1st Edition
Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics A History of Arabic Sciences and Mathematics Volume 5
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.
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
Biography
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.
