Table Of ContentPTOLEMYINPERSPECTIVE
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
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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
