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Author:   Roshdi Rashed (Centre National de la Recherche Scientifique (CNRS) in Paris, France) ,  Nader El-Bizri
Publisher:   Taylor & Francis Ltd
Imprint:   Routledge
Weight:   0.840kg
ISBN:  

9780415582186

ISBN 10:   0415582180
Pages:   450
Publication Date:   04 September 2012
Audience:   College/higher education ,  Tertiary & Higher Education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

CONTENTS Preface ..................................................................................... xi Note ....................................................................................... xiii INTRODUCTION: IBN AL-HAYTHAM AND HIS WORK ON INFINITESIMAL MATHEMATICS 1. Ibn al-Haytham: from Basra to Cairo .............................................. 1 2. Al-Îasan ibn al-Îasan and MuÌammad ibn al-Îasan: mathematician and philosopher ......................................................... 11 3. The works of al-Îasan ibn al-Haytham on infinitesimal mathematics ......... 25 CHAPTER I: THE QUADRATURE OF LUNES AND CIRCLES 1.1. INTRODUCTION ....................................................................... 39 1.2. MATHEMATICAL COMMENTARY ................................................ 42 1.2.1. Treatise on lunes ................................................................. 42 1.2.2. Treatise on the quadrature of the circle ........................................ 46 1.2.3. Exhaustive treatise on the figures of lunes .................................... 49 1.3. TRANSLATED TEXTS 1.3.1. Treatise on Lunes ............................................................... 93 1.3.2. Treatise on the Quadrature of the Circle .................................... 99 1.3.3. Exhaustive Treatise on the Figures of Lunes .............................. 107 CHAPTER II: CALCULATION OF VOLUMES OF PARABOLOIDS AND SPHERES AND THE EXHAUSTION METHOD 2.1. INTRODUCTION ....................................................................... 143 2.2. MATHEMATICAL COMMENTARY ................................................ 144 2.2.1. Calculation of volumes of paraboloids ........................................ 144 2.2.2.1. Arithmetical lemmas ................................................... 144 2.2.2.2. Volume of a paraboloid of revolution ................................ 151 2.2.2.3. The volume of the second species of paraboloid ................... 160 2.2.2.4. Study of surrounding solids .......................................... 164 2.2.3. Calculation of the volume of a sphere ......................................... 168 2.3. TRANSLATED TEXTS: 2.3.1. On the Measurement of the Paraboloid ...................................... 177 2.3.2. On the Measurement of the Sphere .......................................... 221 2.3.3. On the Division of Two Different Magnitudes as Mentioned in the First Proposition of the Tenth Book of Euclid’s Elements .............. 235 CHAPTER III: THE PROBLEMS OF ISOPERIMETRIC AND ISEPIPHANIC FIGURES AND THE STUDY OF THE SOLID ANGLE 3.1. INTRODUCTION ....................................................................... 239 3.2. MATHEMATICAL COMMENTARY ................................................ 242 x CONTENTS 3.3. TRANSLATED TEXT: On the Sphere which is the Largest of all the Solid Figures having Equal Perimeters and On the Circle which is the Largest of all the Plane Figures having Equal Perimeters ...................................... 305 APPENDIX: THE APPROXIMATION OF ROOTS 4.1. MATHEMATICAL COMMENTARY ................................................ 343 4.2. TRANSLATED TEXTS 4.3.1. On the Cause of the Square Root, its Doubling and its Displacement ... 351 4.3.2. On the Extraction of the Side of a Cube ........................................ 357 SUPPLEMENTARY NOTES 1. On the Arithmetic of Transactions ................................................ 361 2. The Configuration of the Universe: a Book by al-Îasan ibn al-Haytham ? . 362 3. Ibn Sinæn and Ibn al-Haytham on the subject of ‘shadow lines’ ................ 377 4. Commentary in the Resolution of Doubts by Ibn al-Haytham on Proposition X.1 of the Elements ...................................................... 381 5. List of Ibn al-Haytham’s works .................................................... 391 BIBLIOGRAPHY ............................................................................. 429 INDEXES Index of names ........................................................................... 439 Subject index ............................................................................. Index of works .........................................................

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Author Information

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 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. Nader El-Bizri is a Reader at the University of Lincoln, and a Chercheur Associe at the Centre National de la Recherche Scientifique in Paris (CNRS, UMR 7219). He has lectured on 'Arabic Sciences and Philosophy' at the University of Cambridge since 1999. He held a Visiting Professorship at the University of Lincoln (2007-2010), and, since 2002, he continues to be a senior Research Associate affiliated with The Institute of Ismaili Studies, London.

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