This book is a translation of Les Mathématiques infinitésimales du IXe au XIe siècle, vol. IV: Méthodes géométriques, transformations ponctuelles et philosophie des mathématiques. The French version, published in London in 2002, also included critical editions of all the Arabic mathematical texts that were the subjects of analysis and commentary in the volume.
It also included: 1. Les emprunts d’Ibn Hūd aux Connus et à L’Analyse et la Synthèse (Ibn Hūd’s borrowings from The Knowns and On Analysis and Synthesis); 2. Al-Baghdādī critique d’Ibn al-Haytham (Al-Baghdādī as a critic of Ibn al-Haytham), with the critical edition of the Arabic text, French translation and mathematical commentaries.
The whole book, apart from these two appendices, has been translated, with great scholarly care, by Dr J. V. Field. The translation of the primary texts was not simply made from the French; I checked a draft English version against the Arabic. This procedure converged to give an agreed translation. The convergence was greatly helped by Dr Field’s experience in the history of the mathematical sciences and in translating from primary sources. I should like to take this opportunity of expressing my deep gratitude to Dr Field for this work.
Very special thanks are due to Aline Auger (Centre National de la Recherche Scientifique), who helped me check the English translations against the original Arabic texts, prepared the camera ready copy and compiled the indexes.
Roshdi Rashed