sidereal period of the planet4 ,thus ,mars1 as seen from ,earth1 which is near ,c the centre of the deferent1 makes a great circle through all the zodiac in two years1 ,jupiter in twelve1 and so on4 ,but meanwhile the epicycle is rotating round its own centre1 ,c#a1 and when the planet reaches the point marked ,s1 the two motions neutralize one another1 so that it appears stationary1 as ,mars did on ,august #bb1 #aiji4 ,after this1 the motion of the epicycle more than counter-balances the motion of the deferent1 and the planet seems to reverse its direction until it reaches the point on the epicycle marked ,s4 ,after this the two motions are once more in the same direction1 so the planet is seen to move rapidly forward1 as ,mars did after ,october #bf4 ,illustration3 ,fig4 #bh4 ,the ,path of ,mars among the ,stars1 #aiji4 ,illustration3 ,fig4 #bi4 ,the ,epicycle4 ,ptolemy's method of accounting for movements such as those shown in ,fig4 #bh4 ,illustration3 ,fig4 #cj4 ,planet retrograding1 and in opposition 7i4e4 in opposition to the sun47 ,in this extremely ingenious way the strange planetary oscillations were accounted for1 without violating the law of uniform circular motion1 and in a more convenient and satisfactory way than by the concentric spheres of ,eudoxus or the moveable eccentrics of ,apollonius4 ,each of the five planets was provided with an epicycle and a deferent1 and these were made of the proper relative size and given the right speed1 so that the motions should correspond with what we see in the sky4 ,ptolemy calls the oscillation a planet's 8anomaly with regard to the sun10 because 7as we have seen when discussing the moveable eccentrics7 it was known to be connected in every case with a planet's angular distance from the ,sun4 ,on ,september #bd1 when ,mars was in the middle of his retrograde arc in ,pisces1 the sun was exactly opposite1 in the constellation of ,virgo4 ,this is found to be always the case1 not only with ,mars1 but with ,saturn and ,jupiter too4 ,whenever one of these planets has the position ,o on its epicycle1 and therefore is retrograding1 the sun will be found to be exactly opposite in the sky4 ,mars comes into this position1 and is opposite the sun1 once in #ghj days2 this1 therefore1 ,ptolemy called the period of his epicycle1 while a little less than two years was the period of the deferent4 ,the two periods of ,saturn are #cgh days and #bi years nearly2 of ,jupiter #cii days and nearly #ab years4 ,illustration3 ,fig4 #ca4 ,venus1 ,mercury1 and the sun4 ,venus and ,mercury betray their dependence upon the sun in more striking fashion1 for since these planets simply oscillated from one side to the other of the sun1 their epicycles must be supposed to be keeping pace with him all the way round the zodiac4 ,fig4 #ca shows their relation to one another4 ,on ,september #be1 #aiaa1 ,mercury was seen from ,earth as a morning star as far west of the sun as it is possible for him to travel1 while ,venus1 after shining as an evening star all the summer1 had come into line with the sun and become invisible4#ea ,on ,december #g following1 the rotation of the epicycles 7,ptolemy would say7 had brought both planets to new positions1 ,mercury now being an evening star at his 8greatest elongation east10 and ,venus a morning star4 ,but the centres of the two epicycles always remain in a line with one another and the sun1 and so their periods on the deferents are the same as his1 viz4 one year4 ,the epicyclic periods1 or intervals between two 8greatest elongations0 west or east1 are #aaf days for ,mercury1 #ehd days for ,venus4 ---------------------------------------- -------------------------------- #ea ,venus had passed her 8inferior conjunction with the sun0 on ,sept4 #ae4 ---------------------------------------- -------------------------------- ,we still explain the complicated course of the planets by resolving it into two approximately circular motions1 but we know now that only one belongs to the planet itself1 the other is ,earth's own motion4 ,the reason why the sun's position affects the position of every planet is simply that the epicycles of ,mars1 ,jupiter1 and ,saturn1 and the deferents of ,venus and ,mercury are reflections of ,earth's yearly journey round the sun4 ,ptolemy had by no means finished with the planets when he had provided each one with an epicycle to represent the 8anomaly with regard to the sun40 ,hipparchus had noticed that there was another lesser irregularity1 which seemed to be periodical likewise1 although no former system had taken it into account2 and this he called the 8anomaly with regard to the zodiac10 because the speed of each planet and the amplitude of its loop varies slightly according to the part of the zodiac it happens to be in4 ,he suggested that this might be dealt with by combining the two theories of epicycles and eccentrics1 and this suggestion ,ptolemy adopted with success4 ,he placed each deferent with its centre not exactly at the earth1 but at a certain small distance which was different for each planet4 7,this is not shown on our small-scale diagrams1 therefore ,earth appears at the exact centre47 ,the true explanation of this irregularity is that each planet's path is not strictly circular1 but elliptical4 ,besides this1 ,ptolemy had to represent the planet's movements north and south 7note how this varies in fig4 #bh474 ,this was partly managed by the aid of small wheels1 rotating in such a way that they lifted and lowered the epicycle as required4 ,although ,ptolemy quotes ,babylonian observations of lunar eclipses dating back as far as the eighth century ,b4,c41 the oldest planetary observations that he uses were made only four hundred years before his time1 and they were probably ,greek4 ,even these were generally very rough4 ,for instance3-- ,in the #difth year of ,nabonassar1 on the #agth day of ,choeac1 in the morning1 ,mercury was three moon-breadths north of the tail of ,capricorn4 ,in the same year1 ,phamenoth the #cjth1 ,mercury was three moon-breadths south of the horn of ,taurus which is also the foot of the ,charioteer4 ,the first year of ,nabonassar 7a ,babylonian epoch7 corresponds with ,b4,c4 #gdg1 so the #difth year is ,b4,c4 #bea4 ,the months used by ,ptolemy are usually ,egyptian4 ,the later observations1 made with an astrolabe1 were much more precise2 ,ptolemy quotes one from ,theon of ,smyrna1 which states that ,mercury was #c #ej in advance of the ,heart of the ,lion 7,regulus71 and for his own observations he also usually gives the sign1 degree1 and minute4 ,sometimes the planets had been observed so near stars that their positions could be very accurately determined by the aid of ,hipparchus' star catalogue4 ,timocharis1 on a certain morning in the #acth year of ,ptolemy ,philadelphus 7,b4,c4 #bgc71 saw ,venus beside the last star in the wing of the ,virgin 7,beta ,virginis72 ,ptolemy himself saw her so close behind a certain star in ,aquarius that she seemed to touch it with her rays2 and in the #hcrd year after the death of ,alexander1 ,jupiter had been observed to eclipse the ,southern ,ass1 that is the southernmost of the pair of stars on either side of the little cluster in ,cancer which the ancients called the ,manger4 ,illustration3 ,fig4 #cb4 ,the sun's ,deferent4 7,its eccentricity is exaggerated74 ,the sun was much easier to manage than the planets4 ,moving always in the same direction1 he needed no epicycle1 and remaining always in the ecliptic1 no wheels4 ,his one irregularity1 the varying speed in different parts of the zodiac1 which ,meton had discovered and ,calippus confirmed1 ,hipparchus accounted for by placing him on eccentric deferent2 ,ptolemy adopted this without change1 and made the year the same length as ,hipparchus had done4 ,as the slowest motion was observed when the sun was in the sign of ,gemini 7at the time of year corresponding with the end of our month of ,may71 the eccentric was placed as in the diagram2 and the sun1 supposed to be revolving uniformly round the centre ,c1 had a slower motion as seen from ,earth when he went north1 because he was then more distant4 ,we know now that it is really ,earth which revolves round the sun1 but the elliptical shape of her orbit is not unlike the eccentric deferent which the ,greeks gave to the sun1 and they guessed quite rightly from his motion that he is further from us in one part of the year than in the other4 ,this is easily proved to-day by the fact that he grows apparently smaller1 as shown by photographs or measurements taken at different times of year1 but the change was not perceptible to the rougher methods of the ancients4 ,it was a pity that ,ptolemy did not take more pains to verify the work of ,hipparchus on the sun1 for the sun's 8apogee10 or point of greatest distance from ,earth1 has an extremely slow motion among the stars which ought to have been quite perceptible in nearly three centuries2#eb but here again he seems to have thought that where ,hipparchus had given so much attention he might pass on to something else1 and so missed an interesting discovery4 ---------------------------------------- -------------------------------- #eb ,it amounts to #e degrees of longitude in #cjj years4 ---------------------------------------- -------------------------------- ,illustration3 #aiaa1 ,july #a4 #aiab1 ,jan4 #c4 ,fig4 #cc4 ,apparent ,variation in the ,size of the ,sun4 ,to face p #adf ,two half photographs of the ,sun1 taken at ,kodaikanal ,observatory4 ,the smaller was taken two days before apogee1 the larger on the day of perigee4 ,instead1 he worked very hard at the moon1 and added another periodical irregularity to those already known4 ,perhaps his feelings were somewhat mixed when this happened1 his pride and pleasure in his important discovery being counter-balanced by the consciousness that it would still further complicate his lunar theory4 ,our satellite is acted upon by ourselves as well as by the sun1 so that she suffers many perturbations1 for ,earth1 though so small compared with the sun1 is comparatively near4 ,ptolemy's discovery was a difference in her speed at full and new1 as compared with her intermediate phases1 and this periodic difference is called by modern astronomers the 8evection40 ,it was already known that her nodes1 or the points at which she crosses the ecliptic1 are in constant retrogressive motion1 just like the equinoctial points1 where the sun crosses the equator2 but the moon's crossing points1 instead of taking thousands of years to circle the zodiac1 run round in about eighteen years4 ,this was discovered early1 because observations were chiefly made during eclipses1 and at these times the moon is always at a node1 that is to say1 she is crossing the ecliptic1 the sun's path2 otherwise the eclipse could not happen4 ,it was also known that she has a varying speed in the zodiac1 and that her apogee1 where the motion is slowest1 instead of being apparently fixed1 like that of the sun1 also runs round the zodiac1 but with a direct motion1 and in a period of about nine years4 ,we need not enter into all the details of ,ptolemy's arrangements for the moon1 which are exceedingly complicated1 but it is interesting to note that he does not explain her varying velocity by an eccentric1 as with the sun and the planets4 ,she has an eccentric1 but ,ptolemy needed it for representing his own discovery1 the evection1 so he gave her an epicycle1 using it in quite a different way from the epicycles of the planets4 ,this epicycle also revolved while moving on the eccentric1 but in the opposite direction1 and there was so little difference in speed between the two motions that it never brought the moon to a stop1 nor reversed her direction1 but simply increased and retarded her motion alternately during her monthly revolution4 ,thus1 when the moon was at ,m1 in what ,ptolemy called the upper apsis 7or arc7 of her epicycle1 or as we should say in her apogee1 the motion on the epicycle was contrary to her motion on the eccentric1 and made it seem slower4 ,when the epicycle had travelled halfway round the eccentric1 it had also made nearly half a revolution on its own axis3 consequently the moon was at ,m1 near the lower apsis1 or perigee1 and the motion on the eccentric seemed to be accelerated4 ,illustration3 ,fig4 #cd4 ,the moon's epicycle and deferent4 ,the slight difference in speed between the two motions accounted for the continuous displacement of the apogee in the zodiac1 as may be seen from the diagram4 ,for suppose that when in apogee at ,m the moon is seen from ,earth among the stars in the middle of ,taurus4 ,at the return of the epicycle to this place next month1 she has not yet quite completed a revolution on her epicycle but is at ,m1 and will not be in apogee until the centre of her epicycle is advanced #c further in ,taurus4 ,after some time 7five months71 apogee does not occur until the moon is in ,gemini1 and it will be nine years before it occurs again in ,taurus4 ,these are the leading features of the system by which ,ptolemy represented the motions of the planets1 the sun1 and the moon4 ,he is uncomfortably conscious that it may strike us as very complicated1 and in his last book he makes a kind of apology4 ,we must remember1 he says1 that we are not dealing with earthly machines which jar and wear1 but with celestial bodies which have no weight1 cause no friction1 and are eternally the same4 ,delambre somewhat cruelly retorts that he need not have wasted time in writing such rubbish1 but have been content to put his results into tables4 ,but what true astronomer could be content with tables and nothing more8 ,he must try to understand their significance4 ,nearing the end of his great work1 which had cost so much labour1 and was so brilliant a success within its limits1 ,ptolemy allows us to see in this little paragraph that he felt he had but touched the hem of ,nature's veil1 and longed in vain to lift it4 ,the circles which he manipulated so skilfully were only mathematical abstractions to him3#ec what was the reality behind8 ,what were the stars8 whence came their unwearied strength1 their eternal calm8 ,the power of ,egypt1 of ,assyria1 and of ,persia had declined1 ,greece was now laid low1 and it was the day of ,rome1 but still ,venus pursued her ancient path among the little stars of ,aquarius1 and when all faded in the solemn dawn1 the sun arose in his ancient majesty4 ,then ,ptolemy looked at his circles and triangles1 and felt how inadequate they were2 yet it was the nearest approach he could make to truth4 ---------------------------------------- -------------------------------- #ec ,this is evident from the way he treats them1 picking up an epicycle or a deferent just as best suits the purpose in hand and explaining sometimes that either would answer equally well4 ---------------------------------------- -------------------------------- ,they did indeed represent very beautifully the celestial motions1 and also in a general way the variations in brightness or diameter1 but their unreality is betrayed by the fact that the latter was often grossly exaggerated1 as for instance with the moon1 whose epicycle had to be so large1 in order to represent her motions1 that at perigee she ought to appear twice as large in diameter as at apogee6 ,ptolemy can hardly have failed to notice this1 though he does not mention it4 ,with regard to the planets1 he is careful to tell us that he knows no way of finding their real distances3 the ratios of their epicycles to their deferents he had carefully computed in each case1 but to estimate the diameters in stadia was utterly beyond his powers4 ,he believed1 however1 that all were very much nearer than the stars1 and more distant than the moon1 and he found universal agreement among astronomers in placing ,saturn1 ,jupiter1 and ,mars1 beyond the sun1 in order of the periods of their deferents1 which were all longer than a year4 ,venus and ,mercury1 however1 had periods the same as the sun3 on which side of him1 then1 must they be placed8 ,some modern authors1 ,ptolemy says1 thought they were beyond the sun1 but he agrees with the most ancient1 and places them between sun and moon4 ,the general disposition of the heavenly bodies according to ,ptolemy is shown in ,fig4 #ce1 with the periods of epicycles and deferents1 and the directions of the several movements1 but epicycles and spaces between deferents are all made equal4 ,it will be noted that the sun has no epicycle and that the moon turns on hers in a reverse direction1 that the centres of those of ,mercury and ,venus are in a line with the sun1 while the lines joining ,mars1 ,jupiter1 and ,saturn to the centres of theirs are in each case parallel with the line joining ,earth and ,sun4 ,beyond all the wandering stars is the sphere of the fixed stars1 moving in its vast period of #cf1jjj years2 and the whole system is carried round ,earth in one great revolution of a day and a night4 ,illustration3 ,fig4 #ce4 ,the ,ptolemaic system4 ,the arcs of circles are portions of the deferents which carry round the smaller circles 7the epicycles7 in the periods named at the side4 ,and here we have to note one astonishing fact4 ,although the planets were all beyond reach of measurement1 it was not so with the moon1 which the ,greeks rightly recognized as our nearest neighbour4 ,they had actually achieved the long-desired feat of measuring her real size and distance4 ,the fundamental principle on which they worked is easily explained4 ,if we look out of a window at a tree in the garden1 it appears against a background of some distant scenery2 if we alter our position by walking to another window1 the tree changes its place with regard to the relatively motionless background1 and its apparent change of place bears a definite proportion to its distance from us4 ,a tree near the house changes its position greatly1 a tree at the far end of the garden much less4 ,from careful measurements of the angle through which the tree appears to have moved and the distance we have walked between the two windows1 the distance of the tree from the house may be easily deduced4 ,the tree in the garden is the moon1 the distant landscape is the star-spangled sky4 ,the space between the two windows must be increased to thousands of miles1 but the astronomer need not walk it4 ,if he makes his first observation when the moon has just risen1 carefully measuring her position among the stars1 the revolving ,earth will carry him to a new position in a few hours1 when with the moon high in the sky he can once more compare her position with the same stars1 and from the change he then finds he can deduce her distance4 ,the ,greeks thought it was the sky1 and not the earth which moved1 but this makes no difference1 as the question is one of relative motion only4 ,the problem1 however1 when applied to the moon1 is a complicated one1 implying not only skill in trigonometry and the possession of suitable instruments for measuring the necessary angles1 but also accurate knowledge of the size of the earth and the motions of the moon1 since her progress eastward among the stars during the interval between the two observations must be allowed for4 ,hipparchus and the astronomers of ,alexandria were the first to qualify themselves for attacking this difficult problem1 and the proof of their success is that ,ptolemy's value for the distance of the moon is very near the truth as obtained by modern methods4 ,the same method is now used1 only it is found better to do what was not possible for the ,greeks1 namely to compare observations made at places several thousands of miles distant1 for instance ,greenwich and the ,cape1 instead of allowing the same place to be moved by the earth's rotation4 ,when the distance of the moon had been thus discovered1 it was a very simple matter to find her real size from her apparent size4 ,the distances of all other heavenly bodies are too great to be determined by naked eye methods1 for the displacement 7technically called 8parallax07 is so small that it is quite invisible without a telescope4 ,hipparchus had tried repeatedly to measure the distance of the sun1 but recognized that neither the method of ,aristarchus nor any other was really conclusive4 ,it was1 however1 the best attempt that had been made1 and ,ptolemy assumed that he knew the distance to be about twenty times that of the moon1 so he gave the sizes and distances of these two bodies as follows1 taking ,earth's semi-diameter as unit3-- ,according to ,ptolemy4 ,modern ,values4 ,semi-diameter4 ,distance4 ,semi-diameter4 ,distance4 ,moon _/ 7#jbij7 #ei #jbgc #fjc ,sun #e #abaj #ajid #bc1dci ,in ,books ,,vii and ,,viii of the ,almagest ,ptolemy describes the #dh ancient constellations and the course of the ,milky ,way among them4 ,the position of each star is noted as it appears in its constellation-figure1 but the celestial latitude and longitude is also given1 and this great catalogue is evidently taken from ,hipparchus4 ,,ptolemy',s ,,forty-,,eight ,,constellations4#ed ---------------------------------------- -------------------------------- #ed ,taken from the ,almagest catalogue1 as given in ,delambre's ,history4 ---------------------------------------- -------------------------------- ,ursa ,minor ,pegasus ,ursa ,major ,andromeda ,draco ,triangulum ,cepheus ,cetus ,auriga ,orion ,corona ,borealis ,the ,river 7,eridanus7 ,the ,kneeler 7,hercules7 ,lepus ,lyra ,the ,dog 7,canis ,major7 ,the ,bird 7,cygnus7 ,canis ,minor 7,procyon7 ,cassiopeia ,argo ,perseus ,hydra ,botes ,crater ,ophiuchus ,corvus ,serpens ,centaur ,sagitta ,the ,wild ,beast 7,lupus7 ,aquila ,ara ,delphinus ,corona ,australis ,equuleus ,piscis ,australis1 ,aries1 ,taurus1 ,gemini1 ,cancer1 ,leo1 ,virgo1 ,libra1 ,scorpio1 ,sagittarius1 ,capricornus1 ,aquarius1 ,pisces4 ,ptolemy sometimes remarks on the colour of the brighter stars1 and always mentions the brightness1 or 8magnitude0 as we call it now1 for the classification of ,ptolemy 7or ,hipparchus87 was found convenient and accurate enough to be retained by modern astronomers1 and the same system is now continued with the faint telescopic stars4 ,the stars ranked as 8first-magnitude10 or brightest of all1 are fifteen in number1 and as these are evidently the 8quindici stelle0#ee alluded to by ,dante in ,par4 xiii4 #d1 it will be interesting to give a list of them here4 ---------------------------------------- -------------------------------- #ee ,fifteen stars4 ---------------------------------------- -------------------------------- ,,ptolemy',s ,,first-,,magnitude ,,stars4 ,name and ,description ,modern ,name and ,meaning4 in the ,catalogue4 #a4 ,arctouros1 fire-coloured ,arcturus 7the ,bear-,watcher74 #b4 ,the brightest star in the ,vega1 in ,lyra4 7,falling ,eagle1 ,lyre ,arabic74 #c4 ,aichs 7the ,goat7 ,capella 7,little ,goat1 ,latin74 #d4 ,the brightest star of the ,aldebaran4 7,the follower1 ,hyades1 fire-coloured because following the ,pleiades1 ,arabic74 #e4 ,basiliskos 7the royal71 on ,regulus 7,latin equivalent74 the heart 7of ,leo74 #f4 ,the tip of the tail 7of ,leo 7 ,denebola 7,lion's ,tail1 ,arabic74 #g4 ,stachys 7,ear-of-,corn7 ,spica 7,latin equivalent74 #h4 ,the last of the ,water and ,fomalhaut4 7,mouth of the ,mouth of the ,southern ,fish1 ,arabic74 ,fish4 #i4 ,the fire-coloured bright ,betelgueux4 7,shoulder of star on the shoulder ,giant1 ,arabic74 of ,orion4 #aj4 ,on the left foot of ,orion1 ,rigel4 7,foot of the ,giant1 common to the ,water4 ,arabic74 #aa4 ,the last of the ,river ,achernar 7,arabic equivalent74 #ab4 ,the very brilliant star1 ,sirius 7,greek ,seirios1 or fire-coloured1 at the ,sothis1 from the ,egyptian mouth of the ,dog1 ,sept71in ,canis ,major4#ef called the ,dog4 #ac4 ,prokuon 7the preceding ,procyon 7in ,canis ,minor71 which ,dog71 on the thigh of rises before ,canis ,major4 ,prokuon #ad4 ,canopos1 on the rudder ,canopus 7an ,egyptian god1 and 7of ,argo7 a town on the ,nile delta74 #ae4 ,the tip of the right forefoot ,alpha ,centauri4 7of the ,centaur74 ,altair and ,antares were counted as second magnitude1 though we now class them among the first4 ---------------------------------------- -------------------------------- #ef ,lockyer1 ,dawn of ,astronomy1 p4 #aif4 ---------------------------------------- -------------------------------- ,it will be seen from the above that only two of these fifteen brightest stars of ,ptolemy's still bear their ,greek names1 ,arcturus1 and ,procyon2 but most of the other modern names are direct translations1 either into ,latin or ,arabic1 of ,ptolemy's description or name for the star1 while ,vega and ,aldebaran have preserved their original ,arabic names 7much corrupted71 and ,canopus and ,sirius are derived from the ,egyptian4 ,regulus-,basiliskos apparently comes from ,babylon1 for the name of this star on tablets of the second century ,b4,c4 was ,shar-ru1 which means 8royal40 ,ptolemy's 8,last of the ,river0 was taken by his ,arab and other commentators to be the first-magnitude star which consequently they named ,achernar1 but this was too far south to be visible at ,alexandria1 though possibly he heard of it or saw it himself at ,syene1 where it rose over the horizon in his times4 ,delambre thinks it is the same as ,fomalhaut1 which already belongs to two other constellations in the star catalogue2 ,brown suggests it was ,theta ,eridani1 which may have been brighter sixteen centuries ago4 ,perhaps it was the star we now call ,alpha in the ,phoenix1 for this lies between the last bend of the ,river and the ,water of ,aquarius1 and its magnitude is between first and second4 ,the stars of the ,southern ,cross are included by ,ptolemy in the stars about the hind feet of the ,centaur1 though it is difficult to identify each one with certainty3 the positions are not very accurately given4 ,ptolemy wrote also on ,astrology1 or as it was then called ,judicial ,astronomy1 and his work on the subject1 which is in four books1 received the name of the ,tetrabiblios4 ,it seems that astrology was not very much believed in by the ,greeks1 for he protests that the influences of the stars are real1 and can be known and predicted1 but allows that this part of astronomy is much more difficult than the mathematical part1 with which he had dealt in the ,syntax1 and that it has not yet been perfected1 and therefore it is sometimes slandered as untrue4 ,astrologers sometimes make mistakes1 like doctors1 yet both astrology and medicine are useful arts4 ,he mentions especially the ,egyptians as practising it4 ,only second in importance to the ,almagest1 and even better known in old days1 was ,ptolemy's work on ,geography4 ,in this he shows how the size of the earth and the latitudes and longitudes of places on ,earth1 can be discovered by observations of the heavens4 ,for ,earth's diameter he adopts the value found by ,poseidonius4 ,his terrestrial globe had a moveable half-circle attached to the poles1 which was divided into #ij from the equator in both directions1 so that by placing this against any spot on the globe1 its latitude north or south of the equator could be immediately read off4 ,only half the equator was marked on this globe1 and divided into #ahj1 for the known part of the earth all lay within these limits4 ,the parallels of latitude marked were not the same as we use1 though the most northerly fell very close to the ,arctic ,circle3 it showed the latitude of the ,island of ,thule1 far away 8towards the ,bears10 as ,ptolemy expresses it1 meaning that it lay under the constellations near the ,north ,pole4 ,the most southerly was not far below the equator1 and others were marked between these which divided the known ,earth into 8climates10 according to the height of the ,pole and the length of the longest day in each4 ,among the many towns which figured on this globe we may mention ,alexandria1 ,rome1 ,athens1 ,jerusalem1 ,florence1 ,cadiz1 ,paris1 ,strasburg1 ,london1 ,bath4 ,meridians were marked at every #e degrees4 ,from this globe ,ptolemy shows how a plane map may be constructed4 ,he took ,rhodes as the central meridian1 because it had a nearly central position among the 8climates10 and was the place in which ,hipparchus had observed4 ,ptolemy also wrote books on ,optics1 on the theory and construction of ,dials1 and on ,music6 ,v4 ,,retrospect4 ,the ,almagest is the last word of ,greek astronomy4 ,we have seen how from the dawn of ,greek history1 as far as we can trace it back in literature1 the ,greeks were familiar with the skies1 and how the most ancient of their philosophers had tried1 chiefly by abstract reasoning1 to discover the cause of the circling motions--never changing1 never ceasing--of sun and stars4 ,when the seemingly unruly movements of the planets were known1 they still felt sure that there must be some underlying principle which would bring all into harmony4 ,inspired by ,plato1 and helped by the ,egyptians1 ,eudoxus took the first step towards finding this principle by careful study of the planetary motions1 and at last1 after many generations of observers and mathematicians1 ,ptolemy was able to describe these motions as accurately as was possible with the methods available4 ,at first the heavenly bodies had been thought of as gods1 then as worlds like our own1 then as spheres of ethereal fire4 ,they were swept round by a mighty wind1 they ran on wheels1 they floated in the ether1 they were set in crystal spheres2 the controlling force was the principle of number or harmony1 an all-pervading ,world-,soul1 a host of immaterial intellectual ,beings subject to one eternal ,first ,mover4 ,it was also suggested that the greater part of the motions were apparent only1 that ,earth was really in motion1 spinning on her axis1 revolving round a ,central ,fire1 or revolving round the ,sun4 ,but these ideas had not enough evidence to support them when suggested4 ,had a great imaginative thinker1 a ,pythagoras or an ,aristarchus1 arisen after ,ptolemy1 he could have shown in detail how by assuming these two motions the phenomena could be more simply accounted for1 and he could have made out a very good case for their probability4#eg ,but the time was past then for such bold originality1 and the explanation of ,aristotle was universally adopted4 ,he1 as we saw1 placed the abode of the gods1 the rulers of the universe1 beyond the outermost sphere1 and found the principle for which all were seeking1 which should be the key to all celestial motions1 in the law of circular motion4 ---------------------------------------- -------------------------------- #eg ,the changing latitudes of the planets1 for instance1 which gave ,ptolemy much trouble1 are much more easily explained when it is granted that they partly depend upon ,earth's motion in an orbit whose plane is slightly inclined to the planes of their orbits4 ---------------------------------------- -------------------------------- ,the ,greeks had at first thought that the earth was a disc1 under a tent-like sky2 then it was a cylinder1 with the sky in tiers above2 then a huge hemisphere filling half the universe4 ,but they discovered that it was a sphere1 surrounded on every side by the heavens2 and they found its true size1 and that the portion of it which was known to them was less than a quarter of its whole extent4 ,they explained the marvel of ,earth's remaining unsupported in space by the known facts of gravity1 arguing that the falling of every particle of earth towards ,earth's centre proved that it was also the centre of the ,universe1 and that every heavy thing tended thither by a law of nature4 ,they also knew the size and the distance of the moon2 they realized that the planets were all immeasurably remote1 and the stars vastly more distant still4 ,they believed that there were great intervals between the planets1 corresponding to the differences in their periods of revolution1 but the stars were always thought of as set in a great sphere1 and therefore all at the same distance from ,earth at its centre4 ,the relative positions of the stars on this great sphere1 and times of rising and setting of many of them had been known in a rough way for many ages1 through the familiar appearance of the constellations1 named we know not by whom2 but ,hipparchus measured their positions in degrees1 and was able to foretell where any star would be in the sky for any place or time4 ,he also discovered the ,precession of the ,equinoxes1 and this was thought to prove a slow rotation of the star sphere4 ,astrology was learned by the ,greeks in ,egypt and the ,east1 but was never practised with the enthusiasm shown by their teachers4 ,as regards the division of time1 the ,greeks adopted from the ,babylonians the twenty-four hour day which we still use1 and their months began with the young moon4 ,their year therefore had to contain a whole number of months1 and it had sometimes twelve1 and sometimes thirteen1 as with the ancient ,babylonians1 but the system by which this was arranged was quite different1 as they did not depend upon observations of the stars1 but counted the number of days between equinox and equinox by means of gnomons4 ,great difficulties were found in trying to reconcile the lunar and solar periods4 ,the ancient #ab-month year1 used in the time of ,hesiod1 was found to be much too short1 and alternate years of #ab and #ac months made the period too long2 then an eight-year cycle was invented1 but this had to be constantly corrected1 which led to great confusion4 ,as we have seen how carefully ,meton and ,euctemon had determined the length of the tropical year1 even before the days of ,eudoxus1 surprise may be felt that a calendar year was not fixed to correspond accurately with the movements of the sun1 ignoring the irreconcileable movements of the moon1 but it is difficult for us to realize in these days how wrong and strange it seemed if a new moon occurred in the middle or at the end of a month1 instead of at the beginning4 ,in ,aristophanes' play of ,the ,clouds1 which was acted in ,b4,c4 #dbc1 the moon was said to grumble because men would not keep the months as she showed them3-- 8,yet you will not mark your days ,as she bids you1 but confuse them1 jumbling them all sorts of ways1 ,and she says the gods in chorus shower reproaches on her head1 ,when in bitter disappointment they go supperless to bed1 ,not obtaining festal banquets duly on the festal day40 ,then ,meton made his celebrated discovery that nineteen tropical years correspond almost exactly with #bce synodic months 7the difference is in fact only a few hours71 and a cycle of #ai years was arranged1 which was adopted by all ,greek states and dependencies4 ,some of the years had twelve and some thirteen months1 and some of the months #bi and others #cj days1 but all followed in a regular order1 and when one cycle was completed another was begun4 ,the total number of days in each cycle was #fidj1 and as this is only #i hours longer than #ai true tropical years1 it follows that the average year in the ,metonic cycle was only half an hour longer than it should have been4#eh ,the average month was not quite two minutes longer than the true synodic month4 ---------------------------------------- -------------------------------- #eh ,it therefore really approached more nearly the sidereal year1 although the cycle was based on the tropical year4 ---------------------------------------- -------------------------------- ,an improvement even on ,meton's cycle was made by ,calippus1 who proposed to correct its too great length by quadrupling the period1 and then deducting one day from the whole4 ,this would have given a cycle of #gf calendar years1 in which the average year was #cfe days1 or only #aa minutes too long4 ,it does not seem1 however1 to have been ever brought into actual use as a calendar1 but ,ptolemy often refers to the ,calippic epoch as a date from which to calculate celestial phenomena4 ,sidenote3 ,theon of ,alexandria c4 #chj ,a4,d4 ,after ,ptolemy1 the ,alexandrian school of astronomy produced only copyists and commentators1 the last of whom was ,theon1 who saw his daughter ,hypatia murdered and the library burned by fanatical mobs4 ,it only remains for us to see how the ,greek system of astronomy1 brought to so great perfection in the ,almagest1 was neglected for many centuries1 and by whom it was at length rediscovered and made to live again4 ,,vi4 ,,astronomy ,,under ,,imperial ,,and ,,christian ,,rome4 ,b4,c4 #df ,,to ,a4,d4 #ajjj4 ,vos ,o clarissima mundi ,lumina labentem clo qu ducitis annum4 ,georgic ,i4 ,no new school of astronomy arose under the ,roman ,empire1 nor do we even know of one ,roman who devoted his life to the science4 ,the genius of this people lay in other directions1 and ,dante truly says3-- #88,nature ordained in the world a place and a people for universal command 444 to wit1 ,rome and her citizens or people4 ,the which our poet too has touched upon right subtly in the sixth ,virgil1 in the sixth book of the neid1 introducing ,anchises admonishing neas1 the father of the ,romans1 thus3-- 8,others shall beat out the breathing bronze more softly1 ,i do well believe it6 ,and shall draw the living features from the marble2 shall plead causes better1 and trace with the rod the movements of the sky1 and tell of the rising stars4 ,roman6 do thou be mindful how to sway the peoples with command4 ,these be thy arts3 to lay upon them the custom of peace1 to spare the subject and fight down the proud40'#ei ---------------------------------------- -------------------------------- #ei ,de ,mon4 ,,ii4 vii41 8,temple ,classics0 edition4 ---------------------------------------- -------------------------------- ,yet there were some enthusiastic amateur astronomers in ,rome1 for ,cicero tells us of one who had felt old age to be no burden because he was so eager over his astronomical studies1 sitting up sometimes all night to finish his calculations1 and delighted when an eclipse he had foretold came to pass4#fj ,this ardent amateur1 ,sulpicius ,gallus by name1 had found such knowledge of practical value in his younger days1 when he was with the legions in ,macedonia1 for he had been able to persuade the troops not to be alarmed by an eclipse of the moon which was about to happen1 explaining how it was due to natural causes2 and while the soldiers in the opposite camp were shrieking and moaning1 believing that the eclipse portended the death of their king1 the ,roman soldiers remained quite calm4 ,this was on the eve of the battle of ,pydna1 in ,b4,c4 #afh1 a little before the time of ,hipparchus4 ---------------------------------------- -------------------------------- #fj ,de ,senectute4 ---------------------------------------- -------------------------------- ,sidenote3 ,ovid ,b4,c4 #dc-;,a4,d4 #ag4 ,sidenote3 ,virgil ,b4,c4 #gj-ai4 ,sidenote3 ,manilius c4 ,a4,d4 #aj4 ,sidenote3 ,cicero ,b4,c4 #ajf-dc4 ,in ,cicero's own life-time1 and throughout the early days of the ,empire1 it was the fashion to have at least a smattering of ,greek astronomy4 ,ovid tells legends of the constellations2 ,virgil1 at his farm where he lingered happily among his vines1 his cattle1 and his bees1 studied the varying aspects of the constellations in connection with the seasons and the weather2 ,manilius wrote a long poem in five books on astronomy and astrology2 ,cicero himself was quite learned in the subject1 and made a translation of ,aratus1 which had a great vogue4 ,very popular also1 both in classical and medival times1 was his ,dream of ,scipio1 which was an imitation of ,plato's fable of the vision of ,er1 in the ,republic4 ,the moral is that earthly fame is valueless1 since ,earth itself is insignificant compared with the starry heavens1 but that those who practice virtue for its own sake shall return to the stars whence their souls originally came4 ,the youthful ,scipio is transported to the skies in a dream1 and meets the souls of his father and of the elder ,scipio ,africanus in 8a radiant circle of dazzling whiteness1 which you have learned from the ,greeks to call the ,milky ,way40 ,there he sees 8stars which we never saw from this place1 and their magnitudes were such as we never imagined1 the smallest of which was that which1 placed upon the extremity of the heavens1 but nearest to the earth1 shone with borrowed light40 ,but the shining globes of the stars are so great that ,earth seems to have contracted to a point1 and ,scipio gazes at it1 grieved4 8,how long will your gaze be fixed on ,earth80 cries ,africanus4 8,do you not see into what temples you have entered80 and he points out nine spheres which compose the whole universe4 ,the outermost1 in which the stars are fixed1 is most divine1 and within this are seven1 one of which contains the planet called ,saturn upon earth1 the next the glorious ,jupiter1 friendly and helpful to mankind1 then ,mars1 ruddy and terrible1 and the next place in the middle region is held by the sun1 the leader1 prince1 and governor of all other luminaries1 the soul of the world1 filling all things with his light4 ,venus and ,mercury follow him in their courses1 like attendants1 and in the lowest sphere rolls the moon1 kindled by his rays4 ,below this1 all is mortal and transitory1 except the souls given to the human race by the grace of the gods2 above the moon all is eternal4 ,earth1 which is at the centre and forms the ninth sphere1 is immoveable and below all the rest2 and all weights1 by their natural gravitation1 fall towards her4 ,scipio then asks what is the sound which fills his ears1 so loud and yet so sweet8 and he is told that he hears the music of the spheres1 which is too great for mortal ears1 just as the sun is too bright for human eyes to look upon4 ,yet those who make music upon ,earth1 with strings or voice1 like all others who follow heavenly pursuits1 are opening for themselves a path by which to return to the stars1 the true home of the soul4 ,sidenote3 ,strabo born c4 ,b4,c4 #fc4 ,sidenote3 ,seneca ,b4,c4 #c-;,a4,d4 #fe4 ,sidenote3 ,pliny c4 ,a4,d4 #bc-gi4 ,sidenote3 ,proclus died c4 #dhj ,a4,d4 ,sidenote3 ,martianus ,capella1 #eth century ,a4,d4 ,sidenote3 ,simplicius #eth century ,a4,d4 ,other famous ,latin authors who wrote on astronomy were ,strabo1 ,seneca1 and ,pliny1 who quote ,eudoxus and ,aristotle1 ,poseidonius1 and ,hipparchus4 ,when ,ptolemy's work was done there was no great writer to popularize it4 ,three hundred years later ,proclus writes a commentary on it1 and ,martianus ,capella mentions it1 but ,simplicius1 in his commentary on ,aristotle's ,de ,clo1 though he speaks of 8the admirable ,ptolemy10 is evidently unacquainted with his work4 ,no ,roman added anything new to astronomy1 and the most precious parts of their writings for the history of astronomy are some fragmentary notes of early ,greek astronomers whose original works are lost4 ,the practical use of astronomy for measuring time appealed1 however1 to the ,roman people4 ,the most ancient ,roman year 7said to have been introduced by ,romulus7 had only ten months1 ,march being the first1 which explains why the ninth to the twelfth of our present months have the names of ,september1 ,october1 ,november and ,december1 as if they came in the order of seventh to tenth4 ,two more months were added later1 and at some unknown date the old ,octennial or #h-year ,cycle was adopted from the ,greeks4 ,this involved the use of intercalary months of varying length1 and the priests were entrusted with the business of arranging them4 ,but the priests thought it much more important that the length of the year should suit their convenience than that it should conform to the celestial movements1 so they made it long or short according as they approved or not of the persons holding office at the time2 and by the time of ,julius ,csar the calendar had fallen into such confusion that ,march #be1 which was supposed to be the date of the spring equinox1 came in the middle of winter6 ,sidenote3 ,julius ,csar and ,sosigenes ,b4,c4 #df4 ,a drastic reform was necessary4 ,julius ,csar called in the ,alexandrian astronomer ,sosigenes1 and gave the ,empire the calendar which1 with the exception of one small reform made since1 we still use4 ,the moon was thrown over altogether3 there were to be no more intercalary months1 and every year was to be exactly like the last1 except for the addition of one day in every fourth year1 so as to make the average year equal to #cfe days4 ,since the tropical solar year is only #aa minutes1 #ad seconds shorter than this1 many centuries would elapse before the months of this calendar would depart from their proper seasons4 ,march #be was restored to the time of the vernal equinox1 but the first day of the new year was to be ,january #a1 and ,julius ,csar gave his own name to the old fifth month of ,quintilis4 ,each month was to be alternately of #ca and #cj days1 except ,february1 which would only have its full complement of #cj days in the fourth year 7,leap ,year71 and #bi every other year4 ,this reform was regarded by some as an unwarrantable interference by a despot4 ,cicero1 when some one mentioned that the constellation ,lyra would rise at a certain hour1 answered bitterly1 8,yes1 if the edict allows it60 ,unfortunately1 the simplicity of the scheme was a good deal spoiled by the folly of ,augustus1 who could not bear that the month of his predecessor should have #ca days while the next1 the old ,sextilis1 which he turned into ,august1 named after himself1 should have only #cj4 ,so he made two months of #ca days come together1 and took away a day from ,february4 ,afterwards1 ,nero gave his name to ,april1 and ,domitian his to ,october1 but this was more than a long-suffering world could bear1 and the new names were gladly forgotten as soon as the tyrants were dead4 ,although1 therefore1 ,rome was obliged to apply to ,alexandria1 that is to ,greek astronomy1 to carry out the project1 it was ,rome that gave us the most correct and convenient calendar which exists1 better in both respects than that which had been used in ,greece itself4#fa ---------------------------------------- -------------------------------- #fa ,the average year was the same1 #cfe days1 in the old #h-year cycle of the ,greeks1 and also in the ,calippic cycle1 which did not come into practical use4 ,the average year of the ,metonic cycle was longer1 and therefore departed further from the true tropical year4 ---------------------------------------- -------------------------------- ,but alas6 the celestial science1 a willing servant as time-measurer for the daily uses of humanity1 a docile captive to adorn the triumph of literature1 was doomed to a baser servitude4 ,it was in the early days of the ,empire1 and all through the ,middle ,ages1 that the pseudo-science of ,astrology was pursued with passion1 and men spent their lives in studying the paths of planets and positions of the stars1 urged solely by the delusive hope of being able therefrom to read the book of fate and guide the lives of their superstitious clients4 ,from ,chaldea1 its ancient home1 came the most famous astrologers1 but their art was soon learned in every country of ,europe1 and its professors were sought after by peasants and kings--now reviled and banished as impious and leagued with devils1 now loaded with honours and rewards1 revered1 hated1 welcomed1 forbidden1 but always believed in4 ,although when ,christianity was established the seven planets could no longer be regarded as great gods ruling over the lesser gods of the stars1 they were still thought to be mighty revealers of fate4 ,each had his special attributes and influence over man3 the fiery colour of ,mars no doubt suggested the warlike and hostile spirit ascribed from time immemorial to this planet-god2 the slow motion of ,saturn in his distant sphere gave an impression of a mournful morose being1 the 8frigida ,saturni stella0 of ,virgil2 ,venus was the planet of love2 the sun1 of honour and power1 and so forth4 ,each planet was also mysteriously connected with a colour1 and1 the alchemists said1 with a metal2 the sun with gold1 the moon with silver1 ,saturn with pale heavy lead1 etc4 ,each also influenced a special part of the body3 thus1 if ,mercury were unfavourably placed at the moment of a child's birth it would be liable to suffer from lung-disease2 the moon's position affected the brain2 the sun's the heart1 etc4 ,as the planets had distinct and often contrary influences in different positions1 it was necessary1 in determining a man's fate1 to consider the aspect of the whole heavens1 especially at the moment of his birth1 but horoscopes were also cast for any period in his career1 past1 present1 or to come1 enabling him to guard against threatening evils or bad tendencies1 and to seize favourable opportunities4 ,the method was as follows3 the sky-sphere1 as it appeared at the given time and place1 was divided into twelve 8houses10 by drawing meridians 7called 8circles of position07 #cj apart4 ,the house just about to rise on the eastern horizon was called the 8ascendant10 and was the first and most important1 planets situated there having more power than anywhere else2 but each house had its special significance1 the second 7just above the eastern horizon7 being the ,house of ,riches1 the seventh of ,marriage1 the twelfth of ,enemies1 etc4 ,the kind and the strength of each planet's influence depended mainly upon the house in which it happened to be1 and was strongest when the planet was in its own house and also in its favourite zodiacal sign4 ,the sun was considered to be most at home in ,leo1 the moon in ,cancer1 and each of the other five planets owned two of the remaining signs4 ,another important point was the 8aspect0 of the planets with regard to one another1 that is1 their angular distance apart on the sky-sphere4 ,if ,mars and ,jupiter1 for instance1 were in 8opposition10 i4e4 #ahj apart1 the portent was unfavourable1 but in 8trine0 or 8sextile0 aspect 7#abj or #fj apart71 favourable4 ,it is evident that for casting horoscopes it was necessary to be able to calculate for any given time or place the positions of the heavenly bodies2 and for this the skies must be watched1 and the movements known of the stars1 of sun and moon1 and of planets4 ,to this extent1 therefore1 an interest in genuine astronomy was kept alive2 but on the other hand1 the system fostered belief in the overwhelming importance of ,earth in the ,universe1 and the existence of the heavenly bodies for the sole purpose of ruling and foretelling human destinies3 no one cared to inquire what were the underlying laws1 and what the real nature1 of the heavenly phenomena4 ,closely allied to this superstitious belief in planetary influences1 was the dread of comets1 meteors1 and eclipses1 which were everywhere regarded as omens4 ,it was in vain that ,seneca urged the greater importance of investigating the nature of the heavenly bodies about which something was already known1 and of trying to solve the problem worthy of highest consideration1 viz4 whether the earth1 as some had asserted1 was turning rapidly1 or was stationary in a turning ,world4 ,his very protest1 as well as his lengthy dissertation on comets1 shows how far less interesting1 alike to philosophers and public1 were the ordered courses of stars and planets1 than the startling apparition of such rare objects as that great 8hairy star0 which1 appearing suddenly during the games instituted by ,augustus after the assassination of ,julius ,csar1 was thought to be the soul of the dead ,emperor4 ,augustus erected a temple in its honour4 ,rome1 considered as the metropolis of the dominant temporal power1 failed to encourage astronomy2 ,rome as the centre of the spiritual power directly discouraged it4 ,sidenote3 ,cosmas c4 #edj ,a4,d4 ,sidenote3 ,augustine #ced-dcj ,a4,d4 ,in the fourth and fifth centuries after ,christ 8the old heathen theory0 that ,earth is a sphere was opposed by some of the ,fathers1 as inconsistent with certain expressions in the ,bible2 and in the sixth an ,egyptian monk1 ,cosmas ,indicopleustes1 formulated a scheme of the ,universe according to which the ,jewish ,tabernacle was a type and pattern of the ,world4 ,the earth is the flat oblong floor1 surrounded by four seas2 these are enclosed by four massive walls which support a roof 7the firmament or sky71 and above this live the angels1 who move the sun1 moon1 and stars across the firmament1 and let down rain through its window4 ,this childish cosmogony1 supposed to be in entire accordance with ,genesis1 ,isaiah1 and the ,psalms1 bears a curious similarity to one of the oldest 8heathen theories0 of all1 born in the land where ,cosmas lived4#fb ,saint ,augustine1 however1 author of the paralysing doctrine3 8,nothing is to be accepted save on the authority of ,scripture10 does not seem to have considered belief in a spherical ,earth forbidden1 but it was to him a matter of perfect indifference1 while he upheld as an article of faith that in no case could any antipodean inhabitants exist4 ,for they could not be descendants of ,adam1 nor ever hear the ,gospel1 since everyone knew the torrid zone to be an impossible barrier between north and south4 ,another favourite ,church doctrine was that ,jerusalem was the centre of the earth3 this idea1 which it will be remembered has a place in ,dante's cosmogony1 was based on the words in ,ezekiel3#fc 8,this is ,jerusalem3 ,i have set it in the midst of the nations and countries that are round about her40 ,good bishop ,arculf1 and other pilgrims1 were shown a pillar 8on the north side of the holy places1 and in the middle of the city10 which marked the exact spot1 and were told in proof of the assertion that at midday at the summer solstice this pillar cast no shadow6 ,how this proved its central position is a mystery1 and if true the pillar must have been deplorably crooked1 for the sun can never pass overhead in ,jerusalem1 in a latitude of nearly #cb north4 ---------------------------------------- -------------------------------- #fb ,see p4 #de4 #fc ,ezekiel1 v4 #e4 ---------------------------------------- -------------------------------- ,the ,church1 like the ,state1 saw that astronomy had one use1 and applied1 like the ,state1 to ,greek astronomy for a calendar4 ,it was necessary that the ecclesiastical calendar should be luni-solar1 since ,easter1 which corresponds with the ,jewish passover1 must fall on the ,sunday following the first full moon after the ,vernal ,equinox4 ,by #cbe ,a4,d41 when the ,council of ,nice was held1 at which this question was settled1 the ,vernal ,equinox fell on ,march #ba instead of ,march #be1 owing to the neglected eleven minutes in the ,julian year4 ,march #ba was therefore adopted by the ,church as the date of the equinox1 which was assumed to remain constant2 and the old luni-solar cycle of ,meton was used1 and still is used in all churches which celebrate ,easter1 as a basis for the ecclesiastical calendar4 ,the custom of reckoning years forwards and backwards from the birth of ,christ was first introduced by a ,roman abbot1 ,dionysius ,exiguus1 in the sixth century1 but it did not become general in ,christian countries until the ninth century4 ,dionysius adopted as the first day of the epoch1 not ,january #a1 but ,march #be1 the old ,roman date of the vernal equinox4 ,this was because it was ,annunciation ,day1 and it was a belief of the ,middle ,ages that the ,annunciation and also the ,crucifixion actually took place on this day1 and also that the ,creation began on the same date4 ,sidenote3 ,martianus ,capella #eth cent4 ,a4,d4 ,sidenote3 ,cassiodorus c4 #ecj ,a4,d4 ,sidenote3 ,bothius died #ebe4 ,at the break-up of the ,roman ,empire some fragments of classical learning were saved from the wreck1 mainly in the text-books of the 8heathen0 writers1 ,capella1 ,cassiodorus1 and ,bothius4 ,these were preserved by the ,church1 now the only repository of learning4 ,the secular instruction given to churchmen included astronomy1 for while the 8,trivium0 comprised the three elementary sciences of ,grammar1 ,rhetoric1 and ,dialectic1 the 8,quadrivium0 comprised the four advanced sciences of ,arithmetic1 ,astronomy1 ,geometry1 and ,music4 ,but only a mere smattering of the 8,quadrivium0 was taught in this period1 and scarcely more of astronomy than was necessary for determining the date of ,easter4 ,the intimate knowledge and ingenious theories of the ,greeks concerning the celestial motions interested no one any more4 ,sidenote3 ,charlemagne #gcb-had4 ,sidenote3 ,isidore died #fcf4 ,sidenote3 ,bede c4 #fgc-gce ,sidenote3 ,fergil1 #gde4 ,sidenote3 ,dicuil1 #hbe ,from the seventh century1 however1 the ignorance began to be less dense4 ,charlemagne established many schools1 and there were enlightened monks here and there--,saint ,isidore of ,seville1 the ,venerable ,bede1 and ,irish scholars like ,fergil and ,dicuil--whose teachings show that the elements of astronomy as taught by the ,greeks were not totally forgotten everywhere4 ,from the beginning of the ninth century all famous monasteries had schools for laymen as well as for monks4 ,in ,italy the darkness was never quite so deep as in northern ,europe1 for traditions of classical culture never quite died out4 ,and although throughout the long period from ,ptolemy to the end of the tenth century1 astronomy had been almost completely neglected in ,europe1 the way was slowly being made plain for a great revival4 ,the ideal ,empire1 governing the whole world from the ,eternal ,city1 and the ideal ,church making all men brothers1 though neither has ever existed in fact1 did so in men's minds1 as we see clearly in ,dante1 and both exercised a powerful influence4 ,the ,roman ,empire and the ,roman ,church did impress a kind of unity on ,europe as it grew3 there was one civilization1 one religion1 one language in which new thoughts could be conveyed to all4 ,thus the ground was prepared1 and whenever a new school of astronomy should arise or be imported1 it would not remain the property of one nation surrounded by barbarians1 but might at once be shared in and advanced by the whole of ,europe4 ,,vii4 ,,arab ,,astronomy4 ,a4,d4 #gej ,,to #abej4 ,,arab ,,astronomy4 ,once more the scene changes4 ,while ,european science is at low ebb1 if we look to the banks of the ,tigris1 not many miles from the ruins of ancient ,babylon1 we find the centre of a new and famous school of astronomy4 ,sidenote3 ,al ,mansur #gec-gge ,a4,d4 ,from the deserts of ,arabia an immense empire had arisen1 which in less than a century spread eastwards as far as ,india1 and westwards to ,morocco and ,spain4 ,its first capital was ,damascus1 but in #gee1 after the defeat of the ,omeyyad dynasty1 the new ,caliph fixed his capital at ,baghdad1 the wondrous city of the ,thousand and one ,nights4 ,this ,caliph was the renowned ,al ,mansur4 ,to his court there came one day a scholar from ,india1 who was skilled in the knowledge of the stars1 and he laid before the ,caliph a book which treated of things celestial and showed how to foretell eclipses4 ,al ,mansur was profoundly interested1 and ordered a translation of the book to be made into ,arabic4 ,the astronomical system of the ,hindus was at that time very similar to the ,greek1 and there can be no doubt that ,greek astronomy had found its way to ,india several centuries before this4 ,sidenote3 ,haroun al ,raschid #ghf-hji ,a4,d4 ,shortly after this the writings of ,greek philosophers and astronomers were brought to the court at ,baghdad4 ,they had been carefully preserved1 copied1 and translated into ,syriac1 by ,nestorian monks in some of the many monasteries which were founded in ,persia and other countries of the ,east when these heretic ,christians were driven out of ,europe in the fifth century2 and many of the ,court physicians of ,baghdad came from a ,nestorian school of medicine4 ,haroun al ,raschid1 son of ,al ,mansur1 gave orders for ,ptolemy's ,syntax to be translated into ,arabic1 and it now received its name of ,almagest3 several other translations were made later1 and ,aristotle was eagerly studied4 ,this ,caliph sent an embassy to ,charlemagne1 and among the presents sent by the ,east to the ,west were an elephant and a clepsydra4 ,sidenote3 ,al ,mamun #hac-hcc ,a4,d4 ,al ,mamun1 son and successor of ,haroun ,al ,raschid1 is said to have learned astronomy under a ,persian teacher4 ,he also added to his father's library1 and one of the terms of a treaty he made with ,michael1 the ,greek emperor1 was that a collection of ,greek writings should be made throughout the empire1 and forwarded 7originals or copies7 to ,baghdad4 ,moreover1 he was not content with merely reading astronomy1 ,greek1 ,persian1 or ,hindu3 he ordered ,ptolemy's estimate of the size of the earth to be tested1 by measuring an arc of a meridian in his own country1 and he founded a splendid observatory in the province of ,baghdad4 ,the instruments were of the same kinds as the ,alexandrian1 but they were larger1 and better made1 and the circles were more accurately divided4 ,the ,arab astronomers were good observers1 and among them for the first time we hear of astronomers winning fame by skill in instrument making4 ,their dials were superior to those of any other race1 and they made some important improvements in mathematics1 which were immensely useful to astronomers4 ,one great service was the introduction of the decimal notation1 which they learned from the ,hindus4 ,astrology is forbidden by the ,koran1 but it was practised eagerly1 nevertheless1 by the ,arabs1 who constructed tables for this purpose1 and made improvements in the methods used4 ,traces of ,arab contributions to astronomy survive in our words 8zenith0 and 8nadir10 and 8almanac02 our word for a 8cipher0 is the ,arabic 8zifra10 and indicates the main advantage of the decimal notation in arithmetic2 while 8sine0 is the ,latin translation of an ,arabic word1 and reminds us of the great improvements made in trigonometry4#fd ---------------------------------------- -------------------------------- #fd ,arabic gib ,latin sinus1 a fold2 i4e4 the chord folded in two4 ---------------------------------------- -------------------------------- ,sidenote3 ,alfraganus c4 #hdj ,a4,d4 ,sidenote3 ,albategnius c4 #ijj ,a4,d4 ,sidenote3 ,abul ,wefa #idj-iih4 ,among the many names of ,ptolemy's successors at ,baghdad1 strange and uncouth to our ears1 the three most famous are ,mohammed ebn ,ketir of ,fargana1 ,mohammed ben ,geber ,albatani1 and ,mohammed ,abul ,wefa al ,buzjani1 which became known to the ,west under the shortened forms of ,alfraganus1 ,albategnius1 and ,abul ,wefa4 ,sidenote3 ,ebn ,jounis died #ajji4 ,egypt too had her ,arab school of astronomy1 as she had had her ,greek4 ,a little later than ,abul ,wefa1 ,ebn ,jounis drew up the famous ,hakemite ,tables of the sun1 moon1 and planets1 under the patronage of the ,caliph ,hakem of ,cairo4 ,at the western end of the ,arab dominions there were centres of intellectual activity in ,morocco and southern ,spain4 ,cordova1 the city of the marvellous mosque1 had also1 in the tenth century1 an ,academy1 and a library which rivalled that of ,baghdad2 and here1 in the midst of almost ceaseless public strife and agitation1 in a strangely mingled atmosphere of cultured refinement unknown to the rest of ,europe1 and of ferocious barbarism1 of tyranny and tolerance1 heroic deeds of chivalry and treacherous intrigues1 there lived and dreamed and worked men of science and philosophers1 poets1 and artists4 ,sidenote3 ,arzachel c4 #ajhj4 ,sidenote3 ,averros #aabf-aaih4 ,sidenote3 ,al ,betrugi c4 #aaej4 ,sidenote3 ,abul ,hazan c4 #abjj4 ,the best known of the ,spanish ,arabs whose names are connected with astronomy are ,arzachel1 who drew up the ,tables of ,toledo2 ,averros1 the great philosopher1 author of ,de ,substantia ,orbis1 and a commentary on ,aristotle's ,metaphysics1 who saw 8a black spot on the sun0 on the day he had predicted a transit of ,mercury2 and ,al ,betrugi 7or ,alpetragius7 who wrote on the ,spheres4 ,there was also a certain ,abul ,hazan1 a renowned geographer1 who travelled across ,north ,africa1 and made a catalogue of #bdj stars1 including some not given by ,ptolemy4 ,of all the astronomical writings of the ,arabs1 one of those which became earliest and best known in ,europe was the ,elements of ,astronomy and ,chronology of ,alfraganus4 ,this was actually used by ,dante as his favourite text-book1 and he mentions it in the ,convivio4 ,i shall therefore give a short account of its contents1 following the edition of ,golius1 printed in ,arabic and ,latin at ,amsterdam in #affi4 ,in the first chapter ,alfraganus gives an account of the calendars used by different nations--,arabs and ,berbers1 ,syrians1 ,romans1 ,persians1 and ,egyptians4 ,after this he plunges at once into a description of the ,universe1 as portrayed by ,ptolemy1 and follows his master so closely that his book is almost a much-abridged and simplified ,almagest1 with a few additions1 and with all the mathematics left out4 ,it is accepted almost without dispute among learned men1 says ,alfraganus1 that the sky is spherical1 and rotates on two fixed poles1 one north1 one south4 ,this is proved by the observed movements of the stars4 ,equally undisputed among the learned is the fact that ,earth and water together form a globe1 which is surrounded by air4 ,the spherical form of ,earth is proved by the fact that phenomena such as lunar eclipses and shooting stars are seen at a later hour by observers in the ,east1 and by the changing height of stars above the horizon as one travels north or south4 ,earth is at the centre of the universe1 and is but a point compared with the heavens4 ,there are two principal celestial motions3 7#a7 the 8prime motion0 which causes the whole sky to revolve with every celestial body1 and produces day and night2 7#b7 the proper motions of the sun and other stars in the opposite direction and round other poles4 ,the great circle of the first motion ,alfraganus calls the ,equator of the ,day2 that of the second1 the ,star-bearing ,circle1 i4e4 the zodiac1 or more precisely1 the ecliptic4 ,the twelve zodiacal signs are then described1 with the division of each into degrees and minutes1 the positions of the equinoxes at the beginning of ,aries and ,libra1 and of the solstices at the beginning of ,cancer and ,capricorn4 ,the ,colure is described as a great circle cutting the zodiac 7i4e4 ecliptic7 and equator at the points where they are furthest apart 7i4e4 at the solstices74 ,this greatest difference was found by ,ptolemy to be #bc #ea but according to the measurement ordered to be made by ,al ,mamun of pious memory1 which was carried out by a number of experts1 it is #bc #ce4 ,this value is adopted and quoted subsequently throughout the book of ,alfraganus4 ,alfraganus then proceeds to explain very clearly how the movements of sun and stars appear from different latitudes on ,earth--on the equator1 at stations further north1 and finally at the pole4 ,he shows how it happens that on the equator day and night are always of equal length1 and the sun passes exactly overhead twice a year2 whereas day and night vary more and more in length1 according to season1 as one travels further north1 and the sun is lower2 until at last at the pole the year consists of one long day and one equally long night1 the celestial pole is in the zenith and the celestial equator on the horizon1 so that the sky revolves like a mill-stone 7i4e4 the stars do not rise and set1 but trace out horizontal circles1 like a wheel which is not upright but flat on the ground74 ,the circumference of ,earth1 as determined by ,al ,mamun of glorious memory1 is #bj1djj miles1 and the diameter1 therefore1 is nearly #fejj4fe ,alfraganus deduces from this the area of the whole ,earth and also of the habitable portion of ,earth4 ,the latter extends only from the equator to #ff #be ,north1 and its longitude at the equator is equal to #ahj or #aj1bjj miles1 at the northern limit to #djhj miles4 ,this is divided into seven 8,climates18 as in ,ptolemy's ,geography1 the first lying a little north of the equator4 ,alfraganus gives for each the length of the longest day1 the height of the pole above the horizon1 the extent of territory1 and the principal regions and towns comprised4 ,he admits that south of the first climate as far as #j is some land1 surrounded by sea1 and sparsely inhabited1 and north of the seventh climate are a few towns1 but these are of no account4 ---------------------------------------- -------------------------------- #fe ,the ,arabian mile was equal to #djjj 8black cubits10 and if this is the ,egyptian and ,babylonian cubit1 the values are rather too large1 being in round numbers #bf1ejj and #h1ejj ,english miles1 instead of #be1jjj and #hjjj4 ---------------------------------------- -------------------------------- ,our author treats next of the risings and settings of the zodiacal signs1 and of the division of the day into #bd equal or #bd 8temporary0 hours 7see p4 #bf74 ,after this1 the unanimous opinion of wise and learned men concerning the spheres is duly set forth in seven chapters2 how there are eight great ,orbs1 the smaller enclosed within the greater1 the star sphere being the outermost and largest of all2 how epicycles are fixed in these2 how only the star sphere has its centre exactly in ,earth1 the others being slightly eccentric2 what are the positions of the poles and centres of the great spheres and the small epicycles1 their relative sizes1 and their different velocities as they turn2 finally1 how well the system represents the movements of sun1 moon1 stars1 and planets4 ,the moon's mean daily motion1 resulting from a wonderful combination of five circular motions1 amounts to about #ac #aa2 the sun's is #ei1 and he completes a revolution in #cfe days 8less an insignificant fraction40 7,this being a popular treatise ,alfraganus apparently thinks it unnecessary to state the length of the year more precisely74 ,the sluggish motion 78motus tardissimus07 of the star sphere1 which is communicated to all the rest in addition to their own motions1 is #a in a century1 according to ,ptolemy1 so that it completes a revolution in #cf1jjj years4 ,coming now to the fixed stars1 their number1 and brightness1 ,alfraganus does not copy ,ptolemy's great catalogue1 but informs us that learned men 78sapientes07 did number all the fixed stars as far south as they could see in the #crd climate1 and divided them according to magnitude into six classes4 8,to the first class they assigned the bright and shining stars such as ,canis 7,sirius7 and ,procyon1 ,vultur ,cadens 7,vega7 and ,cor ,leonis 7,regulus74 ,stars a little less bright they called second magnitude3 such are ,alfarcatein and ,benet ,naax10 ,arab constellations which the ,latin version describes as the two bright stars of ,ursa ,minor1 and those brilliant ones in the tail of ,ursa ,major4 ,thus they proceeded with the other magnitudes1 the smallest measured being of the sixth magnitude4 ,the number of stars in each class is given1 and the total of #ajbb2ff then a list of the #ae first-magnitude stars1 which are the same as ,ptolemy's 7,see p4 #aee74 ,this is followed by a list of the ,arab 8,mansions of the moon40 ---------------------------------------- -------------------------------- #ff ,the ,catalogue of ,hipparchus is said to have contained #ajhj stars1 but ,ptolemy's has only #ajbb4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #cf4 ,method 7erroneous7 of estimating planetary distances1 described by ,alfraganus4 ,the distance ,e ,a being known1 and ,e p being assumed equal to it1 the distance ,e a can be calculated from the known ratio ,e a3 p a4 ,so far 7with the exception of the mansions of the moon7 the ,arab writer has followed the ,greek1 but we have now reached a point where he diverges4 ,ptolemy1 he says1 only tells us the distances and sizes of the sun and moon1 and said nothing about the other heavenly bodies2 but if we suppose the greatest distance of the moon to be the same as the least distance of ,mercury1 and from this calculate his greatest distance 7for the ratio is known71 and if we proceed in the same way with ,mercury and ,venus1 we shall find that the greatest distance of ,venus equals the least distance of the sun as given by ,ptolemy4 ,ptolemy's least distance for the sun1 which was totally wrong1 was #aafj ,earth-radii3 the greatest distance of ,venus1 calculated in this way from ,ptolemy's figures1 was #aaej4 ,alfraganus takes this unlucky coincidence as an indication that there is only just sufficient space between each sphere and the next to allow their respective epicycles to pass one another1 and upon this entirely erroneous assumption he proceeds to lay down the distances of each planet from the earth1 and finally of the stars1 which are all supposed to be at the same distance1 equal to the greatest distance of ,saturn4 ,who first suggested this method of estimating distances we do not know3 the first mention of it occurs in ,europe in the fifth century ,a4,d4 ,the following table shows the distances obtained in this way3-- ,,greatest ,,distance4 ,in ,semi-,diameters of ,earth4 ,moon #fd ,mercury #afg ,venus #aabj ,sun #abbj ,mars #hhgf ,jupiter #ad1dje ,saturn and ,stars #bj1aaj ,in this1 the moon's distance is approximately correct1 but the sun's is not much more than one-twentieth of its true value4 ,to set the stars at a distance of only twenty thousand times ,earth's semi-diameter seems to us to bring them very close1#fg but they would still be beyond measurement by naked eye methods1 so it is no contradiction to ,alfraganus' earlier statement that ,earth is a point compared with the heavens4 ---------------------------------------- -------------------------------- #fg ,earth's diameter1 and even ,earth's distance from the sun1 is too small a unit4 ,light1 travelling #ahf1jjj miles a second1 takes #d years to reach us from the nearest star4 ---------------------------------------- -------------------------------- ,the ,arabs also believed that they had succeeded in measuring the apparent diameters of the planets and even of the points of light which are all we can see of stars1 so ,alfraganus gives the accepted sizes of all4 ,i give them below in descending order of size4 ,the modern values in the third column show how false were the results obtained by this mistaken method4 ,,diameter3 ,,earth #a4 ,alfraganus4 ,modern ,values4 ,sun #e #aji ,the #ae first-magnitude ,arcturus1 ,sirius1 stars #d ,spica1 and others1 much larger than the sun4 ,jupiter #d_/ #aa ,saturn #d #i ,other stars1 in order of ,various4 ,some certainly magnitude1 #bnd to #fth 444 larger than the sun4 ,mars #a ,earth #a #a ,venus _/ _/ ,moon _/ ,mercury _/ ,in the above table the size of the moon 7whose parallax had been found by the ,greeks7 is the only one which is nearly right4 ,the sun is far too small1 and so are the stars4 ,we cannot yet know with certainty the diameter of any star1 but they are all comparable with the sun1 and many are enormously larger4#fh ,as their distances are all different1 some of the brightest may be comparatively small1 and some of the faintest the largest of all4 ---------------------------------------- -------------------------------- #fh ,it is impossible to measure the diameter of any star1 even with the help of the most powerful telescopes1 but in the case of a double star at a known distance the movement of the components as they travel round their common centre of gravity enables us to determine the gravitational force they exercise on each other1 and thus their combined mass2 and their spectra give some idea of their density4 ,for instance1 the mass of the double star ,alpha ,centauri is nearly twice that of our sun2 and as the components appear to be about equal to each other1 and both show a spectrum resembling that of the sun1 we may conclude that ,alpha ,centauri consists of two stars1 each of which has about the same diameter as our sun4 ,arcturus has a diameter far greater1 some say ten times1 some not less than twenty-five times as great as the sun6 ---------------------------------------- -------------------------------- ,the ,arabs took a backward step in adopting these imaginary measurements1 for ,hipparchus had recognized that only the moon was near enough to measure1 and although ,ptolemy accepted ,aristarchus' value for the sun1 he distinctly stated that the planets had no parallaxes and he could not tell their distances4 ,the next four chapters describe briefly the risings1 settings1 and meridian transits of stars as seen from different latitudes on ,earth2 the heliacal risings and settings and the conjunctions with the sun of planets1 stars1 and moon3 the phases of the moon and the direction of her horns at different times of the year4 ,parallax is then clearly defined and discussed4 ,a description follows of the earth's shadow1 thrown by the sun into space--its tapering form1 its position1 always pointing away from the sun1 its width at the distance of the moon1 and its length according to ,ptolemy4 ,this is stated to be #bfh times ,earth's semi-diameter1 which is nearly correct1#fi for although ,alfraganus believed 7from ,ptolemy's erroneous parallax7 that the sun1 was much nearer than it really is1 it followed from this--since the size was deduced from the distance--that he also thought it much smaller1 and the length of a shadow thrown by any dark body is longer the nearer it is to the light-source1 but shorter1 the smaller is the light-source4 ---------------------------------------- -------------------------------- #fi ,the mean length of ,earth's shadow 7which varies a little with her distance from the sun17 is #heg1jjj miles1 or #baf times her semi-diameter4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #cg4 ,earth's ,shadow4 ,the two last chapters are devoted to eclipses1 lunar and solar1 and ,alfraganus points out that1 unlike lunar eclipses1 eclipses of the sun vary in duration and magnitude according to the place on ,earth from which they are viewed4 ,the book concludes3 8,enough having now been said concerning the eclipses of sun and moon1 by the goodness of ,god we have been enabled to bring this writing to an end2 and for this ,deo ,laus et ,gloria40 ,the time at which ,alfraganus lived is not precisely known1 but it seems to have been in the first half of the #ith century1 since from internal evidence he wrote after1 but probably not much after1 the death of ,al ,mamun4 ,his name indicates that he was a native of the beautiful and fertile country1 shut in by lofty mountains1 which lies on either side of the ancient river ,jaxartes4 ,he was surnamed the ,calculator1 and wrote on sun dials and the astrolabe1 but we do not know of any observational work of his4 ,later ,arab writers although they all continued to base their work on that of ,ptolemy1 improved on some of his estimates4 ,albategnius began his book 8,on the ,number and ,motions of the ,stars0 by saying that having studied ,ptolemy's ,syntax and mastered the ,greek methods1 and having noticed some errors in the positions of the stars1 he felt impelled to add to ,ptolemy's observations1 as the latter had added to those of ,abrachis 7,hipparchus71 for it is not given to man to attain perfection4 ,he gives a much more accurate value for precession than ,alfraganus had done1 who merely copied ,ptolemy1 for he makes it #ed seconds yearly1 or one degree in #ff instead of in #ajj years4 ,his tropical year1 too1 is only two minutes shorter than the modern value1 so that he improved upon ,hipparchus in this respect2 and he made the discovery which ,ptolemy missed1 the motion of the sun's apogee4 ,he merely notes1 however1 that the position found by himself differed from that given in the ,almagest1 so it is doubtful whether he realized his discovery1 