Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism. With an Appendix on Pappus and the History of Platonism

193 Pages·1998·15.49 MB·English

by  Jaap Mansfeld

PROLEGOMENA MATHEMATICA
PHILOSOPHIA ANTIQUA
A SERIES OF STUDIES
ON ANCIENT PHILOSOPHY
FOUNDED BY J.H. WASZINKt AND W.J. VERDENIUSt
EDITED BY
J. MANSFELD, D.T. RUNIA
J.C.M. VAN WINDEN
VOLUME LXXX
JAAP MANSFELD
PROLEGOMENA MATHEMATICA
PROLEGOMENA MATHEMAT ICA
FROM APOLLONIUS OF PERGA TO LATE NEOPLATONISM
With an Appendix on
of
Pappus and the History Platonism
BY
JAAP MANSFELD
BRILL
LEIDEN · BOSTON · KOLN
1998
This book is printed on acid-free paper.
Library of Congress Cataloging-in-Publication Data
Mansfeld, Jaap.
Prolegomena mathematica : from Apollonius of Perga to late
Neoplatonism : with an appendix on Pappus and the histmy of
Platonism I by Jaap Mansfeld.
p. em. (Philosophia antiqua, ISSN 0079-1687 ; v. 80)
Includes bibliographical references (p. - ) and indexes.
ISBN 90041126 77 (acid-free paper)
1. Mathematics, Greek. I. Title. II. Series.
QA22.M34 1998
510'.938-dc21 98-38382
CIP
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Mansfeld, Jaap:
Prolegomena mathematica : from Apollonius of Perga to late
Neop1atonism. With an appendix on Pappus and the history of
Platonism. By Jaap Mansfe1d. - Leiden ; Boston; Ko1n: Brill, 1998
(Philosophia antiqua ; Vol. 80)
ISBN 9G-04-11267-7
ISSN 0079-1687
ISBN 90 04 11267 7
© Copyright 1998 by Koninldijke Brill NV, Leiden, 7he Netherlu.nds
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TABLE OF CONTENTS
PREFACE............................................................................................. VII
CHAPTER I PRELIMINARIES ............................................................ 1
CHAPTER II PAPPUS' COLLECTIO................................................... 6
II 1 Introduction......................................................................... 6
II 2 Collectio Book VII................................................................. 9
II 3 Collectio Book VI .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 14
II 4 Further Evidence from the Collectio................................. 20
CHAPTER III CoMMENTARIES ON EucLID, THE ScHOLIA ON
EUCLID'S ELEMENTS AND PAPPUS' COMMENTARY ON
BOOK X......................................................................................... 23
III 1 Comments and Commentaries on the Elements
andData................................................................................... 23
III 2 The Scholia in Euclidem: Prod us, Pappus and Others... 26
III 3 Pappus' Commentary on Elements Book X.................... 31
CHAPTER IV APOLLONms' PROEMS AND EuTocius'
COMMENTARY.............................................................................. 36
IV 1 The Proems of Apollonius' Conica................................. 36
IV 2 Eutocius' Commentary on Apollonius' Conica I-IV.... 40
CHAPTER V EuTocius' CoMMENTARIES ON ARcHIMEDES,
AND THE VITA............................................................................. 44
V 1 Archimedes' Proems........................................................ 44
V 2 Eutocius' Commentaries on Archimedes..................... 45
V 3 The Vita of Archimedes ................ ............. ............ .......... 48
CHAPTER VI HERON OF ALEXANDRIA......................................... 49
VI 1 Introduction....................................................................... 49
VI 2 The Belopoiica.. .... .... . ....... ..... ... .... ...... ..... ........ ......... ... .... ... 49
VI 3 The Pneumatica.... ....................................... ........ .... ........ ... 50
VI 4 The Automata..................................................................... 51
VI 5 The Catoptrica........................ ................... .......................... 52
VI 6 The Metrica.................................................... ..... .... ........ .... 53
VI 7 The Dioptra......................................................................... 54
VI 8 A Theoretical Work: the So-called Definitiones, i.e.
Ta 7tpo tile; yeroJ.le-rpucJic; o-rotxnc.OOeroc;..... .... ...... ..... ............... 55
