Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics: Translation and Commentary

142 Pages·2012·2.43 MB·English

by  Michael N. Fried (auth.)

Sources and Studies
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Michael N. Fried
Edmond Halley’s
Reconstruction of the Lost
Book of Apollonius’s Conics
Translation and Commentary
ABC
MichaelN.Fried
ProgramforScienceandTechnologyEducation
Ben-GurionUniversityoftheNegev
MarcusFamilyCampus
Beer-Sheva84105
Israel
[email protected]
ISBN978-1-4614-0145-2 e-ISBN978-1-4614-0146-9
DOI10.1007/978-1-4614-0146-9
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Preface
The present translation of Halley’s reconstruction of Book VIII of Apollonius’s
Conicswascarriedoutoverthecourseofseveralyears.IttookthatlongbecauseI
wearanotherhat;namely,thatofalecturerinaprogramforscienceandtechnology
education.And,inthatfield,translatingandcommentingonearly18thcenturyre-
constructionsofancientGreekmathematicalworks,unfortunately,hasasomewhat
lowpriority.
Still, though my interest in Halley’s reconstruction of Conics VIII grew origi-
nally outof previouswork I haddoneon ApolloniusofPerga,the moreI worked
onthetranslationandthoughtaboutHalley,themoreIbegantoseethattheproject
actuallyspoketomyeducationalinterestsaswell.Ihavelongbeenconcernedwith
therolethathistoryofmathematicscanplayinmathematicseducation.Ihavehadto
askmyselfinthisconnectionwhatexactlydoesastudentofmathematicsgainfrom
history?ThiswasthequestionthatpreoccupiedmemoreandmoreaboutEdmond
Halley. Thoughhe was a master of the modern and increasingly powerfulmathe-
maticsofhistime,Halleytreatedtheancientmathematicianswithgreatseriousness.
Why? What did he see himself learning fromengagingwith mathematicianssuch
asApollonius?
This really became for me the main question in the backgroundof the present
work.OfcourseoneshouldalsoaskhowfarHalley’sreconstructionofBookVIII
succeededinreproducingApollonius’sownthoughtandthislostbookoftheCon-
ics.Afterall,thatwasHalley’simmediategoal,andwhatheproducedinthisregard
washardlytrivial.Indeed,asapersonwhohasspentmanyyearsstudyingtheCon-
ics, I am tremendously impressed by the profundity of Halley’s understanding of
Apollonius.Ultimately,Halley’sreconstructionofBookVIIIismoreaboutHalley
than about Apollonius. It is, in a way, the portrait of this man’s deep relationship
withthepast.
AsIremarkedattheoutset,myownhistoricalworkhasoftenhadtotakeaback-
seat to otherinstitutionalobligations.Duringa periodwhen I feltthis particularly
acutelyanddespairingly,IwasurgedtotakeuptheHalleyprojectbyadearfriend
and, by all accounts, a brilliant anthropologist, Tania Forte. Tania persuaded me
thatwithoutsuchaprojectIwoulddriftinexorably,asahistorianofmathematics,
vii
viii Preface
toward the River of Lethe. So, to Tania I must offer my very first thanks. Sadly,
Tania will never read this: she died suddenly and tragically in 2005, just as she
wasbeginningherownpromisingcareerandjustasIwasmakingmyfirststepsin
thistranslationandcommentary.AfterTania,ImustthanknextJohnNeufromthe
historyofsciencelibraryattheUniversityofWisconsinwhogenerouslymadethe
text of Halley’s reconstruction available to me when I was working on my Ph.D.
some ten yearsago. I am still touched by the kindnesshe showed me then. I also
want to thank Gideon Freudenthal, who managed to find for me Halley’s preface
totheentire1710editionoftheConics,whichIcouldnotfindinthebestlibraries
hereinIsrael.MayerGoldberghelpedmeobtainpapersonHalley’sactuarialwork
and,moreimportantly,providedinvaluablehelpinallthingsdigital,nottospeakof
wonderfullonghoursofconversationovercoffee.ThroughoutmyworkonHalley’s
Book VIII, Sabetai Unguruwas my constant advisor:he was always the first per-
sonIturnedtowhenIhadquestions,doubtsorideasthatneedingworkingthrough
andheneverfailedme.Iowetohimdeepthanks,notonlyforthis,butalsoforhis
encouragementandwarmfriendship.
ThanksarealsoduetoMarinusTaisbakwhoneverturnedmeawaywhenIcame
to him with Latin problems. I also want to thank my friend and fellow historian
of Greek mathematics, Alain Bernard, with whom I discussed the reconstruction
onseveraloccasions.Theintroductionbelowowesmuchtomyconversationswith
Alain. LennartBerggren,who read the manuscriptwith a fine-toothedcomb, also
deservesthanks:hismanycommentsandsuggestionshavemadethisamuchbetter
workthanitwaswhenhefirstreceivedit.
Finally,Iamgratefultomywife,Yifat,whotrulysupportedmeinthisproject,
saying often, “I think you should put everything else away today and work on
Halley.” Although the work might have been begun without her, without her, it
wouldneverhavebeencompleted.
Beer-Sheva MichaelN.Fried
April,2011
Contents
PartI Introduction
1 EdmondHalley:AncientandModern ............................ 3
2 Apollonius’sConics............................................. 7
3 ThePathtoHalley ............................................. 13
4 Halley’sGeneralStrategyforReconstructingConics, BookVIII .... 17
5 Halley’sDialoguewiththePast .................................. 23
6 ANoteontheTranslation....................................... 33
PartII ApolloniusofPerga’sOnConics:BookEightRestored
APOLLONIUS OF PERGA’S ON CONICS: BOOK EIGHT
RESTOREDORTHEBOOKONDETERMINATEPROBLEMS
CONJECTURED................................................... 37
PartIII SynopsisandAppendices
SynopsisoftheContentsofHalley’sConics,BookVIII .................117
PropositionsI-IV:TheParabolaandInitialPropositionsfortheEllipse
andHyperbola .............................................117
PropositionsV-XVIII:ConjugateDiameters.........................117
ScholiumSpecialCasesofthe“ApplicationofAreas”.................119
PropositionsXIX-XXXIII:DiametersandtheirLateraRecta...........119
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