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Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics Volume 5: Culture and Civilization in the Middle East

Editat de Roshdi Rashed
en Limba Engleză Paperback – 12 dec 2019
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.
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Specificații

ISBN-13: 9780367865290
ISBN-10: 0367865297
Pagini: 678
Dimensiuni: 156 x 234 x 35 mm
Greutate: 0.45 kg
Ediția:1
Editura: Taylor & Francis
Colecția Routledge
Seria Culture and Civilization in the Middle East

Locul publicării:Oxford, United Kingdom

Public țintă

Postgraduate and Undergraduate

Cuprins

 

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

Notă biografică

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.

Descriere

This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. It also includes extensive commentary from one of world’s foremost authorities.