or merely thought that a large error had been made4 ,although some of ,ptolemy's values were thus corrected by the ,baghdad astronomers1 no change was made in his theory of epicycles and eccentrics1 which all accepted as having a concrete existence1 partly because at first they did not distinguish between these and the spheres discussed by ,aristotle1 which he had described as formed of the same material as the planets4 ,as ,ptolemy does not explicitly state that his circles were only symbols1 this is not surprising4 ,they are formed1 say the ,arabs1 of the fifth essence al-acir 7the ther72 and they conceived the epicycle as gliding over the outer surface of the deferent1 like a small soap-bubble on the back of a big one4 ,this notion1 coupled with ,ptolemy's erroneous distance of the sun1 misled them1 as we have seen1 into their imaginary discovery of planetary distances4 ,sidenote3 ,tabit ben ,korra #hbf-ija4 ,it was also partly due to ,ptolemy's unfortunate habit of adopting the doubtful or merely provisional results of his predecessors1 and representing them as well established and confirmed by himself1 that they fell into another error4 ,tabit ben ,korra1 noting the discrepancy between the ,greek and the ,arab value of precession1 investigated the question1 and put forward a theory that the motion varies both in amount and direction4 ,in his book 8,on the ,motion of the ,eighth ,sphere0 he describes an elaborate apparatus which he had invented to account for this variation1 but he is very modest about it1 and after narrating the results obtained by others1 and how they had left them to be judged by posterity1 he adds 8,and this is what we have done1 with ,god's blessing40 ,then follow his figures and tables4 ,this imaginary discovery was accepted by some of the ,arab school1 and it appears in many medival tables1 instead of precession1 under the name of the 8trepidation40 ,the belief in the material reality of the spheres caused the ,arabs to add a ninth sphere to the eighth of ,ptolemy and ,alfraganus1 for they thought it was enough to demand of the eighth that it should carry all the stars and give them their slow movement of precession 7or trepidation74 ,this ninth sphere1 therefore1 enveloped the whole universe3 upon it were fixed no epicycles1 no stars1 no planets1 but it originated the 8prime motion0 by turning once in a day and night1 and communicating this revolution to all the inner spheres4 ,it became known in medival astronomy as the ,primum ,mobile or first moving4 ,sidenote3 ,nasir-ed-din #abja-abgd4 ,sidenote3 ,alfonso #abbc-abhd4 ,the ,baghdad school of astronomy came to an end with ,abul ,wefa in #iih1 and the ,spanish schools died out when ,seville and ,cordova were captured by the ,christians in the thirteenth century2 but the impetus given to the study of ,greek astronomy and astronomical observation was carried on by other nations4 ,in ,persia a fine observatory was founded by ,nasir-ed-din2 in ,spain the ,christian king1 ,alfonso ,x1 ordered tables to be drawn up to replace those of ,arzachel1 and the ,libros de ,saber to be compiled4 ,the movement in ,persia was short-lived1 but in ,europe the revival of astronomy had begun4 ,,viii4 ,,the ,,return ,,of ,,greek ,,astronomy ,,to ,,europe4 ,a4,d4 #ajjj ,,to #acjj4 8,he hath made everything beautiful in ,his time2 also ,he hath set the infinite in their heart40 ,in the whole cycle of the changing year there is no moment so wonderful in northern climes as that which comes in early ,february1 when winter is not yet past1 but for the first time the promise of spring is felt in the air4 ,not a leaf has unfolded its green1 but the swelling buds on the trees make a purple flush all over the woods1 the blackbird sings an exultant strain1 and in some sheltered copse you may find a delicate daring primrose already in bloom4 ,such a moment in the history of ,europe was the year #ajjj ,anno ,domini4 ,after the apathy1 the ignorance1 the despair of the ,dark ,ages1 a new spirit began to breathe hope into the hearts of men4 ,a love of beauty1 a new religious fervour1 a passionate desire for knowledge took possession of them4 ,yet it was nearly a hundred years before the great universities which were one expression of this new spirit sprang up in ,paris1 ,bologna1 ,oxford1 to be followed later by similar centres of intellectual activity in all parts of ,europe4 ,by the end of the twelfth century it is said that there were #ajj1jjj students in ,bologna4 ,a large number were foreigners from many lands1 for as ,latin was the universal tongue in education1 all nations could understand each other1 and scholars often wandered from one university to another1 attracted by the fame of some great master4 ,similarly the doctors would teach first in one town and then another4 ,men of all ages and classes met together1 for among the students were young boys and elderly ecclesiastics1 poor scholars who begged their bread1 and rich nobles who came with a tutor1 a chaplain1 and a whole suite of servants4 ,there were no colleges or even lecture-halls3 the students joined together in small groups to take a house and share expenses1 and the professor lectured in his own house1 or in a hired room1 or1 if the audience was large1 in a city square1 speaking from an open-air pulpit4 ,all were united in the ardent pursuit of learning1 and none complained if the floors were merely covered with straw1 and the lectures1 which often lasted three hours1 began before sunrise on winter mornings in rooms which had no light and no fire4 ,was it not enough that when leaving at the end of university life one was technically said to be 8going home a wise man08 ,one cause of this intellectual fervour was the influence of ,arab culture1 with which ,europe came into contact through the crusades1 and through the ,saracens in ,sicily1 and the ,moors in ,spain4 ,for this reason astronomy and astrology took a high rank among the new studies4 ,to distinguish between the two is quite a modern idea1 and in medival times either name was used indifferently to cover both subjects4 ,in ,bologna university in the thirteenth century an important school of medicine and arts arose1 through ,arab influence1 and the ,arab doctors of medicine introduced the system of astronomy which they had learned from the ,greeks4 8,a doctor without astrology10 it was said1 8is like an eye that cannot see20 and before prescribing for a patient it was thought quite as important to determine the positions of the planets1 as the nature of the disease4 ,by the beginning of the fourteenth century there were salaried professors of astrology in ,bologna1 and they were more highly esteemed than any other professors except those of philosophy4 ,illustration3 ,a ,,medi,,val ,,astronomer4 ,to face p4 #bjj4 ,from a painting by ,gerard ,dow4 ,sidenote3 ,cecco d',ascoli d4 #acbg4 ,one of their duties was to provide 8judgments0 7i4e4 to cast the horoscope7 gratis for students4 ,but the dignity was a perilous one4 ,legitimate prediction by astrology bordered close on necromancy1 which was banned by the ,church1 and one of ,bologna's most famous professors in astrology1 the learned ,cecco d',ascoli1 was burned at the stake in ,florence in #acbg for the crime of sorcery4 ,astronomy1 like other subjects1 was taught chiefly by lectures and 8repetitions10 or classes for catechizing the students on what they had already heard4 ,books could also be had1 though they were dear1 on hire or purchase1 from the university 8stationers0 or librarians4 ,the first books on ,greek astronomy which found their way into ,european universities were ,latin translations of ,arabic commentaries and paraphrases of ,aristotle1 which travelled from ,moorish academies in ,spain to ,paris4 ,the astronomical treatises with strange technical terms in ,arabic were hard work to translate1 especially when they had already passed through several languages1 as often happened4 ,thus it was possible to possess a work of ,aristotle which was a ,latin translation of a ,hebrew translation of a commentary upon an ,arabic translation of a ,syriac translation of the original ,greek text6 ,sidenote3 ,urban ,,iv41 pope #abfa-abfd4 ,but meanwhile some of ,aristotle's works in the ,greek entered ,italy from the ,east1 as a result of the crusading conquest of ,constantinople in #abjd4 ,the first translations of these into ,latin were very poor1 but later on ,st4 ,thomas ,aquinas1 with the help of ,pope ,urban ,,iv41 had a better version made4 ,sidenote3 ,frederick ,,ii4 #aaid-abej4 ,sidenote3 ,sacrobosco died c4 #abef4 ,sidenote3 ,roger ,bacon c4 #abad to c4 #abid4 ,it was long before a good ,latin version of ,ptolemy's ,almagest could be obtained4 ,a translation was made from the ,arabic in #abcj1 at the bidding of the ,emperor ,frederick ,,ii41 who did much1 at his ,sicilian court1 to encourage ,arab literature1 but this translation was not much known or used4#gj ,the teachings of the ,almagest became known chiefly through popular expositions such as those of ,alfraganus1 ,albategnius1 and ,john ,halifax of ,holywood1 an ,english monk who became famous under his ,latinized name of ,sacrobosco4 ,he was not an astronomer but had studied ,greek and ,arab writings1 and finding that the study of astronomy was neglected because books on the subject were difficult both to procure and to understand1 he compiled a useful handbook1 which became widely popular and remained so for several centuries4 ,several other writers1 notably ,roger ,bacon1 wrote on the spheres1 on the use of astrolabes1 and on astrology4 ,the books prescribed in ,bologna for the course in ,astrology and ,mathematics were as follows3-- ---------------------------------------- -------------------------------- #gj ,it was also translated from ,arabic into ,latin at ,toledo1 in #aage4 ---------------------------------------- -------------------------------- ,a work on ,arithmetic or ,algebra4 ,euclid1 with a thirteenth century commentary4 ,the 8,theorica ,planetarum10 which was either a free translation of ,ptolemy's ,almagest or an exposition of its principles4 ,the ,alfonsine ,tables4 ,the ,canons of ,de ,lignires 7of ,amiens1 #accj ,a4,d471 i4e4 rules for the use of astronomical tables to determine the motions of the heavenly bodies4 ,portions of the ,canon of ,avicenna 7the ,arab philosopher74 ,a treatise on the ,astrolabe by a ,jewish astrologer of the ninth century4 ,a treatise on the ,quadrant4 ,the astrological works of ,ptolemy1 with a commentary4 ,a book by ,alchabicius 7fl4 c4 #hej ,a4,d471 probably his work on astrology4 ,a book on astrological medicine4 ,sidenote3 ,alfonso ,x4 #abbc-abhd4 ,from the above we gather that a past master in ,astrology would understand the elements of mathematics1 and all the astronomy that ,ptolemy's translator or commentator could teach2 that he had learned--at least in theory--the use of astronomical instruments and tables1 and a good deal of astrology1 including its use in medical practice4 ,the tables were intended mainly for astrological predictions4 ,the standard ,alfonsine ,tables had been drawn up in #abeb by ,christians1 ,jews1 and ,moors1 under the direction of ,alfonso ,x4 king of ,castile4 ,they contained lists of positions of the planets1 dates of ,easter moons1 8golden numbers0 and 8dominical letters0 of the ecclesiastical calendar1 times and other details of eclipses1 together with methods for finding the places of planets1 and for casting horoscopes4 ,this is the ,alfonso who was so much shocked at the complexity of ,ptolemy's multitudinous circles that 8the ointment of his name is marred10 says ,fuller1 8with the dead fly of his atheisticall speech03 8,if only the ,creator had consulted me1 when ,he made the world1 ,i would have given some good advice60 ,sidenote3 ,sylvester ,,ii4 7,gerbert7 ,pope1 #iii-ajjc4 ,not one of all these books pretended to add any new discovery to astronomy3 all intellectual energy was absorbed in eagerly assimilating the knowledge stored by ,greeks and ,arabs4 ,nor were any great observatories founded in ,europe yet1 in imitation of ,alexandria1 ,rhodes1 or ,baghdad4 ,the instruments in use were celestial globes and small portable astrolabes and quadrants for determining positions and angular distances between the heavenly bodies4 ,the learned pope1 ,sylvester ,,ii41 who had studied astronomy among the ,moors in ,spain1 was so skilful in making astrolabes that some accused him of gaining the art by selling his soul to the devil6 ,sidenote3 ,albertus ,magnus #aaic-abhj4 ,sidenote3 ,aquinas #abbe-abgd4 ,when ,aristotle first came to ,paris 7about #abjj ,a4,d471 in ,oriental dress1 and accompanied by ,moslem authors1 the ,council of ,paris denounced him as an infidel2 yet in less than fifty years all his works were placed on the list of books prescribed in the university course4 ,this was brought about by the ,dominicans4 ,in six of his twenty-one ponderous volumes the ,german friar ,albertus ,magnus paraphrased the whole of ,aristotle's works1 and stripping his philosophy of the pantheistic and materialistic garb in which the ,spanish ,arab ,averros had clothed it1 presented the ,greek philosopher as an ally of ,christianity4 ,the ,italian saint1 ,thomas ,aquinas1 pupil of ,albertus1 in his much more readable commentaries and treatises1 popularized this idea so successfully that ,aristotle--the ,philosopher1 as he was called--speedily became as great an authority on every other subject as he had always been on logic4 ,it was a mutual victory4 ,aquinas captured the ,greek for the ,christian faith2 ,aristotle won the western world to accept his theories4 ,no longer was the doctrine of a spherical ,earth called 8an old heathen theory03 it was almost an integral part of the ,catholic faith4 ,aristotle's demonstration that there must be a ,first ,mover1 himself unmoved1 became an argument for the existence of the ,christian ,deity2 the intelligences which preside over the celestial movements were interpreted as the nine hierarchies of angels whose existence was taught by the ,church4 ,to the eight spheres of the ,greeks and the ,primum ,mobile of the ,arabs1 the thirteenth-century ,christians added the all-embracing heaven of heavens1 the ,empyrean1 to be the abode of the ,creator and blessed spirits4 ,within the central immoveable earth they placed ,purgatory and the fires of ,hell4 ,they accepted the limits of the habitable earth as laid down by ,ptolemy1 but kept ,jerusalem as the centre by asserting that it was situated #ij from the ,pillars of ,hercules1 and #ij from the mouths of the ,ganges4 ,eden1 the earthly paradise of ,adam and ,eve1 was represented on contemporary maps as in the extreme ,east1 separated by sea from the eastern boundary of the inhabited earth4 ,thus theology and science supported one another4 ,all learning was sacred1 and all that man's mind is capable of understanding he might aspire to know1 for the search if rightly pursued would lead at last to the perfect bliss of beholding with unveiled eyes the ,source of all ,truth4 ,,second ,,part4 ,,the ,,astronomy ,,of ,,dante4 ,i4 ,,popular ,,astronomy ,,in ,,italy ,,in ,,dante',s ,,time4 ,in the first part of this book we have sketched the story of man's thoughts about the stars1 from primitive days until the thirteenth century of our era4 ,we have seen what a wealth of imagination and invention the ,greeks brought to bear on the purely empirical science of ,egypt and ,babylon and ,homeric ,greece1 and how out of all the systems devised by them between #fjj ,b4,c4 and #ajj ,b4,c4 one survived1 which was completed and expounded by ,ptolemy in the second century after ,christ in his great ,syntax or ,almagest4 ,its fundamental principles were that ,earth is a sphere1 at rest in the centre of the ,universe1 surrounded on all sides by spherical heavens1 and that the movements of all the heavenly bodies are explained by a combination of uniform circular movements4 ,in the succeeding centuries there were few who could appreciate his work1 and during the ,dark ,ages it was scarcely known in ,europe1 but was preserved by ,nestorian ,christians in schools and monasteries of ,persia1 whence it was unearthed by ,mahomedan princes1 five centuries after ,ptolemy's death2 and when another five centuries had passed it was brought back to ,europe1 tinged with ,oriental thought1 and almost immediately became immensely popular among scholars4 ,then there arose one of the world's greatest poets1 and1 a thousand years after ,ptolemy's death1 immortalized his work1 writing in a tongue unknown to ,ptolemy1 and for nations which in his day were only just struggling into existence4 ,as ,homer reflects to us man's primitive conceptions of the ,universe1 so ,dante reflects the ideas of ,ptolemy and his school4 ,and because he lived just at this time he was able to write with perfect confidence1 quoting ,ptolemy and the ,catholic ,faith side by side as infallible authorities in astronomy4 ,had he lived in the early ,christian centuries he would have been obliged to choose between classical and orthodox views2 had he been born three centuries later1 he would have found ,copernicus and ,galileo ranged against ,ptolemy and the ,church4 ,even ,milton writing a hundred years after the death of ,copernicus1 could not make up his mind which system to adopt1 and the astronomy of ,paradise ,lost is a curious jumble of ancient1 modern1 and transitional ideas4 ,he describes the ,primum ,mobile as a 8firm opacous globe0#ga on which ,satan alights and walks about1 yet later on tells us that we need not believe in its existence if ,earth is turning on her axis2#gb the archangel ,raphl describes to ,adam the ,creation1 at which he was present1 yet declares that he himself does not know whether the sun circles round ,earth1 or ,earth round the sun4 ,this the great ,architect had wisely concealed from man and angel1 ---------------------------------------- -------------------------------- #ga ,paradise ,lost1 ,,ii4 #dah4 #gb ,paradise ,lost1 ,,viii4 #cd-ch4 8perhaps to move ,his laughter at their quaint opinions wide1 ,hereafter when they come to model heaven1 ,and calculate the stars1 how they will wield ,the mighty frame1 how build1 unbuild1 contrive1 ,to save appearances2 how gird the sphere ,with centric and eccentric scribbled o'er1 ,cycle and epicycle1 orb in orb40#gc #gc ,paradise ,lost1 ,,viii4 #gg-hd4 ---------------------------------------- -------------------------------- ,such inconsistencies are not found in ,dante's work1 and nothing could have been further from his thoughts than to imagine the ,creator mocking at man's mistakes and ignorance4 ,like the angelic doctor1 ,thomas ,aquinas1 he considered man's desire for knowledge as one of his highest attributes1 and believed that it had been given to him in order to be satisfied4 ,but before we examine ,dante's writings1 it will be interesting to form an idea of the spirit in which astronomy was generally regarded by his fellow-countrymen1 and what were his opportunities of studying it4 ,dante ,alighieri was born in ,florence in or about the year #abfe1 and died in #acba4 ,there can be no doubt that the part of star-lore which appealed most to the general public in ,italy at this time1 educated and ignorant alike1 was the art of the astrologers4 ,the movements of the heavenly bodies were regarded not merely as omens1 but as the actual instruments by which every event on ,earth was brought to pass4 ,every class of plants1 every race of animals1 was thought to be under the protection of some planet or constellation2 so if it was a bad year for certain fruits1 or if an epidemic broke out among the cattle1 this was because the guardian planet was unfavourably placed1 or an evil planet was in the protecting constellation4 ,floods and drought1 prosperity and death1 properties of minerals such as the lodestone's attraction for iron or the emerald's alleged power of blinding serpents1 the instincts of animals and the impulses of men1 all were subject to the influences of the stars2 and naturally the men who understood and interpreted their movements were held in great repute4 ,some of them were unscrupulous quacks1 like the one-eyed prophet of ,brescia1 mentioned by the gossiping friar ,salimbene4#gd ,he 8called himself an astrologer and diviner10 and received daily 8ten great pennies of silver1 and nightly three great ,genoese candles of the purest wax0 from a political party in ,modena1 as a recompense for advising them how to act4 ,on one occasion he prophesied a victory for them1 but he had little faith in his own words1 for being threatened with violence if his prophecy should fail1 he 8carried off all that he had gained and went his way without saluting his hosts40 8,then10 adds the friar1 8the men of ,sassuolo began to mock them1 as men who sacrifice to devils and not to ,god1 as it is written in ,deuteronomy40 ---------------------------------------- -------------------------------- #gd ,all quotations from ,salimbene's ,chronicle are taken from ,coulton's ,from ,saint ,francis to ,dante4 ---------------------------------------- -------------------------------- ,but most of these men1 like ,asdente of ,parma1 sincerely believed in their own ability to foretell events1 and they usually combined some other favourite forms of soothsaying1 as well as a little alchemy1 with astrology4 ,asdente is described by ,salimbene as 8a poor working cobbler1 pure and simple1 and fearing ,god1 and courteous and urbane2 illiterate1 but with great illumination of mind40 ,his proper name was ,master ,benvenuto1 but he was 8commonly called ,asdente1 that is1 toothless1 by way of contrary1 for he hath great and disordered teeth and an impediment in his speech1 yet he understands and is understood well4 ,he dwells at the bridge-head of ,parma1 hard by the city moat and the well1 along the street which goes to ,borgo ,san ,donnino40 ,this humble prophet was said by ,dante to be the best known citizen of all ,parma 7,conv41 ,,iv4 xvi4 #fe-ga73 he was asked to dinner by a bishop1 and consulted by the warring factions of ,reggio and ,parma4 ,he was said to have foretold the death of two popes1 and a naval defeat of ,pisa by ,genoa4 ,the greatest generals of the day governed their tactics by the advice of astrologers who regularly accompanied them to the field and the camp4 ,the famous ,ghibelline1 ,guido of ,montefeltro1 who is called by ,villani the cleverest soldier of his times#ge retained ,guido ,bonatti#gf in his service and was believed to have gained his great victory at ,forli 7in #abhb7 through the advice of this astrologer4 ,bonatti is diversely described as a tiler and a lawyer1 but whatever his original occupation may have been he found that the position of private astrologer brought him both more fame and more money4 ,he wrote a book on ,judicial ,astronomy1 and ,vincent de ,beauvais describes him as celebrated throughout the western world for his knowledge of the art4 ---------------------------------------- -------------------------------- #ge ,croniche ,fiorentine1 ,bk4 ,,vii4 par4 #hj4 #gf ,inf4 xx4 #aah4 ---------------------------------------- -------------------------------- ,but ,bonatti's fame was faint and fugitive compared with that of the wizard ,michael ,scot4 ,he is one of the picturesque figures of the thirteenth century1 round whom so many legends have gathered that the facts of his life are difficult to glean4 ,it seems that he was born in ,fifeshire of a noble ,scottish family1 at the end of the twelfth or beginning of the thirteenth century1 that he studied in ,oxford and ,paris1 and then spent some time in ,toledo4 ,here he learned ,arabic1 and probably also astrology1 for it was so commonly practised there1 especially among the ,arabs and the ,jews1 that it was sometimes called the ,toletan art4 ,afterwards he went to ,germany1 and was discovered by ,frederick ,,ii41 who took him to ,italy4 ,his great learning earned the admiration of ,pope ,gregory ,,ix41 who speaks of him quite affectionately in a letter to the ,archbishop of ,canterbury2 and it is said that ,honorius ,,ii4 would have liked to make him an archbishop4 ,but ,sir ,michael the ,scot found ,frederick's court more congenial4 ,the ,emperor1 who was himself a poet1 was a munificent patron of literature and art1 and attracted to himself men of talent from all parts of the world4 ,the culture of both ,east and ,west met at that brilliant ,sicilian court#gg which was his for fifteen years before the title of ,emperor was added to that of ,king of ,naples and ,sicily4 ,indeed it was his 8fellowship with ,saracens0#gh which was one great reason for the accusation of heresy on account of which ,dante placed him among the ,epicureans in the ,inferno4 ,he knew ,arabic1 as well as ,french1 ,german1 ,italian1 ,latin1 and ,greek4 ,michael ,scot's acquaintance with ,moorish literature and language was a bond of sympathy between them2 he became astrologer to ,frederick1 and at the ,emperor's wish he superintended a new translation of ,aristotle's works from ,arabic into ,latin4 ,his taste for astronomy is evidenced by the fact that out of these he chose to translate the ,de ,clo himself4 ---------------------------------------- -------------------------------- #gg ,v4 ,e41 ,i4 xii4 #bj-ce4 #gh ,villani1 ,croniche ,fiorentine1 ,,vi4 #a and #bd4 ---------------------------------------- -------------------------------- ,an absurd story is told by ,salimbene about ,frederick and ,michael ,scot1 which1 however1 shows what was believed of his capabilities as an astronomer4 ,the ,emperor one day asked him1 when they were in the palace together1 how far they were from the sky1 and the astrologer told him the distance4 ,they then took a long journey together1 during which the palace was secretly lowered1 and on their return ,frederick asked casually whether the sky could really be so distant as ,michael had said4 8,whereupon he made his calculations1 and made answer that certainly either the sky had been raised or the earth lowered2 and then the ,emperor knew that he spake truth40 ,michael ,scot is said to have warned ,frederick that he would die in ,florence1 for which reason the ,emperor would not enter that city2 but having thoughtlessly gone to a town called ,florentiola he died there2 8for this10 adds the historian1 8is almost always the way1 the devil tricks one by a play upon words40 ,it is curious to contrast this remark1 attributing ,michael's prophecy to the evil powers1 with ,salimbene's quotation from him1 in exactly the same spirit as if he were quoting from an ,old ,testament prophet3--8that the word of ,michael ,scot may be fulfilled in them1 which he wrote in his verses wherein he predicted the future1 #8,and the factions at ,reggio shall hold ill words together4'0 ,the same author brackets him with others who have foretold the future1 in a list which reads curiously to us--8,abbot ,joachim1 ,merlin1 ,methodius and the ,sybil1 ,isaiah1 ,jeremiah1 ,hosea1 ,daniel1 and the ,apocalypse1 and ,michael ,scot who was astrologer to the deposed ,emperor ,frederick ,,ii40 ,besides these prophetic verses1 ,michael wrote several books which treat almost exclusively of astrology1 alchemy1 and other occult 8sciences10 and even in the fifteenth century it was said that his magic books could not be opened without danger1 because of the fiends who were thereby invoked6 ,he seems to have returned to his native ,scotland to die1 but the date is very uncertain4 ,we do not know whether ,dante's picture of him is drawn from memory1 or hearsay of some who had seen the lanky ,scotsman among the southerners1 by nature taller and thinner than they1 and worn by his prolonged studies4 8,quell' altro che ne' fianchi cos poco ,michele ,scotto fu1 che veramente ,delle magiche frode seppe il gioco40#gi 7,inf4 xx4 #aae-aag74 ---------------------------------------- -------------------------------- #gi 8,that other1 round the loins ,so slender of his shape1 was ,michael ,scot1 ,practised in every sleight of magic wile40 ,carey4 ---------------------------------------- -------------------------------- ,it was perhaps the winning personality or the prudence of the canny ,scot which enabled him to bring a brilliant career to a peaceful close1 favoured by the ,church as well as by the excommunicated ,emperor1 although his studies were of so dubious a nature1 and he was intimate with heretic ,mahomedans and ,jews4 ,cecco d',ascoli was not so fortunate4 ,this learned ,italian received the high and honoured post of professor of astrology in ,bologna1 where he lectured and cast horoscopes for his students4 ,he was well versed in natural science1 but the shady side of astrology had a fatal attraction for him3 he fell under suspicion as a sorcerer1 was condemned1 and burned at the stake in ,florence in #acbg 7six years after ,dante's death74 ,the reputations achieved by these and other thirteenth-century astrologers in ,italy1 belonging to such different ranks of life1 show what an immense importance was attached to their art by the general public4 ,yet we shall be greatly mistaken if we think that it was only to acquire skill in this fascinating pursuit that men thronged to hear ,cecco lecture1 or pored over ,latin manuscripts4 ,the intense ardour for knowledge which marks this period made them eager to understand the world around them and the sky above their heads4 ,illustration3 ,,astronomy4 ,from a fresco in the ,spanish ,chapel of ,santa ,maria ,novella1 ,florence4 ,to face p4 #bag4 ,it would be a shame1 writes one1 to live in a house and not know how it is built or what shape it has1 never to examine the walls1 and floors1 and ceilings1 nor to consider the use of the wooden beams used in its construction4 ,in like manner we should not be content without understanding the form and structure of the ,universe in which we live4 ,man1 with his upright attitude and his head held high1 unlike the animals1 was designed by his ,creator to look and listen1 to know and comprehend this marvellous ,universe1 and especially that noblest part of it above him1 the heavens and their wonderful movements4 ,for thus alone can he learn to know ,god ,himself1 the great ,architect of the ,world4 ,in writing thus1 ,ristoro1 the monk of ,arezzo1 was not only echoing the thoughts of ,plato and ,cicero1 he was expressing the feeling for astronomy as a noble and elevating study which was general among thoughtful men of his time4 ,it was expressed also in contemporary art4 ,visitors to the 8,spanish ,chapel0 in the cloisters of a ,florentine church will remember seeing on the frescoed walls the figure of ,astronomy as she was personified in ,tuscany in the fourteenth century4 ,she sits among her peers1 the sciences of the ,trivium and ,quadrivium1 the only one who wears a crown2 her fair hair frames a spiritual face1 one hand is lifted heavenwards1 the other holds a celestial sphere1 on which the broad band of the zodiac crosses the 8equator of the day40 ,at her feet sits a kingly figure in flowing robes1 also crowned1 and with a face of singular beauty and refinement2 he gazes up into the skies with a rapt expression1 and on his knee is a book in which he writes what he sees4 ,this nameless figure was identified doubtfully by ,ruskin as ,zoroaster1 who was considered by many as the inventor of astrology1 but surely it can be no other than ,ptolemy with his ,almagest4 ,for ,ptolemy1 the prince of astronomers1 was often and naturally confused with the royal race who had patronized astronomy at ,alexandria2 as for instance by ,omons1 a thirteenth-century writer1 who says in his ,image du ,monde that 8,ptolemy king of ,egypt0 wrote the ,almagest4 ,the curious mode of dressing the hair and beard may have been thought by the artist to represent an ancient ,egyptian fashion4 ,ptolemy1 we know1 was universely acknowledged at the time to be 8,master of ,astronomy10 as ,brunetto ,latini calls him4 ,his ,almagest was only known indirectly1 but it was believed to contain all that could be known about the movements and the nature of the heavens4 ,some minor additions and corrections had been made1 as we have seen1 by the ,arab astronomers1 but the system was accepted as a complete and satisfactory explanation of all celestial phenomena4 ,hence no professional astronomer was expected to make discoveries2 he was simply well versed in the work of those who went before him1 skilful in the use of a few simple instruments and tables1 and practised in applying the principles of astrology4 ,a general notion of the ,ptolemaic system was widely diffused4 ,for those who could not read ,latin there were encyclopdic works written in the vernacular and in a popular style1 such as the ,trsor of ,brunetto ,latini1 and these always contained a section on astronomy4 ,the average educated man probably had only vague ideas about epicycles and eccentrics1 and perhaps had never heard of the ,arab estimates of the sizes of the planets2 but he would know that astronomy taught that ,earth is a globe1 motionless at the centre of the universe1 and smaller than any of the stars2 he would know the names of the seven planets 7including among these the sun and moon71 and probably also their colours1 their periods1 and their astrological significance2 the zodiacal constellations would be familiar1 especially as they were often used decoratively2 and he would believe that stars and planets are set in crystalline transparent spheres4 ,moreover1 he would often be more of an astronomer than he knew1 for he would learn almost unconsciously many things of which modern men are ignorant4 ,the ill-lighted streets and the dangers of night journeys would force him to be better acquainted with the motions and phases of the moon than most of us are to-day2 he would know when and where to look for different stars2 and the want of a watch would make it necessary for him to be able to take his time from the sun at any season of the year4 ,he could1 however1 sometimes consult a sundial on a church wall or in a private garden1 and the church chimes rang out at tierce1 and nones1 and vespers4 ,these were heard at intervals which were much longer in summer than in winter1 for the system of 8temporary hours0 was used by the ,church1 and the service of tierce was held halfway between sunrise and noon 7or nones71 and vespers was halfway between noon and sunset4 ,,ii4 ,,dante',s ,,studies4 ,,dante',s ,,studies4 ,dante was far above the level of the average educated man4 ,not that his scientific ideas were in advance of his age3 on the contrary1 one special interest that they have for us is that they illustrate1 like his political and religious views1 the beliefs and feelings of the period4 ,his authorities were the authorities of all1 but he had studied them and made their thoughts his own1 as few others did1 except some churchmen and professed scholars4 ,the extent and depth of his reading is evident from his own writings1 and his great learning is noted with admiration by all his biographers4 ,giovanni ,villani1 in the earliest account we possess of ,dante1 says that he was 8a great scholar in almost every branch of learning1 although he was a layman40 ,boccaccio would have us believe that while still a child1 so young that he might be expected to spend his time playing with other children or sitting on his mother's knee1 he gave the whole of his time to reading and learning4 ,lionardo ,bruni1 however1 assures us that though he was an ardent student1 and showed unusual powers at an early age1 he by no means tried to 8sever himself from the world1 but living and moving about amongst other young men of his age1 he approved himself gracious and skilful in every youthful exercise40 ,it was wonderful1 he says1 how ,dante maintained all his social and civic intercourse while he pursued his studies so fervently4 ,in truth1 the poet's troubled life was far removed from that life of calm retirement which one thinks suitable for a scholar4 ,in his early youth he experienced a passionate love and sorrow2 a year before the death of ,beatrice he was fighting for ,florence in the great battle of ,campaldino1 nor was it the first time he had borne arms2 in #abif he spoke in the council of the ,hundred2 in #acjj he was ambassador for the ,tuscan ,league to ,san ,gemignano1 and was elected to the highest office a citizen could hold in his native city1 that of ,prior2 in #acja he was ambassador to the ,pope in ,rome1 and in the year following he was exiled4 ,after this he was always wandering1 often in great poverty1 dependent on first one patron and then another1 always hoping that some turn of affairs would restore him to ,florence1 always taking a keen and active interest in ,italian politics1 until he died1 still in exile1 at ,ravenna4 ,add to this the difficulties common to all scholars of his day1 viz4 absence of printed books1 public libraries1 and journals1 etc41 and we must marvel how he ever found the opportunities and the serenity of mind for his prolonged studies4 ,boccaccio adds another obstacle--his wife6 ,to console him for the death of ,beatrice1 his friends and relatives persuaded him to marry a wife of their choosing with melancholy results3-- 8,dante formerly had been used to spend his time over his precious studies whenever he was inclined1 and would converse with kings and princes1 dispute with philosophers1 and frequent the company of poets4444 ,now1 whenever it pleased his new mistress he must at her bidding quit this distinguished company1 and bear with the talk of women1 and to avoid a worse vexation must not only assent to their opinions1 but against his inclination must even approve them4 ,he who1 whenever the presence of the vulgar herd annoyed him1 had been accustomed to retire to some solitary spot1 and there to speculate on the motions of the heavens1 or the source of animal life1 or the beginnings of created things1 or may be to indulge some strange fancy1 or to compose somewhat which after his death should make his name live into future ages1 he now1 as often as the whim took his new mistress1 must abandon all such sweet contemplation1 and go in company with those who had little mind for such things40#hj ---------------------------------------- -------------------------------- #hj ,boccaccio's ,vita di ,dante2 ,translation from ,toynbee's ,dante ,alighieri 7,oxford ,biographies71 pp4 #ib1 #ic4 ---------------------------------------- -------------------------------- ,however1 after a long tirade against wives1 ,boccaccio owns that as far as concerns ,dante the picture is entirely imaginary4 ,he believes the marriage was an unhappy one1 because after his exile ,dante and his wife never met again1 but we have no evidence whatever that while they were together their life was as ,boccaccio depicts it4 ,doubtless family life and the care of four children interfered to some extent with ,dante's studies1 but the one detail ,boccaccio affirms as fact among his fancies1 namely that the poet refused for nineteen years to see his wife1 seems rather to imply that one thing poor ,gemma did know how to do was to leave her husband in peace when he did not desire her company4 ,when and where ,dante began to study astronomy seriously it is not easy to say4 ,his favourite study in his youth was poetry1 but his parents 7says ,bruni7 gave him a good general education1 engaging such teachers as could be found in ,florence1 where as yet there was no university4 ,but seeing how clever the boy was1 his relatives and friends helped and encouraged him1 and among the latter ,bruni mentions ,brunetto ,latini4 ,this famous ,florentine was a very learned lawyer1 who during ,dante's infancy and boyhood held high offices of state in the city4 ,it is not possible1 therefore1 that he should have had pupils at this time1 and he cannot have been ,dante's master in any strict sense of the word1 as ,vasari affirms1 and as many commentators have assumed on the strength of the moving interview between these two in the ,inferno4#ha ,dante's affectionate greeting mingled with reverence1 and the fatherly solicitude of ,brunetto1 suggest just such a connection as ,bruni indicates4 ,the elderly man had taken an interest in the budding genius of the boy1 and had held inspiring conversations with him from time to time on serious subjects1 and by his own example had encouraged the youth to win fame through his pen4 ,for ,dante was no doubt well acquainted with ,brunetto's ,tesoretto1 and his more ambitious and voluminous ,trsor1 which ,brunetto specially commends to his care4#hb ,this was a compendium of knowledge1 a small part of which was devoted to the elements of astronomy1 and it may well be that this short epitome was ,dante's first introduction to the science4 ---------------------------------------- -------------------------------- #ha ,inf4 xv4 #bc et seq4 #hb ,inf4 xv4 #aai4 ---------------------------------------- -------------------------------- ,some have thought that ,brunetto's advice to ,dante to follow his star 8,se tu segui tua stella 44410#hc indicates that he had cast the poet's horoscope2 but there is no evidence that ,brunetto had ever practised astrology1 or even that he took special interest in it above other branches of learning4 ---------------------------------------- -------------------------------- #hc 8,if thou follow thy star10 ,inf4 xv4 #ee4 ---------------------------------------- -------------------------------- ,villani and other biographers tell us that after his banishment from ,florence1 therefore in middle age1 ,dante went to the ,university at ,bologna1 but they seem to have made this statement rather because of its probability than because they knew it for fact4 ,it is1 however1 quite possible that he spent a couple of years there1 between #acjd and #acjf4 ,he probably left his 8primo rifugio0#hd at ,verona when ,bartolommeo della ,scala#he died in ,march #acjd1 and we know nothing of his whereabouts till ,august #acjf1 when he was in ,padua1 as is proved by a fifteenth century document4#hf ,now in #acjf a number of ,ghibelline students and professors left ,bologna for ,padua2 and we know that ,dante had friends among the ,bolognese professors1 for later on he seems to have corresponded with ,cecco d' ,ascoli1#hg and ,del ,virgilio entreated him to come and receive the laurel crown1 an invitation which the poet refused in one of his ,latin ,eclogues4 ,bologna and the ,bolognese are referred to several times in ,dante's works1 and the friar ,catalano is no doubt alluding to the school of theology at the ,university when he says in ,inf4 xxiii4 #adb-add that he used to hear at ,bologna much about the wickedness and the lies of the ,devil4 ,one vivid passage can hardly be anything but a personal reminiscence of the ,carisenda1 the leaning tower at ,bologna4 ,the poet compares his fear when he saw the giant ,antus stooping over ,virgil and himself to the sensation of looking up at the ,carisenda from beneath the leaning side1 when a cloud is passing over it1 and the spectator feels that the tower is about to fall upon him4#hh 7,the tower was much higher in ,dante's day than it is now1 part having been pulled down in the middle of the fourteenth century74 ---------------------------------------- -------------------------------- #hd 8,first refuge10 ,par4 xvii4 #gj4 #he ,par4 xvii4 #ga1 #gb4 #hf ,imbriani1 ,dante a ,padova4 #hg 8,torno a ,ravenna e de l non mi parto 7,i am going back to ,ravenna1 and shall not leave it again71 is a line in the ,acerba which ,cecco d' ,ascoli puts into the mouth of ,dante1 as though from a letter written to himself from the divine poet at the time0 7about the year #acai74 ,dante and ,giovanni del ,virgilio1 by ,wicksteed and ,gardner1 p4 #hd4 #hh ,inf4 xxxi4 #acf-ada4 ---------------------------------------- -------------------------------- ,the ,university at ,padua was also famous1 and as it was originally an offshoot from ,bologna and modelled on the same plan1 it is sure to have included astronomy in its curriculum4 ,but ,dante does not seem to have stayed here more than a few months4 ,there is also a tradition that he went to ,paris1 the greatest intellectual centre of his times1 and that he himself heard those lectures of ,sigieri1 the philosopher1 in the ,street of ,straw1 of which he makes mention in ,par4 x4 #acg4 ,this is possible1 but quite uncertain2 the allusion to ,sigieri is no proof1 since it has lately been discovered that he died in ,italy1 and his story was well known there4 ,after sifting all the evidence available1 we can only echo ,boccaccio1 and say of ,dante that 8,as it was at divers ages that he studied and learned the divers sciences1 so likewise it was at divers places of study that he mastered them under divers teachers40 ,,iii4 ,,books ,,on ,,astronomy ,,used ,,by ,,dante4 ,,books ,,on ,,astronomy ,,used ,,by ,,dante4 ,we shall probably be right if we conclude that ,dante's knowledge of astronomy was principally gained from independent reading1 and from conversation and discussion with learned men4 ,like a true scholar1 he was learning all his life1 for in the ,paradiso he corrects the opinion expressed earlier in the ,convivio about the origin of the markings in the moon4 ,boccaccio's description of his planning out a course of study and attacking some subjects alone in his youth agrees with his own account of his lonely struggles with ,latin authors2#hi and it is quite credible that he suffered heat and cold1 and went without food and sleep in his eagerness to learn1 since he himself mentions quite casually that at one time he injured his sight by constant reading1 so that the stars appeared blurred to him1 until by rest and bathing with cold water it became strong again4#ij ---------------------------------------- -------------------------------- #hi ,conv4 ,,ii4 xiii4 #bb-bf4 #ij ,conv4 ,,iii4 ix4 #adf-aeg4 ---------------------------------------- -------------------------------- ,his diligence must have been great1 and his memory wonderful1 judging from the numerous quotations from classical and contemporary authors to be found in his writings4 ,they seem to be chiefly from memory1 and it is not likely that he can often have had many books by him when writing4 ,if he gives a reference it is often a vague one1 and occasionally wrong3 his authorities on astronomical questions are sometimes 8the mathematicians10 8the astrologers10 or 8the sages of ,egypt10 by whom he means the ,alexandrian astronomers4 ,one does not1 of course1 expect medival writers to verify their references1 or to have our modern scruples about quoting other authors without acknowledgement3 in those days they were only too glad to get their information wherever they could1 often at second or third hand1 and to make it their own by storing it in their memories4 ,nevertheless1 from a careful study of ,dante's direct quotations1 and his allusions and reminiscences1 which are sometimes unconscious1 a good idea may be gained of his range of reading1 and of the books and authors on whom he chiefly relied for his astronomical data4 ,his supreme authority was of course ,ptolemy4 ,but it would only be by a rare chance that he could see the ,almagest1 even in a translation1 and all the evidence that we can find in his own writings points to its being entirely unknown to him4 ,on each of the three occasions that he quotes ,ptolemy's opinion on subjects dealt with in the ,almagest he is wrong3 once it is ,ptolemy's view on the physical nature of the ,galaxy1#ia as to which none had been expressed1 although its appearance was carefully described2 in another case he implies that ,ptolemy discovered precession1 and says that he added a ninth heaven to account for it1#ib and this double mistake was apparently copied from ,albertus ,magnus or ,averros4#ic ,as we know1 it was ,hipparchus who discovered precession1 and ,ptolemy gives him the credit for in the ,almagest2 it was the ,arabian astronomers who added the ninth sphere4 ---------------------------------------- -------------------------------- #ia ,conv4 ,,ii4 xv4 #gc-gg4 #ib ,conv4 ,,ii4 iii4 #cf-eb1 ,v4 ,n4 xxx4 #ic ,averros1 in his commentary on ,aristotle's ,de ,clo1 says that the ancients believed the eighth1 or starry1 heaven1 to be the outermost1 but that ,ptolemy assumed a ninth1 8because he said that he had discovered a slow motion along the signs of the zodiac in the fixed stars40 ,albertus ,magnus1 in his ,de ,clo et ,mundo1 ,book ,,ii41 says also that the ancients1 including ,aristotle1 believed that there were only eight heavens1 but that ,ptolemy1 so far as he can understand1 believed in ten1 on philosophical not mathematical grounds 7compare ,conv4 ,,ii4 iii4 #dj1 #da74 ,albertus accepted the theory of 8trepidation10 and thought this was the only movement which ought to be assigned to the star sphere2 there remained1 therefore1 two motions1 which affect all the planetary spheres and the star sphere1 for which two more spheres must be assumed1 a ninth sphere for precession1 and a tenth1 the primum mobile1 for the diurnal motion4 ,outside all was the ,empyrean4 ,dante never mentions trepidation1 and evidently did not believe in it3 he needed only nine moving spheres1 therefore1 but counts the ,empyrean as a tenth heaven4 ---------------------------------------- -------------------------------- ,on the other hand ,dante quotes twice quite correctly from the ,tetrabiblios1 which was more widely known4#id ,he may1 therefore1 possibly have read it1 and he alludes to it in the ,convivio1 though by a curious slip he does not give its name1 thinking he has done so already3 8,tolommeo dice nello allegato libro44440#ie ,this is in the fourteenth chapter of the second treatise1 but so far from having just quoted any special work by ,ptolemy he has said nothing at all about him since the third chapter1 and then it was only his opinion and name that were mentioned4 ,i have not been able to trace the quotation given in the ,qustio de ,aqua et ,terra 7xxi4 #bi-ca71 where ,ptolemy is said to have asserted that things on earth resemble things in heaven1 but this probably comes also 7or was supposed to come71 from the 8judicial astronomy0 of the ,tetrabiblios4 ,it is not taken from the ,almagest4 ---------------------------------------- -------------------------------- #id ,conv4 ,,ii4 xiv4 #aih-bjb4 ,ibid4 #bdi-bec4 #ie 8,ptolemy says in the book above cited40 ---------------------------------------- -------------------------------- ,the elements of ,ptolemy's system1 however1 could be learned indirectly1 and it seems that ,dante had recourse to the excellent epitome of the ,arab astronomer ,alfraganus4 ,it is true that his name is only mentioned once1 and his book once2 but nearly all ,dante's astronomical data appear to have been taken from him1 and his very expressions are sometimes repeated4 ,one of the most striking examples of borrowing from the ,elementa ,astronomica of ,alfraganus occurs in the ,paradiso1 where ,dante likens twenty-four spirits to as many brilliant stars4#if ,he makes up the number by taking fifteen specially bright stars from different parts of the sky1 and adding to them the stars of ,ursa ,major and two stars of ,ursa ,minor4 ,the seven chief stars of ,ursa ,major are well known1 but ,beta and ,gamma ,urs ,minoris are not conspicuous nor specially familiar2 and why1 if he takes fifteen unnamed1 should he name any of the twenty-four8 ,turning to chapter #ai of ,alfraganus' book1 we find that he follows ,ptolemy in enumerating fifteen first-magnitude stars in different parts of the sky1 and then he gives as examples of the second magnitude 7i4e4 next in brightness7 ,benet ,naax and ,alfarcatein1 ,arab constellations which correspond with the tail of ,ursa ,major1 and ,beta and ,gamma of ,ursa ,minor4 ---------------------------------------- -------------------------------- #if ,par4 xiii4 #a-ac4 ---------------------------------------- -------------------------------- ,there is no reason to suppose that ,dante knew ,arabic1 but there were several versions of ,alfraganus in ,latin1 and it is even possible to determine with some certainty which of them he used4 ,speaking of the movements of the planet ,venus1 he says that they may be found1 summarized from the best demonstrations of the astrologers1 in the ,book of the ,collection of the ,stars3-- 8,li quali1 secondoch nel ,libro dell' ,aggregazione delle ,stelle epilogato si trova1 dalla migliore dimostrazione degli astrologi 44440 7,conv4 ,,ii4 vi4 #acc-acf74 ,although the usual name for the book of ,alfraganus in ,latin was ,elementa ,astronomica1 the version for which medival students were indebted to the indefatigable translator ,gerard of ,cremona bears in the ,,mss4 the title ,alfragani liber de aggregationibus ,scienti ,stellarum et de principiis clestium motuum4 ,it is this book1 therefore1 that ,dante means1 though he has translated the title somewhat inaccurately4#ig ---------------------------------------- -------------------------------- #ig ,see ,schiaparelli's letter in ,lubin's ,dante e gli ,astronomi ,italiani4 ,the name is1 however1 also used as a sub-title in the printed edition of ,christmann1 ,frankfort1 #aeij1 which was based not on the translation of ,gerard but of ,johannes ,hispalensis of ,seville2 and ,toynbee thinks that this ,frankfort edition represents most nearly the version of ,alfraganus used by ,dante4 ,it is the only one of the five printed editions which gives the same figure for the diameter of ,mercury as that quoted by ,dante4 ,see ,toynbee1 8,dante's ,obligations to ,alfraganus0 in ,romania xxiv4 #ie1 and ,moore1 ,studies in ,dante iii4 p4 #c1 note4 ---------------------------------------- -------------------------------- ,there were several other books known to ,dante from which he must have gleaned information about ,ptolemy's system1 but ,alfraganus we may regard as his standard reference book4 ,many versions of ,alfraganus are still extant1 and it is pleasant to feel that we can hold in our own hands ,dante's text-book on astronomy4 ,the best known is the printed edition of ,golius1 published in ,amsterdam in #affi3 it is in both ,latin and ,arabic1 and opening in the middle we may turn the pages backwards to see the beautiful ,arabic letters of ,alfraganus' own language1 which is written from right to left1 or forwards to look at the ,latin in which he became known to ,dante4 ,next in importance to ,alfraganus among ,dante's authorities on astronomy was ,aristotle4 ,we have seen how overwhelming his authority became in natural science in the second half of the thirteenth century1 and how for some time scholars failed to distinguish between the system of spheres devised by ,eudoxus1 which was the scheme upheld by ,aristotle1 and the epicycles and eccentrics of ,ptolemy4 ,among all ,aristotle's admirers none was more devoted than ,dante3 for him ,aristotle is not only 8,il ,filosofo10 the ,philosopher par excellence1 as he was generally called in that age2 he is 8quello glorioso filosofo al quale la ,natura pi aperse li suoi segreti10 his intellect was 8quasi divino10 and his words are of 8somma e altissima autoritade40#ih ,throughout ,dante's own writings his references to ,aristotle are so frequent that ,dr4 ,moore observes3 8,the amount and variety of ,dante's knowledge of the contents of the various works of ,aristotle is nothing less than astonishing40#ii ---------------------------------------- -------------------------------- #ih 8,that glorious philosopher to whom ,nature most fully revealed her secrets10 ,conv4 ,,iii4 v4 #ed-ef2 8almost divine10 ,conv4 ,,iv4 vi4 #acc2 8supreme and highest authority10 ,ibid4 #eb4 #ii ,moore1 ,studies in ,dante ,i4 7,scripture and ,classical ,authors in ,dante71 from which much of the information in this chapter has been taken4 ---------------------------------------- -------------------------------- ,he does not1 however1 consider ,aristotle infallible as regards the details of astronomy1 for in these the philosopher was only following the observers and mathematicians2#ajj but in all matters which depend upon first principles1 in which ,dante would include the form of the earth1 ,aristotle's authority may not be called in question4#aja ,in cosmical physics1 such as the doctrine of the four elements1 and in meteorology1 ,dante follows 8il mio ,maestro0#ajb implicitly1 and it is also largely from the ,de ,clo that he gained his knowledge of early ,greek speculations regarding the universe4 ---------------------------------------- -------------------------------- #ajj ,conv4 ,,ii4 iii4 #ai-ba4 #aja ,conv4 ,,iii4 v4 #fb-fe4 #ajb 8,my master40 ---------------------------------------- -------------------------------- ,dante knew little more of ,greek than of ,arabic4 ,his occasional use of ,greek words is enough to prove this--for example when he discusses the ,pythagorean theory of 8,antictona10 using the accusative as if it were a nominative4#ajc ,in several passages he implies that the language was not known to him1 and he distinctly states that he used translations of ,aristotle's works4 ,here again we are able to identify the versions he used4 ,in ,conv4 ,,ii4 xv4 #ei-gc he complains that it is impossible to know what ,aristotle believed about the ,milky ,way1 because in the 8old translation0 he is made to say one thing1 and in the 8new translation0 quite another4 ,from his quotations of these two conflicting opinions1 we are able to deduce that the 8old translation0 was that which ,michael ,scot made from the ,arabic1 and the 8new translation0 that of ,aquinas1 which was made direct from the ,greek4 ---------------------------------------- -------------------------------- #ajc ,conv4 ,,iii4 v4 #cb4 ---------------------------------------- -------------------------------- ,he had access1 therefore1 to more than one ,latin translation of ,aristotle2 and beside this1 his quotations seem to have been often taken from commentators and compilers of his own times1 especially ,aquinas and ,albertus ,magnus4 ,this was frequently the case with the ,meteorologica of ,aristotle1 for the ,de ,meteoris of ,albertus ,magnus seems to have been much used by ,dante in place of ,aristotle's own work4 ,dante quotes it by name as ,meteora in ,conv4 ,,ii4 xiv4 #afi1 and also in ,conv4 ,,iv4 xxiii4 #abe-abf1 where he mentions 8,alberto0 as the author4 ,these two1 then1 the ,arab ,alfraganus and the ,greek ,aristotle1 were ,dante's chief authorities in astronomy1 both in ,latin translations4 ,besides these1 there is evidence in his writings that he was familiar with several classical authors who treated of astronomy4 ,he quotes frequently from many of ,cicero's works1 and we find echoes1 in two passages1 of the ,dream of ,scipio1#ajd which he is almost certain to have read1 since it was a favourite book in his time4 ,there are several references to ,seneca1 but the only time that an astronomical phenomenon recorded by him is mentioned#aje ,dante is evidently quoting at second-hand from ,albertus ,magnus4 ,with all the works of ,virgil1 and with the ,metamorphoses of ,ovid 7from which he took his astronomical myths7#ajf he was evidently very familiar2 and ,lucan is one of his authorities for the position of the earth's equator4 ,in this case the name of the author and the number of the book are precisely stated4#ajg ---------------------------------------- -------------------------------- #ajd ,inf4 ii4 #gf-gh2 ,par4 xxii4 #acd-ach4 #aje ,conv4 ii4 xiv4 #agd-agf4 #ajf ,phathon1 ,conv4 ,,ii4 xv4 #ec-ee1 ,purg4 xxix4 #aah-abj2 ,latona1 ,purg4 xx4 #acj-acb2 the ,horses of the ,sun1 ,conv4 ,,iv4 xxiii4 #acd-aci1 etc41 etc4 #ajg ,conv4 ,,iii4 v4 #aae-aag4 ---------------------------------------- -------------------------------- ,dante had a great reverence for ,plato1 whom he calls 8uomo eccellentissimo10#ajh and of whom he repeats the medival legend that he was a prince who gave up all for the sake of acquiring wisdom4#aji ,of his writings he only knew the ,timaeus1 probably the ,latin translation and commentary of ,chalcidius1 which was widely known4 ,or he may have been acquainted with ,aquinas' commentary1 which has since been lost4 ,he also knew something of ,plato's teachings through ,aristotle and ,cicero1 ,albertus ,magnus1 and ,aquinas1 and perhaps ,st4 ,augustine4 ,when he feels obliged to dissent from the great philosopher's doctrine that the souls of men come from the stars1 he does so with reluctance and great gentleness4#aaj ---------------------------------------- -------------------------------- #ajh 8,a man of supreme excellence40 ,conv4 ,,ii4 v4 #ba1 #bb4 #aji ,conv4 ,,iii4 xiv4 #gf-gi4 #aaj ,par4 iv4 #bb-bd1 #di-fj4 ---------------------------------------- -------------------------------- ,among other ,greek philosophers who speculated on astronomy1 ,dante mentions ,thales#aaa and ,pythagoras4 ,the date when the latter flourished he takes 7he tells us7 from ,livy1 and his theory that the ,universe is governed by the principle of number from ,aristotle's first book of ,metaphysics4 ,the astronomical theories of his school are also doubtless taken from ,aristotle4 ,dante tells the story of ,pythagoras that he was the first man to be called 8philosopher10 because when asked if he considered himself a wise man1 he replied1 8,no1 but only a lover of wisdom40#aab ,dionysius the ,academician and ,socrates are referred to for their opinions on the influence of the stars upon human souls2#aac and ,anaxagoras and ,democritus for their galactic theories1#aad which ,dante obtained from ,albertus ,magnus4 ---------------------------------------- -------------------------------- #aaa ,conv4 ,,iii4 xi4 #ci2 ,inf4 iv4 #acg4 #aab ,conv4 ,,iii4 xi4 #bb-cc2 ,,ii4 xiv4 #add-adg2 ,,iii4 v4 #bi-dd2 ,,iii4 xi4 #da-dg4 #aac ,conv4 ,,ii4 xiv4 #cd1 #ce4 #aad ,conv4 ,,ii4 xv4 #ef4 ---------------------------------------- -------------------------------- ,except for ,alfraganus1 ,dante refers but seldom to ,arab astronomers4 ,he does not seem to have known ,albategnius4 ,the ,de ,substantia ,orbis of ,averros is quoted in the ,qustio de ,aqua et ,terra1#aae and it is possible that from this book ,dante derived a theory about the moon which he expounds in the ,convivio4 ,he quotes ,alpetragius on circular existence 7dependent on the spheres71#aaf ,avicenna on the ,galaxy1 and again with ,algazel on the influence of the spheres1#aag and ,albumassar on meteors4#aah ,the quotation from the latter1 however1 is second-hand from ,albertus ,magnus1 and is a mistake1 for the passage is not to be found in that astronomer's works4 ,he was born in ,turkestan1 in #hje4 ---------------------------------------- -------------------------------- #aae ,qu4 xviii4 #ch1 #ci4 #aaf ,conv4 ,,iii4 ii4 #cg4 #aag ,conv4 ,,ii4 xv4 #gg1 ,,ii4 xiv4 #cb4 #aah ,conv4 ,,ii4 xiv4 #agj-agd4 ---------------------------------------- -------------------------------- ,we may here remind our readers that the three ,latin poets1 ,virgil1 ,ovid1 and ,lucan1 were among the world's five greatest poets met by ,dante in ,limbo2 that next to ,aristotle among the philosophers stood ,socrates and ,plato1 and near these were ,democritus1 ,anaxagoras1 and ,thales1 ,cicero and ,seneca1 ,ptolemy1 ,avicenna and ,averros4#aai ---------------------------------------- -------------------------------- #aai ,inf4 iv4 #hj1 #ha1 #ij1 #aca-add4 ---------------------------------------- -------------------------------- ,among ,christian writers1 ,dante may have gathered some information about ancient ,greek speculations from ,st4 ,augustine and ,peter ,lombard2 and ,orosius1 the ,spanish friend of ,augustine1 was his chief authority for that geographical system which1 in connection with astronomy1 plays an important part in the time-indications of the ,divina ,commedia4 ,orosius had a great reputation among geographers and map-makers4 ,he had travelled much between ,spain1 ,africa1 and ,palestine1 and he devotes a chapter to describing the different parts of the earth in his history ,adversus ,paganos1 which he wrote to prove that ,christianity had not injured but benefitted the countries in which it had been accepted4 ,this fifth century geography seems to have been largely based on the first-century geography of ,strabo1 who quotes ,eratosthenes1 ,posidonius1 and ,hipparchus among his authorities4 ,orosius states that the land is entirely surrounded by ,ocean1 and is divided into three continents--,asia1 with the mouths of ,ganges in the middle of its eastern coast1 ,europe stretching vaguely very far to the north-east1 and ,africa a narrow and long strip from east to west between the ,mediterranean and the southern ocean4 ,this chapter is quoted in ,de ,mon4 ,,ii4 iii4 #hg-ij and ,qu4 xix4 #dc2 and ,orosius is almost certainly 8quell' avocato dei tempi cristiani10#abj seen by ,dante among the learned doctors in the ,heaven of the ,sun4 ---------------------------------------- -------------------------------- #abj 8,the advocate of the ,christian centuries40 7,par4 x4 #aii74 ,orosius is also mentioned by name in ,conv4 ,,iii4 xi4 #bg2 ,v4 ,e4 ,,ii4 vi4 #hd2 and ,de ,mon4 ,,ii4 ix4 #bf4 ---------------------------------------- -------------------------------- ,the speaker who points him out in these words also mentions his own name and that of the spirit nearest to him3-- 8,questi che m' a destro pi vicino ,frate e maestro fummi1 ed esso ,alberto di ,cologna1 ed io ,thomas d',aquino40#aba ---------------------------------------- -------------------------------- #aba 8,he who is nearest to me on the right ,my brother and master was1 and he ,albertus ,is of ,cologne1 ,i ,thomas of ,aquinum40 7,par4 x4 #ig-ii74 ---------------------------------------- -------------------------------- ,these two1 so near in heaven1 had been close companions on earth4 ,the youthful ,thomas1 son of ,count d',aquino in southern ,italy1 after six years' study at the ,university of ,naples joined the ,dominican ,order1 and went to ,cologne to learn from ,albert1 who was also of noble family but born in ,suabia on the ,danube4 ,together they went to ,paris1 together returned to ,cologne1 but after six more years there their paths separated3 ,albert rose to be ,bishop of ,ratisbon2 ,aquinas1 after lecturing in ,paris1 ,rome1 and ,bologna1 became a professor at ,naples1 and died in ,italy in #abgd4 ,his master survived him by six years1 dying at ,cologne at the advanced age of eighty-seven in #abhj4abb ---------------------------------------- -------------------------------- #abb ,toynbee1 ,dante ,dictionary2 the source also of many other details given in this chapter4 ---------------------------------------- -------------------------------- ,these two are in the foremost rank among authors of his own time who influenced ,dante4 ,he quotes both writers and several of their books by name1#abc and though he never mentions it he was very familiar with the ,summa ,theologica of ,aquinas4 ,to the works of these famous authors he was frequently indebted for astronomical facts1 theories1 and history1 as already noted4 ,besides this1 his reverence for ,aristotle1 his belief in the essential harmony between religion and science1 and his whole attitude towards knowledge1 are greatly due to the influence of ,st4 ,thomas and his 8brother and master10 ,albert of ,cologne4 ---------------------------------------- -------------------------------- #abc ,albert in ,conv4 ,,iii4 v4 #aac-aae1 vii4 #bf-bh2 ,,iv4 xxiii4 #abe-f2 ,aquinas in ,conv4 ,,ii4 xv4 #abe-f2 ,,iv4 viii4 #c-f1 xv4 #abe-acj1 xxx4 #bf-cj2 ,de ,mon4 ,,ii4 iv4 #e-h2 and see ,purg4 xx4 #fi4 ---------------------------------------- -------------------------------- ,there are also three of ,dante's own fellow-countrymen and contemporaries whose books he is most likely to have read1 although he does not mention them3--,brunetto ,latini the ,florentine1 ,cecco d' ,ascoli1 professor at ,bologna1 and ,ristoro the monk of ,arezzo4 ,brunetto ,latini is only mentioned once in ,dante's works1 besides the passage in the ,inferno already referred to4 ,in the ,de ,vulgari ,eloquentia ,brunetus ,florentinus is mentioned with admiration as a distinguished man of letters1 but blamed with other ,tuscans for writing in his own local dialect4#abd ,brunetto1 who was born in ,florence about #abaj1 was sent on an embassy in #abfj to ,alfonso ,x4 of ,castile1 the learned king under whose guidance the famous astronomical ,tables had been drawn up4 ,but on his way back to ,florence he was met by the news that the ,florentine ,guelphs had been defeated at the disastrous battle of ,montaperti1#abe and expelled from ,florence2 and as he belonged to this party he took refuge in ,france1 first at ,montpellier and afterwards in ,paris4 ,when the ,guelphs had regained the ascendancy through their victory at ,benevento in #abff 7where ,manfred lost his life71#abf ,brunetto returned to ,florence1 and his name subsequently appears in no less than thirty-five public documents as having been consulted by the government of his native city on various important matters4 ,for the most part1 moreover1 it is recorded that his advice was followed4 ,he died at a venerable old age in ,florence in #abid1 and was buried in the church of ,santa ,maria ,maggiore4 ---------------------------------------- -------------------------------- #abd ,v4 ,e41 ,i4 xiii4 #a-aa4 #abe ,inf41 xxxii4 #ha1 and x4 #he1 #hf4 #abf ,purg41 iii4 #aab-abi4 ---------------------------------------- -------------------------------- ,it was while exiled in ,france that ,brunetto wrote the ,italian poem ,il ,tesoretto1 in which he represents himself as a pilgrim on an allegorical journey2 and from this ,dante perhaps derived some suggestions for his ,vision4 ,the poem is incomplete1 and breaks off at a tantalizing point1 for ,brunetto has just met ,ptolemy on ,mount ,olympus1 and has put a question to him3 ,ptolemy 8rispose in questa guisa0#abg--;and here the poem ends6 ---------------------------------------- -------------------------------- #abg 8,replied after this fashion40 ---------------------------------------- -------------------------------- ,in ,france also he wrote ,li ,louvres dou ,trsor1 a great compendium of learning1 in ,french prose4 ,the first part treats of the ,creation and ,biblical history1 and of the natural sciences2 the second of ethics1 rhetoric1 and politics4 ,in the section on astronomy which is included in the first part1 ,brunetto gives a very brief account of ,ptolemy's system1 and the sizes and distances of the heavenly bodies as estimated by the ,arabs3 it seems to be based chiefly on ,alfraganus4 ,but beside the periods of the planets he adds in each case their astrological properties1 as for instance3-- 8,saturnus1 qui est le souverain sor tous1 est cruex et felons et de froide nature 444 ,jupiter 444 ast dous et piteus et plains de biens4444 ,mars et chaus et bataillereus1 et mauvais1 et est apelez ,diex de batailles40#abh ---------------------------------------- -------------------------------- #abh ,li ,louvres dou ,trsor1 ,chabaille1 ,paris #ahfc4 ---------------------------------------- -------------------------------- ,when speaking of the two principal movements of the skies1 he quotes a curious old idea which had been mentioned by ,isidore of ,seville1 that they are in contrary directions because the tremendous speed of the diurnal motion would shake the whole universe to pieces if it were not that the seven planets go as it were to meet it1 and soften its vehemence3-- 8,li firmamenz court de orient en occident entre jor et nuit une fois1 si roidement et si fort que sa pesanteur et so grandor la feroient tout tressaillir1 se ne fussent les ,,vii4 planetes qui vont aussi comme a l'encontre dou firmament1 et atemprent son cours selonc son erre40#abi ---------------------------------------- -------------------------------- #abi ,ibid4 ---------------------------------------- -------------------------------- ,the ,acerba of ,cecco d',ascoli was another encyclopdic work1 but in ,italian verse4 ,it was very much the fashion in those days to undertake a compilation of all kinds of knowledge1 and this was doubtless very useful when few books could be owned by any single reader4 ,cecco had a considerable knowledge of natural science1 and astrology was of great importance in his eyes4 ,though ,dante never mentions him or his work1 he can hardly have been ignorant of it1 especially as he himself is mentioned in it4 ,nor does he mention ,ristoro of ,arezzo1 yet we find many ideas and expressions in ,dante's writings which are also in the ,composizione del ,mondo4 ,even if he did not borrow from it1 the book is worth study by anyone interested in the popular astronomy of the thirteenth century4 ,we learn from the author that he wrote his book in ,arezzo1 finishing it in the year #abhb1 that is about thirty years before ,dante's ,convivio appeared4 ,the opening words run3-- 8,incominiciasi il libro della ,composizione del ,mondo colle sue cagioni3 composto da ,ristoro di ,arezzo in quella nobilissima citt 444 etc40#acj ---------------------------------------- -------------------------------- #acj 8,here beginneth the book of the ,composition of the ,world together with its ,causes3 written by ,ristoro of ,arezzo in that most noble city40 ---------------------------------------- -------------------------------- and the closing words are3-- 8,compiuto e questo libro sotto li anni di ,cristo nel mille dugento ottantadue4 ,ridolfo imperadore aletto4 ,martino quarto papa residente4 ,amen40#aca ---------------------------------------- -------------------------------- #aca 8,here endeth this book1 in the year of our ,lord one thousand two hundred and eighty-two4 ,rudolph ,emperor at this date4 ,martin ,,iv4 resident ,pope40 ,amen4 ---------------------------------------- -------------------------------- ,we learn further that he was a monk and a native of ,arezzo in an interesting passage where he describes a total eclipse of the sun seen by himself from his monastery3 the sky was very clear1 and it must have been a specially dark eclipse1 for besides ,mercury he saw many stars2 totality lasted for as long as a man could easily walk #bej steps2 there was a feeling of chill1 and birds and wild animals were so frightened that they allowed themselves to be caught4 ,fra ,ristoro made a calculation and found that on that day sun and moon were in the same position in the sky4 ,it was perhaps this event which induced him to study astronomy4 ,the extent and depth of ,ristoro's reading evidently bore no comparison to ,dante's1 but he was able to sit writing in his quiet cell1 day after day1 and had such books as he wanted at hand4 ,the monastery seems to have been furnished with astronomical tables1 a celestial globe1 and the books of ,alfraganus and other ,arab writers4 ,all these he had studied1 and he was something of an observer too4 ,alfraganus must have been always at his elbow when writing1 for he turns to it constantly1 quoting 7unlike ,dante7 the chapter referred to3-- 8,alfragano pose nell' ottavo capitolo20 8 testimonio l',alfragano nelli venti e due capitoli del suo libro20#acb ---------------------------------------- -------------------------------- #acb 8,alfraganus said in the #hth chapter02 8,alfraganus bears witness in the #bbnd chapter of his book40 ---------------------------------------- -------------------------------- one chapter is avowedly taken whole from ,alfraganus1 and where the opinions of 8il grande ,tolommeo0#acc are quoted they are evidently copied from the same source4 ,other ,arab writers are quoted once or twice1 for instance1 ,albumassar1 ---------------------------------------- -------------------------------- #acc 8,the famous ,ptolemy40 8il quale fu altissimo maestro d'astrologia10#acd #acd 8,who was a very great teacher of astrology40 ---------------------------------------- -------------------------------- and several lines are copied from a ,latin translation of ,algazel1#ace giving some astrological jargon about the twelve zodiacal signs4 ---------------------------------------- -------------------------------- #ace 8,an ,arabian philosopher of ,baghdad1 #ajeh-aaaa40 ---------------------------------------- -------------------------------- ,we have already quoted from ,ristoro's preface1 showing the high opinion he held of astronomy4 ,but it is disappointing to find that the greatest part of his book is devoted to the 8cagioni10 that is1 to purely fanciful 8reasons10 for all the facts and fallacies concerning nature which he has here brought together4 ,he gravely argues about the constellation figures as if they were real pictures of animals and things pricked out by nature in stars on the vault of heaven1 and not a human convention4 ,he notes their paucity in the southern hemisphere1 and that nearly all have their heads towards the north1 and from this he draws the conclusion that the northern part of the sky is the nobler1 for we can see it is the upper side1 just as we know the top side of a book by the position of its letters4 ,it is for this reason1 he thinks1 that only the northern hemisphere of the earth contains land and is inhabited4 ,some1 especially the great ,averros1 had indeed held that there is inhabited land south of the equator1 because the sun goes there4 ,but this is because his movements of recession and approach are necessary to produce the seasons1 and hence the growth of plant life1 in the north4 ,the constellations are upside down for the south1 so they can have no effect there1 therefore1 there are no animals there 7since every race of animals is under the protection of a constellation72 therefore no plants1 since they exist for animals1 and therefore1 ,ristoro concludes his chain of argument triumphantly1 there are no men1 and no lands1 for land without life would be useless4 ,ristoro reproduces ,alfraganus' description of the sun's movements as seen in different latitudes1 quotes him as saying that the equatoral regions are inhabited1 and ,avicenna that the temperature there is equable because days and nights are always equal4 ,the city ,arym which is exactly on the equator has a perfect climate1 and as it has two summers and two winters there are two harvests2 moreover1 all the stars in the sky are visible at the equator2 therefore1 the best astronomers1 and the wisest and richest men1 ought to live there1 says ,ristoro4 ,when writing thus1 he seems to have had before him one of the 8climate maps0 which were common in ,europe in the eleventh and following centuries1 having been introduced by ,arab cartographers1 who adopted the idea from ,greek maps4 ,for he goes on to point out that the first 8climate0 is much the longest1 and that the others diminish gradually towards the pole1 all the 8terra scoperta0#acf being thus contained in one quarter of the earth1 and having the shape of the moon when we see it half full4#acg ---------------------------------------- -------------------------------- #acf 8,the uncovered earth10 i4e4 not hidden under the ocean4 #acg ,bk4 ,,vi4 cap4 xi4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #ch4 ,the half-moon shape of the habitable earth4 7,ristoro74 ,there is nothing but sea south of the equator1 and the habitable earth lies wholly in one half of the northern hemisphere1 the other half being sea4 ,the habitable earth1 therefore1 is the same shape as the half-moon1 i4e4 a quarter sphere4 ,the accompanying climate map shows all these features1 the famous city ,arym--occupying nearly half the space1 although it is supposed to be merely on the equator--the seven climates1 and the region beyond the seventh1 near the north pole1 marked as uninhabitable through the cold4 ,the half-moon shape of ,earth's habitable quarter is obvious4 ,the map betrays ,arab influence in the orientation1 the south being at the top2 and ,arym1 or ,aren1 was an ,arab myth1 perhaps derived from the ,mount ,meru of the ,hindus1 which is said in the ,vedas to be 8in the middle of the earth40 ,according to ,ristoro1 the positions of the constellation figures do not only explain why one hemisphere of earth has land and the other none2 they also explain the movements of the skies4 ,for the figures of the zodiac face west 7those that have faces71 and this is why the diurnal movement of the whole heaven is towards the west1 so that the constellations may move straightforward1 in the natural way4 ,on the other hand1 the planets move in the opposite direction because it would not be seemly for them to pass each figure of the zodiac arriving first at the back and moving on to the head4 ,this is the true reason of the contrary direction of the two principal celestial movements4 ,ristoro does not approve of the solution quoted by ,brunetto ,latini4 ,he adds that the width of the zodiac was designed to contain the figures of the animals6 ,after this1 we are not surprised to hear that the red colour of the planet ,mars is the cause of its martial nature 7not the reason for which such a nature is attributed to it74 ,the markings on the moon ,ristoro explains by saying that some body must exist in the ,world which is neither polished and shining all over1 like the stars1 nor altogether rugged and dark1 as the earth was supposed to be1 but partaking of both natures2 and this body must be the moon1 because of her intermediate position between the earth and the nearest of the other planets 7,mercury74 ,illustration3 ,,climate ,,map1 ,,of ,,about ,a4,d4 #aaaj4 ,to face p4 #bdh4 ,reproduced by permission from ,beazley's 8,dawn of ,modern ,geography40 ,of the influence of the heavens on the earth ,ristoro has very much to say1 from general statements such as that the spheres impress their influence on things of ,earth1 just as a seal impresses wax1 down to details about the births of horses4 ,if the moon is strong in ,aries1 and ,aries is powerful1 then1 because the moon signifies white among the colours and ,aries signifies the head1 the horse will be born with a white mark on its head1 and if the influence is very strong it will be a beautifully-shaped mark4 ,again and again he tells us about the various properties and 8virtues0 of the seven planets1 but he does not omit to mention that the powers which move the planets and cause them to influence ,earth are spirits1 which we call ,angels1 and the philosophers call ,intelligences4 ,these have their several dwelling-places in the spheres1 and the nobler their nature the higher is the sphere which they inhabit4 ,from these quotations the reader may judge of the general trend of the eight books comprised in ,la ,composizione del ,mondo colle sue ,cagioni3 we shall have occasion to refer to it again1 by way of comparison and contrast1 when dealing with ,dante's works in detail4 ,it is rather curious that there is no trace in ,dante's writings of acquaintance with the great ,roger ,bacon1 or with ,sacrobosco1 especially as ,brunetto ,latini knew the former personally1 and ,cecco d',ascoli wrote a commentary on the latter1 but ,dante may have known them1 and also the works of ,isidore and ,bede1 who are both mentioned in ,par41 x4 #aca1 as well as other books which are now completely lost4 ,those we have described above would1 however1 be enough to supply him with all the astronomical data1 except one1 which we find in his writings4 ,it is now time to examine these1 and see what use he made in literature of the knowledge he possessed4 ,,iv4 ,,astronomy ,,in ,,dante',s ,,writings4 ,,astronomy ,,in ,,dante',s ,,writings4 ,if we except the seven ,penitential ,psalms and the ,profession of ,faith1 which are only paraphrases1 and are very doubtfully ascribed to ,dante1 no work of his can be mentioned which does not contain some reference to the heavenly bodies4 ,when writing the ,vita ,nuova1 that story of his love for ,beatrice which he calls the work of his boyhood1#ach he was haunted by the sublime idea of the rolling spheres4 ,beatrice at her first appearance as a little girl of eight1 and ,beatrice when she died1 suggested thoughts of the nine heavens2#aci almost the first words of the book allude to the circling spheres of the sun and of the stars3#adj and the last sonnet soars beyond them all to the ,empyrean4#ada ,already he seems to have read ,alfraganus1 for he takes a suggestion which occurs in the first chapter of the ,elementa ,astronomica et ,chronologica4 ,alfraganus there describes the different methods of reckoning days1 months1 and years1 in use among different nations1 and gives a special list of the ,syrian months with their corresponding ,roman months2 and ,dante1 by using the ,arabian system of days and the ,syrian months1 is able to prove to himself that the day and the month when ,beatrice died were both at the sacred number of nine4#adb ,according to our method of reckoning1 the time was sunset on the eighth of ,june1 but this was the first hour of the ninth day according to ,arabian usage1 and our sixth month corresponds with the ninth of the ,syrians4 ---------------------------------------- -------------------------------- #ach ,conv4 ,i4 i4 #abe1 #abf4 ,compare ,conv4 ,,iv4 xxiv4 #a-ac4 #aci ,v4 ,n4 ii4 #i-ab1 xxx4 #ac-bd4 #adj ,v4 ,n4 ii4 #a-ab4 #ada ,v4 ,n4 xlii4 #dg4 #adb ,v4 ,n4 xxx4 #a-f4 ---------------------------------------- -------------------------------- ,dante had also read at this time ,aristotle's doctrines about the spheres and their ,movers1 for he quotes from the ,metaphysics1#adc and this is the work in which they are found4 ---------------------------------------- -------------------------------- #adc ,v4 ,n4 xlii4 #cj4 ---------------------------------------- -------------------------------- ,yet a familiarity with ,alfraganus and ,aristotle so early as this is hardly consistent with the difficulty he says he found in understanding ,latin books of philosophy some time after the death of ,beatrice4#add ,perhaps the latter part of the ,vita ,nuova was written a good deal later2 or it may be not altogether frivolous to suggest that in his youth ,dante had read the first chapters of ,alfraganus1 which are easy1 but did not master the rest of the book till later4 ---------------------------------------- -------------------------------- #add ,conv4 ,,ii4 xiii4 #bb-bf4 ---------------------------------------- -------------------------------- ,out of his fifty-three short poems 7including all in ,moore's ,oxford ,edition1 except those which form part of the ,vita ,nuova or ,convivio71 twelve1 or nearly a quarter1 contain some reference to sun1 moon1 or stars1 planets1 or spheres2 and from these alone we could form some idea of ,dante's acquaintance with astronomy4 ,he speaks of the sun as measuring time1#ade and giving light to the stars#adf 7according to the general belief72 the moon#adg and each of the planets#adh is mentioned1 some of the constellations also1#adi especially with reference to the seasons2 the theory of the several heavens and their ,first ,mover1#aej and the supposed influences of the stars and planets are alluded to4#aea ,these poems were written at different times1 and some belong to a much later period than the ,vita ,nuova4 ---------------------------------------- -------------------------------- #ade ,son4 xxxvi4 #b2 ,canz4 xx4 #hi4 #adf ,canz4 xix4 #aag2 ,canz4 ix4 #af1 #ag4 #adg ,canz4 xx4 #hi2 ,son4 xxviii4 #aa4 #adh ,son4 xxviii42 ,canz4 xv4 #d1 #g4 #adi ,canz4 xv4 #c1 #bi1 #da4 #aej ,son4 xxviii4 #b4 #aea ,son4 xxviii4 ,canz4 xix4 #gg1 ,ball4 vi4 #aa1 #ab1 ,canz4 xv4 #da41 ,son4 xxvi4 #ad4 ---------------------------------------- -------------------------------- ,it is when we come to examine the ,convivio1 the work of his manhood1#aeb that we find the clearest evidence of ,dante's careful study of astronomy4 ,this book was written with the professed intention 7as one of its aims7 of sharing with others the learning he had been happy enough to acquire--not indeed as one of the guests at the ,table of ,wisdom1 but as one sitting at their feet and gathering up the crumbs4#aec ,the thread which connects his discourse is a collection of his own ,odes1 on each of which he had intended to write a treatise or commentary1 but the book never advanced beyond the fourth treatise4 ,these ,odes were nearly all love-poems1 but the poet explains that they are a figurative expression of his devotion to ,philosophy1 and the whole book is a glorification of the pursuit of knowledge4 ,in the opening sentences1 with the reference to ,aristotle1 the manner of reasoning1 the assumptions of our innate desire for absolute knowledge and the bliss brought by its attainment1 ,dante is the spokesman of his period4 ---------------------------------------- -------------------------------- #aeb ,conv4 ,i4 i4 #aaa-aac and #abe-abg4 #aec ,conv4 ,i4 i4 #fg-hf4 8,siccome dice il ,filosofo nel principio della ,prima ,filosofia1 ,tutti gli uomini naturalmente desideranno di sapere3 ,la ragione di che puote essere1 che ciascuna cosa1 da providenza di propria natura impinta1 inclinabile alla sua perfezione4 ,onde1 accioch la scienza l'ultima perfezione della nostra anima1 nella quale sta la nostra ultima felicit1 tutti naturalmente al suo desiderio siamo soggetti40#aed #aed 8,as the ,philosopher says at the beginning of the ,first ,philosophy1 #8,all men naturally desire to have knowledge4' ,the reason of this may be that everything1 being impelled by foresight belonging to its own nature1 tends to seek its own perfection4 ,wherefore inasmuch as knowledge is the final perfection of our soul in which our final happiness consists1 all men are naturally subject to the desire for it40 ,conv4 ,i4 i4 #a-aa4 ---------------------------------------- -------------------------------- ,and from a study of the ,convivio we may learn much of the authors most esteemed1 the methods of study pursued1 and the results obtained1 by thirteenth-century scholars seeking to gain the ultimate perfection of the soul4 ,astronomy is frequently introduced1 especially in the second and third treatises4 ,the ,ode which forms the text of the second treatise is that which is quoted by ,charles of ,hungary in ,par4 viii4 #cg--8,voi che intendendo il terzo ciel movete10#aee and it gives ,dante the occasion to speak first of the heaven of ,venus1 explaining ,ptolemy's system of epicycles1 and later of all the heavens in their order1 and the celestial bodies contained in them4 ,the ode of the third treatise contains the line 8,non vede il ,sol1 che tutto il mondo gira 4440#aef and upon this he hangs a complete little essay describing the movements of the sun1 and how they appear from different parts of the earth1 as well as a short dissertation on the question whether it is ,sun or ,earth which actually moves4 ---------------------------------------- -------------------------------- #aee 8,oh ye whose intellectual ministry ,moves the third heaven40--,carey4 #aef 8,the sun sees not1 though circling all the world40 ---------------------------------------- -------------------------------- ,the ,latin works1 ,de ,monarchia1 ,de ,vulgari ,eloquentia1 the ,eclogues1 and the ,letters1 do not give much scope for astronomical references2 yet there are many similes drawn especially from the sun and moon1 and the thought of the spheres as instruments of ,god's ,will in bringing about events on earth is constantly recurring4 ,in the curious work ,qustio de ,aqua et ,terra1 ,dante argues learnedly about the spheres1 the orbit of the moon1 and her effect on the tides1 and the influences of the stars4 ,the book purports to have been written at ,verona in #acbj as the outcome of a discussion in which ,dante had taken part as to the respective heights of land and ocean1 a problem which had been dealt with by ,ristoro d' ,arezzo some forty years earlier4 ,its authenticity has been questioned1 partly under the mistaken idea that facts such as gravity1 the spherical form of ,earth1 and the connection of tides with the moon were not known until much later2 but as a matter of fact the discussion is quite in the manner of ,dante's day1 and no facts or theories are put forward which he could not have learned from books with which we believe he was acquainted4#aeg ,the internal evidence of his authorship is strong1 and belief in it seems to be gaining ground among experts4#aeh ---------------------------------------- -------------------------------- #aeg ,the spherical form of ,earth1 and the action of gravity at the earth's surface1 were commonplaces with the ,greeks1 as we have seen in ,part ,i4 of this book4 ,posidonius1 ,strabo1 and other classical writers speak of the tides as following the revolution of the heavens1 and having periods similar to those of the moon2 ,albertus ,magnus and ,aquinas ascribe them to the influence of the moon1 and so does ,dante himself in ,par4 xvi4 #hc4 #aeh ,see ,moore1 ,studies in ,dante1 ,,ii4 8,the ,genuineness of the ,qustio de ,aqua et ,terra10 for a complete discussion of the question4 ---------------------------------------- -------------------------------- ,finally1 the ,divine ,comedy1 the work of ,dante's maturity1 which took him so many years to write1 and for which he had studied ever since he closed the ,vita ,nuova with the resolve to write more worthily one day of ,beatrice1#aei focuses in one unique and finished work the thoughts and ideals1 the knowledge and fancies1 of the poet and his age4 ,the subject of the poem1 taken in its literal sense1 is cosmical1 for it describes a journey in which the author penetrates to the centre of the universe1 and passes from planet to planet until he reaches the outermost sphere4 ,moreover1 the journey is assumed to take a definite space of time1 and the passing of the hours by day and by night is indicated by the successive positions of sun or stars1 and the phases and movements of the moon4 ,the ,divine ,comedy contains more than twice as many allusions to the heavenly bodies as all the other works of ,dante put together4 ---------------------------------------- -------------------------------- #aei ,v4 ,n4 xliii4 #c-g4 ---------------------------------------- -------------------------------- ,but we must discriminate in drawing conclusions from these astronomical references so freely distributed in all ,dante's writings4 ,if he wrote the ,qustio1 it is his only professedly scientific work1 written for scientific men1 and astronomy is only brought in incidentally4 ,the ,convivio1 in which astronomical facts and theories are set forth in much greater detail and fulness than elsewhere1 was a popular work meant for those who had no inclination1 or else no opportunity1 for prolonged serious studies4 ,we expect1 therefore1 that technical details will be avoided4 ,still more will they be omitted in the ,divine ,comedy and other poetical works1 where difficult problems and pedantical accuracy would be most unsuitable4 ,we can infer the knowledge which lay in ,dante's mind1 behind his popular use of it in literature2 and we can often find an explanation in the prose of the ,convivio for a slight allusion in the poetical works2 but we must not deal with any as if they were text-books1 and set forth precisely and completely all that ,dante knew of his favourite science4 ,it is the poet's artistic use of the astronomy of his day which merits our admiration quite as much as the scholar's proficiency4 ,this being premised1 we may now proceed to quote from his works1 showing how he has dealt with first the facts1 and secondly the theories1 of astronomy4 ,finally we shall be able to form a clear mental picture of the universe as it was believed to exist by ,dante1 and not only by his contemporaries but by his successors for many generations4 ,v4 ,,observational ,,astronomy4 8,the heavens declare the glory of ,god2 and the firmament sheweth ,his handy-work4 ,day unto day uttereth speech1 and night unto night sheweth knowledge4 ,there is no speech nor language where their voice is not heard4 ,their line is gone out through all the earth1 and their words to the end of the world4 ,in them hath he set a tabernacle for the sun2 which is as a bridegroom coming out of his chamber1 and rejoiceth as a strong man to run a race40 #a4 ,,movements ,,of ,,the ,,moon4 ,of all the seven sciences of the ,trivium and ,quadrivium1 ,astronomy1 ,dante thought1 was the noblest1 and for two reasons4 ,aristotle had said that a science is noble in proportion to the nobility of its subject1 and the certainty of its conclusions2 and in both of these ,astronomy excels4 ,its subject is the ,movement of the ,heavens1 and its certainty is perfect4 8,e nobile e alta per nobile e alto suggetto1 ch' del movimento del cielo3 alta e nobile per la sua certezza1 la quale senza ogni difetto40#afj ,if astronomers are sometimes mistaken1 the fault lies in them1 as ,ptolemy said1 and not in the science4 ---------------------------------------- -------------------------------- #afj ,conv4 ,,ii4 xiv4 #bdd-bag4 8,it is noble and lofty because of its noble and lofty subject1 which is the movement of the heavens2 it is lofty and noble because of its certainty1 which is without flaw40 ---------------------------------------- -------------------------------- ,this quotation from ,ptolemy is from his book on 8judicial astronomy10#afa and it may be that ,dante was partly thinking of astrological predictions1 as he almost certainly was in the passage that follows1 where he adds that astronomy takes a long time to learn1 not only because of its great range1 but because experience is necessary to form a correct judgment4 ,nevertheless1 it is probable that by its flawless certainty he meant that unchanging laws govern the celestial phenomena1 so that they may always be predicted without error when the laws are known4 ---------------------------------------- -------------------------------- #afa ,see p4 #aef4 ---------------------------------------- -------------------------------- ,his definition of astronomy was accurate1 for it was not until the middle of the nineteenth century that physical astronomy began to take its place beside the old 8astronomy of position10 and in ,dante's day practically the only subject open to research concerning the heavenly bodies was their movements4 ,of these1 and especially the 8prime motion0 of the diurnal revolution1 he was vividly conscious4 ,his favourite name for the heavens is 8wheels0--8le ruote magne10 8eterne ruote10 8stellate ruote02#afb and he often refers to them as a standard of motion4 ,thus when with ,beatrice he was rapt from the summit of ,mount ,purgatory1 to express the swiftness of their flight he says it was almost as rapid as the movement of the sky--8veloci1 quasi come il ciel vedete40#afc ,constantine moving the capital of the ,roman ,empire eastwards is described as turning the ,roman ,eagle contrary to the course of the sky--8contra il corso del ciel10#afd and the sky itself is described as a sphere which is ceaselessly at play like a lively child3-- ---------------------------------------- -------------------------------- #afb 8,the great wheels10 8eternal wheels10 8starry wheels40 #afc 8,swift1 almost as the heaven ye behold40 ,par4 ii4 #ba4 #afd 8,against the course of the sky40 ,par4 vi4 #b4 444 8la spera1 ,che sempre a guisa di fanciullo scherza40#afe #afe 444 8,that sphere1 ,which aye in fashion of a child is playing40 ,purg4 xv4 #b1 #c4 7,longfellow74 ---------------------------------------- -------------------------------- ,to ,dante1 as to the ,greeks1 it is not the unusual or startling that appeals1 but the unfailing harmony of the regular celestial movements4 ,comets he mentions only twice1 and shooting stars twice1 eclipses seven times2 but there are scores of allusions to the rhythmical progression of ,sun and stars1 ,moon and planets4 ,the skies were familiar to him in all their daily aspects--sunset and dawn and radiant noons2 cloudy nights 8sotto pover cielo10#aff brilliant starlit nights1 nights of clear moonlight4 ,he had seen the stars fade one by one1 till at last even the brightest vanished in the glow of dawn3-- ---------------------------------------- -------------------------------- #aff 8,under a poor sky40 ,purg4 xvi4 #b4 8,e come vien la chiarissima ancella ,del sol pi oltre1 cos il ciel s chiude ,di vista in vista1 infino alla pi bella40#afg #afg 8,and as advances1 bright exceedingly1 ,the handmaid of the sun1 the heaven is closed1 ,light after light1 to the most beautiful40 ,par4 xxx4 #g-i4 7,longfellow74 ---------------------------------------- -------------------------------- he had watched for their first appearance in the evening twilight3-- 8,e s come al salir di prima sera ,comincian per lo ciel nuove parvenze1 ,s che la vista pare e non par vera44440#afh ---------------------------------------- -------------------------------- #afh 8,as at evening hour ,of twilight1 new appearances through heaven ,peer with faint glimmer1 doubtfully descried40 ,par4 xiv4 #gj-gb4 7,carey74 ---------------------------------------- -------------------------------- ,numberless other passages and expressions will occur to every ,dante reader1 proving how keenly he felt the beauty of the skies4 ,but they prove more than this4 ,other authors have felt and have described poetically the beauties of the skies1 but they often remember imperfectly what they saw1 or draw upon their imagination without any knowledge of the celestial movements1 and so fall into absurd mistakes4 ,the moon especially is a stumbling-block1 and it is quite a rare thing for a modern novelist to introduce one without making it do something impossible4 ,a new moon will rise at midnight1 or a waning moon at sunset2 she has even been known to rise and then to set in the dark hours of one short midsummer night2#afi and a well known author sees her in two phases at the same moment3 8the full moon rose1 yellow and gibbous60#agj ---------------------------------------- -------------------------------- #afi ,in ,kenneth ,grahame's delightful book1 full of sympathy with ,nature1 ,the ,wind in the ,willows4 ,the moon rose when it was 8past ten o'clock10 and 8sank earthwards reluctantly and left them0 before dawn4 #agj ,h4 ,g4 ,wells1 ,the ,time ,machine4 ---------------------------------------- -------------------------------- ,dante's moon does indeed give us a little trouble once or twice1 but he never makes flagrant mistakes of this kind4 ,his consistency and truth of description prove his knowledge of astronomy1 and also imply intelligent thoughtful watching of the celestial movements2 for it is notorious that book-knowledge1 if unassisted by acquaintance at first-hand with the facts of a subject like astronomy1 will not save a writer from glaring inaccuracies4 ,his allusions to the motions of the moon1 both diurnal and monthly1 show plainly that he understood them well4 ,his new moon appears in the evening1 his waning moon rises late at night and sets in morning sunshine1#aga and his full moon comes on the meridian at midnight1 for when he wishes to describe her at her brightest1 as a comparison with a very brilliant light1 he places her in a clear sky at midnight in her mid-month4#agb ,in the middle of a lunar month the moon is full1 and being exactly opposite the sun will reach the meridian at midnight3 this therefore is the time when she gives all the light she possibly can4 ,in the ,qustio#agc ,dante mentions that the moon does not move in the celestial equator1 but sometimes north of it1 and sometimes an equal amount south2 in the ,convivio he indicates the length of her period1 and briefly describes her phases and their cause--8,ora luce da un lato1 e ora luce dall' altro1 secondo che 'l sole la vede40#agd ---------------------------------------- -------------------------------- #aga ,inf4 xv4 #ah1 #ai2 ,purg4 xviii4 #gf-ha2 ,purg4 x4 #ad1 #ae1 ,cf4 ix4 #dd4 #agb ,purg4 xxix4 #ec1 #ed4 #agc ,qu4 xx4 #fa-fc4 #agd 8,now she shines on one side1 and now on the other1 according to the way the sun looks upon her40 ,conv4 ,,ii4 xiv4 #gg-gi4 ---------------------------------------- -------------------------------- ,her position in the zodiac is mentioned several times4 ,in one passage he indicates a very brief space of time in the following curious way3-- 8,quando ambo e due i figli di ,latona1 ,coperti del ,montone e della ,libra1 ,fanno dell' orizzonte insieme zona1 ,quant' dal punto che il zenit inlibra4 ,infin che l'uno e l'altro da quel cinto1 ,cambiando l'emisperio1 si dilibra1 ,tanto1 col volto di riso dipinto1 ,si tacque ,beatrice40#age ---------------------------------------- -------------------------------- #age 8,at what times both the children of ,latona1 ,surmounted by the ,ram and by the ,scales1 ,together make a zone of the horizon1 ,as long as from the time the zenith holds them ,in equipoise1 till from that girdle both ,changing their hemisphere disturb the balance1 ,so long1 her face depicted with a smile1 ,did ,beatrice keep silence40 ,par4 xxix4 #a-h4 ---------------------------------------- -------------------------------- ,that is to say1 when ,sun and ,moon 7the children of ,latona7 are both on the horizon1 but one being in ,aries and the other in ,libra they are opposite one another1 the zenith for a moment holds them1 as it were1 in balance2 but the next moment one will drop below the horizon while the other rises above it1 thus changing from the visible to the invisible hemisphere and vice versa1 as each frees itself 78si dilibra07 of the common horizon that girdled them4 ,the pause of ,beatrice was as brief as the time during which sun and moon would thus hang in the balance4 ,yet1 though ,dante shows that he was familiar with the movements and appearances of the moon1 his allusions to her are cold and comparatively rare4 ,unlike modern poets1 moonlight does not seem to have had any great fascination for him4 ,in all his works there are only fifty-one references to the moon1 and far the greater number of these are remarks about the measurement of time1 or else her phases1 her markings1 her share in causing eclipses etc4 ,in all his short poems 7including those of the ,vita ,nuova and ,convivio7 there are but two references1 and those as dry as possible4 8,pi lune0#agf is once used1 meaning several months1 and in a sonnet which describes the influences of each heaven on his lady1 all he can find to say of the moon's is 8,e 'l primo ciel di s gi non l' duro40#agg ---------------------------------------- -------------------------------- #agf 8,many moons40 ,canz4 xx4 #hi4 #agg 8,and the first heaven is not grudging to her40--,sonetto xxviii4 ---------------------------------------- -------------------------------- ,the chill of moonlight is spoken of as with a shudder on the hill of ,purgatory2#agh and its usefulness is recognized rather grudgingly when ,virgil remarks that yesternight the moon was full1 and adds that ,dante must remember it1 since it did him no harm in the depths of the ,forest4#agi ,it is true there is some beauty in the description of the aurora which preceded moonrise#ahj on the first night in ,purgatory1 but ,dante gives it an ugly name1 and the waning moon when seen on the following night1 four days after full1 is oddly compared to a bucket in shape4 ,dante did not admire this gibbous form1 for he instances the outline of the moon when not quite full as an ignoble curve1 contrasting it with the beauty of a perfect circle4#aha ---------------------------------------- -------------------------------- #agh ,purg4 xix4 #a1 #b4 #agi ,inf4 xx4 #abg-abi4 #ahj ,purg4 ix4 #a-i4 #aha ,conv4 ,,iv4 xvi4 #hi-ic4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #ci4 ,sun1 moon1 and zenith4 ,to illustrate ,par4 xxix4 #a-f4 7,see p4 #bfe74 ,in the first figure the sun and moon are balanced1 as it were1 being at equal distances from the zenith3 in the second1 a few minutes later1 by the rising of the sun and the setting of the moon1 the balance is disturbed1 and each changes its hemisphere4 ,hardly ever does he find a beautiful epithet for her3 she is ruler of ,hell1#ahb ,cain and the ,thorns#ahc 7in reference to the legend which sees this figure in her dark markings72 or she is simply ,delia1#ahd ,trivia1#ahe the daughter of ,latona1#ahf or with a little warmth the sister of the sun1#ahg and with the sun one of the two ,eyes of ,heaven4#ahh ,one exception to this harsh treatment is in the beautiful description of reaching the heaven of the moon1#ahi for there she is the first star1 the eternal pearl2 and the sudden burst of eloquence in the midst of a grave argument in ,de ,monarchia startles us doubly when we find that ,justice is compared to the moon--not1 as one might expect1 resplendent in a dark sky1 but ,phbe gazing at her brother opposite1 in the purple of the morning calm4#aij ,the passage from ,par4 xxix4 quoted above helps us to understand why the moon in this position should symbolize ,justice1 for here again is suggested the perfect balancing of the two great orbs1 as the sun rises and the full moon sets4 ---------------------------------------- -------------------------------- #ahb ,inf4 x4 #hj4 #ahc ,inf4 xx4 #abf4 #ahd ,purg4 xxix4 #gh2 ,ep4 vi4 #ed4 #ahe ,par4 xxiii4 #bf4 #ahf ,par4 x4 #fg2 xxii4 #aci2 xxix4 #a4 #ahg ,purg4 xxiii4 #abj4 #ahh ,purg4 xx4 #acb4 #ahi ,par4 ii4 #be-cf4 #aij ,de ,mon4 ,i4 xi4 #ce-cg4 ---------------------------------------- -------------------------------- ,add to these passages two similes drawn not indeed from the moon itself but from the halo surrounding her1#aia and two descriptions of brilliant moonlight nights1#aib and we have all that ,dante has written in praise of the moon4 ,it is true that throughout the ,inferno and ,purgatorio the sun typifies ,divine ,grace1 and the moon is his opposite1 but this cannot altogether explain the difference in their treatment1 even in the ,divine ,comedy4 ,a deeper reason seems to be ,dante's true southerner's love of the sun2 and he doubtless had the astronomer's feeling that moonlight always means loss of starlight1 which he dearly loved 7see ,purg4 xviii4 #gf1 #gg74 ,perhaps too the astrological views of the moon influenced him1 consciously or not4 ,according to ,ristoro1 the moon represents the poorest and lowest classes of people1 who are servants and messengers to the rest2 and as all the planets were supposed to be either masculine or feminine1 he ungallantly adds--8,e questa ,luna1 a cagione di sua vilt1 potemo dire per ragione ch'ella sia femmina40#aic ,her only house1 too1 which is ,cancer1 is also poor and base4 ,the moon1 moreover1 is nearer ,earth than any other planet1 and shows by her dark markings that she is less pure than the rest4 ---------------------------------------- -------------------------------- #aia ,par4 x4 #fg-fi2 and ,purg4 xxix4 #gh4 #aib ,purg4 xxix4 #ec1 #ed2 and ,par4 xxiii4 #bf4 #aic 8,and this moon1 because of her inferiority1 is rightly called feminine40 ---------------------------------------- -------------------------------- #b4 ,,movements ,,of ,,the ,,sun4 ,whatever the reason1 ,dante's fifty-one references to the moon are in strong contrast to his allusions to the sun4 ,these are four times as many1 and they include warm expressions of admiration and delight1 and beautiful epithets and similes4 ,the sun is ,titan with his chariot and horses1#aid he is a ,mirror1 a ,car of ,light1 the ,lantern of the ,world1 the ,prince of the ,stars1 the ,father of all mortal life4#aie ,his beautiful form is admired1 8la perfetta sua bella figura10#aif and his intense brilliance often noted4#aig ,he is the guide that leads all aright1#aih to whom ,virgil appeals3-- ---------------------------------------- -------------------------------- #aid ,ecl4 ii4 #a-d4 #aie ,purg4 iv4 #fb1 #fc2 ,purg4 iv4 #ei2 and xxix4 #aag1 #aah2 ,par4 i4 #ch2 ,canz4 xix4 #aad2 ,par4 xxii4 #aaf4 #aif 8,the perfection and beauty of his shape40 ,canz4 xix4 #gf4 #aig ,v4 ,n4 xlii4 #bi2 ,canz4 ix4 #b2 ,conv4 ,,ii4 xiv4 #abf1 #abg2 ,purg4 xvii4 #eb1 #ec2 ,par4 i4 #ed2 and x4 #dh1 etc4 #aih ,inf4 i4 #ag1 #ah4 8,o dolce ,lume1 a cui fidanza i' entro ,per lo nuovo cammin1 tu ne conduci40#aii #aii 8,o pleasant light1 my confidence and hope6 ,conduct us thou10 he cried1 8on this new way40 ,purg4 xiii4 #af1 #ag4 7,carey74 ---------------------------------------- -------------------------------- ,under his rays the rose expands1 the air is gladdened1 mists are dispelled1 snow melts1 and all things are quickened into life4#bjj ,unlike the moon1 the sun is the bringer of warmth and comfort1 chasing away cold and darkness1#bja sunrise is the hour of renewed hope and confidence1#bjb it strengthens our limbs1 paralysed by the cold of night1#bjc it is eagerly awaited through the darkness by the little bird on her nest2#bjd and delicate flowers1 bowed and closed during the cold night1 rise upright on their stems and open as soon as the sun shines once more upon them4#bje ,the exquisite sunsets and sunrises of the ,purgatorio are favourite passages with all readers4 ---------------------------------------- -------------------------------- #bjj ,par4 xxii4 #ee1 #ef2 ,inf4 vii4 #abb2 ,de ,mon4 ,,ii4 i4 #cg-ci2 and ,par4 ii4 #ajf-ajh2 ,canz4 xi4 #cg2 ,conv4 ,,iii4 xii4 #ei1 #fj1 etc4 etc4 #bja ,canz4 ix4 #e4 #bjb ,inf4 i4 #da-dc4 #bjc ,purg4 xix4 #aj1 #aa4 #bjd ,par4 xxiii4 #a-i4 #bje ,inf4 ii4 #abg-abi4 ---------------------------------------- -------------------------------- ,love is compared with the summer sun1#bjf the generosity of a noble nature resembles 8the great planet40#bjg ,the ,emperor ,henry ,,vii41 from whom ,dante expected the regeneration of ,italy and the whole ,christian world1 is likened to the rising sun2#bjh the birth of ,st4 ,francis is described as 8nacque al mondo un sole10#bji and his birthplace ought rightly to be called not ,assisi but ,orient4#baj ,virgil is addressed as 8,o ,sol che sani ogni vista turbata20#baa ,beatrice is 8,il sol degli occhi miei40#bab ,finally the sun is the best symbol of ,god1#bac and so it is used many times in the ,divine ,comedy3 8,il ,sol degli angeli10#bad 8,il ,sol che raggia tutto nostro stuolo20#bae a spirit turns to 8il ,sol che la riempie10#baf and when ,virgil laments that he is shut out of heaven it is in these words3 8,ho i' perduto ,di veder l' alto ,sol che tu disiri40#bag ---------------------------------------- -------------------------------- #bjf ,de ,mon4 ,,ii4 i4 #cf-da42 ,canz4 ix4 #bjg ,canz4 xix4 #if-aad4 #bjh ,ep4 v4 #aj2 and vii4 #ai1 #bj1 #be4 #bji 8,a sun rose upon the world40 ,par4 xi4 #ej4 #baj ,par4 xi4 #eb-ed4 #baa 8,o sun that healest all imperfect vision10 ,inf4 xi4 #ia4 #bab 8,the sun of my eyes40 ,par4 xxx4 #ge 7,see also ,par4 iii4 #a-c74 #bac ,conv4 ,,iii4 xii4 #eb-fc4 #bad 8,the ,sun of the angels40 ,par4 x4 #ec4 #bae 8,that ,sun which enlightens all our company40 ,par4 xxv4 #ed4 #baf 8,the ,sun which satisfies it40 ,par4 ix4 #h4 #bag 8,i have lost the sight of that high ,sun whom thou desirest40 ,purg4 vii4 #be1 #bf4 ,compare ,par4 xxx4 #abf2 xv4 #gf2 xviii4 #aje4 ---------------------------------------- -------------------------------- ,but we may not dwell on those thoughts of the sun as the typical giver of light and life2 we must ask what ,dante says about his movements1 since this was the chief subject-matter of medival astronomy4 ,his daily course1 8il cammin del ,sole10#bah is often spoken of1 and is indicated both by his position in the sky1 and the length and direction of shadows4 ,the second ,eclogue begins with a description of a breathlessly hot midday1 when objects1 which are usually shorter than their own shadows1 now surpassed them in length4 ---------------------------------------- -------------------------------- #bah 8,the path of the sun40 ,purg4 xii4 #gd4 8,resque refulgentes1 solitae superarier umbris1 ,vincebant umbras40 ,ecl4 ii4 #e1 #f4 ---------------------------------------- -------------------------------- ,at this time the sun appears most brilliant1 and seems to move most slowly1 since he is scarcely changing his position with regard to the horizon4 8,e pi corrusco1 e con pi lenti passi1 ,teneva il sole il cerchio di merigge40#bai ---------------------------------------- -------------------------------- #bai 8,shining more brightly and with slower steps1 the sun had gained the circle of midday40 ,purg4 xxxiii4 #ajc1 #ajd4 ---------------------------------------- -------------------------------- ,the greatest number of references to the sun's daily journey occur in the ,purgatory1 and we shall quote them in a later chapter4 ,his yearly journey through the zodiac is also very often referred to4 ,when relating his first meeting with ,beatrice1 ,dante names his age1 not by simply saying that he was nearly nine years old1 but by counting the number of the times that the 8heaven of light10 that is1 of the sun1 had returned to the same point since his birth3-- 8,nove fiate gi1 appresso al mio nascimento1 era tornato lo cielo della luce quasi ad un medesimo punto1 quanto alla sua proprio girazione40#bbj ---------------------------------------- -------------------------------- #bbj 8,nine times already since my birth had the heaven of light returned to the selfsame point almost1 as concerns its own revolution40 ,v4 ,n4 ii4 #a-d4 7,rossetti74 ---------------------------------------- -------------------------------- ,the sun's 8own revolution0 is of course its apparent yearly movement1 as distinct from the diurnal movement which it shares with all the heavenly bodies4 ,the same thought is expressed in a sonnet3 8,io sono stato con ,amore insieme ,dalla circolazion del ,sol mia nona40#bba ,we know further that ,dante was born in either ,may or ,june1 because he says1 when he finds himself among the stars of ,gemini1 that the sun was rising and setting in this sign at the time of his birth4#bbb ---------------------------------------- -------------------------------- #bba 8,i have dwelt with ,love since my ninth revolution of the sun40 ,son4 xxxvi4 #a1 #b4 #bbb ,see diagram on p4 #bgf4 8,o gloriose stelle ,con voi nasceva e s'ascondeva vosco ,quegli ch' padre d'ogni mortal vita1 ,quand' io senti' da prima l' aer tosco40#bbc #bbc 8,o glorious stars 444 ,with you was born1 and hid himself with you1 ,he who is father of all mortal life1 ,when first ,i tasted of the ,tuscan air40 ,par4 xxii4 #aab-aag4 7,longfellow74 ,at this date the sun entered the constellation of ,gemini on ,june #a 7,old ,style71 but was in the sign from ,may #aa to ,june #aa1 and it is always to the signs that ,dante refers in the ,divine ,comedy4 ,the anonymous fourteenth century commentator known as 8l',ottimo0 interprets this passage as indicating the time 8between the middle of ,may and the middle of ,june40 ---------------------------------------- -------------------------------- ,boccaccio tells us that a ,mayday feast1 given by the father of ,beatrice1 was the occasion of ,dante's first meeting with her1 and also that not long before his death in ,ravenna he told a friend that he had completed his fifty-sixth year in the preceding ,may1 so we may conclude that ,may was the month of his birth4 ,dante seems to have taken some trouble to find out the exact period of the sun's revolution4 ,his text-book1 the ,elementa of ,alfraganus1 only gives it as #cfe days nearly3--8,sol 444 orbem confecit diebus #cfe et prop 40 ,ristoro d',arezzo and ,brunetto ,latini were content to repeat this rough estimate1 and call the year #cfe days #f hours1 but ,dante wished to be more exact1 and somehow contrived to obtain a value which was much nearer the modern estimate of #cfe days1 #e hours1 #dh minutes1 #df seconds4 ,we know this from two passages4 ,in the ,convivio he gives the half period as less than #ahb days #ae hours2 and in the ,paradiso ,beatrice says that ,january will in time cease to be a winter month1 because of a neglected fraction of time4 8,prima che gennaio tutto si sverni ,per la centesma ch' laggi negletta40#bbd ---------------------------------------- -------------------------------- #bbd 8,ere ,january be unwintered wholly ,by the centesimal on ,earth neglected40 ,par4 xxvii4 #adb-adc4 7,longfellow74 ---------------------------------------- -------------------------------- ,january was in fact receding from the winter1 and steadily though slowly advancing towards the spring1 because the ,julian year 7as we saw1 p4 #aga7 was #aa minutes #ad seconds longer than the true solar tropical year4 ,when ,julius ,csar reformed the ,calendar1 ,march #be was made 7as of old7 to coincide with the spring equinox1 but by ,dante's time this date was #ac days late1 and the true equinox fell on ,march #ab4 ,consequently though the day called ,january #a still came #hd days before ,march #be1 it was only #ga days before the spring equinox4 ,if ,beatrice meant to speak with scientific precision1 and was correct in her hundredth part of a day per annum1 that is1 if the difference between the astronomical and the ,julian year was one day in a hundred years1 it would be #gajj years before the first of ,january came to coincide with the spring equinox1 and ,january became a spring month4 ,but the error quoted is really rather too large1 for a hundredth part of a day is #ad minutes #bd seconds1 and it was in fact only #aa minutes #ad seconds4 ,it would be interesting to know where ,dante found this value1 which is practically the only astronomical datum not given in ,alfraganus4 ,ptolemy1 following ,hipparchus1 had given the tropical year as _/ part of a day less than #cfe2 ,albategnius gave a more accurate figure1 and one which agrees well with the 8centesma10 for his tropical year differs from the ,julian by a little less than _/ of a day2 but he also improved the value of precession1 and ,dante does not seem to have known this1 so he was probably not acquainted with this astronomer's work4 ,the ,alfonsine ,tables gave a value which was very close indeed to the correct one1 making the tropical year only #cj seconds longer than the modern value1 and the difference between the ,julian and true year _/ of a day4 7,the correct value is _/74 ,either of these figures may have been known to ,dante indirectly3 perhaps he had obtained the ,alfonsine value in conversation with ,brunetto ,latini1 who had visited ,alfonso's court4 ,his fraction was evidently only approximate1 but it is interesting to know that he had found out more than popular books could tell him about the period of the sun's revolution1 and that he had been sufficiently struck by the small difference between the calendar and astronomical years to mention it in a picturesque way in his poem4 ,it is possible that he had heard of ,roger ,bacon's appeal to the ,pope in #abfg to correct the calendar because the date of the spring equinox was of importance in connection with the observation of ,easter4 ,it is hardly necessary to remind my readers that this was done by another ,pope three hundred years later1 before ,january had made much more advance towards becoming a spring month4 ,the hundredth part of a day1 of which ,beatrice complained1 is now subtracted from the year by omitting to make century years leap years2 but as the error was really not quite so great as she said1 an exception is made for century years divisible by #djj4 ,thus #afjj was a leap year1 but not #agjj1 #ahjj1 or #aijj4 ,illustration3 ,fig4 #dj4 ,the ,zodiac and the ,months4 ,dante seems to have connected any season of the year with the sun's path in the zodiac as readily as with the name of a month4 ,the sun's yearly course through the signs is shown diagrammatically in figure #dj1 and a glance at this will make clear a number of allusions without any explanation4 ,starting from the first point of ,aries at the spring equinox1 which in ,dante's time fell in the middle of ,march1 and taking one-twelfth of the year to traverse each sign1 it is evident that during the end of ,march and beginning of ,april the sun was in ,aries2 he entered ,cancer and reached the summer solstice in ,june1 the autumnal equinox in ,libra in ,september1 and the winter solstice when he entered ,capricornus in ,december4 ,the six signs above the horizontal line are northern1 the six below are southern4 ,the following are a few typical examples4 ,when ,dante wishes to express the transition of his feelings from despondency to courage1 at seeing the stern and troubled face of his guide melt suddenly to a smile1 he compares himself to a poor shepherd who wakes early and sees the fields covered1 as he thinks1 with snow1 but in a short time finds that it is only hoar-frost which has put on the semblance of her white sister1 and seeing the face of the world changed he gladly leads out his sheep to pasture4 ,the time at which this may happen is 8,quella parte del giovinetto anno1 ,che il sole i crin sotto l',aquario tempra1 ,e gi le notti al mezzod sen vanno40#bbe ---------------------------------------- -------------------------------- #bbe 8,in that part of the youthful year wherein ,the sun his locks beneath ,aquarius tempers1 ,and now the nights draw near to half the day40 ,inf4 xxiv4 #a-c4 7,longfellow74 ---------------------------------------- -------------------------------- ,that part of the youthful year when the sun cools his locks beneath ,aquarius is clearly the end of ,january or beginning of ,february1 but the last line may bear one of two meanings4 ,if we translate 8mezzod0 as 8half the day0 it means that the nights are growing shorter1 and very soon 7in ,march7 when the sun will have reached the equinox1 they will be just twelve hours long4 ,if we take 8mezzod0 as meaning 8the south10 we must interpret the passage in the light of others in the ,divine ,comedy where ,night is personified1 and considered as circling in the zodiac always opposite to the sun4 ,for instance in ,purg4 ii4 #a-f 7a passage which will be more fully explained later7 ,night is described as circling opposite to the sun1 8,la notte1 che opposita a lui cerchia10#bbf and as the sun at that time was in ,aries1 ,night was in ,libra1 8le ,bilance40 ,henceforth for six months the sun will be in the northern signs1 and the days longer than the nights1 but as soon as ,night begins to assert her supremacy1 and the nights begin to be longer than the days1 the sun enters ,libra and then it is not visible all night4 ,this is the meaning of ---------------------------------------- -------------------------------- #bbf 8,night that opposite to him revolves40 7,longfellow74 8le ,bilance1 ,che le caggion di man quando soverchia40#bbg #bbg 8,the ,scales1 that from her hands are dropped ,when she reigns highest40 ,purg4 ii4 #e1 #f4 7,carey74 ---------------------------------------- -------------------------------- ,when ,night becomes dominant1 the ,scales fall from her hand1 for the sun is in that sign4 ,applying this idea to the passage quoted above1 it will mean 8,the nights are going southward10 for the sun in ,aquarius is not far from the point where he crosses the equator to the north1 therefore ,night circling opposite to him is nearing the point where she goes south4 ,either interpretation is faithful to fact1 but perhaps the circumstance that the plural noun is used favours the first4 ,illustration3 ,fig4 #da4 ,the ,ram on the ,ecliptic4 ,to face p4 #bgi4 ,from the 8,cosmi ,historia0 of ,robert ,flud1 a4d4 #afab4 7,reproduced from ,brown's ,phainomena of ,aratos47 ,conrad ,malaspina prophesied to ,dante that his favourable opinion of the ,malaspina family would be justified 8before the sun had come to rest again seven times in the bed which the ,ram covers and bestrides with his four feet40 8,ed egli3 ,or va1 che il ,sol non si ricorca ,sette volte nel letto che il ,montone ,con tutti e quattro i pie copre ed inforca ,che cotesta cortese opinione 4440#bbh ---------------------------------------- -------------------------------- #bbh 8,and he3 ,now go1 for the sun shall not lie ,seven times upon the pillow which the ,ram ,with all his four feet covers and bestrides4 ,before that such a courteous opinion 4440 ,purg4 viii4 #acc-acf4 7,longfellow74 ---------------------------------------- -------------------------------- ,the sun was at the time in the ,ram1 and ,malaspina means that less than seven years would elapse1 before his prophecy was fulfilled4 ,the aptness of the description may be seen by the figure of ,aries as portrayed in an old seventeenth century book in which the ,ram is uncomfortably trying to sit on the ecliptic4 ,another instance is in the beautiful midwinter ,ode1 8,io son venuto al punto della rota40#bbi ,each stanza pictures a feature of a severe winter--snow and rain1 the absence of summer birds1 bare trees and dead flowers1 the favourite walk become a torrent2 but the first describes the position of stars and planets4 ,when the sun sets1 the ,twins appear on the eastern horizon1 hence we know at once that the sun is in ,sagittarius and the time is ,november or ,december4 ,to confirm his melancholy1 the poet adds that the ,star of ,love 7,venus7 is hidden from us by the sun's rays which now shine athwart her1 and that the planet which strengthens the cold 7,saturn1 the 8frigida stella0 of ,virgil7 displays himself in that arc of the sky in which all the seven planets cast the shortest shadow2#bcj that is1 either he is on the meridian at sunset1 or he is in the most northerly part of the zodiac1 in ,gemini or ,cancer4 ,a planet in this place1 as for instance the sun at midsummer1 is visible longer1 describes a longer arc1 and casts shorter shadows1 than in any other part of the zodiac4 ,and as this is the part which rises over the eastern horizon as the sun sets1 ,saturn would also rise at that time and remain visible all night4 ---------------------------------------- -------------------------------- #bbi 8,i have come to that part of the wheel40 ,canz4 xv4 #bcj ,like all medival writers1 ,dante includes the sun and moon among the seven planets4 ,the others do not cast perceptible shadows1 except ,venus and ,jupiter at their brightest4 ,the opening lines of the ,ode run thus3-- 8,io son venuto al punto della rota1 ,che l'orizzonte1 quando il ,sol si corca1 ,ci parturisce il geminato cielo2 ,e la stella d'amor ci sta rimota ,per lo raggio lucente1 che la 'nforca ,s di traverso1 che le si fa velo2 ,e quel pianeta che conforta il gelo ,si mostra tutto a noi per lo grand' arco1 ,nel qual ciascun de' sette fa poca ombra40#bca #bca 8,i to that point in the great wheel have come1 ,wherein the horizon1 when the sun doth set1 ,brings forth the twin-starred heaven to our sight2 ,and ,love's fair star away from us doth roam1 ,through the bright rays obliquely on it met ,in such wise that they veil its tender light2 ,that planet which makes keen the cold of night ,shows himself to us in the circle great1 ,where each star of the seven casts little shade40 7,plumptre74 ---------------------------------------- -------------------------------- ,it is astonishing that ,giuliani should so completely miss the point of the 8twinned sky10 that he substitutes 8ingemmato0 for 8geminato10 and reads-- 8 444 la rota1 ,ch' all orizzonte1 quando il ,sol si corca1 ,ci parturisce l'ingemmato cielo40#bcb ---------------------------------------- -------------------------------- #bcb 8,the ,wheel which1 when the sun sets1 brings forth for us on the horizon the jewelled sky40 ---------------------------------------- -------------------------------- ,he understands the hour of evening to be meant1 when the ,wheel of ,day and ,night brings a jewelled1 i4e4 starry sky on the horizon as the sun sets4 ,but it is not only on the horizon that stars appear at sunset2 and the mention of ,gemini to indicate the time of year is thoroughly characteristic of ,dante4 ,the ,wheel is the revolving year which has carried the sun into ,sagittarius4 ,angelitti remarks that the whole description was literally true for ,december #abif1 since ,venus was then in conjunction with the sun1 and ,saturn in ,cancer2#bcc and as this poem is a complaint of the hardness of his lady1 to whom the poet is nevertheless wholly devoted1 it may well have been written in that time when the lady ,philosophy refused to smile upon her lover4#bcd ---------------------------------------- -------------------------------- #bcc ,sulla ,data del ,viaggio ,dantesco p4 #ij1 note4 #bcd ,comparing ,conv4 ,,ii4 ii4 #ab1 xiii4 #di-eb1 and ,,iv4 i4 #fj-fb1 we learn that in ,august #abic 7vide infra1 p4 #cad71 ,dante first became acquainted with the ,lady ,philosophy2 that in the early part of #abif he was completely under her spell2 and that some time afterwards she for a while estranged herself from him4 ---------------------------------------- -------------------------------- ,further on in the same poem the effects of the sun in spring1 when he is in the sign of ,aries1 are alluded to as 8the virtue of ,aries03-- 8,passato hanno lor termine le fronde1 ,che trasse fuor la virt d',ariete1 ,per adornare il mondo1 e morta l' erba40#bce ---------------------------------------- -------------------------------- #bce 8,scattered and faded now is all the foliage ,which had burst forth1 beneath the power of ,aries1 ,to beautify the world1 the grass is withered40 ,canz4 xv4 #dj-db4 ---------------------------------------- -------------------------------- ,contrast with this the passage in the ,paradiso where 8nocturnal ,aries0 is used as a synonym for autumn4 8,questa primavera sempiterna ,che notturno ,ariete non dispoglia40#bcf ---------------------------------------- -------------------------------- #bcf 8,this everlasting spring ,nocturnal ,aries never can despoil40 ,par4 xxviii4 #aaf-aag4 ---------------------------------------- -------------------------------- ,for although ,aries may be seen during some part of the night in the greater part of the year1 it is most emphatically a noctural sign when it rises as the sun sets1 and remains above the horizon until he rises2 this happens when the sun is in the opposite sign of ,libra1 which he enters at the autumnal equinox4 ,a rather curious passage in the ,paradiso is incomprehensible unless we think of the sun's path in the zodiac1 and realize that ,dante is comparing the brightness of the spirit of ,st4 ,john in an indirect way with the brightness of the sun4 8,poscia tra esse un lume si schiar1 ,s che1 se il ,cancro avesse un tal cristallo1 ,l'inverno avrebbe un mese d'un sol d40#bcg ---------------------------------------- -------------------------------- #bcg 8,thereafterward a light among them brightened ,so1 that if ,cancer one such crystal had ,winter would have a month of one sole day40 ,par4 xxv4 #ajj-ajb4 7,longfellow74 ---------------------------------------- -------------------------------- ,if a light as dazzling as this spirit were to shine forth in ,cancer1 there would be perpetual day for a whole month in winter4 ,for when the sun entered ,capricornus1 which he does in ,december1 he would be exactly opposite1 so that as one light set the other would rise1 and there would be no darkness until the sun passed into another sign4 ,to many similar instances the diagram 7p4 #bgf7 will be found to supply a key1 and some we shall have occasion to notice presently in another connection4 #c4 ,,the ,,stars4 ,if our poet did not love moonlight1 there is no doubt that starlight was very dear to him4 ,never are stars spoken of as cold1 or placed in antithesis to the sun4 ,rather are they classed together1 as in the pathetic letter1 written when he heard of the possibility that the ,florentines might receive him again if he would consent to return as a disgraced but pardoned criminal4 ,if this is the only path to ,florence1 never will he re-enter the beloved city4 8,what then80 he cries4 8,can he not see the mirrors of the sun and of the stars1 wherever he may be8 can he not meditate on precious truths under any sky80#bch ---------------------------------------- -------------------------------- #bch ,ep4 ix4 #df-di4 ---------------------------------------- -------------------------------- ,he describes the ,inferno as bereft of stars as well as of sun2#bci he hopes to escape those dark abysses to see the beautiful stars again1#bdj and the terror of the sounds of weeping and crying is heightened indescribably by the simple words3--8risonavan per l'aer senza stelle40#bda ,when he does at length come forth to see 8le cose belle che porta il ciel0#bdb how eagerly he gazes1 not only at ,venus1 but at the new stars in the south6 how his 8greedy eyes0#bdc seek the same region as soon as dusk begins to fall6 and how radiantly the stars look down upon him on that last night on the rocky slopes of the ,mountain1 near the summit6#bdd ---------------------------------------- -------------------------------- #bci ,inf4 iii4 #bc4 #bdj ,inf4 xvi4 #hb1 #hc4 #bda 8,resounded through the air without a star40 ,inf4 iii4 #bc4 #bdb 8,the fair things that heaven holds40 ,inf4 xxxiv4 #acg1 #ach4 #bdc ,purg4 viii4 #he4 #bdd ,purg4 xxvii4 #hi1 #ij4 ---------------------------------------- -------------------------------- ,this is all allegorical1 no doubt1 but it is because of ,dante's feeling for the real 8belle stelle0#bde that he uses them as symbols of truth and holiness1 and concludes each ,cantica of the ,divine ,comedy with their name3-- ---------------------------------------- -------------------------------- #bde 8,beautiful stars10 ,inf4 xvi4 #hc4 8,e quindi uscimmo a riveder le stelle40#bdf 8,puro e disposto a salire alle stelle40#bdg 8,l',amor che move il sole e l'altre stelle40#bdh #bdf 8,thence issuing we beheld again the stars40 #bdg 8,pure and disposed to mount unto the stars40 #bdh 8,the ,love that moves the sun and the other stars40 ---------------------------------------- -------------------------------- ,here 8stelle0 has the wider meaning of the ,french 8astres10 for which we have no equivalent in ,english except the clumsy 8heavenly bodies20 but most of ,dante's hundred references are to stars in the more special sense1 and often to particular stars or constellations4 ,over eighty occur in the ,divine ,comedy4 ,stars are jewels1 torches1 flames1 immortal nymphs adorning every region of the sky4#bdi ,heaven is made beautiful by their light1 and the joy of the angels is expressed in their shining1 as mortal joy shines forth in human eyes4#bej ,if the spirits in the fourth heaven are described as glowing suns1#bea the 8splendours0 that descend upon the golden ladder in the seventh1 make ,dante think that all the stars in the sky are gathered together there4#beb ---------------------------------------- -------------------------------- #bdi ,purg4 ix4 #d2 ,purg4 viii4 #hi2 ,purg4 i4 #be2 ,par4 xxiii4 #bf4 #bej ,par4 ii4 #acj1 #adb-add4 #bea ,par4 x4 #gf4 #beb ,par4 xxi4 #bh-cc4 ---------------------------------------- -------------------------------- ,the eyes of ,beatrice shone brighter than stars2#bec light comes as from many stars in reading the sacred books2#bed faith gleams like a star in the sky2#bee and truth appears in a mind cleared of falsehood and error like the radiance of stars in a sky which has been wholly swept of cloud and mist by a north wind4 ---------------------------------------- -------------------------------- #bec ,inf4 ii4 #ee4 #bed ,par4 xxv4 #gj4 ,see also ,conv4 ,,ii4 xvi4 #d-ab1 where the writings of ,bothius and ,cicero1 and all instructive books1 are called stars full of light4 #bee ,par4 xxiv4 #adg4 8,come rimane splendido e sereno ,l'emisperio dell' aer1 quando soffia ,borea da quella guancia ond' pi leno1 ,perch si purga e risolve la roffia ,che pria turbava1 s che il ciel ne ride ,con le bellezze d'ogni sua paroffia3 ,cos fec' io1 poi che mi provvide ,la ,donna mia del suo risponder chiaro1 ,e come stella in cielo il ver si vide40#bef #bef 8,even as remaineth splendid and serene ,the hemisphere of air1 when ,boreas ,is blowing from that cheek where he is mildest1 ,because is purified and resolved the wrack ,that erst disturbed it1 till the welkin laughs ,with all the beauties of its pageantry3 ,thus did ,i likewise1 after that my ,lady ,had me provided with her clear response1 ,and like a star in heaven the truth was seen40 ,par4 xxviii4 #gi-hg4 7,longfellow74 ---------------------------------------- -------------------------------- ,stars1 as well as the sun1 are used as symbols for the objects of ,dante's deepest reverence2 for the ,blessed ,virgin is called 8la viva stella10#beg and the ,final ,vision in which the redeemed find their ultimate bliss is a ,trinal ,light seen as a single star3-- ---------------------------------------- -------------------------------- #beg 8,the shining star40 ,par4 xxiii4 #ib4 8,o trina ,luce1 che in unica stella ,scintillando a lor vista s gli appaga1 ,guarda quaggi alla nostra procella40#beh #beh 8,o ,trinal ,light1 that in a single star ,sparkling upon their sight so satisfies them1 ,look down upon our tempest here below60 ,par4 xxxi4 #bh-cj4 7,longfellow74 ---------------------------------------- -------------------------------- ,the diurnal motion of the stars is referred to many times4 ,as ,dante watched the mystical procession in the ,earthly ,paradise1 and saw one group follow in the footsteps of another across the flowers and the grass1 he thought of the stately procession of stars which we see here by night1 star following star across the sky4#bei ,their movement marks for him the passage of time1 as we see in the first sonnet of the ,vita ,nuova3-- ---------------------------------------- -------------------------------- #bei ,purg4 xxix4 #ia4 8,gi eran quasi ch' atterzate l' ore ,del tempo che ogni stella piu lucente40#bfj #bfj 8,of those long hours wherein the stars above ,wake and keep watch1 the third was almost nought40 ,v4 ,n4 iii4 #ha1 #hb4 7,rossetti74 ---------------------------------------- -------------------------------- and in the ,inferno1 where ,virgil hastens ,dante1 saying that all the stars are sinking which were rising when he started on his long journey4#bfa ---------------------------------------- -------------------------------- #bfa ,inf4 vii4 #ih1 #ii4 ---------------------------------------- -------------------------------- ,the motion of those stars which neither rise nor set1 but are always seen circling round the pole1 is clearly described4 ,in the heaven of the sun1 spirits gather round ,dante and ,beatrice1 and circle round them1 8,come stelle vicine ai fermi poli20#bfb and the motion of the stars near the pole is said to be slow1 like the part of a wheel which is near the axle4#bfc ,we may compare these descriptions with the statement of ,alfraganus3--8,e stell 7i4e4 the northern circumpolar7 vertuntur omnes circa idem punctum4 ,et quei ex iis puncto huic est vicinior1 minorem conficit circulum3 motusque ejus appret lentior40#bfd ,dante assumes that his readers understand this motion when he describes himself as seeing unknown stars near the ,south ,pole4 ,the ,mount of ,purgatory is supposed to be situated in the southern hemisphere1 and at his first arrival1 before dawn1 he turns to the right1 after looking at ,venus in the east1 therefore to the south1 and sees near the pole four stars so brilliant that the whole sky seems to rejoice in their radiance1 and he pities the 8widowed0 northern hemisphere because they are invisible there4#bfe ,in the evening1 as soon as it begins to grow dark1 although he is engaged in an interesting discourse with a friend with whom he had exchanged warm greetings1 he looks eagerly once more towards the pole 7note the intensity expressed by the repeated 8pure07-- ---------------------------------------- -------------------------------- #bfb 8,like unto stars neighbouring the stedfast poles40 ,par4 x4 #gh4 #bfc ,purg4 viii1 #hf1 #hg4 #bfd 8,these stars all revolve round the same point1 and the nearer a star is to this point1 the smaller is the circle that it makes1 and the slower its motion appears40 ,el4 ,ast4 cap4 ii4 #bfe ,purg4 i4 #bb-bg4 8,gli occhi miei ghiotti andavan pure al cielo1 ,pur l dove le stelle son pi tarde1 ,s come rota pi presso allo stelo40#bff #bff 8,my insatiate eyes ,meanwhile to heaven had travelled1 even there ,where the bright stars are slowest1 as a wheel ,nearest the axle40 ,purg4 viii4 #he-hg4 7,carey74 ,he now sees three bright stars which make this pole glow with light1 and ,virgil says that the stars he saw in the morning are low1 while those now visible have risen higher to take their place4 8,ed egli a me3 ,le quattro chiare stelle ,che vedevi staman son di l basse1 ,e queste son salite ov' eran quelle40#bfg #bfg 8,and he to me3 ,the four resplendent stars ,thou sawest this morning are down yonder low1 ,and these have mounted up to where those were40 ,purg4 viii4 #ia-ic4 7,longfellow74 ---------------------------------------- -------------------------------- ,the diurnal movement of the starry heaven is also alluded to in the ,convivio1 and contrasted with that immensely slow movement which was discovered by ,hipparchus1 and is called by us ,precession4 ,the starry heaven1 says ,dante1 displays one of its poles to us1 and keeps the other hidden2 and in like manner it displays only one movement to us1 and keeps the other almost hidden4 ,by the first1 it revolves once in every day from east to west2 the other is nearly insensible1 being only one degree in a hundred years1 and it is from west to east4#bfh ,this is the value of precession as given by ,alfraganus1 following ,ptolemy4 ---------------------------------------- -------------------------------- #bfh ,conv4 ,,ii4 xv4 #aj-ad1 and #if-ajd4 ---------------------------------------- -------------------------------- ,it was this stupendous and mysterious cycle which was used by ,dante to measure the age of ,beatrice1 though for his own he used 7as we saw7 the ordinary measure of the sun's period4 ,when he first saw 8la gloriosa donna0#bfi she had only been in this life so long that the starry heaven had moved towards the east one-twelfth part of a degree4 ,therefore1 she was one-twelfth of a hundred years old1 or #h years #d months1 8so that it was near the beginning of her ninth year that she appeared to me1 and ,i saw her nearly at the end of my ninth40#bgj ---------------------------------------- -------------------------------- #bfi 8,the glorious ,lady40 #bgj ,v4 ,n4 ii4 #i-ae4 ---------------------------------------- -------------------------------- ,dante tells us how many stars had been counted by 8the sages of ,egypt10 by whom he means ,ptolemy and the other ,alexandrians3 he did not know that the star catalogue of the ,almagest was originally made by ,hipparchus of ,rhodes4 8,dico ch' il cielo stellato ci mostra molto stelle2 ch1 secondoch li savi d',egitto hanno veduto1 infino all'ultima stella che appare loro in meridie1 mille ventidue corpora di stelle pongono1 di cui io parlo40#bga ---------------------------------------- -------------------------------- #bga 8,i say that the starry heaven displays a multitude of stars to us1 for as the ,sages of ,egypt have perceived1 including the last star which appears to them in the south1 they reckon one thousand and twenty-two starry bodies1 of which ,i am now speaking40 ,conv4 ,,ii4 xv4 #ah-bb4 7,jackson74 ---------------------------------------- -------------------------------- ,it will be noted that he carefully avoids saying that this is the number of all the stars visible from the whole earth4 ,had he1 like ,ristoro1 run away with the idea that a blank space on the globe meant a blank in the sky1 his night sky seen from ,purgatory would have been strangely bare and dull6 ,yet both writers used the same text-book4 ,dante is here following ,alfraganus closely1 for he had written in his nineteenth chapter3-- 8,sciendum itaque sapientes inivisse mensuram stellarum fixarum omnium1 quoad instrumentis observari e potuerunt1 extremam usque meridiei partem1 in tertio climate ipsis conspicuam4444 ,stell universae quarum agi mensura potuit sunt mille viginti du40#bgb ---------------------------------------- -------------------------------- #bgb 8,you are to know that the ,sages measured the places of all the fixed stars as accurately as possible with their instruments1 as far south as they could see in the third climate4444 ,the number of all the stars which he was able to measure is one thousand and twenty-two40 ---------------------------------------- -------------------------------- ,both in the ,qustio and the ,paradiso ,dante notes how stars differ1 not only in their brightness or 8magnitude10 but also in the quality of their light1 by which he probably means their colour3-- 8,videmus in eo sc4 clum stellatum differentiam in magnitudine stellarum et in luce40#bgc ---------------------------------------- -------------------------------- #bgc 8,we see in it 7the starry heaven7 a difference in the magnitude of the stars and in their light40 ,qu4 xxi4 #ai-ba4 8,lumi1 li quali nel quale e nel quanto ,notar si posson di diversi volti40#bgd #bgd 8,lights many the eighth sphere displays to you ,which in their quality and quantity ,may noted be of aspects different40 ,par4 ii4 #fe-ff4 7,longfellow74 ---------------------------------------- -------------------------------- ,it seems as if it were the beauty and the movement of the starry sky as a whole which appealed to ,dante1 rather than the distinguishing of special stars and constellations4 ,those which he mentions are almost all either in the zodiac1 and used to denote the hour1 the season1 or the position of one of the seven planets2 or else they are near one of the poles and illustrate the circumpolar motion4 ,all the zodiacal constellations are mentioned except ,virgo and ,sagittarius4 ,besides the ordinary names of 8,ariete10 8,libra10 etc41 ,aries is called 8il ,montone20#bge ,gemini 8il segno che segue il ,tauro10 8gli eterni ,gemelli10 and 8il bel nido di ,leda10#bgf in reference to the mother of ,castor and ,pollux1 its two brightest stars2 ,libra is 8le ,bilance02#bgg ,scorpio 8il freddo animale02#bgh ,capricornus is 8il ,capra del ciel02#bgi and ,pisces 8la celeste ,lasca40#bhj ---------------------------------------- -------------------------------- #bge 8,the ,ram40 ,purg4 viii4 #acd2 ,par4 xxix4 #b4 #bgf 8,the sign which follows ,taurus10 ,par4 xxii4 #aaj1 #aaa2 8,the eternal ,twins10 xxii4 #aeb2 8,the fair nest of ,leda10 xxvii4 #ih4 #bgg 8,the ,balance40 ,purg4 ii4 #e4 #bgh 8,the cold creature40 ,purg4 ix4 #e4 #bgi 8,the ,goat of the sky40 ,par4 xxvii4 #fi4 #bhj 8,the celestial ,carp40 ,purg4 xxxii4 #ed4 ---------------------------------------- -------------------------------- ,in one place ,castor and ,pollux are mentioned1 but merely as a synonym for the whole constellation of ,gemini4#bha 8,il petto del ,leone ardente0#bhb is perhaps ,cor ,leonis1 the ,heart of the ,lion1 for this is the name given to ,regulus by both ,ptolemy and ,alfraganus4 ,the 8,maggior ,fortuna0#bhc of ,purg4 xix4 #d1 is a group of stars belonging to the two constellations of ,aquarius and ,pisces1 in which the geomancers1 who told fortunes by means of certain points traced at random1 thought they saw a special series of these points1-33344 ---------------------------------------- -------------------------------- #bha ,purg4 iv4 #fa4 #bhb 8,the burning ,lion's breast40 ,par4 xxi4 #ad4 #bhc 8,greater ,fortune40 ---------------------------------------- -------------------------------- ,it is generally agreed that the 8gemme0 of ,purg4 ix4 #d1 8poste in figura del freddo animale1 ,che con la coda percote la gente10#bhd are some stars of ,scorpio which were shining on the eastern horizon just before the moon rose on the first night in the ,island of ,purgatory4 ---------------------------------------- -------------------------------- #bhd 8,gems 444 set in the shape of that cold animal ,which with its tail doth smite amain the nations40 7,longfellow74 ---------------------------------------- -------------------------------- ,the zodiacal constellations in general are spoken of as 8all the lights of his the sun's path30 8,tutti i lumi della sua strada40 7,par4 xxvi4 #aba1 #abb74 ,the pole star is described as the point of the axle round which the first sphere revolves4#bhe ,the first sphere 7or wheel1 as it is called1 with reference to its circling motion7 is here the ,primum ,mobile1 which was thought to cause the diurnal motion4 ,this unique position gains for the pole star the name of 8the star10 as for instance in ,conv4 ,,iii4 v4 #hd1 #he1 where ,dante says that a man standing at the north pole would have 8la stella0 directly over his head4 ,and in ,paradise he hears a voice among the spirits which makes him turn in its direction as the needle turns to the star-- ---------------------------------------- -------------------------------- #bhe ,par4 xiii4 #aa1 #ab4 8,voce1 che l'ago alla stella ,parer mi fece in volgermi al suo dove40#bhf #bhf 8,a voice1 ,that made me seem like needle to the star1 ,in turning to its whereabout40 ,par4 xii4 #bi1 #cj4 7,carey74 ---------------------------------------- -------------------------------- ,this property of the magnet was known in ,dante's day1 as well as its power of attracting iron1 though only the latter had been known to ,ptolemy and the classical world4 ,whether the discovery came from ,china1 where it is said that some form of compass has been used since the second century ,a4,d41 or whether it had been discovered independently by ,arab or ,italian navigators1 we do not know3 but scholars and poets in the twelfth and early thirteenth centuries write of the 8ugly brown stone0 used by sailors to make an instrument that cannot lie4 ,for a needle1 rubbed by it and run through a straw1 when floated on water turns so surely to 8the star0 that one need never doubt its guidance4 ,thus writes ,guyot1 the poet of ,languedoc1 about #abjj3-- 8,un art font qui mentir ne puet1 ,par la vertu de la manete1 ,une pierre laide et brunete1 ,ou le fers volentiers se joint1 ,ont3 si esgardent le droit point1 ,puis c'une aiguile i ont touchie1 ,et en un festu l'ont couchie1 ,en l'eve la metent sanz plus1 99 99 99 99 99 ,puis se torne la pointe toute ,contre l'estoile si sanz doute1 ,que ja nas hom n'en doutera40 ,and thus ,ristoro3-- 8,l'angola1 che guidi li marinari1 ch per la virtu del cielo tratta e rivolta alla stella la quale chiamata tramontana40#bhg ---------------------------------------- -------------------------------- #bhg 8,the needle which guides mariners1 for by the virtue of the heavens it is attracted and turned towards that star which is called the ,north ,star40 ,composizione del ,mondo1 ,bk4 ,,vii4 part iv4 ch4 #b4 ---------------------------------------- -------------------------------- ,albertus ,magnus speaks of it in the same way1 as something well known to mariners4 ,it seems strange to us how ,dante and his contemporaries failed to see the importance of this discovery2 ,brunetto ,latini1 when the ugly stone was shown to him on his visit to ,roger ,bacon at ,oxford1 even professing to regard it as a mere toy1 of no practical use4 ,dante discusses the number of the stars known to ,ptolemy1 and describes the last mad voyage of ,ulysses1 who saw all the stars of the other pole1 while ours sank low on the ocean floor2#bhh but he does not seem to guess that the new toy would make possible even longer voyages than these1 and that in time the blank in his celestial globe would be filled4 ---------------------------------------- -------------------------------- #bhh ,inf4 xxvi4 #abg-abi4 ---------------------------------------- -------------------------------- ,yet even in his own life-time plucky little ,genoa fitted out two galleys which ventured through the forbidden ,straits1 with intent to circumnavigate ,africa and find a new route to ,india4 ,and meanwhile1 travelling by old overland or coasting routes1 ,italian missionary monks1 and ,italian traders1 were visiting southern countries and describing southern skies4 ,friar ,giovanni de ,monte ,corvino1 who was in ,south ,india with ,nicolo of ,pistoia1 writes home in #abia1 telling of his disappointment that he had never been able to see 8the other pole star0 7l'altra tramontana71 though he saw new stars moving round and evidently near to it1 close to the southern horizon4 ,a few years later ,marco ,polo the ,venetian was dictating the story of his travels to a ,pisan in ,genoa3 he had been further south than the missionaries1 for in a certain island 7probably ,sumatra7 he had seen the south pole 8a spear's length0 above the horizon2 and in the land of ,zinzi 7,zanzibar87 he had seen a marvellous star as big as a sack 7which was evidently the ,greater ,magellanic ,cloud74 ,this he drew a picture of with his own hand4 ,dante's silence1 and probable incredulity1 regarding these experiences of his own countrymen and contemporaries is characteristic of his age2 for scholars were too eager to explore the precious classical lore lately recovered from oblivion1 to realize that they were on the threshold of a new era in knowledge1 of which these men were pioneers4 ,it is sometimes thought1 however1 that ,dante made use of contemporary observations of southern skies in his description of the stars he feigned himself to have seen when the ,wain disappeared under his northern horizon4#bhi ,quite correctly1 he does not place any single bright star to mark the south pole2 his two constellations1 one of four bright stars seen above the pole in the morning1#bij one of three which takes its place after sunset1#bia are these real or fictitious8 ---------------------------------------- -------------------------------- #bhi ,purg4 i4 #cj4 #bij ,purg4 i4 #bf4 #bia ,purg4 viii4 #hi4 ---------------------------------------- -------------------------------- ,it is a fact that there are four bright stars in the form of a cross1 lying between #ef and #fc south3 are these ,dante's 8quattro chiare stelle10 8quattro luci sante80#bib ,they were not recognized as a separate constellation until the beginning of the sixteenth century1 when ,amerigo ,vespucci described them in his letters about his southern voyages1 and the ,florentine ,andrea ,corsali wrote about the marvellous ,cross which was so beautiful that in his opinion no other constellation in the sky was worthy to be compared with it4 ,this1 he believed1 was the very cross of which ,dante had spoken in a prophecy4 ---------------------------------------- -------------------------------- #bib 8,four bright stars1 four sacred lights40 ---------------------------------------- -------------------------------- ,even among ,dante's most enthusiastic admirers1 ,i suppose none will be found to-day to support this view2 but many think that he must have heard of the ,cross from travellers4 ,true1 these stars are visible during at least part of the year in all places south of #cd north1 and therefore in ,north ,africa1 and they had been catalogued by ,ptolemy as part of the ,centaur1 so that no astronomer could take them to be a newly-found constellation1 but might not some unscientific traveller like ,marco ,polo have brought a vague report of their position8 ,illustration3 ,,map ,,of ,,stars ,,visible ,,before ,,dawn ,,in ,,purgatory4 ,to face p4 #bie ,to this we might reply that ,dante never says his four stars were in the form of a ,cross2 that there had to be four to represent the four ,pagan virtues1 the other constellation of three representing the three ,christian virtues 7compare the group of four handmaidens who sing1 8,noi siam qui ninfe1 e nel ciel siamo stelle10#bic and are followed by a group of three72#bid and that this other constellation was certainly imaginary1 since there is no group of three bright stars anywhere near the south pole4 ---------------------------------------- -------------------------------- #bic 8,we are nymphs here1 and in heaven we are stars40 ,purg4 xxxi4 #ajd-ajf4 #bid ,purg4 xxxi4 #aaa4 ---------------------------------------- -------------------------------- ,but the fact is that conjectures and arguments are unnecessary1 since ,dante has expressly said that his four stars had never been seen before by anyone except the first people--8non viste mai fuor che alla prima gente10 7,purg4 i4 #bd7--that is1 our first parents1 in that ,eden of his imagining which was in the southern hemisphere1 and on the island where he was then standing in his vision4 ,as a matter of curiosity ,i have included a map showing what stars would have been really visible to ,dante at the supposed latitude of ,purgatory1 when ,pisces was on the eastern horizon1 as described in ,purg4 i4 ,it will be seen that the ,southern ,cross is low1 and would have been hidden behind the ,mountain of ,purgatory at five o'clock in the morning4#bie ---------------------------------------- -------------------------------- #bie ,antonelli thinks the four stars were and ,crucis1 and ,centauri1 all of which had been mentioned by ,ptolemy1 and all lie near the circle which marks the limit of circumpolar stars in the supposed latitude of ,purgatory 7#cb south74 ,the three stars he says were ,navis1 ,canopus1 and ,achernar3--,antonelli1 ,accenni alle ,dottrine ,astronomiche nella ,divina ,commedia4 ---------------------------------------- -------------------------------- ,among northern constellations1 ,ursa ,major is frequently spoken of by ,dante1 under different names1 but always with reference to its high northern latitude4 ,as the ,wain1 8il ,carro10 it is said to be lying in the north-west when ,pisces is on the eastern horizon1 and to have disappeared from view in the southern hemisphere4#bif ,the wain-pole or shaft is pictured as sweeping round in the diurnal revolution1 but always remaining above our horizon day and night1 throughout its turning3 ---------------------------------------- -------------------------------- #bif ,inf4 xi4 #aac1 #aad2 ,purg4 i4 #cj4 8,quel ,carro1 a cui il seno ,basta del nostro cielo e notte e giorno1 ,s ch' al volger del temo non vien meno40#big #big 8,the ,wain1 that in the bosom of our sky ,spins ever on its axle1 night and day40 ,par4 xiii4 #g-i4 7,carey74 ---------------------------------------- -------------------------------- ,the same idea is expressed in the ,midwinter ,ode1 where the constellation is called the ,seven ,frosty ,stars1 never lost to sight in ,europe3-- 8,fuggito ogni augel che 'l caldo segue ,dal paese d',europa1 che non perde ,le sette stelle gelide unquemai40#bih ---------------------------------------- -------------------------------- #bih 8,fled is every bird that seeks the warmth1 ,from ,european lands which never lose ,the seven cold stars40 ,canz4 xv4 #bg-bi4 ---------------------------------------- -------------------------------- ,this is a reminiscence of some lines of ,bothius quoted by ,dante in ,de ,monarchia1 in which the northern nations are described as under the sway of the 8septem gelidi triones40#bii ,the ,septem ,triones1 the ,seven ,ploughing ,oxen1 was one of the ,latin names for ,ursa ,major1 whence comes 8septentrional0 for ,north4 ,this name also is used by ,dante in ,purg4 xxx4 #a1 where the ,seven ,candlesticks of the mystic procession seen in the ,garden of ,eden are likened to these seven stars1 and are named the ,septentrion of the ,first ,heaven 7the ,empyrean74 ,this divine ,septentrion was guiding the ,procession1 as the starry ,septentrion of a lower heaven guides the mariner into port3 ---------------------------------------- -------------------------------- #bii 8,seven cold oxen40 ,de ,mon4 ,,ii4 ix4 #if4 8faceva l ciascuno accorto ,di suo dover1 come il pi basso face ,qual timon gira per venire a porto40#cjj #cjj 8,to duty there ,each one convoying1 as that lower doth ,the steersman to his port40 ,purg4 xxx4 #d-f4 7,carey74 ---------------------------------------- -------------------------------- ,like the seven stars1 also1 the heavenly ,septentrion is said figuratively to know neither setting nor rising1 but unlike them it knows no cloud except of sin4#cja ,because it is spoken of as guiding mariners1 some commentators have taken the above to refer rather to ,septentrio ,minor 7,ursa ,minor71 which also has seven chief stars1 and is a better guide because nearer the ,pole1 as ,thales taught2 but the comparatively faint stars of the ,little ,bear would not be so apt a comparison with the celestial lights4 ---------------------------------------- -------------------------------- #cja ,purg4 xxx4 #a-c4 ---------------------------------------- -------------------------------- ,by the name of the ,bears1 both ,ursa ,major and ,minor are referred to as guides at sea in ,par4 ii4 #i4 ,in the strange new seas on which ,dante warns his readers he is about to enter1 ,minerva will blow a favouring wind1 ,apollo will steer the barque1 and the nine ,muses will guide his course by the ,bears4 ,they are also spoken of together in ,purg4 iv4 #fe1 to indicate the northern part of the sky4 ,a fifth name for ,ursa ,major is derived from the fable 7known to ,dante probably from ,ovid's ,metamorphoses7 of the nymph ,helice1 who was turned into a she-bear by ,juno1 and was hunted by her own son1 ,orcas4 ,jupiter transformed them into ,ursa ,major and ,botes4 8,se i barbari1 venendo di tal plaga ,che ciascun giorno d',elice si copra1 ,rotante col suo figlio ond' ell' vaga1 ,vedendo ,rome e l' ardua sua opra1 ,stupefaciensi44440#cjb ---------------------------------------- -------------------------------- #cjb 8,if the barbarians coming from some region ,that every day by ,helice is covered1 ,revolving with her son whom she delights in1 ,beholding ,rome and all her noble works ,were wonder-struck44440 ,par4 xxxi4 #ca-ce4 7,longfellow74 ---------------------------------------- -------------------------------- ,here we have the same idea as of the ,wain wheeling round but never setting1 with the addition of a neighbouring constellation describing a circle in the same time4 ,the ,barbarians who lived in a region always dominated by ,ursa ,major1 and came to marvel at the mighty buildings of ancient ,rome1 are probably the races of northern ,europe in general2 and this reminds us again of the lines of ,bothius quoted above1 for it is among the peoples ruled by ,rome that he mentions 8quos premunt septem gelidi triones40#cjc ,if1 however1 ,dante meant a country where the seven stars pass exactly overhead1 the barbarians must have inhabited ,scotland1 or southern ,scandinavia1 or central ,russia4 ,if he means that ,botes also remained always above the horizon1 they must have come from within the ,arctic ,circle1 but this is not likely4 ---------------------------------------- -------------------------------- #cjc 8,those under the sway of the seven cold oxen40 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #db4 ,ursa ,minor as a ,horn4 ,par4 xiii4 #aj4 ,in one of the passages just quoted other constellations and stars are mentioned together with ,ursa ,major4 ,in ,par4 xii4 ,dante has compared the two circles of spirits which surround ,beatrice and himself to a double rainbow1 and to two garlands of immortal roses4 ,in the next canto he finds a new simile3 in imagination he takes some of the brightest and most familiar stars from our sky1 and makes of them two new constellations in the form of two crowns4 ,the stars are these3 fifteen from different parts of the sky1 which are so brilliant that they shine through air dense enough to quench lesser orbs2 the ,wain1 which never sets in our sky2 and the mouth of the horn whose tip is the axis on which the ,primum ,mobile revolves4 ,that is to say1 as we have before remarked1 ,dante takes the fifteen first-magnitude stars and the stars instanced by ,alfraganus as of second magnitude4 ,ursa ,minor is aptly compared to a horn1 the wide mouth of which is formed by its two bright stars ,beta and ,gamma1#cjd while the narrow end is ,alpha1 the ,pole ,star4 ,these twenty-four bright stars we must then imagine to group themselves into two constellations like that into which ,ariadne1 the daughter of ,minos1 was changed when she died2 this is ,corona ,borealis or the ,northern ,crown1 otherwise called ,ariadne's ,crown1 which suggests a circle1 though it is not a perfect one4 ,dante uses the word 8segni0 for any constellations1 a custom we find in ,ristoro also1 although the modern usage is to restrict 8signs0 to mean only divisions of the zodiac4 ---------------------------------------- -------------------------------- #cjd ,i do not know whether this comparison originated with ,dante1 but it was well known to ,spanish sailors two centuries later4 ,in the ,arte of ,navigation which was 8,englished out of the ,spanyshe10 by ,richard ,eden in #aefa1 ,beta and ,gamma of ,ursa ,minor are referred to as 8two starres called the ,guardians1 or the mouth of the horne40 ---------------------------------------- -------------------------------- ,the star-like spirits1 thus grouped into a surpassingly brilliant double constellation1 begin to sing their ineffable heavenly song1 and to circle round the centre where ,dante stands1 in a marvellous dance1 whose swiftness1 when compared with anything known on earth1 is as the movement of that swift heaven which carries with it all the rest1 when compared with the flowing of the sluggish river ,chiana4#cje ---------------------------------------- -------------------------------- #cje ,par4 xiii4 #a-bh4 ---------------------------------------- -------------------------------- ,this passage helps us to understand expressions which often strike one as very strange1 describing the circling movements of the spirits in ,paradise4 ,for the likeness to stars is clear throughout4 ,their brightness is an expression of their happiness1#cjf and increases in each succeeding heaven4 ,only in the lowest can ,dante see the forms and features of ,piccarda and the other blessed spirits2 in the next they clothe themselves in light1 and although at first the radiant eyes of ,justinian are seen1 the first words addressed to him cause him to shine more brilliantly than before1 and as the sun conceals himself by his own light1 so the spirit conceals himself by the splendour which grows with his joy4#cjg ,in the third heaven the spirits shine in the star of ,venus like sparks seen in flame2#cjh in the fourth they are called suns1 and surpass the sun in brilliancy2#cji in the fifth they are compared with the ,galaxy#caj and with shooting stars1#caa in the seventh and eighth with stars#cab and with spheres of light1 turning on fixed poles and flaming like comets4#cac ---------------------------------------- -------------------------------- #cjf ,par4 viii4 #eb1 #ec4 #cjg ,par4 v4 #acf1 #acg4 #cjh ,par4 viii4 #af4 #cji ,par4 x4 #gf1 #dj-db4 #caj ,par4 xiv4 #ig-aja4 #caa ,par4 xv4 #ac1 #ad4 #cab ,par4 xxi4 #cb1 #cc2 xxiii4 #bf1 #bg4 #cac ,par4 xxii #bc2 xxiv4 #aa1 #ab4 ---------------------------------------- -------------------------------- ,in like manner the swiftness of their motion increases in proportion to the clearness with which each beholds eternal truth4#cad ,the almost incredible speed with which ,dante himself soars from sphere to sphere1 and with which the spirits move--whether in coming towards him1 impelled by ,divine charity1 in returning to the heaven of heavens1 or in circling with one another in mystic dance--is frequently dwelt upon1 and illustrated by many striking similes4 ,the dance is always a circling or wheeling movement 78il giro10 8la rota10 ,par4 viii4 #bj and #bf2 ix4 #fe74 ,and besides this1 individual spirits turn with a rapid motion1 remaining on the same spot4 ,descending the celestial ,ladder in the heaven of ,saturn1 step by step1 they revolve3-- ---------------------------------------- -------------------------------- #cad ,par4 viii4 #bj1 #ba2 and xxviii4 #ajj-ajb4 8,vid' io pi fiamelle ,di grado in grado scendere e girarsi1 ,ed ogni giro le facea pi belle40#cae #cae 8,saw ,i many little flames ,from step to step descending and revolving1 ,and every revolution made them fairer40 ,par4 xxi4 #acf-ach4 7,longfellow74 ,compare #hj1 #ha and #ci2 and ,par4 xxiv4 #aj1 #aa4 ---------------------------------------- -------------------------------- ,now these two things1 their light and their movements1 were all the facts concerning the stars which medival astronomers could observe2 and the movements were thought to be in circles and inconceivably rapid4 ,motion in circles1 and especially the movement of rotation on an axis1 remaining in the same place1 had been said by ,aristotle to be the most noble form of motion1 and the fittest for celestial bodies4 ,therefore1 when ,dante represents the redeemed and the angels as expressing their bliss by radiance and marvellously rapid motion in circles1 he makes them resemble the heavenly spheres and stars among which they manifest themselves to him4 ,the motions are directly compared with those of stars in the passage already quoted3-- 8,poi1 s cantando1 quegli ardenti soli ,si fur girati intorno a noi tre volte1 ,come stelle vicine ai fermi poli40#caf ---------------------------------------- -------------------------------- #caf 8,as soon as singing thus those burning ,suns ,had round about us whirled themselves three times1 ,like unto stars neighbouring the steadfast poles40 ,par4 x4 #gf-gh4 7,longfellow74 ---------------------------------------- -------------------------------- ,remembering this significance of circular motion we shall feel a little less strange the similes of a mill and a top applied to the spirits of ,paradise4#cag ,a third way in which the spirits express their joy is by the sweetness of their song1#cah and here also they resemble the heavenly bodies1 which make sweet music as they circle4 ,this doctrine of ,pythagoras was very popular throughout the ,middle ,ages4 ---------------------------------------- -------------------------------- #cag ,par4 xxi4 #hj1 #ha2 xii4 #c2 xviii4 #da1 #db4 #cah ,par4 xxiv4 #bb-bd1 x4 #gc1 and many others4 ---------------------------------------- -------------------------------- #d4 ,,the ,,galaxy4 ,the ,galaxy or ,milky ,way is twice referred to in the ,divine ,comedy4 ,in ,inf4 xvii4 #ajf-ajh1 it is in connection with the myth of ,phaeton1 who being allowed by his father ,jove to drive the chariot of the sun for one day1 lost control of his chargers1 and going all astray1 burned the sky in a part which still shows signs of this catastrophe1 i4e4 the ,milky ,way4 8,quando ,fetn abbandon li freni1 ,per che il ciel1 come pare ancor1 si cosse40#cai ---------------------------------------- -------------------------------- #cai 8,what time abandoned ,phaton the reins1 ,whereby the heavens1 as still appears1 were scorched40 ,inf4 xvii4 #ajg-ajh4 7,longfellow74 ---------------------------------------- -------------------------------- ,this of course is only a poetical myth4 ,but in the ,paradiso1 in three lines the appearance1 colour1 and approximate position of the ,galaxy are described1 and allusion is made to the difference of opinions between learned men with regard to the puzzling question of its nature4 ,dante is in the heaven of ,mars4 ,he sees the soldier saints1 star-like and fiery red1 some larger and some less1 thronging thick in two great bands1 which1 crossing one another in the depths of the planet1 form a marvellous ,crucifix4 ,the crowded lights make him think of the ,galaxy1 with its multitudinous points of light1 differing in brightness1 although that is white1 and lies in a great circle between the celestial poles4 8,come1 distinta da minori e maggi ,lumi1 biancheggia tra i poli del mondo ,galassia s che fa dubbiar ben saggi1 ,s costellati facean nel profondo ,marte quei rai il venerabil segno ,che fan giunture di quadranti in tondo40#cbj ---------------------------------------- -------------------------------- #cbj 8,even as1 distinct with less and greater lights1 ,glimmers between the two poles of the world ,the ,galaxy that maketh wise men doubt1 ,thus constellated in the depths of ,mars ,those rays described the venerable sign ,that quadrants joining in a circle make40 ,par4 xiv4 #ig-ajb4 7,longfellow74 ---------------------------------------- -------------------------------- ,if we now turn to the fifteenth chapter of ,treatise ,,ii4 of the ,convivio1 we shall find the ,phaeton myth and the various theories about the ,milky ,way set forth in due order1 and shall learn which of these ,dante considered to be true4 ,he is comparing the two sciences of ,metaphysics and ,physics with the ,heaven of the ,fixed ,stars1 and takes the opportunity to tell us some of the most important facts known about it4 ,here he calls the ,galaxy a circle3--8,la ,galassia1 cio quello bianco cerchio che il vulgo chiama la ,via de ,santo ,jacopo40#cba ,this popular name perhaps arose through a confusion of ,galaxy and ,galicia1 where was a famous shrine of ,st4 ,james1 and hence came the belief in ,italy that the ,galassia was a sign by night to guide pilgrims on their way to this shrine at ,compostella in ,galizia4 ---------------------------------------- -------------------------------- #cba 8,the ,galaxy1 that is1 the white circle commonly called ,st4 ,james's ,way40 ---------------------------------------- -------------------------------- ,dante proceeds as follows with his comparison3-- 8,e per la ,galassia1 ha questo cielo grande similitudine colla ,metafisica4 ,perch da sapere che di quella ,galassia li filosofi hanno avuto diverse opinioni4 ,ch li ,pittagorici dissero che 'l sole alcuna fiata err nella sua via1 e1 passando per altre parti non convenienti al suo fervore1 arse il luogo1 per lo quale pass2 e rimasevi quell' apparenza dell' arsura4 ,e credo che si mossero dalla favola di ,fetonte1 la quale narra ,ovidio nel principio del secondo di ,metamorfoseos4 ,altri dissero 7siccome fu ,anassagora e ,democrito7 che ci era lume del sole ripercosso in quella parte4 ,e queste opinioni con ragioni dimostrative riprovarono4 ,quello che ,aristotile si dicesse di ci1 non si pu bene sapere1 perch la sua sentenza non si trova cotale nell' una traslazione come nell' altra4 ,e credo che fosse l'errore de' traslatori2 che nella ,nuova par dicere che ci sia uno raunamento di vapori sotto le stelle di quelle parte1 che sempre traggono quelli2 e questa non pare avere ragione vera4 ,nella ,vecchia dice1 che la ,galassia non altro che multitudine di stelle fisse in quella parte1 tanto picciole che distinguere di quaggi non le potemo1 ma di loro apparisce quello albore il quale noi chiamiamo ,galassia4 ,e puote essere che il cielo in quella parte pi spesso1 e per ritiene e ripresenta quello lume e questa opinione pare avere1 con ,aristotile1 ,avicenna e ,tolommeo4 ,onde conciossiacosach la ,galassia sia uno effetto di quelle stelle le quali non potemo vedere1 se non per lo effetto loro intendiamo quelle cose1 e la ,metafisica tratta delle prime sustanze1 le quali noi non potemo simigliantemente intendere se non per li loro effetti2 manifesto che 'l cielo stellato ha grande similitudine colla ,metafisica40#cbb ---------------------------------------- -------------------------------- #cbb 8,and in the ,galaxy this heaven has a close resemblance to ,metaphysics4 ,wherefore it must be known that the ,philosophers have had different opinions about this ,galaxy4 ,for the ,pythagoreans affirmed that the sun at one time wandered in its course1 and in passing through other regions not suited to sustain its heat1 set on fire the place through which it passed2 and so these traces of the conflagration remain there4 ,and ,i believe that they were influenced by the fable of ,phaton1 which ,ovid tells at the beginning of the second book of the ,metamorphoses4 ,others 7as for instance ,anaxagoras and ,democritus7 said that the ,galaxy was the light of the sun reflected in that region4 ,and these opinions they confirmed by demonstrative reasons4 ,what ,aristotle may have said about it cannot be accurately known1 because the two translations give different accounts of his opinion4 ,and ,i think that any mistake may have been due to the translators1 for in the ,new ,translation he is made to say that the ,galaxy is a congregation1 under the stars of this part of the heaven1 of the vapours which are always being attracted by them2 and this opinion does not appear to be right4 ,in the ,old ,translation he says that the ,galaxy is nothing but a multitude of fixed stars in that region1 stars so small that they are not separately visible from our earth1 but the appearance of whiteness which we call the ,galaxy is due to them4 ,and it may be that the heaven in that part is more dense1 and therefore retains and reproduces that light and this opinion ,avicenna and ,ptolemy appear to share with ,aristotle4 ,therefore1 since the ,galaxy is an effect of those stars which cannot be perceived except so far as we apprehend these things by their effect1 and since ,metaphysics treats of primal substances which in the same way we cannot apprehend except by their effects1 it is plain that there is a close resemblance between the starry heaven and ,metaphysics40 ,conv4 ,,ii4 xv4 #dd-hf4 7,jackson74 ---------------------------------------- -------------------------------- ,this characteristic passage is interesting for several reasons4 ,it illustrates the medival fondness for allegory1 the reluctance to believe that ,aristotle could ever be wrong1 and the interest in ancient ,greek speculations1 in all of which ,dante expresses the feelings of his age3 and it brings vividly before us the methods and the difficulties of medival authors4 ,for ,dante is repeating from ,albertus ,magnus all these ancient speculations3 the officious copyist who altered ,aristotle's words1 the fact that ,aristotle could only be read in ,latin1 and the variety of translations1 were all everyday obstacles to study2 and ,dante's own book has suffered from one of them in this very passage4 ,the words placed between brackets are evidently an interpolation 7as ,mr4 ,wicksteed observes in the 8,temple0 ,convivio73 without them the passage goes on smoothly and logically to its end4 ,on the assumption that the ,galaxy is composed of a multitude of small stars1 but not that the sky is denser in that part1 the parallel with ,metaphysics holds good4 ,dante therefore held the true opinion about the ,milky ,way1 but he was mistaken in thinking that he had the support of ,aristotle4 ,it was the 8,new ,translation0 7made by ,aquinas from the ,greek7 which gave his opinion correctly2 in the 8,old0 7made by ,michael ,scot from the ,arabic7 his statement had been apparently changed without comment into one which seems to ,dante--and also to us--to represent the truth about the ,galaxy4 #e4 ,,the ,,planets4 ,all the planets which were known before the days of the telescope are mentioned by ,dante several times4 ,each has its peculiar beauty1 but 8la lucentissima stella di ,venere0#cbc is brighter and more beautiful than any other4 ,he speaks of 8la chiarezza del suo aspetto1 ch ' soavissima a vedere pi che altra stella40#cbd ---------------------------------------- -------------------------------- #cbc 8,that most brilliant star1 ,venus40 ,conv4 ,,ii4 iv4 #hh4 #cbd 8,the brightness of her appearance1 which is more lovely to behold than that of any other star40 ,conv4 ,,ii4 xiv4 #aab1 #aac4 ---------------------------------------- -------------------------------- ,no reader of the ,purgatorio can ever forget that matchless morning on which ,dante1 escaping at last from the murky gloom of the ,inferno1 sees the sky once more1 pure blue even to its furthest limits1 and the planet of love shining in the east4 8,dolce color d'oriental zaffiro1 ,che s'accoglieva nel sereno aspetto ,dell' aer1 puro infino al primo giro1 ,agli occhi miei ricominci diletto1 ,tosto ch' i' uscii fuor dell' aura morta1 ,che m'avea contristati gli occhi e il petto1 ,lo bel pianeta che ad amar conforta ,faceva rider tutto l'oriente1 ,velando i ,pesci ch'erano in sua scorta40#cbe ---------------------------------------- -------------------------------- #cbe 8,sweet colour of oriental sapphire1 ,which was gathering in the serene aspect ,of the sky1 pure even to the first circle1 ,to my eyes restored delight1 ,so soon as ,i had come forth from that dead air1 ,which had troubled eyes and breast4 ,the fair planet that inspires love ,was making all the orient smile1 ,veiling the ,fishes which were in her train40 ,alternative rendering of the first three lines3-- 8,sweet colour of oriental sapphire1 ,which was diffused over the tranquil scene1 ,from mid-heaven even to the first circle40 ,purg4 i4 #ac-ba4 ---------------------------------------- -------------------------------- ,strange to say1 the beginning of the above beautiful passage which conveys so direct and vivid an impression of blue sky and pure air1 presents some difficulties when one comes to translate it word by word1 especially as the texts offer more than one reading4 ,by some commentators the 8primo giro0#cbf has been understood to mean the sphere of the moon1#cbg or even the highest sphere 7the ,primum ,mobile72 but this is certainly inadmissible1 as ,dante supposed the atmosphere to reach only as far as the sphere of ,fire1 which came between it and the moon4 ,the prime circle is here evidently the horizon1 the fundamental circle of observers1 the ,first ,circle of the astrologers1 from which they reckoned all the rest4 ,it is here that the sky usually becomes pale and misty1 however blue and clear it may be above4 ,the colour was gathering and deepening1#cbh especially in the east1 where ,dante was looking1 as dawn began to appear in a perfectly cloudless sky2 for during the darkness of the night it would have appeared almost black4 ---------------------------------------- -------------------------------- #cbf ,first1 or prime1 circle4 #cbg ,conv41 ,,ii4 iv4 #a-c4 #cbh ,literally1 8was assembling10 or 8was being collected40 ---------------------------------------- -------------------------------- ,dr4 ,moore thinks the authority better for a different reading1 viz4 8,dal mezzo0#cbi instead of 8,dell' aer40#ccj ,in this case1 we must take 8mezzo puro0 to mean mid-heaven1 that is the zenith1 8puro0 being used as a noun1 and meaning a cloudless sky 7like 8sereno0 in ,purg4 v4 #ch72 and 8il sereno aspetto0 must mean 8the quiet scene40 ---------------------------------------- -------------------------------- #cbi 8,from the middle40 #ccj 8,of the air40 ---------------------------------------- -------------------------------- ,venus appears again in the ,purgatorio1 shining upon the ,mountain from the east before sunrise2 and this time she is called ,cytherea1 after the island near which she was fabled to have risen from the sea1 and in which she received a special worship4 8,dell' oriente 444 raggi nel monte ,citerea1 ,che di foco d'amor par sempre ardente40#cca ---------------------------------------- -------------------------------- #cca 8,from the east there shone upon the ,mountain ,cytherea1 who in the flame of love seems to be always burning40 ,purg4 xxvii4 #id-if4 ---------------------------------------- -------------------------------- ,the position of ,venus in her course through the zodiac is indicated in the previous passage by the expression 8velando i ,pesci40#ccb ,the oscillating motion1 by which she appears first on the morning and then on the evening side of the sun is referred to several times4 ,in prose ,dante speaks of her two apparitions1 the morning and the evening3 8la sua apparenza1 or da mane1 or da sera20#ccc in poetry1 he describes her as wooing the sun1 first following and then facing him3-- ---------------------------------------- -------------------------------- #ccb 8,veiling the ,fishes0 7the zodiacal constellation74 #ccc 8,her appearance1 now in the morning1 and now in the evening40 ,conv4 ,,ii4 xiv4 #aad1 #aae4 ---------------------------------------- -------------------------------- 8la stella ,che il sol vagheggia or da coppa or da ciglio40#ccd ---------------------------------------- -------------------------------- #ccd 8,the star ,that woos the sun1 now following1 now in front40 ,par4 viii4 #aa-ab4 7,longfellow74 ---------------------------------------- -------------------------------- ,mercury and ,venus 7called rather oddly after their mothers71 are said both to move closely round the sun3-- 444 8vidi com' si move ,circa e vicino a lui ,maia e ,dione40#cce ---------------------------------------- -------------------------------- #cce 8,i saw how move themselves1 ,around and near him1 ,maia and ,dione40 ,par4 xxii4 #adc-add4 ---------------------------------------- -------------------------------- 8,quel bel pianeta di ,mercuro0#ccf keeps closest1 for he is more hidden than any other in the rays of the sun4 ,here again the fact is expressed in simple prose in the ,convivio3-- ---------------------------------------- -------------------------------- #ccf 8,that fair planet1 ,mercury40 ,son4 xxviii4 #i4 ---------------------------------------- -------------------------------- 8,mercurio 444 pi va velata de' raggi del sole che null' altra stella40#ccg ---------------------------------------- -------------------------------- #ccg 8,mercury 444 as it moves is more veiled by the rays of the sun than any other star40 ,conv4 ,,ii4 xiv4 #ii-ajj4 ---------------------------------------- -------------------------------- which explains 7if necessary7 the more poetical language of the ,paradiso3-- 8,la spera1 ,che si vela ai mortal con altrui raggi40#cch ---------------------------------------- -------------------------------- #cch 444 8,the sphere ,that veils itself from men in alien rays40 ,par4 v4 #abh1 #abi4 ---------------------------------------- -------------------------------- ,in the same way we may compare the descriptions of ,mars in the ,paradiso with a statement in the ,convivio3-- 8,questo fuoco10#cci and 8l'affocato riso della stella10#cdj and 8,marte rosseggia10#cda with ---------------------------------------- -------------------------------- #cci 8,this ,fire40 ,par4 xvi4 #ch4 #cdj 8,the burning smile of the star40 ,par4 xiv4 #hf4 #cda 8,mars shows red40 ,purg4 ii4 #ad4 ---------------------------------------- -------------------------------- 8,esso ,marte 444 il suo calore simile a quello del fuoco2 444 esso appare affocato di colore40#cdb ---------------------------------------- -------------------------------- #cdb 8,this ,mars 444 his heat is like the heat of a fire 444 his colour is as if he were on fire40 ,conv4 ,,ii4 xiv4 #afb-afe4 ---------------------------------------- -------------------------------- ,the famous occultation of ,mars by the moon1 seen by ,aristotle1 is quoted by ,dante in ,conv4 ,,ii4 iii4 #ei-fe4 ,jupiter is the 8dolce stella0#cdc and the 8giovial facella40#cdd ,he is silvery white1 the whitest of all the stars3--8,intra tutte le stelle bianca si mostra1 quasi argentata40#cde ---------------------------------------- -------------------------------- #cdc 8,sweet star40 ,par4 xviii4 #aae4 #cdd 8,the torch of ,jove40 ,par4 xviii4 #gj4 #cde 8,amongst all the stars it shows white1 as if silvered over40 ,conv4 ,,ii4 xiv4 #bjb-bjd4 ---------------------------------------- -------------------------------- ,therefore when ,dante saw the planet filled with brilliant spirits1 he says3 8,giove pareva argento l d' oro distinto40#cdf ,comparisons between the colours of ,jupiter and ,mars are made in ,par4 xviii4 #fd-fi1 and xxvii4 #ac-ae4 ---------------------------------------- -------------------------------- #cdf 8,jupiter ,seemed to be silver there with gold inlaid40 ,par4 xviii4 #ie-if4 7,longfellow74 ---------------------------------------- -------------------------------- ,finally ,saturn is the slowest and the most distant of all the planets4 ,these two characteristics are thus described in the ,convivio3-- 8,l'una si la tardezza del suo movimento per li dodici segni2 ch ventinove anni e pi1 secondo le scritture degli astrologi1 vuole di tempo lo suo cerchio3 l'altra si che esso alto sopra tutti gli altri pianeti40#cdg ---------------------------------------- -------------------------------- #cdg 8,one is the slowness of its movement through the twelve signs2 for twenty-nine years and more1 according to the writings of the astrologers1 are required for its revolution3 the other is that it is high above all other planets40 ,conv4 ,,ii4 xiv4 #bbf-bca4 ---------------------------------------- -------------------------------- ,in the ,paradiso ,saturn is called a ,mirror1#cdh a ,crystal1#cdi a splendour2#cej his circling motion is alluded to1 and his position at the time in the zodiac3-- ---------------------------------------- -------------------------------- #cdh ,par4 xxi4 #ah4 #cdi ,par4 xxi4 #be4 #cej ,par4 xxi4 #ac4 ---------------------------------------- -------------------------------- 8,cerchiando il mondo40#cea 8,sotto il petto del ,leone ardente40#ceb ---------------------------------------- -------------------------------- #cea 8,circling the world40 ,par4 xxi4 #bf4 #ceb 8,beneath the burning ,lion's breast40 ,par4 xxi4 #ad4 ---------------------------------------- -------------------------------- ,some of the most beautiful similes in the ,divine ,comedy are drawn from the planets4 ,the angel-pilot of ,purgatory1 when first seen far off over the sea1 is likened to the planet ,mars1 glowing red through morning mists1 low in the west above the ocean floor2#cec and the angel that welcomes the poet to the second circle on the ,mountain is beautiful as the ,morning ,star4 ---------------------------------------- -------------------------------- #cec ,purg4 ii4 #ac-ae4 8,a noi venia la creatura bella1 ,bianco vestita1 e nella faccia quale ,par tremolando mattutina stella40#ced #ced 8,towards us came the being beautiful1 ,vested in white1 and in his countenance ,such as appears the tremulous morning star40 ,purg4 xii4 #hh-ij4 7,longfellow74 ---------------------------------------- -------------------------------- ,although any of the planets when rising just before the sun may be called a morning star1 ,venus is probably intended here1 as also where ,st4 ,bernard1 in his devotion to the ,virgin1 is compared with the ,morning ,star which takes its beauty from the sun3-- 8,colui ch'abbelliva di ,maria1 ,come del sole stella mattutina40#cee ---------------------------------------- -------------------------------- #cee 8,he who drew beauty from ,mary1 as the ,morning ,star does from the ,sun40 ,par4 xxxii4 #ajg1 #ajh4 ---------------------------------------- -------------------------------- ,all the seven planets 7that is1 including sun and moon71 are occasionally mentioned together1 8tutti e sette10#cef and their movement in the ecliptic is referred to in ,par4 x1 #ad3 8,l'obbliquo cerchio che i pianeti porta40#ceg ,in the #adth and #aeth chapters of the second treatise of the ,convivio1 already so often quoted1 ,dante draws an elaborate comparison between the seven planets and the seven sciences of the ,trivium and ,quadrivium4 ,the moon is ,grammar1 ,mercury ,dialectic1 ,venus ,rhetoric1 the ,sun ,arithmetic1 ,mars ,music1 ,jupiter ,geometry1 and ,saturn ,astrology4 ,the reasons given for the latter are the slow movement and the height 7i4e4 distance from ,earth7 of ,saturn1 which ,dante compares with the length of the time taken in learning astronomy1 and the loftiness of its subject4 ---------------------------------------- -------------------------------- #cef 8,all the seven40 ,son4 xxviii4 #ad1 and ,par4 xxii4 #adh4 #ceg 8,the oblique circle which carries the planets40 ---------------------------------------- -------------------------------- ,in the same way the star sphere is said to resemble ,physics and ,metaphysics1 the ,primum ,mobile ,ethics1 and the ,empyrean ,theology4 ,the argument is very fanciful1 but just what would appeal to readers of ,dante's day1 who loved to find allegories everywhere2 and it gives him an opportunity of instructing them very simply in his beloved science4 ,he sometimes uses the planetary periods as divisions of time 7as ,plato said they should be used71 for computing earthly events1 and in him this does not seem affectation1 as it would with almost anyone else4 ,it seems quite natural that ,cacciaguida1 when speaking in the heaven of ,mars1 and answering a question regarding the date of his birth1 should count the time not by solar but by ,martian years1 saying that from the beginning of the ,christian ,era to the day of his birth1 ,mars had returned to his ,lion 7the constellation of ,leo7 five hundred and eighty times4#ceh ,the length of the ,martian year according to ,alfraganus is #a ,persian year1 #aj months1 and #bb days nearly4 ,the ,persian year 7as he tells us in the first chapter of the ,elementa7 consists of #ab months of #cj days each plus #e extra days1 making #cfe days exactly 7not #cfe days like the ,roman71 so the ,martian year is #fhg days 7the modern estimate is #fhfi74 #fhg days #ehj gives us #ajia a4d4 as the date of ,cacciaguida's birth4 ,this is consistent with the date of his death1 for he had just told ,dante that he fell in the ,crusade to which he followed the ,emperor ,conrad1 and we know that this was fought in the year #aadg4 ,some commentators think that ,dante did not intend the ,martian year to be taken so precisely1 but only as approximately two solar years1 since he gave it thus in ,conv4 ,,ii4 xv4 #ade4 ,but there he specially states that he is quoting an approximate figure only 78uno anno quasi0#cei is half the period of ,mars7 whereas in the ,paradiso it is used to fix a date4 ,since by taking #ehj #b years we get #aafj1 an impossible date of birth for a man who died in #aadg1 the only way to support this theory that ,dante was speaking loosely here is to adopt another reading of the passage1 and substitute 8tre0 for 8trenta40#cfj ,then #eec 7instead of #ehj7 #b years would give the date #aajf2 but the reading is not supported by good authority4 ---------------------------------------- -------------------------------- #ceh ,par4 xvi4 #cd-ci4 #cei 8,about a year40 #cfj 8,three10 for 8thirty40 ---------------------------------------- -------------------------------- ,the period of ,venus is used with equal appropriateness when ,dante is relating how love for the ,gentil ,donna found a way to his heart1 coming on the rays of ,venus1#cfa the star of love4 8,la stella di ,venere due fiate ere rivolta in quello suo cerchio che la fa parere serotina e mattutina1 secondo i due diversi tempi1 appresso lo transpassamento di quella ,beatrice beata1 che vive in cielo con gli angioli e in terra colla mia anima1 quando quella ,gentil ,donna1 di cui feci menzione nella fine della ,vita ,nuova1 apparve primamente accompagnata d',amore agli occhi miei1 e prese alcuno luogo nella mia mente40#cfb ---------------------------------------- -------------------------------- #cfa ,conv4 ,,ii4 vii4 #hh1 #hi4 #cfb 8,the star of ,venus had twice revolved in that circle of hers which makes her appear as evening and morning star1 according to her two seasons1 since the translation of that holy ,beatrice who lives in heaven with the angels and on earth in my soul1 when that ,gentle ,lady1 of whom ,i made mention at the end of the #8,new ,life1' appeared first before my eyes1 escorted by ,love1 and took some place in my mind40 ,conv4 ,,ii4 ii4 #a-ab4 ---------------------------------------- -------------------------------- ,venus runs through her changes1 appearing first as ,evening and then as ,morning star1 in #ehd days2 and1 as the reader will remember1 this movement was ascribed by ,ptolemy to her epicycle 78quello suo cerchio10 8that circle of hers074 ,dante would find #ehd days given for it in his ,alfraganus4#cfc ,twice #ehd is #aafh days1 or three years and a little more than #b months4 ,therefore1 since we know from ,v4 ,n4 xxx4 that ,beatrice died in ,june #abij1 ,dante wishes to say that he first saw the ,lady of ,pity in ,august #abic4 ---------------------------------------- -------------------------------- #cfc 8,venus ambitum epicycli peragit anno ,persico #a1 mensibus #g1 et diebus prope #i10 that is1 the period of ,venus on her epicycle is #cfe #baj #i #ehd days nearly1 according to ,alfraganus4 ,the modern mean value is also #ehd days4 ---------------------------------------- -------------------------------- ,the period has been taken by some modern commentators to refer to the #bbe days in which ,venus revolves round the sun1 but this period has no place in the ,ptolemaic system4 ,we cannot here discuss ,dante's allegory of the ,gentle ,lady and ,philosophy1 but in this passage he has stated without ambiguity or uncertainty the date of her first appearance4#cfd ---------------------------------------- -------------------------------- #cfd ,see ,lubin's ,dante e gli ,astronomi ,italiani4 ,the period of #bbe days may be easily deduced from ,ptolemy's system1 for it is the time in which the epicycle of ,venus would make an absolute revolution round its centre1 the diameter becoming parallel to its former position4 ,but the ,greeks invariably reckoned the period as the time in which it revolved relatively to ,earth1 that is #ehd days4 ---------------------------------------- -------------------------------- #f4 ,,eclipses4 ,we find solar eclipses mentioned six times in ,dante's works4 ,as in all old records1 there is no allusion to the features which chiefly strike modern astronomers--the pearly corona1 and the blood-red prominences standing out like flames round the black disc4 ,the terror of the sudden darkness1 even when foreseen1 seems to have absorbed all attention1 and only the appearance of stars in the daytime and the frightened behaviour of animals was noted by ,ristoro1 and by others until quite modern times4 ,in his letter to the ,cardinals of ,italy1 ,dante speaks of the shameful and grievous removal of the ,papacy from ,rome to ,avignon as an eclipse of the sun4#cfe ,in his dream of the death of ,beatrice1 he sees the sun so darkened that the stars appear1 to his great terror3-- ---------------------------------------- -------------------------------- #cfe ,ep4 viii4 #aeh1 #aei4 8,poi mi parve vedere appoco appoco ,turbar lo ,sole ed apparir la stella40#cff #cff 8,the while1 little by little1 as ,i thought1 ,the sun ceased1 and the stars began to gather40 ,v4 ,n4 xxiii4 #agf1 #agg4 7,rossetti74 ,see also the prose description just before1 lines #ce-cg4 ---------------------------------------- -------------------------------- ,he also refers to the disputed idea that the darkness at the time of the ,crucifixion was caused by an eclipse of the sun1#cfg and to the figurative eclipse which then took place in heaven4#cfh ---------------------------------------- -------------------------------- #cfg ,par4 xxix4 #ig-ajb4 #cfh ,par4 xxvii4 #ce1 #cf4 ---------------------------------------- -------------------------------- ,if he had ever seen one in reality1 it would have made more impression upon him1 and we should surely have found it referred to several times and vividly described4 ,the only suggestion of a personal experience is where he temporarily loses the power of sight by gazing too fixedly upon the spirit of ,st4 ,john2 and he compares this to a man who looks so intently at the sun1 just before an eclipse1 that he becomes incapable of seeing it at the critical moment4#cfi ,this incident may have been told him by an observer of the total eclipse of ,june #abci1 which was visible in ,italy1 and seems to be the one described by ,ristoro4 ,lastly1 he mentions the discovery that the moon comes between us and the sun1 which we have learned from eclipses1 as an example of the proper method of reasoning3 for we must first ask whether a thing is1 and afterwards why it is4 ,thus man's wonder leads him to knowledge4#cgj ---------------------------------------- -------------------------------- #cfi ,par4 xxv4 #aah-aba4 #cgj ,qu4 xx4 #c-e1 #bf-bi4 ---------------------------------------- -------------------------------- ,the eclipsed moon is only once mentioned1 viz4 in ,de ,mon4 ,,iii4 iv4 #adj-adb1 where she is described as not wholly dark4 ,with his usual indifference to her ,dante fails to note the often extraordinary beauty of her colouring when the eclipse is total4 #g4 ,,comets ,,and ,,meteors4 ,the connection between these two classes of heavenly bodies seems to be real1 though its exact nature is still a mystery4 ,in old days little or no distinction was drawn between them1 so that it is sometimes difficult to know whether a writer is describing a large meteor1 or a comet1 or a shower of falling stars4 ,dante only mentions comets once1 very briefly1 when he describes spirits in ,paradise as 8fiammando forte a guisa di comete40#cga ,he says nothing of the magnificent comet described by ,ristoro1 which rose at three o'clock in the morning1 huge as a mountain1 and with great rays like a mane2 but travelling always towards the south grew gradually fainter1 and disappeared after #fj days4 ,yet it was seen in ,tuscany shortly before ,dante's birth1 and it was thought to herald the death of the ,pope 7,urban ,,iv4 in #abfd7 and the terrible war in which first ,manfred and afterwards ,conradin were slain4 ,these events are familiar to every reader of the ,divine ,comedy1#cgb but there is never any mention of the comet4 ---------------------------------------- -------------------------------- #cga 8,blazing brilliantly like comets40 ,par4 xxiv4 #ab4 #cgb ,inf4 xxviii4 #af-ag2 ,purg4 iii4 #aab-acb4 ---------------------------------------- -------------------------------- ,nor does he describe in any detail the fiery cross which was seen in the sky above ,florence 8in the beginning of her destruction10 which does not mean1 as one might think1 the legendary sack of the city by ,totila1 but the treacherous entry of ,charles of ,valois1 8,totila secundus10#cgc in ,november #acja4 ,this portent was of course considered as of ill omen for the ,republic1 and although ,dante was still absent on his embassy to ,rome1 and cannot have seen it himself1 it is rather remarkable that he says so little about it4 ,it is described by an eye-witness1 8,io1 che chiaramente la viddi0#cgd as a red cross which appeared in the evening over the ,priors' ,palace2 the vertical arm seemed to be #bj ells long1 the transverse one a little shorter1 and it remained visible for as long as it would take a horse to gallop two furlongs4 ,villani the historian describes it as like a comet with an immense trail1 as of smoke1 behind it4 ,dante merely mentions it1 together with the ball of fire seen by ,seneca at the death of ,augustus1 which1 judging by ,seneca's own words1 was also a large meteor1 for he describes it as flashing into sight and moving very rapidly1 disappearing as it moved4#cge ---------------------------------------- -------------------------------- #cgc ,v4 ,e4 ,,ii4 vi4 #dh4 #cgd 8,i1 who saw it clearly40 #cge ,naturales ,qustiones1 ,bk4 ,i4 ---------------------------------------- -------------------------------- ,dante calls meteors 8kindled vapours10#cgf in accordance with the doctrines of ,aristotle1 but the popular idea of them is shown by his observation that they might be taken for stars in motion1 only that no star vanishes from its place1 and they are only seen for a short time4#cgg ,ristoro d',arezzo had already alluded to this fallacy3-- ---------------------------------------- -------------------------------- #cgf ,conv4 ,,ii4 xiv4 #afh-aga1 and ,purg4 v4 #cg4 #cgg ,par4 xv4 #af-ah4 8,alquanti non savi credono ch'elle sieno stelle1 che caggino del cielo e vengano meno40#cgh #cgh 8,some ignorant people think that they are stars which fall from heaven and vanish40 ,comp4 del ,mondo1 ,,vii4 v4 ---------------------------------------- -------------------------------- ,he gives the same reason as ,dante for disbelieving this1 and ,seneca had expressed it more forcibly1 saying that if true there would be no more stars in the sky1 for some meteors are seen every night4 ,albertus ,magnus1 who seems to have had a genius for mistaking his authorities1 quotes ,alfraganus as stating that shooting stars are most frequent in evening twilight1 though nothing of the kind is said in the ,elementa4 ,dante perhaps accepted the statement1 though it is by no means necessarily implied in his 8di prima notte30#cgi moreover there is some authority for the alternative reading of 8mezza notte40#chj ,wherever the idea originated1 its sole foundation must have been the circumstance that more persons are awake in the early than in the late hours of the night3 the fact is that more meteorites are captured by the morning side of the earth1 which is turned in the direction towards which she is moving in her orbit4 ---------------------------------------- -------------------------------- #cgi 8,early in the night40 #chj 8,midnight40 ,purg4 v4 #ch4 ---------------------------------------- -------------------------------- ,shooting stars were necessarily familiar to a lover of starry skies1 and ,dante has given us an exquisite description of the suddenness with which they startle quiet eyes1 while their brilliancy and swiftness of flight provides him with two beautiful similes4 ,in the first he compares them1 and also flashes of summer lightning1 with messenger spirits in ,purgatory hastening to bring their friends to him3-- 8,vapori accesi non vid' io s tosto ,di prima notte mai fender sereno1 ,n1 sol calando1 nuvole d'agosto1 ,che color non tornasser suso in meno1 ,e giunti l1 con gli altri a noi dier volta40#cha ---------------------------------------- -------------------------------- #cha 8,vapours enkindled saw ,i ne'er so swiftly ,at early nightfall cleave the air serene1 ,nor1 at the set of sun1 the clouds of ,august1 ,but upward they returned in briefer time1 ,and on arriving with the others1 wheeled ,towards us40 ,purg4 v4 #cg-da4 7,longfellow74 7,by 8vapours that cleave the clouds of ,august10 flashes of lightning without thunder are meant4 ,aristotle believed both these and meteorites to be ignited vapours74 ---------------------------------------- -------------------------------- ,the second illustrates the brightness and beauty1 as well as the movement1 of the star-like spirits in ,mars3-- 8,quale per li seren tranquilli e puri ,discorre ad ora ad or subito foco1 ,movendo gli occhi che stavan sicuri1 ,e pare stella che tramuti loco1 ,se non che dalla parte ond' ei s' accende ,nulla sen perde1 ed esso dura poco 4440#chb ---------------------------------------- -------------------------------- #chb 8,as through the pure and tranquil evening air ,there shoots from time to time a sudden fire1 ,moving the eyes that steadfast were before1 ,and seems to be a star that changeth place1 ,except that in the place where it is kindled ,nothing is missed1 and this endureth little40 ,par4 xv4 #ac-ah4 7,longfellow74 ---------------------------------------- -------------------------------- #h4 ,,the ,,sun',s ,,path ,,in ,,the ,,sky ,,seen ,,from ,,different ,,parts ,,of ,,the ,,earth4 ,we have now seen how familiar ,dante was with the aspects of the skies above his head4 ,his writings show also that he had pictured clearly to himself what they must be in other parts of the world--in regions far east or west1 in the southern hemisphere1 at the equator1 and at either pole4 ,science could not tell him all that he would have liked to know about the stars1 so that although he can speak of regions where ,ursa ,major passes overhead1 and where it sinks out of sight below the horizon1 he has to fall back upon his imagination and invent new constellations for the southern hemisphere4 ,but astronomy could tell him1 and his habit of accurate thought1 as well as his imagination1 helped him to grasp how the sun would appear at any latitude on the earth1 and what would be the results on the length of day and night1 and on the seasons4 ,a very interesting little disquisition on this subject is found in the ,convivio1 in illustration of some lines in one of his ,odes1 which speak of the sun circling the whole world4 ,in order to understand this completely1 ,dante says1 we must know exactly in what way the sun circles the world4 ,the chief point to bear in mind while reading his description is that the sun1 besides the simple daily motion in a circle1 has a constant slow motion north or south1 and therefore his path in the sky1 as we see it day after day1 is really spiral4 ,the passage is much too long to quote in full1 but if the reader will follow me1 taking his ,convivio and opening it at chapter v4 of ,treatise ,,iii4 and beginning at line #ff1 ,i will give a rsum which will form a running commentary on the text1 and an explanation of any points which may not at once be clear4 ,we see the sky1 says ,dante1 continually revolving round ,earth as centre2 and it has two fixed poles of revolution--the northern1 which is visible to nearly all the land not covered by sea1 and the southern1 which is hidden from nearly all of it4 ,and the circle which is equi-distant from these two poles the celestial equator is that part of the sky in which we see the sun when he is in ,aries and in ,libra4 ,now if a stone could be dropped from this pole of ours the northern1 it would fall far away yonder in the ocean just where1 if a man were standing1 he would always have the ,pole ,star exactly overhead4 8,la stella0#chc is the ,pole ,star1 see p4 #bia4 ,and ,i believe 7,dante says7 that from ,rome to the north pole1 in a direct line1 is a distance of about #b1gjj miles4 ,to fix our ideas1 let us imagine that at this spot there is a city called ,maria1 and let us imagine another city1 called ,lucia1 at the spot exactly opposite1 where a stone would fall if dropped from the other pole4 ,and ,i believe that from ,rome southwards to this second place would be a distance of about #gejj miles4 ,thus the distance between the two cities1 in whatever direction the measuring cord be stretched1 would be #aj1bjj miles1 that is1 half the circumference of the globe1#chd and the inhabitants of ,maria would have their feet opposite the feet of those of ,lucia4 ,if any two spots on a sphere are exactly antipodal1 but in no other case1 the distance may be measured in an infinity of directions1 and always come out the same4 ---------------------------------------- -------------------------------- #chc 8,the star40 #chd ,as this is the value given by ,alfraganus1 we must here understand ,arabian miles4 ,the distances from ,rome to the north and south pole are therefore probably equal to #cejj to #igej ,english miles1 and both are a little too large1 because the half circumference of ,earth is too large4 ,the proportion is about right1 however1 for ,rome is nearly three times as far from the south pole as the north1 her latitude being #db ,n4 ,alfraganus placed her in the fifth climate1 at the northern boundary of which he said the pole was elevated #dc4 ---------------------------------------- -------------------------------- ,lastly1 let us imagine a circle on the globe1 which will be at equal distances everywhere from ,maria and ,lucia the equator4 ,according to the opinions of the astrologers1 if ,i understand them aright1 and according to what is said by ,albertus ,magnus and by ,lucan1 this circle would divide the dry land from the ocean there in the south1 approximately along the extremity of the ,first ,climate1 where amongst others live the ,garamantes1 who go almost always naked1 to whom ,cato went when fleeing from ,csar4 8,approximately10 because the southern extremity of the ,first ,climate1 according to ,alfraganus1 lay a little north of the equator1 although land extended1 and was sparsely inhabited1 as far the equator 7see p4 #ahf74 ,dante speaks again of these extra-climatal races in ,de ,mon4 ,i4 xiv4 #dc-ea1 where he contrasts the ,scythians who live beyond the seventh climate1 and therefore endure extreme inequality of days and nights1 and suffer almost intolerable cold1 with the ,garamantes who live under the equator1 where days and nights are always equal1 and the heat is so intense that they can scarcely bear any clothing4 ,since 8the astrologers who determine the climates0#che had fixed their northern limit at #ej1 nearly the whole of ,britain also lay1 like barbarous ,scythia1 in this scarcely habitable region of long nights and bitter cold6 ---------------------------------------- -------------------------------- #che ,qu4 xix4 #cf4 ---------------------------------------- -------------------------------- ,when we have marked these three places on the globe1 i4e4 the two poles and the equator1 it is easy 7,dante goes on7 to see how the sun circles4 ,i say then1 that the heaven of the sun turns from west to east1 not directly against the diurnal movement--that is1 the movement which produces day and night--but obliquely against it1 and so that its middle circle1 which is similarly between its two poles1 and on which is the body of the sun i4e4 the ecliptic1 cuts in two opposite points the circle of the two first poles the equator1 that is1 at the beginning of ,aries and the beginning of ,libra2 it diverges from that circle in two arcs1 one north and the other south4 ,the highest points of these arcs are equally distant from the first circle in either direction1 being #bc degrees and a little more2 and the one summit is at the beginning of ,cancer1 and the other at the beginning of ,capricorn4 ,therefore1 when the sun is in the beginning of ,aries1 travelling in the mid-circle of the first poles the equator1 ,maria will see this sun circling the world1 low down on the ground1 or on the sea1 like a mill-stone only half of which is seen1 and day after day he will be seen to rise1 like the screw of a press1 until he has performed about ninety revolutions1 or a little more4 ,when these revolutions are accomplished1 he will be as high in the sky above ,maria as he stands in the sky of the ,garamantes at middle-tierce at the time of equal days and nights4#chf ---------------------------------------- -------------------------------- #chf ,adopting the reading of ,dr4 ,moore3 8nella mezza terra1 alla mezza terza10 that is1 8at the equator at middle-tierce40 ,see ,studies in ,dante ,,iii4 #ajg1 #ajh4 ---------------------------------------- -------------------------------- ,from ,conv4 ,,iv4 xxiii4 and ,,iii4 vi41 where ,dante explains the use of temporal hours1 we learn that mid-tierce on the day of the equinox is an hour and a half after sunrise1 or #g4cj ,a4,m4 ,since the sun moves through #cfj degrees divided by #bd1 that is #ae degrees1 in an hour1 and his motion is vertical in equatorial countries at the equinox1 it would bring him in #a hours to #bb degrees above the horizon4 ,his greatest height above the horizon at the pole is only one degree more than this1 for it is obviously equal to the greatest distance between the equator and the ecliptic1 i4e4 #bc degrees1 since at the pole the equator coincides with the horizon4 ,this gives a good idea1 therefore1 of the appearance of the sun in the sky to the people at ,maria1 and is a striking illustration of the difference between the polar sun and the equatorial4 ,for at the time mentioned1 the sun has only a quarter the height which it will attain at noon1 when it will pass through the zenith of the ,garamantes2 yet this is the highest position in which the inhabitants of ,maria can ever see it4 ,if a man stood upright in ,maria1 and kept turning his face to the sun1 he would see it move to his right as we do4 ,after reaching his greatest height in the sky1 the sun would begin to descend again1 in the same spiral way like a screw turning1 for another ninety revolutions or so1 until once more he was circling down on the horizon1 only half his body visible4 ,then he would be lost to sight altogether1 and would begin to be seen in ,lucia1 where he would rise and descend in just the same way as in ,maria4 ,but if a man faced the sun in ,lucia1 he would see it moving to his left as one does in ,australia where it goes north at noon4 ,illustration3 ,fig4 #dc4 ,the ,sun at the ,equinox1 seen from the poles and the equator4 ,conv4 ,,iii4 v4 7,maria1 ,lucia1 imaginary cities at the ,north and ,south poles74 ,we see1 then1 that these places have one day in the year which is six months long1 and one night of equal length1 and when it is day with one1 it is night with the other4 ,now on the circle on the globe where the ,garamantes live the equator1 the sun when in ,aries goes exactly overhead1 not circling horizontally like a mill-stone1 but vertically like a wheel1 and exactly half of this wheel is visible above the horizon4 ,after this1 the sun is seen to depart and go towards ,maria for about #ia days2 then in about the same time it returns1 and enters ,libra2 then it goes towards ,lucia for about #ia days1 and in the same period returns4 ,and this place1 which circles the entire globe1 always has equal day and night1 on whichever side of it the sun is2 and twice in the year it has a very hot summer1 and twice a mild winter4 ,the regions which are between the two imaginary cities and the mid-circle1 see the sun in different ways1 according to their distance from these places1 but the details1 our author says1 he will leave to the ingenious reader1 8,siccome omai1 per quello che detto 1 puote vedere chi ha nobile ingegno1 al quale bello un poco di fatica lasciare40#chg ---------------------------------------- -------------------------------- #chg 8,for now1 after what has already been said1 the rest may be understood by whomsoever has a noble mind1 to which it is well to leave a little labour40 7,cf4 ,par4 x4 #bb-be74 ---------------------------------------- -------------------------------- ,he draws attention to the interesting fact1 which follows from the above1 that in the course of a year 7when the heaven of the sun has made a complete revolution and returned to the same place71 every part of this globe on which we live has received an equal amount of daylight4 ,and the essay ends in an apostrophe which recalls the reproof of ,virgil to those who will not look up to the skies3#chh 8,o ineffabile ,sapienza che a cos ordinasti1 quanto povera la nostra mente a ,te comprendere6 ,e voi1 a cui utilit e diletto io scrivo1 in quanta cecit vivete1 non levando gli occhi suso a queste cose1 tenendoli fissi nel fango della vostra stoltezza40#chi ---------------------------------------- -------------------------------- #chh ,purg4 xiv4 #adh-aea4 #chi 8,o unspeakable ,wisdom who hast thus ordained1 how poor is our intellect to understand ,thee6 ,and you1 for whose benefit and pleasure ,i am writing1 in what blindness you live1 not lifting up your eyes to these things1 but keeping them fixed on the slough of your folly40 ---------------------------------------- -------------------------------- ,it is interesting to compare this passage with the parallel passages in ,alfraganus and ,ristoro4 ,the astronomer is concise and clear2 the monk is diffuse and apt to repeat himself2 the poet is quaintly picturesque4 ,both the ,italians evidently draw the main facts from the ,arab1 and all use the illustration of a mill-stone to explain the horizontal motion of the heavens at the pole3 here are the three corresponding passages3-- 8,coelumque mol trusatilis instar gyrum vertitur40#cij 8,l si volgera il cielo attorno con tutte le sue stelle1 in modo di macina40#cia 8,conviene che ,maria veggia 444 esso sole #8girare il mondo' 444 come una mola40#cib ---------------------------------------- -------------------------------- #cij 8,and the sky revolves like a mill-stone40 ,el4 ,ast4 ch4 vii4 #cia 8,there the sky will revolve1 with all its stars1 mill-stone fashion40 ,comp4 del ,mondo4 ,i4 xxiii4 #cib 8,it follows that ,maria must see this sun #8circling the world' like a mill40 ,conv4 ,,iii4 v4 #adb-adg4 ---------------------------------------- -------------------------------- ,dante alone uses the figure of a wheel to illustrate the vertical motion at the equator2 he perhaps takes from ,ristoro the idea of the spiral4 ,for the latter describes the path of the sun as a 8via tortuosa1 la quale i savi chiamano spira20#cic but he explains it as like a string wound round a stick1 ,dante like the screw of a press4 ,dante is dealing only with the sun1 and does not enter into details about the visibility of the zodiacal signs like the other two authors2 but on the other hand he goes south to the other pole1 which apparently does not interest the others1 perhaps because the southern hemisphere was thought to be uninhabited4 ,but the poet has added life to his description by supposing both poles inhabited1 placing there his imaginary1 mysteriously-named cities of 8,maria0 and 8,lucia40 ,on the equator1 where ,ristoro has the mythical city of ,arym1 whose wise and prosperous citizens enjoy a perfect climate1 ,dante1 relying more on the classics1 lets his barbarous ,garamantes run about naked most of the year1 under the fierce equatorial sun4 ,needless to say1 his little homily in conclusion is all his own2 it is more interesting to find that he alone mentions the opposite movements of the ,sun1 to right and left respectively in the north and south hemispheres1#cid and the fact that every part of the earth receives the same amount of sunlight in a year4 ,this may have been suggested by someone else1 but one would like to think he arrived at it independently1 when thinking over the facts4 ---------------------------------------- -------------------------------- #cic 8,a winding path1 which the learned call a spiral40 #cid 8,lucan1 who was well known to ,dante1 had observed that shadows cast by the sun in the southern hemisphere travel to the right instead of to the left1 and fall southwards when with us they fall to the north40 ,moore1 ,studies in ,dante i4 p4 #bci4 ---------------------------------------- -------------------------------- ,in the light of this treatise1 which describes so truthfully the path of the sun1 and its effect on the seasons in different latitudes1 we may explain two rather puzzling passages in the ,divine ,comedy4 ,one is at the beginning of the tenth canto of the ,paradiso1 where ,dante wishes his readers to realize the position of the sun when he entered it with ,beatrice1 and the great importance of this position4 8,lift your eyes with me1 reader10 he says1 8to that place in the lofty heavens where the one motion meets the other1 and see how the oblique circle which carries the planets branches off from that point40 ,the reader is now familiar with the 8two chief motions10 and knows that one is the diurnal1 from east to west1 the other the planetary periodical motions in the opposite direction2 they meet at the equinoxes1 where the ecliptic cuts the equator4 ,it is the spring equinox which ,dante is speaking of1 for a little further on he says that the sun1 situated in the place above-mentioned1 was circling in those spirals which bring him to us earlier every day 7lines #ca-cc74 ,now if the path of the planets were not thus oblique1 he continues1 much virtue in heaven would be lost1 and almost every earthly power dead4 ,even if the obliquity were merely less or more1 the universal order of both heaven and earth would suffer greatly4 ,but why this should be so he leaves his readers to think out for themselves1 having a greater matter in hand which demands all his attention4 ,it is easy to see that if the sun always moved in the equator1 without departing from it either north or south1 he would rise every day to the same height in the sky1 and there would be no change of seasons anywhere on the earth2 he would always be overhead at noon to ,dante's ,garamantes1 living on the equator1 and always just on the horizon1 day and night1 to the people of 8,maria0 and 8,lucia0 at the ,poles4 ,if the ecliptic made a greater angle with the equator the seasons would be more marked1 and the sun would rise higher in summer in high latitudes4 ,if the angle were less1 the reverse would be the case4 ,moreover if sun and moon and all the planets followed the same track1 they would be constantly eclipsing one another4 ,but if we would understand the full meaning of-- 8,se la strada lor non fosse torta1 ,mota virt nel ciel sarebbe in vano1 ,e quasi ogni potenza quaggi morta40#cie ---------------------------------------- -------------------------------- #cie 8,if their pathway were not thus inflected1 ,much virtue in the heavens would be in vain1 ,and almost every power below here dead40 ,par4 x4 #af-ah4 7,longfellow74 ---------------------------------------- -------------------------------- we must turn to thirteenth-century ,ristoro of ,arezzo1 who has set forth in detail the results which he believed would follow from a change in the ecliptic4 ,if all the seven planets moved in the same narrow path1 there would be much less variety in their 8aspects10 and therefore in their influences upon the earth2 and in the frequent eclipses one would prevent the other from looking at the earth 78impedimenterebbe l'uno l'altro a guardare la terra071 and so hinder its action4 ,and since it is the northward movement of the sun which causes our plants to blossom1 and later to bear fruit1 if there were no such motion we should see no renewal of life4 ,he argues further that if the obliquity of the ecliptic were greater1 countries in high latitudes would have too severe a winter to be inhabited2 while if it were less1 the summer there would not be warm enough for the ripening of harvests2 therefore in whichever way it differed from the actual value1 a smaller part of the earth would be habitable4 8,or ti riman1 lettor1 sopra il tuo banco1 ,dietro pensando a ci60#cif ---------------------------------------- -------------------------------- #cif 8,and now remain1 reader1 on your bench1 thinking over this60 ,par4 x4 #bb1 #bc4 ---------------------------------------- -------------------------------- ,how much of this was in ,dante's mind it is hardly possible to say1 but it is evident that the 8via tortuosa0 of the seven planets1 and its effects on the earth1 was a favourite subject for thought in his time4#cig ---------------------------------------- -------------------------------- #cig ,thus ,petrarch3 8,le stelle vaghe e lor viaggio torto40 78,the wandering stars and their winding way407 ,sonetto de ,morte di ,madonna ,laura4 ---------------------------------------- -------------------------------- ,but the most famous passage relating to the sun's path and its aspect in strange latitudes is ,purg4 iv4 #eb-hd4 ,here ,dante is able at once to understand the startling appearance of the sun travelling to his left instead of his right1 as seen on the first morning in ,purgatory1 for he grasps the full meaning of ,virgil's explanation1 and caps it1 in a way which seems astonishingly quick-witted to unastronomical readers6 ,the two poets had begun to climb the mountain just at sunrise1 and sat down to rest on a ledge at about half-past nine1 looking east4 ,dante at first looked down at the shore1 whence he had so painfully climbed1 then raised his eyes to the sun1 and was amazed to find that its rays struck him on the left shoulder4 ,virgil1 seeing his astonishment1 explains why the sun is going north instead of south as it climbs the sky4 ,the sun is now in ,aries1 and therefore on the equator1 as we know from several passages1 but ,virgil begins by saying that if it were in ,gemini a more northerly sign and kept to its ancient path1 ,dante would see it travelling still further northwards in its daily course4 8,if ,castor and ,pollux stars in ,gemini were in company with that ,mirror the sun which carries his light up and down i4e4 goes north and south alternately1 you would see the glowing zodiac that part in which the sun is revolving still closer to the ,bears40 ,gemini is literally nearer to the constellations of the ,bears than ,aries1 but this is not the sense of ,virgil's statement3 he means merely to indicate the north in general 7see ,ptolemy1 p4 #aeg74 8,to understand why the sun goes north10 ,virgil says1 8you must know that this mountain and ,zion ,jerusalem are so situated on the earth that one is precisely antipodal to the other2 and so1 the sun's path being between them1 when he is viewed in one direction from ,jerusalem1 he is viewed in the opposite direction from ,purgatory4 ,if you turn from the east to your right to see him from ,jerusalem1 you must turn to your left in ,purgatory40 ,virgil speaks of the sun's path or the ecliptic as the path which ,phaton was not able to keep1 and he describes the two antipodal places as having one and the same horizon but two entirely different hemispheres4 8,certainly10 replies ,dante1 8,i have never seen anything so clearly as ,i now perceive what at first puzzled me4 ,for the middle circle of the celestial motion1#cih which is called the equator in a certain art astronomy1 and which always remains between the sun and winter1 the sun crosses it departing from us in either hemisphere at the autumnal equinox1 here lies to the north of us1 for the reason you have given namely1 that we are in the southern hemisphere1 whilst the ,hebrews inhabitants of ,jerusalem see it towards the hot region the south40 ,observe that the expression used of the equator 8che sempre riman tra il sole e il verno10#cii distinctly suggests the reversed seasons in the southern and northern hemispheres1 so that ,dante has no intention1 as ,dr4 ,moore suggests1 of assuming by a poetic licence that it is spring in ,purgatory as well as in ,italy4#djj ,it is autumn in the southern hemisphere1 but this need not distress us3 the holy ,mountain knows no inclement weather1#dja and in the ,garden of ,eden on its summit spring flowers and autumn fruits eternally flourish together4#djb ,an allusion is made to a tropical summer in 8la terra che perde ombra40#djc ,tropical ,africa is intended1 where the sun at certain times passes directly overhead1 and therefore casts no shadows1 as the ,alexandrian astronomers had observed 7see p4 #aag74 ---------------------------------------- -------------------------------- #cih ,cf4 ,conv4 ,,iii4 v4 #gf1 #aia4 #cii 8,which always remains between the sun and the winter40 ,purg4 iv4 #ha4 #djj ,studies in ,dante iii4 p4 #aff4 #dja ,purg4 xxi4 #df-dh2 ,purg4 xix4 #ch4 #djb ,purg4 xxviii4 #adc4 #djc 8,the land where shadows are lost40 ,purg4 xxx4 #hi4 ---------------------------------------- -------------------------------- ,did ,dante believe that no land exists anywhere in the southern hemisphere8 ,there are some indications that he thought it possible to push the limits of the habitable earth a little beyond the equatorial boundary of ,alfraganus4 ,there would be no heresy in lengthening the southward extremities of ,africa or ,asia1 because all that the ,church forbade was to plant another land in the south1 separated from us by a vast ocean or impassable torrid zone1 and to people it with inhabitants1 who could not therefore be descendants of ,adam or have the ,gospel preached to them4 ,nor would there be any inconsistency with the poet's own description of our hemisphere as that covered by 8la gran secca10#djd or with the voyage of ,ulysses1 on which he saw no land but the ,mountain of ,purgatory2 for he sailed south-west1 not due south1 and the 8mondo senza gente0#dje was 8diretro al ,sol40#djf ---------------------------------------- -------------------------------- #djd 8,the great dry land40 ,inf4 xxxiv4 #aac4 #dje 8,the unpeopled world40 ,inf4 xxvi4 #aag4 #djf 8,behind the sun40 ,ibid4 ---------------------------------------- -------------------------------- ,the indications are as follows3-- 7#a7 ,the passage quoted above1 where it is said that the equator 8divides the uncovered land from the ocean0#djg is ambiguous in the original1 and might mean 8divides the land uncovered by ,ocean40 ---------------------------------------- -------------------------------- #djg ,conv4 ,,iii4 v4 #aag1 #aah4 ---------------------------------------- -------------------------------- 7#b7 ,shortly before1 he has distinctly admitted that there is some land in the southern hemisphere1 by saying that the north celestial pole is visible to nearly all the land not covered by sea1 and the south is hidden from nearly all of it4 ,the first is true in any case1 since though the pole is theoretically visible as far as the equator1 it is often hidden by mist or rising land on the northern horizon2 but unless the second 8nearly0 has been added by a 7somewhat natural7 mistake of a copyist1 it can only apply to lands in the southern hemisphere4#djh ---------------------------------------- -------------------------------- #djh ,refraction makes the pole visible a little before one reaches the equator1 but such refinements need not be considered in dealing with a popular work like the ,convivio4 ---------------------------------------- -------------------------------- 7#c7 ,there is a stanza in ,canzone ,,xv4 which suggests that ,dante believed ,ethiopia to be on the south side of the equator4 ,classical and medival cosmographers had very vague ideas about the extent and position of this country4 ,dante describes a wind raised in its deserts by the sun1 which now is heating it 7implying the time of summer872 but the same wind1 crossing the sea to ,europe1 darkens all this hemisphere1 bringing clouds which fall in snow4 8,levasi della rena d',etiopia ,un vento pellegrin1 che l' aer turba1 ,per la spera del sol1 ch' or la riscalda1 ,e passa il mare1 onde n'adduce copia ,di nebbia tal1 che s' altro non la sturba ,questo emisperio chiude tutto1 e salda2 ,e poi si solve1 e cade in bianca falda ,di fredda neve1 ed in noiosa pioggia40#dji ---------------------------------------- -------------------------------- #dji 8,there riseth up from ,ethiopia's sands ,a wind from far-off clime which rends the air1 ,through the sun's orb that heats it with its ray4 ,the sea it crosses2 thence1 o'er all the lands ,such clouds it brings that but for wind more fair ,o'er all our hemisphere 'twould hold its sway2 ,and then it breaks and falls in whitest spray ,of frozen snow and pestilential showers40 ,canz4 xv4 #ad-ba4 7,plumptre74 ---------------------------------------- -------------------------------- ,however1 it may be said that 8or la riscalda0#daj means merely that it is always hot in the tropics1 even when we have winter1 and that 8questo emisperio0#daa cannot possibly mean the whole of the terrestrial northern hemisphere from equator to pole1 but simply describes the appearance of the hemispherical sky1#dab completely covered with cloud4 ,these doubtful passages are not strong enough to set against the explicit statement in the ,qustio that the habitable earth extends from the equator to the ,arctic circle and no further4#dac ,letters and reports from missionaries and traders1 none of them scientific1 did not shake ,dante's faith in the limits laid down by ,ptolemy and ,alfraganus4 ,his geography was utterly wrong1 but his astronomy was right2 and therefore1 although he had no idea of what he would see on our globe in untravelled latitudes1 he knew exactly1 and has described vividly1 what he would see in the sunny sky4 ---------------------------------------- -------------------------------- #daj 8,now heats it40 #daa 8,this hemisphere40 #dab ,just as in ,par4 xxviii4 #hj4 #dac ,qu4 xix4 #ec-eg1 and repeated in xxi4 #cf-dj4 ---------------------------------------- -------------------------------- #i4 ,,celestial ,,phenomena ,,and ,,time4 ,the foregoing quotations have shown how well ,dante understood the changing appearances of the celestial phenomena as viewed from different latitudes3 it now remains to be seen what were his conceptions of longitude4 ,a difference in longitude between two places makes no difference in the stars1 nor in the apparent paths of the heavenly bodies1 but they come to the meridian sooner in the more easterly place2 and as it is the meridian passage of the sun which determines local time1 this will vary in exact