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E-raamat: Classical Mathematics from Al-Khwarizmi to Descartes

4.67/5 (6 hinnangut Goodreads-ist)

Roshdi Rashed (Centre National de la Recherche Scientifique (CNRS) in Paris, France)

Formaat: 758 pages
Sari: Culture and Civilization in the Middle East
Ilmumisaeg: 21-Aug-2014
Kirjastus: Routledge
Keel: eng
ISBN-13: 9781317622390

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Formaat: 758 pages
Sari: Culture and Civilization in the Middle East
Ilmumisaeg: 21-Aug-2014
Kirjastus: Routledge
Keel: eng
ISBN-13: 9781317622390

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This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat.

‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics.

This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture.

Arvustused

This comprehensive history of mathematics from the 8th to the 17th centuries is organized by fields. The most interesting part is "Algebra" because of its unifying role. - M. Bona, University of Florida

Foreword

xiii

Translator's Note

xiv

Preface

Introduction: Problems Of Method

1 The history of science: between epistemology and history

(16)

2 The transmission of Greek heritage into Arabic

(38)

1 Transmission and translation: setting up the problem

(16)

1 Towards a new approach

(2)

2 Cultural transmission, scientific transmission

(2)

3 Scholarly transmission: one myth and several truths

(1)

3.1 The rebirth of research

(4)

3.2 Institution and profession: the age of the Academies

(4)

3.3 An ideal type of translator: Hunayn ibn Ishaq's journey

(2)

3.4 Third phase: from translator-scientist to scientist-translator

(1)

2 Translation and research: a dialectic with many forms

(19)

1 Coexisting and overtaking: optics and catoptrics

(9)

2 Translation and recursive reading: the case of Diophantus

(5)

3 Translation as a vehicle of research: the Apollonius project

(3)

4 Ancient evidence of the translation-research dialectic: the case of the Almagest

(2)

3 Prospective conclusion

(2)

3 Reading ancient mathematical texts: the fifth book of Apollonius's Conies

(26)

4 The founding acts and main contours of Arabic mathematics

(22)

PART I

I ALGEBRA

1 Algebra and its unifying role

105

(44)

1 The beginning of algebra: al-Khwarizmi

107

(6)

2 Al-Khwarizmi's successors: geometrical interpretation and development of algebraic calculation

113

(4)

3 The arithmetization of algebra: al-Karaji and his successors

117

(8)

4 The geometrization of algebra: al-Khayyam (1048--1131)

125

(10)

5 The transformation of the theory of algebraic equations: Sharaf al-Din al-TusI

135

(10)

6 The destiny of the theory of equations

145

(4)

2 Algebra and linguistics: the beginnings of combinatorial analysis

149

(22)

1 Linguistics and combinatorics

150

(10)

2 Algebraic calculation and combinatorics

160

(2)

3 Arithmetic research and combinatorics

162

(2)

4 Philosophy and combinatorics

164

(1)

5 A treatise on combinatorial analysis

165

(4)

6 On the history of combinatorial analysis

169

(2)

3 The first classifications of curves

171

(68)

1 Introduction

171

(5)

2 Simple curves and mixed curves

176

(12)

3 Geometrical and mechanical: the characterization of conic sections

188

(7)

4 Geometrical transformation and the classification of curves

195

(4)

5 The intervention of the algebraists: the polynomial equation and the algebraic curve

199

(5)

6 The classification of curves as mechanical and geometrical

204

(21)

7 Developments of the Cartesian classification of algebraic curves

225

(9)

8 Conclusion

234

(5)

Appendix: Simplicius: On the Euclidean definition of the straight line and of curved lines

237

(2)

4 Descartes's Geometric and the distinction between geometrical and mechanical curves

239

(20)

1 The geometrical theory of algebraic equations: the completion of al-Khayyam's program

241

(7)

2 From geometry to algebra: the curves and the equations

248

(11)

5 Descartes's ovals

259

(22)

6 Descartes and the infinitely small

281

(20)

7 Fermat and algebraic geometry

301

(32)

1 The geometrical loci and the pointwise transformations

303

(8)

2 The equations of geometrical loci

311

(5)

3 Solution of equations by the intersection of two curves

316

(3)

4 The solution of algebraic equations and the study of algebraic curves

319

(14)

II ARITHMETIC

1 Euclidean, neo-Pythagorean and Diophantine arithmetics: new methods in number theory

333

(32)

1 Classical number theory

333

(13)

1.1 Euclidean and neo-Pythagorean arithmetic

334

(2)

1.2 Amicable numbers and the discovery of elementary arithmetic functions

336

(4)

1.3 Perfect numbers

340

(1)

1.4 Equivalent numbers

341

(1)

1.5 Polygonal numbers and figurate numbers

342

(3)

1.6 The characterization of prime numbers

345

(1)

2 Indeterminate analysis

346

(19)