vi TABLE OF CONTENTS
CHAPTER VII THEON(?)'s PREFACE TO EucLID's 0PTICA........ 58
CHAPTER VIII MARINUS oN EucLID's DATA............................. 61
CHAPTER IX PTOLEMY's PREFACES............................................... 66
IX 1 The Mathematike Suntaxis.................................................. 66
IX 2 The Apotelesmatica ............................................................. 71
CHAPTER X CoMMENTARIES ON PTOLEMY.................................. 76
X 1 Pappus and Theon on the Mathematike Suntaxis
and Handy Tables................................................................... 76
X 2 The Anonymous Introduction to the Mathematike
Suntaxis. ............ ... ... ............... ........... ... ... ... ... . ........ ... ......... ....... 79
X 3 Commentaries on the Apotelesmatica............................... 81
CHAPTER XI NICOMACHUS OF GERASA AND HIS
COMMENTATORS......................................................................... 82
XI 1 The Introductio Arithmetica............... ... .. . . .. ... . .. ... . ...... ... . . . .. . 82
XI 2 Iamblichus' Version and Asclepius' and Philoponus'
Commentaries....................................................................... 87
XI 3 The Anonymous Prolegomena to the Introductio
Arithmetica................................................................................ 89
CHAPTER XII CoNCLUSION............................................................ 92
APPENDIX 1: THE TITLE OF PTOLEMY's AsTROLOGICAL
TREATISE...................................................................................... 96
APPENDIX 2: PAPPUS AND THE HISTORY OF PLATONIS]VJ ......... 99
COMPLEMENTARY NOTES............................................................... 122
BIBLIOGRAPHY................................................................................. 133
INDEX LocoRUM PoTIORUM ......................................................... 151
INDEX RERuM ET NoMINUM ANTIQUORUM............................... 168
PREFACE
This little book grew out of a paper I was invited to write for a
Festschrift. Because, alas, things got out of hand I have to publish the
results of my enquiries separately. I worked on it from September
1997 to February 1998, adding the indexes later, at the proof stage,
and making a few small changes at the same time. One may note
that ANRW 11.37.5, which according to the announcement is to
contain a number of survey chapters on ancient mathematics, will
appear only a few years from now. This is a pity, because the
contents of this volume certainly would have been a great help.
The reason why I started working on this theme at all is that I
discovered that in an earlier book I had overlooked quite a lot of
important evidence, as is explained in the first paragraph on p. 1
below.
A short version of Appendix 2 was delivered as a Mededeling
(lecture) at the Netherlands Royal Academy on March 9 1998; a
longer version, based on a hand-out containing the more important
texts, was presented in the context of the seminaire Les philosophes et
la philosophic at the Sorbonne on March 26 1998. David Runia
persuaded me to include a revised English version of this piece in
the book. I hope to have profited from the critical remarks made at
these oral presentations.
Thanks are due to friends and colleagues who helped in various
ways. Keimpe Algra, Pierluigi Donini, Tiziano Dorandi, Frans de
Haas, David T. Runia, and Carlos Steel commented on and criti
cized draft versions, including that of Appendix 2. Petri Maenpaa
kindly sent me a copy of his important dissertation on Analysis, a
difficult topic on which we also exchanged e-mail letters. Needless
to say I take full responsibility for such errors as undoubtedly
remain. Henri van de Laar weeded out typing errors and gave
indispensable assistance with the bibliography and proofs. My
student assistants Ivo Gerardts and Johannes Rustenburg indefatig
ably brought the books and journals I needed from the University
Library. Gonni Runia with her usual expertise again gave the
finishing touches to the camera-ready copy.
Bilthoven, July 1998