PTOLEMYINPERSPECTIVE Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUME 23 EDITOR Jed Z. Buchwald, Dreyfuss Professor of History, California Institute of Technology, Pasadena, CA, USA. ASSOCIATE EDITORS FOR MATHEMATICS AND PHYSICAL SCIENCES Jeremy Gray, The Faculty of Mathematics and Computing, The Open University, Buckinghamshire, UK. Tilman Sauer, California Institute of Technology ASSOCIATE EDITORS FOR BIOLOGICAL SCIENCES Sharon Kingsland, Department of History of Science and Technology, Johns Hopkins University, Baltimore, MD, USA. Manfred Laubichler, Arizona State University ADVISORY BOARD FOR MATHEMATICS, PHYSICAL SCIENCES AND TECHNOLOGY Henk Bos, University of Utrecht Mordechai Feingold, California Institute of Technology Allan D. Franklin, University of Colorado at Boulder Kostas Gavroglu, National Technical University of Athens Paul Hoyningen-Huene, Leibniz University in Hannover Trevor Levere, University of Toronto Jesper Lützen, Copenhagen University William Newman, Indian University, Bloomington Lawrence Principe, The Johns Hopkins University Jürgen Renn, Max-Planck-Institut für Wissenschaftsgeschichte Alex Roland, Duke University Alan Shapiro, University of Minnesota Noel Swerdlow, California Institute of Technology ADVISORY BOARD FOR BIOLOGY Michael Dietrich, Dartmouth College, USA Michel Morange, Centre Cavaillès, Ecole Normale Supérieure, Paris Han-Jörg Rheinberger, Max Planck Institute for the History of Science, Berlin Nancy Siraisi, Hunter College of the City University of New York Archimedes has three fundamental goals; to further the integration of the histories of science and technology with one another: to investigate the technical, social and practical histories of specific developments in science and technology; and finally, where possible and desirable, to bring the histories of science and technology into closer contact with the philosophy of science. To these ends, each volume will have its own theme and title and will be planned by one or more members of the Advisory Board in consultation with the editor. Although the volumes have specific themes, the series itself will not be limited to one or even to a few particular areas. Its subjects include any of the sciences, ranging from biology through physics, all aspects of technology, broadly construed, as well as historically-engaged philosophy of science or technology. Taken as a whole, Archimedes will be of interest to historians, philosophers, and scientists, as well as to those in business and industry who seek to understand how science and industry have come to be so strongly linked. Ptolemy in Perspective Use and Criticism of his Work from Antiquity to the Nineteenth Century ALEXANDERJONES InstitutefortheStudyoftheAncientWorld,NewYorkUniversity Editor AlexanderJones 15East84thStreet NewYorkNY10028 USA [email protected] ISSN1385-0180 ISBN978-90-481-2787-0 e-ISBN978-90-481-2788-7 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2009940670 (cid:2)c SpringerScience+BusinessMediaB.V.2010 Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Acknowledgements The 2007 Caltech conference “Ptolemy in Perspective” that gave rise to this volume was generously funded by the Francis Bacon Foundation, and expertly organized by the Division of Humanities and Social Sciences at Caltech. The editor also acknowledges the Institute for the Study of the Ancient World, New York University, for providing resources and technical support in the book’s preparation. v Contents AnUnpublishedAstronomicalPapyrusContemporarywithPtolemy..... 1 AnneTihon AncientRejectionandAdoptionofPtolemy’sFrameofReferencefor Longitudes ........................................................ 11 AlexanderJones Ptolemy’sDoctrineoftheTermsandItsReception .................... 45 StephanHeilen TheTraditionofTextsandMapsinPtolemy’sGeography ............... 95 FlorianMittenhuber IslamicReactionstoPtolemy’sImprecisions........................... 121 F.JamilRagep TheUseandAbuseofPtolemy’sTetrabiblosinRenaissanceandEarly ModernEurope:TwoCaseStudies(GiovanniPicodellaMirandolaand FilippoFantoni) ...................................................135 H.DarrelRutkin Tycho,Longomontanus,andKepleronPtolemy’sSolarObservations andTheory,PrecessionoftheEquinoxes,andObliquityof theEcliptic... 