INTRODUCTION MOTION AND TRANSFORMATIONS IN GEOMETRY
CHAPTER I: THE PROPERTIES OF THE CIRCLE
2. Euclid, Pappus and Ibn al-Haytham: on homothety
3. Ibn al-Haytham and homothety as a point by point transformation
TRANSLATED TEXT: On the Properties of Circles
CHAPTER II: THE ANALYTICAL ART IN THE TENTH TO ELEVENTH CENTURIES
2. Analytical art: discipline and method
3. The analytical art and the new discipline: ‘The Knowns’
I. ANALYSIS AND SYNTHESIS: MATHEMATICAL METHOD AND DISCIPLINE
1. The double classification of Analysis and Synthesis
Analysis and synthesis in arithmetic
Analysis and synthesis in geometry
Analysis and synthesis in astronomy
2. Applications of analysis and synthesis in number theory and in geometry
Two indeterminate systems of equations of the first degree
Problem solved with the help of transformations
Construction of a circle to touch three given circles
Geometrical commentary on the problem
Algebraic commentary on the auxiliary problem
TRANSLATED TEXT: On Analysis and Synthesis
II. THE KNOWNS: A NEW GEOMETRICAL DISCIPLINE
1. Properties of position and of form and geometrical transformations
2. Invariant properties of geometrical loci and geometrical transformations
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
3.2. On the Properties of the Triangle
On the Properties of the Triangle in Regard to Height
CHAPTER III: IBN AL-HAYTHAM AND THE GEOMETRISATION OF 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
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
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 for 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
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 for Determining Geometrical Propositions
3. Letter of Aḥmad ibn Muḥammad ibn ‘Abd al-Jalīl <al-Sijzī> 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
I. Fakhr al-Dīn al-Rāzī:
Ibn al-Haytham’s critique of the notion of place as envelope