Ibn al-Haytham's geometrical methods and the philosophy of mathematics
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Bibliographic Information
Ibn al-Haytham's geometrical methods and the philosophy of mathematics
（Culture and civilization in the Middle East, 55 . A history of Arabic sciences and mathematics ; v. 5）
Routledge, 2017
- : hbk
- Other Title
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Les mathématiques infinitésimales du IXe au XIe siècle
Méthodes géométriques, transformations ponctuelles et philosophie des mathématiques
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"Center for Arab Unity Studies"
"This book is the translation of Les Mathématiques infinitésimales du IXe au XIe siècle, vol. IV: Méthodes géométriques, transformations ponctuelles et philosophie des mathématiques" -- Foreword
Includes bibliographical references (p. [639]-648) and indexes
Description and Table of Contents
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.
Table of 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 ge
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