proportion to the distance east4 ,when it is early morning in ,england1 it is noon in ,burmah1 and evening in ,fiji4 ,as ,alfraganus had observed 7following ,ptolemy71 a celestial phenomenon such as a lunar eclipse1 which is caused by an actual darkening of the moon's surface when immersed in ,earth's shadow1 is visible in every place where the moon is above the horizon1 though the local hour differs4 ,it is otherwise with a total solar eclipse1 for this is only visible from the very small portion of ,earth on which the moon's shadow falls as she passes between us and the sun 7see fig4 #dd72 and as this shadow moves on1 owing to her own motion and the diurnal revolution combined1 the eclipse becomes visible successively from different parts of the earth4 ,dante realized this when he quoted the argument of some theologians that the miraculous three hours' darkness described in the ,gospels could not have been caused by an eclipse of the sun1 as ,aquinas and others had suggested1 because it was visible all over the earth at the same absolute time1 that is1 during the ,crucifixion4#dad ,some said1 he tells us1 that the moon went back and placed herself between us and the sun 7for the moon at ,passover time was always full1 and therefore opposite the sun71 so that the sun's light should not come down 7to us on the earth72 others1 that the sun hid itself1 for a corresponding eclipse was seen by ,spaniards and ,indians as well as ,jews4#dae ,spaniards and ,indians were supposed to live at the extreme western and eastern limits of the habitable earth3 they were #ahj in longitude1 or #ab hours in time1 apart1 and ,jerusalem was midway between them4 ,therefore the sun would be visible to all1 though only just rising in ,india and just setting in ,spain2#daf but it could not have been an eclipse that darkened it to all at the same time4 ---------------------------------------- -------------------------------- #dad ,luke xxiii4 #dd4 #dae ,par4 xxix4 #ig-ajb4 #daf ,dante believed the death of ,christ to have taken place when it was noon in ,jerusalem4 ,conv4 ,,iv4 xxiii4 #aje-ajf4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #dd4 ,lunar and ,solar ,eclipses4 ,this passage shows that ,dante was entirely orthodox and conservative in his geography1 as far as longitude was concerned1 and confirms us in the conclusion that he was so also with regard to latitude1 and was not likely to accept contemporary evidence about lands south of the equator1 or stars unknown to ,ptolemy4 ,in the ,divine ,comedy there are several passages which refer to the same system1 as for instance where ,night is described as covering the whole region from 8the ,shore0 to ,morocco1#dag or where the time is stated to be noon on the ,ganges1 sunrise at ,jerusalem1 and midnight in ,spain4#dah ,and in the ,qustio de ,aqua et ,terra the system is thus clearly explained3-- 8,as all these agree in believing the naturalists1 the astrologers1 and the cosmographers1 this habitable earth extends in longitude from ,gades1 which lies on the western boundaries of ,hercules1 as far as the mouths of the ,ganges1 as ,orosius writes4#dai ,that longitude is such that at the equinox the sun is setting upon those who are at one of these boundaries1 while it is rising upon those who are at the other1 as astrologers have discovered by eclipses of the moon4 ,therefore the aforesaid boundaries must be #ahj degrees distant in longitude1 which is half the distance of the whole circumference40#dbj ---------------------------------------- -------------------------------- #dag ,purg4 iv4 #acg-aci4 #dah ,purg4 xxvii4 #a-e4 #dai ,orosius says3 8,europ in ,hispania occidentalis oceanus termino est1 maxime ubi apud ,gades insulas ,herculis column visuntur4444 ,asia ad mediam frontem orientis habet in oceano ,eoo ostia fluminis ,gangis40 #dbj ,qu4 xix4 #ch-eb4 ---------------------------------------- -------------------------------- ,gades is not the city of ,cadiz1 but two islands 7the 8,gades ,insul0 of ,orosius71 on which ,hercules was said to have set up his ,pillars1 as a sign that no one should venture further2 and they were thought to lie in the mouth of what we call the ,straits of ,gibraltar3#dba-- ---------------------------------------- -------------------------------- #dba ,moore1 ,studies in ,dante iii4 p4 #abd4 ---------------------------------------- -------------------------------- 8quella foce stretta1 ,ov' ,ercule segn li suoi riguardi1 ,accioch l'uom pi oltre non si metta40#dbb ---------------------------------------- -------------------------------- #dbb 8,the strait pass1 where ,hercules ordained ,the boundaries not to be o'erstepped by man40 ,inf4 xxvi4 #ajg-aji4 7,carey74 ---------------------------------------- -------------------------------- ,through these ,ulysses sailed1 never to return4#dbc ---------------------------------------- -------------------------------- #dbc ,inf4 xxvi4 #ajf-adb4 ---------------------------------------- -------------------------------- ,it is difficult to believe that a lunar eclipse had ever been observed simultaneously1 and the local time compared1 on the ,ganges and at ,gibraltar1 as the above quotation from the ,qustio declares3 and if it had been1 the astrologers1 the cosmographers1 and the naturalists would have found out that they were greatly mistaken1 for the distance is little more than half what they thought4 ,all that ,ptolemy had said was that this was the right method for calculating longitudes1 and he gave as an example an eclipse which had been seen at ,arbela at the fifth hour and at ,carthage at the second hour4#dbd ,it was1 in fact1 an excellent method1 and the only one before the day of chronographs and telegraphs2 and it seems to have been assumed that ,ptolemy's guess of #ahj for the extent in longitude of the inhabited earth was based upon it4 ---------------------------------------- -------------------------------- #dbd ,ptolemy's ,geography1 ,bk4 ,i4 ---------------------------------------- -------------------------------- ,then this #ahj was considered1 in the ,middle ,ages1 as divided into two equal parts1 the western half containing ,europe and ,africa1 the eastern containing ,asia4 ,on the western front of ,asia lay ,jerusalem1 thus holding the central position in the inhabited earth which was thought to be her right1 on the authority of certain ,scripture texts1 as we saw4#dbe ,this gave the ,mediterranean a length of #ij1 which of course is vastly too great4 ,even ,ptolemy had only estimated it at #fb1 and the ,alfonsine ,tables made it #eb1 while the true distance is only about #db4 ---------------------------------------- -------------------------------- #dbe ,see p4 #agf4 ---------------------------------------- -------------------------------- ,latitude1 however1 was much more easily measured than longitude1 for it was only necessary to take the height of the pole star above the horizon with an astrolabe2 and the latitude of ,jerusalem is really just about midway between the supposed limits of the habitable earth1 the equator and arctic circle1 for it is nearly #cb north4 ,some daring spirits ventured to suggest that the dry land stretched much further round the globe than was commonly supposed1 so that one might sail from ,spain to ,asia in quite a short time1 and they sheltered themselves behind the great names of ,aristotle1 ,seneca1 ,pliny1 and ,esdras4#dbf ,albertus ,magnus quotes ,aristotle to this effect1 although in another part of the same book 7his ,de ,clo et ,mundo71 he repeats the usual phrase about the habitable ,earth being all contained within one of the northern quadrants of earth4 ,roger ,bacon expresses himself more boldly1 and it is possible that he was impressed by the long journey of the ,franciscan friar ,rubruquis1 on his mission to ,central ,asia1 from ,st4 ,louis of ,france to the ,emperor of the ,mongols4 ,besides relating the story of this journey1 ,bacon speaks of men who were known to live in tropical ,taprobane 7,ceylon71 and if there1 why not also south of ,capricorn8 ,there may be delightful countries there1 since it is the better and nobler part of the world1 as ,aristotle and ,averros taught4 ,moreover1 ,dante's own countryman1 the learned ,pietro d',abano1 maintained that there are habitable lands on1 and even beyond the equator1 and did not hesitate to quote conversations with ,marco ,polo as evidence1 although this 8most extensive traveller and most diligent enquirer0 was accounted a romancer by most of his contemporaries4 ,had not ,messer ,marco told him that in islands south of the equator he had seen not only great rams with coarse stiff wool like the bristles of pigs1 but human beings8#dbg ---------------------------------------- -------------------------------- #dbf ,esdras ,,ii4 vi4 #db4 #dbg ,beazley1 ,dawn of ,geography iii4 #bh1 #bi4 ---------------------------------------- -------------------------------- ,roger ,bacon was banished from ,oxford on a charge of heresy and witchcraft3 ,pietro d',abano escaped the ,inquisition by dying1 in #acaf4 ,men such as these belonged to the new age that was coming1 the age that would throw away the old lesson-books1 and begin to discover for itself--and they suffered in consequence4 ,dante belonged heart and soul to his own era1 and clung passionately to its ideals and traditions4 ,for him the ,ganges still flowed into the all-surrounding ocean on the east coast of ,asia1 #ij degrees from ,jerusalem1 as ,orosius had pictured it1 and there is not the faintest echo in his writings of the voyages of his countrymen1 ,corvino and his bishops1 or ,polo and his companions1#dbh between 8,greater ,india0 and 8,zayton0 7,amoy harbour71 although they surely must have recognized1 when they praised the great rivers of ,china1 that these flowed into a sea many days' journey beyond that into which the ,ganges rolled its waters4 ,nor is there1 on the other hand1 any hint of the monstrous races with which ,dark-,age superstition had peopled the remote regions of the earth1 although they were regularly represented on the maps of that time4 ,it is true that the 8portolani10 or handy charts1 of which the earliest known date from ,dante's life-time1 showed none of these things1 but depicted the coast-lands of the ,mediterranean and ,black ,seas with marvellous accuracy3 but they were only for pilots and merchant captains1 and had nothing to do with scholars4 ,the maps ,dante would see were hung on church or monastery walls1 or illustrated learned books2 and the mappe-monde of ,cardinal ,heinrich of ,mainz may be taken as typical of them all4 ,it much resembles our great ,hereford ,map of the ,world1 and was probably copied from the same original design4 ---------------------------------------- -------------------------------- #dbh ,corvino and ,marco ,polo made the voyage in the same year1 #abib1 but in reverse directions4 ---------------------------------------- -------------------------------- ,it is two hundred years older than ,dante1 but so stationary was geography throughout the ,middle ,ages that it might have been executed in his day1 or1 except for a few details1 several centuries earlier4 ,medival maps are as fascinating as a fairy tale1 which indeed they much resemble4 ,the shape is conventional1 and not supposed to represent the true shape of the habitable earth2 it is sometimes circular1 sometimes quadrilateral1 occasionally oval1 as in the present instance4 ,the east is here1 as usual1 at the top1 and there we see the ,paradise of ,adam and ,eve1 and close beside it1 to the north1 the ,river ,ganges1 flowing into the great ocean which surrounds all the land4 ,at the opposite or western extremity are the ,pillars of ,hercules1 which two angels appear to be guarding4 ,in the centre1 but not so exactly or conspicuously central as in some other maps1 we find 8,hierusalem40 ,along the south is the long narrow continent of ,africa1 with the ,atlas and ,ethiopian mountains2 and the ,nile1 rising far in the south-west1 after mysterious submergences and reappearances1 finally flows into the ,mediterranean1 past the pictured ,pyramids1 here strangely called 7according to ,dark-,age myth7 the ,barns of ,joseph4 ,in the north another ,angel points to the country where dwell the ,gog-,magogs1 and not far off are the lands of the ,hyperboreans1 here described as untroubled by disease or discord1 of the 8most wicked0 ,gryphons1 and of the ,dog-headed folk1 adjoining the ,arctic ,ocean4 ,italy is a very large country1 roughly triangular1 and in the ,mediterranean to the south lie ,sicily1 the whirlpool ,charybdis1 the rock ,scylla1 ,sardinia1 ,corsica1 and other islands4 ,rome is figured as a battlemented city1 about halfway between ,jerusalem and the ,pillars of ,hercules4 ,illustration3 ,,map ,,of ,,the ,,world ,,by ,,heinrich ,,of ,,mainz1 ,,about ,a4,d4 #aaaj4 ,to face p4 #cdd4 ,reproduced by permission from ,beazley's 8,dawn of ,modern ,geography40 ,this is where ,dante also places the imperial city1 for in his system it is about #de1 or #c hours1 east of ,gades and west of ,jerusalem4 ,he tells us in one place that it was vespers in ,naples when the sun rose in ,purgatory1#dbi and in another that when it was vespers or three o'clock in the afternoon in ,purgatory1 it was midnight 8here0#dcj which may mean ,florence or ,italy in general2 both these statements indicate a difference of nine hours or #ace between ,italy and ,purgatory4 ,purgatory in the ,divine ,comedy is exactly antipodal to ,jerusalem1 and therefore twelve hours distant in time2#dca and for the sake of his allegory ,dante has so far departed from tradition as to place the ,earthly ,paradise here also4#dcb ,these five places may therefore be diagramatically represented thus3-- ---------------------------------------- -------------------------------- #dbi ,purg4 iii4 #be4 #dcj ,purg4 xv4 #a-f4 #dca ,purg4 iv4 #fh-ga2 xxvii4 #a-e4 #dcb ,purg4 xxviii4 #adb4 ,opinions differed as to its exact site1 and some placed it in the ocean beyond the eastern limit of the habitable earth4 ,in ,v4 ,e4 ,i4 viii4 #f-aj1 ,dante says that the root of the human race was planted in eastern lands1 but this refers to ,adam's home after the expulsion from ,paradise4 ---------------------------------------- -------------------------------- ---------------------------------------- ----------------- ,,early ---------------- ,,time ---------------------- ,,late #ab hours #f;hrs4 #c;hrs4 #f;hrs4 #ab hours ---------------------------------------- ------------ ,purgatory ,gades ,italy ,jerusalem ,ganes ,purgatory ---------------------------------------- ------------ #ahj #ij #de #j #ij #ahj ,,west --------------- ,,longitude -------------------- ,,east ---------------------------------------- ----------------- ,with this key1 ,dante's fondness for describing the time at one place by mentioning one of the others need be no stumbling-block1 as it is to many readers4 ,the fact is that though ,dante had none of our opportunities for changing time-reckoning by long journeys1 nor for communicating with friends at the other side of the world1 who wake while we sleep1 the marvellous daily revolution of the skies had a fascination for him1 and he delighted to picture a glorious sunrise taking place in one country while in another it was high noon1 or the middle of the night4 ,thus1 the beautiful description of the stars fading in the growing light of dawn1 which we quoted above1 is preceded by a picture of the sun glowing on the meridian some #fjjj miles away 7rather more than a quarter the circumference of the globe71 while with us ,earth's shadow has sunk almost to a level plane4#dcc ,again1 ,folco of ,marseilles1 when describing his birthplace1 says that the greatest of all the seas 7the ,mediterranean7 except the ocean which encircles all the habitable earth1 stretches so far against the sun 7i4e4 from west to east71 that the line of sky which is on its horizon at one end is on its meridian at the other4#dcd ,if the sun were seen just rising on the eastern horizon at ,gades1 it would be on the meridian at ,jerusalem and the time would there be noon4 ---------------------------------------- -------------------------------- #dcc ,par4 xxx4 #a-c4 #dcd ,par4 ix4 #hb-hg4 ---------------------------------------- -------------------------------- ,dante's hours are always reckoned from sunrise1 and they are the 8temporary0 or ,church hours4 ,he defines both kinds in the ,convivio4 ,the same lines of his ,ode which provided him with a text whereon to discourse of the sun's movements1 give him occasion to treat of the division of each day into hours1 thus3-- 8,i say that the sun1 in circling round the world1 ne'er beholdeth aught so noble as this lady1 from which it follows that she is1 as the words affirm1 the most noble of all the things on which the sun shines4 ,and ,i say in that hour1 etc4 ,wherefore we must know that the hour is understood in two senses by astrologers4 ,one sense is employed when they assign twenty-four hours to the day and night1 that is1 twelve to the day and twelve to the night1 however long or short the day may be4 ,and these hours become short or long in the day and in the night1 according as the day and night wax and wane4 ,and the ,church uses hours in this sense when she speaks of ,prime1 ,tierce1 ,sext1 and ,none2 and these are called temporal hours4 ,the other sense is employed when1 of the twenty-four hours alloted to the day and night1 the day has sometimes fifteen and the night nine1 and sometimes the night has sixteen and the day eight assigned to it1 according as the day and the night wax and wane2 and these are called equal hours4 ,and at the equinox these latter are always one and the same with those which are called temporal2 for it must needs be so when the day and the night are of the same length40#dce ,the choice of these two examples of unequal days and nights seems to be another instance of ,dante's dependence upon ,alfraganus1 for in ,chapter ,,viii4 of the ,elementa ,astronomica we read that the middle of the seventh climate 7in which the inequality is greatest7 has a longest day of #af hours1 and the middle of the fifth1 of #ae hours2 and in chapter ,,ix4 we find that ,magna ,roma is situated in the fifth climate4 ,in the fourth treatise of the ,convivio1 ,dante returns to the same subject1 and enters into further detail about ,church hours and divisions of the day4#dcf ,our lives1 like the arch of heaven which is always above us1 consist of a rise and a decline1 with a culminating point1 and this point he fixes as normally reached at a man's #ceth year1 as ,ristoro had also done4#dcg ,in the same way the day rises and declines1 and culminates at the sixth hour2 and it is the most noble hour of the day and the most virtuous 7in the old ,latin sense of virtue as strength1 efficacy74 ---------------------------------------- -------------------------------- #dce ,conv4 ,,iii4 vi4 #g-cb4 #dcf ,conv4 ,,iv4 xxiii4 #ej to end4 #dcg ,comp4 del ,mondo1 ,i4 xxii4 8,la sesta ora1 cio il mezzo del d1 la pi nobile di tutto il d1 e la pi vertuosa40#dch #dch 8,the sixth hour1 that is1 the middle of the day1 is the most noble of all the day1 and the most virtuous40 ---------------------------------------- -------------------------------- ,this means the whole of the sixth hour 7as we should say1 from #aa to #ab o'clock73 the beginning of the seventh hour is the exact moment of noon1 after which the day begins to decline4 ,it was for this reason1 ,dante believes1 that ,christ chose to die during the sixth hour1#dci and during his #cdth year1 for then the day and his human life were both at their culmination1 and had not begun to decline4 ---------------------------------------- -------------------------------- #dci ,luke xxiii4 #dd-df4 ,dante understands this to mean that death took place at about the sixth hour1 not the ninth4 ---------------------------------------- -------------------------------- ,there was some difference in the methods of reckoning the hours for ,church offices1 but ,dante tells in this same passage which of them he considered right1 and he follows it consistently in his works4 ,the ,church day was divided into four parts1 viz43-- ,at the equinox ,tierce1 ,sunrise to the end of the third hour #f to #i a4m4 ,sext1 ,fourth to end of sixth hour #i a4m4 to #ab noon ,nones1 ,seventh to end of ninth #ab noon to #c p4m4 ,vespers1 ,tenth hour to sunset #c to #f p4m4 ,two of the ,church offices were to be said at the beginning1 and one at the end1 of these periods1 as follows3-- ,tierce1 at the end i4e4 #i a4m4 at the equinox4 ,nones1 at the beginning i4e4 #ab noon4 ,vespers1 0 0 i4e4 #c p4m4 at the equinox4 ,thus sext is omitted altogether1 and ,dante says that the reason for the arrangement is to approximate in every case to that hour which is the noblest of the whole day1 the sixth4 ,mid-tierce was halfway through the period from sunrise to the end of the third hour1 that is1 #g4cj a4m4 at the time of the equinox2 and mid-nones and mid-vespers were counted in the same way4 ,as an instance of reckoning hours by the sun1 we may quote the reply of ,adam when ,dante desired to know how long time he had spent in ,eden3 8,dalla prim' ora a quella che seconda1 ,come il sol muta quadra1 l'ora sesta40#ddj ---------------------------------------- -------------------------------- #ddj 8,from the first hour to that which cometh next 7,as the sun changes quarter7 to the sixth40 ,par4 xxvi4 #ada-adb4 7,carey74 ---------------------------------------- -------------------------------- ,just as the time of day may be told1 if one is accustomed to watch the sun1 by noting how much of the daily course has been run1 so the time of day or night 7according to her phase7 may be told by the moon2 only with her we must take into consideration the rapid and variable motion eastwards in the zodiac4 ,alfraganus says that her mean daily motion in longitude is #ac and nearly #aa minutes1#dda but that a small amount must be added or subtracted every day in order to find her true motion4 ,as a clock1 therefore1 for use in daily life1 she leaves much to be desired4 ,this daily motion makes her fall constantly behind the sun1 so that she loses time every day1 and not even the same amount of time2 for though she crosses the meridian on an average #ej minutes later each day1 the interval is sometimes only #ch minutes and sometimes as much as #ff minutes4 ,and her times of setting and rising are even more variable4 ---------------------------------------- -------------------------------- #dda ,it is easily seen that this is correct1 if we divide the #cfj of the moon's path through the zodiac by the #bg days and eight hours in which she traverses it1 and returns to the same star4 ,brunetto ,latini says 8,la lune s'esloigne dou ,soleil chascun jor xiii degrez po s'en faut10 but he is wrong1 having apparently forgotten that the sun is also moving in the same direction1 at the average rate of nearly #a daily4 ---------------------------------------- -------------------------------- ,this is easily understood if we remember how much the sun's time of setting varies throughout the year1 according to the part of the zodiac in which he is travelling1 and consider that what the sun does in a year the moon does in a month4 ,and in her case the effect is sometimes exaggerated1 sometimes diminished1 for her path in the zodiac is inclined to the sun's path2 moreover1 her greatest departure from it to north and south takes place in different parts of the zodiac at different times4 ,these facts were well known to ,ptolemy and to medival astronomers1 and everyone who watches the moon must have noticed how variable are the intervals between one moonrise or one moonset and the next4 ,the extent of variability also depends upon our latitude 7just as with sunrises and sunsets72 and in ,florence the retardation in one day may sometimes be only twenty minutes1 sometimes an hour and twenty minutes4 ,the difference would be less in ,dante's ,purgatory1 since this was in latitude #cb south1 and the intervals between moonset and moonset become less variable in length as we approach the equator1 just as the days become less unequal all the year round4 ,still1 they would vary a good deal1 so we must conclude that ,dante only means to indicate the time quite roughly when he uses the moon as a clock4 ,as a matter of fact1 he seldom does so in the ,divine ,comedy without giving us another clue to the time as well4 ,these passages all belong to a most interesting series of time indications1 which we may now proceed to examine4 ,,vi4 ,,dante',s ,,journey ,,through ,,the ,,three ,,realms3 ,,indications ,,of ,,time ,,and ,,direction ,,by ,,means ,,of ,,the ,,skies4 #a4 ,,time ,,references ,,in ,,the ,,divine ,,comedy4 ,the plan of the universe through which ,dante feigns himself to have journeyed is familiar to all readers of the ,divine ,comedy4 ,hell1 as the ,fathers taught1 was a subterranean cavity1 and ,dante pictures it as an inverted cone1 whose apex reaches the exact centre of ,earth and therefore of the universe4 ,it is situated vertically underneath ,jerusalem1 the centre of the inhabited ,earth4 ,he departs from the ,fathers1 however1 in removing ,purgatory from these dim regions1 and placing it on an island in the midst of the ocean of the uninhabited hemisphere1 exactly at the antipodes of ,jerusalem4 ,on this island rises a mountain whose immensely lofty summit reaches the upper regions of the atmosphere1 and upon the summit is the ,eden of our first parents4 ,this original conception is an extraordinary gain1 both from the artistic and the allegorical points of view2 and it is in harmony with the idea of ,aristotle1 and of many medival writers1 that the southern hemisphere was the 8nobler0 part of ,earth4 ,here1 then1 man was permitted to dwell before the ,fall1 and hither come repentant souls1 saved from ,hell1 but not yet pure enough to enter ,heaven4 ,paradise consists of all the spheres of medival astronomy1 and the poet rises from one to another until he finally reaches the all-embracing ,empyrean1 where his vision ends4 ,nowhere does he describe this scheme in full1 but it was evidently clear in his own mind1 and by following him step by step in his journey it is easily reconstructed1 and is represented in the accompanying diagram4 ,in the same way he never states how long a time he spent on this visionary journey1 yet this also he had definitely determined1 and in each ,cantica he refers once to the period of time alloted to each realm4 ,in the last ,circle but one of the ,inferno1 he is warned by ,virgil that the time allowed is drawing to a close2#ddb in the last but one of the ,purgatorio ,virgil urges him to make the best use of the time appointed2#ddc and in the ,paradiso1 just before the final vision1 ,st4 ,bernard tells him that the time of his trance is nearly over4#ddd ---------------------------------------- -------------------------------- #ddb ,inf4 xxix4 #aa4 #ddc ,purg4 xxiii4 #e1 #f4 #ddd ,par4 xxxii4 #aci4 ---------------------------------------- -------------------------------- ,in the first ,canto1 which is introductory to the whole ,commedia1 he mentions the time at which he assumes that his vision began4 ,it was 8nel mezzo del cammin di nostra vita10#dde which may mean simply that he was middle-aged1 or comparing it with the passage in the ,convivio quoted earlier 7see p4 #cdg71 we may suppose it to mean that he was exactly in his #ceth year4 ,the season was spring--8la dolce stagione10#ddf and when night was over the sun rose among those stars which were with him at the ,creation1 which was believed to have taken place at the vernal equinox some sixty-five centuries before4 ---------------------------------------- -------------------------------- #dde 8,midway in the journey of our life40 ,inf4 i4 #a4 #ddf 8,the sweet season40 ,inf4 i4 #dc4 8,il ,sol montava su con quelle stelle ,ch' eran con lui quando l',amor ,divino ,mosse da prima quelle cose belle40#ddg #ddg 8,aloft the sun ascended with those stars ,that with him rose when ,love ,divine first moved ,those its fair works40 ,inf4 i4 #ch-dj4 7,carey74 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #de4 ,the ,universe of ,dante4 ,the expression 8quelle stelle10#ddh however1 shows us that ,dante does not intend to be pedantically accurate1 which would indeed be inartistic in a poem4 ,he speaks several times of the supposed slow motion of the star sphere1#ddi and although he never mentions its effect in shifting the place of the equinox continually among the stars1 we can hardly imagine that he failed to understand this4 ,he knew quite well1 therefore1 that the stars which accompanied the sun in that first springtime of the world could not be the same stars which rose with him now4 ,but astronomers had agreed to call the part of the sky which contains the vernal equinox by its old name1 and it would be exceedingly tiresome if he were to distinguish1 every time he mentioned them1 between the zodiacal constellations and the zodiacal signs2 there shall be no occasion1 therefore1 to stop and consider which he means1 and no ambiguity3 he assumes once for all that they always have been and always are identical1 that the 8first point of ,aries0 or vernal equinox is now and always at the beginning of the constellation ,aries4 ,to this assumption he is consistent throughout4 ---------------------------------------- -------------------------------- #ddh 8,those stars40 #ddi ,purg4 xi4 #ajh2 ,conv4 ,,ii4 xv4 #ab-ad4 ---------------------------------------- -------------------------------- ,another important point to notice is that1 since it is the time of the equinox1 there is no difference between 8temporary0 and 8equal0 hours4#dej ,days and nights are of equal length2 sunrise and sunset are nearly at #f a4m4 and #f p4m41 according to our modern method of reckoning4#dea ,in this way also1 and without any sacrifice of astronomical accuracy1 the poet has simplified his time references for his readers4 ---------------------------------------- -------------------------------- #dej ,conv4 ,,iii4 vi4 #bh-cj4 #dea ,on the day of the spring equinox the sun rises and sets a few minutes after six o'clock1 because we set our clocks not by the real sun but the more convenient 8mean sun40 ---------------------------------------- -------------------------------- ,we must observe1 however1 that the day is as uncertain as the year2 for1 although it is certainly near the equinox1 8quelle stelle0 may mean exactly the first point of ,aries or only the constellation ,aries in general4 ,from this ,canto alone1 therefore1 we cannot be sure of the exact date4 ,from other allusions of various kinds1 scattered throughout the ,divine ,comedy1 we gather that ,dante did intend a definite date to be understood1 but unfortunately the data by which he means to fix it are themselves so ambiguous that commentators differ as to the day1 the month1 and the year4 ,the question has so direct a bearing on ,dante's astronomy that we cannot shirk it2 but for the present1 leaving it aside1 let us deal merely with the hour1 which is distinctly stated from the first1 and indicated in a number of passages so clearly that readers with an elementary knowledge of the apparent movements of the heavenly bodies can find little difficulty in following ,virgil and ,dante through their journey1 seeing exactly how many days it required1 and frequently at what hour of day or night they were in a particular spot4 ,if my readers are not now in possession of this elementary knowledge1 this book has been written in vain4 ,i give below a list of all the hour-indications1 astronomical and others1 for the sake of clearness and completeness2 but ,i omit for the present those that indicate only the date1 and merely call the days the first1 second1 etc4 ,these passages1 though they are only to be understood in a popular sense1 prove quite as clearly as the elaborate astronomical explanations in the ,convivio how deep an interest ,dante always took in astronomy2 and a study of them shows that he had carefully considered the positions of the heavenly bodies and their movements during the progress of the action in his poem4 ,,time ,,references ,,in ,,the ,,divine ,,comedy ,night4 ,in the ,forest4 ,moon full 7see below1 ,inf4 xx4 #abg-abi1 and ,purg4 xxiii4 #aah-aba74 8,la notte ch' i' passai40 ,inf4 i4 #ba4 8,the night that ,i had spent40 ---------------------------------------- ------------------------ #ast day4 ,just before sunrise4 ,at the foot of the ,hill4 8,ma poi ch' io fui al pi d'un colle giunto1 4 4 4 4 4 ,guardai in alto1 e vidi le sue spalle ,vestite gi de' raggi del pianeta ,che mena dritto altrui per ogni calle40 ,inf4 i4 #ac-ah4 8,but after ,i had reached a mountain's foot1 4 4 4 4 4 4 ,upward ,i looked1 and ,i beheld its shoulders ,vested already with that planet's rays ,which leadeth others right by every road40 ---------------------------------------- ------------------------ ,sunrise #f a4m4#deb ,climbing the ,hill4 8,tempo era dal principio del mattino1 ,e il sol montava su con quelle stelle ,ch'eran con lui quando l' ,amor divino ,mosse da prima quelle cose belle40 ,inf4 i4 #cg-dj4 8,the time was the beginning of the morning1 ,and up the sun was mounting with those stars ,that with him were1 what time the ,love ,divine ,at first in motion set those beautous things40 ---------------------------------------- -------------------------------- #deb ,the clock-hours in this column are not to be regarded as if taken from a railway time-table6 ,sunrise is at #f a4m4 within a few minutes only1 for the reasons above stated1 viz43 our clocks are regulated by the 8mean0 sun1 and it is not necessarily the exact day of the equinox when the vision begins4 ---------------------------------------- -------------------------------- ,evening twilight4 ,at the ,gate of ,hell4 8,lo giorno se n'andava1 e l' aer bruno44440 ,inf4 ii4 #a4 8,day was departing1 and the brown air44440 ---------------------------------------- ------------------------ ,midnight4 ,crossing the fourth circle4 8,gi ogni stella cade1 che saliva ,quando mi mossi40 ,inf4 vii4 #ih1 #ii4 8,already sinks each star that was ascending ,when ,i set out40 ---------------------------------------- ------------------------ #bnd day4 ,about #b hrs4 before sunrise 7#d a4m47 ,on the edge of the cliff1 preparing to descend to the #gth circle4 8,i ,pesci guizzan su per l' orizzonta1 ,e il ,carro tutto sovra il ,coro giace40 ,inf4 xi4 #aac1 #aad4 8,quivering are the ,fishes on the horizon1 ,and the ,wain wholly over ,caurus lies40 ---------------------------------------- ------------------------ 7,dante refers to the previous day47 ,in the #gth circle4 8,mi smarri' in una valle4 4 4 4 4 4 ,pur ier mattina le volsi le spalle40 ,inf4 xv4 #ej-eb4 8,i lost me in a valley4 4 4 4 4 4 ,but yestermorn ,i turned my back upon it40 ---------------------------------------- ------------------------ ,after sunrise1 between #f and #g a4m4 ,leaving the #dth ,pit of ,circle ,,viii4 7,virgil reminds ,dante of the night before last1 spent in the ,forest47 8,gi tiene il confine ,d' ambedue gli emisperi e tocca l' onda ,sotto ,sibilia ,caino e le spine2 ,e gi iernotte fu la luna tonda2 ,ben ten dee ricordar1 ch non ti nocque ,alcuna volta per la selva fonda40 ,inf4 xx4 #abd-abi4 8444 ,already holds the confines ,of both the hemispheres1 and under ,seville ,touches the ocean-wave1 ,cain and the thorns2 ,and yesternight the moon was round already2 ,thou shouldst remember well3 it did not harm thee ,from time to time within the forest deep40 ---------------------------------------- ------------------------ #g a4m4 ,on the bridge over the #eth ,pit4 8,ier1 pi oltre cinq' ore che quest' otta1 ,mille dugento con sessanta sei ,anni compi che qui la via fu rotta40 ,inf4 xxi4 #aab-aad4 8,yesterday1 five hours later than this hour1 ,one thousand and two hundred sixty-six ,years were complete that here the way was broken40 ---------------------------------------- ------------------------ ,about #a p4m4 ,leaving the #ith ,pit4 8,e gi la ,luna sotto nostri piedi1 ,lo tempo poco omai che n' concesso40 ,inf4 xxix4 #aj1 #aa4 8,and now the moon is underneath our feet4 ,henceforth the time allotted us is brief40 ---------------------------------------- ------------------------ ,nightfall4 ,at the bottom of the world4 8,la notte risurge2 ed oramai da partir1 ch tutto avem veduto40 ,inf4 xxxiv4 #fh1 #fi4 8,night is reascending1 and 'tis time ,that we depart1 for we have seen the whole40 ---------------------------------------- ------------------------ #crd day4 7no night intervening7 #g4cj a4m4 ,in the new hemisphere 8,gi il sole a mezza terza riede40 ,inf4 xxxiv4 #if4 8,and now the sun to middle-tierce returns40 ---------------------------------------- ------------------------ #dth day4 ,about an hour before sunrise 7#e a4m474 ,on the island of ,purgatory4 8,e quindi uscimmo a riveder le stelle40 ,inf4 xxxiv4 #aci4 8,thence we came forth to see again the stars40 8,lo bel pianeta che ad amar conforta ,faceva tutto rider l' oriente1 ,velando i ,pesci ch' erano in sua scorta40 ,purg4 i4 #ai-ba4 8,the beauteous planet that to love incites ,was making all the orient to laugh1 ,veiling the ,fishes that were in her escort40 ---------------------------------------- ------------------------ ,dawn4 8,lo sol vi mostrer1 che surge omai40 ,purg4 i4 #ajg4 8,the sun1 which now is rising1 will direct you40 8,l' alba vinceva l' ora mattutina40 ,purg4 i4 #aae4 8,the dawn was vanquishing the matin hour40 ---------------------------------------- ------------------------ ,sun just below east horizon4 ,on the ,shore of the ,island4 8,gi era il sole all' orizzonte giunto ,lo cui meridian cerchio coperchia ,jerusalem col suo pi alto punto2 ,e la notte1 che opposita a lui cerchia1 ,uscia di ,gange fuor con le bilance ,che le caggion di man quando soperchia2 ,si che le bianche e le vermilie guance1 ,l dove io era1 della bella ,aurora1 ,per troppa etate divenivan rance40 ,purg4 ii4 #a-i4 8,already had the sun the horizon reached ,whose circle of meridian covers o'er ,jerusalem with its most lofty point2 ,and night1 that opposite to him revolves1 ,was issuing forth from ,ganges1 with the scales ,that fall from out her hand when she exceedeth2 ,so that the white and the vermilion cheeks ,of beautiful ,aurora1 where ,i was1 ,by too great age were changing into orange40 ---------------------------------------- ------------------------ ,sun risen4 8,da tutte parti saettava il giorno ,lo sol1 ch'avea con le saette conte ,di mezzo il ciel cacciato il ,capricorno40 ,purg4 ii4 #ee-eg4 8,on every side was darting forth the day ,the sun1 who had with his resplendent shafts ,from the mid-heaven chased forth the ,capricorn40 ---------------------------------------- ------------------------ ,soon after sunrise4 ,walking westward1 towards the ,mountain of ,purgatory4 8,lo sol che retro fiammeggiava roggio40 ,purg4 iii4 #af4 8,the sun that in our rear was flaming red40 ---------------------------------------- ------------------------ ,shortly after #f a4m4 7#c p4m4 in ,italy74 8,vespero gi col dov' sepolto ,lo corpo dentro al quale io facea ombra40 ,purg4 iii4 #be1 #bf4 8',tis vespers there already where is buried ,the body within which ,i cast a shadow40 ---------------------------------------- ------------------------ ,about #i4cj a4m4 ,at the foot of the ,mountain4 8,ben cinquanta gradi salito era ,lo sole40 ,purg4 iv4 #ae1 #af4 8,fifty full degrees uprisen was ,the sun40 ---------------------------------------- ------------------------ ,midday4 ,on a ledge of the ,mountain 7,anti-purgatory74 8,vedi ch' tocco ,meridian dal sole1 e dalla riva4 ,copre la notte gi col pi ,morrocco40 ,purg4 iv4 #acg-aci4 8,see1 the sun has touched ,meridian1 and from the shore the night ,covers already with her foot ,morocco40 ---------------------------------------- ------------------------ ,afternoon4 ,climbing the eastern slope of the ,mountain4 8,vedi omai che il poggio l' ombra getta4 4 4 4 4 4 ,prima che sii lass tornar vedrai ,colui che gi si copre della costa1 ,s che i suoi raggi tu romper non fai40 ,purg4 vi4 #ea-eg4 8,see1 e'en now the hill a shadow casts4 4 4 4 4 4 ,ere thou art up there1 thou shalt see return ,him1 who now hides himself behind the hill1 ,so that thou dost not interrupt his rays40 ---------------------------------------- ------------------------ ,evening4 8,vedi gi come dichina il giorno40 ,purg4 vii4 #dc4 8,see already how the day declines40 ---------------------------------------- ------------------------ ,sunset 7#f p4m474 ,in the ,flowery ,valley1 on the ,mountain-side4 8,era gi l'ora che volge il disio ,ai naviganti e intenerisce il core1 ,lo di ch'han detto ai dolci amici addio2 ,e che lo nuovo peregrin d' amore ,punge1 se ode squilla di lontano ,che paia il giorno pianger che si more40 ,purg4 viii4 #a-f4 8',twas on the hour that turneth back desire ,in those who sail the sea1 and melts the heart1 ,the day they've said to their sweet friends farewell2 ,and the new pilgrim penetrates with love1 ,if he doth hear from far away a bell ,that seemeth to deplore the dying day40 ---------------------------------------- ------------------------ ,evening twilight4 8,tempo era gi che l' aer s'annerava40 ,purg4 viii4 #di4 8,already now the air was growing dark40 ---------------------------------------- ------------------------ 7,dante refers to the morning of the same day47 8,per entro il lochi tristi ,venni stamane40 ,purg4 viii4 #eh1 #ei4 8,through the dismal places ,i came this morn40 ---------------------------------------- ------------------------ ,early night3 about #g p4m4 8,le quattro chiare stelle ,che vedevi staman1 son di l basse1 ,e queste son salite ov' eran quelle40 ,purg4 viii4 #ia-ic4 8,the four resplendent stars ,thou sawest this morning are down yonder low1 ,and these have mounted up to where those were40 ---------------------------------------- ------------------------ ,shortly before moonrise1 between #h and #i p4m4 8,la concubina di ,titone antico ,gi s'imbiancava al balco d'oriente1 ,fuor delle braccia del suo dolce amico2 ,di gemme la sua fronte era lucente1 ,poste in figura del freddo animale ,che con la coda percote la gente2 ,e la notte de' passi con che sale ,fatti avea due nel loco ov' eravamo1 ,e il terzo gi chinava in giuso l' ale40 ,purg4 ix4 #a-i4 8,the concubine of old ,tithonus now ,gleamed white upon the eastern balcony1 ,forth from the arms of her sweet paramour2 ,with gems her forehead all relucent was1 ,set in the shape of that cold animal ,which with its tail doth smite amain the people2 ,and of the steps with which she mounts the ,night ,had taken two in that place where we were1 ,and now the third was bending down its wings40 ---------------------------------------- ------------------------ #eth day4 ,dawn4 ,at the ,gate of ,purgatory4 8,nell' ora che comincia i tristi lai ,la rondinella presso alla mattina40 ,purg4 ix4 #ac1 #ad4 8,just at the hour when her sad lay begins ,the little swallow1 near unto the morning40 7,see also ix4 #eb 8nell' alba che precede al giorno10 and ix4 #ei 8come il di fu chiaro407 7,see also 8,at dawn1 which doth precede the day40 and 8,as day grew bright074 ---------------------------------------- ------------------------ ,more than #b hours after sunrise 7after #h a4m474 8,il sole er' alto gi pi che due ore48 ,purg4 ix4 #dd4 8,and now the sun was more than two hours high40 ---------------------------------------- ------------------------ ,about #i4cj a4m4 ,on the #ast ,cornice of the ,mountain4 8,pria lo scemo della luna ,rigiunse al letto suo per rcorcarsi1 ,che noi fossimo fuori di quella cruna40 ,purg4 x4 #ad-af4 8,sooner had the moon's decreasing disc ,regained its bed to sink again to rest4 ,than we were forth out of that needle's eye40 ---------------------------------------- ------------------------ #ab noon4 ,ascent to the #bnd ,cornice4 8,pi era gi per noi del monte volto1 ,e del cammin del sole assai pi speso ,che non stimava l'animo non sciolto4 4 4 4 4 4 444 ,vedi che torna ,dal servigio del d l'ancella sesta40 ,purg4 xii4 #gc-ha4 8,more of the mount by us was now encompassed1 ,and far more spent the circuit of the sun1 ,than had the mind preoccupied imagined4 4 4 4 4 4 444 ,lo1 returning is ,from service of the day the sixth handmaiden40 ---------------------------------------- ------------------------ #c p4m4 7midnight in ,italy74 ,ascent to the #crd ,cornice4 8,quanto tra l#8ultimar dell' ora terza ,e il principio del d par della spera ,che sempre a guisa di fanciullo scherza1 ,tanto pareva gi in ver la sera ,essere al sol del suo corso rimaso2 ,vespero l1 e qui mezza notte era4 ,e i raggi ne ferian per mezzo il naso1 ,perch per noi girato era si il monte1 ,che gi dritti andavamo in ver l'occaso40 ,purg4 xv4 #a-i4 8,as much as 'twixt the close of the third hour ,and dawn of day appeareth of that sphere ,which aye in fashion of a child is playing1 ,so much1 it now appeared1 towards the night ,was of his course remaining to the sun2 ,there it was evening1 and 'twas midnight here4 ,and the rays smote the middle of our faces1 ,because by us the mount was so encircled1 ,that straight towards the west we now were going40 ---------------------------------------- ------------------------ ,evening4 ,on the #crd ,cornice4 8,noi andavam per lo vespero1 attenti ,oltre1 quanto potean gli occhi allungarsi ,contra i raggi serotini e lucenti48 ,purg4 xv4 #aci-ada4 8,we passed along athwart the twilight1 peering ,forward1 as far as ever eye could stretch ,against the sunbeams serotine and lucent40 ---------------------------------------- ------------------------ ,sunset at sea-level1 #f p4m4 8,io rividi ,lo sole in pria1 che gi nel corcare era40 ,purg xvii4 #h1 #i4 8,i saw again ,the sun at first1 that was already setting40 ---------------------------------------- ------------------------ ,on the #crd ,cornice4 8,i raggi1 morti gi1 nei bassi lidi48 ,purg4 xvii4 #ab4 8,rays already dead on the low shores40 ---------------------------------------- ------------------------ ,ascent to the #dth ,cornice4 8,procacciam di salir pria che s'abbui40 ,purg4 xvii4 #fb4 8,let us make haste to mount ere it grow dark40 ---------------------------------------- ------------------------ ,sunset on the ,mountain1 shortly after #f p4m4 ,on the #dth ,cornice4 8,gi eran sopra noi tanto levati ,gli ultimi raggi che la notte segue1 ,che le stelle apparivan da pi lati40 ,purg4 xvii4 #gj-gb4 8,already over us were so uplifted ,the latest sunbeams which the night pursues1 ,that upon many sides the stars appeared40 ---------------------------------------- ------------------------ ,towards midnight4 8,la luna1 quasi a mezza notte tarda1 ,facea le stelle a noi parer pi rade1 ,fatta com' un secchione che tutto arda2 ,e correa contra il ciel per quelle strade ,che il sole infiamma allor che quel da ,roma ,tra i ,sardi e i ,corsi il vede quando cade40 ,purg4 xviii4 #gf-ha4 8,the moon1 belated almost unto midnight1#dec ,now made the stars appear to us more rare1 ,formed like a bucket that is all ablaze2 ,and counter to the heavens ran through those paths ,which the sun sets aflame when he of ,rome ,sees it 'twixt ,sardes and ,corsicans go down40 ---------------------------------------- -------------------------------- #dec ,or 8almost at late midnight40 ---------------------------------------- -------------------------------- #fth day4 ,nearly #b hours before sunrise1 about #d a4m4 ,on the #dth ,cornice4 8,nell' ora che non pu il calor diurno ,intepidar pi il freddo della luna1 ,vinto da terra1 o talor da ,saturno2 ,quando i geomanti lor ,maggior ,fortuna ,veggiono in oriente1 innanzi all' alba1 ,surger per via che poco le sta bruno40 ,purg4 xix4 #a-f4 8,it was the hour when the diurnal heat ,no more can warm the coldness of the moon1 ,vanquished by ,earth1 or peradventure ,saturn2 ,when geomancers their ,fortuna ,major ,see in the orient1 before the dawn1 ,rise by a path that long remains not dim40 ---------------------------------------- ------------------------ ,early morning4 ,ascent to #eth ,cornice4 8,su mi levai1 e tutti eran gi1 pieni ,dell' alto d i giron del sacro monte1 ,ed andavam col sol nuovo alle reni40 ,purg4 xix4 #cg-ci4 8,i rose1 and full already of high day ,were all the circles of the sacred mountain1 ,and with the new sun at our back we went40 ---------------------------------------- ------------------------ ,about #aj a4m4 ,on the #fth ,cornice4 8,e gi le quattro ancelle eran del giorno ,rimase addietro1 e la quinta era al temo1 ,drizzando pure in su l' ardente corno40 ,purg4 xxii4 #aah-abj4 8,and four handmaidens of the day already ,were left behind1 and at the pole the fifth ,was pointing upwards still its burning horn40 7,dante refers to 8the other day0 when he began the journey47 8,di quella vita mi volse costui ,che mi va innanzi1 l' altr' ier1 quando tonda ,vi si mostr la suora di colui-- ,e il sol mostrai40 ,purg4 xxiii4 #aah-aba4 8,out of that life he turned me back who goes ,in front of me1 some days agone1 when round ,the sister of him yonder showed herself-- ,and to the sun ,i pointed40 ---------------------------------------- ------------------------ ,between #b and #d p4m4 ,ascent to the #gth ,cornice4 8,il sole avea lo cerchio di merigge ,lasciato al ,tauro1 e la notte allo ,scorpio40 ,purg4 xxv4 #b1 #c4 8,the sun bad his meridian circle ,to ,taurus left1 and ,night to ,scorpio40 ---------------------------------------- ------------------------ ,evening4 ,on the #gth ,cornice1 west side of the ,mountain4 8,feriami il sole sull' omero destro1 ,che gi1 raggiando1 tutto l' occidente ,mutava in bianco aspetto di cilestro40 ,purg4 xxvi4 #d-f4 8,on the right shoulder smote me now the sun1 ,that1 raying out1 already the whole west ,changed from its azure aspect into white40 ---------------------------------------- ------------------------ ,sunset at sea-level1 #f p4m4 ,about to cross the zone of fire4 8,s come quando i primi raggi vibra ,la dove il suo ,fattore il sangue sparse1 ,cadendo ,ibero sotto l' alta ,libra1 ,e l' onde in ,gange da nona riarse1 ,s stava il sole2 onde il giorno sen giva40 ,purg4 xxvii4 #a-e4 8,as when he vibrates forth his earliest rays ,in regions where his ,maker shed his blood1 ,the ,ebro falling under lofty ,libra1 ,and waters in the ,ganges burnt with noon1 ,so stood the sun2 hence was the day departing40 ---------------------------------------- ------------------------ ,sun about to set on the mountain heights4 ,at the foot of the last stairway4 8,lo sol sen va1 soggiunse1 e vien la sera40 ,purg4 xxvii4 #fa4 8,the sun departs1 it added1 and night cometh40 ---------------------------------------- ------------------------ ,sun sets4 ,climbing the last stairway4 8,io toglieva i raggi ,dinanzi a me del sol ch'era gi basso4 4 4 4 4 4 ,il sol corcar1 per l' ombra che si spense ,sentimmo40 ,purg4 xxvii4 #fe-fi4 8,i cut off the rays ,before me of the sun1 that now was low4 4 4 4 4 4 ,by the vanished shadow the sun's setting ,behind us we perceived40 ---------------------------------------- ------------------------ ,night4 ,on the last stairway4 8,vedev' io le stelle40 ,purg4 xxvii4 #hi4 8,i beheld the stars40 ---------------------------------------- ------------------------ #gth day4 ,about #d a4m4 8,nell' ora1 credo1 che dell' oriente ,prima raggi nel monte ,citerea40 ,purg4 xxvii4 #id1 #ie4 8,it was the hour1 ,i think1 when from the east ,first on the mountain ,cytherea beamed40 ---------------------------------------- ------------------------ ,dawn4 8,e gi per gli splendori antelucani 4 4 4 4 4 ,le tenebre fuggian da tutti i lati40 ,purg4 xxvii4 #aji-aab4 8,and now before the antelucan splendours 4 4 4 4 4 ,the darkness fled away on every side40 ---------------------------------------- ------------------------ ,early morning4 ,in the ,earthly ,paradise4 8,vedi l il sol che in fronte ti riluce40 ,purg4 xxvii4 #acc4 8,behold the sun that shines upon thy forehead40 8,l' re prime40 ,purg4 xxviii4 #af4 8,the hours of prime40 ---------------------------------------- ------------------------ ,midday4 ,by the fountain of ,euno4 8,teneva il sole il cerchio di merigge40 ,purg4 xxxiii4 #ajd4 8,the sun was holding the meridian circle40 ,ascent to ,paradise4 8,fatto avea di l mane e di qua sera ,tal foce quasi1 e tutto era l bianco ,quello emisperio1 e l' altra parte nera40 ,par4 i4 #dc-de4 8,almost that passage had made morning there ,and evening here1 and there was wholly white ,that hemisphere1 and black the other part40 ---------------------------------------- ------------------------ #hth day4 ,a lapse of #f hrs4 since entering the #hth heaven4 7,cf4 ,par4 xxii4 #aea-aec74 ,sunset in ,jerusalem 7sunrise in ,purgatory74 ,in the eighth heaven among the stars of ,gemini4 8,dall' ora ch'io avea guardato prima ,io vidi mosso me per tutto l'arco ,che fa del mezzo al fine il primo clima2 ,si ch'io vedea di l da ,gade il varco ,folle d',ulisse4 e di qua presso il lito ,nel qual si fece ,europa dolce carco2 ,e pi mi fora discoperto il sito ,di questa ,aiuola1 ma il sol procedea ,sotto i miei piedi un segno e pi partito40 ,par4 xxvii4 #gi-hg4 8,since the first time that ,i had downward looked ,i saw that ,i had moved through the whole arc ,which the first climate makes from midst to end2 ,so that ,i saw the mad track of ,ulysses ,past ,gades1 and this side well nigh#ded the shore ,whereon became ,europa a sweet burden2 ,and of this threshing-floor the site to me ,were more unveiled1 but the sun was preceding ,under my feet1 a sign and more removed40 ---------------------------------------- -------------------------------- #ded ,or 8nigh me30 8presso0 may mean either4 ---------------------------------------- -------------------------------- #b4 ,,the ,,inferno4 ,using the above table as a guide1 we may now see how ,dante uses the movements of the heavenly bodies both for time and direction1 and we shall discover how long his journey takes4 ,dante has spent a night in a dark forest4 ,the moon was then full2 but we only learn this later1 when ,virgil reminds him of it1 and he himself mentions it to ,forese1 when talking in the ,purgatorio4 ,at dawn he finds himself at the foot of a hill on which are already shining the first rays of the morning sun--the planet which leads all aright by every path4 ,the sun rises3 it is in ,aries1 consequently the moon1 being full1 must be in ,libra1 and must have set as the sun rose1 i4e4 at about #f a4m4 ,virgil appears1 rescues the poet from three terrible beasts1 and announces that he has come to conduct him through ,hell and ,purgatory1 and to lead him to ,beatrice1 who will guide him to ,paradise4 ,on the evening of the same day1 at twilight1 the poets enter the ,inferno4 ,this great subterranean cavity1 shaped like an inverted cone 7see fig4 #de71 is divided into nine circles1 in which the different classes of sinners are punished4 ,in this blind world of eternal darkness no star shines1 and the sun is never once mentioned as timegiver2 when ,virgil wishes to remind ,dante that they must hasten1 he refers to the position of moon or stars1 and the former is called 8,la ,donna che qui regge40#dee ---------------------------------------- -------------------------------- #dee 8,the ,lady who rules here40 ,inf4 x4 #hj4 ---------------------------------------- -------------------------------- ,after passing through four circles1 ,virgil says that every star is now sinking which was ascending when he started1 indicating that it is now six hours since they entered the ,inferno1 or soon after midnight4 ,he does not mean that all these stars are setting1 but that they have crossed the meridian1 and are at some point of their descent towards the west4 ,strictly speaking this does not apply to stars north of the equator1 since they take more than six hours to reach the meridian1 being above the horizon for more than twelve4 ,perhaps ,virgil is thinking chiefly of the constellations of the zodiac4 ,the poets cross the fifth circle1 enter the 8basso ,inferno0#def or city of ,dis1 and on the edge of the precipice which borders the circle of the ,heretics they sit while ,virgil explains the system of the several circles4 ,then he expresses a wish to continue the journey1 for the ,fishes 7of the zodiac7 are quivering on the horizon1 and the ,wain lies to the north-west4 ,as it is the time of the ,vernal ,equinox1 and the sun is in ,aries1 ,pisces is the zodiacal sign immediately preceding the sun1 and begins to rise about four in the morning4 ,the part of ,ursa ,major called the ,wain is somewhat less than #ahj distant from ,pisces2 hence when the latter appears on the eastern horizon the former will be in the west 7and of course always in the north74 ,the 8,caurus0 of the ,latins was the wind from the north-west4 ---------------------------------------- -------------------------------- #def 8,lower ,hell40 ,inf4 viii4 #ge4 ---------------------------------------- -------------------------------- ,they descend a cliff over loose stones which roll under the unaccustomed weight of ,dante's living feet4 ,virgil tells him that both here and elsewhere in ,hell the ancient rocks were riven by an earthquake which immediately preceded the triumphant descent of ,christ after ,his crucifixion4 ,so mighty was the shock that he thought the universe was dissolving into chaos by the force of love1 as ,empedocles had said must happen periodically4 ,at the base of the cliff they cross the river ,phlegethon1 then pass through the wood of the ,harpies1 and walk along the stone banks of a conduit which afterwards falls with thunderous roar down a steep precipice4 ,on the burning sand through which the conduit runs1 ,dante sees ,brunetto ,latini1 and tells him that it was only yesterday that he escaped from the ,forest4 ,the monster ,geryon carries them down the precipice1 and they reach the ten ,pits of ,malebolge1 which like so many moats surround the central ,depth4 ,when looking down upon the astrologers in the fourth ,pit1 ,virgil again hastens ,dante on1 telling him that now ,cain and the thorns--by which he means the moon1 alluding to the legend#deg--;is on the boundary of the two hemispheres1 and already touching the waves below ,seville4 ,the two hemispheres are those of the habitable earth whose centre is ,jerusalem1 and the uninhabitable with ,purgatory at its centre3 the moon1 therefore1 is just setting as seen from ,jerusalem1 and in the ,inferno the time is ,jerusalem time4 ,it is here that ,virgil adds1 8,and yesternight the moon was full30 did we not know this1 the fact that she was setting would give no clue to the time4 ,when full1 she set as the sun rose1 that was at #f a4m42 now1 therefore1 she is setting after sunrise1 between six and seven in the morning2#deh and this is how ,virgil tells ,dante1 without mentioning the sun1 that a new day has begun4 ---------------------------------------- -------------------------------- #deg ,cf4 ,par4 ii4 #dh-ea4 #deh ,the retardation is not likely to be more than the average of #ej minutes1 and may be less1 because the moon is in ,libra1 and therefore going south4 ,this tends to diminish the interval between one moonset and the next in the northern hemisphere1 just as the days get shorter when the sun goes south in autumn4 ---------------------------------------- -------------------------------- ,the poets accordingly hasten on to the bridge above the next ,pit1 the fifth1 and here the demons treacherously mislead them by assuring them that the next bridge directly on their way is broken down1 but the one to the left is standing4 ,the anniversary of the catastrophe is precisely determined by ,malacoda1 the chief demon of the band1 as five hours later than the present hour on the preceding day4 ,there can be no doubt that he refers to the same earthquake as ,virgil described when descending the stony cliff1 and all commentators are agreed to this4 ,the time now1 therefore1 is five hours before midday1 i4e4 #g a4m41 since it was at midday that ,dante believed ,christ to have died4#dei ---------------------------------------- -------------------------------- #dei ,some think the interval between this reference and the last almost too short1 but the words do not indicate that ,malacoda spoke on the stroke of seven6 and the moon may have set at about #f4cj4 ---------------------------------------- -------------------------------- ,the scenes with the demons follow1 the breathless escape into the next ,pit1 of the ,hypocrites1 and the horrors of the ,pit of the ,thieves4 ,then for a short space1 when the suffering and the murk of ,hell is becoming almost intolerable1 we are suddenly lifted into the upper air by the narrative of ,ulysses--into the pure air and the vast spaces of the southern ocean1 and we see once more the skies4 ,we follow the adventurers to the regions beyond the sun1 the world where no one lives2 we see all the stars of the other pole1 and the moon shines down upon us4 ,too soon comes the tragic end of the story1 and the waters close over the ship2 the shade of ,ulysses passes on1 and we are once more in the 8buio d' inferno40#dfj ---------------------------------------- -------------------------------- #dfj 8,darkness of ,hell40 ,purg4 xvi4 #a4 ---------------------------------------- -------------------------------- ,at the next ,pit1 that of the ,schismatics1 as ,dante stands ready to weep for pity on the bridge above it1 ,virgil reproaches him for delaying1 for little remains now of the time permitted for seeing the ,inferno1 and already the moon is beneath their feet4 ,this is about an hour after midday2 for if the moon were full she would be just opposite the sun1 hence under our feet when the sun is on the meridian1 i4e4 at noon2 but this is one day after ,full ,moon1 and therefore she does not reach the position till about an hour later4 ,the tenth and last ,pit is traversed1 and when the giant ,antus has lifted them down into the sorrowful pit towards which all the rest of ,hell converges1 the poets have nearly reached the centre of the earth4 ,for they have been descending continually1 finding a slight fall between each circle1 and between the great divisions of different classes of sin1 three sharp steep falls--the cliff descending to the ,river of blood and other circles of the violent1 the precipice down which ,geryon carried them to the ,malebolge of ,fraud1 and the ,dark ,pit to the bottom of which ,antus conveyed them1 where in the ,frozen ,lake treachery was punished4 ,last of all1 at the very centre and bottom of the whole 8dolorous kingdom0 of ,lucifer1 they see its ,king1 and ,virgil says all has been seen1 and it is time to depart1 for ,night is rising again4 ,thus we see that the journey through the ,inferno has taken exactly the time from one sunset to another1 twenty-four hours4 ,now ,virgil seizes the shaggy side of the fiend1 while the monstrous wings are raised1 and with ,dante clinging to him climbs down the side1 as far as the hip2 here with difficulty and labour the master turns round1 so that his head is where his feet were1 and climbs up1 panting1 so that ,dante thinks they are returning4 ,but when the ascent has been made1 and both poets sit down to rest1 ,dante sees to his astonishment that the frozen lake is gone1 the head and wings of ,lucifer are gone1 they are looking down upon him1 and see only his legs which are directed upwards6 ,to add to ,dante's bewilderment1 ,virgil now says1 8,rise1 for the way is long and the road is bad1 and the sun has already returned to middle-tierce10 which1 as we have seen1 means at the time of the equinox #g4cj in the morning4 ,night was just beginning in the dreadful place they have so recently left1 but now for the first time ,virgil mentions the sun as giving them the time1 and it is early morning4 ,the explanation is that the point which they passed with so great an effort is the exact centre of the world2 they are now on its further side1 and above them is the other hemisphere1 where all is ocean save the island of ,purgatory4 ,virgil explains how it was through the fall of ,lucifer from ,heaven that all the land except ,purgatory is in one hemisphere1 and that there is a cavity through which they may now climb to the opposite hemisphere4 ,when ,lucifer fell1 all the land which then existed in the unknown hemisphere fled for fear of him1 sinking under the sea1 and then escaping round the globe settled in the inhabited hemisphere4 ,it may be1 he adds1 that then the earth in the interior fled away from him upwards to form land in this hemisphere 7,purgatory7 and thus an empty space is left here4 ,up this1 which is the same length as the tunnel of the ,inferno1 they climb1 guided through the darkness by the sound of a little brook which has worn its winding way down the rock4 ,on this route there is nothing to detain them1 for they are alone in the darkness1 but it presumably takes much longer to ascend than it did to descend1 for climbing without a pause it takes about twenty-three hours 7from the centre7 to reach that round hole in the rocks through which at last they once more see the stars1 just before the dawn of a new day4 #c4 ,,purgatory4 ,leaving ,earth's centre at sunset by ,jerusalem time1 sunrise by ,purgatory time1 the poets emerge next morning by starlight when the morning star is making all the orient smile4 ,henceforth ,dante does not need to be told how moon or stars are standing in the sky3 he has but to look up1 and see the sun and sometimes the moon by day1 the stars and sometimes the moon by night4 ,the ,inferno was like one long dark night1 ,paradise will be one brilliant day2 in ,purgatory the sun rises four times and sets three times1 before ,dante reaches the summit1 and thence rises to ,paradise with ,beatrice4 8,lo bel pianeta che ad amar conforta0#dfa is of course ,venus3 if there were any doubt about this1 the words used concerning the dawn of the last morning on the ,mountain would solve it1 for there 8,cytherea0 is spoken of as shining in the east on the mountain4 ,she is in ,pisces1 the sign which rises about two hours before ,aries1 or #d a4m4 at this season1 and as the stars are still clearly visible1 it is about #e a4m4 ,the poets have evidently come up from the subterranean passage facing east1 for they see ,venus first1 then ,dante turns to his right 7south7 and sees the four brilliant stars near the south pole1 then turning towards the north pole he sees that the ,wain has disappeared beneath the horizon1 and close beside him he finds ,cato1 on whose face the ,four ,stars are shining4 ,cato tells them that the sun1 which is about to rise1 will be their guide to reach the ,mountain1 and as they first go down to the shore1 following his instructions1 daylight begins to appear4 ---------------------------------------- -------------------------------- #dfa 8,the fair planet which kindles love40 ---------------------------------------- -------------------------------- ,while they are still on the shore the sun reaches the point just below the horizon1 for he is described as just touching the western horizon of the other hemisphere1 whose zenith is above ,jerusalem1 and night is just rising on the eastern horizon of that hemisphere4 ,where the poets are the rose colour in the east is turning to orange1 just before the sun rises4 ,it rises over their horizon while they are watching a light far over the sea1 which with almost incredible rapidity draws near1 becomes visible as a vessel1 touches land1 the spirits disembark1 and the celestial pilot 8sen g1 come venne1 veloce40#dfb ,the sun has now driven ,capricorn from the mid sky with his bright beams1 that is1 the stars have become invisible in bright daylight1 and fig4 #df shows that when ,aries rises over the eastern horizon ,capricorn will be overhead4 ,but the sun is still very low1 so swift was the coming of the spirits1 for ,dante's shadow is not yet visible to them3 it is by his breathing that they perceive he is a living man4 ,it is only after the meeting with ,casella1 and the dispersal of the spirits by ,cato1 that the sun1 still red with sunrise tints1 makes ,dante's shadow fall in front of him as the poets are walking westward towards the mountain4 ,he is alarmed not to see ,virgil's shadow on the ground beside it1 and is told that the body within which ,virgil once had cast a shadow lies buried in a country where it is now the time of vespers4 ,that is1 in ,italy it is three o'clock in the afternoon3 hence in ,purgatory1 where they now are1 it is six in the morning4 ---------------------------------------- -------------------------------- #dfb 8,departed1 as he came1 swiftly40 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #df4 ,the ,signs of the ,zodiac as seen at sunrise from the ,mountain of ,purgatory at the autumnal equinox there 7the vernal equinox in the ,northern ,hemisphere74 ,purg4 ii4 #ee4 ,at #f a4m4 ,aries is just rising1 ,libra the opposite constellation is just setting1 while ,capricornus has just reached the meridian4 ,the signs follow one another in their diurnal course over the sky in the direction shown by the arrows1 circling parallel to the celestial equator4 ,at the foot of the mountain they are joined by a band of spirits1 and walking very slowly with them1 conversing with ,manfred1 so much time passes that to ,dante's surprise1 when they reach the place where the ascent is to be made 7still on the eastern side71 the sun has travelled fully fifty degrees since rising4 ,as the sun passes over #cfj in #bd hours1 this indicates about #c hours after sunrise1 or #i4cj a4m4#dfc ,the climb to the first ledge is slow and very arduous1 for as ,virgil explains1 the lower slopes are the most difficult1 since the act of climbing becomes more and more easy as the ascent is made4 ,resting on a ledge1 they look back and at the sun1 and note how it has travelled north1 so that it now strikes their left shoulders2 and after a conversation with ,belacqua ,virgil begins to mount again1 saying that it is noon4 ,the other hemisphere consequently is all in darkness1 from ,ganges 78la riva0#dfd7 to ,morocco4 ---------------------------------------- -------------------------------- #dfc ,if the meaning is that the sun is now #ej above the horizon1 this would indicate a later hour1 nearing midday1 for the sun does not rise vertically in this latitude1 and reaches only #eh at noon at the time of the equinox4 ,but the first explanation is the more probable4 #dfd 8,the shore40 ---------------------------------------- -------------------------------- ,other spirits have been met and spoken with1 and they are still climbing when evening comes1 and ,dante1 thinking he is to reach the summit of the mountain and see ,beatrice that day1 entreats ,virgil to hasten4 8,see10 he says1 8how the mountain now casts a shadow40 ,for the sun has travelled round to the west1 and the poets1 still on its eastern side1 are in deep shadow3 this explains how1 when they meet ,sordello1 he does not recognize that ,dante is a living man1 as all the spirits until now have done4 ,but ,virgil assures him that the way is longer than he knows3 before they reach the summit1 the sun1 now hidden behind the mountain and not causing ,dante to cast any shadow1 will return again to the east4 ,illustration3 ,fig4 #dg4 ,northern slope of the ,mountain of ,purgatory1 up which ,dante climbed4 ,being in the southern hemisphere1 this was the sunny side1 and he followed the sun's course1 from east through north to west4 ,immediately after this1 they meet with ,sordello1 who tells them that it is impossible to climb even one step on the mountain after sunset1 and leads them to a flowery valley1 in which to rest for the night4 ,the spirits in the valley sing the evening hymn while the sun sets2 and it begins to grow dark while ,dante is talking with judge ,nino1 explaining whence he came that morning4 ,as soon as the stars become visible1 his eyes seek the southern pole1 and fix themselves on three brilliant stars which have taken the place of that constellation of four which he saw some fourteen hours before4 ,the latter have travelled to the south-west1 and are hidden behind the mountain1 and the new constellation is above the pole towards the east4 ,night has risen two steps and part of a third in this place when ,dante falls asleep1 and the most natural meaning of this is that it is somewhat more than two hours after sunset1 or after #h o'clock1 in ,purgatory4 ,the moon has not yet risen1 since she is like a clock which loses on an average #ej minutes every day4 ,since the first morning in the ,forest1 when she was exactly #ab hours behind the sun and set at six o'clock1 three whole days have elapsed1#dfe and if she has lost #c times #ej minutes1 or #b hours1 she will rise #ad hours after the sun rises1 that is #b hours after sunset1 or at about #h4cj4 ,as the retardation varies much1 let us say simply that she rises to-night between eight and nine o'clock4 ,she has also moved among the stars1 about #ac degrees each day1 and as #c #ac #ci1 and there are #cj in a zodiacal sign1 she has passed out of ,libra and is in ,scorpio4 ,libra begins to rise at #f p4m41 and ,scorpio at a little before #h1 therefore part of ,scorpio is now above the horizon4#dff ,this1 then1 is the meaning of the first two stanzas of ,canto ix43 the mistress of ,tithonus is the aurora before moonrise 7the solar aurora being his wedded wife1 according to classical mythology71 and this pale aurora is showing white in her balcony of the eastern sky1 while on her forehead shine the stars of ,scorpio1 the cold creature with the stinging tail4 ---------------------------------------- -------------------------------- #dfe ,see table on p4 #cfa4 #dff 8,we must not assume1 as some commentators have done1 that the signs rise at equal intervals of two hours1 although each circles the star sphere in #bd hours4 ,see fig4 #df1 where the dotted line shows how e4g4 ,cancer1 circling parallel with the celestial equator1 will rise at a point considerably north of east1 and having had to traverse more than #ij degrees since ,aries rose due east1 will not rise until about #g hours later1 i4e4 #a p4m4 ,conversely ,scorpio1 following ,libra1 will rise south of east1 and a little less than #b hours later4 ,the moon's retardation1 therefore1 is less in this part of the zodiac than it would otherwise be1 and the hour is probably nearer eight than nine40 ---------------------------------------- -------------------------------- ,this curious passage has been otherwise interpreted by some commentators1 and ,scartazzini calls it 8oscuro al superlativo10#dfg a riddle which still waits its dipus4 ,according to him1 8,titone0 should be read 8,titan10 the sun-god1 and his mistress is ,tethys the ocean1 which is now shining not under his rays 78fuor delle braccia del suo dolce amico0#dfh7 but under the rays of the rising moon4 ,this seems far-fetched1 and the reading doubtful4 ,in any case1 it would indicate the same hour and the same phenomenon 7moonrise74 ---------------------------------------- -------------------------------- #dfg 8,superlatively obscure40 #dfh 8,out of the arms of her lover40 ---------------------------------------- -------------------------------- ,others think that the solar aurora is intended1 and explain the 8freddo animale0#dfi as ,pisces1 and the 8steps0 as the watches of the night4 ,but why a terrible tail should be ascribed to a fish is not clear1 nor is it easy to see how the third step with which ,night ascends could be the hour of dawn4 ,night1 which circles opposite to the sun1 surely reaches the culminating point and begins to descend at midnight1 just as midday is 8il colmo del d40#dgj ,moreover1 the third watch would bring us at latest to a little before #c a4m4 ,to make the 8steps0 signs of the zodiac is no better2 for if ,libra1 ,scorpio1 and ,sagittarius have risen1 it is midnight2 what then can be shining in the east8 and on whose forehead are the stars of ,scorpio glittering8 ,on the other hand1 all accords well if we accept the first interpretation--the light of the moon just about to rise whitening the eastern sky1 some brilliant stars of ,scorpio shining there1 and ,dante falling asleep at the third hour of the night1 wearied after his sleepless nights1 and the hardest day's climb that he will have4 ,we need not grudge him his long sleep of nearly twelve hours1 as those do who take this passage to indicate midnight or early morning4#dga ---------------------------------------- -------------------------------- #dfi 8,cold creature40 #dgj 8,the climax of the day40 #dga ,see ,moore1 ,studies in ,dante iii4 pp4 #ge-hd1 for a detailed discussion of this passage4 ,several commentators have held that lines #a to #f describe the dawn of day elsewhere2 and it is true that it would be nearly #f a4m4 and ,pisces would be on the horizon in ,italy when the hour was nearly #i p4m4 in ,purgatory4 ---------------------------------------- -------------------------------- ,when ,dante wakes the sun has already been up for more than two hours1 but a dream which had come to him in the early dawn1 at the time when the swallow begins to twitter1 has had its counterpart in the truth1 that the lady ,lucia came at that time and carried him up the mountain side1 leaving him outside the ,gate of ,purgatory when the day was bright4 ,when this ,gate has been passed through1 a narrow chasm between the rocks has to be climbed1 and the passage is so difficult that it is at least an hour before the poets emerge on the open space of the ,first ,cornice4 ,for the waning moon has already set1 and as she has lost another half hour or so during the night1 the time of her setting this morning was about #i a4m4 ,when ,dante next notices the position of the sun1 which he is too intent to do for some time1 they have travelled some distance along the ,first ,cornice1 with its outer edge on their right1 and the sixth handmaid is returning from the service of the day1 that is1 the sixth hour is ended3 it is midday1 and they have spent nearly three hours here1 looking at the rock sculptures and conversing with the spirits4 ,the ascent to the ,second ,cornice is made with marvellously little fatigue1 as ,virgil had promised4 ,there they at first find no one to direct them1 so ,virgil looks at the sun1 and turns westward towards it1 taking it as their guide1 and they walk for about a mile before encountering any spirits in this circle4 ,the stairway to the next ,cornice is reached at the time of vespers1 that is1 #c p4m42 and ,dante describes the position of the sun by saying that the portion of sky which it still had to traverse before evening was equal to the portion which is brought into view between the beginning of the day and the end of the third hour1 that is1 it was three hours before sunset2 and he compares this ceaseless motion of the sky1 which according to the ,ptolemaic system caused the motion of the sun1 to an ever-playing child4 ,we need not particularly enquire whether he is thinking of the heaven of the sun1 or the ,primum ,mobile3 it may be either1 but is most likely simply the diurnal movement in general1 made strikingly evident by the sun4 ,the sun's rays now strike their faces1 for they have so far circled the mountain that they are walking towards the west2 8,vespero l0#dgb means in ,purgatory1 and 8qui0#dgc is ,italy1 where it is midnight now4 ---------------------------------------- -------------------------------- #dgb 8,vespers there40 #dgc 8,here40 ---------------------------------------- -------------------------------- ,the sun is low when they reach the third ,cornice1 and when they emerge from the dense cloudy fog which here envelopes the spirits1 ,dante gradually sees the ball of the sun as when mists clear away1 and he sees that it is just about to set4 ,in fact the low shores at the