2.1 Rational Diophantine analysis

346

(9)

2.2 Integer Diophantine analysis

355

(8)

2.3 Arithmetic methods in number theory

363

(2)

2 Algorithmic methods

365

(34)

1 Numerical equations

368

(21)

1.1 The extraction of roots

368

(9)

1.2 The extraction of roots and the invention of decimal fractions

377

(2)

1.3 Numerical polynomial equations

379

(10)

2 Interpolation methods

389

(10)

3 Thabit ibn Qurra and amicable numbers

399

(12)

4 Fibonacci and Arabic mathematics

411

(14)

5 Fibonacci and the Latin extension of Arabic mathematics

425

(20)

6 Al-Yazdi and the equation nΣi-1x2i = x2

445

(8)

7 Fermat and the modern beginnings of Diophantine analysis

453

(20)

PART II GEOMETRY

1 The Archimedeans and problems with infinitesimals

473

(82)

1 Calculating infinitesimal areas and volumes

475

(42)

1.1 The Pioneers

475

(24)

1.2 The Heirs

499

(7)

1.3 Later developments

506

(11)

2 The quadrature of lunes

517

(8)

3 Equal perimeters and equal surface areas: a problem of extrema

525

(13)

3.1 Al-Khazin: the mathematics of the Almagest

527

(1)

3.1.1 Isoperimeters

528

(2)

3.1.2 Equal areas

530

(1)

3.2 Ibn al-Haytham: a new theory

531

(1)

3.2.1 Isoperimeters

532

(1)

3.2.2 Equal surface areas

533

(5)

4 The theory of the solid angle

538

(17)

2 The traditions of the Conies and the beginning of research on projections

555

(46)

1 Cylindrical projections

557

(18)

1.1 Al-Biruni's testimony and his priority claim

557

(2)

1.2 Al-Hasan ibn Musa's study of the ellipse

559

(1)

1.3 Thabit's treatise on the cylinder

560

(5)

1.4 Ibn al-Samh's study of plane sections of a cylinder and the determination of their areas

565

(6)

1.5 The theory of projections: al-Quhi and Ibn Sahl

571

(4)

2 Conic projections

575

(26)

2.1 Ptolemy's Planisphere

575

(3)

2.2 Al-Farghani's treatise, al-Kamil fi san at al-asturlab

578

(5)

2.3 Al-Quhi's treatise and Ibn Sahl's commentary on it

583

(8)

2.4 Al-Saghani's study of the projection of the sphere

591

(6)

2.5 The construction of the sumut

597

(4)

3 The continuous drawing of conic curves and the classification of curves

601

(20)

1 Introduction

601

(4)

2 Ibn Sahl: a mechanical device to trace conic sections

605

(2)

3 Al-Quhi: the perfect compass

607

(7)

4 Al-Sijzi: the improved perfect compass

614

(4)

5 Continuous drawing and classification of curves

618

(3)

4 Thabit ibn Qurra on Euclid's fifth postulate

621

(16)

1 Introduction

621

(4)

2 Thabit ibn Qurra's first treatise

625

(5)

3 Thabit ibn Qurra's second treatise

630

(7)

PART III APPLICATION OF MATHEMATICS: ASTRONOMY AND OPTICS

1 The celestial kinematics of Ibn al-Haytham

637

(44)

1 Introduction

637

(12)

1.1 The astronomical work of Ibn al-Haytham

637

(8)

1.2 The Configuration of the Motions of the Seven Wandering Stars

645

(4)

2 The structure of The Configuration of the Motions

649

(32)

2.1 Research on the variations

650

(9)

2.2 The planetary theory

659

(22)

2 From the geometry of the gaze to the mathematics of the phenomena of light

681

(14)

CONCLUSION: The philosophy of mathematics

695

(38)

1 Mathematics as conditions and models of philosophical activity: al-Kindi and Maimonides

699

(9)

2 Mathematics in the philosophical synthesis and the `formal' inflection of the ontology: Ibn Sina and Nasir al-Din al-Tusi

708

(18)

3 From ars inveniendi to ars analytica

726

(7)

INDEX

Index of names

733

(10)

Index of works

743

Roshdi Rashed is one of the most eminent authorities on Arabic mathematics and the exact sciences. A historian and philosopher of mathematics and science and a highly celebrated epistemologist, he is currently Emeritus Research Director (distinguished class) at the Centre National de la Recherche Scientifique (CNRS) in Paris, and is the former Director of the Centre for History of Medieval Science and Philosophy at the University of Paris (Denis Diderot, Paris VII). He also holds an Honorary Professorship at the University of Tokyo and an Emeritus Professorship at the University of Mansourah in Egypt.

Michael H. Shank is professor of the History of Science at the University of Wisconsin-Madison, were he teaches surveys of the history of science from antiquity to Newton. His research interests focus on, and often stray beyond, the late-medieval Viennese astronomical and natural philosophical traditions.

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