Geometry and Dioptrics in Сlassical Islam

Geometry and Dioptrics in classical Islam By Rushdai Raashid
Publisher: Al-Furqaan Islamic Heritage Foundation 2005 | 1178 Pages | ISBN: 1873992998 | File type: PDF | 16 mb


CONTENTS
PREFACE TO THE TRANSLATION V
NOTICE XIII
CHAPITRE I: THE MATHEMATICIANS: SCIENTIFIC MILIEU AND WORKS 1
1. Ibn Sahl . . . . . 1
1.1. Ibn Sahl and his Time . 1
1.2. Ibn Sahl's Scientific Work. 4
1.2.1. On Squaring the Parabola. 5
1.2.2. On Centers of Gravity. . 5
1.2.3. Geometrical Problems Cited by al-Sijzi 6
1.2.4. On Lines of Diorism . 7
1.2.5. Al-Shanni's Book on the Synthesis of the Problems Analysed by Abu Sa'd al-'Ala' ibn Sahl 7
1.2.6. On the Properties of the Three Conic Sections . 10
1.2.7. The Book on the Astrolabe by the Demonstration of al-Quhi and the Commentary of Ibn Sahl 11
1.2.8. Burning Instruments . . . . . . 12
1.2.9. Proof that the Celestial Sphere is not of Extreme Transparency . 15
2. Al-Quhi. . . 16
2.1. The Mathematician and the Artisan 16
2.2. Al-Quhi's Scientific Work 19
2.2.1. The Book on the Astrolabe by Demonstration 19
2.2.2. On the Perfect Compass . . . 20
2.2.3. Lemma to the Division of the Straight Line by Archimedes 23
2.2.4. On the Construction of an Equilateral Pentagon in a Given Square. . . . . 23
2.2.5. On the Determination of the Division of a Known Angle into Three Equal Parts . . 26
2.2.6. On the Division of an Angle Enclosed by Two Straight Lines into Three Equal Parts 27
2.2.7. On the Determination of Two Straight Lines Between Two Straight Lines, so that the Four Succeed One Another in Continuous Proportion, and on the Division of an Angle into Three Equal Parts . . . . 27
2.2.8. On the Trisection of an Angle and the Construction of a Regular Heptagon in the Circle 28
2.2.9. On the Knowledge of the Magnitude of the Distance between the Center of the Earth and the Position of a Shooting Star in the Night 28
2.2.10. On the Knowledge of the Magnitude of what is Seen of the Sky and of the Sea from the Top of an Elevated Thing 29
2.2.11. In Finite Time, there is Infinite Movement . 30
3. Al-Quhi's Predecessors: On the Trisection of an Angle . 30
3.1. Ahmad ibn Shakir: On the Trisection of an Angle Enclosed by Two Straight Lines . 30
3.2. Thabit ibn Qurra 30
3.2.1. On the Construction of Two Means and the Division of a Known Angle into Three Equal Parts . 30
3.2.2. The Division of an Angle into Three Equal Parts 31
3.3. Abu Ja'far Muhammad ibn al-Husayn al-Khazin 31
3.3.1. On the Division of an Angle into Three Equal Parts and the Determination of Two Straight Lines Between Two Straight Lines that Succeed One Another in Continuous Proportion . 31
3.3.2. On the Determination of Two Straight Lines Between Two Straight Lines that Succeed One Another in Continuous Proportion by a Method of Fixed Geometry . 31
4. Al-Sijzi . 32
4.1. On the Construction of the Perfect Compass. 32
4.2. On the Properties of the Hyperbolic Dome and the Parabolic Dome . 32
4.3. On the Properties of the Elliptical, Hyperbolic and Parabolic Solids . 33
5. Ibn al-Haytham 33
5.1. Book Seven of the Optics 34
5.2. The Treatise on the Burning Sphere 37
6. Al-Farisi: The Commentary on the Burning Sphere 38

Dioptrics
CHAPTER II: IBN SAHL AND THE BEGINNINGS OF DIOPTRICS
I. Introduction
2. The Parabolic Mirror
3. The Ellipsoidal Mirror
4. Refraction and Snell's Law
5. Piano-Convex and Biconvex Lenses
6. Conclusion . 43
TEXTS AND TRANSLATION
1. On Burning Instruments.
2. Proof that the Celestial Sphere is not of Extreme Transparency
CHAPTER III : THE DIOPTRICAL RESEARCH OF IBN AL-HAYTHAM AND AL-
FARISI 151
1. The Spherical Diopter 153
2. The Spherical Lens . 160
3. The Burning Sphere . 162
4. The Burning Sphere and the Quantitative Study of al-Farisi 170
5. Ibn Sahl, Ibn al-Haytham, and Snell's Law. 177
TEXTS AND TRANSLATION
Ibn al-Haytham
1. Optics - Seventh Book: The Spherical Diopter.
2. Optics - Seventh Book: The Spherical Lens .
3. Treatise on the Burning Sphere
4. Treatise on the Burning Sphere - Redaction of al-Farisi

Geometry
CHAPTER IV: ON CONIC SECTIONS AND THEIR APPLICATIONS . 295
I. Conics and Harmonic Division 297
1.1. Ibn Sahl on Harmonic Division. . 297
1.2. Projective Interpretation of Ibn Sahl's Study . 303
2. Ibn Sahl on Conic Sections and Geometrical Constructions. 306
2.1. The Synthesis by al-Shanni of Ibn Sahl's Analysis of Geometrical Problems . . . . . . 306
2.2. Ibn Sahl on the Construction of a Triangle by Means of an Ellipse and a Circle 334
3. Conic Sections and Geometrical Constructions: al-Quhi and his Predecessors. . . . . . 336
3.1. Introduction . 336
3.2. The Two Mean Proportionals. 338
3.2.1. The Legacy of the Ancients 338
3.2.2. The New Tradition: Thabit ibn Qurra and al-Khazin 341

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