foot of the mountain are already in shadow4 ,virgil urges that they make the ascent to the next ,circle before darkness comes1 and1 as each ascent is easier than the last1 they are able just to reach the summit before the sun is quite gone4 ,here ,dante sees the stars begin to appear1 while he is wondering at the strange law which robs him of power to proceed 7as ,sordello had warned them7 after the sun has set4 ,they employ this time of forced inaction by talking of the sins which are punished in the several ,circles1 until all ,dante's questions are answered1 and he is beginning to fall asleep4 ,it is at this moment that he first mentions the moon3 she is glowing1 shaped like a bucket in her present phase1 and the stars are paled by her light4 ,she is 8belated almost till midnight10 if the epithet 8tarda0 belongs to her2 if it applies to 8mezza notte10 then it is almost late midnight when she is seen paling the stars4 ,she ought to have risen about ten o'clock1 but ,dante does not speak of her rising1 so this may mean simply that it was moonlight and starlight at the time of which he is about to speak1 viz4 nearly the late hour of midnight2 or else that since he is now on the northern slope of the mountain1 and the moon is in a southern sign1 she did not become visible to him till towards midnight4 ,in any case1 the 8quasi0 shows that he is only giving us a rough idea of the time4 ,but in what sign was she8 ,her position in the zodiac is described in a peculiarly round-about fashion4 ,dante says that her course against the sky1 that is1 her monthly motion which is contrary to the diurnal1 had taken her to that part of her track in which the sun is when from ,rome he is seen to set between ,sardinia and ,corsica4 ,the straits between these islands lie west and a little south of ,rome1 therefore the sun sets in that direction when he is going south after passing the autumnal equinox in ,libra1 and this is just what the moon is doing now4 7,the sun passes the same point again when coming north1 before entering ,aries at the spring equinox1 but ,dante has either forgotten this1 or considers it obvious that the first position is meant here74 ,this is probably all that he means to convey1 and if we ask for more exact information1 it is almost impossible to tell what degree or even what sign in the zodiac he intends us to understand2 for as the straits are nearly two hundred miles from ,rome they are quite invisible thence1 and we do not know what he thought was their precise direction4 ,the medival commentator ,benvenuto da ,imola says that the position intended is in ,scorpio2 the moderns usually say ,sagittarius1 but without explaining how they draw this conclusion4 ,benvenuto's is probably simply the position which he thought the moon ought to have in order to agree with what ,dante says about her1 just as he states that ,venus was in ,pisces in ,march #acjj1 although this was not the case at all1 as we shall presently see4 ,a calculation based on the difference in latitude between ,rome and the ,straits shows that they are only about #i south of west1 and that the sun1 when setting in this direction is about #f south of the equator3 this is the case #ae days after the equinox1 which in the beginning of the fourteenth century fell on ,september #ad4 ,therefore the date at which the sun was seen from ,rome setting in the direction between ,sardinia and ,corsica was the #bith of ,september1 and its position in the zodiac was then the middle of the sign ,libra4 7,owing to precession1 it would be in the constellation ,virgo1 but we have seen that ,dante ignores precession in these references47 ,but the moon ought now1 on this second night in ,purgatory1 to have reached at least the last degrees of ,scorpio1 since on the previous night she rose when the first part was already above the horizon4 ,dante has therefore made a flagrant mistake with his moon1 running her back into ,libra again1 and falsifying all his previous descriptions--if he knew as much about geography as we do now4 ,but it is only necessary to glance at the map of ,henry of ,mainz to see that such a supposition would be grotesque4 ,the portolan maps did indeed show the relative positions of ,rome1 ,sardinia1 and ,corsica1 with remarkable accuracy2#dgd but as we have already said1 it is not in the least likely that ,dante had ever seen one of these sailing charts4 ,it was on the classics1 and especially on ,orosius1 that he relied for his geography1#dge and the suggestion of ,dr4 ,moore seems most plausible1 that he was here thinking of the ,spaniard's description of ,sardinia3--8,habet ab oriente et borea ,tyrrenicum mare quod spectat ad portum urbis ,romae40#dgf ,this implies that ,sardinia lay south-west of ,rome1 in a direction such as the sun might have had when setting in ,november1 in ,scorpio or ,sagittarius4 ---------------------------------------- -------------------------------- #dgd ,see for instance the 8,carte ,pisane18 and the ,central ,mediterranean map of ,vesconte1 dating from about #acjj and #acaa respectively1 in ,beazley's ,dawn of ,geography1 iii4 ,latitudes and longitudes are not given1 but from certain centres lines radiate to all points of the compass1 like great spiders' webs4 #dge ,de ,mon4 ,,ii4 iii4 #hg-ij4 etc4 #dgf 8,it is bounded on the east and north by the ,tyrrhenian sea1 which lies towards the port of ,rome10 ,moore1 ,studies in ,dante iii4 p4 #gb4 ---------------------------------------- -------------------------------- ,or possibly1 when the poet was in ,rome in #acja1 he may have been watching a sunset in the second week in ,november1 and may have been told1 among other pieces of misinformation which are so readily given to visitors to great cities1 that he was looking towards the straits which separate ,sardinia from ,corsica4 ,we can imagine his replying1 or thinking3 8,then the sun sets behind them when he has nearly finished his course in ,scorpio1 and is about to yoke his steeds under another star60#dgg ---------------------------------------- -------------------------------- #dgg ,purg4 xxxii4 #ef1 #eg4 ---------------------------------------- -------------------------------- ,it is while the moon is shining on this ,cornice that the spirits who purge their sins on it appear1 rushing past in haste4 ,then at last ,dante sleeps1 and dreams again in the cold moonlit dawn when ,aquarius and ,pisces are on the horizon 7see p4 #bij74 ,the mountain is full of daylight when ,virgil wakes him1 and the newly-risen sun shines behind them as they continue their journey1 for they had reached the north point of the circle1 and are walking now due west4 ,they mount almost immediately to the ,fifth ,cornice1 where presently they are startled by a violent trembling of the mountain followed by a mighty shout of 8,gloria in excelsis0 from all the spirits4 ,statius joins them1 and from him they learn that this was no earthquake1 for since passing the gate of ,purgatory they are in a region too lofty for such disturbances to be felt1 or for rain or snow or dew to fall2 the mountain trembles1 and the shout of praise follows1 when a soul rises1 purified and ready to ascend to ,paradise4 ,with ,statius they climb to the ,sixth ,cornice1 and then1 looking round1 they see that the fifth handmaid of the sun's chariot is directing its upward course1 that is1 it is the fifth hour1 or between #aj and #aa a4m4 ,as usual1 they walk on with the outer edge of the circle on their right4 ,it is here that we are reminded1 as once in the ,inferno1 that only a certain time is allowed1 for while ,dante is looking eagerly at the first mysterious tree ,virgil gently urges him onward3-- 8,lo pi che padre mi dicea1 ,figliuole1 ,vienne oramai1 ch il tempo che c' imposto ,pi utilmente compartir si vuole40#dgh ---------------------------------------- -------------------------------- #dgh 8,my more than father said unto me1 ,son1 ,come now1 because the time that is ordained us ,more usefully should be apportioned out40 ,purg4 xxiii4 #d-f4 7,longfellow74 ---------------------------------------- -------------------------------- ,it is here also that ,dante informs his old friend ,forese ,donati and other spirits1 who are all astonished at the sight of his shadow1 that he is a living man who was rescued by ,virgil some days ago1 when the sister of the sun was round 7referring of course to the full moon in the forest71 and he points to the sun4 ,now a curious question arises3 ,dante was in sunshine in the early morning2 he is in sunshine now1 and has been walking all morning in the same direction in which the sun was moving2 how is it then that ,statius did not notice his shadow1 but had to be told that he was not a spirit8#dgi ,if the ,mountain had been a small hill1 it would have been quite easy to walk so large a part of a circle round it1 in a short time1 that the poets would have been in shadow until the sun caught them up again when they lingered talking on the ,sixth ,cornice2 but the ,mountain was so large that a whole day's walking only brought them a quarter of the way round1 i4e4 from the east side to the north1 and it was evidently a distance of many miles4#dhj ,it is difficult to believe that ,dante has forgotten1 because he is so careful throughout to mention the surprise of the spirits except when his shadow could not be seen for one reason or another4 ,it is true that in the latitude of ,purgatory 7#cb south1 as that of ,jerusalem is #cb north71 the sun rises rather steeply1 which makes it easier to get into the shade in the early morning while circling a mountain4#dha ,on the other hand a simpler solution offers itself in the text4 ,statius approaches ,dante and ,virgil from behind1 and they only stop and turn their faces to him for a few moments while ,virgil returns his greeting1 then walk on quickly while ,statius makes his surprised reply3 8,what6 if you are spirits44440 ,if he has not yet quite overtaken them he cannot see ,dante's shadow1 which ,dante himself is screening from view as it falls in front of him1 the morning sun being still at his back1 and ,virgil explains at once that his companion is a living man4 ---------------------------------------- -------------------------------- #dgi ,purg4 xxi4 #bj-bg4 #dhj ,purg4 xiii4 #bb-bc4 #dha ,on an ,astronomical ,point in ,dante's ,purgatorio1 by ,p4 ,h4 ,cowell1 ,f4,r4,a4,s41 ,the ,observatory1 ,december #aijf4 ---------------------------------------- -------------------------------- ,in spite of their haste1 the three poets remain about four hours in this sixth ,cornice2 and when they reach the ascent to the next it was indeed time to climb without any delay1 for the sun had left the meridian to the sign which follows ,aries1 viz4 ,taurus1 and ,night1 8che opposita a lui cerchia10#dhb had left the meridian of the opposite hemisphere to ,scorpio4 ,aries at the time of the equinox begins to cross the meridian at midday1 ,taurus at two o'clock1 and ,gemini at four#dhc3 therefore it is now between two and four in the afternoon4 ,the three poets hasten therefore 7,statius still accompanying ,virgil and ,dante71 like men who pause for nothing on their way1 whatever the road be like2 and a question ,dante is longing to ask with regard to the form of purgation last seen is put and answered as they follow one another up the narrow stair2 as soon as they reach the top1 they turn to the right1 as usual1 without hesitation or delay4 ,as ,dante walks cautiously between the outer edge of this ,cornice and the fire which bursts forth from the inner wall of rock1 all the blue of the western sky is already changing into ash-white1 and he has come so far round the ,mountain that the evening rays strike his right shoulder4 ,with one of the many touches which show ,dante's close observation and his vivid realization of the scene he is describing1 he says here that his shadow falling on the flame makes it appear a deeper red1 and this is observed by the spirits4 ,when they reach the spot where1 on the further side of the flames1 the chanting ,angel guides them across to the last ascent1 the sun is very near to its setting4 ,its burning noonday beams are shining on the waves of ,ganges1 its first morning beams quiver over ,jerusalem1 and ,spain lying under ,libra is wrapped in midnight gloom2 hence it is beginning to set at sea-level in ,purgatory4 ,high on the ,mountain it still shines1 but when the poets have crossed the flames1 the voice of the ,angel persuades them to hasten their steps before the darkness comes4 ,the stair mounts through the rock on the west side of the ,mountain so that the low sun casts ,dante's shadow in front of him as he climbs4 ,and he has only climbed a few steps when they are all aware that the sun has completely set because the shadow disappears4 ,before the colour has all faded from the west1 and the whole vast range of the horizon seen from this height has become one uniform tint1 each of the three makes a bed of one step1 and between the high and narrow enclosing rocky walls ,dante sees the stars come out1 much brighter and much larger than he has ever seen them before4 ,no moonlight dims them1 for moonrise will be late to-night1 long after ,dante has fallen asleep4 ---------------------------------------- -------------------------------- #dhb 8,that circles opposite to him40 ,purg4 ii4 #d4 #dhc ,the signs follow one another on the meridian at intervals of exactly #b hrs4 ---------------------------------------- -------------------------------- ,once again1 for the third and last time1 he has a prophetic dream in the early dawn2 and if we compare these three parallel passages1 we find that each begins with the same words 8,nell' ora40#dhd ,the first time the ideas connected with the time are wholly sorrowful1 for it is said to be the hour when the swallow begins to twitter1 perchance in memory of her former woes--alluding to the tragic tale of ,procne and ,philomel4 ,the second is a depressing time1 for it is the cold hour when1 the day's heat being all spent1 the chilled earth cannot overcome the influence of the cold planets such as the moon or ,saturn1 but there is a thought of hope in the stars of the ,greater ,fortune seen rising in the east1 in a sky which is now scarcely dark to them4 ,the third is all joy1 for it is the hour when ,cytherea 7the planet ,venus71 burning ever in the fire of love1 shines first upon the mountain4 ,dante's sleep flees from him as the shades of darkness flee on all sides1 chased by the brightness before sunrise2 and when ,virgil tells him that to-day he shall reach the goal of his desires1 he speeds up the remaining steps of the stair1 almost as if on wings4 ---------------------------------------- -------------------------------- #dhd 8,at the hour40 ---------------------------------------- -------------------------------- ,the poets arrived on the shores of ,purgatory1 as we saw1 facing east1 and now that they have attained the summit of the mountain1 coming up the western slope1 they again face east1 and the just risen sun shines in their faces4 ,dante walks towards it3 a breeze fans his forehead and causes all the trees to bend in the direction of the shadow thrown at sunrise by the ,mountain 7i4e4 westwards71 and the murmur of this gentle wind in the branches forms a bass to the treble of the singing birds who are greeting the morning hours4 ,for a few steps the stream of ,lethe stays his steps in this direction1 but he soon reaches a bend1 and once more 8a levante mi rendei40#dhe ,the symbolical procession which accompanies ,beatrice comes towards him from the east1 and after he has crossed the river ,lethe and joined the procession beside the ,car in which ,beatrice is throned1 all turn to the sun1 which by this time must have travelled some distance towards the north4 ,after the vision of the disasters which befell the holy ,car1 and after ,beatrice has spoken with ,dante again1 they reach the fountain whence ,eunoe flows1 and now the sun is on the meridian and it is noon1 though 7as ,dante reminds us7 different places have different meridians1 so that it is not noon everywhere else4 ,he is bathed in the holy waters1 and thus1 all having been accomplished for which he has visited these regions1 he is 8puro e disposto a salire alle stelle40#dhf ---------------------------------------- -------------------------------- #dhe 8,i turned to the east40 #dhf 8,pure and ready to rise to the stars40 ,purg4 last line4 ,hell was entered at twilight1 ,purgatory at dawn1 the ascent to ,paradise is made at noon1 8il colmo del d40#dhg ,the time spent in ,purgatory is three days and the morning of a fourth1 which is the seventh from the beginning of the vision4 #dhg 8,the climax of the day40 ---------------------------------------- -------------------------------- #d4 ,,paradise4 ,that the time of ascent to the spheres was noon is again stated in the opening ,canto of the ,paradiso1 where ,dante says that the sun had brought morning there 7,purgatory7 and evening here 7the inhabited hemisphere71 and that now the whole of that hemisphere was bright while the whole of this was dark4#dhh ,the sun is therefore now due north4 ,while ,beatrice stood beside the waters of ,eunoe1 after walking towards the sun1 it had moved to her left1 so she now turns in that direction to gaze upon it4#dhi ,she1 like ,virgil1 takes as her guide that sun which ,dante has said is the fittest symbol of ,god1 and it is through the power of this heavenly light that he is raised from earth4 ,compare #dhh ,it has been suggested to read the line ,par4 i4 #dd4 8,tal foce2 e quasi tutto l era bianco10 transferring the 8quasi0 7almost7 so that the meaning should be 8almost was wholly white that hemisphere10 and to interpret that it is now morning of the day following the events in the last ,canto of the ,purgatorio4 ,but if so1 ,dante would have spent a whole night in the ,earthly ,paradise without mentioning it1 or explaining this long delay after he had become 8pure and ready to rise to the stars40 7,for the meaning of 8foce10 the 8passage10 see later1 p4 #djj74 ---------------------------------------- -------------------------------- #dhi ,par4 i4 #df1 #dg4 8,amor che il ciel governi 444 col tuo lume mi levasti40#dij #dij 8,love that rules the heavens1 with thy light ,thou didst raise me40 ,par4 i4 #gd1 #ge4 ---------------------------------------- -------------------------------- ,he is not conscious of any effort1 or even movement1 but is astonished by a great light and strange music1 and learns that he is in the sphere of fire and listening to the harmony of the spheres4 ,his soul1 freed from all that bound it to earth1 is soaring towards its natural goal1 as fire mounts up and rivers run down4 ,the upward gaze to the sun or to the skies1 and its power to raise them1 is again described in ,par4 i4 #adb3 ,beatrice 8rivolse inver lo cielo il viso10#dia and in ii4 #bb1 8,beatrice in suso ed io in lei guardava40#dib ,thus they rise to the ,first ,heaven1 of the moon4 ,in answer to an eager question of ,dante's about the markings of the moon1 ,beatrice is led to discourse on the spheres and their movers4 ,spirits appear1 and ,dante learns that although all the redeemed dwell in the ,empyrean1 those of different degrees of blessedness will manifest themselves to him in each sphere4 ,after explaining this and other things1 ,beatrice once more ---------------------------------------- -------------------------------- #dia 8,turned her eyes again towards heaven40 #dib 8,beatrice gazed upwards1 and ,i at her40 8si rivolse tutta disiante ,a quelle parte ove il mondo pi vivo10#dic #dic 8,turned again with yearning to that part where the world is most living40 ,par4 v4 #hf1 #hg4 ---------------------------------------- -------------------------------- and swift as an arrow that strikes its mark before the cord has ceased to quiver1 they ascend to the ,second ,heaven1 of ,mercury4 ,to understand the above lines we must remember that the sun1 as ,dante told us in the introductory ,canto1#did is at the equinox1 or near it1 and therefore on the equator2 also that the equator of a sphere1 where motion is quickest1 is its most living part4#die ,beatrice is therefore looking again at the sun4 ,some understand 8quella parte0#dif to refer directly to the sun1 8quegli ch' padre d'ogni mortal vita10#dig some to the equinoctial point2#dih others think that the east is meant2 others the ,empyrean1 in which is the true life of all the ,universe4 ---------------------------------------- -------------------------------- #did ,inf4 i4 #ch-dj4 #die ,conv4 ,,ii4 iv4 #eb-fb4 #dif 8,that part40 #dig 8,he who is father of all mortal life40 ,par4 xxii4 #aaf2 see also ,de ,mon4 ,i4 ix4 #f1 #g4 #dih ,see ,par4 x4 #g-ba4 ---------------------------------------- -------------------------------- ,equally swiftly and unconsciously1 ,dante ascends to the successive heavens of ,venus1 the sun1 ,mars1 ,jupiter1 and ,saturn1 finding himself always in the planet which occupies each sphere4 ,mounting the mysterious golden ladder which is set up in ,saturn1 with a rapidity inconceivable on earth1 the poet finds himself in the ,heaven of ,stars1 in the constellation of ,gemini4 ,now that he is so near the final blessedness his eyes are clear and keen1 and that his heart may be filled with joy ,beatrice bids him look down and see how much of the universe is already beneath his feet4 ,there lie the seven spheres1 and there is the little globe of ,earth1 so small that1 like ,scipio1 he smiles at its paltry appearance2 there is the moon1 showing him the face turned away from ,earth1 which has no dark markings3 there is the sun1 at which for once he is able to gaze2 and near it circle ,mercury and ,venus2 the temperate ,jupiter moves between his father ,saturn and his son ,mars2 with a new power of vision ,dante can grasp all their sizes and distances and the various speeds of their movements2 and the poor little disc of the earth1 small and round as a threshing floor1#dii about which we quarrel so fiercely1 is all visible to him at a glance1 its highest hills and its lowest river-valleys running down to the sea4 ,he turns away his eyes to look into the beautiful eyes of his guide4 ,she is standing1 erect1 intent1 watching eagerly for that glorious ,procession1 whose coming is making a growing brightness in the sky4 #dii ,longfellow says3--8,looking down from the terrace of ,monte ,cassino upon the circular threshing-floor of stone in a farm lying below1 ,i first felt the aptness of ,dante's phrase4 ,this very scene may have suggested it to him40 8,la donna mia si stava eretta ,ed attenta1 rivolta inver la plaga ,sotto la quale il sol mostra men fretta40#ejj ---------------------------------------- -------------------------------- #ejj 8,so my lady stood1 erect and intent1 turned towards that place under which the sun shows least haste40 ,par4 xxiii4 #aj-ab4 ---------------------------------------- -------------------------------- ,no other intimation is given as to the direction from which the ,procession comes4 ,the sun's daily motion appears slowest on the meridian1 as ,dante remarked in ,purg4 xxxiii4 #ajc1 #ajd1 because he is scarcely changing his position with regard to the horizon2 or in the south 7where we in this hemisphere see him when on the meridian72 he shows least haste to leave us in the long summer days1 near the solstice4 ,if the ,procession descends from the heaven of heavens to show itself here symbolically to ,dante1 as we know that the spirits in other heavens did1#eja then ,beatrice was gazing upwards1 and the meridian may be meant1 particularly that part of it which passes directly overhead4 ,if the ,procession came from the east1 like the ,procession in ,eden1#ejb the summer solstice in ,cancer is meant1 which lies east of ,gemini4 ,it is difficult to see any special meaning in its coming from the south1 for although some commentators say that this suggests the consummate glory of the midday sun1 the same idea is conveyed by the meridian4 ,a constellation like ,cancer perhaps corresponds better than a circle like the meridian with the expression 8plaga10#ejc and the idea of the east makes more perfect the beautiful simile which the poet has just drawn between the little bird on the spray beside its nest waiting for the sun to rise1 and ,beatrice watching for the advent of ,him who is likened to a sun among the starry company of ,his saints4#ejd ---------------------------------------- -------------------------------- #eja ,see ,par4 iv4 #cd-ci4 #ejb ,purg4 xxix4 #ab and #cd4 #ejc 8,region40 #ejd ,par4 xxiii4 #bi1 #cj4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #dh4 ,dante's first view of ,earth from the ,stars4 ,par4 xxii4 7see p4 #cig74 ,when this glorious company has at length vanished1 she bids him look down once more1 this time that he may realise how he has been revolving with the spheres1 the little earth lying immoveable at his feet4 ,he looks down1 and notes what parts of ,earth are lighted by the sun1 and what parts are wrapped in darkness1 for now he is able to see what he had often imagined1 the shadow of night sweeping westward over the globe4 ,the ,atlantic ,ocean1 where ,ulysses sailed beyond ,gades1 is all in daylight1 and so is the ,mediterranean1 but the sun is setting over ,jerusalem1 for he says that its position prevents him from seeing beyond the coast whence ,europa was carried 7i4e4 ,phnicia or ,palestine74 ,it must therefore be midday at ,gades1 and the sun is on the meridian there2 it is 8a sign and more10 or something between #cj and #fj1 advanced to the west beyond the meridian over which ,dante stands4 ,he does not define his own position more exactly than this1 but we may conjecture that he was #de 7a sign and a half7 east of the sun1 since this would be the meridian of ,rome1 and there would be a peculiar fitness in such a position at such a moment1 when he has just received a message of warning and prophecy from ,st4 ,peter to bear to this city4#eje ---------------------------------------- -------------------------------- #eje ,par4 xxvii4 #fd-ff4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #di4 ,the view six hours later4 ,par4 xxvii4 ,fig4 #di shows these positions of ,dante and the sun1 and the consequent limits of his vision4 ,jerusalem is 8near10 in comparison with the much more distant sunlit space of ocean in the opposite direction4 ,we place the sun in the middle of ,aries1 because we shall see presently 7when discussing the date7 that this is its most probable position1 and ,dante in the first degree of ,gemini because this is #de east of the sun1 and also because the fact that he is above ,earth's 8first climate0 suggests that he is in the beginning of this sign4 ,for the northern limit of the first climate was #bj1 according to ,alfraganus1 and the ecliptic in the sign of ,gemini rises gradually from #bj north of the equator to #bc at its end1 where it adjoins ,cancer4 ,since the time when he looked down before1 he sees that he has revolved over an arc equal to half the climate1 that is #ij1 for the climates only extended over the habitable earth1 which was #ahj in longitude4 ,his former position1 then1 must have been #ij further east1 halfway between ,jerusalem and ,ganges2 and it was then noon at ,jerusalem1 while all the ocean east of ,ganges lay in the black darkness of night4 ,fig4 #dh shows this position4 ,in this interpretation of a difficult passage1 the meaning given to the first lines seems a little forced2 but if we take them in the more natural sense that ,dante had moved from above the centre to the end of the climate1 that is1 from the meridian of ,jerusalem to ,gades1 we are met by a difficulty in the following lines4 ,for to say that he is standing over ,gades1 and in the same breath that the sun is more than #cj further to the west1 means that it is setting more than #cj west of ,jerusalem3 he cannot therefore possibly see ,jerusalem1 nor is it 8near0 him4 ,it does not help us to take 8presso0 in its alternative meaning1 and say that he could see 8nearly as far as0 ,jerusalem1 for however little more than #cj 8a sign and more0 may mean1 it brings the 8terminator0 7as astronomers call the dividing line between light and darkness on a planet7 a long way from ,jerusalem and much nearer ,italy1 according to ,dante's reckoning of distances in the ,mediterranean4 ,this is shown on fig4 #ej1 where the data are made as favourable as possible1 by putting the sun at the very end of ,aries4 ,on the whole1 it is easier to accept a round-about expression in the first lines than an inaccurate one later4 ,the former is quite characteristic of ,dante1 and we have already met some like it in the ,divina ,commedia in descriptions of the positions of heavenly bodies4#ejf ---------------------------------------- -------------------------------- #ejf ,compare ,purg4 xv4 #a-e1 where the course the sun still has to run between vespers and sunset is described as equal to the space between the third hour and sunrise4 ---------------------------------------- -------------------------------- ,looking back to the earlier position1 as described in ,canto xxii41 we find no light thrown on the question2 for here he does not mention any particular place as visible1 nor say where the terminator lay4 ,his words are3-- 8,l'aiuola che ci fa tanto feroci1 ,volgendom' io con gli eterni ,gemelli1 ,tutta m'apparve dai colli alle foci40#ejg ---------------------------------------- -------------------------------- #ejg 8,the threshing-floor that maketh us so proud1 ,to me revolving with the eternal ,twins1 ,was all apparent made from hill to harbour40 ,par4 xxii4 #aea-c4 7,longfellow74 ---------------------------------------- -------------------------------- ,this seems to express simply a bird's eye view of ,earth1 as it lay stretched out like a map below the observer4 ,it is1 however1 often taken to mean that the whole habitable earth was visible4 ,this could never be unless the sun1 as well as ,dante1 was over the meridian of ,jerusalem1 which is obviously impossible while one is in ,aries and the other in ,gemini2 and as he refers back to the first passage from the second he cannot have forgotten this4#ejh ---------------------------------------- -------------------------------- #ejh ,della ,valle boldly assumes that they were over the same meridian1 by a poetical licence1 although at the same time the sun was in a different sign4 ,dante only mentions the latter fact1 he thinks1 in order to show that he was a few degrees north of the sun 7,gemini being more northerly than ,aries72 therefore he could see over the edge1 as it were1 of the sun-lighted hemisphere of ,earth4 ,this is desperately subtle4 ---------------------------------------- -------------------------------- ,it is1 however1 the only way in which the passages can be reconciled with his further assumption1 shared by some other commentators1 that ,dante1 in his flight through the spheres1 simply ascended without any movement in longitude except that he was carried round by the daily revolution of the spheres4 ,all the planets1 therefore1 were ranged one above the other1 in the sign of ,gemini1 and it was always noon on the earth below his feet1 since that was the hour at which he ascended from the ,earthly ,paradise1 and his movement was the same as the sun's4 7,here ,della ,valle is inconsistent1 however1 for he maintains that the ascent was made in the early morning47 ,but this is a very artificial conceit1 and not indicated by ,dante4 ,he implies that ,beatrice1 in leading him to each sphere1 chose the part of it which he was to enter 7see ,par4 xxvii4 #ajb71 and he tells us that ,saturn was in ,leo1 ,venus in ,pisces1 and the sun in ,aries4 ,illustration3 ,fig4 #ej4 ,an impossible interpretation of ,par4 xxvii4 ,a book which aims at explaining ,dante's ,paradiso to young people#eji suggests an original way of reconciling the two passages1 for the author gravely asserts that the sun was at first below ,dante's feet in ,gemini1 but that by the time he looked down again it had moved a good distance onward1 and was then in the sign of ,taurus6 ,according to this1 a whole month must have elapsed1 and time had gone backwards1 from ,may to ,april6 ---------------------------------------- -------------------------------- #eji ,il ,paradiso di ,dante dichiarato ai giovani1 by ,angelo de ,gubernatis4 ---------------------------------------- -------------------------------- ,a suggestion much more worthy of attention is that of ,professor ,rizzacasa d',orsogna1 who thinks the key is to be found in the line1 8,volgendom' io con gli eterni ,gemelli40 ,this1 he suggests1 is in anticipation of the second passage1 for although ,dante could not see the whole habitable earth at any one time1 his change of position1 as he revolved with the ,twins1 enabled him to do so in the course of time which elapsed between his two views4 ,a comparison of figures #dh and #di will make this clear4 ,one more suggestion may perhaps be made1 though it is rather a hazardous one4 8,dai colli alle foci0#eaj may mean from the ,apennine ,hills to the mouths of ,ganges4 ,this would be decisive for the correctness of the explanation illustrated by our diagram4 7,see fig4 #dh74 ---------------------------------------- -------------------------------- #eaj 8,from the hills to the river-mouths40 ---------------------------------------- -------------------------------- ,in any case1 the points which ,dante specially wishes us to understand are clear and simple3 at the first glance he was struck by the insignificance of the ,earth2 at the second1 he became conscious that he was moving with the spheres1 having passed over #ij of arc1 or a quarter of the diurnal revolution1 and he saw that it was now sunset at ,jerusalem4 ,he next ascends to the ,primum ,mobile1 though he cannot tell us to which part of it ,beatrice chose to lead him1 since it is perfectly uniform throughout4 ,beatrice explains that this most swift and living sphere1 although it contains no star by which its motion is made visible1 causes the 7diurnal7 motion of all the lower spheres2 and thus it is like a flower-pot in which are hidden the roots of ,time1 while in the others we see the leaves4 ,here he sees the nine hierarchies of angels who direct the nine moving spheres2 and finally he soars to the ,empyrean1 where ,beatrice returns to her seat among the blessed spirits who form the ,celestial ,rose1 and ,st4 ,bernard encourages him to lift his eyes to 8,l',amor che move il sole e l' altre stelle40#eaa ,this is the end and consummation of the ,vision4 ---------------------------------------- -------------------------------- #eaa 8,love which moves the sun and the other stars40 ,par4 last line4 ---------------------------------------- -------------------------------- ,the reader will have observed that although there are several indications of direction in ,dante's journey through ,paradise1 all referring to the heavenly bodies1 there are no time references after he has left ,earth and entered the regions of eternity1 except the passage discussed above1 which indicates a period of six hours spent in the eighth heaven1 since #ij of the diurnal revolution correspond with six hours of time4 ,but it tells us also that at the close of this period the sun was setting over ,jerusalem3 consequently another morning was dawning in ,purgatory4 ,eighteen hours have passed1 therefore1 since ,dante left the ,earthly ,paradise at noon2 and he rises to the ,primum ,mobile and thence to the ,empyrean on the eighth day of his ,vision4 ,the whole ,vision1 therefore1 occupied an octave1 or eight days4 #e4 ,,positions ,,of ,,sun1 ,,moon1 ,,and ,,planets ,,among ,,the ,,stars ,,during ,,dante',s ,,vision4 ,the allusions to sun1 moon1 and stars in the ,divine ,comedy1 when thus brought together1 are seen to follow one another according to a regular scheme1 and they form a very good guide by which to time ,dante on his journey4 ,there is a little inaccuracy in one passage about the stars1 and the moon is ambiguous once1 but quite explicable4 ,taking the allusions in a simple popular sense1 as he seems to intend us to do1 assuming that the signs and the constellations of the zodiac are identical1 and that the moon1 which at first is opposite the sun1 traverses about #ac in the zodiac daily1 and loses about an hour of time more or less1 there is very little difficulty in following him4 ,it is quite enough to know that the sun is somewhere in ,aries throughout1 and that the moon is therefore in ,libra at the beginning4 ,illustration3 ,fig4 #ea4 ,the rising sun at the ,spring ,equinox4 ,but if we wish to know a little more accurately the positions of sun and moon among the stars1 we must carefully compare the passages bearing on this question4 ,commentators differ so much that while some think the sun's annual motion is ignored1 and it is assumed to be at the equinox all the time1 others maintain that it was at the equinox on the first day and moved on through ,aries at the rate of about one degree a day 7as it should do1 since there are #cfe days in a year and #cfj in the circumference of the sphere72#eab while others again say that it was merely somewhere in ,aries from the beginning4 ---------------------------------------- -------------------------------- #eab ,alfraganus1 as we saw1 gives the daily movement of the sun eastward in the zodiac as about #ei minutes of arc4 7,a degree contains #fj minutes74 ---------------------------------------- -------------------------------- ,what are the actual indications of its position8 ,no one questions that it was in ,aries throughout the ,vision1 for this is often indicated1 sometimes directly1 as in ,inf4 i4 #ch-dj1 sometimes by mentioning ,taurus as the sign following the sun1#eac or ,pisces as the sign preceding4#ead ---------------------------------------- -------------------------------- #eac ,purg4 xxv4 #b1 #c4 #ead ,inf4 xi4 #aac2 ,purg4 i4 #ba1 xix4 #d-f4 ---------------------------------------- -------------------------------- ,there are four detailed descriptions3-- 7#a7 ,on the first morning1 the sun rose among those stars which were with him at the ,creation4#eae ,as we have seen1 this may mean merely some point in ,aries1 or the first point of ,aries1 at which the sun was thought to have been placed when created4 ---------------------------------------- -------------------------------- #eae ,inf4 i4 #ch-dj4 ---------------------------------------- -------------------------------- 7#b7 ,on the seventh day it rose near a point where three crosses are formed by the intersection of four circles4#eaf ,one naturally thinks of the horizon as one of these circles2 the equator and ecliptic1 whose intersection define the equinox1 suggest themselves as two more2 the fourth is doubtless the colure which passes through the equinoctial points and the poles1 although curiously enough this is not mentioned by ,ptolemy or ,alfraganus1 who only speak of the solstitial colure4 ,fig4 #ea shows how the horizon makes a cross with each of the other three when the equinox is upon it4 ,the sun is at the point of intersection when rising with the equinox1 and it was near there when it rose this morning--8quasi40 ,it was therefore near1 but not exactly at the equinox1 and we know that it was the vernal1 not the autumnal equinox1 from the many allusions to ,aries4 ---------------------------------------- -------------------------------- #eaf ,par4 i4 #ch1 #ci4 ---------------------------------------- -------------------------------- 7#c7 ,when ,dante rises to the sun 7on the same day7 he directs our attention once more to this point where 8the one motion strikes the other10 that is1 where the ecliptic--the oblique circle which bears the planets--branches off from the equator1 and he reminds us of the supreme importance of this divergence4 ,the sun1 he says1 was in this place4 ,he does not mean at the exact point of intersection1 or this passage would be in flat contradiction to the last3 8quella parte0#eag is no more precise than 8quelle stelle10#eah and means only this part of the sky1 or the constellation of ,aries4 ,the words which follow not only specify that it was the spring equinox1 but suggest that the sun had already traversed several of those spirals which bring him to us earlier each morning1 i4e4 it was several days after the equinox4#eai ---------------------------------------- -------------------------------- #eag 8,that part40 #eah 8,those stars40 #eai ,par4 x4 #g-cc4 ---------------------------------------- -------------------------------- 7#d7 ,on the same day the sun was 8one sign and more0 removed from some point in ,gemini4#ebj ,this is very vague1 but at least the sun cannot now have been at the first point of ,aries1 or it would have been two whole signs from even the first degree of ,gemini4 ---------------------------------------- -------------------------------- #ebj ,par4 xxvii4 #hf1 #hg4 ---------------------------------------- -------------------------------- ,it seems1 then1 that we cannot possibly agree that the sun was at the equinox throughout the poem4 ,it is clear that it was past the equinox towards the end2 but from these four passages we cannot be sure whether it was there on the first morning1 or whether it moved through some undefined part of ,aries during the ,vision4 ,one consideration gives us some help1 however4 ,we know from ,inf4 xxi4 #aab-aad that the first day was either ,march #be1 which was believed in the ,middle ,ages to be the true anniversary of the ,crucifixion1 or ,good ,friday1 which was kept by the ,church as such4 ,march #be is four days after the date which the ,church still kept as the day of the ,equinox 7,march #ba71 and #ac days after the true equinox1 which at this time fell on ,march #ab4 ,good ,friday also almost inevitably must fall after the equinox1 since ,easter follows the full moon which follows the equinox4 ,it is true that some of ,dante's readers may still have regarded the old traditional date of ,march #be as the true day of the equinox1 and possibly it was to suit all shades of knowledge that he left the sun's position vague2 but he himself certainly knew better1 and probably had ,march #ab in his mind4 ,then those who held to ,march #be might consider the sun as exactly at the equinox on the first day of the ,vision1 but all better-informed readers and ,dante himself must have regarded it as somewhat past this point4 ,if we take it that1 e4g41 it was a week past the equinox1 the sun was in about #g of ,aries1 and this position agrees with the four crucial passages mentioned above4 ,the stress laid on the equinox seems to demand that the sun should be at least as near it as this on the first day2 and a week later it would have reached the middle of ,aries1 which is the position we assigned to it from a discussion of ,par4 xxvii4 #hf1 #hg4 ,this also agrees well with the course of the moon in the zodiac1 which must depend upon the sun's4 ,we have seen that she was opposite the sun on the first morning1 that her light paled the first-risen stars of ,scorpio while she was yet beneath the eastern horizon three days later1 and that she was proceeding south on the following night4 ,if the sun was in the #gth degree of ,aries on the first morning1 the moon must have been in the #gth degree of ,libra2 her mean daily motion of #ac would bring her to the #afth degree of ,scorpio three days later and to the last degree on the day following2 so even if we allow a deviation of a few degrees from the average1 she was just where she should have been on each occasion4 ,we have assumed for convenience that she became full and was opposite the sun just as she set on the first morning1 but this may have happened at any time during the previous night 7in the ,forest73 ,dante has not specified the hour1 and it is of no consequence1 since the indications of time by the moon must necessarily be vague4 ,the time of sunrise will still differ little from #f o'clock1 a week after the equinox4 ,in ,london it is a quarter of an hour earlier1 but the difference is less in ,italy1 and still less in the latitude of ,jerusalem4 ,besides the sun and moon1 two of the planets are mentioned as in a particular place among the stars4 ,venus1 before sunrise on the fourth morning1 is seen among the stars of ,pisces2#eba and she is also mentioned as a morning star before sunrise on the seventh day4#ebb ,saturn is in ,leo4 8,il petto del ,leone0#ebc may mean the western part of the ,lion1 the part which first rises and contains the head and breast1 or it may refer to the star ,regulus1 which is called by ,ptolemy and ,alfraganus 8,cor ,leonis40#ebd 8,sotto il petto0#ebe may mean the position of the planet as seen projected in the sky or a map1 that is1 a little south of this part of the constellation2 more probably1 perhaps1 ,dante is thinking of the supposed position of ,saturn's sphere below that of the stars4#ebf ---------------------------------------- -------------------------------- #eba ,purg4 i4 #ba4 #ebb ,purg4 xxvii4 #ie4 #ebc 8,the ,lion's breast40 ,par4 xxi4 #ad4 #ebd 8,the ,lion's ,heart40 #ebe 8,beneath the breast40 #ebf ,cf4 ,purg4 xxxii4 #ef1 #eg1 where the sun is spoken of as under another star4 ---------------------------------------- -------------------------------- ,mars is spoken of as having returned to his own ,lion a number of times3 8al suo ,leon 444 venne10#ebg but this does not necessarily imply that he was in that constellation at the time4 ,mercury and ,jupiter are not noted as seen anywhere in the sky1 nor does ,dante say in what constellation they were when he entered them with ,beatrice4 ,there are a number of pitfalls into which ,dante might have stumbled1 with this disposition of the skies1 and the change to the southern hemisphere2 and that he has avoided all is as clear a proof of his familiarity with astronomical phenomena as the positive evidence of his truthful1 consistent descriptions4 ,for instance1 he might very well have represented the cold planet ,saturn as actually aiding the cold moon in driving away the heat of the day during the night1 in ,purg4 xix4 #a-c1 instead of only saying 8talor da ,saturno20#ebh but if so1 this would have been inconsistent with the position of ,saturn in ,leo1 since ,leo was below the horizon when dawn was drawing near and ,pisces was rising4 ,again1 we have already mentioned that he evidently did not forget that it was autumn in the southern hemisphere4 ,he never suggests that it was spring in ,purgatory1 and in the passage quoted above1 where he describes sunrise at the ,march equinox1 saying that the sun then moves 8con miglior corso e con migliore stella10#ebi this happiest effect on the world is restricted to 8mortals10 who as he thought all dwelt in the northern hemisphere1 8surge ai mortali40#ecj ,i do not mean that the expression was used for this reason1 but it is an example of how instinctively he avoided mistakes into which any other author would almost certainly have fallen4 ---------------------------------------- -------------------------------- #ebg 8,to his ,lion has come40 ,par4 xvi4 #cg1 #ch4 #ebh 8,sometimes by ,saturn40 #ebi 8,with a better course and better star40 ,par4 i4 #dj4 #ecj 8,rises upon mortals40 ,par4 i4 #cg4 ---------------------------------------- -------------------------------- #f4 ,,the ,,assumed ,,date ,,of ,,the ,,vision4 ,even among ,dante enthusiasts there must be many who are astonished at the warmth of the controversy concerning the assumed date of his ,vision4 ,to know whether he feigned himself to have entered the ,inferno with ,virgil in ,march or in ,april1 in the year #acjj or in #acja1 really does not help us to appreciate the music of his verse nor the depth of his thought2 yet a wealth of learning and research has been poured out upon this problem1 and some commentators seem ready to defend their opinions with their lives1 if that would avail to convince their readers6 ,the date is indeed intimately connected with the narrative of the ,divine ,comedy1 since there are constant allusions to current events4 ,by choosing a year earlier than the time at which he was writing1 ,dante is able not only to tell the spirits what is passing on the earth they have left1 but to endow them with the power of prophesying to him events which are to come4#eca ,the peculiar interest of the problem for us just now is that astronomy has been called in to solve it4 ,we have seen that the positions and movements of the heavenly bodies are all consistent with one another in his poem1 but it is interesting to ask whether they are merely a consistent fiction or whether they correspond with facts4 ,did ,dante arrange his moon and planets according to his feeling for scenery and the convenience of his time references1 or did he take the positions as they really were at some particular date8 ,if so1 the full moon1 ,venus a morning star in ,pisces1 and ,saturn in ,leo1 all together near a spring equinox1 ought to help to fix that date4 ,the year which is almost universally accepted1 by the oldest as well as the most modern commentators1 is #acjj1 chiefly on the authority of ,inf4 xxi4 #aab-aad4 ,here ,malacoda says that yesterday 7the day of ,dante's entering the ,inferno7 it was #abff years since the earthquake which accompanied the ,crucifixion 7see p4 #cgj74 ,adding to this the #cd years which ,dante has told us he believed to have elapsed between the ,nativity and the ,crucifixion1#ecb we get #abff #cd #acjj4 ,and the day is either the ,church ,festival commemorating the ,crucifixion1 i4e4 ,good ,friday1 which in #acjj fell on ,april #h1 or ,march #be1 which was believed to be the actual anniversary4 ---------------------------------------- -------------------------------- #eca ,inf4 x4 #ajj-aje4 #ecb ,conv4 ,,iv4 xxiii4 #if-ih4 ---------------------------------------- -------------------------------- ,if this is the right interpretation of the passage1 we may say at once that ,dante's astronomical data are imaginary1 for the moon was not full on the night preceding either of these dates1 but on ,march #e1 and ,april #d3 ,saturn was indeed in ,leo1 but ,venus was so near the ,sun as to be invisible in ,march1 and began to appear as an evening star in ,taurus on about the #ith of ,april4 ,these positions were all carefully calculated by ,prof4 ,angelitti1 who is a professional astronomer as well as a ,dante scholar2 and he made the thrilling discovery that the positions agree wonderfully well for the year #acja6 ,in this year the moon was full on the early morning of the #beth of ,march2 ,venus entered ,pisces three days later1 and was a morning star1 near her greatest elongation west1 and very brilliant2 ,saturn was not only still in ,leo but was just three degrees west of ,regulus2 and ,mars was also in ,leo4 ,if the anniversary of the ,crucifixion means ,good ,friday1 the day would be ,march #ca in #acja1 and the moon would be wrong1 but ,march #be has some claims to be considered the more probable date4 ,a fixed calendar date is more appropriate to use for calculating an exact number of years than a changing festival1 which might rather be regarded as an 8ideal date40#ecc ,moreover1 ,march #be is suggested by the allusion to the ,creation in the opening ,canto2 this day was also the traditional date for the spring equinox1#ecd and it was one of the most important days in the year to ,florentines1 being their ,new ,year's ,day as well as ,lady ,day4 ---------------------------------------- -------------------------------- #ecc ,moore1 ,studies in ,dante iii4 p4 #adf4 #ecd ,see p4 #agg4 ---------------------------------------- -------------------------------- ,we know that the idea of writing his great work was in ,dante's mind even when he wrote the last words of the ,vita ,nuova1#ece and we need only suppose that he was thinking of it when he looked at the sky on the evening before ,lady ,day in #acja1 that he saw the full moon1 and the two bright planets ,mars and ,saturn making a striking asterism with ,regulus2 also that in the early dawn about the same time he rejoiced in the sight of ,venus veiling the ,fishes in the east4 ---------------------------------------- -------------------------------- #ece ,v4 ,n4 xliii4 #a-aa4 ---------------------------------------- -------------------------------- ,but is this attractive theory admissible8 ,can we take ,dante's words elsewhere as referring to the year #acja8 ,take first the one passage in which he explicitly states the day and year1 the words of ,malacoda quoted above4 ,this is usually taken to indicate the year #acjj1 as shown above 7p4 #daj71 but it is easy to interpret it another way--thus3 #acjj years had been completed since the ,nativity on the day ,dante entered the ,inferno4 ,now the year #a is not one year after the ,nativity1 but the year of the ,nativity itself2 hence the year #b is one year after1 the year #c two years after1 444 the year #acjj is #abii years after1 and the year #acja is #acjj years after4 ,the year #acjj was completed on ,march #be1ecf and the date then changed1 according to ,florentine usage1 to #acja4 7,it had already been called #acja for three months1 according to ,roman usage1 so fortunately for us1 there is no disagreement between the two calendars from this part of the year74 ---------------------------------------- -------------------------------- #ecf ,exactly at midday1 moreover1 according to one system then in vogue1 though it seems to have been more usual to begin the day at sunrise4 ---------------------------------------- -------------------------------- ,it must also be noted that in several old ,,mss41 considered authoritative by some of the very early commentators1 the passage reads3--8,mille dugent 'uno con sessanta sei40#ecg ,although it is impossible to believe that ,dante wrote such a faulty line1 this shows that some early copyist felt a difficulty either in accepting the date #acjj or in understanding how ,dante arrived at it by ,malacoda's computations4 ,this passage1 therefore1 is inconclusive for #acjj or #acja4 ---------------------------------------- -------------------------------- #ecg 8,a thousand two hundred and one1 added to sixty-six40 ---------------------------------------- -------------------------------- ,then there is the first line of the ,divina ,commedia 8,nel mezzo del cammin di nostra vita10#ech which is usually taken to mean that ,dante was in his #ceth year1 since in ,conv4 ,,iv4 xxiv4 #cj1 #ca1 and xxiii1 #hh-id1 he says that in normal natures the 8punto sommo10 the 8colmo10#eci of the ,arch of ,life is reached at this age4 ,but is it to be taken as indicating a precise year8 ,if so1 it points to one which has never been suggested for the ,vision1 so far as ,i know1 for in another passage of the ,convivio he says when speaking of his exile1 that he had lived in ,florence 8fino al colmo della mia vita10#edj and we know that the year of his exile was #acjb4 ,but if we look again at the discussion concerning the arch of human life1 we find that the whole period of 8gioventute10#eda which is from the #beth to the #deth year 8veramente colmo della nostra vita0#edb 7,conv4 ,,iv4 xxiv4 #bb1 #bc74 ,if1 nevertheless1 it is said that the 8mezzo del cammin di nostra vita0 means ,dante's #ceth year1 we must know the date of his birth with certainty before we can deduce the year at which he had reached this age4 ,and this is not quite easy4 ,this very line is used indifferently to show that he was born in #abfe because the date of the ,vision was #acjj1 or that the date was #acjj because he was born in #abfe6 ,no registers of births or baptisms were kept in those days4 ,most of the old biographers give #abfe for the date1 but not all1 and some of those who do betray ignorance or confusion in the matter3 ,boccaccio says the year #abfe1 when ,urban the ,fourth was ,pope1 yet ,urban we know died in #abfd2 ,lionardo ,bruni says 8#abfe1 a little after the return to ,florence of the ,guelfs1 who had been in exile by reason of the defeat of ,montaperti10 but this return was in ,september #abff6 ,dante himself says that his ancestors shared in this exile1#edc and as he also often refers to the fact that he was born in ,florence1#edd it is difficult to see how that could have been in #abfe4 ---------------------------------------- -------------------------------- #ech 8,midway in the journey of our life40 #eci 8,the highest point10 the 8summit40 #edj 8,until the summit of my life40 ,conv4 ,i4 iii4 #bd1 #be4 #eda 8,youth40 #edb 8,is in truth the summit of our life40 #edc ,farinata alludes to the two ,guelf banishments of #abdh and #abfj4 ,inf4 x4 #db-ej4 #edd ,conv4 ,i4 iii4 #bb-bd2 ,inf4 xxiii4 #id1 #ie1 etc4 ---------------------------------------- -------------------------------- ,again1 he says that there was a difference of less than #h months between the age of ,beatrice and himself 7she was #h years #d months old when he was nearly nine71#ede that she died in ,june #abij1edf and was then on the threshold of her 8second age10#edg that is in her #bdth year1 or #bc years old4 ,this gives #abfg for the year of her birth1 and he must have been born in the same or the preceeding year4 ,historical documents show that ,dante spoke in the ,council of the ,hundred in #abie1 and ,brunetto ,latini says no man could hold office in ,florence under thirty years of age2 but ,brunetto wrote in exile in ,france and died in #abij1 and in a translation from his original ,french into ,italian the age has been altered to #be1 so it is possible that the age had been lowered before #abie4edh ,there remains the story told by ,boccaccio1 that a ,ser ,piero di ,messer ,giardino 7a notary whose name occurs in legal documents of the time71 heard from ,dante himself shortly before his death that he had been #ef years old in the preceding ,may4 ,the date of his death is unanimously given as #acba1 so this story1 if we may accept it as authentic1 is one clear piece of evidence that ,dante was born in #abfe4 ---------------------------------------- -------------------------------- #ede ,v4 ,n4 ii4 #a-ae4 #edf ,v4 ,n4 xxx4 #d-ac4 #edg ,purg4 xxx4 #abd1 #abe2 ,cf4 ,conv4 ,,iv4 xxiv4 #aa-ac4 #edh ,imbriani3 ,quando nacque ,dante8 and ,che ,dante probabilissimamente nacque nei ,,mccclxvii4 ---------------------------------------- -------------------------------- ,on the whole1 we must say that it is doubtful whether the 8mezzo del cammin0 means ,dante's #ceth year1 and if it does1 we are not certain that he reached that age in #acjj4 ,another passage which is often quoted as clearly indicating the year of the ,jubilee1 #acjj1 for the assumed date of the ,vision is ,casella's explanation of his late arrival in ,purgatory4#edi ,dante is surprised to witness this arrival1 knowing that it is some time since his friend's death2 and ,casella replies that the ,angel of the ,passage had refused many times to bring him1 until three months ago1 when every one who wished to come had been graciously received4 ,this is believed to refer to the ,bull of ,pope ,boniface published at ,christmas #abii1 that is just three months before ,march #acjj4 ,but this ,bull gave no indulgence to the dead2 it was in favour of those who performed certain spiritual exercises in the churches of ,rome during the ,jubilee year4 ,on the other hand1 there was a ,bull published just a year later1 which was for the benefit of departed souls3 it extended the indulgences to those who had died on their way to ,rome1 or before the spiritual exercises were completed there4 ,we do not know when ,casella died1 but if it was some time in #acjj1 with his purpose of gaining the indulgence unfulfilled1 the ,angel's refusal at first1 and acceptance afterwards--after ,december #acjj--;and his arrival in ,purgatory in ,march #acja1 would be explained4 ,the fact that his arrival was still three months after the ,bull1 and that all without exception were welcomed by the ,angel1 are difficulties which apply to both interpretations4 ,but perhaps that just given is a little too clever4 ,it is most natural to consider the ,indulgence as the famous one of #acjj1 and to understand that in the ,jubilee year the way of salvation was made easier for all souls1 living or dead4#eej ---------------------------------------- -------------------------------- #edi ,purg4 ii4 #ia-ajc4 ---------------------------------------- -------------------------------- #eej ,for this point and a full discussion of the date1 especially from the astronomical data1 see ,angelitti's ,sulla ,data del ,viaggio ,dantesco1 and ,sull' anno della ,visione ,dantesca1 and ,moore's 8,the ,date assumed by ,dante for the ,vision of the #8,divina ,commedia1'0 ,studies in ,dante ,,iii4 ,if however these1 and many other passages quoted in the controversy1 are unconvincing1 the same cannot be said of ,cunizza's 8,questo centesim' anno40#eea ,prof4 ,angelitti's suggestion that she was reckoning by the ,easter year1 which was used in some parts of ,france and ,italy1 so that the date was still #acjj for her1 though for most ,italians it was #acja1 is too ingenious2 and it is hard to believe that she means 8this century year0 applying it to #acja4 ,though this might be correct1 it is clear that #acjj was regarded as the century year1 because the words 8centesimo anno0 occur in the ,bull of ,boniface ,,viii4 with reference to the year #acjj4 ,this then speaks strongly and clearly against our astronomical theory of #acja4 ---------------------------------------- -------------------------------- #eea 8,this hundredth year40 ,par4 ix4 #dj4 ---------------------------------------- -------------------------------- ,the historical events alluded to in the ,divine ,comedy are so often of unknown date to us1 that few of them help as much as might be expected4 ,judge ,nino's widow remarried on ,june #bd1 #acjj1 and as he speaks of her as having already put off her widow's weeds1#eeb this might indicate that we are in #acja1 but it is not conclusive1 since they would probably be discarded three months before she was actually the wife of another4 ,on the other hand1 ,can ,grande della ,scala1 who is said in a fourteenth century chronicle to have been born on ,march #i1 #abia1 is described as only nine years old4#eec ,dante might possibly have been mistaken by a year in the date of his birth1 but he cannot have been ignorant of the death of his friend ,guido ,cavalcanti4 ,the cry of anguish from ,guido's father will be remembered by all readers of the ,inferno1 after ,dante has spoken of his friend in the past tense3-- ---------------------------------------- -------------------------------- #eeb ,purg4 viii4 #gd4 #eec ,par4 xvii4 #hj1 #ha4 8,di subito drizzato grid3 ,come1 ,dicesti egli ebbe8 ,non viv' egli ancora8 ,non fiere gli occhi suoi lo dolce lome80#eed #eed 8,up starting suddenly he cried out3 ,how ,saidst thou8 #8he had8' ,is he not still alive8 ,does not the sweet light strike upon his eyes80 ,inf4 x4 #fg-fi4 ---------------------------------------- -------------------------------- ,and as ,dante hesitates a little1 ,cavalcante sinks back into his tomb of punishment1 and does not reappear4 ,before ,dante leaves the place1 feeling compunction1 he charges ,farinata to tell the father that his son is still among the living1 and that the sinister hesitation was due to another cause than he thought4 ,now it is beyond dispute that ,guido died in ,august #acjj1 for he was buried in the cemetery of ,st4 ,reparata in ,florence on ,august #bi1 #acjj1 according to official records still extant2#eee and ,dante had a share in banishing him amongst other exiles to the unhealthy place where he contracted the illness of which he died4 ,the year #acjj1 in which ,dante held the official position which obliged him to do this1 was burned into his mind1 as we see in his letter1 mentioned by ,lionardo ,bruni1 in which he says that all his misfortunes sprang from the time of his priorate4 ---------------------------------------- -------------------------------- #eee ,toynbee's ,dante ,dictionary1 under 8,cavalcanti40 ---------------------------------------- -------------------------------- ,how then can we believe that he here imagines himself speaking in the spring of #acja1 unless we assume that ,cavalcanti had really guessed the true cause of his hesitation1 and that what ,dante said afterwards was a kindly lie8 ,is this in character with his uncompromising1 even ruthless straightforwardness8 ,unless therefore some really satisfactory way of escape can be found from this incident and the 8centesim' anno0 ,i fear we must reluctantly abandon the theory of #acja1 championed so skilfully by ,angelitti and others1 and must agree with the majority that ,dante means us to understand the year #acjj4 ,the early commentators seem to have taken for granted that ,dante was correct in his astronomical data1 without taking any particular trouble to verify them4 ,jacopo della ,lana in commenting ,par4 xxi4 #ad says that in #acjj in the month of ,march ,saturn was in ,leo1 and was in the #hth degree of that sign2 and in order that we should know what was the disposition of the whole sky at that time he further informs us that ,jupiter was in ,aries in the #bdth degree1 and ,mars in ,pisces in the #aath degree1 that the sun was near the beginning of ,aries1 and ,venus in ,pisces 7these two are evidently taken simply from ,dante74 ,mercury was in ,virgo 7with the sun in ,aries6 in this case ,mercury would have been visible nearly the whole night71 and the moon in 4 ,here there is said to be a blank in all the ,,mss4 ,the moon was too much for ,della ,lana1 whether the difficulty was in finding her position or in reconciling it with that given by ,dante4 ,the ,ottimo and ,benvenuto da ,imola copy ,della ,lana with little change1 both giving the positions of ,saturn1 ,jupiter1 and ,mars in degree and sign1 but the sun only as near the beginning of ,aries1 ,venus in ,pisces1 and ,mercury in ,virgo4 7,it is astonishing that neither should have noticed this gross error47 ,benvenuto boldly adds that the moon was in ,libra1 doubtless because ,dante's description so required it at the beginning of his poem4 ,nor do these early commentators seem to feel any difficulty about the date on which the ,vision began4 ,from ,inf4 i4 #ch-dj they generally conclude that it was the day of the equinox1 which they say vaguely fell in the middle of ,march 8mezzo ,marzo10 and from ,inf4 xxi4 #aab-aad all except ,boccaccio 7who interprets ,march #be7 take it to be ,good ,friday4#eef ,no discrepancy seems to have been felt here3 they merely remark that in #acjj ,easter fell in ,march1 and more than two hundred years passed before anyone pointed out that this was wrong4 ---------------------------------------- -------------------------------- #eef ,moore1 ,studies in ,dante ,,iii4 p4 #adf4 ---------------------------------------- -------------------------------- ,at last a work appeared in #aeed1 called 8,del ,sito1 ,forma1 et ,misure dello ,inferno di ,dante10 in which the author1 ,giambullari1 remarked that according to astronomical calculations the ,paschal ,moon was not full on the night between ,thursday and ,good ,friday in #acjj1 but on the morning of ,april #eth4 ,this excited a good deal of interest1 and many theories have since been put forth to reconcile ,dante's astronomical data with the facts of the year #acjj4 ,dr4 ,moore thinks the date of entering the ,inferno was ,good ,friday1 ,april #h1 #acjj1 but that ,dante uses instead of the real moon the ecclesiastical moon1 which1 as we know1 is a conventional body revolving according to ,meton's cycle1 and sometimes appearing on tables as full two or three days before or after the real ,full ,moon4 ,dr4 ,moore finds that this ecclesiastical moon1 was full on ,april #g1 #acjj4eeg ,but would ,dante trouble about the ecclesiastical moon1 and would his readers know anything about it8 ,its only use was for determining ,easter1 and this was done for the people by the ,church4 ,the real moon was extremely important for astrologers1 for whose benefit ,tables and ,almanachs were chiefly drawn up2 the real moon was useful to everyone as light-giver and time recorder4 ,it is surely inconceivable that a ,florentine who wished to arrange a midnight festival1 or to start on a night-journey1 would consult a calendar to find out on what date the ecclesiastical moon would be full6 ,and the ecclesiastical moon does not alter the position of ,venus4 ---------------------------------------- -------------------------------- #eeg 8,the ,astronomy of ,dante10 in ,studies ,,iii41 and ,time ,references in the ,divina ,commedia4 ---------------------------------------- -------------------------------- ,according to another suggestion1 ,dante followed a tradition as to the position of all the 8seven planets0 at the ,creation1 and for this reason not only was his sun in ,aries1 but the moon full and opposite1 and ,venus in ,pisces4 ,venus is said to have this position in a picture of the ,creation in a ,church at ,san ,gemignano4#eeh ,compare also ,milton's moon at her creation3-- ---------------------------------------- -------------------------------- #eeh ,note on ,purg4 i4 #ai-ba in the 8,temple0 edition of ,dante4 8 444 ,less bright the moon1 ,but opposite in levelled west1 was set1 ,his mirror1 with full face borrowing her light ,from him40#eei #eei ,par4 ,lost vii4 #cge-cgh4 ---------------------------------------- -------------------------------- ,or again1 it is sometimes held that the day and all the celestial positions are ideal4 ,dante means us to understand that the first day of his ,vision was ,good ,friday1 but without troubling as to what day it fell on in #acjj2 the equinox and the full moon are naturally connected with ,good ,friday1 since they determine ,easter2 ,venus is connected with the idea of dawn1 and when the ,sun is in ,aries the morning star may well be in ,pisces4 ,either of these views might be correct1 and no one will dispute a poet's right to arrange his skies as he thinks fit1 if he is consistent with them1 as ,dante was4 ,but how did these positions1 if they are purely imaginary1 come to coincide exactly with the real positions of #acja8 ,if we examine the positions of #acja1 and accept nothing that is doubtful in ,dante's own words1 what does the coincidence amount to8 ,saturn was near ,regulus1 but he was also in the forepart of ,leo in #acjj1 and we are not sure that ,dante means more than this2 ,mars was in ,leo1 but we are not sure that ,dante wanted him there2#efj the moon was full on the morning of ,march #be1 but we are not sure whether ,dante means ,march #be or ,good ,friday4 ,venus was a morning star in ,pisces1 and this till very lately was the one astronomical fact incontestably in favour of #acja and against #acjj4 ---------------------------------------- -------------------------------- #efj ,see p4 #djg4 ---------------------------------------- -------------------------------- ,but in #aijh there was printed in ,florence1 for the first time1 a medival ,almanach1 which suggests so simple an explanation of this most striking coincidence that it seems to leave nothing more to be said for the #acja hypothesis4 ,this ,almanach1 which has been published under a title which perhaps takes things a little too much for granted--,almanach ,dantis ,aligherii--was compiled by a learned ,jew1 ,jacob ben ,machir ben ,tibbon1 who was born in ,marseilles about #abcf1 and died at the beginning of the fourteenth century4 ,using the ,toledan ,tables1 he constructed this so-called perpetual almanach1 which gives the positions of sun1 moon1 and planets1 at intervals of a few days for whole cycles of years4 ,each has a cycle of a different length1 that of ,venus for instance being #h years1 as on the ,babylonian tablets of ephemerides2 and at the end of each cycle nearly the same positions come over again4 ,it was written in ,hebrew1 and translated into ,latin by an unknown author1 and must have been popular1 since there were an immense number of ,latin ,,mss4 in the fourteenth century4 ,in the original1 all the cycles begin in #acja1 but in the ,latin they begin in #acjj1 except the cycles of ,venus and the sun1 which begin in #acja4 ,yet #acja is not written over the first column for ,venus1 but merely #a1 or nothing at all1 or even in some copies #acjj1 and in both the ,hebrew and ,latin prefaces the beginning of all the cycles is stated to be #acjj4efa ---------------------------------------- -------------------------------- #efa ,preface to ,almanach ,dantis ,aligherii1 ,boffito and ,melzi d' ,eril4 ---------------------------------------- -------------------------------- ,if1 therefore1 ,dante looked up the position of ,venus in this almanac1 he would very naturally take the #acja positions for #acjj1 and he would find that ,venus was in ,aquarius throughout ,march1 until the #bgth1 when she passed into the sign of ,pisces1 and therefore was a morning star during the whole month and also in ,april4 ,and he would find that ,saturn was in the #gth and #hth degrees of ,leo in ,march and ,april #acjj 7which was very nearly correct74#efb ---------------------------------------- -------------------------------- #efb ,it is important to observe that this suits the description of the 8,lion's breast0 better than the #bjth and #bast degrees 7,almanach positions for #acja71 if ,dante1 as usual in the ,divina ,commedia1 identifies the constellation with the sign4 ---------------------------------------- -------------------------------- ,it appears then that while certain expressions used in the ,divine ,comedy prove clearly that #acja is not the year assumed as the date of the ,vision1 the astronomical argument in favour of it is not strong enough to be convincing1 especially in the light of this recent discovery4 ,granting that #acjj was the year1 what was the day8 ,probably not ,march #be1 for the early commentators1 excepting only ,boccaccio in one passage1 are all in favour of ,good ,friday1 and ,dante might see in the ,almanac that the moon was not full on that date4 ,but neither was she full on the actual date of ,good ,friday1 which fell on ,april #h in #acjj2 moreover the sun was then so far advanced in ,aries that seven days later1 when ,dante describes it as a little past the equinox1 it would really have been in ,taurus4 ,the third and only possibility is to accept the theory that his moon and his day were ideal2 that is1 he simply assumed ,good ,friday and a full moon to occur together soon after the equinox1 with which both are so intimately associated4 ,the date of ,easter is not given in the old almanac1 and we have seen that the early commentators who knew that the equinox fell in 8mezzo ,marzo0#efc were content to accept ,easter as falling in that month also4 ,we must not forget the convenience of an equinox and a full moon for simplifying the time references also4 ---------------------------------------- -------------------------------- #efc ,the middle of ,march4 ---------------------------------------- -------------------------------- ,we conclude1 then1 that the year chosen by ,dante was #acjj 7as has been most generally believed71 and the day ,good ,friday1 which he assumes to have fallen about a week after the equinox1 and at a time of full moon4 ,saturn in his poem1 and also in fact1 was in ,leo2 ,venus was not actually a morning star1 nor in ,pisces1 but he may have been led to assign this position to her through an error in a contemporary almanac4 ,i must confess to a great feeling of disappointment in coming to the conclusion that ,prof4 ,angelitti's enticing theory must be rejected1 but a careful study of ,dante's own words1 and ,prof4 ,boffito's discovery of the 8,almanach perpetuum ad annum #acjj inchoatum0 seem to leave no other choice4 ,last ,april1#efd when helping to photograph ,halley's ,comet in beautiful early dawns1 this problem was much in my mind4 ,venus once more had the ,fishes in her train1 and oddly enough ,good ,friday had fallen on ,march #be6 ,i could not help wishing that these things had happened in #acjj as well as in #aiaj6 ---------------------------------------- -------------------------------- #efd ,this was written in #aiaj4 ---------------------------------------- -------------------------------- ,if in spite of all arguments to the contrary1 any readers are convinced that ,dante's celestial positions were taken from the real skies1 it remains to them to imagine that he saw them in ,march of #acja and wove them into the narrative of his poem1 although for some reason he adopted another date4 ,the following tables 7pp4 #dbe-bf7 summarize the foregoing pages4 ,it will be noted with what appropriate symbolism ,dante enters ,hell on the evening of ,good ,friday1 spends that night and the whole of ,saturday in the depths1 and rises out of them on ,easter ,day before the dawn4 ,for although he reaches ,earth's centre on ,saturday evening by ,jerusalem time1 the change of hemisphere there makes his time suddenly go back twelve hours1 so that it is again ,saturday morning1 and he spends the day and night of ,saturday 7,purgatory time7 in climbing to ,earth's surface4 ,,days ,,of ,,the ,,vision ,,and ,,positions ,,of ,,the ,,sun1 ,,moon1 ,,and ,,planets4 ,dante's ,jerusalem,purgatory ,positions of ,sun1 ,journey4 ,time4 ,time4 ,moon and ,planets ,references4 in ,zodiac4 ---------------------------------------- ------------------------ ,night ,moon full in ,libra1,inf4 xx4 #abg4 about #gth degree ,day ,i4 ,sun in ,aries1 ,inf4 i4 #ch-dj4 ,forest ,good about #gth degree ,friday 7#acjj7 ---------------------------------------- ------------------------ ,night ,inferno ,day ,,ii4 ,saturday ---------------------------------------- ------------------------ ,night ,day ,,iii4 ,saturday ,earth's ,day in ,interior 7,sunday7 ,purgatory ,easter ,night ,day ,day ,,iv4 ,venus in ,pisces ,purg4 i4 #ai-ba4 7,sund47 at dawn ,easter ,day in ,purgatory ,night ,moon in the middle ,purg4 ix4 #a-f4 of ,scorpio ---------------------------------------- ------------------------ ,day ,v4 7,mond47 ,night ,moon at end of ,scorpio or ,purgatory beginning of ,purg4 ,sagittarius xviii4 #gi-ha4 ,day ,,vi4 7,tues47 ,night ---------------------------------------- ------------------------ ,earthly ,day ,,vii4 ,sun in the middle ,par4 i4 #cg-dd2 ,paradise1 7,wed47 of ,aries x4 #g-cc2 planetary ,saturn in ,leo xxvii4 #hf1hg4 stellar spheres ---------------------------------------- ------------------------ ,primum ,day ,,viii4 ,par4 xxi4 ,mobile 7,thur47 #ac-ae4 and ,empyrean ,summary4 ,arguments for #acjj or #acja4 ,from ,expressions and ,incidents in the ,d4,c4 ,malacoda4 ,inconclusive3 method of reckoning uncertain4 ,inf4 xxi4 #aab-aad4 8,nel mezzo del ,inconclusive3 a precise year possibly not cammin40 indicated1 and date of ,dante's birth not ,inf4 i4 #a4 certainly known4 ,casella4 ,inconclusive3 may refer to ,bull of #abii1 ,purg4 ii4 #ih-ii4 but possibly of #acjj4 ,can ,grande4 ,for #acjj3 ,can ,grande #i years old in ,par4 xvii4 #hj1 #ha4 ,march #acjj4 ,cunizza4 ,for #acjj3 8questo centesim' anno0 can only ,par4 ix4 #dj4 mean #acjj4 ,nino's widow4 ,inconclusive3 might put off widow's weeds ,purg4 viii4 #gd4 before re-marriage4 ,guido ,cavalcanti4 ,for #acjj3 ,guido1 ,dante's intimate friend1 ,inf4 x4 #aaa4 died in ,august #acjj4 ,the ,astronomical ,data4 7,true ,equinox1 ,march #ab4 ,ecclesiastical1 ,march #ba4 ,traditional1 ,march #be74 ,in ,d4,c4 ,on ,good ,friday1 #acjj4 ,on ,march #be1 #acja4 ,,sun near ,day assumed to fall soon after,date of traditional ,,equinox4 equinox 7actually ,april #h47 equinox 7#ac days after true equinox74 ,,moon full on ,assumed full1 since ,easter ,full4 first day4 associated with equinox and full moon4 7,actually full ,march #e1 and ,april #d47 ,,venus in ,pisces ,supposed in ,pisces from error ,entered ,pisces on #dth