1st Edition

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

Edited By

Roshdi Rashed





ISBN 9780367865290
Published December 11, 2019 by Routledge
678 Pages

USD $48.95

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Book 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, 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.

Table of 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 ge

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Editor(s)

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.