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Al-Khwarizmi: The Beginnings of Algebra [Hardback]

  • Format: Hardback, 340 pages, height x width x depth: 235x165x30 mm, weight: 847 g
  • Pub. Date: 12-Nov-2009
  • Publisher: Saqi Books
  • ISBN-10: 0863564305
  • ISBN-13: 9780863564307
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  • Format: Hardback, 340 pages, height x width x depth: 235x165x30 mm, weight: 847 g
  • Pub. Date: 12-Nov-2009
  • Publisher: Saqi Books
  • ISBN-10: 0863564305
  • ISBN-13: 9780863564307
Other books in subject:
Al-Khwarizmi's Algebra (Kitab al-Jabr wa-al-muqabala), written around 820, was the first scientific text in history to systematically present algebra as a mathematical discipline that is independent of geometry and arithmetic. Roshdi Rashed has produced the first Arabic critical edition of Al-Khwarizmi's work, containing an annotated translation into English, an introductory essay, and extensive commentaries on the text.
Roshdi Rashed is a leading authority in the history and philosophy of science and mathematics. He is senior director of research at the Centre National de la Recherche Scientifique in Paris, and is a former professor at the University of Tokyo.

Al-Khwarizmi was a mathematician, astronomer and geographer. He worked most of his life as a scholar in the House of Wisdom in Baghdad during the first half of the 9th century and is considered by many to be the father of algebra.

His Algebra (Kitab al-Jabr wa-al-muqabala), written around 820 AD, was the first scientific text in history to systematically present algebra as a mathematical discipline independent of geometry and arithmetic. This groundbreaking work was divided into two main sections: one dealing with algebraic theory, and the other focusing on the calculation of inheritances and legacies.

Al-Khwarizmis book laid down the groundwork for a scientific field where mathematics and juridical learning meet, which was further developed by successive generations of mathematicians and jurists. This text also highlighted for the first time the deep-rooted possibilities in algebra to extend the use of mathematical disciplines from one to another, such as the application of arithmetic to algebra, or of geometry into algebra, and vice-versa for these three disciplines into one another; hence opening up novel areas of mathematical research. Latin translations of al-Khwarizmis book began in the 12th century, and these texts held a continuous influence over algebra and mathematics until the 16th century

Roshdi Rashed's book is the first Arabic critical edition of al-Khwarizmi's Algebra. It is also the first scholarly annotated translation into English that contains an introductory essay and extensive commentaries on the text that bring the reader back as faithfully as possible to al-Khwarizmi's original text.

Roshdi Rashed is a leading authority in history and philosophy of science and mathematics. He is Senior Director of Research at the Centre National de la Recherche Scientifique (CNRS) in Paris, and a former Professor at the University of Tokyo. He has published widely in French and Arabic, and his books in English include: The Development of Arabic Mathematics: Between Arithmetic and Algebra (1994), Encyclopaedia of the History of Arabic Science (1996), Omar Khayyam, The Mathematician (2000), and Geometry and Dioptrics in Classical Islam (2005).

Al-Khwarizmi’s Algebra (Kitab al-Jabr wa-al-muqabala), written around 820, was the first scientific text in history to systematically present algebra as a mathematical discipline that is independent of geometry and arithmetic. Roshdi Rashed has produced the first Arabic critical edition of Al-Khwarizmi’s work, containing an annotated translation into English, an introductory essay, and extensive commentaries on the text.

Roshdi Rashed is a leading authority in the history and philosophy of science and mathematics. He is senior director of research at the Centre National de la Recherche Scientifique in Paris, and is a former professor at the University of Tokyo.



The first critical edition of Al-Khwarizmi's Algebra.
Preface vii
Critical apparatus and abbreviations ix
I Al-Khwarizml Mathematician
Introduction
3(8)
I Traditions of Calculation in the Eighth Century and Al-Khwarizmi's Algebra
1.1 Introduction
11(3)
1.2 Al-Khwarizmf s language
14(2)
1.3 Al-Khwarizmi and the culture of the eighth century
16(2)
1.4 Linguists' calculation methods. A priori classification and combinatorics
18(6)
1.5 Juridical calculations
24(6)
II Al-Khwarizmi's Knowledge of the Mathematical Literature
2.1 Introduction
30(1)
2.2 Euclidean mathesis and al-Khwarizmi's idea of algebra
31(1)
2.2.1 Equations and algorithms
31(12)
2.2.2 Quadratic irrational quantities (surds)
43(6)
2.2.3 Geometrical proof and algebraic proof
49(8)
2.3 Euclid, Heron and al-Khwarizmi
57(4)
2.4 Diophantus and al-Khwarizmi
61(3)
2.5 Aryabhata, Brahmagupta and al-Khwarizmi
64(19)
II Text and Translation
Edition and Translation
83(9)
Book on Algebra and Muqabala
92(241)
Squares are equal to roots
96(2)
Squares are equal to a number
98(1)
Roots are equal to a number
98(2)
Squares plus roots are equal to a number
100(4)
Squares plus a number are equal to roots
104(2)
Roots plus a number are equal to squares
106(16)
Chapter on multiplication
122(8)
Chapter on addition and subtraction
130(4)
Division <and multiplication of roots>
134(10)
Chapter on the six problems
144(1)
The first of the six problems
144(2)
Second problem
146(2)
Third problem
148(2)
Fourth problem
150(2)
Fifth problem
152(2)
Sixth problem
154(2)
Chapter on various problems
156(40)
Chapter on transactions
196(6)
Chapter on <surface>-measurement
202(8)
Problems on measurement
210(22)
Book on wills
232(1)
Chapter on assets and debt
232(4)
Another chapter on wills
236(2)
Another chapter on wills
238(8)
On another kind of wills
246(4)
On another kind of wills
250(6)
On another kind of wills
256(14)
Chapter on the will with a dirham
270(12)
Chapter on complement
282(10)
Calculation of the return <of inheritance>
292(1)
A chapter thereof on marriage during illness
292(4)
Chapter on freeing <slaves> during illness
296(24)
Chapter on the return of the dowry
320(8)
Chapter on forward buying during illness
328(5)
Additional Notes 333(14)
Arabic-English Glossary 347(24)
Arabic-Latin mathematical Glossary 371(6)
Index of proper names 377(2)
Index of concepts 379(2)
Index of treatises 381(2)
Index of manuscripts 383(2)
Bibliography 385
Roshdi Rashed is a leading authority in history and philosophy of science and mathematics. He is Senior Director of Research at the Centre National de la Recherche Scientifique (CNRS) in Paris, and a former Professor at the University of Tokyo. He has published widely in French and Arabic, and his books in English include: The Development of Arabic Mathematics: Between Arithmetic and Algebra (1994), Encyclopaedia of the History of Arabic Science (1996), Omar Khayyam. The Mathematician (2000), and Geometry and Dioptrics in Classical Islam (2005).