day4 in contemporary almanac1 ,march #bg4 confounding #acja with #acjj4 ,,saturn 8on the ,in forepart of ,leo1 ,in ,leo1 #bast degree ,lion's breast40 #hth degree of the sign4 of the sign1 close to ,regulus4 ,,mars possibly ,not near ,leo4 ,in ,leo4 intended to be in ,leo4 ,early commentators understand ,good ,friday1 not ,march #be4 ,,vii4 ,,theoretical ,,and ,,speculative ,,astronomy4 8,thou shalt learn the burning nature of the pure clear sun1 thou shalt hear the wandering nature of the round-eyed moon1 and thou shalt learn of the surrounding heaven1 whence it arose1 and how ,necessity guiding it compelled it to hold fast the bounds of the stars40 ,parmenides4 #a4 ,,the ,,spheres4 ,dante's astronomical phenomena1 though they are just the same that are familiar 7or ought to be familiar7 to us1 have led us into some strange by-ways1 because they are so intimately connected with his works of imagination4 ,his astronomical theories1 by which these phenomena were explained1 will also take us into paths which are now seldom trodden by astronomers or others1 because medival astronomy was mingled with magic1 with metaphysics1 and with religion1 in a way which seems very strange to us4 ,the second treatise of the ,convivio has for its text the ,ode which is quoted in ,paradiso viii4 #cg1 8,voi che intendendo il terzo ciel movete40#efe ,when speaking of the literal meaning of this ,ode1 ,dante takes the occasion to discourse on the system of astronomy which he had learned1 and describes how all the apparent movements of the heavens are explained by postulating the existence of spheres and epicycles1 entering with special detail into the system of ,venus1 the third heaven2 and later on1 when expounding the allegorical meaning of the ,ode1 he draws an elaborate comparison between the spheres and the different branches of science and philosophy1 in which he incidentally gives his readers a good deal of information about the heavens4 ---------------------------------------- -------------------------------- #efe 8,oh ye whose intellectual ministry ,moves the third heaven40 7,carey74 ---------------------------------------- -------------------------------- ,from this interesting treatise1 therefore1 as well as from many scattered passages in all his works1 we learn what ,dante thought were the real movements of the heavenly bodies1 their dimensions1 their nature1 and the forces which move them2 and it forms a valuable commentary on the ,paradiso1 in reading which he supposes us to understand the elements of the ,ptolemaic system1 and the ideas of the philosophers and the ,fathers of the ,church concerning the organization of the ,universe4 ,of these ultimate truths concerning the heavens1 ,dante says1 very little can be known1 but the little which is within the reach of human reason1 gives more delight 7as ,aristotle says7 than the abundance and the certainty of other things easier to be understood4#eff ,this thought finds an echo in the ,paradiso1 where the poet reminds us of the beautiful order to be found throughout the universe1 and invites us to contemplate the skill of the architect as shown in the movements of the planets4#efg ---------------------------------------- -------------------------------- #eff ,conv4 ,,ii4 iii4 #h-ad4 #efg ,par4 x4 #a-ab4 ---------------------------------------- -------------------------------- ,dante knew that great men in ancient days had speculated on the possibility that it was ,earth1 and not the skies1 that moved in the diurnal period1 but the balance of authority was against them1 and they had been confuted by the ,master of those who ,,know1#efh that glorious philosopher to whom ,nature most fully revealed her secrets1#efi ,aristotle4 ,in ,treatise ,,iii4 of the ,convivio he gives a clear and concise account of the theory of ,philolaus1 and of what he understood to be the theory of ,plato4#egj ,in the former he seems to have been struck with the deduction that1 if ,fire were at the centre of the ,universe1 the real motion of fire on ,earth1 which to us appears always to ascend1 would in reality be a descent towards its own place at the centre4 ---------------------------------------- -------------------------------- #efh ,inf4 iv4 #aca4 #efi ,conv4 ,,iii4 v4 #ed-ef4 #egj ,conv4 ,,iii4 v4 #bi-eb4 ,see ,part ,i4 of this book ,pythagoras and his ,followers1 and ,plato1 for a description of their astronomical systems4 ---------------------------------------- -------------------------------- ,both these hypotheses he had evidently learned from ,aristotle's ,de ,clo1#ega and when thus presented they seem entirely fanciful2 so although ,dante had reverence for both ,pythagoras and ,plato it is not surprising that he rejected the systems of both4 ,he adds that it is not his intention to recount here the arguments by which ,aristotle confutes them and establishes the truth3 it is enough for his readers to know1 on so great an authority1 that the earth is fixed1 and does not revolve1 and is at the centre of the ,world4 ,dante has to confess reluctantly that ,aristotle made two mistakes in his astronomy3 he said that there were only eight spheres1 those of the seven planets1 and that of the stars1 8e che di fuori da esso non fosse altro alcuno20#egb also he placed the heaven of the sun immediately above that of the moon1 that is to say second in order1 counting from ,earth outward4 ,aristotle's loyal admirer hastens to add that these serious mistakes 8questa sua sentenza cos erronea0#egc are explicable and excusable because1 as ,aristotle himself shows in the ,metaphysics1 when he treated of astrology he was merely following the opinions of others4 ,that is to say1 he took his facts from others1 and they cannot all be depended upon1 but his philosophical deductions are his own1 and are never in error4 ,in the above question of the possible movements of ,earth1 we saw 7pp4 #aja-b7 that ,aristotle's arguments were almost entirely drawn from metaphysics4 ---------------------------------------- -------------------------------- #ega ,see ,part ,i4 8,aristotle40 #egb 8,and that outside the latter there was no other40 ,conv4 ,,ii4 iii4 #bd1 #be4 #egc 8,this entirely mistaken opinion of his40 ,ibid4 #bh4 ---------------------------------------- -------------------------------- ,there have been many opinions regarding the number and the positions of the spheres1 ,dante says1 but the truth about them has at length been found4 ,the scheme which he expounds is that of ,ptolemy1 modified by the ,arabs and adapted to the doctrines of the ,church by ,christian writers4 ,in the ,vita ,nuova he almost seems to imply that the nine moving spheres form an article of faith4 8,secondo ,tolommeo e secondo la ,cristiana verit1 nove siano li cieli che si muovono40#egd ---------------------------------------- -------------------------------- #egd 8,according to ,ptolemy and according to ,christian ,truth1 nine is the number of the moving heavens40 ,v4 ,n4 xxx4 #af-ah4 ---------------------------------------- -------------------------------- ,quoting from ,albertus ,magnus1 or ,averros1 he apparently credits ,ptolemy with the discovery of precession1 for he says that it was ,ptolemy who added a ninth sphere to the eight of ,aristotle1 because he perceived that otherwise the outer sphere would have a double movement1 and so he felt obliged to assume a sphere beyond the star sphere which should have only the one simple motion of the diurnal east to west revolution4 ,the period of this revolution 7the sidereal day7 ,dante gives as #bc hours and _/ths of an hour1 8grossamente assegnando10#ege i4e4 #bc hours #ef minutes1 which is the correct value ignoring the #d seconds4 ,we know that it was not ,ptolemy in fact who thought it necessary to add a ninth sphere2 he was not sufficiently interested in spheres1 since to him they were only mathematical abstractions3 but the ,arabs of ,baghdad noted that he had added another movement1 the discovery of ,hipparchus2 and they1 accepting the spheres as material instruments of celestial motions1 felt obliged to assume the existence of the ,primum ,mobile or #ith sphere4 ,that ,dante should believe the spheres to exist as actual entities was inevitable1 for his principal authorities1 ,greek1 ,arab1 and ,christian1 all taught this4 ,and there is abundant evidence that he did think of them thus4 ,he calls them bodies3--8omnia corpora10#egf 8questi corpi grandi10#egg 8cerchi corporai10#egh 8il maggior corpo10#egi etc4 ,they are transparent1 one sphere not obstructing the light from another2#ehj and composed of ther1 8questo etera tondo40#eha ,they have a certain thickness1 and would be visible if near enough1 for ,dante speaks of the inner margin of the ,primum ,mobile1 and says that it was too far above him for him to have seen it yet1 when he was in the ,star ,sphere4#ehb ---------------------------------------- -------------------------------- #ege 8,roughly speaking40 ,conv4 ,,ii4 iii4 #cf-dh4 #egf 8,all bodies40 ,ep4 x4 #dde4 #egg 8,these vast bodies40 ,par4 viii4 #ii4 #egh 8,material circles0 7here compared with the ,angels1 who are purely spiritual74 ,par4 xxviii4 #fd4 #egi 8,the greatest body40 ,par4 xxx4 #ci4 #ehj ,purg4 iii4 #bi1 #cj4 #eha 8,this rounded ether40 ,par4 xxii4 #acb4 #ehb ,par4 xxiii4 #aab-aag4 ---------------------------------------- -------------------------------- ,he gives the order of the eight heavens as in ,ptolemy1 and adds the ninth1 which is only perceived by the diurnal movement of which it is the cause2 and it is called by many the ,crystalline1 that is1 the diaphanous or completely transparent ,heaven4#ehc ,the order of these spheres has been discovered by observation and reasoning1 with the use of the principles of ,perspective1 ,arithmetic1 and ,geometry4 ,dante gives as an instance the experience of ,aristotle1 who with his own eyes saw the moon pass below ,mars1 and so hide it for some time2 and he mentions also how in eclipses it is evident that the moon is below the sun 7i4e4 nearer to us74#ehd ,to these nine spheres of the astronomers1 the ,catholic ,church1 8which cannot lie10 adds a tenth1 the ,empyrean ,heaven1 which means the heaven of flame or light1 and is the abode of the blessed spirits and of ,god ,himself4#ehe ,and here ,dante is able to give himself the pleasure of adding that ,aristotle seems to have been of this opinion also2 8,ed anco ,aristotile pare ci sentire1 a chi bene lo intende1 nel primo ,di ,cielo e ,mondo40#ehf ,he is no doubt alluding to what ,aristotle says about the existence beyond the finite universe4#ehg ,the whole passage is thus translated in the 8,temple0 ,dante3#ehh 8,nor is there any change of any of those things which are ranged above the outmost rotation1 but they are unchangeable and passionless1 enjoying the superlative existence1 and passing in absolute self-sufficiency their eternal life40 ---------------------------------------- -------------------------------- #ehf 8,and ,aristotle also1 to one who rightly understands him1 seems to mean the same thing1 in his first book of ,the ,heaven and the ,earth40 ,conv4 ,,ii4 iv4 #cb-cd4 #ehc ,conv4 ,,ii4 iv4 #a-ac4 #ehd ,conv4 ,,ii4 iii4 #eb-fe4 #ehe ,conv4 ,,ii4 iv4 #ac-af1 #cj-cb4 ,see also ,ep4 x4 #ddh-deb4 #ehg ,see p4 #ig4 #ehh ,the ,convivio of ,dante1 8,temple0 ,edition1 note on ,,ii4 iv4 ---------------------------------------- -------------------------------- ,the ninth sphere rotates on two poles1 which are absolutely fixed1 8fermi e fissi e non mutabile1 secondo alcuno rispetto10#ehi the eight within it have each two poles which are only relatively fixed 7for they move with the movement of the ,primum ,mobile71 and every sphere has an equator1 every point on which is equally distant from the two poles of rotation1 as anyone may see who will turn round an apple1 or any other spherical thing4 ,any point on the equator moves more quickly than any other point on the sphere1 and each part moves more quickly the nearer it is to the equator1 more slowly as it is far from it and nearer to the pole1 since all the circling is done in the same time1 and some parts have a greater1 and some a less distance to go1 according to their distance from the equator4 ,dante adds that the nearer any part of a heaven is to its equator1 the nobler it is compared with its poles1 for it has more movement1 and more actuality1 more life1 and more form1 and it touches more of the heaven just above1 and in consequence is more noble4#eij ---------------------------------------- -------------------------------- #ehi 8,firm and fixed and not moveable1 from any point of view40 ,conv4 ,,ii4 iv4 #ej1 #ea4 #eij ,conv4 ,,ii4 iv4 #fh-ge4 ---------------------------------------- -------------------------------- ,besides these ten heavens there are others which1 strictly speaking1 should be included in the number3 these are the little spheres which are called 8epicycles0 by astronomers1 and they also have equators and poles of rotation1 and are fixed on the large spheres1 or heavens4 ,dante does not enter into any particulars about these1 but only mentions 7as belonging specially to the subject in hand7 that the brilliant star of ,venus is carried 8on the back0 of an epicycle1 which is itself fixed on the back of the third ,heaven4#eia ,the apparent movement of ,venus is therefore compounded of no less than four movements3 that of her epicycle1 of her whole heaven 7the 8deferent0 ,dante does not name1 probably as introducing too technical a word71 of the west to east motion of the star sphere 7precession71 and the diurnal4 ,the epicycle of ,venus is also called in this treatise1 as we have already seen1 8quello suo cerchio che la fa parere serotina e mattutina1 secondo i due diversi tempi10#eib and the 8terzo epiciclo0#eic is referred to in ,par4 viii4 #c4 ---------------------------------------- -------------------------------- #eia ,conv4 ,,ii4 iv4 #gh-ajd4 #eib 8,that circle of hers which makes her appear as evening and morning star1 according to the two different periods40 ,conv4 ,,ii4 ii4 #c-e4 #eic 8,third epicycle40 ---------------------------------------- -------------------------------- ,a little further on in the same treatise1 ,dante tells us the periods in which all these nine spheres revolve4 ,it is an interesting passage1 and illustrates the poet's vivid way of bringing home to his own mind and those of his readers the effects of the different celestial motions4#eid ,the ninth sphere1 which is the ,crystalline or ,primum ,mobile1 causes by its daily revolution the daily revolution of all the other spheres1 which are within it2 it is1 as ,beatrice says1 8costui1 che tutto quanto rape l'altro universo seco40#eie ,therefore if we imagine it possible for the motion of this ,crystalline ,heaven to cease1 what will be the effect on the motions of the other heavens8 ,obviously their diurnal movement from east to west will cease1 and we shall only see them revolving1 each in its own period1 from west to east4 ,there will be no alternation of day and night1 or rather1 there will be one long day of six months1 and one long night of the same length1 in any given place all over the earth4 ,in the same way the moon will be invisible for half the month2 and all the planets will be invisible to us for half their periods2 and as ,dante believed only the known hemisphere of ,earth to be inhabited1 he could say that during one half of each period no one would see the planet at all4 ,he enumerates the half period in each case1 as follows3-- ---------------------------------------- -------------------------------- #eid ,conv4 ,,ii4 xv4 #acb-aee4 #eie 8,that one which sweeps the whole of the rest of the universe along with it40 ,par4 xxviii4 #gj1 #ga4 ---------------------------------------- -------------------------------- ,half ,period ,whole ,period given by ,alfraganus 8,planets40 7approximate7 7,el4 ,ast4 ch4 xvii47 given by ,dante4 ,years ,months ,days ,saturn #ad years #bi #e #h ,jupiter #f 0 #aa #aj #ad about4 ,mars about a year #a #aj #bb nearly4 ,sun #ahb days1 #ad hrs4 444 #cfe nearly4 about the same ,venus as the sun4 444 0 ,mercury 0 0 444 444 0 ,moon #ad days 444 7nearly7 #bg1 #g hrs4 7,paris edition1 #bi days1 #ab hrs47 ,if we compare these with the zodiacal periods given by ,alfraganus1 we see that ,dante has taken those of ,saturn1 ,jupiter1 and ,mars at the nearest whole number of years and halved them1 but with the sun he seems to have used that more exact value with which we have already seen that he was acquainted4 ,for to divide the #cfe days of ,alfraganus by #b would have given him exactly #ahb days #ae hours2 but dividing #cfe days #e hours1 and neglecting minutes gives #ahb days #ad hours4 ,the large oscillations of ,venus and ,mercury would make their periods of visibility very irregular1 but the mean period would be1 as ,dante says1 about the same as that of the sun4 ,he has made a slip with the moon1 for of course it is her sidereal period of #bg days #g hours which he should have taken1 giving a half period of less than #ad days1 whereas he has evidently taken the mean synodic period of #bi days #ab hours1 and ignored the hours4 ,all the printed editions of ,alfraganus give the sidereal period in this passage1 except the ,paris edition of #aedf2 but that gives the synodic1#eif so it doubtless appeared on some medival ,,mss4 ,dante must have had the misfortune to possess or consult one of these4 ---------------------------------------- -------------------------------- #eif ,toynbee1 8,dante's ,obligations to ,alfraganus in ,vita ,nuova and ,convivio10 in ,romania xxiv4 #ie4 ---------------------------------------- -------------------------------- ,as for the stars1 one third of their sphere would not yet have been seen4 ,this is not difficult to understand if we remember what the movement of the star sphere was supposed to be1 and how long it was since man had first begun to look upon it1 according to ,dante's chronology4 ,the movement which makes the equinoctial point shift its place among the stars was thought to be a movement of revolution of the whole star sphere1 and its rate to be one degree in a century2 the age of the world1 we learn from ,par4 xxvi4 #aah-abc1 was over sixty centuries when ,dante wrote4 ,for ,adam said that he had spent #icj years on ,earth and #dcjb in the ,limbo1 so that ,dante evidently counted #ebcb years from the ,creation to the ,crucifixion1 that is 7#ebcb-cc 7 #eaii to the beginning of our era at the birth of ,christ1 which is the date given by ,orosius2 adding #acjj years to this1 we find that the age of the world in ,dante's day was more than #fjjj years4 ,therefore the star sphere had revolved1 since the beginning of the world1 through more than #fj degrees4 ,the first inhabitants of this earth saw half the starry sky or #ahj1 and since then it had revolved through #fj1 which together is equal to #bdj2 therefore there would still remain #abj1 or one third of a revolution1 to be made to complete the whole #cfj1 and bring every part of the star sphere into view4 ,just before this passage ,dante had expressed the same idea in another way4 ,this movement proper to the star sphere1 he says1 will never have an end1 for the end of a revolution is to return to the same point2 and this heaven will never do so1 for since the beginning of the world it has turned through a little more than the sixth part of its whole revolution 7#fj of #cfj71 and we are already in the last age of the world1 and indeed are awaiting the consummation of the celestial motion4#eig ---------------------------------------- -------------------------------- #eig ,conv4 ,,ii4 xv4 #ajh-aah4 ---------------------------------------- -------------------------------- ,if the premises be granted1 the conclusions are correct4 ,as regards sun1 moon1 and planets1 they are correct even from the point of view of modern knowledge4 ,for if the diurnal motion 7that is ,earth's rotation7 were to cease1 while her other motions1 and those of the rest of the solar system remained as at present1 her motion round the sun would cause it to rise and set once in a year1 and the appearance of moon and planets also would be as described4 ,the vastly distant stars would have no appreciable motion1 save that caused by precession1 for if the earth revolved round the sun without turning on her axis1 the same stars would always remain on the meridian at any given place4 ,precession1 however1 would not have the result which ,dante supposed4 ,he considered it to be a rotation of the star sphere1 but we know that it is merely a nodding4 ,hence at any given place a star at the pole would describe1 in the course of centuries1 a small circle in the sky1 and those at the equator would move in short lines first north and then south1 while stars between would move in ellipses which become narrower as they approach the equator4 ,all round the horizon1 therefore1 there would be slight very slow changes1 bringing a few fresh stars into view1 and causing others to disappear4 ,the whole amount of the sky actually seen would vary but little1 even if the world should last much longer than ,dante expected4 ,dante evidently took his value of precession from ,alfraganus1 for he was one of the few ,arab astronomers who accepted ,ptolemy's erroneous figure4 ,in the ,paradiso1 as the poet mounts with ,beatrice from sphere to sphere he mentions the number of each one in its order4 ,the moon is 8la prima stella10#eih ,mercury 8il secondo regno10#eii ,venus 8il terzo ciel10#fjj the spirits met in the sun are 8la quarta famiglia10#fja ,mars is 8questa quinta soglia10#fjb and 8pi levato0#fjc than the last heaven1 ,jupiter is the 8stella sesta10#fjd ,saturn 8il settimo splendore40#fje ,the starry heaven is alluded to as 8la spera ottava40#fjf ,the ,primum ,mobile is 8il ciel velocissimo10#fjg 8il maggior corpo40#fjh ,the ,empyrean1 8il ciel ch' pura luce10#fji is called 8l'ultima spera10#faj but this has no limits and no movement1 and therefore no poles3-- ---------------------------------------- -------------------------------- #eih 8,the first star40 ,par4 ii4 #cj4 #eii 8,the second realm40 ,par4 v4 #ic4 #fjj 8,the third heaven40 ,par4 viii4 #cg4 #fja 8,the fourth family40 ,par4 x4 #di4 #fjb 8,the fifth threshold40 ,par4 xviii4 #bh4 #fjc 8,more lofty40 ,par4 xiv4 #he4 #fjd 8,sixth star40 ,par4 xviii4 #fh1 #fi4 #fje 8,the seventh splendour40 ,par4 xxi4 #ac4 #fjf 8,the eighth sphere40 ,par4 ii4 #fd4 #fjg 8,the swiftest heaven40 ,par4 xxvii4 #ii4 #fjh 8,the greatest body40 ,par4 xxx4 #ci4 ,compare ,v4 ,n4 xlii4 #dg4 8,oltre la spera che pi larga gira10 78beyond the sphere which has the largest circle740 #fji 8,the heaven of pure light40 ,par4 xxx4 #ci4 #faj 8,the last sphere40 ,par4 xxii4 #fb4 8 444 ,in quella sola ,e ogni parte l dove sempr' era2 ,perch non in loco1 e non s'impola40#faa #faa 8 444 ,within that one alone ,is every part where it has always been2 ,for it is not in space1 nor turns on poles40 ,par4 xxii4 #fe-fg4 7,longfellow47 ---------------------------------------- -------------------------------- ,in ,conv4 ,,ii4 iv4 #ce-ci it is thus described3-- 8,questo il sovrano edificio del mondo1 nel quale tutto il mondo s'inchiude2 e di fuori dal quale nulla 2 ed esso non in luogo1 ma formato fu solo nella ,prima ,mente1 la quale li ,greci dicono ,protonoe40#fab ---------------------------------------- -------------------------------- #fab 8,this is the sovereign edifice of the world1 in which all the world is enclosed1 and beyond which is naught2 and it exists not in space1 but received form only in the ,primal ,mind1 which the ,greeks call ,protonoe40 ,see also ,ep4 x4 #ddb-ddg4 ---------------------------------------- -------------------------------- ,we must remember1 however1 that the spheres are sometimes counted in the other direction1 from the outermost to the innermost or lowest1 and therefore this 8ultima spera0#fac is elsewhere spoken of as 8il primo cielo10#fad 8il primo giro10#fae 8clum primum40#faf ---------------------------------------- -------------------------------- #fac 8,last sphere40 #fad 8,the first heaven40 ,purg4 xxx4 #a4 #fae 8,the first circle40 ,par4 iv4 #cd4 #faf 8,first heaven40 ,qu4 iv4 #g4 ---------------------------------------- -------------------------------- #b4 ,,the ,,spheres ,,and ,,the ,,four ,,elements4 ,the pure region of the spheres1 8il paese sincero10 is immortal as the spirits themselves2#fag but below the lowest celestial sphere 78la celestial c'ha men salita0 ,par4 iv4 #ci7 all is mortal and transitory1 as the ,greeks and the ,latin poets had said4 ,this is expressed in the ,letter to ,can ,grande1 when ,dante contrasts the spheres 7clum7 and the elements1 and says3 8illud incorruptibile1 illa vero corruptibilia sunt40#fah ,it is also implied in ,virgil's address to ,beatrice3 ---------------------------------------- -------------------------------- #fag ,par4 vii4 #acj-acb compared with #fg1 #fh4 ,see also ,par4 i4 #fd and #gf4 #fah ,ep4 x4 #dce-dcg4 ---------------------------------------- -------------------------------- 8,o donna di virt1 sola per cui ,l'umana specie eccede ogni contento ,da quel ciel che ha minor' li cerchi sui40#fai ---------------------------------------- -------------------------------- #fai 8,o ,lady of ,virtue1 thou alone through whom ,the human race exceedeth all contained ,within the heaven that has the lesser circles40 ,inf4 ii4 #gf-gh4 7,longfellow74 ---------------------------------------- -------------------------------- ,it is only through the spiritual teaching which ,beatrice symbolizes that the human race can rise above all that is comprised within the heaven of the smallest sphere4 ,and it is taught by ,beatrice herself when1 in the heaven of ,mercury1 she discourses on the mysteries of the creation and redemption4 ,the angels1 the souls of men1 and the spheres1 were created directly by ,god1 she says1 and are therefore immortal1 but the elements1 water1 fire1 air1 earth1 and all things that are formed out of them1 also the souls or living principles of all animals and plants1 were created through intermediate instruments and are mortal4 ,these intermediate instruments are the heavenly bodies4 ,pure or inchoate matter was created at the beginning by ,god1 and a power infused into the stars to give it form4#fbj ---------------------------------------- -------------------------------- #fbj ,par4 vii4 #abd-adc4 ,compare with ,plato's account of the creation of living beings 7,part ,i41 ,plato74 ---------------------------------------- -------------------------------- ,dante follows the classics and agrees with his contemporaries in arranging the four elements in four spheres1 which are below the celestial spheres4 ,the sphere of ,fire is immediately within that of the moon1 below this comes ,air1 then ,water1 and lastly the solid sphere of ,earth4 ,the contrast between ,fire which constantly tends to rise towards the moon1 and ,earth which sinks towards the centre of the universe1 is a favourite thought with him2#fba and lightning striking the earth is described as fleeing its proper place4#fbb ,aristotle seems to have regarded the four elements as flowing into one another1 so that these lowly spheres beneath the moon were not sharply divided1 but his medival disciples1 following the ,greek idea to its logical conclusion1 conceived them with boundaries as definite as those of the celestial spheres4 8,exhalations0 could pass from one to another1 but each particle of every element tended always to revert to its own place1 which was distinct from the others4 ---------------------------------------- -------------------------------- #fba ,par4 i4 #aae1 #aag2 ,de ,mon4 ,i4 xv4 #ch-da2 and ,,iii4 vii4 #cj1 #ca1 etc4 #fbb ,par4 i4 #ib1 #acj-acd4 ---------------------------------------- -------------------------------- ,and here they encountered a serious difficulty4 ,if the sphere of water is naturally higher than that of earth1 how comes it that in one quarter of the globe land rises above the ocean8 ,it was recognised as necessary that this should happen in some part of the world1 in order for an opportunity to be given for the elements to combine and to form all those substances and all those living creatures1 including man1 for which this earth was prepared2 it was also agreed that the celestial spheres were the agency by which the ,creator had first chosen to 8let the dry land appear10 and by which it was maintained above the ocean2 but the exact nature of this force and the way in which it acted was a question sometimes discussed4 ,albertus ,magnus was of opinion that the rays of the sun and the stars1 which had more power in the temperate and tropic zones than in the arctic1 had here dried up the ocean1 and he quotes ,albumassar's statement that this proves the existence of land on the southern side of the equator also4 ,ristoro1 on the other hand1 believed that the waters had been drawn up and rolled back from the habitable earth1 and he attributes the elevating force to the stars of the north1 bringing in his favourite theory that in this hemisphere they are far more numerous1 and the constellations1 from their upright position1 are far more powerful than in the south4 ,he compares this lifting force of the stars to the attractive power of a magnet over iron1 and argues that it must be the waters which are drawn away from the earth1 not the earth which is lifted above the water1 because the starry influence in its downward course would meet first the sphere of water1 and moreover it is lighter and easier to move than ,earth4 ,he also thinks that the presence of springs on mountain tops is to be explained by the fact that the ocean is preserved at a higher level1 hence water percolating through the porous land1 as through a sponge1 is forced up to its utmost height4 ,it does not seem as if ,dante had paid much attention to this problem when he was writing the ,convivio1 for although he calls the habitable part of the earth 8the uncovered land10 8la terra discoperta0 7,conv4 ,,iii4 v4 #gc71 he speaks of ,earth and ocean as if they formed a globe together1 8,questa terra 444 col mare centro del cielo10#fbc in the manner of ,alfraganus1 8,inter sapientes convenit1 terram un cum aqua globosam esse40#fbd ,but if we may believe that ,dante is the author of the ,qustio de ,aqua et ,terra--a belief shared by many experts--he became greatly interested in the problem later on4 ,according to the introduction and the final colophon1 he attended a discussion on the subject and joined in it himself1 when in ,mantua1 and afterwards in ,verona less than two years before his death he wrote and read in public a ,latin treatise in which his arguments and conclusions are set forth4 ---------------------------------------- -------------------------------- #fbc 8,this earth1 together with the sea1 is the centre of heaven40 7,conv4 ,,iii4 v4 #fc-fe47 #fbd 8,it is agreed among learned men that earth and water together form a globe40 7,el4 ,ast4 iii474 ---------------------------------------- -------------------------------- ,he seems to have had in mind ,ristoro's book1 and while refuting some of the conclusions agrees with others4 ,as a thirteenth century scholar he admits1 as a matter of course1 that the centre of the earth is the centre of the ,universe and the goal towards which all heavy things tend2 that earth as the heaviest element ought to be everywhere nearest this centre1 while water ought to occupy the nobler place above it1 that is1 nearer to the most noble sphere of all which envelops all the others 7the ,empyrean74 ,he also reasons1 in true ,dantesque and true medival fashion that there must be some place in the universe where all the elements may meet and mingle so that all potential forms of matter may be realized2 otherwise the ,mover of heaven1 in whom all these forms 7,plato's ,ideas7 actually exist1 would fail to give complete expression to his goodness1 which is impossible4#fbe ---------------------------------------- -------------------------------- #fbe ,qu4 xviii4 #bh-ed4 ,this may be compared with ,par4 xxix4 #ac-ah4 ---------------------------------------- -------------------------------- ,the author of the ,qustio denies1 however1 that this was accomplished by the removal of part of the sphere of water from the underlying earth4 ,the ocean cannot have been drawn away and heaped up1 he says1 for water would always flow down again1 being fluid and naturally seeking its own level2 nor can the sphere of water be eccentric to that of ,earth so that the latter emerges from it in one part4 ,the reason for this is interesting since it implies a curious and apparently novel theory of gravity4 ,aristotle's theory was that all heavy things tend by a natural law towards the centre of the universe1 and therefore necessarily range themselves in spheres round it2 the writer might therefore have made short work of ,water's eccentric sphere by stating briefly that it could not exist2 instead of this1 however1 he suggests a new law of gravity1 apparently invented on the spur of the moment1 according to which everything which has weight tends towards the centre of its own circumference4 ,if then earth and water had two separate centres1 they would fall naturally in different directions1 or as he puts it 8to different downs40 ,yet we know that the law of gravity is the same for both1 and therefore their spheres must be concentric4 ,the centre of the universe must be also the centre of the sea4#fbf ,it had apparently been urged 7perhaps in the discussion at ,mantua7 that since water follows the moon in the tides1 its sphere may also imitate hers in being eccentric1 but although ,dante takes for granted that a connection between moon and tides is proved 7and indeed it had been noted by the ,greeks71#fbg he replies that imitation in one particular need not imply imitation in all4 ,again1 if the sphere of earth emerged from the sphere of water in the way proposed1 the outline of the emergent earth must be circular1 instead of which it is that of a half-moon1 or nearly so1 its width from east to west being much greater than its length from north to south4 ---------------------------------------- -------------------------------- #fbf ,qu4 xv4 #aj1 #aa4 #fbg ,see p4 #acd4 ---------------------------------------- -------------------------------- ,dante has been blamed for assigning this shape to the emergent earth1 but the comparison of ,earth's habitable quadrant with the illuminated quadrant of the moon is perfectly just1 as we saw with ,ristoro1#fbh from whom ,dante is perhaps quoting here4 ,the qualifying 8vel quasi0#fbi is added because the truly habitable regions did not extend over the whole quadrant1 but stopped short at the arctic circle4 ---------------------------------------- -------------------------------- #fbh ,see p4 #bdg4 #fbi 8,or nearly40 ,qu4 xix4 #fa-fc4 ---------------------------------------- -------------------------------- ,the existence of springs on mountain tops is explained by the fact that water rises thither not in the form of water but of vapour4 ,another upholder of ,ristoro's theory that ,water was rolled away from ,earth seems to have brought forward as evidence that sailors can see distant land from the mast which is invisible from the deck1 and that therefore it evidently lies below the ocean2 but this is confuted by the true and well known explanation that it is the convex shape of the sea which hides the distant land4 ,our author adds to his other arguments1 in the curiously casual way so characteristic of his age1 the ordinary observation which would be the first to occur to us1 and quite sufficient in itself1 viz4 that instead of seeing a great wall of ocean rising above our sea-coasts1 we invariably see the coast rising above the sea4 ,his own idea is that though the sphere of ,water in general rises above ,earth1 in one part of the northern hemisphere ,earth has been drawn up above the ocean4 ,earth must be subject to an uplifting influence1 as well as to the downward drag of gravity1 just as man is susceptible to the influence of reason as well as to the sway of his lower passions4 ,this uplifting influence is not inherent in ,earth herself1 an upward impulse would be contrary to her own nature2 nor can it be in water1 or air1 or fire1 since all these are homogeneous bodies1 and their virtue is evenly distributed1 so that they could not cause a local and partial effect4 ,it must be therefore in one of the heavens1 and it remains for us to enquire which4 ,it cannot be in the heaven of the moon1 for in the moon herself resides whatever influence comes from her sphere2#fcj and she goes as far south of the equator as she does north3 therefore she would raise land beyond the equator as well as on this side1 but this is not so4 ---------------------------------------- -------------------------------- #fcj ,compare with ,conv4 ,,ii4 vii4 #hh-ajj1 where the poet says that the influence from each sphere comes on the rays of the planet in that sphere1 also ,de ,mon4 ,,iii4 iv4 #aci1 #adj4 ---------------------------------------- -------------------------------- ,then follows a passage of which commentators can make nothing as it stands3-- 8,nec valet dicere quod illa declinatio non potuit esse propter magis appropinquare terr per excentricitatem2 quia si hc virtus elevandi fuisset in luna1 7quum agentia propinquiora virtuosius operentur7 magis elevasset ibi quam hic40#fca ---------------------------------------- -------------------------------- #fca 8,nor does it avail anything to say that that declination could not take place because of approaching nearer the earth through eccentricity2 for if this elevating virtue were in the moon1 since agents act the more powerfully the nearer they are1 she would elevate there rather than here40 ,qu4 xx4 #fe-ga4 ---------------------------------------- -------------------------------- ,mr4 ,wicksteed suggests reading 8elevatio0 instead of 8declinatio10 and apparently deletes the 8non10#fcb and ,dr4 ,moore seems to read the same way1#fcc for both agree in interpreting as follows3--the author is stating an argument that the elevation of land 7in only one hemisphere7 might be due to the moon's coming nearer to ,earth in one part of her orbit1 owing to its eccentricity2 to which he replies that if that were the cause the elevation would be greater in the south than here in the north1 because the moon is nearer to the earth when she goes south4 ---------------------------------------- -------------------------------- #fcb ,note on this passage in 8,temple0 ,dante4 #fcc ,studies in ,dante1 ii4 p4 #cci4 ---------------------------------------- -------------------------------- ,this is supposed to imply a belief that the moon is always in perigee#fcd when south of the equator1 whereas the fact that her perigee revolves all round the zodiac was as well known to ,ptolemy and ,alfraganus as it is to modern astronomers4 ,the interpretation therefore convicts the author of the ,qustio of so serious and inexplicable a blunder that these commentators find themselves obliged to consider it as evidence either that it was not written by ,dante1 or that his knowledge of astronomy was much less extensive than has been supposed4 ,it is suggested that there may have been a popular fallacy in his time that the moon was like the sun in this respect--although to know that the sun has a perigee1 and that it is situated in the south1 requires some acquaintance with astronomy6 ,however1 ,dr4 ,moore has searched ,alfraganus and other works in vain to find a suggestion of this kind4 ---------------------------------------- -------------------------------- #fcd ,nearest ,earth4 ---------------------------------------- -------------------------------- ,illustration3 ,fig4 #eb4 ,the moon's epicycle and deferent4 7,the dotted line represents the southern half of the deferent74 ,yet an explanation and a source of this statement is not far to seek1 and instead of proving ignorance it indicates that the author of the ,qustio knew his ,alfraganus well4 ,the passage is evidently slightly corrupt1 but the clue to its meaning lies in the word 8eccentricity40 ,in two other places of the ,qustio the moon's eccentric 8orbis0 is alluded to1#fce but if we translate this as 8orbit0 we shall be introducing modern ideas which meant nothing to ,dante or his contemporaries4 ,according to ,alfraganus and ,ptolemy the moon's orb or sphere#fcf was eccentric1 but this was not the main cause of her varying distance from ,earth4 ,it was the revolution of her epicycle round its centre ,c1 which caused her to move continually from apogee ,m to perigee ,p2 and as the whole epicycle was meanwhile revolving on the deferent round ,c1 and these two periods were not quite equal1 the moon was as often in the perigee of her epicycle when it was south as when it was north4 ,but besides this1 the deferent1 being eccentric to ,earth1 had also a perigee and apogee2 and ,alfraganus says that the perigee of the eccentric is always in the south4 8,saturnus1 ,jupiter1 atque ,mars eccentricorum suorum absidas summas et imas habent declinatas a zodiaco1 illas ad boream1 hasce ad austrum1 secundum eandem semper deflexus mensuram3 quedadmodum res in ,luna obtinet40#fcg ---------------------------------------- -------------------------------- #fce ,qu4 vii4 #d1 #f1 and xxiii4 #eb4 #fcf 8,orbis0 and 8sphra0 are used indifferently by ,alfraganus to indicate the celestial spheres3 thus1 in ch4 xii4 he says 8,orbes1 qui stellarum omnes motus complectantur1 numero esse octo10 and on the next page1 8unamquamque harum sphrarum octo40 #fcg 8,the upper and lower apsides of the eccentrics of ,saturn1 ,jupiter1 and ,mars1 have a certain declination from the zodiac1 the former to the north1 the latter to the south1 the amount always remaining constant3 and it is just the same with the moon40 ,el4 ,ast4 xviii4 par4 #f4 ---------------------------------------- -------------------------------- ,the upper and lower apsides are defined in chapter xii4 as the positions of apogee and perigee respectively4#fch ,in this quotation the word 8declinatas0 also supplies us with the meaning of ,dante's 8declinatio10 which need not be changed for 8elevatio40 ,he is using it in the astronomical sense of position north or south1 like ,alfraganus and modern astronomers1 and it refers here to the 8declinet0 of five lines earlier4 8,luna 444 tantum declinet per zodiacum ab quinoctiali versus polum antarcticum quantum versus arcticum40#fci ---------------------------------------- -------------------------------- #fch ,in the edition of ,golius ch4 vii4 par4 #e1 the position of greatest distance is called the perigee1 of least the apogee1 but this mistake is corrected in the next paragraph4 #fci 8,the moon's declination in the zodiac from the equator towards the south pole is as great as towards the north40 ,qu4 xx4 #fa-fc4 ---------------------------------------- -------------------------------- ,it is only necessary to delete 8quod0 and 8non potuit10 and the whole passage becomes clear and1 from the point of view of medival astronomy1 correct4 ,the author has shown that the moon cannot be supposed to exert any preponderating influence in the northern hemisphere1 because her declination south is equal to that in the north4 ,nor is it of any use1 he adds1 to say that this declination 7south7 results from her approaching the earth more nearly on her eccentric orb 7see diagram72#fdj for 7although this does imply an unequal influence7 if the elevating influence came from the moon1 it would act more powerfully in the south than here in the north1 since the nearer an agent is the more powerfully it acts4 ,he goes on to say that the same reasoning rules out the planetary spheres1 and here ,alfraganus still supports him1 for ,saturn1 ,jupiter1 and ,mars are said to have the perigees of their eccentrics in the south1 just like the moon1 while those of ,venus and ,mercury are continually changing4#fda ---------------------------------------- -------------------------------- #fdj ,the deferent was the equator of her orb or sphere4 #fda ,ristoro also defines apogee and perigee 78auge0 and 8opposito d'auge07 as effects of movements on an epicycle1 and says that the deferent is 8declined0 from the ecliptic 78declinato della via del sole107 part being north and part south1 but he does not say whether its perigee is north or south4 ,comp4 del ,mondo4 ,i4 xii4 xiv41 and ,,iii4 vii4 ---------------------------------------- -------------------------------- ,as for the ,primum ,mobile1 or ninth sphere1 it is uniform throughout1 and consequently quite uniform in virtue1 therefore there is no reason why it should elevate land here rather than elsewhere4 ,since1 then1 there are no more moving bodies except the star sphere1 or eighth heaven1 it must be from this that the lifting power proceeds4 ,and it is specially adapted to exercise such an influence since it contains a number of stars1 all of which have different 8virtues40 ,without repeating ,ristoro's nave assertions about the greater number and the upright positions of the northern constellations1 our author bids us remark that star differs from star1 constellation from constellation1 and that their influences are also diverse1 so that those in the north have different virtues from those in the south4 ,the lifting virtue which raises the land must reside in those stars which are between the equator and #fg north1 since those are above the habitable earth2 but we do not know the nature of the force they exercise1 whether it attracts the land as a magnet attracts iron1 or forces it up by generating underground vapours1 such as have raised some mountains 7,aristotle had said in his ,meteorologica that volcanic hills were formed by pent-up winds beneath them74 ,after so elaborate a search for a power capable of raising land only in the north and not in the south1 we naturally inquire why in the east and not in the west8 ,but to this we only receive the reply that there was not enough material to go round1 and that we must not ask presumptuous questions4 ,let us seek to approach divine and immortal things as nearly as is possible to human nature1 but leave those which are too high for us4 ,this somewhat lengthy description of the contents of the ,qustio has been given because1 even if it is not ,dante's work1 it illustrates well the current ideas concerning the ,cosmos1 its form and forces4 ,so many of the ideas1 however1 and even the expressions find parallels in the unquestioned writings of ,dante1 that the internal evidence for its genuineness is strong4#fdb ---------------------------------------- -------------------------------- #fdb ,for a thorough discussion of this question see ,moore's ,studies in ,dante ii4 pp4 #cjc-cgd4 ---------------------------------------- -------------------------------- ,in his poems ,dante is faithful to his own descriptions of the universe in prose1 and in the visionary journey of the ,divine ,comedy he passes successively through all the spheres which are enumerated in the ,convivio and the ,qustio4 ,the central sphere of earth1 the lowest of all the elements1 8il suggetto dei vostri elementi10#fdc is completely traversed1 from side to side1 and on the further side is seen the vast sphere of ocean which envelopes three-quarters of the earth4 ,the ,mountain which the poet has placed here 7his only innovation7 rises out of the water towards the heavens higher than any other1 8inverso il ciel pi alto si dislaga10#fdd and in climbing it he reaches that region in the sphere of air into which no cold exhalations can rise from earth or sea1 neither the 8secco vapor0#fde which causes wind and earthquake1 nor the 8esalazion dell' aqua0#fdf from which are formed rain and hail1 cloud and dew4 ,hot exhalations ascend to the sphere of fire1 there to become meteors or comets 7see p4 #ajc72 but the cold vapours rising as high as they can towards the sun which draws them up 78retro il calor0#fdg71 are unable to ascend beyond the ,gate of ,purgatory4#fdh ,therefore ,purgatory is exempt from all changes except those caused by that which heaven receives from itself into itself4 ,this was ingeniously conjectured by ,venturi to be light1 since there is change of day and night in ,purgatory2 but from the context it seems clear that human souls are meant4 ,souls come forth from their ,creator1 whose special abode is the heaven of heavens1 and return thither after purification4 ,and it was the rising of the purified soul of ,statius1 ready to return to heaven1 which had been the cause of that trembling of the ,mountain of which he is here speaking4 ---------------------------------------- -------------------------------- #fdc 8,the foundation of your elements40 ,par4 xxix4 #ea4 #fdd 8,rises highest towards heaven out of the sea40 ,purg4 iii4 #ae4 #fde 8,dry vapour40 #fdf 8,exhalations from the water40 #fdg 8,behind i4e4 following the heat40 #fdh ,purg4 xxviii4 #ig-ii and xxi4 #eb-ec4 ,the gate is meant by 8i tre gradi0 78the three steps071 and 8ove si serra0 78where it is locked074 ,see ,purg4 ix4 #gf1 #ajf-ajh4 ---------------------------------------- -------------------------------- ,after learning this1 ,dante is surprised to find1 on the summit of the ,mountain1 that his brows are caressed by a gentle breeze which comes from the east and bends all the trees of the ,forest in one direction4 ,matilda tells him that it is true no atmospheric changes are felt on this ,mountain1 and it was for this that it was made to rise so high1 so that man in the ,garden of ,eden1 on the top of the ,mountain1 should be untroubled by the disturbances which occur lower down3 what he feels now is no fluctuating wind4 ,on this lofty mountain1 remote from any other land in the midst of the hemisphere of sea1 he feels for the first time the revolution of the atmosphere uninterruptedly following the movement of the celestial spheres4 ,the idea that ,eden was on a lofty mountain1 secure from stormy weather1 and inaccessible to fallen man1 was a familiar one with medival writers3 it was sometimes located on ,adam's ,peak in ,ceylon1 and ,bede thought it might rise as high as the moon1 but ,albertus ,magnus says this was only meant figuratively4 ,but the connection with ,purgatory1 and the thought that here the movement of the heavens might be felt as a soft breeze1 is1 so far as ,i know1 all ,dante's own4 ,in all the ,divine ,comedy there is no more beautiful allegory than this4 ,man in the age of innocence1 man to-day when purified from sin1 is already partly in heaven1 though he still walks the earth4 ,and like many another allegory of ,dante's1 it follows naturally from the science of his day4 ,aristotle had said that the upper air 8flows in a circle1 because it is drawn along with the circulation of the ,whole10 and ,aquinas3-- 8,thus the air which exceeds the greatest altitude of the mountains flows round1 but the air which is contained within the altitude of the mountains is impeded from this flow by the immoveable parts of ,earth40 ,purg4 xxviii4 #ajc-ajh is almost a poetical paraphrase of this3-- 8 444 ,in circuito tutto quanto ,l'aer si volge con la prima volta1 ,se non gli rotto il cerchio d'alcun canto3 ,in questa altezza1 che tutta disciolta ,nell' aer vivo1 tal moto percote ,e fa sonar la selva1 perch ' folto40#fdi ---------------------------------------- -------------------------------- #fdi 8 444 ,the universal atmosphere ,turns in a circuit with the primal motion1 ,unless the circle is broken on some side3 ,upon this height1 that all is disengaged ,in living ether1 doth this motion strike1 ,and make the forest sound1 for it is dense40 7,longfellow74 ---------------------------------------- -------------------------------- ,the whole body of the air1 everywhere in the world1 is turning with the ,first ,revolution 7the ,primum ,mobile71 wherever it is not interrupted by any obstruction 7of hills etc472 and as at this height the ,mountain is altogether free and open to the pure air1 this motion strikes the thick forest and makes it murmur4#fej ---------------------------------------- -------------------------------- #fej ,scartazzini takes the passage as referring to ,eden only1 and interprets that all the air here is moving evenly and noiselessly unless it meets with any obstacle such as this forest1 when a murmuring sound results4 ---------------------------------------- -------------------------------- ,from this region of pure air1 ,dante rises with ,beatrice through the sphere of ,fire1 into which already in a dream he had been rapt1 on the first night in ,purgatory1 by the ,eagle with golden feathers1 when the burning heat of the dream-fire roused him from his sleep4#fea ,now he feels no heat1 but is amazed at the vast extent of light1 greater than any river or lake ever seen on earth1 and at the same moment he begins to hear the music of the eternal spheres1#feb for he is approaching the heaven of the moon4 ,in each one he hears it until the seventh is reached1 but here1 in pity for his mortal senses1 which are not yet strong enough to bear so much divine beauty1 not only does ,beatrice forbear to smile1 but the sweet symphonies of heaven are silent4#fec ---------------------------------------- -------------------------------- #fea ,purg4 ix4 #cj-cc4 #feb ,par4 i4 #gf-ha4 #fec ,par4 xxi4 #eh-fc4 ---------------------------------------- -------------------------------- ,did ,dante then1 in spite of ,aristotle1 believe in the music of the spheres8 ,perhaps the fact that only the ,commedia1 of all his works1 makes mention of it indicates that he only thought of it as a poetical fiction1 an allegory8 ,yet it was fully believed in by many in his day1 although opinions varied greatly as to what note each planet sang4 ,the favourite idea among ,greek and ,latin writers seems to have been that the notes made up a musical scale1 the lowest sphere sounding forth the lowest note1 and the star sphere its octave2 but others thought that only the seven planets took part in the harmony1 corresponding with the seven strings of the lyre3 the moon being at the shortest distance from ,earth1 was the shortest string and gave the highest note1 ,saturn was the longest and gave the deepest4 ,our own ,milton1 when he prays1 8,ring out1 ye crystal spheres10 bids the ,primum ,mobile join in1 as well as the star sphere3 8,and with your nine-fold harmony ,make up full concert to the angelic symphony40#fed ,and ,shakespear lets every separate star swell the chorus3 8,there's not the smallest orb which thou beholdest ,but in his motion like an angel sings1 ,still quiring to the young-eyed cherubins40#fee ,in the same spirit1 but more literally perhaps than these1 are we to understand the music of ,dante's spheres1 which accompanies the singing of the angels3-- 8,il cantar di quei che notan sempre ,dietro alle note degli eterni giri40#fef ---------------------------------------- -------------------------------- #fed ,hymn on the ,nativity4 #fee ,merchant of ,venice4 #fef 8,the song of those who sing for ever ,after the music of the eternal spheres40 ,purg4 xxx4 #ib1 #ic4 7,longfellow74 ---------------------------------------- -------------------------------- #c4 ,,dimensions ,,and ,,physical ,,nature ,,of ,,the ,,universe4 ,we have seen that ,dante believed the circling of the nine moving spheres and their epicycles to be the immediate cause of the movements which he saw in stars and planets4 ,if we ask what were his ideas with regard to their sizes and distances the question is easily answered4 ,it is a curious fact that although our ideas about the size of anything we see depend upon the distance at which it appears to be1 and no one can say how far away the sun looks1 most of us nevertheless have a quite definite idea as to how large it looks1 about the size of a dinner-plate1 a cart-wheel1 c4 ,cleomedes1 in the days of ,augustus1 quotes ,lucretius and the ,epicureans as believing that the sun is no larger than it looks1 that is a foot in diameter2 and he rightly remarks1 amongst other arguments to the contrary1 that if it were only that size it would be invisible unless nearer than the tops of the mountains1 yet we see islands and hills projected against it when rising1 which shows that its distance is greater4 ,dante twice quotes the same fallacy1 as an instance of the folly of trusting to the impression of our senses1 when not corrected by reason1 and he tells us what he believes the true size of the sun to be4 ,in ,conv4 ,,iv4#feg he says3-- 8,thus we know that to most people the sun appears to be a foot wide in diameter2 and this is so utterly false that according to the investigation and discovery made by human reason with her attendant arts1 the diameter of the sun's body is five times that of the earth's1 and a half besides4 ,for whereas the earth has a diameter of six thousand five hundred miles1 the diameter of the sun1 which when measured by sense-impressions seems to be a foot in extent1 is thirty-five thousand1 seven hundred and fifty miles40 7,see also ,ep4 x4 #db-df74 ,when speaking of the planet ,venus he says she is 8far off from us1 being distant even when she is nearest to us one hundred and sixty-seven times the distance of the distance of the centre of the earth from us1 which is three thousand two hundred and fifty miles40#feh ---------------------------------------- -------------------------------- #feg ,conv4 ,,iv4 viii4 #ea-fd4 #feh ,conv4 ,,ii4 vii4 #ajd-ajh4 ---------------------------------------- -------------------------------- ,mercury is spoken of in the ,paradiso as a small star1 8,questa picciola stella10#fei and in ,conv4 ,,ii4#ffj ,dante says3--8,mercury is the smallest star in the sky2 for the length of its diameter is not more than #bcb miles1 according to ,alfraganus1 who says that it is one twenty-eighth of the diameter of the earth1#ffa which is six thousand five hundred miles40 ---------------------------------------- -------------------------------- #fei 8,this small star40 ,par4 vi4 #aab4 #ffj ,conv4 ,,ii4 xiv4 #ib-ih4 #ffa ,the ,frankfort printed edition and some ,latin ,,mss of ,alfraganus agree with this3 the edition of ,golius gives _/4 ---------------------------------------- -------------------------------- ,it is only in the last passage that our poet quotes his authority1 but in the others also the diameter or the semi-diameter of the earth is used as the unit of measure1 and it is the same as that given by ,alfraganus2 so are the sizes of ,mercury and the ,sun1 and the least distance of ,venus is the value given by ,alfraganus for the greatest distance of ,mercury1 which he asserted to be equal4 ,it seems quite clear1 therefore1 that the figures given in the tables on pp4 #ahi-ij represent ,dante's belief as to the dimensions of the ,universe4 ,these passages also are another proof that ,dante had not studied ,ptolemy's own work1 for ,ptolemy had said that the distances of ,venus and ,mercury could not be accurately known4#ffb ---------------------------------------- -------------------------------- #ffb ,almagest1 ,bk4 ,,ix4 ---------------------------------------- -------------------------------- ,we do not expect exact measures of distance in ,dante's descriptions of his soaring flight through the spheres1 but he so constantly speaks of the marvellous speed with which he passes from star to star that we are not required to ignore the stupendous distances between4 ,the one indication he does give us of the space which separates him from earth is full of poetry and symbolic meaning3 ,i refer to ,folco's words in the heaven of ,venus3-- 8,questo cielo1 in cui l'ombra s'appunta ,che il vostro mondo face0 444#ffc ---------------------------------------- -------------------------------- #ffc 8,this heaven1 where ends the shadowy cone ,cast by your world40 ,par4 ix4 #aah1 #aai4 7,longfellow74 ---------------------------------------- -------------------------------- ,this is the last of the three heavens in which ,dante has met spirits whose lives did not reach the perfection of the saints in higher heavens1 but were marred by broken vows1 earthly ambition1 earthly love2 and here he is reminded that he has not yet soared high enough to be beyond reach of the cone of shadow thrown by the earth4 ,this is another allegory resting on what was to the poet an astronomical fact4 ,for ,earth's shadow was said by ,ptolemy and ,alfraganus to extend to #bfh times the distance of her semi-diameter1 and the distance of ,venus from ,earth varied1 according to ,alfraganus1 between #afg and #aabj times this unit1 while the next planet1 the sun1 at his least distance was #aabj units distant 7the same as ,venus' greatest74 ,therefore the spheres of ,venus and the two nearer planets ,mercury and the ,moon1 were all within reach of ,earth's shadow1 but the sun and the rest were far beyond it4#ffd ,venus and ,mercury themselves never could be actually touched by the shadow like the moon1 however1 because they keep too near the sun for ,earth to interpose herself between them and the source of light4 7,though the length of the shadow thrown by ,earth is nearly accurate1 see pp4 #aia-ib1 the planets are a great deal further than ,alfraganus supposed2 for the least distance of ,venus is nearly #fjjj times ,earth's semi-diameter1 and the least distance of ,mercury #ab1jjj74 ---------------------------------------- -------------------------------- #ffd ,rabbi ,abraham ben ,chija1 in his ,sphra ,mundi1 written about #aajj ,a4,d41 says that ,earth's shadow extends as far as the distance of ,mercury1 not of ,venus 7,delambre1 ,histoire de l'astronomie ancienne1 and ,dreyer1 ,planetary ,systems72 but this does not agree with the figures given by ,alfraganus4 ---------------------------------------- -------------------------------- ,except for this we have only the passage in the ,paradiso already referred to1 where ,dante1 standing among the stars of ,gemini1 found the sphere above him too distant to be seen1 but turning his gaze downwards was able to survey all the planets and the earth at the centre of the ,world4 ,he knew very well that at a distance from ,earth #bj1jjj times her own semi-diameter it would be impossible to see her as a disc1#ffe far less to distinguish oceans and continents1 hills and river-mouths4 ,it would in fact be like looking at an object one foot in diameter at a distance of two miles4 ,but as we have before observed1 his power of vision here was more than human3 at every step in this marvellous journey it had grown clearer and stronger1 and in the fourth heaven he had been able to look on spirits which shone in the sun more brilliantly than the sun itself1 although on earth no eye can look upon the sun4#fff ,in the ,empyrean1 distinctions of space1 and impediments to vision vanished altogether4#ffg ---------------------------------------- -------------------------------- #ffe ,her diameter would look no larger than the diameter of ,saturn1 as we see it when nearest to him2 but like ,saturn she would be visible as a bright point1 because shining by reflected sunlight4 ,ancient and medival astronomers never realized this1 however1 but thought of ,earth as a dark body1 receiving light but giving none4 #fff ,conv4 ,,ii4 xiv4 #abf1 #abg2 ,par4 x4 #dj-db1 #dh4 #ffg ,par4 xxii4 #fg2 xxxi4 #ai-bd2 xxx4 #aah-abc4 ---------------------------------------- -------------------------------- ,with regard to the physical nature of the heavenly bodies1 ,dante and his contemporaries had no means whatever of investigation1 and could only profess ignorance or accept one or other of the guesses of their predecessors4 ,some of the ,greek philosophers1 as we saw1 guessed that the planets were worlds somewhat like the earth1 others thought they were composed of fire or of air4 ,but the general belief in the thirteenth century was that planets and spheres alike were composed of a kind of celestial matter1 called by ,aristotle and the ,greeks 8ther10 by the ,arabs 8al-acir10 an immortal substance which had neither heaviness nor lightness1 and was altogether distinct from any of the four elements existing below the sphere of the moon4 ,beatrice speaks of 8this sphered ether10 8questo etera tondo40 ,par4 xxii4 #acb4 ,dante's description of this celestial substance when he first enters the ethereal world is one of the finest instances of his faithfulness to the teachings of astronomy as he had learned it1 combined with poetical imagination1 and at the same time his power of using material facts 7as he conceived them7 to present an allegory of the deepest religious mysteries4 ,if we merely listen to the magic of the words1 an impression is conveyed of something mysteriously beautiful and dazzling1 unlike anything known on earth2 but if we look into the meaning1 we find that the globe of the moon has just those strange1 contrasting qualities1 just the colour and the form which a sphere of ether may be imagined to have4 ,it is white and rounded like a pearl1 8polished0 as ,plato said of the universal orb1 it is thick and shining1 soft as cloud but hard as diamond2 and it offers no more resistance to ,dante as he enters into it than does water to a ray of light4#ffh ,then follows a discussion concerning the substance not only of the moon but of all the heavenly bodies4 ,on hearing that he has reached the boundaries of the immortal world1 and has entered 8la prima stella10#ffi ,dante eagerly enquires of ,beatrice what are those dark markings in the body of this planet which are seen from ,earth and have given rise to the fable of ,cain4 ,she smiles a little1 and bids him tell her first what is his own opinion4 ,he advances the theory which he had taught in the ,convivio1 viz4 that the parts of the moon which look dark to us are less dense than the rest1 and therefore the rays of the sun when striking them are not stopped and reflected back to us2 hence the brightness is less than in other parts of her surface4 8,l'ombra ch' in essa1 444 non altro che rarit del suo corpo1 alla quale non possono terminare i raggi del sole e ripercuotersi cos come nell' altre parti40#fgj ---------------------------------------- -------------------------------- #ffh ,par4 ii4 #be-de4 #ffi 8,the first star40 #fgj 8,the shadow which is in her is nothing but rare parts of her substance1 which cannot stop the rays of the sun and reflect them back like the other parts40 ,conv4 ,,ii4 xiv4 #gb-gf4 ---------------------------------------- -------------------------------- ,this explanation seems to have been first suggested by ,averros1 the ,arab philosopher and astronomer of ,cordova1 who was known in the ,middle ,ages as 8,the ,commentator10 from his famous commentary of ,aristotle4 ,the suggestion occurs in his ,de ,substantia ,orbis1 and as it follows a quotation from ,aristotle 7to the effect that the moon is more nearly related to ,earth in her nature than to the stars71 it was believed by many to be originally due to ,aristotle himself4 ,the strange circumstance that the moon alone1 among all the heavenly bodies1 appeared to have dark shadows on her bright face1 had roused much curiosity already among the ,greeks2 and ,plutarch1 in his dialogue 8,on the ,face in the ,moon10 mentions the different explanations suggested in his day4 ,some thought that the polished surface of the moon reflected1 like a mirror1 parts of the earth2 the ,stoics said that air was enclosed within her globe of fire and obscured it in certain places1 but this view was rejected with contumely by ,plutarch4 8,it is a slap in the face to the moon when they fill her with smuts and blacks1 addressing her in one breath as ,artemis and ,athena1 and in the very same describing a caked compound of murky air and charcoal fire1 with no kindling or light of its own1 a nondescript body smoking and charred like those thunderbolts which the poets address as lightless and sooty60#fga ---------------------------------------- -------------------------------- #fga ,plutarch1 ,on the ,face in the ,moon1 translation by ,prickard4 ---------------------------------------- -------------------------------- ,the third hypothesis1 which was favoured by most of the speakers in the dialogue1 was that the moon was not a star at all1 but a kind of more beautiful ,earth2 and it was even suggested that men might dwell on her who thought their world the only place fit for human beings1 looking down with contemptuous pity on our ,earth1 as a sort of sediment and slime of the ,universe1 appearing through damps and mists and clouds1 a place 8unlighted1 low1 motionless10 entirely incapable of supporting moving breathing warm-blooded animals6 ,this was not a view which could possibly be held by medival ,christians1 and in a treatise on ,aristotle's ,de ,clo1 attributed to ,albert of ,saxony1 we find others put forward4 ,the author disproves the old theory of a mirror-like moon reflecting parts of ,earth1 and also another that the moon draws up cold vapours which are seen like clouds on her surface1 and upon which she is nourished--for how should an eternal heavenly body need nourishment8--and finally he expounds the theory of 8,the ,commentator10 with which he agrees4 ,the markings are rare parts of the moon's substance1 which cannot shine so brightly as the denser parts1 and this varied surface he compares with alabaster1 in which 8the dense and not translucent part is very white1 while that which is translucent like glass is obscure and tends to blackness4 ,and if10 he adds1 8it is asked why the moon is thus dissimilar in her parts1 the reply is that this is her nature40#fgb ---------------------------------------- -------------------------------- #fgb ,see ,paget ,toynbee1 ,le ,teorie ,dantesche sulle ,macchie della ,luna1 in ,giornale ,storico della ,letteratura ,italiana1 vol4 xxvi4 pp4 #aef-afa4 ---------------------------------------- -------------------------------- ,this theory was perhaps the most popular one with medival scholars1 though there was some difference of opinion as to whether the dense or the rare parts of the moon were those that showed dark4 ,ristoro perhaps alludes to it1 in the passage where he speaks of the moon's markings1 but in a very confused way1 and the contrast of 8polished0 and 8rugged0 surface is what he chiefly lays stress upon4 ,after upholding this theory in the ,convivio1 ,dante rejects it in the ,paradiso3 perhaps because it was more or less bound up with the idea that the moon was partly of an earthy nature1 and this was inconsistent with the other theory of ,aristotle1 so popular among classical writers1 that all within and above the sphere of the moon was eternal and heavenly4 ,he is evidently very anxious to convince us of the falsity of his old belief1 for he is not content with a simple assertion1 but lets ,beatrice reason like a learned doctor1 using arguments which would appeal to his readers1 drawn now from experiments which might be used in a school1 and now from the accepted astrological beliefs of the day4 ,first she reminds him that the numerous stars scattered over the surface of the eighth sphere differ in brightness1 like the different parts of the moon's surface1 but they differ in the quality 7colour87 of their light1 as well as the quantity1 and we know that there are essential differences between them1 because their 8virtues0 are different4 ,it cannot be1 therefore1 that they differ simply in density or rarity of their substance4 ,then she shows that in no circumstances is the theory of varying density in different parts of the moon capable of explaining the observed variety of brightness4 ,for if the parts which look dark are less dense than others1 either they must be so right through the planet1 or there must be an alternation of dense and rare matter in those parts1 like fat and lean in a material body1 one behind the other like pages in a book4 7,the double metaphor is characteristic of ,dante47 ,now if the first be true1 the sunlight would shine through the moon is those parts1 during an eclipse2#fgc and if the second1 the sun's rays must penetrate to the lower-lying denser part1 and be reflected thence just as from the dense parts of the moon's surface4 ,a possible objection that in that case the reflecting surface would be further away1 and therefore appear fainter1 may be disproved by an experiment4 ,take two mirrors and place them at an equal distance from you2 place a third between them but further away1 face the three mirrors1 and place a light behind you so that it may be reflected from them all3 the distant one will appear smaller1 but no less bright than the two near ones4 ,this reasoning is perfectly sound4 ,then follows the explanation for which all this is a preparation4 ,it involves an exposition of ultimate causes which we need not enter into here3 for the present we need only say that difference of brightness is not caused by differences of much or little of the same substance4 ,there are intrinsic differences between star and star1 and between different parts of the moon1#fgd but all are manifestations of divine intelligence2 just as the different members and faculties of a human body are manifestations of a human soul4 ---------------------------------------- -------------------------------- #fgc ,albert of ,saxony notes this objection1 but says the rarity is not sufficiently great to make these parts transparent4 #fgd ,this is in agreement with modern belief4 ,some parts of the moon's surface reflect sunlight less well than others1 and therefore look dark1 just as a peaty soil looks darker than limestone4 ---------------------------------------- -------------------------------- ,the diversity of the celestial matter is also touched upon in the ,convivio1 where it is said that the epicycle of ,venus is 8not of the same essence as that which carries it the deferent or large sphere1 although it is more nearly of one nature with it than with the rest40#fge ,differences of colour are indicated in the glowing masses of the planets1 which are entered by ,dante and ,beatrice4 ,as with the moon1 they do not merely alight upon the surface1 but penetrate the planetary ether4 8,quel ch' era dentro al sol10#fgf 8,nel profondo ,marte10#fgg 8,la temprata stella sesta1 che dentro a s m'avea ricolto40#fgh ,mercury is called a pearl--8la presente margarita0#fgi--while ,mars is 8questo fuoco10#fhj and the astronomer poet says he knew the planet by its burning smile1 for it seemed to him even more ruddy than its wont4 ---------------------------------------- -------------------------------- #fge ,conv4 ,,ii4 iv4 #id-if4 #fgf 8,that which was within the sun sc4 the spirits40 ,par4 x4 #da4 #fgg 8,in the depths of ,mars40 ,par4 xiv4 #ajj1 #aja4 #fgh 8,the temperate sixth star1 which within itself had received me40 ,par4 xviii4 #fh1 #fi4 #fgi 8,the present pearl40 ,par4 vi4 #abg4 #fhj 8,this fire40 ,par4 xvi4 #ch4 8,ben m' accors' io ch' io era pi levato1 ,per l'affocato riso della stella1 ,che mi parea pi roggio che l'usato40#fha #fha 8,well was ,i 'ware that ,i was more uplifted ,by the enkindled smiling of the star ,that seemed to me more ruddy than its wont40 ,par4 xiv4 #he-hg4 7,longfellow74 ---------------------------------------- -------------------------------- ,and when1 without being conscious of any movement1 he found that the red light shining on ,beatrice had turned to purest white1 like a blush fading from a fair face1 he knew that the sixth star 7,jupiter7 had received him within itself4 8,e quale il trasmutare in picciol varco ,di tempo1 in bianca donna1 quando il volto ,suo si discarchi di vergogna il carco1 ,tal fu negli occhi miei1 quando fui volto1 ,per lo candor della temprata stella ,sesta1 che dentro a s m'avea ricolto40#fhb ---------------------------------------- -------------------------------- #fhb 8,and such as is the change1 in little lapse ,of time1 in a pale woman1 when her face ,is from the load of bashfulness unladen1 ,such was it in mine eyes1 when ,i had turned1 ,caused by the whiteness of the temperate star1 ,the sixth1 which to itself had gathered me40 ,par4 xviii4 #fd-fi4 7,longfellow74 ---------------------------------------- -------------------------------- ,this contrast between the colours of ,jupiter and ,mars is referred to more than once4 ,in ,par4 xxvii41 the flaming spirit of ,st4 ,peter1 flushed with righteous indignation1 becomes brilliant as the planet ,jupiter1 and red as ,mars3-- 8,e tal nella sembianza sua divenne1 ,qual diverrebbe ,giove1 s'egli e ,marte ,fossero augelli1 e cambiassersi penne40#fhc ---------------------------------------- -------------------------------- #fhc 8,he in semblance such became ,as ,jove might be1 if he and ,mars were birds1 ,and interchanged their plumes40 ,par4 xxvii4 #ac-ae4 7,carey74 ---------------------------------------- -------------------------------- ,and when ,dante looks down upon the seven planets he sees 8il temperar di ,giove ,tra il padre e il figlio40#fhd ---------------------------------------- -------------------------------- #fhd 8,the temperate light of ,jove1 between his father and his son40 ,par4 xxii4 #ade-adf4 ---------------------------------------- -------------------------------- ,to understand which we must turn to the oft-quoted fourteenth chapter of the second treatise in the ,convivio4 ,here we find that ,jupiter 8moves between two heavens0 which 8are antagonistic to its excellent temperateness1 that is to say the heavens of ,mars and that of ,saturn10#fhe and ,dante quotes ,ptolemy as saying that ,jupiter is a star of temperate constitution1 between the cold of ,saturn and the heat of ,mars4 ,it seems that these ideas of cold and heat1 as applied to the planets1 were taken literally1 not merely as poetical descriptions of colour1 nor of astrological significance2 for ,dante says explicitly in the same chapter of the ,convivio that ,mars is hot like fire1 that this is the cause of his colour1#fhf and that he dries up and burns things4#fhg ---------------------------------------- -------------------------------- #fhe ,conv4 ,,ii4 xiv4 #aif-aih4 #fhf ,cf4 ,ristoro1 ,comp4 del ,mondo1 ,,iii4 iii4 #fhg ,conv4 ,,ii4 xiv4 #afa-afe4 ---------------------------------------- -------------------------------- ,similarly he appears to have believed that ,saturn and the moon were literally of a cold nature4 8,quel pianeta che conforta il gelo10#fhh in ,canzone xv4 is doubtless ,saturn2 and the chill of the hour before dawn is described as due not only to loss of heat by the earth but sometimes also to the influence of the cold moon or of ,saturn4#fhi ,besides her shadowy markings1 the moon had another peculiarity which distinguished her from all other heavenly bodies1 for she was the only planet then known to vary in apparent size and shape 8according to the way in which the sun looks upon her40#fij ,she was therefore a very dark body1 though it was believed that she had some light of her own1 and ,dante argues in favour of this that she does not become totally invisible during an eclipse4#fia ,this was a very natural conclusion3 it would not readily occur to anyone that the reddish light of the eclipsed moon is sunlight refracted 7i4e4 bent out of its direct course7 in passing through the earth's atmosphere4 ---------------------------------------- -------------------------------- #fhh 8,the planet that strengthens the cold40 ,canz4 xv4 #g4 #fhi ,purg4 xix4 #a-c4 #fij ,conv4 ,,ii4 xiv4 #gh1 #gi4 #fia ,de ,mon4 ,,iii4 iv4 #adj-adb4 ---------------------------------------- -------------------------------- ,the sun1 although the astrologers made him not very much larger than the brightest fixed stars and the largest planets1 was much brighter and hotter than any1 and it was universally agreed that all obtained their light from him4 ,even if1 like the ,moon1 they had some light of their own1 and did not only reflect like mirrors1 this inherent light had originally come from the sun and was but