Travelling Mathematics - The Fate of Diophantos' Arithmetic
In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we kn
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R. Halleux, Liège S. Hildebrandt, Bonn Ch. Meinel, Regensburg J. Peiffer, Paris W. Purkert, Bonn D. Rowe, Mainz A.I. Sabra, Cambridge, Mass. Ch. Sasaki, Tokyo R.H. Stuewer, Minneapolis H. Wußing, Leipzig V.P. Vizgin, Moskva
Ad Meskens
Travelling Mathematics The Fate of Diophantos' Arithmetic
Ad Meskens Artesis Hogeschool Antwerpen Department Bedrijfskunde, Lerarenopleiding en Sociaal Werk Verschansingstraat 29 2000 Antwerpen Belgium e-mail: [email protected]
Fig. 1.1 © Stephen Chrisomalis, published with kind permission. All drawings by Paul Tytgat, with kind permission.
ISBN 978-3-0346-0642-4 e-ISBN 978-3-0346-0643-1 DOI 10.1007/978-3-0346-0643-1 Library of Congress Control Number: 2010935851 © Springer Basel AG 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained.
Cover illustration: From Waller Ms de-00215, August Beer: Über die Correction des Cosinusgesetzes bei der Anwendung des Nicol’schen Prismas in der Photometrie, after 1850. With friendly permission by The Waller Manuscript Collection (part of the Uppsala University Library Collections). Cover design: deblik Printed on acid-free paper Springer Basel AG is part of Springer Science + Business Media www.birkhauser-science.com
Contents Preface 1 Arithmetic and the beginnings 1.1 In the beginning. . . . . . . . . 1.2 Classical Greece . . . . . . . . 1.3 The Greek written heritage . 1.4 Numbers in Classical Greece . 1.5 All is number . . . . . . . . .
vii of algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Alexandria ad Aegyptum 2.1 The capital of memory . . . . . . . . . . . . . . 2.2 Diophantos’ Alexandria . . . . . . . . . . . . . 2.3 Education and the culture of paideia . . . . . . 2.4 Heron of Alexandria: a Diophantine precursor?
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3 Diophantos and the Arithmetika 3.1 The manuscripts . . . . . . . . . . . . . . . . 3.2 Diophantos . . . . . . . . . . . . . . . . . . . 3.3 The book On Polygonal Numbers and the lost 3.4 Symbolism in the Arithmetika . . . . . . . . . 3.5 The structure of a Diophantine problem . . . 3.6 The Arithmetika . . . . . . . . . . . . . . . . 3.7 The algebra of the Arithmetika . . . . . . . . 3.8 Interpretations of algebra in the Arithmeti
