Lacroix and the Calculus
Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal
- PDF / 4,327,624 Bytes
- 475 Pages / 467.716 x 666.141 pts Page_size
- 105 Downloads / 194 Views
Editorial Board: K. Andersen, Aarhus D. Buchwald, Pasadena H.J.M. Bos, Utrecht U. Bottazzini, Roma J.Z. Buchwald, Cambridge, Mass. K. Chemla, Paris S.S. Demidov, Moskva E.A. Fellmann, Basel M. Folkerts, München P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
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
João Caramalho Domingues
Lacroix and the Calculus
Birkhäuser Basel · Boston · Berlin
João Caramalho Domingues Centro de Matemática da Universidade do Minho Campus de Gualtar 4710-057 Braga Portugal e-mail: [email protected]
2000 Mathematical Subject Classification: Primary: 01A50; Secondary: 01A55
Library of Congress Control Number: 2008920493 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-7643-8637-5 Birkhäuser Verlag AG, Basel - Boston - Berlin 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. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF∞ Cover illustration: Figure 30 in volume II of Lacroix’s Traité du Calcul différentiel et du Calcul intégral: construction of a first-order partial differential equation in three variables (see pages 247-248). Printed in Germany ISBN 978-3-7643-8637-5
e-ISBN 978-3-7643-8638-2
987654321
www.birkhauser.ch
Abridged contents 0
Introduction
1 A short biography of Silvestre-François Lacroix
1 7
2 An overview of Lacroix’s Traité
21
3 The principles of the calculus
53
4 Analytic and differential geometry
89
5 Approximate integration and conceptions of the integral
141
6 Types of solutions of differential equations
179
7 Aspects of differences and series
257
8 The Traité élémentaire
283
9 The second edition of the Traité
321
10 Final remarks
343
A Two memoirs by Lacroix
353
B Lacroix’s historical appraisal of his own Traité
397
C Syllabi of Lacroix’s course of analysis at the École Polytechnique
403
D Biographical data on a few obscure characters
423
Bibliography
427
Index
461
Contents Acknowledgments 0 Introduction 0.1 Lacroix and his Traité in the literature 0.2 This study . . . . . . . . . . . . . . . . 0.2.1 Comparisons . . . . . . . . . . 0.2.2 Structure . . . . . . . . . . . . 0.2.3 Notations . . . . . . . . . . . .
xiii
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . .
Data Loading...