151 N.M.Swerdlow Dunthorne,Mayer, andLalandeontheSecularAccelerationoftheMoon..203 J.M.Steele Bibliography.......................................................217 vii Contributors Stephan Heilen Institut für Romanistik/Latinistik, Universität Osnabrück, Germany, [email protected] Alexander Jones Institute for the Study of the Ancient World, New York University, New York, NY, USA, [email protected] Florian Mittenhuber Ptolemaios-Forschungsstelle, Institut für Klassische Philologie, Universität Bern, Schweiz, [email protected] F. Jamil Ragep Institute of Islamic Studies, McGill University, Montreal, Quebec, Canada, [email protected] H. Darrel Rutkin Institute for the study of the Ancient World, New York University, New York, NY, USA, [email protected] J. M. Steele Department of Egyptology and Ancient Western Asian Studies, Brown University, Providence, RI, USA, [email protected] N. M. Swerdlow Humanities and Social Sciences, California Institute of Techno- logy, Pasadena, CA, USA, [email protected] Anne Tihon Université Catholique de Louvain, Louvain-la-Neuve, Belgium, [email protected] ix Introduction AmongthescientificauthorsoftheancientGreco-Romanworld,nonegivesussuch a strong impression of writing for posterity as Ptolemy. He lives in a time when learned and eloquent men seek and attain public adulation and private patronage, when the physician Galen performs dissections of pigs and sheep before the elite of Rome and when the sophist Alexander the “Clay Plato” dazzles the Athenian massesasmuchbyhisgroominganddeportmentasbyhisdeclamation.Fromthis milieuPtolemyisutterlyremote.Outsideofhisbooksheisnothing;nocontempo- rary mentions the man, and no later account of his life or person will preserve an authentic report. He addresses his books without flourish to a certain Syros, about whomweknownothing,andinthemthereisnopersonality,noreferencetohimself exceptasanobserver,scholar,andtheoretician,noallusiontohisenvironment.His criticisms of other scientific practitioners are free of polemic. He habitually uses sesquipedalianverbsandwritesvast,labyrinthinesentences;buthisvocabularyand phrasingare repetitive,eschewingfigurativelanguage,andhistangledsyntaxresults from the impulse to express the conditions and consequences of a thought all at once, and is worlds away from self-conscious rhetoric. Galen cannot refrain from bragginghowprofitableanybookascribedtohimselfisforthebooksellersofRome; onesuspectsthateveninstudiousAlexandriaPtolemy’stechnicaltreatisesarenot exactly bestsellers. Nor is there anything meretricious about Ptolemy’s efforts to give his science a public face: the inscription he erects at Canopus represents his cosmosasabarelistofhighlyprecisenumericalparameters,andhisworldmapis ageometricalconstructionunembellishedbycrocodilesandpygmies. AndsoPtolemy’sbiographyispracticallycompletewhenwehavesaidthathis fullnamewasKlaudiosPtolemaios,andthathelivedinornearAlexandria,made astronomical observations between the mid-120s and the early 140s of our era, and wrote books on scientific topics of which about a dozen have come down to us.1 Abouthalfareastronomical,andofthese,threeareespeciallyimportant.The MathematicalComposition(Mathematikeˆ Syntaxis),betterknownsincetheMiddle Ages as the Almagest, is a systematic treatise in thirteen books in which Ptolemy deduces the structure and quantitative parameters of geometrical models for the heavenlybodiesfromempiricalevidenceincludingspecificdatedobservations.The Almagestalsousesthesemodelstoderivetablesforcalculatingthepositionsofthe heavenlybodiesonanygivendate,togetherwithotherphenomenasuchaseclipses xi xii Introduction andplanetaryfirstandlastvisibilities,butthetablesalsohadalifeoftheirownin slightlyrevisedformasaseparatepublicationthatPtolemycalledtheHandyTables (Prokheiroi Kanones). Lastly, Ptolemy’s Planetary Hypotheses (Hypotheseis toˆn Planoˆmenoˆn), a treatise in two books, gives a technical description, again slightly revised,ofPtolemy’scelestialmodels,suggestshowtheyarelikelytobearranged relative to each other and what their absolute dimensions would be, and offers a physicalinterpretationofthegeometricalmodelsintermsofsystemsofrevolving bodiescomposedofaitheˆr,theAristotelianfifthelement. AllPtolemy’sotherwritingshaveatleastaglancingconnectiontohisastronomy, buttwoareespeciallyclose.TheTetrabiblos(againanickname—wedonotknow Ptolemy’s own title, but a credible guess is Apotelesmatika, roughly “Astrological Influences”)isafour-booktreatisearguingfortheviabilityofastrologyasaphys- ical science of the effects of celestial bodies on the terrestrial environment and on individuals, and on this basis Ptolemy undertakes a systematic reform of the gen- eralprinciplesofastrologicalprediction.TheGeography(GeoˆgraphikeˆHypheˆgeˆsis, “GuidetoWorld-Cartography,”alsocommonlyknownbeforemoderntimesasthe Cosmography)providestheprinciplesandmaterialsforthedrawingofamapofthe knownpartsoftheworldbasedonacriticalanalysisofastronomicalmeasurements andothergeographicalreports. Ptolemy crafted each of his major treatises to be self-standing, so that no reader would have to be familiar with other texts on the same topic to follow Ptolemy’sargumentonitsownterms.Perhapsinpartforthatveryreason,Ptolemy’s tended to be the only works of their genres to survive into late antiquity and the medieval Byzantine and Arabic traditions. (The exception is astrology, which was handed down through many other