absorbed sunlight4#fib ,we meet constantly with this idea in ,dante's works4 ,in one of his ,odes the sun is said to 8donar luce alle stelle20#fic in the ,convivio he says1 8,il sole 444 di sensibile luce s prima1 e poi tutti i corpi celestiali ed elementali allumina40#fid ,the ,morning ,star is described as deriving her beauty from the sun2#fie and after the sun has set he shines forth again in the light of all the stars4#fif ,so also says ,brunetto ,latini1 8,sans faille li solaus est fondemenz de touts lumieres et de toute chalor40 ---------------------------------------- -------------------------------- #fib ,see quotations from ,albertus ,magnus and ,roger ,bacon in ,moore's ,studies1 iii4 p4 #de1 note4 #fic 8,bestow light on the stars40 ,canz4 xix4 #aag4 #fid 8,the sun illumines first himself and then all celestial and elemental bodies with visible light40 ,conv4 ,,iii4 xii4 #ed-ef4 #fie ,par4 xxxii4 #ajg1 #ajh4 #fif ,par4 xx4 #a-f2 compare xxiii4 #bh-cj4 ---------------------------------------- -------------------------------- #d4 ,,influence ,,of ,,the ,,spheres ,,on ,,human ,,affairs4 ,if we are to believe a fifteenth century biographer1 we have so far omitted to mention ,dante's greatest claim to be considered a proficient in astronomy4 8,he foretold10 says ,filelfo1 8many of the calamities of ,florence1 the wars of ,italy1 and other political changes1 all of which would have been impossible without an accurate knowledge of the movements of the celestial bodies40 ,filelfo was a poet1 and his authority for this surprising statement can be no other than that on which1 ,dr4 ,moore says1 he mainly depends1 and which seldom or never fails him1 8his own most airy and lively imagination unembarrassed by any references to documents40#fig ,the prophecies of the ,divina ,commedia are obviously written after the events1 and in no single instance are they supposed to have any connection with the art of the astrologers4 ,on the contrary1 it is remarkable how very little we find in ,dante's writings about the fate-predicting and character-reading which passed as the chief part of astronomy with the large majority of his contemporaries1 and played a considerable part even in the scientific writings of his fellow authors4 ---------------------------------------- -------------------------------- #fig ,moore1 ,dante and his early ,biographers1 p4 #ie4 ---------------------------------------- -------------------------------- ,not that he disbelieved in the art3 it would have been almost a miracle if he had4 ,the astrologers in the fourth ,bolgia were punished with other soothsayers not because they deceived credulous clients1 but because they had desired to look too deeply into the future1#fih which was impiety4 ,for this reason the learned ,michael ,scot1 the honoured of ,popes1 was there1 as well as poor ,asdente1 and ,guido ,bonatti1 and ,aruns who from his solitary cave had watched the stars1 and prophesied the victories of ,csar over ,pompey4#fii ,this orthodox sentiment that 8judicial astronomy10 was apt to be a snare1 and lead to practices condemned by the ,church1 may have been one reason for ,dante's avoidance of it2 but we cannot read his works without feeling that it was the beauty of the skies1 and the keen desire to understand the structure of the universe which inspired him to study astronomy1 and that he had no superstitious fear of the heavenly bodies1 no greedy wish to make use of his knowledge to pry into the future4 ,there is no evidence that he was acquainted with the details of astrology4 ,the few allusions made in his works to special effects of certain stars or planets are only to those most familiarly known1 and parallel instances might be found to many of them in modern poems4 ,with this difference1 however1 that to-day they are figures of speech3 with ,dante they represented facts4 ,venus was to him in serious truth 8la stella d'amor10#gjj 8lo bel pianeta che ad amar conforta10#gja and exercised a real power over ,folco#gjb and ,cunizza1#gjc and his own heart4#gjd ,he even tells us1 in serious prose1 that it is the planet and not the whole sphere1 which is the source of this influence1 and that it is borne to us upon her rays4#gje ,so also the moon has a special influence1 which is communicated by her rays4#gjf ---------------------------------------- -------------------------------- #fih ,inf4 xx4 #ch4 #fii ,inf4 xx4 #aae-aah1 #df-ea4 #gjj 8,the star of love40 ,canz4 xv4 #d4 #gja 8,the fair planet which incites to love40 ,purg4 i4 #ai4 #gjb ,par4 ix4 #id-if4 #gjc ,par4 ix4 #cb1 #cc4 #gjd ,conv4 ,,ii4 ,canz4 #a-f4 #gje ,conv4 ,,ii4 vii4 #hh-ajj4 #gjf ,de ,mon4 ,,iii4 iv4 #aci1 #adj4 ---------------------------------------- -------------------------------- ,to the strong star of ,mars the noble warlike nature of ,can ,grande was partly due2#gjg ,jupiter is a temperate star1 not only in the purity of his colour1 but his influence is felt where justice is worked on earth4#gjh ,saturn's influence is modified when he shines in ,leo1#gji the sun has special powers in ,aries1#gaj and to his presence in ,gemini at the time of ,dante's birth the poet attributes his literary gift4#gaa ,in ,inf4 xxvi4 #bc1 he again suggests that his mental powers may be due to the influence of a good star1 and ,brunetto ,latini bids him follow his star4#gab ,dante also quotes ,albumassar1 and ,seneca1 and the events of his own day1 to show that those fiery vapours1 meteorites1 portend the death of kings and the downfall of states1 adding that this is because they are effects of the sovereignty of ,mars4#gac ,this passage explains why the warrior ,malaspina is called a vapour drawn by ,mars from ,valdimagra1 which in the tempest of battle at ,piceno shall suddenly split the clouds and deal death to the combatants4#gad ---------------------------------------- -------------------------------- #gjg ,par4 xvii4 #gf-gh4 #gjh ,par4 xviii4 #aae-aag4 #gji ,par4 xxi4 #ac-ae4 #gaj ,par4 i4 #dj-db2 ,canz4 xv4 #da4 #gaa ,par4 xxii4 #aab-aag4 ,the ,ottimo1 commenting this passage1 says that ,gemini 8is the house of ,mercury1 who signifies1 according to the astrologers1 literature1 science1 and learning4 ,and in this direction it disposes those who are born when it is in the ascendant1 and more powerfully if the sun is in it40 #gab ,inf4 xv4 #ee4 #gac ,conv4 ,,ii4 xiv4 #agj-ahj4 #gad ,inf4 xxiv4 #ade-aej4 ---------------------------------------- -------------------------------- ,the results of the right disposition of sphere with sphere are spoken of in ,canz4 xix4 #gg-gi2 all the nine were in perfect accord when ,beatrice1 herself a nine or miracle of perfection1 was to be born2#gae and every star rained its light and its virtue into her beautiful eyes4#gaf ,there is also a charming sonnet1 in which the poet tells us how all the seven planets influence his lady4 ---------------------------------------- -------------------------------- #gae ,v4 ,n4 xxx4 #bb-bd4 #gaf ,ball4 vi4 #aa1 #ab4 8,da quella luce che il suo corso gira ,sempre al volere dell' empiree sarte1 ,e stando regge tra ,saturno e ,marte1 ,secondo che l'astrologo ne spira2 ,quella che in me col suo piacere aspira1 ,d'essa ritragge signorevol arte3 ,e quei che dal ciel quarto non si parte ,le d l'effetto della mia desira4 ,ancor quel bel pianeta di ,mercuro ,di sua virtute sua loquela tinge1 ,e 'l primo ciel di s gi non l' duro4 ,colei1 che 'l terzo ciel di s costringe ,il cor le fa d'ogni eloquenza puro2 ,cos di tutti e sette si dipinge40#gag #gag 8,from that bright star which moveth on its way ,for ever at the ,empyrean's will1 ,and between ,mars and ,saturn ruleth still1 ,e'en as the expert astrologer doth say1 ,she who inspires me with her beauty's ray ,doth subtle art of sovereignty distil2 ,and he whose glory doth the fourth heaven fill ,gives her the power my longing soul to sway4 ,and that fair planet known as ,mercury ,colours her speech with all its virtue rare1 ,and the first heaven its boon does not deny4 ,she who the third heaven ruleth as her share ,makes her heart full of utterance pure and free2 ,so all the seven to perfect her agree40 ,sonnet xxviii4 7,plumptre74 ---------------------------------------- -------------------------------- ,in more serious vein is the discourse in ,par4 ii4 on the different virtues of the different stars2#gah and this should be compared with passages in the ,qustio and the ,convivio4 8,sciendum quod licet clum stellatum habeat unitatem in substantia1 habet tamen multiplicitatem in virtute10#gai sounds like an echo of the words of ,beatrice3 ---------------------------------------- -------------------------------- #gah ,par4 ii4 #fd-gb1 #acj to end4 #gai 8,it should be borne in mind that although the starry heaven has unity in substance it nevertheless has multiplicity in virtue40 ,qu4 xxi4 #ab-ad4 8,cos l'intelligenza sua bontate ,multiplicata per le stelle spiega1 ,girando s sopra sua unitate40#gbj #gbj 8 444 ,e'en so ,the intellectual efficacy unfolds ,its goodness multiplied throughout the stars1 ,on its own unity revolving still40 ,par4 ii4 #acf-ach4 7,carey74 ---------------------------------------- -------------------------------- ,and when comparing ,nobility with the star-spangled sky1 our author says3 8,tante sono le sue stelle che nel cielo si stendono1 che certo non da maravigliare1 se molti e diversi frutti fanno nella umana ,nobilt1 tante sono le nature e le potenze di quelle1 in una sotto una semplice sustanza comprese e adunate1 nelle quali siccome in diversi rami fruttifica diversamente40#gba ---------------------------------------- -------------------------------- #gba 8,so many are the stars which spread themselves over her sky1 that surely we cannot wonder if they make many and diverse fruits grow on human nobility1 so many are their natures and potencies1 concentrated and united in one simple substance2 and on them as on diverse branches she bears fruit in diverse ways40 ,conv4 ,,iv4 xix4 #de-eb4 7,jackson74 ,see also ,conv4 ,,iv4 xxi4 #fb-ff4 ---------------------------------------- -------------------------------- ,the author goes on to say in the ,qustio that the many and diverse stars which we see in the eighth heaven were placed there in order that it might pour down diverse virtues1 and that he who perceives this not1 let him know that he is outside the pale of philosophy4#gbb ,in another place he tells us that the nearer a star is to the mid-circle of the star sphere1 the greater is its virtue3#gbc he no doubt means1 not the celestial equator1 but the zodiac 7or more exactly the ecliptic71 since this was the mid-circle of the star sphere1 parallel to which its slow revolution of #cf1jjj years was made4 ,this would agree with the view of the astrologers1 who paid more attention to the constellations of the zodiac than to any others4 ---------------------------------------- -------------------------------- #gbb ,qu4 xxi4 #ag-ai4 #gbc ,conv4 ,,ii4 iv4 #ge-gg4 ---------------------------------------- -------------------------------- ,but we may search all ,dante's works in vain for any reference to the 8houses0 or 8aspects0 of the planets1 or for any information about the masculine and feminine1 mobile and stable1 signs4 ,all such things1 which seemed to most writers of his day quite as important as the periods of the planets or the positions of the signs1 he entirely ignores4 ,among the circumlocutions by which he describes the signs1 such as 8the fair nest of ,leda10 or 8the sign that follows ,taurus10 we never find 8the house of ,saturn10 or 8the sign in which ,mars is mildest40 ,leo is called ,mars' own ,lion1 probably because the 8leo audax et ferox0 of bestiaries agreed with the fiery colour and nature of ,mars3#gbd astrologically1 his signs were ,scorpio and ,aries4 ,it is quite astonishing that among all the characteristics of the planets and spheres mentioned in ,convivio ,,ii4 chapters xiv4 and xv41 only two relate to astrology1 namely1 the temperate disposition of ,jupiter between the hot ,mars and cold ,saturn1 and the power of ,mars to draw up the hot vapours which become meteors and portend the deaths of kings4 ,all the rest--the markings and phases of the moon1 the small size and proximity to the sun of ,mercury1 the beauty of ,venus and her appearance alternately as morning and evening star1 the brilliance of the sun and his capability of giving light to all the stars1 the position of the sphere of ,mars midway between those of the other planets1 the purity of ,jupiter's colour1 the slow movement and distance of ,saturn--all these are purely astronomical1 to use the modern distinction4 ,so also are the characters of the star sphere--the thousand and twenty-two visible stars1 and the indistinguishable stars of the ,galaxy1 the pole we see and the other which remains hidden1 the conspicuously swift diurnal movement and the almost imperceptible secular revolution of #cf1jjj years4 ,of the ,primum ,mobile it is remarked that it controls the movement of all the rest1 and of the ,empyrean that it is full of peace4 ---------------------------------------- -------------------------------- #gbd ,but see ,tozer's ,english ,commentary on ,dante's ,divina ,commedia1 note on ,par4 xvi4 #cg4 8,in medival astrology ,mars was one of the ,lords of the ,lion40 ---------------------------------------- -------------------------------- ,the symbolism of the spheres assigned in ,paradise to the different saints is partly drawn from astrological ideas1 for in ,venus ,dante meets the lovers1 in ,mars the warriors1 in ,jupiter the just rulers4 ,but those who were not eternally faithful to their vows are in the moon because she has the lowest sphere1#gbe the contemplative saints are in the highest planet1 the theologians who enlightened the faithful are in the sun1 and the ambitious are in the little planet which ever keeps closest to the sun4 ,the heaven of 8many and diverse stars0 shows the poet a host of saints1 and the ,primum ,mobile1 which controls the movement of the other spheres1 reveals to him the ,angels who direct them4 ,it seems1 then1 that ,dante was not interested in technical astrology1 and had never made a study of it2 and ,i think we may adduce this additional evidence that he had not learned astronomy in a university1 or under ,cecco d',ascoli4 ,it is only necessary to look at the list of books prescribed at ,bologna#gbf to feel sure that ,dante had not taken a regular course there4 ,the list1 it is true1 belongs to a somewhat later time1 but there is no reason to suppose that astrology became of more importance in the late fourteenth century than at its beginning4 ---------------------------------------- -------------------------------- #gbe ,par4 iii4 #ee-eg4 #gbf ,see p4 #bjb4 ---------------------------------------- -------------------------------- ,nevertheless1 however little ,dante may have cared for the details of astrology1 we shall never understand all that the skies meant to him unless we realize that a general belief in their influence on man was deeply rooted in his mind4 ,for him it was a tremendous fact1 and one which pervades his writings1 that stars and spheres are the instruments of ,god's providence1 and are ordained by the ,first ,mover to mould the destinies of ,earth4#gbg ,it is their movements which manifest ,his ,will2#gbh they are the hammers1#gbi earth the metal1 they are the seals1#gcj and earth the wax4 ---------------------------------------- -------------------------------- #gbg ,de ,mon4 ,,ii4 ii4 #ae-ah1 #be1 #bf1 #cf-ch2 ,,iii4 ii4 #cj-cb2 xvi4 #ia-aja2 ,ep4 v4 #acc-ace2 ,par4 ii4 #aba1 viii4 #ig-ii4 #gbh ,ep4 v4 #abd1 #abe4 #gbi ,par4 ii4 #abg1 #abh4 #gcj ,par4 ii4 #acj-acb2 xiii4 #gc-ge2 viii4 #abg1 #abh2 i4 #da1 #db4 ,ristoro of ,arezzo uses the same expression1 ,comp4 del ,mondo1 ,bk4 ,,vii4 part ,i4 chapter #b4 ---------------------------------------- -------------------------------- ,three times the stars are invoked to bring justice and righteousness on earth4#gca ,through the spheres the elements were evolved out of the first chaotic matter1 and everything on earth took form2 all life and motion is generated by them4#gcb ,man's soul is a direct creation by ,god1 but the moving heavens play an important part in the formation of his material body1 his mental faculties1 and his disposition4#gcc ,were it not for the action of the spheres1 children would be precisely like their parents1 their whole nature being governed by the law of heredity alone3 it is the different influences of the skies that give them different natures4#gcd ,this1 says ,beatrice1 is perhaps what ,plato meant when he said that souls came from different stars and returned thither3 if his meaning was that the influences of the stars is so great that to them is due the praise or blame which we distribute to men1 there is some truth in the saying4#gce ---------------------------------------- -------------------------------- #gca ,purg4 vi4 #ajj2 xx4 #ac1 #ad2 xxxiii4 #dj-de4 #gcb ,par4 vii4 #acc-ada2 xiii4 #fe1 #ff2 ,conv4 ,,iii4 xv4 #aei-afa2 ,,ii4 xv4 #aeb-aed2 ,,iv4 xxiii4 #ej-eb4 #gcc ,conv4 ,,ii4 xiv4 #bh-cj2 ,,iv4 ii4 #eh-fa2 ,par4 xxvi4 #abh1 #abi4 #gcd ,par4 viii4 #abg-ace4 #gce ,par4 iv4 #di-fj4 ,see also ,ecl4 ii4 #af1 #ag2 and ,conv4 ,,iv4 xxi4 #ag-ai1 #be-bg4 ---------------------------------------- -------------------------------- ,some truth only--8alcun vero02 for the stars are not independent powers1 for good or evil1 which men are unable to resist4 ,this view is expressly combated in ,purg4 xvi4 #eh-hd4 ,dante has asked the spirit of the courtly ,venetian ,marco ,lombardo why the world is so full of wickedness now1 for some say it is the effect of the heavens1 and others seek an earthly cause4 ,marco groans at the blindness of men1 who accuse heaven for the results of their own misdeeds3 it is true that the heavens influence our lower natures1 our instincts1 and desires2 but the soul is free1 and can control them4 ,this is in accordance with the teaching of ,st4 ,augustine and ,aquinas4 ,in one passage of the ,de ,monarchia1 ,dante goes even further than this1 and asserts that the influences of the spheres are only good1 and that evil results from imperfections in the material on which these perfect instruments work4#gcf ---------------------------------------- -------------------------------- #gcf ,de ,mon4 ,,ii4 ii4 #ba-bc2 ,cf4 ,par4 xiii4 #fd-gh4 ---------------------------------------- -------------------------------- ,conceptions such as these give us a new idea of medival astrology4 ,they may be mistaken1 but at least they are grand1 and not unworthy of a philosopher and a ,christian4 #e4 ,,the ,,motive ,,power4 ,dante's ideas regarding the laws and origin of motion in the universe were derived from ,aristotelian metaphysics and ,church doctrines4 ,he believed that there were three kinds of motion proper to three kinds of bodies3 i4e4 heavy bodies tended towards the centre of the universe1 which is also the centre of the earth2 light bodies tended upwards to the region of fire just below the moon2 and bodies of ethereal substance--the stars1 planets1 and spheres--moved eternally in circles round the centre4 ,thus ,beatrice1 when speaking of the instinct implanted in all created things1 which bears them through the great ocean of being each to his destined haven1 says3-- 8,questi ne porta il foco inver la luna1 4 4 4 4 4 ,questi la terra in s stringe ed aduna40#gcg ---------------------------------------- -------------------------------- #gcg 8,this carries fire towards the moon1 this compresses and binds ,earth together40 ,par4 i4 #aae1 #aag4 ,see also ,de ,mon4 ,,iii4 vii4 #cj1 #ca1 and ,i4 xv4 #ch-da2 ,conv4 ,,iii4 iii4 #aj-ac2 ,qu4 xviii4 #aa1 #ab1 and many others4 ---------------------------------------- -------------------------------- ,and ,virgil3-- 8,il foco movesi in altura1 ,per la sua forma1 ch' nata a salire ,l dove pi in sua materia dura40#gch ---------------------------------------- -------------------------------- #gch 8,the fire doth upward move ,by its own form1 which to ascend is born1 ,where longest in its matter it endures40 ,purg4 xviii4 #bh-cj4 7,longfellow74 ---------------------------------------- -------------------------------- ,that is to say the form of a flame fits it to rise to that place where1 being in its own element1 it may last longer than on ,earth4 ,conversely1 the centre of the earth is described as the bottom of the whole universe1 and the point towards which all weights are attracted4#gci ,these opposite forces ,dante calls gravity and levity4#gdj ---------------------------------------- -------------------------------- #gci ,inf4 xxxii4 #h1 and #gd2 xxxiv4 #aaj1 #aaa4 ,see also ,par4 xxxiii4 #bb1 #bc2 ,inf4 ix4 #bh1 #bi2 ,qu4 iii4 #f-i1 etc4 #gdj ,de ,mon4 ,i4 xv4 #df-dh2 ,qu4 xii4 #ci-db4 ---------------------------------------- -------------------------------- ,the most interesting illustration of this force of gravity is the description1 in the last canto of the ,inferno1 of passing the centre of the earth1 8il punto al qual si traggon d'ogni parte i pesi40#gda ,virgil turned here 8con fatica e con angoscia10#gdb and bid ,dante hold him fast1 8ansando com' uom lasso40#gdc ,it was natural to suppose that the force of gravity would increase as one neared the centre1 though the fact is that it decreases4 ,in deep mines it is less than at the surface of earth2 and if we could go to much greater depths we should find that we could stand in any position1 and walk in any direction with almost equal ease1 till at the exact centre the sense of weight and of 8up0 and 8down0 would vanish altogether4 ,this is because it is the whole mass of the earth which attracts1 and when we penetrate beneath the surface the part above is no longer dragging us down1 and its effect is annulled4 ,but at the surface gravity acts as if the force were all concentrated at the centre1 and falling bodies increase their speed as they approach the surface3 before the days of ,newton1 therefore1 it was thought that the whole of the attracting force was actually situated at the centre of the earth4 ,brunetto ,latini speaks of gravity increasing as this point is approached1 and ,dante1 like ,aristotle1 calls it the goal of gravity4#gdd ---------------------------------------- -------------------------------- #gda 8,the point towards which weights are drawn from every direction40 ,inf4 xxxiv4 #aaj-aaa4 #gdb 8,laboriously and painfully40 ,inf4 xxxiv4 #gh4 #gdc 8,panting like a tired man40 ,inf4 xxxiv4 #hc4 #gdd ,qu4 xvi4 #ed1 #ee4 ---------------------------------------- -------------------------------- ,between the physical and the spiritual universe as conceived by ,dante1 there is a very close correspondence4 ,souls burdened with the weight of sin fall towards the centre of the universe1 sinking deeper the heavier is their guilt1 and at the bottom of the whole universe is the personification of all evil4 ,repentant souls1 as they are freed from their sins1 rise higher and higher1 and the ascent becomes always easier1 until at last they soar heavenward as naturally and spontaneously as flames of fire4 ,in ,paradise the motion of the pure spirits is inconceivably rapid1 and their mystic dances expressive of joy are always in circles4 ,motion in circles was the only appropriate kind for the heavenly bodies1#gde but the actual force which originated and preserved their motions was intelligence and will4 ,when ,dante sang1 8,voi che intendendo il terzo ciel movete10#gdf he was not addressing beings created merely by his poet's imagination4 ,his own commentary on the words shows us that they were as real to him as the planets themselves4 ,he can know nothing of them through the senses1 yet is as certain of their existence as one with closed eyes is of light4#gdg ,these beings move the spheres not through any material contact1 but solely by the power of thought3 they are immaterial immortal intelligences1 commonly called ,angels1 and ,dante identifies them with the ,forms of ,aristotle1 the ,ideas of ,plato1 and the gods and goddesses of the ,pagans1 8avvegnach non cos filosoficamente intendessero quelle come ,plato40#gdh ,as the hammer beats out forms in metal1 and thus expresses what is in the mind of the smith1 and as he works from the artist's design1 so the movements and 8virtues0 of the sacred spheres mould earthly events1 but these movements and virtues are the expression of controlling angels1 and they are carrying out the ,will of the ,first ,mover4 ,and as the joy of a happy mortal shines out in the eyes1 so the joy of the angels shines out in stars and planets4#gdi ---------------------------------------- -------------------------------- #gde ,this is nowhere stated1 but everywhere taken for granted1 and in ,conv4 ,,ii4 xiv4 #baa the circle is said to be the most perfect of figures4 #gdf 8,oh ye whose intellectual ministry moves the third heaven40 ,conv4 ,,ii4 canzone2 and ,par4 viii4 #cg4 #gdg ,conv4 ,,ii4 v4 #aai-abf4 #gdh 8,although they did not think of them as philosophically as ,plato40 ,conv4 ,,ii4 v4 #e-cg1 #id1 #ie2 vi4 #aed-aei4 #gdi ,par4 ii4 #abg-abi1 #adb-add4 ---------------------------------------- -------------------------------- ,there were nine ,orders in the angelic hierarchies1 according to the teaching of the ,church1 the chief authority on this subject being a book ,de ,celestia ,hierarchia1 supposed to have been written by ,dionysius the ,areopagite1 a disciple of ,st4 ,paul1 who had learned from the apostle what he had seen when rapt to the third heaven4 ,aquinas assigns to one of these nine orders the guidance of stars and planets1 and to others the rule over earthly affairs4 ,but since the latter follow the celestial motions1 there was no need to separate the two functions1 and ,dante laid down in the ,convivio that a few ,angels from each ,order preside over the movements of each sphere4 ,with ,aristotle1 he agreed that there is one ,intelligence for each movement1 so that for ,venus 7for instance7 there are three movers to direct respectively the circling of the ,epicycle1 the ,deferent1 and the movement of ,precession which every planet shares with the stars2 but whether there is a fourth mover to guide the diurnal motion of ,venus or if all the inner spheres are swept along by the motion of the ,primum ,mobile1 he would not presume to decide4#gej ,when he wrote the ,paradiso1 he no longer thought that a few ,angels were set apart for this ministry3 he implies that all the angels in each order united in the act of moving a whole heaven and perhaps he means to include the beatified human spirits as well4#gea ,he also slightly changes the correspondence between the angelic orders and their respective spheres4#geb ,swiftness of motion in a sphere corresponds with fervour of adoration in the ,movers3 hence the highest and swiftest of the moving heavens1 which is the ,primum ,mobile1 is moved by the highest ,order1 the ,seraphim3 and the lowest and slowest1 which is that of the moon1 by the lowest order1 the ,angels4#gec ---------------------------------------- -------------------------------- #gej ,conv4 ,,ii4 v4 and vi4 #gea ,par4 viii4 #cd-cg4 #geb ,cf4 ,par4 xxviii4 #ih to end1 with ,conv4 ,,ii4 vi4 #dc-ee1 #ajf-aji4 #gec ,par4 xxviii4 #cd-ci1 #fd-ge4 ---------------------------------------- -------------------------------- ,all these movements are a proof of the existence of a ,first ,mover1 ,himself unmoved1 as ,aquinas had said1 following ,aristotle1 and the first words of ,dante's confession of faith in ,paradise are an echo of this3-- 8,io credo in uno ,iddio1 ,solo ed eterno1 che tutto il ciel muove1 ,non moto1 con amore e con disio40#ged ---------------------------------------- -------------------------------- #ged 0,in one ,god ,i believe1 ,sole and eterne1 who moveth all the heavens1 ,with love and with desire1 ,himself unmoved40 ,par4 xxiv4 #acj-acb4 7,longfellow74 ---------------------------------------- -------------------------------- ,here1 as often elsewhere1 ,dante identifies the heavens with their ,movers1 and speaks as if the spheres themselves were moved by love and longing4 ,in the tenth heaven1 or ,empyrean1 this longing was completely fulfilled1 hence this heaven was for ever at rest4#gee ---------------------------------------- -------------------------------- #gee ,conv4 ,,ii4 iv4 #ac-cj2 ,ep4 x4 #ddb-deb1 and #dgb-dhh2 ,par4 i4 #aba-abc4 ---------------------------------------- -------------------------------- ,,viii4 ,,medi,,val ,,and ,,modern ,,views ,,of ,,the ,,universe4 ,,medi,,val ,,and ,,modern ,,views ,,of ,,the ,,universe4 ,let us now gather into one picture the details of medival astronomy which ,dante has taught us1 and try to see the universe as it presented itself to men's minds in his days4 ,motionless1 at the centre of all things1 is the earth1 a massive globe #bj1djj miles in circumference4#gef ,only the northern part of one hemisphere is inhabited2 the rest is covered by ocean4 ,it is surrounded by air1 into which rise the exhalations from land and sea which cause winds1 rain1 etc4 ,above the height to which these rise1 and above the tops of the highest mountains1 the air sweeps uninterruptedly round the earth from east to west1 sharing the movement of the skies4 ,above this again is the region of pure fire3 all fire on ,earth's surface tends to rise into it1 and hot dry vapours ascending here burst into flame1 and are seen from ,earth as shooting stars and comets4 ---------------------------------------- -------------------------------- #gef ,probably equal to #bf1ejj ,english statute miles4 ---------------------------------------- -------------------------------- ,bounding the sphere of fire is the lowest of the celestial spheres1 that of the moon2 and here we pass abruptly from the world of the four elements1 transitory1 changing1 to the celestial world1 eternal1 changeless4 ,sphere rises above sphere1 carrying moon and sun and planets1 until we reach the vast orb in which are set all the stars4 ,all these bodies are composed of a mysterious imponderable substance called ther2 all are perfectly spherical1 and all their movements are circular4 ,the diurnal rotation which we see is caused by an outermost sphere which contains no star3 it communicates its own motion to all the spheres within it4 ,the zodiacal motions of sun1 moon1 and planets1 and the precession of the equinoxes1 are caused by the proper motion of each sphere1 rotating from west to east4 ,the oscillating movements of the five planets and the varying speed of the moon are caused by small rotating spheres called epicycles1 on which planets and moon are fixed1 the epicycles in their turn being attached to the large spheres4 ,the distance from the earth to the nearest heavenly body1 which is the moon1 is #fd times the radius of the earth2 the distance of the fixed stars1 more than #bj1jjj times the radius of ,earth4 ,mercury1 the smallest of the heavenly bodies1 is only #bcb miles in diameter1#geg the moon and ,venus are both rather more than a quarter the size of the earth1 ,mars is a little larger than ,earth2 next in order of size come the stars1 from the faintest visible increasing up to those of the second magnitude2 ,saturn and ,jupiter are much larger than ,earth1 and the fifteen brightest 7first-magnitude7 stars larger still2 the sun is the largest body in the whole universe1 having a diameter #e times ,earth's diameter4 ,it is immensely bright and hot1 is the source of light to the whole universe1 and on ,earth is the chief giver of light1 heat1 and life1 and the chief measure of time4 ---------------------------------------- -------------------------------- #geg #cjj ,english statute miles4 ---------------------------------------- -------------------------------- ,the moon and stars are also useful in this way to ,earth1 and upon her are poured all the influences of the celestial spheres1 the sun1 moon1 and planets3 these are the instruments by which every event on ,earth is brought to pass4 ,it is their nature to move in circles1 as it is ,earth's nature to remain motionless at the centre of the universe2 but all their motions are controlled by the wills of immortal angels1 which are subject to the ,will of the ,first ,mover4 ,the sensible universe is eternal1 but it is finite and measurable1 and of definite form1#geh being bounded by a sphere4 ,beyond this in every direction is infinity4 ---------------------------------------- -------------------------------- #geh ,conv4 ,,iv4 ix4 #bc-be4 ---------------------------------------- -------------------------------- ,such was the medival conception of the ,universe1 as we gather from learned medival books1 and as we find it vividly pictured in ,dante's glowing verse4 ,how do we conceive it now8 ,the heavens are the same to our eyes as to ,dante's4 ,the blue dome of the sky still arches over our heads1 and in it we may see the stars shine out after the sun has set2 we may see ,venus making all the orient smile at early dawn1 and the light of the moon not yet risen paling the stars of ,scorpio4 ,we may also see with our bodily eyes what was only visible to the keen eyes of ,dante's mind1 the rising sun travelling to our left1 and the southern stars circling round the southern pole1 while the stars of the north sink below the ocean floor4#gei ---------------------------------------- -------------------------------- #gei ,compare with ,dante's accurate descriptions a poem by ,kipling in 8,a ,school ,history of ,england03-- 8,south and far south below the line ,our ,admiral leads us on4 ,above1 undreamed-of planets shine40 767 ---------------------------------------- -------------------------------- ,but to one who knows anything of modern astronomy the ideas suggested are widely different4 ,most striking is the absence of that sharp contrast between ,earth and heaven which our forefathers felt4 ,earth is not to us small1 dark1 and inert1 made of the basest material and sunk1 like the dregs of the ,universe1 to its lowest depths4 ,earth is a heavenly body1 as the ,pythagoreans rightly guessed1 a beautiful big planet1 shining brightly by reflected sunlight and moving swiftly1 like her sister-planets4 ,to ,venus she is the brightest star in the sky2 to the moon she shows a far larger disc than the moon shows to us1 and markings more beautiful and wonderful1 brilliant caps of snow at either pole1 oceans coloured blue-green1 and continents varying in tint1 whenever the dazzling white clouds part to reveal her surface4 ,earth is the largest planet among her neighbours1 ,mercury1 ,venus1 and ,mars2 just as ,jupiter is largest among the giant planets--,saturn and the more recently discovered ,uranus and ,neptune4 ,in the gap between these two groups modern astronomers have discovered hundreds of tiny planets1 to which ,earth is a monster1 for many are only a few miles in diameter4 ,the meteorites which shoot across our view1 8startling quiet eyes10 we still regard as a kind of conflagration in our upper atmosphere1 but instead of vapours rising from ,earth's surface we recognise them as visitants from inter-planetary space1 caught by ,earth's great mass as they pass too near1 and flaming up with the heat caused by their sudden rush through the air4 ,they exist in shoals of thousands and millions1 some small as pebbles1 some like great rocks1 but all belonging to our system and pursuing definite paths like planets4 ,the same must be said of comets1 which have just as little to do with a hypothetical fire-sphere round ,earth1 but travel in regular periods1 some long1 some short2 several small ones are seen every year1 and occasionally a great splendour like ,halley's draws near to us in its orbit1 yet even these seem to consist of very small quantities of matter4 ,other members of our celestial family are the moons of ,mars1 ,jupiter1 and the rest1 of which more are still being discovered4 ,the ,earth-,moon system is1 however1 unique in that our satellite is much nearer our own size than the proportionately tiny companions of other planets and the pair must look like a beautiful 8double0 moving through the stars and continually revolving round one another4 ,illustration3 ,fig4 #ec4 ,comparative sizes of the ,sun and his satellites4 p4 #dij ,all these bodies are made1 not of a mysterious ether1 but of something just as wonderful1 beautiful1 and incomprehensible--the same stuff as ,earth4 ,most probably all developed in long-past ages out of a nebula1 or mass of gas which for some unknown reason was intensely hot4 ,small bodies1 like the ,moon and ,mars1 cooled off the most quickly1 and have lost or are losing their air and their water2 larger bodies1 like ,jupiter1 have still some heat1 and are probably in a more or less fluid condition4 ,on the sun an inconceivable heat still rages2 everything is in a gaseous state1 and this globe which men used to think eternally changeless is the scene of the fiercest turmoil2 currents are always ascending and descending1 clouds of fire are flung up thousands of miles high1 and patches which look black compared with the surrounding surface and indicate a mysterious commotion are constantly forming1 developing1 and disappearing4 ,the sun is enormously larger than ,dante thought1 larger than all the planets put together1 large enough for our moon's whole orbit to fit comfortably inside4 ,it is hot enough and brilliant enough to light all the planets3 this1 which was only a guess of medival astronomers1 we know as a fact to-day1 and the planets which are suitably placed show it to us1 when seen in the telescope2 ,venus1 for instance1 changing her phase 8according as the sun looks upon her10 exactly like the moon4 ,and ,earth must show similar phases as seen from ,mars4 ,for ,aristarchus was right3 the sun is the centre of the planetary movements1 including those of the planet ,earth4 ,we saw how ,ptolemy's system hinted at this1 in the significant connection between each planet's movement and the movement of the sun2 but a strong argument against it was that if ,earth were really moving round the sun we ought to see a yearly displacement in the positions of all the stars4 ,modern instruments have at last made it possible to perceive this displacement4 ,about a hundred stars1 our nearest neighbours1 describe a very minute orbit in the sky1 which in every case is an exact reflection of the sun's apparent orbit round the earth4 ,unless1 therefore1 we are going to provide all these stars1 as well as the planets1 with epicycles1 which must all revolve in the same period1 in the same direction1 and in parallel planes1 we must conclude that the movement is really ,earth's yearly movement round the sun4 ,these miniature star-orbits also show us the stupendous distances which lie between ,earth and the nearest stars1 while by far the greater number are too remote to show any displacement at all4 ,aristarchus and those other ancient astronomers were also right who thought that ,earth was turning on her axis1 and thus producing by her own motion the alternation of day and night1 and the apparent circling of the stars4 ,when we look now at stars hastening across the sky1 they no longer present themselves to our thought as fixed on a sphere with a radius of #bj1jjj ,earth-radii1 which is revolving round us at a tremendous speed2 we feel that we are looking into space at glowing globes which are at various and almost inconceivable distances from us2 also that all those we see1 all those that ,hipparchus numbered1 are but an insignificant fraction of all those now known to exist4 ,all have their own real motions1 as well as the apparent motions produced by ,earth1 but these are in different directions1 towards what goal we cannot at present tell4 ,compared with them1 ,earth is indeed insignificant1 in size and also in brightness1 for while she shines with reflected light they glow as the sun does and are his peers4 ,nevertheless1 with them too we have a feeling of kinship1 for analysis of their light shows that they too are made of earth-stuffs3 they are not eternal nor changeless1 for very many vary constantly in their light1 and they are at different stages of development1 some appearing very young1 while others are beginning to burn dim and low1 and some can only be inferred to exist1 for they seem to be wholly dark4 ,more wonderful perhaps than anything else1 we find that the force which binds the whole of our sun's family together is nothing strange and unknown1 but the same familiar force of gravity1 which the ,greeks knew so well but thought only applicable to ,earth4 ,its rule includes the seemingly unruly comets and meteors1 and it extends as far as our search can reach1 to the uttermost star4 ,this sense of unity throughout the world1 which is always growing stronger1 is comforting4 ,and we allow ourselves to wonder whether intelligent life has not developed elsewhere1 as well as on this globe that we inhabit4 ,perhaps each planet that attends our sun is fitted at some period to be the abode of life3 surely among the millions of stars many must have attendant planets1 and on some of them even now are living1 thinking1 beings4 ,dante's world was easier to think about than ours4 ,encompassed by an infinity which gave the imagination free scope1 the material universe within was neatly rounded off1 as it were1 complete1 finished4 ,only in the central spot was any development taking place1 and thither were directed all effects of the circling spheres4 ,our universe is vague1 vast1 mysterious1 without known limits or centre1 offering problem after problem to the thinker4 ,dante's marvellous moon-substance is simple compared with the baffling nature of our ther2 ,dante's ,angel-,movers are intelligible compared with the amazing mystery of universal gravitation4 ,yet when we lift our eyes from earth to heaven1 we share the feeling of our medival forefathers1 of the ancient ,greeks1 of the earliest men whenever and wherever they became men4 ,the unerring courses of the stars speak to us1 8the unperturbed to the perturbed10 of perfect harmony1 untouched by chance or arbitary conflicting wills4 ,now1 however1 we do not believe this is because heaven is essentially different from earth3 it is because we see there only the grand outlines1 only the working of great laws1 of a system which includes our own earth4 ,could we but lose sight of the details here1 and view the history of man as we view the stars1 the harmony would be as grand4 ,,hymn ,,to ,,zeus4 ,most glorious of the ,immortals1 many-named1 ,almighty for ever1 ,zeus1 ,ruler of ,nature1 that governest all things with law1 ,hail6 for lawful it is that all mortals should address thee4 ,for we are thy offspring1 taking the image only of thy voice1 as many mortal things as live and move upon the earth4 ,therefore will ,i hymn thee1 and sing thy might for ever4 ,for thee doth all this universe that circles round the earth obey1 moving whithersoever thou leadest1 and is gladly swayed by thee4 ,such a minister hast thou in thine invincible hands--the two-edged1 blazing1 imperishable thunderbolt4 ,for under its stroke all nature shuddereth1 and by it thou guidest aright the universal ,reason1 that roams through all things1 mingling itself with the greater and lesser lights1 till it has grown so great1 and become supreme king of all4 ,nor is aught done on the earth without thee1 ,o ,god1 nor in the divine sphere of the heavens1 nor in the sea1 ,save the works that evil men do in their folly4 ,yea1 but thou knowest even to find a place for superfluous things1 and to order that which is disorderly1 and things not dear to men are dear to thee4 ,thou dost harmonize into one all good and evil things1 that there should be one everlasting ,reason of them all4 ,and this the evil among mortal men avoid and heed not wretched1 ever desiring to possess the good2 yet they nor see nor hear the ,universal ,law of ,god1 which1 obeying with all their heart1 their life would be well4 ,but they rush graceless each to his own aim1 ,some cherishing lust for fame1 the nurse of evil strife1 ,some bent on monstrous gain1 ,some turned to folly and the sweet works of the flesh1 ,hastening indeed to bring the very contrary of these things to pass4 ,but thou1 ,o ,zeus1 the all-giver1 dweller in the darkness of cloud1 lord of thunder1 save thou men from their unhappy folly1 ,which do thou1 ,o ,father1 scatter from their souls1 and give them to discover the wisdom1 in whose assurance thou governest all things with justice2 ,so that1 being honoured1 they may pay thee honour1 ,hymning thy works continually1 as it beseems a mortal man1 ,since there can be no greater glory for men or gods than this1 ,duly to praise for ever the ,universal ,law4 ,,cleanthes 7#crd century ,b4,c474 ,translation by ,t4 ,w4 ,rolleston4 ,,index4 7,pages #a to #bjf are in ,part ,i43 #bjg onwards1 in ,part ,,ii47 ,abrachis 7,hipparchus71 #aic ,abul ,hazan1 #ahd ,abul ,wefa1 #ahc1 #aid 8,acerba10 #bbg1 #bdc ,achernar1 #ab1 #aee1 #aef1 #bie ,achilles1 ,shield of1 #ec ,adam1 #cdi1 #dch ,albategnius1 #ahc1 #aic1 #bjb1 #bci1 #bge ,albertus ,magnus1 #bjd1 #bcb1 #bcg1 #bci1 #bda1 #bib1 #cjf1 #cbd1 #cdb1 #dcb1 #ddc1 #ded 0 and meteors1 #cai ,albert of ,saxony1 #dfd1 n4#dfe ,al ,betrugi 7,alpetragius71 #ahd ,albumassar1 #bci1 #bde1 #ddc1 #dgc ,alchabicius1 #bjb ,alchemy1 #bab-ac1 #bae ,aldebaran1 #aee1 #aef ,alexander the ,great1 #gi1 #hj1 #aab1 #ade ,alexandria1 #aac1 #aah1 #abb1 #acd1 #ace1 #aef1 #aeg1 #agb 0 ,astronomers of1 #abb1 #abd1 #acg1 #aec1 #afc1 #aga1 #age1 #bhh 0 ,museum and observatory of1 #aac1 #aad1 #aaf1 #aag1 #abb1 #ace 0 ,school of1 #aab et seq41 #afc ,alfarcatein1 #ahg1 #bcd ,alfonso ,x41 #aie1 #bjc1 #bdb ,alfraganus1 #ahc1 #bcc-cg1 #bdc 0 editions of1 #bce1 #dcg1 n4#deh 0 geography of1 #ccg 0 writings of1 #ahd et seq41 #aic-d 0 and climates1 #cbd1 #cig 0 0 colure1 #djc 0 0 ,dante1 #bec1 #bed1 #bgc1 #bge1 #bhf1 #bhh-ij1 #bii1 #cac1 #cae1 #cbh1 #cce1 #cdg1 #djc1 n4#djc1 #dcf-cg1 #ddd1 #ddh-ea1 #deh-i 0 and eclipses1 #cch 0 0 meteors1 #cbj 0 0 moon1 #cdi1 #ddh-di 0 0 precession1 #bhh1 #dci 0 0 ,regulus1 #djf 0 0 ,ristoro1 #bde-dg ,algazel1 #bde ,almagest1 #aad1 n4#aae1 #abc1 #acf1 #aed1 #aei1 #afc1 #ahb1 #ahd1 #aic1 #bji1 #bah1 #bcb1 #bch 0 translations of1 #bja-b ,al ,mamun1 #ahb1 #ahe1 #ahf1 #aib #8,almanach ,dantis ,aligherii1' #dba-bc ,al ,mansur1 #aha ,alpha ,draconis1 #abg 0 ,centauri1 #aee1 #aia 0 ,phnicis1 #aef ,amerigo ,vespucci1 #bid ,anaxagoras1 #fj1 #fa1 #gf1 #ih1 #bci1 #cje ,anaximander1 #bf1 #ef1 #ff1 #ge1 #gf1 #ia1 #ii ,anaximenes1 #fj1 #ih ,andrea ,corsali1 #bid ,angelitti1 ,prof41 #bha1 #daj1 #dae1 #dag1 #dbc ,angels1 #bdi1 #bhd1 #cjb1 #caa1 #chh1 #dad-ae1 #dda1 #dgg1 #dhb-hd1 #dhi1 #did ,angelo de ,gubernatis1 n4#cii ,anomaly1 of planets1 #adj1 #adc ,antus1 #cga ,antares1 #cj ,antichthon1 #ga1 #ge1 #aja1 #bcf ,antipodes1 #ff1 #agf1 #cbd ,antonelli1 n4#bie ,apogee1 #aai2 of moon1 #adh1 #ddi1 #dej2 of sun1 #adf1 #aic ,apollonius1 #aah1 #ada ,aquarius1 #cc1 n4#cf1 #ade1 #adi1 #aef1 #bgg1 #bij1 #che ,aquila1 #ab ,aquinas1 ,st4 ,thomas1 #bja1 #bjd et seq41 #baa1 #bcg1 #bch1 #bda1 #cjf1 #cci1 #ded1 #dgi1 #dhc1 #dhd ,arabs 7see also ,mahomedan7 0 astronomers1 #bah2 year1 #ci2 zodiac1 #cj 0 and astrology1 #bac2 astronomy1 #aha et seq4 ,aratus1 #be ,note1 #ca1 #cb1 #cd1 #ce1 n4#ce1 #eh1 #afh ,archimedes1 #ajg ,arcturus1 #cf1 #eb1 #aee1 #aij1 #aia ,arculf1 #agf ,argo1 n4#cf ,aries 7see also ,ram71 #dj1 n4#dc1 #bfe1 #bgi1 #bha1 #bij1 #cbe1 #cef1 #cfh1 #cgc1 #cgd1 #chg1 #cih1 n4#cii 0 first point of1 #abi1 #ahe1 #bgg1 #ceg1 #djc1 #djd 0 and astrology1 #bdi 0 0 ,jupiter1 #dah 0 0 ,mars1 #dgf 0 0 ,sun1 #bgg1 #bgh1 #bha1 #cbc1 #cbe1 #ccc1 #cfg1 #cfh1 #chc1 #cif1 #cih1 #djb-e1 #dah1 #dai1 #dbb1 #dgc ,aristarchus1 #ajg et seq41 #aaa1 #abj1 #aba1 #aec1 #aia1 #dib ,aristophanes1 #afb ,aristotle1 #eh1 #ff1 #ie et seq4 0 cosmogony of1 #aja-jb1 #ajc et seq41 #abc1 #afj1 #bja1 #bjd 0 influence on science1 #hj1 #acf1 #ahb1 #ahd1 #aic 0 translations of1 #bad1 #bcg 0 and ,arabs1 #ahd 0 0 ,averros1 #dfc 0 0 ,calippus1 #ie1 #ajg 0 0 the ,galaxy1 #bcg1 #cje1 #cjf 0 0 ,dante1 #bce-ch1 #bda1 #bed-ee1 #bfa1 #cja1 n4#cba1 #cdb1 #dca1 #ddb1 #dea1 #ded1 #dfd-fe1 #dhj-hd 0 0 gravity1 #dde 0 0 ,latin authors1 #agj 0 0 ,mars1 #caj1 #dcc 0 0 meteors1 #cai1 #cba 0 0 music of the spheres1 #dee 0 0 ,plato1 #he 0 0 southern hemisphere1 #cec 0 0 spheres #dca1 #dcb1 #dcd1 #dfa ,aruns1 #dgb ,aryabhata1 #aaj-aa ,arym1 #bdg1 #cbi ,arzachel1 #ahd1 #aie ,asdente1 #bab1 #dgb ,assisi1 ,st4 ,francis of1 #bga ,astrolabe1 #aad1 #aae1 #abb1 #add1 #aib1 #bjb1 #bjc1 #cda 0 invention of1 #aae1 #acc ,astrologers1 #bac1 #bca1 #cfi1 #dai1 #dfi1 #dgf 0 of ,brescia1 #baa2 #acth century1 #baf ,astrology 7see also ,star ,influence1 and ,astronomy1 ,judicial71 #f1 #de1 #dg1 #aeg1 #afa1 #agb1 #baa et seq41 #bah1 #bdc1 #bde1 #bdi1 #cjh1 #dga1 #dgf1 #dgh-i 0 ,arab1 #ahc1 #bjj1 #bac 0 books on1 #bjb-c 0 ,egyptian1 #aac1 #aeg 0 ,jewish1 #bac 0 professors of1 #bjj 0 and planets1 #baa ,astronomy1 ,alexandrian1 #aab et seq41 #bah1 #bca1 #bhh1 #cce 0 ,arab1 #aha et seq41 #aij1 #bjd1 #bcb1 #bci1 #bdc1 #bde1 #dfa-c 0 ,babylonian1 #dj et seq41 #bji1 #dba 7see also ,babylonians7 0 ,chinese1 #bi et seq41 #aae 0 ,egyptian1 #bji 7see also ,egyptians7 0 ,greek1 #bji1 #bcf1 #cad1 #dde1 #dfa 7see also ,greeks7 0 ,indian 7see ,hindu1 and ,india7 0 judicial1 #abd1 #bac1 #bcc1 #bfa 7see also ,astrology7 0 ,moorish1 n4#bjj1 #bjc 0 ,persian1 #aie 0 primitive of1 #be et seq4 0 in ,spain1 #ahc1 #aid 0 taught by ,church1 #agf 0 personified1 #bag 0 and ,dante1 #a ,atlas1 #ih2 ,mt4 ,atlas1 #ec ,augustine1 ,st41 #age1 #bch1 #bci1 #dgi ,augustus1 ,emperor1 #aga1 #age1 #cai1 #cei ,auriga 7,charioteer71 #add ,averros1 #ahd1 #bjd1 #bcb1 #bci1 #bdf1 #cdb1 #dcb1 #dfb ,avicenna1 #bjb1 #bci1 #bdg1 #cje ,babylon1 #fi1 #hj1 #aef1 #aha ,babylonia1 #ah1 #cf1 #ha ,babylonians1 #cf-ch2 astronomers1 #aaj1 #abe1 #abg1 #add1 #afa 0 and astronomy1 #dc-d 0 0 calendar1 #dj et seq4 0 0 cosmogony1 #de1 #df1 #dg1 #dh1 #ee1 #eg 0 0 day division1 #bg 0 0 eclipse records1 #hj1 #ha1 #add 0 0 gnomon1 #bf 0 0 occultations of planets1 #aje ,bacon1 ,roger1 #bjb1 #bdi1 #bge1 #bib1 #cdb1 #cdc ,baghdad1 #ada-c1 #aha et seq41 #bde1 #dcb 0 astronomers1 #aid-e 0 observatory1 #adb 7see also ,arab ,astronomers7 ,bartolommeo della ,scala1 #bbf1 #bbg ,bear3 ,great1 #ab1 #be1 #cf1 #eb1 #ef1 #aeg1 #ahg1 #big-h1 #ccd2 ,little1 #be1 #ef1 #ahg1 #big-ih1 #ccd 7see also ,ursa ,major and ,minor7 ,beatrice1 #a1 #bec1 #bcg1 #bhd1 #cgf1 #cij1 #cib1 #cid1 #dja1 #dda1 #dee1 #dgc 0 age of1 #bec1 #bhh1 #dac-d 0 death of1 #bbd1 #bec1 #bed1 #cad1 #caf1 #dad 0 ,dante's first meeting with1 #bec1 #bgb1 #bgc 0 guiding ,dante1 #bfb1 #ccj1 #cfg1 #cgc1 #cib1 #cic1 #djj1 #dja 0 and ,moon1 #dfb1 #dge 0 0 ,sun1 #bga1 #cib ,beazley1 n4#cdb1 n4#chd ,bede1 #agh1 #bej1 #ded ,belacqua1 #cgf ,benet ,naax1 #ahg1 #bcd ,benevento1 #bdb ,benvenuto da ,imola1 #chc1 #dah ,betelgeux1 #aee ,boccaccio1 #bbd1 #bbe1 #bbh1 #bca1 #bgd1 #dac1 #dad1 #dah1 #dbb ,bothius1 #a1 #agg1 #bhd1 #bif ,boffito1 ,prof41 #dbc ,bologna1 #aii et seq41 #bbg1 #bgg 7see also ,universities7 ,botes1 #eb1 #bhd1 #bih ,borneo1 natives of1 and gnomon1 #bf ,british ,astronomical ,association1 ,journal of1 n4#bi1 n4#cd 0 ,museum1 #cf1 #dj ,brown1 ,robert1 #bd ,note1 #cb1 n4#cd1 #ce1 #aef ,brunetto ,latini1 #bah1 #bbe-f1 #bda-b1 #bdh-i1 #bgd-e1 #bib1 n4#cdi1 #cfi1 #dad1 #dgj1 #dgc1 #dha ,bull1 see ,taurus ,cacciaguida1 #c1 #cac ,calendar1 #bi1 #cf1 #dg2 ,ancient1 #cc1 #cd 0 ,arab1 #ci1 #ahd 0 ,babylonian1 #dj1 #da1 #abg 0 ,berber1 ,persian1 ,syrian1 #ahd 0 ,chinese1 #ci 0 ,ecclesiastical1 #agf1 #bjc 0 ,egyptian1 #ci1 #ahd 0 ,greek1 #afa1 #afb1 n4#agb 0 ,hindu and ,parsee1 #abg 0 ,julian1 and ,roman1 #aga1 #agf1 #ahd1 #bgd et seq4 0 luni-solar1 #agf 0 ,mahomedan1 #ci ,calippus1 #ic1 #ajg1 #ade1 #afb2 cycle1 #agb ,callisthenes1 #hj ,campaldino1 #bbd ,cancer1 #ade1 #agd1 #ahe1 #bfi1 #bgg1 #bhj-b1 #cbe1 #cid1 #cig ,can ,grande della ,scala1 #daf1 #dbf1 #dda1 #dgc ,canopus1 #ab1 #fg1 #acd1 #aee1 #bie ,canton1 #bg ,capella 7star71 #aee 0 ,martianus1 #agj1 #agg ,capricornus1 #cc1 #dc1 #add1 #ahe1 #bgg1 #bhb1 #cbe1 #cdb1 #cfj1 #cgd ,carnac1 #bi ,casella1 #cgd1 #dad1 #dbf ,cassiodorus1 #agg ,cassiopeia1 #ab ,castor and ,pollux1 #dc1 #bij1 #ccc ,catalano1 ,friar1 #bbg ,cato1 #cgc-d ,cecco d' ,ascoli1 #bjj1 #baf1 #bbf1 n4#bbg1 #bda-d1 #bdi1 #dgh ,celestial ,movements1 #i-bj1 #be1 #bh1 #bi1 #ch1 #dg1 #ef1 #fb1 #fe1 #hf1 #ajb-c1 #aje1 #acf et seq41 #aei1 #agd1 #bji1 #bdh1 #bfa-d1 #bii1 #ceg1 #cfg1 #dji1 #dbi1 #dcj1 #dcb1 #dch1 #deg1 #dhc1 #dhg 0 direct1 #af1 #adg 0 and ,alfraganus1 #ahe et seq4 0 0 astrology1 #baa 0 0 ,brunetto ,latini1 #bdc 0 0 tables of1 #bb1 #bc 0 0 daily1 #ac 0 0 retrograde1 #af1 #ah1 #dd1 #aaf1 #adg ,centaur1 n4#cf1 #bid2 ,alpha ,centauri1 #aee ,central ,fire1 #ge1 #he1 #aja1 #ajb1 #aji1 #aei ,cetus1 n4#cf ,chalcidius1 #bch ,chaldea1 #agb ,charioteer1 see ,auriga ,charlemagne1 #agh1 #ahb ,charles of ,hungary1 #bef ,charles of ,valois1 #cah ,chinese1 and comets1 #de2 gnomon1 #bj1 #aad2 year1 #ch2 zodiac1 #bi1 #ca ,china1 #bia1 #cdc ,christian ,era1 ,introduction of1 #agg ,church1 ,catholic1 #baj1 #baf1 #bai1 #cce1 #cdf-h1 #daj1 #dai1 #dca1 #dcb1 #dhj1 #dhc2 and spheres1 #dcc ,cicero1 #a1 #aji1 #afg-h1 #aga1 #bag1 #bcg-i ,cleanthes1 #dif ,cleomedes1 #ace1 #deg ,clepsydra1 #bg1 #aae1 #abb1 #acc1 #ada ,climates1 #aeh1 #ahf1 #ahg1 #bdg-h1 #cbd1 #cdg1 #cig ,clocks1 pendulum1 #af2 water1 #bg1 #aae 7see also ,clepsydra7 ,colure1 #ahe1 #djc ,comets1 #de1 #ff1 #ajc1 #agd1 #age1 #agf1 #bfb1 #cah et seq41 #dhg1 #dij1 #dia 8,composizione del ,mondo10 #bdd et seq41 #bib ,conjunction1 #bd1 #adb1 #aia 8,consolations of ,philosophy10 #a ,constantine1 #bfb ,constantinople1 #bja ,constellations1 #ded2 ancient1 #cc1 #cd1 #hj 0 ,arab1 #cj1 #ahh1 #bcd 0 ,egyptian1 #cd2 ,hebrew1 #cd2 ,hindu1 #cj 0 figures of1 #aae1 #aed-ee1 #afh1 #bdf1 #bdh1 #bhi1 #ddc1 #dea 0 influences of1 #bdf1 #dea 0 naming and origins of1 #bd ,note1 #cb1 #cc1 #cf1 #dg1 #ea1 #hj1 #afa 0 southern1 #bdf 0 and ,astrology1 #baa 8,convivio10 #bee1 #beh1 #ceg1 #dfd1 #dff1 #dfh1 #dgf ,copernicus1 #ff1 #aaa1 #acf1 #baj ,cordova1 #ahc ,corona ,borealis1 #bii ,corsica1 #cdd1 #chc1 #chd ,corvino1 #bic1 #cdc ,corvus1 n4#cf ,cosmas ,indicopleustes1 #age ,cosmogonies1 ,ancient1 #de1 #fc1 #afj2 ,babylonian1 #de1 #ec1 #eg2 ,egyptian1 #de1 #ec1 #hc1 #aji2 ,hebrew1 #de1 #dg2 ,hindu1 #de2 ,homeric1 #ec do4 of ,anaximander #eh-ei2 ,aristotle1 #ajc2 ,cosmas1 #age2 ,democritus1 #fc2 ,eudoxus1 #hh2 ,leucippus1 #fc2 ,philolaus1 #gj2 ,plato1 #hc2 ,ptolemy1 #aej2 ,pythagorean1 #ff-ge2 ,thales1 #ee1 #ef ,coulton1 n4#bab ,creation1 #djc1 #daa1 #dai ,crystal ,spheres1 #gd1 #aei 7see also ,spheres7 ,cunizza1 #dae1 #dbf1 #dgb ,cycles1 #de1 #ee ,cyprus1 #ajb ,dante1 birth of1 #baa1 #bgc1 #dac1 #dbf2 childhood1 #bbc2 as ,councillor1 #bbd1 #dad2 as ,prior1 #bbd2 in exile1 #bbd2 in ,ravenna1 #bbd1 #bgc2 in ,mantua1 #ddd2 in ,rome1 #bbd1 #cah2 in ,verona1 #bef1 #ddd2 death1 #afe1 #baf1 #bbd1 #bgc 0 studies1 #bbc et seq42 quoted1 #be 0 shadow of1 in ,purgatory1 #cgd1 #chg-h 0 wife of1 #bbd-e 0 and ,alfraganus1 #bcd1 #bed1 #bhi1 #ddi2 ,asdente1 #bab 0 0 ,aristotle1 #if1 #ajb1 #aje1 #bce1 #bda1 #bed1 #dhj1 #dhb 0 0 ancient writers1 #eg1 #fb1 #gj1 #hb1 #hf 0 0 astrology1 #bfa2 and astronomy1 #be 0 0 ,brunetto ,latini1 #bbe1 #bbf1 #bdb 0 0 ,beatrice1 #a1 #bgc 0 0 calendar1 #bgd1 #bge 0 0 ,date of ,vision1 #ceg1 #dji et seq4 0 0 ,classical authors1 #bcg et seq4 0 0 ,frederick ,,ii41 #bad 0 0 ,greek astronomy1 #aje1 #bfb1 #cjf 0 0 philosophers1 #dfa 0 0 ,homer1 #bji 0 0 geography1 #ccg1 #cci et seq4 0 0 ,jerusalem1 #agf 0 0 ,michael ,scot1 #bae 0 0 ,milton1 #baj 0 0 ,moon1 #bfe et seq4 0 0 music of the ,spheres1 #dee-f 0 0 precession1 #bgd et seq41 #dci 0 0 ,philosophy1 #bee 0 0 ,ptolemy1 #ace1 #aed1 #bji1 #bcb1 #bef1 #deh-i1 #dfh 0 0 ,roman ,empire1 #afg1 #agh 0 0 science1 #a1 #bai1 #beh 0 0 the ,acerba1 #bdd 0 0 stars1 #bhc et seq4 0 0 southern stars1 #bic-e 0 0 universities1 #bbf et seq4 8,dante e gli ,astronomi ,italiani10 n4#bce1 n4#cae ,day1 ,arab1 #bec2 definitions of1 #ad1 #bb1 #be1 #bf2 divisions of1 #eb1 #afa2 length of1 #ahf2 sidereal1 #ab1 definition of1 #bb2 solar1 #ab2 ,church1 #cdh ,decimal ,notation1 introduced1 #ahb ,declination1 definition of1 #abf 8,de ,clo0 78,on the ,heavens071 of ,aristotle1 #if1 n4#if1 #aje1 #agj1 n4#bcb1 #bcf1 #dca1 #dfd translations of1 #bad 8,de ,clo0 of ,albertus ,magnus1 n4#bcb1 #cdb ,deferent1 definition of1 #ach2 #ade1 n4#adi1 #aic ,degrees1 invention of1 #dd ,delambre1 n4#ce1 n4#abf1 #adi1 #aef1 n4#dfj ,della ,lana1 ,jacopo1 #dah ,della ,valle1 n4#cih ,del ,virgilio1 #bbg ,democritus1 #fd et seq41 #ih1 #bci1 #cje ,denebola1 #aee 8,de ,substantia ,orbis10 #ahd ,dicuil1 #agh ,dilgan1 #dj1 #db1 #abg ,dionysius ,exiguus1 #agg 0 the ,academician1 #bci 0 0 ,areopagite1 #dhc ,direct ,motion1 #af ,divine ,comedy1 #bcg-h1 #cec1 #djb1 #dji ,dominicans1 #bjd1 #bda ,domitian1 #aga ,dream of ,scipio1 #aji1 #afi1 #bcg ,dreyer1 n4#dfj ,dupuis1 #cd ,earth1 #cic1 #cie1 #cih-dja1 #dij1 #dia 0 centre of1 #cec1 #cgb1 #dbd1 #dha 0 0 of universe1 #ff1 #ge1 #hc1 #hd1 #he1 #hh1 #ia1 #if1 #ih1 #ii1 #ajj1 #aji1 #aab1 #abj1 #acg1 #afj1 #afi1 #ahe1 #bjc1 #bje1 #bji1 #bai1 #dca1 #ddd1 #dfa1 #dhi 0 ,counter-1 see ,antichthon 0 dimensions of1 #ga1 #ajb1 #aag1 #aah1 #acd1 #aeg1 #afj1 #afi1 #ahb1 #ahe1 #ahf1 #aij1 #baf1 #deh1 #dhg1 #dij 0 distance from sun1 #ajh1 #ahi 0 form of1 #ef1 #ei1 #fc1 #ff1 #fg-h1 #ga1 #gb1 #hc1 #ia1 #if1 #ih1 #ajj1 #afj1 #age1 #ahe1 #ahf 0 habitable part1 #bje1 #bdg1 #bdh1 #cce1 #cdb1 #cec1 #cfi1 #cgb1 #cia1 #cig1 #cih1 #dcf1 #ddd1 #ddf1 #dea1 #dhg 0 in equilibrium1 #ajj 0 measurement of1 #ajc1 #aag1 #acd 0 motion of1 #ag1 #ff1 #gj1 #ga1 #he1 #hh1 #ii1 #aja1 #adb1 #ahf2 0 movement of1 #dca1 #dch 0 resting on air1 #fc2 on water1 #ef1 #ih 0 revolution round sun1 #ac1 #ff1 #ajg1 #aji1 #aaj1 #abj1 #adf1 #aei1 #baj1 #bef1 #dib 0 rotation on axis1 #ac1 #gb1 #ge1 #he1 #hh1 #aja1 #ajh1 #aaj1 #acf1 #aei1 #baj1 #dib 0 shadow of1 #fg1 #if1 #aia1 #cdf1 #dei1 #dfj 0 spherical form of 7see also form of earth71 #ajb1 #bji1 #bai1 #bcg1 #dhg ,earthly ,paradise1 see ,eden ,easter1 #agf1 #agg1 #bjc1 #bge1 #dje1 #dah1 #dbj1 #dbb1 #dbd 0 year1 #dae ,ebn ,jounis1 #ahc ,eccentrics1 #aah1 #aai1 #aba1 #ada et seq41 #aic1 #baj1 #bce ,eclipses1 #ah1 #ee1 #eg1 #fg1 n4#gf1 #aag1 #afh1 #agd1 #age1 #aib1 #bjc1 #bfb1 #bee et seq41 #bff1 #dfe 0 annular1 #dd 0 ,babylonian records1 #hj1 #if1 #aac1 #add 0 lunar1 #dd1 #de1 #ee1 #fg1 #abe1 #ahe1 #cch1 #cdj1 #cda1 #dfi 0 solar1 #bde1 #cch ,ecliptic1 #ah1 #ee1 #aag1 #abf1 #abi1 #acj1 #ade1 #adg1 #ahe1 #bgi1 #cab1 #cbe1 #ccj1 #cca1 #ccc1 #cig1 #djc1 #djd1 #dgf ,ecphantus1 #ge1 #ajb ,eden1 #bje1 #bie1 #bif1 #ccd1 #cdi1 #cec1 #cid1 #dja1 #dec1 #ded 0 ,richard1 #bii #8,egyptian ,system1' #aji1 #abj 0 year1 #ch1 #de ,egyptians 7also ,egypt71 #bg1 #bh1 #cf1 #de1 #fg 0 astronomers1 #ee1 #ef1 #aje1 #abd1 #abe1 #add 0 astrology1 #aac1 #abj1 #aef 0 astronomy1 #cd1 #de1 #df1 #ea1 #hj1 #aac1 #ahd 0 cosmogony1 #de1 #ec1 #ee 0 and ,eudoxus1 #ff1 #hh1 #ajj1 #aea 0 0 ,pythagoras1 #fg 0 0 eclipses1 #de #8,elementa ,astronomica1' #ahd1 #bcd1 #bec1 #bgc1 #cac1 #cbj1 #cdg 0 translations of1 #bcd ,elements1 ,the ,four1 #fb1 #hc1 #ajc1 #bcf1 #dda et seq41 #dfa1 #dgh 0 0 creation of1 #dda 0 0 and ,aristotle1 #bcf1 #ddb ,ellipse1 n4#id ,elongation1 ,greatest1 ,e4 and ,w41 #adb2 definition of1 #ae ,empedocles1 #fj1 #fb1 #ih1 #cfi ,empyrean1 #bjd1 n4#bcb1 #bec1 #bif1 #cac1 #cec1 #cic1 #dja1 #dcc1 #ddj1 #ddd1 #dfb1 #ddg1 #dhd ,epicycles1 def4 of1 #ach et seq41 #aba1 n4#adi1 #ahg1 #aic1 #aid1 #baj1 #bce1 #bef1 #cad1 #dbi1 #dce1 #ddi1 #deg1 #dff1 #dhc1 #dhh1 #dib 0 of ,venus1 #adb1 #dce ,epping and ,strassmeier1 n4#cf ,equator 7celestial71 #aj et seq41 #ah1 #ce1 n4#ce1 #fe1 #aae1 #abf1 #acj1 #ahe1 #cbc1 #ccj1 #ccd1 #cfh1 #chc1 #cib1 #cig1 #djc1 #djd1 #dci1 #ddh1 #dgf 0 terrestrial1 #bch1 #bdf1 #bdg1 #cbb1 #cbd1 #cbi1 #ccf1 #ccg1 #cdb ,equinox1 #cj1 #abd1 #abf1 #bgd1 #bgh1 #bhb1 #cbf1 #ccj1 #ccd1 #cdj1 #cdg1 #cdh1 #cdi1 #ced1 #cef1 #cfh1 #cgb1 #chc1 #chg1 #cib1 #djb-g1 #daj1 #dah1 #dbj-c 0 date of1 #bf1 #agf1 #agg1 #ahe 0 definition of1 #ab 0 observation of1 #ci1 #id1 #aaf1 #abd1 #abe 0 position of1 n4#dd1 #ahe 0 precession of1 #bc1 #bd1 #ce1 #abe1 #acc1 #ace1 #acg1 #afa1 #aic1 #aid1 #bcb1 #bge1 #bhg1 #cef1 #chd1 #dcb1 #dce1 #dci1 #dhc1 #dhh 0 and ,alfraganus1 #dci ,eratosthenes1 #aag1 #acd1 #bdj ,eridanus1 78,the ,river07 n4#ce1 n4#cf1 #aee1 #aef ,eridu1 #df ,esdras1 #cdb ,ether1 #ajd1 #aaj1 #acg1 #aei1 #aic1 #dcc1 #dfa1 #dff1 #dhj1 #dhh1 #dia ,ethiopia1 #ccf2 ,ethiopians1 #ec ,euclid1 #aah1 #bjb ,euctemon1 #ic1 #afa ,eudoxus1 #ff et seq41 #cd1 #hj1 #bce2 spheres of1 #ij1 #ajf1 #ajg1 #aji1 #aab1 #aac1 #aah1 #abc1 #ada1 #aei1 #afa1 #agj 0 and ,calippus1 #ic1 #id2 and ,egypt1 #hj1 #ajj1 #aei2 and ,plato1 #ha1 #hh1 #aei ,eunoe1 #cff1 #cij1 #cib ,evection1 #adg ,farinata1 #dac1 #dag ,fergil1 #agh ,filelfo1 #dga ,fire2 ,central1 #dca2 sphere or region of1 #eh1 #cjh1 #ddb1 #dhj1 #dhg ,first ,mover1 #ajf1 #aei1 #bjd1 #bed1 #ddd1 #dgh1 #dhc1 #dhd1 #dhi ,fishes 7see ,pisces7 ,florence1 #a1 #aeh1 #bja1 #baa1 #bae1 #baf1 #bbd1 #bbe1 #bbf1 #bdb1 #bhc1 #cah1 #cde1 #cej1 #djf1 #daa-ad1 #dag1 #dba1 #dga ,folco1 #cdf1 #dei1 #dgb ,fomalhaut1 #aee1 #aef ,forese1 #cfg ,forest1 ,the1 #bff1 #ceh1 #cfg1 #cfi1 #cgh1 #chf1 #djf ,francis1 ,st41 #bga ,frederick ,,ii41 #bjb1 #bac et seq4 ,gades1 #cdj1 #cde1 #cff1 #cie1 #cig ,galaxy1 #fa1 #ajc1 #aae1 #aed1 #afh1 #bcb1 #bci1 #cja1 #cjc et seq41 #dgg ,galileo1 #ajg1 #baj ,gallus1 ,sulpicius1 #afg ,ganges1 #bje1 #cdj-e1 #cfj1 #cfe1 #chh1 #cig1 #djj ,gardner1 ,e4 ,g41 #bbh ,gemini 7see also ,twins71 #dc1 #dd1 #ade1 #adi1 #bgc1 #bhj-a1 #bij1 #ccc1 #cff1 #chg1 #cic1 #cid1 #cig1 n4#cii1 #djd1 #dfa1 #dgc ,geminus1 n4#ic1 #acd ,genoa1 #bic ,geography1 #bdj1 #cdd2 ,arab1 #bdf1 #bdg2 ,alfraganus'1 #ahf2 ,ptolemy's1 #adf1 #aeg1 #ahf ,geryon1 #cfi ,ghibellines1 #bac1 #bbg ,giambullari1 #dai ,giuliani1 #bhj ,gnomon1 defined1 #ac1 #bf1 #bh1 #dg1 #ef1 #aad1 #aaf1 #abb1 #abe1 #afa 0 introduced into ,greece1 #bf 0 and ,babylonians1 #bf2 ,chinese1 #bi1 #aad2 ,borneo1 #bf ,goat1 see ,capricorn ,golius1 #bce ,good ,friday1 #dbc-bf ,gravity1 #ajj1 #acg1 #afj1 #afi1 #aia1 #bcg1 #dde1 #ddg1 #dhb1 #dic ,greek ,astronomers and ,astronomy1 #bg1 #bh1 #cf1 #ea et seq41 #aab1 #aei1 #afh1 #aga1 #agb1 #agf1 #agh1 #bjj1 #bjd1 #dcc1 #ddf1 #dfc1 #die ,gruppe1 n4#gf ,guelfs1 #dac ,guido ,bonatti1 #bac1 #dgb ,guido ,cavalcanti1 #daf1 #dbf ,guido of ,montefeltro1 #bac ,hades1 #ed ,hammurabi1 #dj ,haroun al ,raschid1 #ahb ,he1 and ,ho1 ,chinese astronomers1 #cj ,heath1 n4#ge-gf ,heaven1 eighth1 #cff1 #djb1 #dge 0 fourth1 #bhd 0 ninth1 #bcc 0 seventh1 #bhd1 #dee 0 third1 #dbi1 #dhc 0 of fire1 #eh 7see also fire7 0 of ,jupiter1 #cic 0 of ,mars1 #cjc1 #cac1 #cic 0 of ,mercury1 #ccb1 #dda 0 of the ,moon1 #cib1 #dca1 #ddg1 #dee1 #dhd 0 of ,saturn1 #cja1 #cic1 #djg 0 of ,stars1 #bhh1 #cjd1 #cic 0 of the ,sun1 #bdj1 #bef1 #bgb1 #cgc1 #cha1 #dca 0 of ,venus1 #bef1 #cic1 #dbi1 #dce1 #dei1 #dhc ,heavens 7see also ,star sphere71 #eh1 #ei1 #fg1 #ia1 #bji1 #bec1 #bed1 #bef1 #bfb1 #cjj1 #cic1 #dbi1 #dca1 #dce1 #dhd1 #ddg 0 influence of1 #bff 0 revolution of1 #i1 #ah1 #bj1 #ea1 #eg1 #fb1 #fc1 #gj1 #gd1 #ge1 #hb1 #he1 #hh1 #ih1 #ajb1 #ajd1 #ajh1 #abd1 #acf1 #acg1 #ahe 7see also ,celestial motions7 ,hebrew cosmogony1 #df1 #eg2 year1 #ci ,heinrich of ,mainz1 #cdc1 #chd ,heliacal rising1 #ci1 #dj1 #dd1 #de1 #eb1 #aia ,hell1 #bje1 #cec1 #ceh1 #cfg to #cga1 #cij1 #dbc ,hemisphere1 ,southern1 #bhf1 #cbb1 #cbi1 #ccj1 #ccd1 #ccf1 #cci1 #cec1 #djg1 #ddc1 #ddg ,henry ,,vii41 ,emperor1 #bga ,heracleides1 #gd1 #ge1 #ajb1 #aji ,hercules1 ,pillars of1 #cd1 #ed1 #ajc1 #bje1 #cdj1 #cdd1 #cde ,herodotus1 #ee ,hesiod1 #ea1 #eb1 #afa ,hesperus1 #eb ,hicetas1 #gd1 #ge ,hindu arithmetic1 #ahb2 astronomy1 #aha2 calendar1 #abg2 constellations1 #cj2 cosmogony1 #de2 zodiac1 #cj ,hindus and eclipses1 #de ,hipparchus1 #ej1 #abb et seq41 #ach1 #adc1 #aec1 #ahi1 #aia1 #aic1 #bcc1 #bdj1 #bge1 #bhg1 #bhh1 #dcb1 #dic 0 ,star ,catalogue of1 #abc1 #add1 n4#ahh 0 and ,ptolemy1 #acc-e1 #acg1 #adc1 #aeh ,homer1 #cd1 #ea1 #eb1 #gb ,horoscope1 #agc1 #agd1 #bja1 #bjc1 #baf1 #bbf ,hose1 ,dr41 #bg ,hours1 ,church1 #cdg1 #cdh2 8,equal10 #bg1 #cdg1 #cef2 8,temporary10 #bg1 #cdg1 #cef ,hyades1 #dc1 #dd ,hypatia1 #afc ,imbriani1 n4#bbg1 n4#dad ,india 7see also ,hindu71 #ajc1 #aaa1 #aha1 #cci1 #cdc ,inferno1 #bhc1 #cjg1 #cfg et seq41 #dji-aj 0 and ,brunetto ,latini1 #bbf 0 0 ,michael ,scot1 #bad ,instruments1 astronomical1 #ac1 #aac1 #acc1 #ace1 #ahb1 #bjc1 #bah ,intelligences1 #bdi1 #dhc ,isaiah1 #cd1 #age ,isidore1 #agh1 #bdc1 #bej ,japanese1 #ch ,jerusalem1 #aeg1 #ccc1 #cci1 #cdj1 #cde1 #cfj1 #cgc1 #cgd1 #chh1 #cie1 #cig1 #djj1 #dja2 centre of earth1 #agf1 #cda1 #cdc1 #cdd1 #cec1 #cfi2 latitude of1 #chg1 #djf ,jews1 #be1 #bac1 #baf2 astrologer1 #bjb2 astronomers1 #bjc1 #dba ,job1 #cd ,johannes ,hispalensis1 n4#bce ,jowett1 n4#hb ,jubilee year 7#acjj ,a4,d471 #dae ,julius ,csar1 #agj1 #age1 #bgd ,jupiter1 #af1 #abj1 #ada1 #ade1 #aej1 #afi1 #ahi1 #caj1 #caa1 #djg1 #dah1 #dea1 #dia 0 colour1 #ag1 #caa1 #dfg1 #dgc1 #dgg2 dimensions1 #dhh1 #dij 0 period1 #bc1 #fi1 #ia1 #aji1 #adb1 #dcf1 #dcg 0 and astrology1 #agd1 #bdc1 #dfh1 #dgc1 #dgf1 #dgg ,justinian1 #cjj ,kepler1 n4#id ,king1 ,l4 ,w41 n4#cg ,knobel1 n4#cj ,kugler1 n4#ce ,leo1 #ca1 #dc1 #add1 #aee1 #agd1 #bij1 #cac1 n4#cii1 #djf1 #djg1 #daj1 #daa1 #dah1 #dbj1 #dbb1 #dbc1 #dgc1 #dgf ,lethe1 #cij ,leucippus1 #fb1 #fc ,libra1 #ca1 #ahe1 #bfe1 #bgh1 #cbe1 #cfe1 #cgh1 #chj1 #chh 0 and moon1 #cfg1 #cgi1 #chc1 #chd1 #djb1 #djf1 #dah 0 and sun1 #bgh1 #cbc1 #chb ,lignires1 ,de1 ,canons of1 #bjb 8,libros de ,saber10 #aie ,lion1 see ,leo ,lionardo ,bruni1 #bbc1 #bbe1 #bcf1 #dac ,livy1 #bch ,lockyer1 ,sir ,norman1 #bi1 #aee ,lodestone 7see also magnet71 #baa1 #bia ,longfellow1 n4#cic ,longitude1 #cch1 #cci ,lucifer1 #cga1 #cgb ,lubin1 n4#bcf1 n4#cae ,lucan1 #bch1 #bci1 #cbd1 n4#ccj ,lucia 7imaginary city71 #cbc-bg 0 the lady1 #chj ,macrobius1 #aji ,magnet 7see also lodestone71 #baa1 #bia1 #bib1 #ddc1 #dea ,mahaffy1 n4#aac ,mahomedans1 #ci1 #bji1 #baf ,malacoda1 #cgj1 n4#cgj1 #daj-ab1 #dbf ,malaspina1 #bgh1 #bgi1 #dgc ,manfred1 #bdb1 #cah1 #cgf ,manilius1 #afh ,maps1 #bje1 #cdc1 #cdd1 #chd2 climate maps1 #bdg1 #bdh2 ,greek maps1 #bdg ,marco ,lombardo1 #dgi ,marco ,polo1 #bic1 #cdb ,mars1 #c1 #af1 #ag1 #bc1 #fi1 #ij1 #ic1 #aji1 #aab1 #aah1 #abj1 #ach1 #aej1 #afi1 #agc1 #ahi1 #bdh1 #caj1 #cba1 #daa1 #dah1 #dbj1 #dea1 #dfg1 #dfh1 #dgf1 #dhh1 #dij 0 colour of1 #ag2 dimensions1 #dhh 0 period1 #dcf 0 occultation of1 #aje1 #caj1 #dcc 0 sphere of1 #dgg 0 and astrology1 #agd1 #bdc1 #dgc1 #dgg ,mathematics1 #gi1 #ha1 #aje1 #ajg1 #aba1 #ace1 #aea1 #ahd1 #bjc ,matilda1 #dec ,maunder1 ,e4 ,w41 #bd ,note1 #ce1 #abg ,mediterranean1 #cie1 #cih ,mercury1 #ae1 #af1 #bc1 #fi1 #gj1 #ia1 #ic1 #aji1 #aba1 #adb et seq41 #add1 #afi1 #ahi1 #bde1 #bdi1 #cji et seq41 #djg1 #dah1 #dea1 #dfg1 #dij 0 diameter1 #bcf2 dimensions1 #deh1 #dgg1 #dhh2 period1 #dcf 0 and astrology1 #agc ,meridian1 #bb1 #bf1 #bhj1 #cch1 #cdf1 #cdi1 #cfa1 #cfe1 #cfh1 #cga1chg1 #cij1 #cid-g1 n4#cih1 #dci ,meroe1 #aah ,meteors1 #fa1 #agd1 #bci1 #cah1 #cai1 #dgc1 #dgf1 #dic2 meteorites1 #dij ,meteorology1 #bcf ,meton1 #ic1 #ade1 #afa1 #afb1 #agb1 #agg1 #dai ,michael ,scot1 #bac et seq41 #bcg1 #cjf1 #dgb ,milky ,way1 see ,galaxy ,milton1 #ff1 #baj1 #dbj1 #def ,mimnermus1 #ec ,montaperti1 #bdb1 #dac ,month1 ,babylonian1 #da2 ,egyptian1 #add2 ,roman1 #bec2 ,syrian1 #bec 0 defined1 #bb1 #cj 0 anomalistic1 #bc2 intercalary1 #ch1 #agj2 sidereal1 #bb1 #cj 0 names of1 #aga 0 synodic1 #ae1 #bj1 #cj1 #eb1 #afb1 #afc 0 and moon1 #bff1 #cej1 #dcf ,moon1 #cjh1 #djb1 #djf1 #djg1 #dah1 #dai1 #def1 #dfi1 #dia 0 apogee of1 #ddi 0 distance1 #aje1 #ajh1 #adh et seq41 #aej1 #aeb1 #afj1 #ahi et seq41 #dhh 0 dimensions of1 #ef1 #aad1 #aeb et seq41 #afj1 #ahh et seq4 0 ecclesiastical1 #dai-dbb 0 eclipses1 #ee 0 epicycle1 #ddi 0 god1 #cg 0 influence of1 #bcg1 #bff1 #dej1 #dgc1 #dhi 0 inhabited1 #ga 0 mansions of1 #cj 0 markings on1 #fa1 #bca1 #bdh1 #bff1 #bfi1 #cib1 #cic1 #dfb et seq41 #dfi1 #dgf 0 movements of1 #ac1 #ad1 #ah1 #bi1 #ajj1 #aje1 #aad1 #aag1 #adf et seq41 #bai1 #beg1 #bfd1 #bfe1 #cci1 #cej1 #chc1 #djb et seq4 0 orbit1 #bef 0 perigee of1 #ddh1 #ddi 0 nodes of1 #adg 0 periods3--sidereal1 #bfd1 #dcf1 #dcg2 synodic1 #dcg 0 phases of1 #ad1 n4#gf1 #aia1 #bfd1 #bff1 #dfi1 #dgf2 full1 #ad1 #bfd1 #bff1 #cfg1 #chf1 #cga1 #djf1 #daj1 #daa1 #dai1 #dbc2 gibbous1 #bfd1 #bff2 half1 #ajh1 #ddf2 new1 #ad1 #bi1 #dj1 #eb1 #bfd 0 positions of1 #djb 0 rising1 #ad1 #bfc1 #bff1 #cej 0 0 in ,purgatory1 #cfc1 #cgh-hj1 #chi 0 setting1 #ad1 #bfc1 #bfe1 #cej1 #cfg1 #cfi 0 0 in ,purgatory1 #chj 0 sphere of1 #afi1 #cjh1 #ddi1 #dfe1 #dgg1 #dhd1 #dhg 0 substance1 #ee1 #ga1 #aad1 #dfc et seq41 #did 0 waning1 #bfb1 #bff1 #chj 0 worship of1 #be 0 and astrology1 #agc1 #agd1 #bdi1 #bfh1 #djg1 #dai1 #dej1 #dgb et seq4 0 0 ,dante1 #bfa et seq4 0 0 ,mars1 #caj1 #dcc 0 0 month1 #ac1 #ad1 #ae1 #bh1 #cj1 #ch1 #da1 #eb1 #aga 0 0 sun1 balancing1 #bfe2 contrasted1 #bfh 0 0 tides1 #ahi et seq41 #bcg1 #dde 0 0 time1 #bff1 #cdi1 #cfg1 #cfi1 #cgj1 #djf1 #dai1 #dhh 0 0 zodiac1 #bfe ,moore1 ,dr4 ,e41 #bcf1 n4#bcf1 n4#bcg1 #cjh1 n4#cbf1 n4#ccj1 #ccd1 n4#cdj1 n4#chj1 #chd1 n4#daa1 n4#dae1 #dai1 #ddh1 n4#deb1 n4#dfi1 #dga1 n4#dga ,moors1 #bja1 #bjc1 #bad ,morning ,star1 #cab1 #cad1 #cgc1 #daj1 #dbj1 #dba1 #dbb1 #dgj1 #dgg ,morocco1 #cdj1 #cfa ,motion1 ,law of1 #ic1 #ajj1 #aba1 #aei1 #dhj ,movers1 see ,first ,mover1 and ,spheres ,mulmul1 #da ,music of the ,spheres1 #fg1 #ajd ,nabonassar1 #add ,naples1 #bdj ,nasir-ed-din1 #aie ,nestorians1 #aha1 #ahb1 #bji ,nero1 #aga ,newton1 #ajj1 #dha ,nineveh1 #cd1 #dd ,night personified1 #bgh ,nino1 #cgh1 #daf1 #dbf ,nile1 #cdd ,nones1 #bai1 #cdh ,observatories1 ,alexandria1 #aac1 #aaf1 #ace2 ,baghdad1 #ahb2 ,greenwich1 #aec2 ,pekin1 #aad2 ,persian1 #aie2 ,the ,cape1 #aec2 of ,eudoxus1 #hh2 of ,hipparchus1 #abb 8,observatory1 ,the10 n4#bd1 #cd 8,on the ,heavens18 see ,de ,clo ,occultations1 #aje1 #ade ,omons1 #bah ,opposition1 defined1 #agd1 #aai1 #ada ,orion1 #ab1 #cf1 #eb1 #aee ,orosius1 #bdj1 #cda1 #cdc1 #chd1 #dch ,ottimo1 #bgc1 #dah1 n4#dgc ,ovid1 #afh1 #bch1 #bci1 #big1 #cje ,padua1 #bbg ,paradise 7see also ,eden71 ,earthly1 #bhe1 #bie1 #cdd1 #cde1 #cec1 #cff1 #cgc1 #che1 #cij1 n4#cia1 n4#cii1 #dja1 #dhb ,paradise ,lost1 #baj ,parallax1 #aec1 #aia ,paris1 #aeh1 #bja1 #bjd2 ,university1 #aed1 #bbh1 #bda1 #bdb ,parmenides1 n4#gf1 #dbh ,parsis1 #abg ,pekin1 #aad1 #aaf ,pericles1 n4#fa ,perigee1 #bc1 #aai1 #adh1 #aej1 #ddh-ea ,persia1 #bji ,petrarch1 n4#ccb ,phaton1 #cjc1 #ccc 8,phainomena10 of ,aratus1 #cb1 #ce ,philolaus1 #gj1 #he1 #dca ,philosophy1 #bee1 #bha1 #cad1 #cae1 #cdf ,phnicians1 #be1 #ef ,phosphor1 #fh1 #hj ,piccarda1 #cjj ,pietro d' ,abano1 #cdb ,pinches1 ,t4 ,c41 #dh ,pisces 7see also ,fishes71 #cb1 #abi1 #ach1 #bij1 #bie1 #cjg1 #cji1 #cei1 #cfj1 #cfh1 #cgj1 #cgc1 n4#chj1 #chc1 #che1 n4#cii1 #djc1 #djf1 #djg1 #daj1 #daa1 #dah1 #dbj1 #dbc1 #did-ie ,planets1 defined1 #af1 #de1 #eb1 #eh1 #fj1 #fc1 #fe1 #fh1 #gj1 #gi1 #bai1 #bed1 #beg1 #bfi1 #bgi1 #bhi1 #cjg et seq41 #cab1 n4#cii1 #dai1 #dfa1 #dff1 #dfh1 #dhh1 #did-ie 0 aspects of1 #bjj1 #dgf 0 astrology and1 #agc-d1 #baa1 #bai1 #bdc1 #bdi1 #dje 0 distances of1 #aej1 #ahi1 #aid 0 houses of1 #agd1 #dgf1 n4#dgc 0 influences of1 #bed1 #dgb1 #dgc1 #dgd 0 movements of1 #ae1 #af1 #bi1 #dd1 #eh1 #fh1 #fi1 #gj1 #gi1 #hj1 #hh-ij1 #ajd1 #aah1 #abc1 #ach1 #aei1 #bdh1 #cab1 #ccj1 #cca 0 names of1 #hj1 #hc 0 nature of1 #dfa 0 periods of1 #bc1 #bi1 #fi1 #hc1 #hi1 #ia1 #ajj1 #aji1 #ada1 #bai1 #cac1 #dcf 0 positions of1 #djb et seq41 #dai 0 shadows cast by1 n4#bhj 0 varying velocity of1 #id1 n4#id 0 and the sciences1 #cab ,plato1 #hj et seq41 #he1 #ia1 #ih1 #aja1 #ajd1 #aei1 #bag1 #bch1 #bci1 #cac1 #dca1 #ddd1 #dfb1 #dgi1 #dhb1 #dhc ,pleiades1 #bh1 #bi1 #ce1 #dj1 #eb1 #aee 0 and ,australian legend1 #bh 0 0 ,tahitan natives1 #bh ,pliny1 #ej1 #abc1 #agj1 #cdb ,plunkett1 ,miss1 #cd ,plutarch1 #he1 #ajg1 #acg1 #dfc ,pole1 celestial1 #ab1 #ah1 #ea1 #fe1 #aje1 #aeg1 #ahe1 #ahf1 #ahg1 #bhf1 #bhg1 #bhi1 #big1 #cjb1 #cbc1 #cce1 #dcd1 #dci1 #dgg2 north1 #cgc2 south1 #bhf1 #bib1 #bic1 #cce1 #cgc1 #cgh1 #dhi 0 terrestrial1 #bdg1 #cbb2 north1 #cbc1 #cgj2 south1 #cbc ,pole star1 #i1 #fg1 #abg1 #bia1 #cbc ,popes1 #bgf1 #caf2 ,boniface ,,viii41 #dae1 #daf2 ,gregory ,,ix41 #bac2 ,honorarius ,,ii41 #bad2 ,urban ,,iv41 #cah1 #dac ,poseidonius1 #acd1 #aeg1 #agj1 #bdj ,precession of ,equinoxes1 see ,equinox ,prickard1 n4#dfc ,primum ,mobile1 #aid1 #bjd1 #baj1 #bii1 n4#bcb1 #bia1 #cjh1 #cac1 #cha1 #djj1 #dja1 #dcb-dcd1 #dcf1 #ddj1 #dea1 #dee1 #def1 #dgg1 #dhd ,proclus1 #agj ,proctor1 ,r4 ,a41 n4#bd1 #cd1 #ce ,procyon1 #aee1 #ahg ,ptolemy1 #e1 #bd n4#bd n4#cd1 #acd et seq41 #aed1 #aef1 #afj1 #afc1 #agj1 #agh1 #ahb1 #ahf1 #bjb1 #bji1 #baj1 #bah1 #bdb1 #bde1 #bfa1 #bge1 #bhh1 #bij1 #bia1 #cje1 #ccc1 #cej 0 ,almagest1 #aac1 #aae1 #abc1 #ahb1 #ahd1 #bja 0 dimensions of earth1 #ahb2 of heavenly bodies1 #aia 0 geography of1 #aeg1 #bje1 #ccg1 #cda 0 quoted1 #acd 0 system of1 #cha1 #dca1 #dcb1 #dia 0 0 0 epicycles1 #bef1 #cae 0 works by1 #aef1 #aeg1 #ahb 0 and ,apollonius1 #aah 0 0 ,aristarchus1 #ajg 0 0 ,arabs1 #adg1 #aeb1 #ahc1 #ahh1 #aib-d 0 0 colure1 #djc 0 0 ,dante1 #bcb1 #bce1 #bci1 #dei1 #dfh 0 0 eclipses1 #cch2 and ecliptic1 #ahe 0 0 ,hipparchus1 #abf1 #acc1 #adc1 #adf 0 0 moon1 #adf1 #ddh1 #ddi 0 0 precession1 #ahg1 #aic1 #dcb 0 0 ,regulus1 #djf 0 0 stars1 #bib1 #bid1 #cci 0 0 ,venus1 #cae ,ptolemy ,philadelphus1 #add 0 ,ptolemies1 ,royal1 #aac ,purgatory1 #aje1 #bje1 #bie1 #cde1 #cfj1 #cfg1 #cgj1 #cgb1 #cgc1 #cij1 #dja1 #djg1 #dec1 #ded 0 gate of1 #cfb1 #chj1 #che1 #dec 0 latitude of1 #bhf1 #cec1 #chg 0 ,mountain of1 #aje1 #bfb1 #bhf1 #bie1 #caa1 #cab1 #ccb-e1 #cec1 #cfj et seq41 #cgc1 #cge1 #cgh1 #cha1 #chb1 #che1 #chf1 #chh1 #cij1 #deb1 #dec1 #dee ,pyramids1 #de1 #ha1 #abg ,pythagoras1 #ff et seq41 #bcf1 #bch1 #cjb1 #dca ,pythagoreans1 #fb1 #ff et seq41 #ge1 n4#gf1 #gi1 #he1 #hh1 #ia1 #if1 #ajj1 #aja1 #ajb1 #ajd1 #aaj1 #aaa1 #cjd1 #dij ,quadrivium1 #agg #8,qustio de ,aqua et ,terra1' #bef1 #beh1 #cdj1 #ddd1 #deb ,ram 7see ,aries71 #bgi ,ravenna1 n4#bbg1 #bgc ,regulus1 #dc1 #add1 #aee1 #ahg1 #bij1 #djf1 #daa1 #dbj ,retrograde ,motion1 #af ,rhodes1 #fg1 #abb1 #acd1 #aeh ,rigel1 #aee ,ristoro1 #bag1 #bda et seq41 #beg1 #bfh1 #bgd1 #bib1 #bhh1 #cjj1 #cbh1 #cbi1 #ddd1 n4#dea1 #dfd1 n4#dgh 0 and comet1 #cah2 constellations1 #ddc1 #dea2 eclipses1 #cag2 ecliptic1 #cca2 habitable earth1 #ddf2 meteors1 #cai ,rizzacasa d',orsogna1 ,prof41 #djj ,rome1 #aaa1 #aeg1 #bda1 #caf1 #cai1 #cbc1 #cde1 #chc1 #che1 #cif1 #dae 0 ,church of1 influence on astronomy1 #age1 #agh 0 ,empire of1 #bfb2 influence on astronomy1 #ach1 #afg1 #agb1 #agh ,rome1 and calendar1 #agb1 #age ,rubruquis1 ,friar1 #cdb ,sacrobosco1 #bjb1 #bdi ,sagittarius1 #bgi1 #bha1 #bij1 #chj1 #chc1 #che ,st4 ,bernard1 #cab1 #ced1 #dja ,st4 ,john1 #bhb1 #cag ,st4 ,louis1 ,king1 #cdb ,st4 ,paul1 #cb1 #dhc ,st4 ,peter1 #cif1 #dfh ,salimbene1 #bab ,saracens1 #bad ,sardinia1 #cdd1 #cfd1 #chc1 #chd ,saturn1 #af1 #bc1 #fi1 #ia1 #aje1 #aji1 #abj1 #ada1 #afi1 #ahi1 #bgi1 #bha1 #caa1 #cfd1 #chi1 #cic1 n4#cih1 #djf1 #djg1 #daj1 #daa1 #dag1 #dbj1 #dbb1 #dbc1 #dej1 #def1 #dfh1 #dfi1 #dij 0 dimensions1 #dhh2 movements1 #caa2 period1 #dcf ,scales1 see ,libra ,scartazzini1 #cgi1 n4#dee ,schiaparelli1 n4#ce1 n4#ci1 n4#bcf ,schwary1 #cd ,scipio1 #afh-fi1 #cic2 ,dream of1 #afh1 #bcg ,scorpio1 #cj1 #ca1 #dc1 #cfe1 #cgh1 #cgi1 #chj1 #chc1 #chd1 #che1 #chg1 #dje1 #dgf1 #dhi ,seleucus1 #aaj ,seneca1 #ff1 #afi1 #agd1 #bcg1 #bci1 #cdb1 #dgc2 and meteors1 #cai ,shakespear1 #def ,sheol1 #df ,sigieri1 #bbh ,simplicius1 #ij1 #agj ,sirius1 #ci1 #eb1 #fg1 #aae1 #aee1 #ahg ,socrates1 #hb1 #hc1 #bci ,solstice1 definition of1 #aa1 #bf1 #bi1 #ajg1 #aag1 #abg1 #ahe1 #bgg1 #cid ,sordello1 #cgh1 #chb ,sosigines1 #aga ,southern ,cross1 #ab1 #aef1 #bid ,spain1 #cci-db1 #chh ,spheres1 #i1 #eg1 #eh1 #fb1 #fe1 #fh1 #hc1 #hd1 #ajd1 #acg1 #afi1 #ahd1 #ahg1 #bjd1 #bai1 #bdi1 #bed1 #beg1 #bfb1 #cjb1 #ceh1 #cib1 #cic1 n4#cii1 #dbi et seq41 #ddd1 #deb1 #deg1 #dgc1 #dgh1 #dah 0 crystalline1 #dcc 0 eighth sphere1 #dff 0 elevating power of1 #ddc 0 homocentric1 #aab 0 influence of1 #bci1 #bdi1 #bed1 #dgh1 #dgi1 #dhe1 #dhh1 #did 0 movement of1 #cie1 #djj1 #dec 0 movers of1 #ajf1 #aei1 #bjd1 #bed1 #djj1 #dhb1 #dhc1 #dhd1 #dif 0 music of1 #fg1 #fh1 #ajd1 #afi1 #cjb1 #cib1 #dee1 #def 0 ninth1 #dcb-c 0 sky as a1 #ea 0 substance of1 #ie1 #ajd1 #aic1 #dcc1 #dfa 0 #8unrolling1' #ie1 #ajb1 #ajf 0 of air1 #ddb1 #deb 0 of ,eudoxus1 #hh1 #hi1 #id1 #ajf1 #ajg1 #aab 0 of fire1 #ajc1 #aei1 #cjh1 #cib1 #ddb1 #dec1 #dee1 #dij 0 of moon1 #ajc1 #cjh1 #dgg 0 of sun1 #hh1 #ic1 #bec 0 of stars1 #ac1 #fg1 #gj1 #gb1 #hi1 #id1 #ie1 #if1 #aji1 #abi1 #acg1 #aeb1 #afj1 #ahg1 #bec1 #cac1 #cef1 #dcc1 #dcg1 #dch1 #def1 #dgf1 #dgg 0 of water1 #ddb1 #ddc 0 and ,arabs1 #aid 0 0 ,roger ,bacon1 #aah1 #bjb 0 0 time1 #dja ,spica1 #abd-f1 #acj1 #aee ,stars1 #bai1 #bhc et seq41 #dhi1 #djb1 #dic-id 0 brightness of1 #abc1 #aed1 #ahg 0 catalogues1 #abc1 #acc1 #add1 #aed1 #ahg1 #bhh2 ,abu ,hazan's1 #ahd2 ,hipparchus'1 #ahh2 ,ptolemy's1 #ahg 0 ,dante's #8quindici stelle1' #aee 0 dimensions of1 #aij1 #dhh 0 globes1 #aae 0 distance of1 #ag1 #ajh1 #aec1 n4#aij1 #dhh1 #dib-ic 0 influence of1 #baa1 #bed1 #bef1 #ddc1 #dej1 #dgc1 #dge1 #dgh1 #dgi1 #dhh 0 magnitudes of1 #aed1 #ahg1 #ahh1 #bcd1 #bhi1 #bii1 #dhh2 first-magnitude1 #aed1 #ahg 0 movements of1 #i1 #ea1 #eb1 #hc1 #hd1 #hf1 #ig1 #acf1 #ahg1 #bhd1 #bhf1 #bhg1 #bhi1 #cja1 #ced1 #dbd1 #die1 #dif 0 new1 #abc 0 number of1 #abc1 #ahg1 #bhh1 #dgg1 #die 0 ,pole1 #bia1 #bii 0 positions of1 #db1 #abc1 #abf1 #aic 0 shooting1 #ajc1 #ahe1 #bfb1 #cja1 #cai1 #dhg1 #dij 0 southern1 #bhc1 #bic1 #cgc1 #cgh1 #dhi 0 substance of1 #ajc1 #ajd1 #acf 0 worship of1 #cg1 #ch1 #ea 0 and human souls1 #hf 0 0 ,milky ,way1 #ajc 0 0 time1 #beg1 #bhe1 #bhi1 #cfg1 #dhh ,stationary points1 #af1 #dd1 #aba ,statius1 #che-g1 #dec ,stilbon1 #hj ,stoics1 #aab1 #acd1 #dfc ,stobus1 #ajg ,stonehenge1 #bi ,strabo1 #agj1 #bdj ,styx1 #ed ,sumerians1 #cf1 #ch2 year1 #ch ,sun1 boat of1 #de1 #df 0 brightness of1 #bgj1 #bhb1 #dfb1 #dgg1 #dhh1 #dfi 0 centre of universe1 #aja1 #aaj 0 dimensions of1 #ef1 #aaj1 #adf1 #aec1 #ahh1 #deg-h1 #dfi1 #dhh1 #dia 0 distance of1 #ajh1 #adf1 #aec1 #ahi1 #aic1 #deg-h 0 door of1 #df 0 god1 #cg1 #dh1 #ed 0 heaven of1 see ,heavens 0 ,lake of1 #ed 0 movements of1 #aj1 #ac1 #ci1 #ec1 #ee1 #fb1 #aae1 #aaf1 #abj1 #ade1 #adf1 #ahe1 #ahg1 #bdg1 #bef1 #bgb-d1 #bgf1 #cbb et seq41 #cch1 #cdf1 #cdi1 #cij-b1 #djb1 #djc 0 perigee of1 #ddh 0 period of1 #dcf 0 positions of1 during ,vision1 #djb et seq4 0 rise1 #aj1 #ac1 #ad1 #be1 #bh1 #ed1 #bfg1 #bgj1 #bga1 #bgc1 #cci1 #cdf1 #cdh1 #cef1 n4#cef1 #djf 0 rise in ,forest1 #ced1 #ceh1 #cfg1 #cfi 0 0 in ,purgatory1 #bga1 #cfj1 #cfb1 #cfc1 #cfd1 #cff1 #cgd1 #che1 #chi1 #djf 0 set1 #aj1 #ac1 #ad1 #dh1 #bec1 #bfb1 #bga1 #bgc1 #bgi1 #bhj1 #bhb1 #bid1 #cci1 n4#ccf1 #cej1 #cef1 #chc1 #che 0 0 in ,purgatory1 #bga1 #cfa1 #cfc to #cff1 #cgh1 #chb1 #chh 0 source of all light1 #dgj1 #dgg1 #dhh 0 worship of1 #be1 #cg1 #de 0 and astrology1 #agc1 #dgc1 #dgg 0 0 comets1 #ajc 0 0 ,dante1 #bfg1 #bgj et seq4 0 0 stars1 #bed1 #dgj1 #dgg 0 0 time1 #bai1 #bed1 #beg1 #cdi1 #cfg1 #cgb1 #dhh ,sundial1 #bg1 #aae1 #aeh1 #ahb1 #aib1 #bai ,syene1 #aag1 #aef ,sylvester ,,ii41 #bjc ,synodic revolution1 #bb1 #cj #8,syntaxis' 7see ,almagest71 n4#abe1 #acf1 #aeg1 #ahb1 #aic1 #bji ,tabit ben ,korrah1 #aid ,tables3-- 0 ,alfonsine1 #aie1 #bjb1 #bjc1 #bdb1 #bge1 #cda2 astronomical1 #bjc1 #bdb1 #bde2 ,greek1 #aag2 ,hakemite1 #ahc2 ,toledo1 #ahd1 n4#bjb1 #dba 0 of constellations1 #ca1 #aed2 ,days of the ,vision1 and positions of sun1 etc41 #dbe2 ,ptolemy's first-magnitude stars1 #aee2 planetary distances and dimensions1 #ahi2 positions of sun and moon1 #aij2 planetary periods1 #ia1 #dcf2 planets in zodiac1 #cbe2 revolutions of sun1 moon1 and planets1 #bb1 #bc2 time references in 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