The Transformation of Mathematics in the Early Mediterranean World_ From Problems to Equations (2007).pdf

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The Transformation of Mathematics in the Early
Mediterranean World: From Problems to Equations
The transformation of mathematics from ancient Greece to the medieval Arab-
speaking world is here approached by focusing on a single problem proposed by
Archimedes and the many solutions offered. In this trajectory Reviel Netz follows
the change in the task from solving a geometrical problem to its expression as
an equation, still formulated geometrically, and then on to an algebraic problem,
now handled by procedures that are more like rules of manipulation. From a
practice of mathematics based on the localized solution (and grounded in the
polemical practices of early Greek science) we see a transition to a practice of
mathematics based on the systematic approach (and grounded in the deuteronomic
practices of Late Antiquity and the Middle Ages). With three chapters ranging
chronologically from Hellenistic mathematics, through Late Antiquity, to the
medieval world, Reviel Netz offers a radically new interpretation of the historical
journey of pre-modern mathematics.
r ev iel netz
is Associate Professor in the Department of Classics at Stanford
University. He has published widely in the field of Greek mathematics:
The Shap-
ing of Deduction in Greek Mathematics: A Study in Cognitive History
(1999) won
the Runciman Prize for
2000,
and he is currently working on a complete English
translation of and commentary on the works of Archimedes, the first volume of
which was published in
2004.
He has also written a volume of Hebrew poetry
and a historical study of barbed wire.
cambridge classical studies
General editors
r . l . h u nt e r , r . g . o sb o r n e, m . d. r e e v e ,
p. d. a . g a r n s e y, m . m i l l e t t, d. n. s e d l e y, g. c. h o r r o c k s
T H E T R A N S F O R M AT I O N O F M AT H E M AT I C S
I N T H E E A R LY M E D I T E R R A N E A N W O R L D :
F RO M P RO B L E M S T O E Q UAT I O N S
REVIEL NETZ
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521829960
© Faculty of Classics, University of Cambridge 2004
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2004
Reprinted 2005, 2006
This digitally printed version 2007
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
The Transformation of Mathematics in the Early Mediterranean World : From
Problems to Equations / Reviel Netz.
p. cm. – (Cambridge classical studies)
Includes bibliographical references.
ISBN 0 521 82996 8
1. Mathematics – Europe – History. I. Title. II. Series.
QA27.E85N48 2004
510´.94 – dc22 2003060601
ISBN 978-0-521-82996-0 hardback
ISBN 978-0-521-04174-4 paperback

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