Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics Volume 5 (Culture and Civilizatio

Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics Volume 5 (Culture and Civilizatio

By: Roshdi Rashed (editor)Hardback

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Description

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, Thabit ibn Qurra and al-Sijzi: 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: Thabit ibn Qurra; The idea of an Ars Inveniendi: al-Sijzi. 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.

About Author

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.

Contents

CONTENTS Foreword Preface 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 problems Problem in plane geometry Problem solved with the help of transformations Construction of a circle to touch three given circles xii CONTENTS 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: The Knowns III: ANALYSIS AND SYNTHESIS: EXAMPLES OF THE GEOMETRY OF TRIANGLES 1. On a geometrical problem: Ibn Sahl, al-Sijzi 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: THABIT IBN QURRA AND AL-SIJZI I. THABIT IBN QURRA: AXIOMATIC METHOD AND INVENTION II. AL-SIJZI: 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 3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzi CONTENTS xiii 4. Analysis and synthesis: variation of the auxiliary constructions 5. Two principal methods of the ars inveniendi III. HISTORY OF THE TEXTS 3.1. Book by Thabit ibn Qurra for Ibn Wahb on the Means of Arriving at Determining the Construction of Geometrical Problems 3.2. To Smooth the Paths in view of Determining Geometrical Propositions, by al-Sijzi 3.3. Letter of al-Sijzi to Ibn Yumn on the Construction of an Acute-angled Triangle 3.4. Two Propositions from the Ancients on the Property of Heights of an Equilateral Triangle: Ps-Archimedes, Aqatun, Menelaus TRANSLATED TEXTS: 1. Book of Abu al-Hasan Thabit ibn Qurra for Ibn Wahb on the Means of Arriving at Determining the Construction of Geometrical Problems 2. Book of Ahmad ibn Muhammad ibn `Abd al-Jalil al-Sijzi to Smooth the Paths in view of Determining Geometrical Propositions 3. Letter of Ahmad ibn Muhammad ibn `Abd al-Jalil to the Physician Abu `Ali Nazif ibn Yumn on the Construction of the Acute-angled Triangle from Two Unequal Straight Lines 4. Two Propositions of the Ancients on the Property of the Heights of an Equilateral Triangle: Pseudo-Archimedes, Aqatun, Menelaus SUPPLEMENTARY NOTES I. Fakhr al-Din al-Razi: Ibn al-Haytham's critique of the notion of place as envelope II. Al-Hasan ibn al-Haytham and Muhammad ibn al-Haytham: the mathematician and the philosopher - On place BIBLIOGRAPHY INDEXES

Product Details

  • ISBN13: 9780415582193
  • Format: Hardback
  • Number Of Pages: 674
  • ID: 9780415582193
  • weight: 1021
  • ISBN10: 0415582199

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