texts in addition to the Tetrabiblos.) Each of Ptolemy’s treatises has a distinct, sometimes complex path of subsequent recep- tion and exploitation as a text of living scientific value, or of criticism that could lead to rejection. In the case of the Almagest, the presence of observation reports that,iftrustworthy,mightcontributetothemeasurementoftheEarth’svariablerate of rotation has kept that work from entirely subsiding into a condition of purely historicalinterestuptoourowntime. From May 31 through June 2, 2007 the Division of the Humanities and Social SciencesattheCaliforniaInstituteofTechnology,withgeneroussupportfromthe FrancisBaconFoundation,hostedaconferenceonusesandcriticismsofPtolemy’s astronomical,geographical,andastrologicalworksfromantiquitythroughmodern times,thefocusbeingontheroleofPtolemyincurrentscientificpracticeanddis- pute.Thepresentvolumegathersmostofthepapersfromthatconferencetogether withanewpaperbytheeditor. IntheAlmagestPtolemytreatsHipparchusashisonlylegitimatepredecessorin theoretical astronomy, making only brief and dismissively vague allusions to the astronomers of the intervening three centuries and his own time. Modern eluci- dation of traces of Greek astronomy in Indian sources (a field of evidence by no meansexhausted,thoughtricky)haverevealedthatPtolemyelidedoveragreatdeal of work in mathematical astronomy that had been done after Hipparchus, and the ongoingdiscoveryofastronomicaltextsandtablesamongthepapyrifromRoman Introduction xiii Egypt is providing the historian with a still small but growing body of material relatingtotheimmediatebackgroundagainstwhichPtolemy’sastronomywasfirst received. In the first paper in this volume, Anne Tihon gives us a first glimpse of a deeply interesting new papyrus manuscript containing passages from a work of unknown authorship written during the years when Ptolemy was still making the observations on which the Almagest was based. The topic is how to calculate the Sun’s longitude in the zodiac using a set of tables that had surprising points of resemblancetoPtolemy’stables,andevenmoresurprisingdifferences.Amongthe lessons offered by this papyrus is that Ptolemy’s was not the only version of solar theory descended from Hipparchus’ researches, and that its correctness would not havebeenastraightforwardmattertohisbetter-informedcontemporaries. Alexander Jones (the editor) takes up a closely related topic, the problem of definingaframeofreferenceforcelestiallongitudes.TheastrologersofPtolemy’s period did not distinguish between the tropical and the sidereal year, and used a frame of reference that was assumed to be tropical but in fact was approximately sidereal. Ptolemy’s tables assume a tropical frame while attributing a precessional motiontothefixedstars.Papyrishowthatfortwocenturiesafterhistime,Ptolemy’s tableswerecommonlyusedonlytogetherwithacorrectionthatbroughtcomputed positionsintoastandardizationoftheprevalentframeofreference;thiscorrection is identical to a formula associated by Theon of Alexandria with the doctrine of trepidation, or oscillating solstitial points. Jones attempts to account for the origin andmotivationofthisformula,andthecauseofitslaterabandonment. IntheTetrabiblosPtolemystateshisdissatisfactionwithtwomethodsofdividing thesignsofthezodiacintoTerms,thatis,zonesofafewdegreesgovernedastrolog- icallybyoneoranotheroftheplanets,andherecountshisdiscoveryofasuperior methodinanoldanddamagedmanuscript.StephanHeilenoffersathoroughcritical treatmentofthequestionwhetherPtolemy’sstoryistrueoranaudaciousfabrication before exploring the reception of Ptolemy’s system of Terms by astrologers from Ptolemy’s day to the Seventeenth Century. This specimen of Ptolemy’s reforming approach to astrology experienced a rather sad fate: transmitted in variously cor- rupted forms, it won little acceptance even from authors who gave lip service to Ptolemy’srationaleforthesystem. The Geography provides a set of resources for drawing maps of the world, includingacatalogueofsomeeightthousandlocalitieswiththeirlongitudesandlat- itudes.TheearliestmanuscriptcopiesoftheGeographythatwehavewereproduced morethanamillenniumafterPtolemy,andmanyofthemhavemapsaccompanying the text. The origin of these maps, and whether they descend through graphical copying from maps made by or for Ptolemy himself, have long been vigorously disputed. Relying on minute study of the manuscript maps and texts, Florian Mit- tenhubermakesalucidandconvincingcasethattheextantmapsaretheendofan unbrokenchainofmapsoriginatinginantiquity,ifnotinPtolemy’stime,contraryto thebeliefofseveralscholars(including,hitherto,theeditor)thattheywererecreated aroundA.D.1300purelyonthebasisofthetransmittedtext. When astronomers or geographers attempted to repeat certain of Ptolemy’s observations and measurements, different sorts of consequences could follow. In