Roshdi Rashed (SPHERE, UMR 7219), Dir.
J. V. Field (Trad.)
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."
: : Routledge
: : Collection Culture and Civilization in the Middle East, London, Centre for Arab Unity Studies
: : xx, 674 p.
: : Langues : anglais
: : ISBN : 9780415582193
: : avril 2017
Précédents volumes de la collection :
- R. Rashed, Founding Figures and Commentators in Arabic Mathematics. A History of Arabic Sciences and Mathematics, vol. 1, Culture and Civilization in the Middle East, London, Centre for Arab Unity Studies, Routledge, 2011.
- R. Rashed, Ibn al-Haytham and Analytical Mathematics. A History of Arabic Sciences and Mathematics, vol. 2, Culture and Civilization in the Middle East, London, Centre for Arab Unity Studies, Routledge, 2012.
- R. Rashed, Ibn al-Haytham’s Theory of Conics, Geometrical Constructions and Practical Geometry. A History of Arabic Sciences and Mathematics, vol. 3, Culture and Civilization in the Middle East, London, Centre for Arab Unity Studies, Routledge, 2013.
- R. Rashed, Ibn al-Haytham. New Spherical Geometry and Astronomy, A History of Arabic Sciences and Mathematics, vol. 4, Culture and Civilization in the Middle East, London, Centre for Arab Unity Studies, Routledge, 2014.
TABLE DES MATIERES [pour téléchargement]
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 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
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 geometrical loci and geometrical transformations
Translated text : 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. Thăbit 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
- 3.1. Analysis and point-to-point transformation
- 3.2 Analysis and variation of one element of the figure
- 3.3. Analysis and variation of two methods of solution of a single problem
- 3.4. Analysis and variation of lemmas
- 3.5. Analysis and variation of constructions carried out using the same figure
- 3.6. Variations on a problem from Ptolemy
- 3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzī
- 4. Analysis and synthesis : variation of the auxiliary constructions
- 5. Two principal methods of the ars inveniendi
III. History of the texts
-
- 3.1. Book by Thābit ibn Qurra for Ibn Wahb on the Means of Arriving at Determining the Construction of Geometrical Problems
- 3.2. To Smooth the Paths in view of Determining Geometrical Propositions, by al-Sijzī
- 3.3. Letter of al-Sijzī to Ibn Yumn on the Construction of an Acute-angled Triangle
- 3.4. Two Propositions from the Ancients on the Property of Heights of an Equilateral Triangle : Ps-Archimedes, Aqāṭun, Menelaus
Translated texts :
- 1. Book of Abū al-Ḥasan Thābit ibn Qurra for Ibn Wahb on the Means of Arriving at Determining the Construction of Geometrical Problems
- 2. Book of Aḥmad ibn Muḥammad ibn ‘Abd al-Jalīl al-Sijzī to Smooth the Paths in view of Determining Geometrical Propositions
- 3. Letter of Aḥmad ibn Muḥammad ibn ‘Abd al-Jalīl
to the Physician Abū ‘Alī Naẓīf ibn Yumn on the Construction of the Acute-angled Triangle from Two Unequal Straight Lines - 4. Two Propositions of the Ancients on the Property of the Heights of an Equilateral Triangle : Pseudo-Archimedes, Aqāṭun, Menelaus
Supplementary notes
I. Fakhr al-Dīn al-Rāzī : Ibn al-Haytham’s critique of the notion of place as envelope
II. Al-Ḥasan ibn al-Haytham and Muḥammad ibn al-Haytham : the mathematician and the philosopher – On place
BIBLIOGRAPHY
INDEXES
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Dans la même rubrique :
- Ibn al-Haytham. New Spherical Geometry and Astronomy
- Ibn al-Haytham’s Theory of Conics, Geometrical Constructions and Practical Geometry
- Ibn al-Haytham and Analytical Mathematics
- Founding Figures and Commentators in Arabic Mathematics
- Angles et grandeur
- Eutocius d’Ascalon. Commentaire sur le traité des "Coniques" d’Apollonius de Perge (Livres I-IV)
- Les "Arithmétiques" de Diophante. Lecture historique et mathématique.
- Abū Kāmil : Algèbre et analyse diophantienne
- Apollonius de Perge. La section des droites selon des rapports.
- APOLLONIUS DE PERGE, CONIQUES
Apollonius de Perge. Coniques. Livre I. - Apollonius de Perge, Coniques. Livres II et III.
- Apollonius de Perge. Coniques. Livre IV.
- Apollonius de Perge. Coniques. Livre V.
- Apollonius de Perge. Coniques. Livres VI et VII.
- Les Mathématiques infinitésimales du IXe au XIe siècle
- Al-Khwarizmi. Le commencement de l’algèbre.
- Le Développement de la géométrie aux IXe-XIIe siècle. Abu Sahl Al-Quhi.
- Al-Khayam Umar. Al-Khayam mathématicien
- Averroès. Commentaire moyen à la Rhétorique d’Aristote
- Fermat et les débuts modernes de la géométrie