Ancient Mathematics (Sciences of Antiquity)

303 Pages·2001·1.87 MB·English

by  Serafina Cuomo

ANCIENT MATHEMATICS
The theorem of Pythagoras, Euclid’s Elements,and Archimedes’ method to
find the volume of a sphere are all parts of the invaluable legacy of ancient
mathematics. Its discoveries and insights continue to amaze and fascinate
the modern reader. But ancient mathematics was also about counting and
measuring, surveying land and attributing mystical significance to the
number six.
This volume offers the first accessible survey of the discipline in all its
variety and diversity of practices. The period covered ranges from the fifth
century BC to the sixth century AD, with the focus on the Mediterranean
region. Topics include:
• mathematics and politics in classical Greece
• the formation of mathematical traditions
• the self-image of mathematicians in the Graeco-Roman period
• mathematics and Christianity
• the use of the mathematical past in late antiquity
There are also segments on historiographical issues – such as the nature
of the evidence on early Greek mathematics, or the problem of the authentic
text of the Elements – as well as individual sections on ancient mathematicians
from Plato and Aristotle to Pappus and Eutocius. Fully illustrated with
plates, drawings and diagrams, and with an extensive bibliography, Ancient
Mathematics will be a valuable reference tool for non-specialists, as well as
essential reading for those studying the history of science.
S. Cuomo is a lecturer at the Centre for the History of Science, Technology
and Medicine, Imperial College, London. She is the author of a book on
Pappus, and of articles on Hero and Frontinus.
i
SCIENCES OF ANTIQUITY
Series Editor: Roger French
Director, Wellcome Unit for the History of Medicine,
University of Cambridge
Sciences of Antiquity is a series designed to cover the subject matter of what
we call science. The volumes discuss how the ancients saw, interpreted and
handled the natural world, from the elements to the most complex of living
things. Their discussions on these matters formed a resource for those who
later worked on the same topics, including scientists. The intention of this
series is to show what it was in the aims, expectations, problems and
circumstances of the ancient writers that formed the nature of what they
wrote. A consequent purpose is to provide historians with an understanding
of the materials out of which later writers, rather than passively receiving
and transmitting ancient ‘ideas’, constructed their own world view.
ANCIENT ASTROLOGY
Tamsyn Barton
ANCIENT NATURAL HISTORY
Histories of nature
Roger French
COSMOLOGY IN ANTIQUITY
M.R. Wright
ANCIENT MATHEMATICS
S. Cuomo
ii
A N C I E N T
M AT H E M AT I C S
S. Cuomo
London and New York
iii
First published in 2001
by Routledge
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by Routledge
29 West 35th Street, New York, NY 10001
Routledge is an imprint of the Taylor & Francis Group
This edition published in the Taylor and Francis e-Library, 2005.
“To purchase your own copy of this or any of Taylor & Francis or Routledge’s
collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”
© S. Cuomo
All rights reserved. No part of this book may be reprinted or reproduced or
utilised in any form or by any electronic, mechanical, or other means, now
known or hereafter invented, including photocopying and recording, or in
any information storage or retrieval system, without permission in writing
from the publishers.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Cuomo, S. (Serafina)
Ancient mathematics / S. Cuomo.
p. cm. – (Sciences of antiquity)
Includes bibliographical references and index.
1 Mathematics, Ancient. I. Title. II Series.
QA22 .C85 2001
510′.93–dc21 2001019499
ISBN 0-203-99573-2 Master e-book ISBN
ISBN 0–415–16494–X (hbk)
ISBN 0–415–16495–8 (pbk)
iv
C O N T E N T S
List of figures and tables vi
List of abbreviations vii
List of places mentioned ix
Acknowledgements xii
INTRODUCTION 1
1 EARLY GREEK MATHEMATICS: THE EVIDENCE 4
2 EARLY GREEK MATHEMATICS: THE QUESTIONS 39
3 HELLENISTIC MATHEMATICS: THE EVIDENCE 62
