The development of Arabic mathematics : between arithmetic and algebra

(Boston Studies in the Philosophy and History of Science)

R. Rashed e  A. Armstrong

Springer | 1994 | 392 páginas | rar - pdf | 8,7 Mb

link (password: matav)

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.
 
CONTENTS
Editorial Note vii
Preface ix
Introduction
CHAPTER I: The Beginnings of Algebra 8
1. AI-KhwarizmI's Concept of Algebra 8
2. AI-KarajI 22
3. The New Beginnings of Algebra in the Eleventh and Twelfth Centuries 34
4. Mathematical Induction: al-KarajI and al-SamawJal 62
CHAPTER II: Numerical Analysis 85
The Extraction of the nth Root and the Invention of Decimal Fractions (Eleventh to Twelfth Centuries)
CHAPTER III: Numerical Equations 147
The Solution of Numerical Equations and Algebra: Sharaf aI-DIn al-lusI and Viete
CHAPTER IV: Number Theory and Combinatorial Analysis 205
1. Diophantine Analysis in the Tenth Century: al-Khazin 205
2. Ibn al-Haytham and Wilson's Theorem 238
3. Algebra and Linguistics: Combinatorial Analysis in Arabic Science 261
4. Amicable Numbers, Aliquot Parts and Figurate Numbers in the Thirteenth and Fourteenth Centuries 275
5. Ibn al-Haytham and Perfect Numbers 320
APPENDIX 1: The Notion of Western Science: "Science as a Western Phenomenon"
APPENDIX 2: Periodization in Classical Mathematics 350
Bibliography 356
Index 367