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The Development of Arabic Mathematics : Between Arithmetic and Algebra - R. Rashed

The Development of Arabic Mathematics

Between Arithmetic and Algebra

By: R. Rashed, A. Armstrong (Translator)

Hardcover

Published: 30th June 1994
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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.

Editorial Note
Preface
Introductionp. 1
The Beginnings of Algebrap. 8
Al-Khwarizmi's Concept of Algebrap. 8
Al-Karajip. 22
The New Beginnings of Algebra in the Eleventh and Twelfth Centuriesp. 34
Mathematical Induction: al-Karaji and al-Samawalp. 62
Numerical Analysis: The Extraction of the nth Root and the Invention of Decimal Fractions (Eleventh to Twelfth Centuries)p. 85
Numerical Equations: The Solution of Numerical Equations and Algebra: Sharaf al-Din al-Tusi and Vietep. 147
Number Theory and Combinatorial Analysisp. 205
Diophantine Analysis in the Tenth Century: al-Khazinp. 205
Ibn al-Haytham and Wilson's Theoremp. 238
Algebra and Linguistics: Combinatorial Analysis in Arabic Sciencep. 261
Amicable Numbers, Aliquot Parts and Figurate Numbers in the Thirteenth and Fourteenth Centuriesp. 275
Ibn al-Haytham and Perfect Numbersp. 320
Appendix 1: The Notion of Western Science: "Science as a Western Phenomenon"p. 332
Appendix 2: Periodization in Classical Mathematicsp. 350
Bibliographyp. 356
Indexp. 367
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792325659
ISBN-10: 0792325656
Series: Boston Studies in the Philosophy and History of Science
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 382
Published: 30th June 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 29.7 x 21.0  x 3.18
Weight (kg): 0.77