Founding Figures and Commentators in Arabic Mathematics: A History of Arabic Sciences and Mathematics Volume 1

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ISBN: 9780415582179 | 0415582172
Cover: Hardcover
Copyright: 11/15/2011

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This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. It also includes extensive commentary from one of world's foremost authorities on the subject.

Editor's Foreword	p. xiii
Preface	p. xix
Note	p. xxiv
Banu Musa and the Calculation of the Volume of the Sphere and the Cylinder
Introduction	p. 1
The Banu Musa: dignitaries and learned	p. 1
The mathematical works of the Banu Musa	p. 7
Treatise on the measurement of plane and spherical figures: a Latin translation and a rewritten version by al-Tusi	p. 10
Title and date of the Banu Musa treatise	p. 34
Mathematical Commentary	p. 38
Organization and structure of the Banu Musa book	p. 38
The area of the circle	p. 40
The area of the triangle and Hero's formula	p. 46
The surface area of a sphere and its volume	p. 47
The two-means problem and its mechanical construction	p. 60
The trisection of angles and Pascal's Limaçon	p. 66
Approximating cubic roots	p. 69
Translated Text: On the Knowledge of the Measurement of Plane and Spherical Figures	p. 73
Thabit Ibn Qurra and his Works In Infinitesimal Mathematics
Introduction	p. 113
Thabit ibn Qurra: from Harran to Baghdad	p. 113
The works of Thabit ibn Qurra in infinitesimal mathematics	p. 122
History of the texts and their translations	p. 124
Measuring the Parabola	p. 130
Organization and structure of Ibn Qurra's treatise	p. 130
Mathematical commentary	p. 133
Arithmetical propositions	p. 133
Sequence of segments and bounding	p. 142
Calculation of the area of a portion of a parabola	p. 154
Translated text: On the Measurement of the Conic Section Called Parabola	p. 169
Measuring the Paraboloid	p. 209
Organization and structure of Ibn Qurra's treatise	p. 209
Mathematical commentary	p. 214
Arithmetical propositions	p. 214
Extension to sequences of segments	p. 218
Volumes of cones, rhombuses and other solids	p. 223
Property of four segments	p. 230
Arithmetical propositions	p. 231
Sequence of segments and bounding	p. 233
Calculation of the volumes of paraboloids	p. 244
Parallel between the treatise on the area of the parabola and the treatise on the volume of the paraboloid	p. 256
Translated text: On the Measurement of the Paraboloids	p. 261
On The Sections of The Cylinder and Its Lateral Surface	p. 333
Introduction	p. 333
Mathermatical commentary	p. 337
Plane sections of the cylinder	p. 337
Area of an ellipse and elliptical sections	p. 341
Concerning the maximal section of the cylinder and concerning its minimal sections	p. 356
Concerning the lateral area of the cylinder and the lateral area of portions of the cylinder lying between the plane sections touching all sides	p. 363
Translated text: On the Sections of the Cylinder and its Lateral Surface	p. 381
IBN Sinan, Critique of Al-Mahani: The Area of The Parabola
Introduction	p. 459
Ibrahim ibn Sinan: 'heir' and 'critic'	p. 459
The two versions of The Measurement of the Parabola: texts and translations	p. 463
Mathematical Commentary	p. 466
Translated Texts
On the Measurement of the Parabola	p. 483
On the Measurement of a Portion of the Parabola	p. 495
Abu Ja'far Al-khain: Isoperimetrics and Isepiphanics
Introduction	p. 503
Al-Khazin: his name, life and works	p. 503
The treatises of al-Khazin on isoperimeters and isepiphanics	p. 506
Mathematical Commentary	p. 507
Introduction	p. 507
Isoperimetrics	p. 509
Isepiphanics	p. 524
The opuscule of al-Sumaysati	p. 546
Translated Texts
Commentary on the First Book of the Almagest	p. 551
The Surface of any Circle is Greater than the Surface of any Regular Polygon with the Same Perimeter (al-Summaysati)	p. 577
Al-quhi, Critique of Thabit: Volume of the Paraboloid of Revolution
Introduction	p. 579
The mathematician and the artisan	p. 579
The versions of the volume of a paraboloid	p. 583
Mathematical Commentary	p. 588
Translation Texts
On the Determination of the Volume of a Paraboloid	p. 599
On the Volume of a Paraboloid	p. 609
IBN Al-Samh: The Plane Sections of A Cylinder and The Determination of Their Areas
Introduction	p. 615
Ibn al-Samh and Ibn Qurra, Successors to al-Hasan ibn Musa	p. 615
Serenus of Antinoupolis, al-hasan ibn Musa, Thabit ibn Qurra and Ibn al-Samh	p. 618
The structure of the study by Ibn al-Samh	p. 622
Mathematical Commentary	p. 623
Definitions and accepted results	p. 623
The cylinder	p. 626
The plane sections of a cylinder	p. 627
The properties of a circle	p. 628
Elliptical sections of a right cylinder	p. 632
The ellipse as a plane section of a right cylinder	p. 632
The area of an ellipse	p. 645
Chords and sagittas of the ellipse	p. 653
Translated Text: On the Cylinder and its Plane Section	p. 667
Ibn HuD: The Measurement of the Parabola and the Isoperimetric Problem
Introduction	p. 721
Kitab al-Istikmal, a mathematical compendium	p. 721
Manuscript transmission of the texts	p. 727
The Measurement of the Parabola	p. 729
Infinitesimal property or conic property	p. 729
Mathematical commentary on Propositions 18-21	p. 733
Translation: Kitab al-Istikmal	p. 749
The Isoperimetric Problem	p. 755
An extremal property or a geometric property	p. 755
Mathematical commentary on Proposition 16 and 19	p. 758
Translation: Kitab al-Istikmaal	p. 764
Supplementary Notes
The Formula of Hero of Alexandria according to Thabit ibn Qurra	p. 767
Commentary of Ibn Abi Jarrada on The Sections of the Cylinder by Thabit ibn Qurra	p. 767
Bibliography	p. 779
Indexes
Index of names	p. 793
Subject index	p. 797
Index of works	p. 805
Table of Contents provided by Ingram. All Rights Reserved.

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Founding Figures and Commentators in Arabic Mathematics: A History of Arabic Sciences and Mathematics Volume 1

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