| Description |
1 online resource (768 pages) |
| Series |
Culture and Civilization in the Middle East |
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Culture and civilisation in the Middle East.
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Foreword; Translator's Note; Preface; Introduction: Problems of Method; 1. The history of science: between epistemology and history; 2. The transmission of Greek heritage into Arabic; 1. Transmission and translation: setting up the problem; 1. Towards a new approach; 2. Cultural transmission, scientific transmission; 3. Scholarly transmission: one myth and several truths; 3.1. The rebirth of research; 3.2. Institution and profession: the age of the Academies; 3.3. An ideal type of translator: Hụnayn ibn Ishạ̄q's journey |
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3.4. Third phase: from translator-scientist to scientist-translator2. Translation and research: a dialectic with many forms; 1. Coexisting and overtaking: optics and catoptrics; 2. Translation and recursive reading: the case of Diophantus; 3. Translation as a vehicle of research: the Apollonius project; 4. Ancient evidence of the translation-research dialectic: the case of the Almagest; 3. Prospective conclusion; 3. Reading ancient mathematical texts: the fifth book of Apollonius's Conics; 4. The founding acts and main contours of Arabic mathematics; Part I; I. Algebra |
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1. Algebra and its unifying role1. The beginning of algebra: al-Khwārizmī; 2. Al-Khwārizmī's successors: geometrical interpretation and development of algebraic calculation; 3. The arithmetization of algebra: al-Karajī and his successors; 4. The geometrization of algebra: al-Khayyām (1048-1131); 5. The transformation of the theory of algebraic equations: Sharaf al-Dīn al-Tụ̄sī; 6. The destiny of the theory of equations; 2. Algebra and linguistics: the beginnings of combinatorial analysis; 1. Linguistics and combinatorics; 2. Algebraic calculation and combinatorics |
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3. Arithmetic research and combinatorics4. Philosophy and combinatorics; 5. A treatise on combinatorial analysis; 6. On the history of combinatorial analysis; 3. The first classifications of curves; 1. Introduction; 2. Simple curves and mixed curves; 3. Geometrical and mechanical: the characterization of conic sections; 4. Geometrical transformation and the classification of curves; 5. The intervention of the algebraists: the polynomial equation and the algebraic curve; 6. The classification of curves as mechanical and geometrical |
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7. Developments of the Cartesian classification of algebraic curves8. Conclusion; Appendix: Simplicius: On the Euclidean definition of the straight line and of curved lines; 4. Descartes's Géométrie and the distinction between geometrical and mechanical curves; 1. The geometrical theory of algebraic equations: the completion of al-Khayyām's program; 2. From geometry to algebra: the curves and the equations; 5. Descartes's ovals; 6. Descartes and the infinitely small; 7. Fermat and algebraic geometry; 1. The geometrical loci and the pointwise transformations |
| Summary |
This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat.'Early modern, ' mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from 'classical mathematics, ' to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Ra |
| Notes |
2. The equations of geometrical loci |
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Print version record |
| Subject |
Mathematics -- History
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MATHEMATICS -- Essays.
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MATHEMATICS -- Pre-Calculus.
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MATHEMATICS -- Reference.
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Mathematics
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| Genre/Form |
History
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| Form |
Electronic book
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| ISBN |
9781317622390 |
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1317622391 |
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9781322074054 |
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1322074054 |
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