The Development of Arabic Mathematics: Between Arithmetic and Algebra

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Springer Science & Business Media, Jun 30, 1994 - History - 382 pages
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An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history.
Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science.
 

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Contents

III
1
IV
8
V
22
VI
34
VII
62
VIII
85
IX
147
X
205
XII
261
XIII
275
XIV
320
XV
332
XVI
350
XVII
356
XVIII
367
Copyright

XI
238

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Page 366 - Recherches sur plusieurs ouvrages de Léonard de Pisé, découverts et publiés par M. le prince B. Buoncompagni , et sur les rapports qui existent entre ces ouvrages et les travaux mathématiques des Arabes, par MF Wœpcke.
Page 366 - III. Traduction d'un fragment anonyme sur la formation des triangles rectangles en nombres entiers, et d'un traité sur le même sujet par Aboà Dja'Jar Mohammed Ben Alhoçaïn (Atti dell' Accademia Pontificia de' Nuovi Lincei, anno i86i, vol.
Page 366 - Grecs. iSSz, in-8. i 5o — Essai d'une restitution de travaux perdus d'Apollonius sur les quantités irrationnelles, d'après un mss. arabe. i853, in ,|. i » — Discussion de deux méthodes arabes pour déterminer une valeur approchée de sin. i'.
Page 358 - Mersenne, Frénicle et l'élaboration de l'analyse combinatoire dans la première moitié du XVIIe siècle...

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