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Ibn al-Haytham and analytical mathematics : a history of Arabic sciences and mathematics. Volume 2

Author: Rushdī Rāshid; Nader El-Bizri
Publisher: London : Routledge, 2013.
Series: Culture and civilisation in the Middle East.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
History
Additional Physical Format: Print version:
Rashid, Rushdi.
Ibn al-Haytham and analytical mathematics Volume 2.
London : Routledge, 2012
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Rushdī Rāshid; Nader El-Bizri
ISBN: 9781136191084 1136191089 0415582180 9780415582186 9781299558465 1299558461
OCLC Number: 844440957
Description: 1 online resource (800 pages).
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-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 ...
Series Title: Culture and civilisation in the Middle East.
Responsibility: by Roshdi Rashed ; edited by Nader El-Bizri.

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