Ibn Al-Haytham's Geometrical Methods and the Philosophy of Mathematics by Rāshid, Rushdī -- Read -- Imperial Library of Trantor

Index

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 Eenturies

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

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

Translated Text: On the Knowns

III: Analysis and Synthesis: Examples of the Geometry of Triangles

1. 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 Invention II. 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

4. Analysis and synthesis: variation of the auxiliary constructions 5. Two principal methods of the ars inveniendi

III. History of the Texts

Translated Texts:

Supplementary Notes

Bibliography Indexes

Index of names Subject index Index of works Index of manuscripts