Ibn al-Haytham and analytical mathematics. A history of Arabic sciences and mathematics 2

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-Iasan ibn al-Iasan and MuIammad ibn al-Iasan:    mathematician and philosopher ... 11    3. The works of al-Iasan 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-Iasan ibn al-Haytham ? . 362    3. Ibn Sinaen 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 ...