4 HELLENISTIC MATHEMATICS: THE QUESTIONS 125
5 GRAECO-ROMAN MATHEMATICS: THE EVIDENCE 143
6 GRAECO-ROMAN MATHEMATICS: THE QUESTIONS 192
7 LATE ANCIENT MATHEMATICS: THE EVIDENCE 212
8 LATE ANCIENT MATHEMATICS: THE QUESTIONS 249
Glossary 263
Bibliography 267
Index 287
v
FIGURES AND TABLES
Figures
1.1 Plan of Metapontum and surrounding area 7
1.2 The Eupalinus tunnel 10
1.3 The so-called Salamis abacus 12
1.4 The so-called Darius vase 13
3.1 Doura Europus with city plan and fortifications
in evidence 64
3.2 A surveying instrument from the Fayum, dating from
Ptolemaic times 68
4.1 The medieval and Renaissance tradition of Euclid’s Elements 127
5.1 Roman abacus (replica) 147
5.2 Gearwork from the Antykythera object 152
5.3 Sundial found in Pompeii 154
5.4 Reconstruction of a groma from Pompeii, c. first
century AD 155
5.5 Centuriation from Africa Proconsularis 156
5.6 Fragment 7 of Cadaster Orange A, c. AD 77 156
Tables
1.1 Milesian or Ionian notation 11
1.2 Acrophonic or Attic notation 11
vi
A B B R E V I AT I O N S
CAG Commentaria Aristotelis Graeca
CMG Corpus Medicorum Graecorum
CIL Corpus Inscriptionum Latinarum
DK H. Diels and W. Kranz (eds), Die Fragmente der
Vorsokratiker, 6th edn, Zurich 1952
DSB Dictionary of Scientific Biography, New York 1969–
IG Inscriptiones Graecae
ILS H. Dessau, Inscriptiones Latinae Selectae, Berlin 1892–
1916
LS H.G. Liddell and R. Scott, A Greek-English Lexicon,
9th edn, rev. H.S. Jones, Oxford 1968
O. Bodl. J.G. Tait, Greek Ostraka in the Bodleian Library and
Other Collections, 1, London 1930
OCD The Oxford Classical Dictionary, Oxford 1996
P. Amh. Amherst Papyri, B.P. Grenfell and A.S. Hunt (eds), 2
vols, London 1900–1
P. Berol. Berlin Papyri
P. British Museum Greek Papyri in the British Museum, F.G. Kenyon and
H.I. Bell (eds), London 1893–1917
P. Cairo B.P. Grenfell and A.S. Hunt (eds), Greek Papyri,
Catalogue général des Antiquités égyptiennes du Musée
du Caire, vol. 10, Oxford 1903
P. Cairo Isidor. The Archive of Aurelius Isidorus, A.E.R. Boak and H.C.
Youtie (eds), Ann Arbor 1960
P. Cairo Zen. C.C. Edgar, Zenon Papyri, Catalogue général des
Antiquités égyptiennes du Musée du Caire, 79, 4 vols,
Cairo 1925–31
P. Col. Zen. W.L. Westermann and L. Sayre Hasenoehrl (eds),
Zenon Papyri. Business Papers of the Third Century B.C.
Dealing with Palestine and Egypt, 2 vols, New York
1934–40
vii
ABBREVIATIONS
P. Ent. Publications de la Société royale égyptienne de
Papyrologie, Textes et Documents, ed. O. Guéraud, 1,
Cairo 1931–32
P. Fayum B.P. Grenfell, A.S. Hunt, D.G. Hogarth, Fayum Towns
and their Papyri, London 1900
P. Flind. Petr. The Flinders Petrie Papyri, J.P. Mahaffy and J.G. Smily
(eds), Dublin 1891–1905
P. Freib. Mitteilungen aus der Freiburger Papyrussammlung, in
Sitzungsberichte der Heidelberger Akademie der
Wissenschaften, Phil.-hist. Klasse, 1914–16
P. Herc. Papyri Herculanenses, see M. Capasso, Manuale di
papirologia ercolanese 1991
P. Lips. L. Mitteis, Griechische Urkunden der Papyrussammlung
zu Leipzig, 1, 1906
P. Lond. Greek Papyri in the British Museum, F.G. Kenyon and
H.I. Bell (eds), London 1893–1917
P. Mich. Michigan Papyri
P. Oxy. Oxyrhynchus Papyri, B.P. Grenfell and A.S. Hunt (eds),
London 1898–
P. Rev. Laws B.P. Grenfell, Revenue Laws of Ptolemy Philadelphus,
Oxford 1896
P. Tebt. Tebtunis Papyri, B.P. Grenfell, A.S. Hunt, J.G. Smyly,
E.J. Goodspeed and C.C. Edgar (eds), 3 vols,
London/New York 1902–38
P. Vindob. Papyrus Vindobonensis
SelPap Select Papyri, Engl. tr. A.S. Hunt and C.C. Edgar, 5
vols, Cambridge, MA/London 1932–34
viii
LIST OF PLACES MENTIONED
LIST OF PL ACES
M E N T I O N E D
Western Mediterranean
1 Agrigentum I8 Màlaga off the map 18 Paestum G9
2 Aosta (Augusta towards I1 19 Pompeii G9
Taurinorum) D6 11 Marseille (Massilia) E5 20 Rimini E8
3 Bologna D7 12 Marzabotto E7 21 Rome F8
4 Canosa (Canusium) F9 13 Metapontum G10 22 Syracuse I9
5 Capua F9 14 Milan D7 23 Tarentum G10
6 Carthage I7 15 Naples G9 24 Thurii G10
7 Cosa F7 16 Orange (Arausius) D4 25 Verona C7
8 Cumae G9 17 Ostia F8 26 Worms A7
9 Enns B9 Osuna (Urso) off the
10 Hippo I6 map towards I1
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