9781873992999
Geometry And Dioptrics In Classical Islam - Rushdai Raashid
Al-Furqaan Islamic Heritage Foundation (2005)
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#6871

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Geometry, Algebraic, Mathematics, Arab

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
3.2.3. Al-Quhi . 352
3.3. The Trisection of an Angle . . . . . 355
3.3.1. Introduction . 355
3.3.2. The Earliest Trisections of an Angle: Pappus, Ahmad ibn Shakir and Thabit ibn Qurra. . 355
3.3.3. Al-Khazin: Trisecting an Angle and the Cleavage between Ancients and Moderns .... 366
3.4. Al-Quhi: Variation on the Trisection of an Angle 370
3.5. The Lemma to Archimedes' Division of a Straight Line 383
3.6. The Inscription of a Pentagon in a Given Square 389
3.7. Conclusion . . . 402
4. A New Orientation in the Geometry of Conics: Quadratic Surfaces 403
4.1. On the Properties of Hyperbolic and Parabolic Domes. 405
4.2. Projective Interpretation of the Problem of the Plane Sections of a Quadric . 417
4.3. On the Properties of Elliptical, Hyperbolic and Parabolic Solids 418
4.3.1. Plane Sections . 419
4.3.2. Hyperbolic and Parabolic Plane Sections. 425
4.4. The Projective Interpretation of the Investigation of Plane Sections of a Cylinder 429
TEXTS AND TRANSLATION
IBN SAHL
1. On the Properties of the Three Conic Sections . 434
2. Book on the Synthesis of the Problems Analysed by Ibn Sahl 444
3. A Fragment on the Construction of a Triangle by Means of an Ellipse and a Circle . 486
4. A Problem of Geometry 490
AL-QOHI
1. On the Determination of the Division of a Known Angle into Three Equal Parts . 494
2. On the Division of an Angle Enclosed by Two Straight Lines into Three Equal Parts. 504
3. 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 . 508
4. On the Trisection of an Angle and the Construction of a Regular Heptagon in the Circle . 514
5. Lemma to the Division of the Straight Line by Archimedes . 522
6. On the Construction of an Equilateral Pentagon in a Given Square 532
AL-QUHI'S PREDECESSORS
1. Ahmad ibn Shakir
On the Trisection of an Angle Enclosed by Two Straight Lines . 550
2. Thabit ibn Qurra
On the Construction of Two Means and the Division of a Known Angle into Three Parts . 554
The Division of an Angle Enclosed by Two Straight Lines into Three Equal Parts . 564
3. AI-Khazin
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 . 574
On the Determination of two Straight Lines Between Two Straight Lines that Succeed One Another in Continuous Proportion by a Method of Fixed Geometry. 586
AL-SUZI
On the Properties of the Hyperbolic Dome and the Parabolic Dome 592
On the Properties of the Elliptical, Hyperbolic and Parabolic Solids. 610
CHAPTER V: A TRADITIONN OF RESEARCH: CONTINUOUS DRAWING OF CONIC CURVES AND THE PERFECT COMPASS 629
Introduction 629
1. The Mechanical Construction of Conics: Ibn Sahl 632
1.1. The Parabola. 632
1.2. The Ellipse . . . . . . . . 633
1.3. The Hyperbola . . . . . 633
2. The Invention of the Perfect Compass: Abu Sahl al-Quhi 635
2.1. AI-QuhI's First Book . 636
2.2. AI-QuhI's Second Book . . 641
2.3. Correspondence between al-QuhI's propositions 4, 5, and 6 and proposition 1.52 to 59 of Apollonius' Conics. . 658
3. Al-Sijzi and the Continuous Drawing of Similar Conic Sections with the Help of the Perfect Compass . 659
4. Continuous Drawing and the Classification of Curves 668
5. Geminus and al-Sijzi: the Classification of Curves 670
6. Ibn 'Iraq and al-Biruni on al-Quhi's Perfect Compass 677
6.1. Ibn 'Iraq: on the Lemmas of al-Quhi 677
6.2. Al-Biruni: al-Quhi's Theory of the Perfect Compass 682
6.2.1. The Parabola 682
6.2.2. The Hyperbola . 684
6.2.3. The Ellipse . 687
7. Kamal al-Din ibn Yunus and his Pupils: On the Perfect Compass. 689
7.1. Introduction . 689
7.2. Al-Abhari and the Perfect Compass 693
8. Conclusion: Drawing Conic Sections: A New Subject Area in Geometry . 722
TEXTS AND TRANSLATION
1. Al-Quhi: On the Perfect Compass. 726
2. Al-Sijzi: On the Construction of the Perfect Compass. 798
3. Ibn 'Iraq: Epistle of Ibn 'Iraq to al-Biruni in Reply to Geometrical Problems 808
4. Al-Biruni: Account of the Perfect Compass. . 816
5. Al-Abhari: Treatise on the Compass of Conic Sections 828
CHAPTER VI: CONICAL AND CYLINDRICAL PROJECTIONS, AND ASTROLABES 849
1. The Astrolabe and the Methods of Projection 849
2. Ibn Sahl on Stereographic Projection. . 870
TEXTS AND TRANSLATION
1. Treatise on the Art of the Astrolabe by Demonstration, composed by Al-Quhi. . 878
2.Ibn Sahl: Commentary on the Treatise on the Art of the Astrolabe by Al-Quhi. . 940
3. A Fragment of Ibn Sahl on Stereographic Projection. 968

APPENDIX I: GEOMETRY AND MECHANICS (KINEMATICS). AL-QUHI, VS ARISTOTLE: ON MOTION . 975
TEXTS AND TRANSLATION
1. Al-Quhi: In Finite Time, there is Infinite Movement 986
2. Fragment of the Treatise of Ibn Butlan: The Refutations of 'Ali ibn Ridwan . . 988
3. Fragment of al-Mu'tabar fi al-hikma of Abu al-Barakat al-Baghdadi 990
APPENDIX II: AL-QUHI: FROM METEOROLOGY TO ASTRONOMY 991
TEXTS AND TRANSLATION
I. 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 . .1008
2. On the Knowledge of the Magnitude of what is Seen of the Sky and of the Sea from the Top of an Elevated Thing . 1018
3. Fi ma'rifat ma yura min al-sama' wa-al-bahr (abridged version) 1033
ADDITIONAL NOTES . 1037
Notes on Ibn Sahl's Treatises on Burning Instruments and the Celestial Sphere . 1037
1. On the parts of the 'instrument' 1037
2. Experimentation . 1039
3. Translation of Ptolemy's Optics 1045
Notes on Ibn al-Haytham's On the Sundial 1045
Notes on al-Shanni's Book on Synthesis 1052
Notes on the Astrolabe . 1055
1. Treatise by al-Quhi . . 1055
2. Ibn Sahl's Commentary on the treatise by al-Quhi 1059
ARABIC-ENGLISH GLOSSARY 1067
INDEX 1139
Index of Names 1139
Subject Index . 1145
Index of Works 1157
Index of Manuscripts. 1163
BIBLIOGRAPHY . 1165
ARABIC PREFACE

Product Details
LoC Classification QA564 .R374 2005
No. of Pages 1178
Height x Width 300 mm