Table Of ContentPythagoras Revived
This page intentionally left blank
Pythagoras Revived
Mathematics and Philosophy in Late Antiquity
Dominic J. O'Meara
CLARENDON PRESS · OXFORD
GreatClarendonStreet,OxfordOX26DP
OxfordUniversityPressisadepartmentoftheUniversityofOxford
ItfurtherstheUniversity'sobjectiveofexcellenceinresearch,scholarship,
andeducationbypublishingworldwidein
OxfordNewYork
AucklandBangkokBuenosAiresCapeTownChennai
Dar esSalaamDelhiHongKongIstanbulKarachiKolkata
KualaLumpurMadridMelbourneMexicoCityMumbaiNairobi
SãoPauloShanghaiTaipeiTokyoToronto
Oxfordisaregisteredtrademark ofOxfordUniversityPress
intheUK andincertainothercountries
PublishedintheUnitedStatesby
OxfordUniversityPressInc., NewYork
©DominicJ. O'Meara1989
Themoralrightsoftheauthorshavebeenasserted
DatabaserightOxfordUniversityPress(maker)
Firstpublished1989
Firstissuedinpaperback1990
Allrightsreserved.Nopartofthispublicationmaybereproduced,
storedinaretrievalsystem,or transmitted,inanyform orbyanymeans,
withoutthepriorpermissioninwriting ofOxfordUniversityPress,
oras expresslypermittedbylaw, or under termsagreedwiththeappropriate
reprographicsrightsorganization.Enquiriesconcerningreproduction
outsidethescopeoftheaboveshouldbesenttotheRightsDepartment,
OxfordUniversityPress,attheaddressabove
Youmustnotcirculatethisbookinanyotherbindingorcover
andyoumustimposethissameconditiononanyacquirer
BritishLibraryCataloguinginPublicationData
Dataavailable
Library ofCongressCataloginginPublicationData
O'Meara,DominicJ.
Pythagorasrevived.
Bibliography:p.Includesindex.
1.Pythagorasand Pythagoreanschool.
2. Mathematics—Philosophy—History.I.Title.
B243.0461989119′.09′01588–25246
ISBN0–19–823913–0 (Pbk.)
PATRI DILECTISSIMO
SACRUM
This page intentionally left blank
Preface
Research begun many years ago with the support of a Junior and Visiting Fellowship at the Dumbarton Oaks Center
for ByzantineStudiesbroughtme to thetexts and theses explored inthisbook. A sabbatical grant and generous leave
ofabsencefromTheCatholicUniversityofAmericaandagrantprovidedinidealcircumstancesbytheAlexander von
Humboldt-Stiftung allowed me to develop these theses. Completion of the book was made possible by the support
made availableby the Universitéde Fribourg. I am also much indebted to friends and colleagues for their assistance.
Henri-Dominique Saffrey made many helpful suggestionsand corrections for whichI am grateful,as I am to Oxford
UniversityPress's reader for constructiveand detailedcomments. Ilsetraut Hadot also proposed improvements to the
book, which is indebted to her research as it is to the work of Pierre Hadot, a longstanding source of inspiration for
me. Leendert Westerink and John Duffy were unfailing in their expert assistance. I am particularly grateful to Werner
Beierwaltes: he putmeonthetrack ofIamblichus and gavemeinvaluableadviceand helpduringmystayinFreiburg-
im-Breisgau and Munich. The deficiencies that remain in the book are of course mine. My wife Carra gave my work
her fullencouragement and support throughout many years. Amy Eiholzer-Silver prepared thetypescriptsof thefinal
revisions of the book with intelligent care.
In an effort to simplify footnotes as far as possible, I have adopted the practice of referring to modern works by the
name of the author and the year of publication: further details may be found in the second part of the Bibliography.
The texts of ancient authors are cited by page and line in the editions listed in the first part of the Bibliography (for
fragments, by fragment number and line). In cases where this seemed appropriate, I have added a chapter number
beforethepage reference(e.g. I ch. 2, 3=vol.I, chapter 2, page 3). Translations are mine,unless otherwisenoted. The
following standard abbreviations are used:
CAG Commentaria in Aristotelem Graeca, Berlin, 1870 ff.
DK H. Diels, W. Kranz, Die Fragmente der Vorsokratiker, Berlin, 1952.
viii PREFACE
LSJ Liddell, Scott, Jones, Greek—English Lexicon.
RE Pauly, Wissowa, Kroll, Realencyclopädie der classischen Altertumswissenschaft.
SVF Stoicorum veterum fragmenta, ed. H. von Arnim, Leipzig, 1905–24.
This book was completed early in 1986. I have tried to include mention of what has been published since, but have
only been able to take account to a limited extent in particular of the important Paris colloquium on Proclus: Proclus,
lecteur et interprète des anciens, ed. J. Pépin, H.-D. Saffrey, Paris 1987.
D.J.O'M.
Fribourg, Switzerland
Christmas 1987
Table of Contents
Introduction
Part I The Revival Of Pythagoreanism In the Neoplatonic School
1. Varieties of Pythagoreanism in the Second and Third Centuries AD 9
1. Numenius of Apamea 10
2. Nicomachus of Gerasa 14
3. Anatolius 23
4. Porphyry 25
2. Iamblichus' Work On Pythagoreanism: Title, Plan, the First Four Books 30
1. The Title and Overall Plan 32
2. Pythagoras (Book I: On the Pythagorean Life) 35
3. Pythagorean Philosophy (Book II: the Protreptic) 40
4. Pythagorean Mathematical Science (Book III: On General Mathematical Science) 44
5. Arithmetic (Book IV: On Nicomachus' Arithmetical Introduction) 51
3. On Pythagoreanism V – VII: The Excerpts in Michael Psellus 53
1. Michael Psellus, Philosophical Excerptor 53
2. Psellus' Excerpts from On Pythagoreanism V – VII 57
3. On Pythagoreanism V 60
(i) General Plan 60
(ii) Physical Number 62
(iii) Formal and Material Causation 62
(iv) Efficient Causation 64
(v) Change 64
(vi) Place 66
(vii) The Void 67
(viii) Conclusion 68
