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Founding Figures and Commentators in Arabic Mathematics: A History of Arabic Sciences and Mathematics Volume 1 [Kietas viršelis]

(Centre National de la Recherche Scientifique (CNRS) in Paris, France), Edited by
  • Formatas: Hardback, 808 pages, aukštis x plotis: 234x156 mm, weight: 1700 g
  • Serija: Culture and Civilization in the Middle East
  • Išleidimo metai: 06-Oct-2011
  • Leidėjas: Routledge
  • ISBN-10: 0415582172
  • ISBN-13: 9780415582179
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 808 pages, aukštis x plotis: 234x156 mm, weight: 1700 g
  • Serija: Culture and Civilization in the Middle East
  • Išleidimo metai: 06-Oct-2011
  • Leidėjas: Routledge
  • ISBN-10: 0415582172
  • ISBN-13: 9780415582179
Kitos knygos pagal šią temą:
In this unique insight into the history and philosophy of mathematics and science in the mediaeval Arab world, the eminent scholar Roshdi Rashed illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The first of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics and sciences in the ninth and tenth centuries.

Extensive and detailed analyses and annotations support a number of key Arabic texts, which are translated here into English for the first time. In this volume Rashed focuses on the traditions of celebrated polymaths from the ninth and tenth centuries School of Baghdad - such as the Ban Ms, Thbit ibn Qurra, Ibrhm ibn Sinn, Ab Ja“far al-Khzin, Ab Sahl Wayjan ibn Rustm al-Qh - and eleventh-century Andalusian mathematicians like Ab al-Qsim ibn al-Samh, and al-Mutaman ibn Hd. The Archimedean-Apollonian traditions of these polymaths are thematically explored to illustrate the historical and epistemological development of infinitesimal mathematics as it became more clearly articulated in the eleventh-century influential legacy of al-Hasan ibn al-Haytham (Alhazen).

Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.
Editor's Foreword xiii
Preface xix
Note xxiv
Chapter I Banu Musa And The Calculation Of The Volume Of The Sphere And The Cylinder
1.1 Introduction
1(37)
1.1.1 The Banu Masa: dignitaries and learned
1(6)
1.1.2 The mathematical works of the Banu Musa
7(3)
1.1.3 Treatise on the measurement of plane and spherical figures: a Latin translation and a rewritten version by al-Tusi
10(24)
1.1.4 Title and date of the Banu Musa treatise
34(4)
1.2 Mathematical Commentary
38(35)
1.2.1 Organization and structure of the Banfi Musa book
38(2)
1.2.2 The area of the circle
40(6)
1.2.3 The area of the triangle and Hero's formula
46(1)
1.2.4 The surface area of a sphere and its volume
47(13)
1.2.5 The two-means problem and its mechanical construction
60(6)
1.2.6a The trisection of angles and Pascal's Limacon
66(3)
1.2.6b Approximating cubic roots
69(4)
1.3 Translated Text: On the Knowledge of the Measurement of Plane and Spherical Figures
73(40)
Chapter II Thabit Ibn Qurra And His Works In Infinitesimal Mathematics
2.1 Introduction
113(17)
2.1.1 Thabit ibn Qurra: from Harran to Baghdad
113(9)
2.1.2 The works of Thabit ibn Qurra in infinitesimal mathematics
122(2)
2.1.3 History of the texts and their translations
124(6)
2.2 Measuring The Parabola
130(79)
2.2.1 Organization and structure of Ibn Qurra's treatise
130(3)
2.2.2 Mathematical commentary
133(36)
2.2.2.1 Arithmetical propositions
133(9)
2.2.2.2 Sequence of segments and bounding
142(12)
2.2.2.3 Calculation of the area of a portion of a parabola
154(15)
2.2.3 Translated text: On the Measurement of the Conic Section Called Parabola
169(40)
2.3 Measuring The Paraboloid
209(124)
2.3.1 Organization and structure of Ibn Qurra's treatise
209(5)
2.3.2 Mathematical commentary
214(47)
2.3.2.1 Arithmetical propositions
214(4)
2.3.2.2 Extension to sequences of segments
218(5)
2.3.2.3 Volumes of cones, rhombuses and other solids
223(7)
2.3.2.4 Property of four segments
230(1)
2.3.2.5 Arithmetical propositions
231(2)
2.3.2.6 Sequence of segments and bounding
233(11)
2.3.2.7 Calculation of the volumes of paraboloids
244(12)
2.3.2.8 Parallel between the treatise on the area of the parabola and the treatise on the volume of the paraboloid
256(5)
2.3.3 Translated text: On the Measurement of the Paraboloids
261(72)
2.4 On The Sections Of The Cylinder And Its Lateral Surface
333(126)
2.4.1 Introduction
333(4)
2.4.2 Mathematical commentary
337(44)
2.4.2.1 Plane sections of the cylinder
337(4)
2.4.2.2 Area of an ellipse and elliptical sections
341(15)
2.4.2.3 Concerning the maximal section of the cylinder and concerning its minimal sections
356(7)
2.4.2.4 Concerning the lateral area of the cylinder and the lateral area of portions of the cylinder lying between the plane sections touching all sides
363(18)
2.4.3 Translated text: On the Sections of the Cylinder and its Lateral Surface
381(78)
Chapter III Ibn Sinan, Critique Of Al-Mahani: The Area Of The Parabola
3.1 Introduction
459(7)
3.1.1 Ibrahim ibn Sian: 'heir' and 'critic'
459(4)
3.1.2 The two versions of The Measurement of the Parabola: texts and translations
463(3)
3.2 Mathematical Commentary
466(17)
3.3 Translated Texts
3.3.1 On the Measurement of the Parabola
483(12)
3.3.2 On the Measurement of a Portion of the Parabola
495(8)
Chapter IV Abu Ja'far Al-Khazin: Isoperimetrics And Isepiphanics
4.1 Introduction
503(4)
4.1.1 Al-Khazin: his name, life and works
503(3)
4.1.2 The treatises of al-Khazin on isoperimeters and isepiphanics
506(1)
4.2 Mathematical Commentary
507(44)
4.2.1 Introduction
507(2)
4.2.2 Isoperimetrics
509(15)
4.2.3 Isepiphanics
524(22)
4.2.4 The opuscule of al-Sumaysati
546(5)
4.3 Translated Texts
4.3.1 Commentary on the First Book of the Almagest
551(26)
4.3.2 The Surface of any Circle is Greater than the Surface of any Regular Polygon with the Same Perimeter (al-Sumaysati)
577(2)
Chapter V Al-Quhi, Critique Of Thabit: Volume Of The Paraboloid Of Revolution
5.1 Introduction
579(9)
5.1.1 The mathematician and the artisan
579(4)
5.1.2 The versions of the volume of a paraboloid
583(5)
5.2 Mathematical Commentary
588(11)
5.3 Translation Texts
5.3.1 On the Determination of the Volume of a Paraboloid
599(10)
5.3.2 On the Volume of a Paraboloid
609(6)
Chapter VI Ibn Al-Samh: The Plane Sections Of A Cylinder And The Determination Of Their Areas
6.1 Introduction
615(8)
6.1.1 Ibn al-Samh and Ibn Qurra, successors to al-Hasan ibn Musa
615(3)
6.1.2 Serenus of Antinoupolis, al-Hasan ibn Musa, Thabit ibn Qurra and Ibn al-Sant
618(4)
6.1.3 The structure of the study by Ibn al-Samh
622(1)
6.2 Mathematical Commentary
623(44)
6.2.1 Definitions and accepted results
623(3)
6.2.2 The cylinder
626(1)
6.2.3 The plane sections of a cylinder
627(1)
6.2.4 The properties of a circle
628(4)
6.2.5 Elliptical sections of a right cylinder
632(7)
6.2.6 The ellipse as a plane section of a right cylinder
639(6)
6.2.7 The area of an ellipse
645(8)
6.2.8 Chords and sagittas of the ellipse
653(14)
6.3 Translated Text: On the Cylinder and its Plane Section
667(54)
Chapter VII Ibn Hud: The Measurement Of The Parabola And The Isoperimetric Problem
7.1 Introduction
721(8)
7.1.1 Kitab al-Istikmal, a mathematical compendium
721(6)
7.1.2 Manuscript transmission of the texts
727(2)
7.2 The Measurement Of The Parabola
729(26)
7.2.1 Infinitesimal property or conic property
729(4)
7.2.2 Mathematical commentary on Propositions 18-21
733(16)
7.2.3 Translation: Kitab al-Istikmal
749(6)
7.3 The Isoperimetric Problem
755(12)
7.3.1 An extremal property or a geometric property
755(3)
7.3.2 Mathematical commentary on Propositions 16 and 19
758(6)
7.3.3 Translation: Kitab al-Istikmal
764
Supplementary Notes
The Formula of Hero of Alexandria according to Thabit ibn Qurra
767(1)
Commentary of Ibn Abi Jarrada on The Sections of the Cylinder by Thabit ibn Qurra
767(12)
Bibliography 779(14)
Indexes
Index of names
793(4)
Subject index
797(8)
Index of works
805
Roshdi Rashed is one of the most eminent authorities on Arabic mathematics and the exact sciences. A historian and philosopher of mathematics and science and a highly celebrated epistemologist, he is currently Emeritus Research Director (distinguished class) at the Centre National de la Recherche Scientifique (CNRS) in Paris, and is the Director of the Centre for History of Medieval Science and Philosophy at the University of Paris (Denis Diderot, Paris VII). He also holds an Honorary Professorship at the University of Tokyo and an Emeritus Professorship at the University of Mansourah in Egypt.

Nader El-Bizri is a Reader at the University of Lincoln, and a Chercheur Associé at the Centre National de la Recherche Scientifique in Paris (CNRS, UMR 7219). He has lectured on Arabic Sciences and Philosophy at the University of Cambridge since 1999. He held a Visiting Professorship at the University of Lincoln (2007-2010), and, since 2002, he continues to be a senior Research Associate affiliated with The Institute of Ismaili Studies, London.