Title Ibn al-Haytham's geometrical methods and the philosophy of mathematics : a history of Arabic sciences and mathematics. Volume 5 / Roshdi Rashed ; translated by J.V. Field

Published London : New York : Routledge, 2017 ©2017

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Description 1 online resource (xiv, 664 pages) : illustrations Series Culture and civilization in the Middle East ; volume 55 History of Arabic sciences and mathematics ; volume 5 Culture and civilisation in the Middle East ; v. 55. History of Arabic sciences and mathematics ; v. 5. Contents Introduction : motion and transformation in geometry -- Chapter I: The properties of the circle -- Chapter II: The analytical art in the tenth to eleventh centuries -- Analysis and synthesis : mathematical method and discipline -- The knowns : a new geometrical discipline -- Analysis and synthesis : examples of the geometry of triangles -- Chapter III: Ibn al-Haytham and the geometrisation of place -- Appendix : the Ars Inveniendi : Thabit ibn Qurra and al-Sijzi -- Thabit ibn Qurra : axiomatic method and invention -- Al-Sijzi : the idea of an Ars Inveniendi -- History of the texts -- Translated texts -- Supplementary notes -- Bibliography -- Indexes Cover; Half Title; Title Page; Copyright Page; Table of Contents; Foreword; Preface; Introduction: Motion and Transformations in Geometry; Chapter I: The Properties of the Circle ; Introduction; 1. The concept of homothety; 2. Euclid, Pappus and Ibn al-Haytham: on homothety; 3. Ibn al-Haytham and homothety as a point by point transformation; 4. History of the text; Mathematical Commentary; Translated Text: On the Properties of Circles; Chapter II: The Analytical Art in the Tenth to Eleventh Centuries; Introduction; 1. The rebirth of a subject; 2. Analytical art: discipline and method 3. The analytical art and the new discipline: 'The Knowns'4. History of the texts; On Analysis and Synthesis; The Knowns; I. Analysis and Synthesis: Mathematical Method and Discipline Mathematical Commentary; 1. The double classification of Analysis and Synthesis; Preliminary propositions; Analysis and synthesis in arithmetic; Analysis and synthesis in geometry; Analysis and synthesis in astronomy; Analysis in music; 2. Applications of analysis and synthesis in number theory and in geometry; Number theory; Perfect numbers; Two indeterminate systems of equations of the first degree Geometrical problemsProblem in plane geometry; Problem solved with the help of transformations; Construction of a circle to touch three given circles; Auxiliary problem; Geometrical commentary on the problem; Algebraic commentary on the auxiliary problem; Translated Text: On Analysis and Synthesis; II. The Knowns: A New Geometrical Discipline; Introduction; Mathematical Commentary; 1. Properties of position and of form and geometrical transformations; 2. Invariant properties of geometrical loci and geometrical transformations; Translated Text: On the Knowns III: Analysis and Synthesis: Examples of the Geometry of Triangles1. On a geometrical problem: Ibn Sahl, al-Sijzī and Ibn al-Haytham; 2. Distances from a point of a triangle to its sides; 3. History of the texts; 3.1. On a Geometrical Problem; 3.2. On the Properties of the Triangle; Translated Texts:; On a Geometrical Problem; On the Properties of the Triangle in Regard to Height; Chapter III: Ibn al-Haytham and the Geometrisation of Place; History of the Text; Translated Text: On Place; Appendix: The Ars Inveniendi: Thābit Ibn Qurra and al-Sijzī I. Thābit Ibn Qurra: Axiomatic Method and InventionII. Al-Sijzī: The Idea of an Ars Inveniendi; 1. Introduction; 2. A propaedeutic to the ars inveniendi; 3. The methods of the ars inveniendi and their applications; 3.1. Analysis and point-to-point transformation; 3.2. Analysis and variation of one element of the figure; 3.3. Analysis and variation of two methods of solution of a single problem; 3.4. Analysis and variation of lemmas; 3.5. Analysis and variation of constructions carried out using the same figure; 3.6. Variations on a problem from Ptolemy Summary "This fifth volume of A History of Arabic Sciences and Mathematics is complemented by four preceding volumes which focused on the main chapters of classical mathematics: infinitesimal geometry, theory of conics and its applications, spherical geometry, mathematical astronomy, etc. This book includes seven main works of Ibn al-Haytham (Alhazen) and of two of his predecessors, Thābit ibn Qurra and al-Sijzī: The circle, its transformations and its properties; Analysis and synthesis: the founding of analytical art; A new mathematical discipline: the Knowns; The geometrisation of place; Analysis and synthesis: examples of the geometry of triangles; Axiomatic method and invention: Thābit ibn Qurra; The idea of an Ars Inveniendi: al-Sijzī. Including extensive commentary from one of the world's foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research."--Provided by publisher Notes "This book is the translation of Les Mathèmatiques infinitèsmales du IXe au XIe siècle, vol. IV: Mèthodes gèomètriques, transformations ponctuelles et philosophie des mathèmatique"--Foreword page 3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzī 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 former 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. J. V. Field is a historian of science, and is a Visiting Research Fellow in the Department of History of Art and Screen Media, Birkbeck, University of London, UK Print version record Subject 880-02 Alhazen, 965-1039. SUBJECT 880-02/(3/r ابن الهيثم Subject 880-03 Sijzī, Aḥmad ibn Muḥammad, -1084 or 1085. SUBJECT 880-03/(3/r سجزي، احمد بن محمد Subject 880-04 Thābit ibn Qurrah al-Ḥarrānī, -901. SUBJECT 880-04/(3/r ثابت بن قرة الحراني Thābit ibn Qurrah al-Ḥarrānī, -901 fast Sijzī, Aḥmad ibn Muḥammad, -1084 or 1085 fast Alhazen, 965-1039 fast Subject Science -- Arab countries -- History Mathematics -- Arab countries -- History Science, Medieval. Mathematics, Medieval. Science -- Arab countries -- Philosophy -- History Mathematics -- Arab countries -- Philosophy -- History HISTORY / Middle East / General MATHEMATICS / History & Philosophy Mathematics Mathematics, Medieval Mathematics -- Philosophy Science Science, Medieval Science -- Philosophy Arab countries Genre/Form History Form Electronic book Author Field, Judith Veronica, translator. ISBN 9781351686006 1351686003 9781315168456 1315168456 9781351686013 1351686011 9781351685993 1351685996

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