From Antiquity until recently, philosophers and mathematicians have continually discussed the concept of angle and its relation to archimedean and non-archimedean theories of measurement. For the first time, this book traces the history of these discussions in Greek and Arabic, from Euclid to Kamāl al-Dīn al-Fārisī, after whom the discussion was not resumed until Newton and Euler. The volume presents first editions of over twenty texts, either in Arabic or Greek and translated into Arabic, of the greatest mathematicians and philosophers (...) of the time. The texts are here translated into French and supplemented with extensive commentary. The book begins with the definitions and propositions of Euclid on angles and measurement, followed by the Greek commentary tradition represented by Proclus and Simplicius (only extant in Arabic) and the writings of the Arabic mathematicians and philosophers from the 9th through 14th century, placing the fundamental contributions by Avicenna and Ibn al-Haytham into their historical context and showing how numerous successors produced new syntheses of their work. (shrink)

Maimonide, philosophe dans la mouvance d'al-Farabi, etait medecin, informe des mathematiques et maitre de la litterature talmudique. Ce livre a pour ambition d'examiner les liens entre philosophie et science dans l'oeuvre de Maimonide, et aussi de placer celle-ci dans son veritable contexte historique entre Cordoue et Le Caire au XIIe siecle. Les etudes rassemblees ici explorent plusieurs facettes de cette oeuvre: logique, savoir et philosophie mathematiques, ecrits medicaux, conception du libre-arbitre ou des rapports entre nature et loi... Elles examinent aussi (...) l'impact qu'a eu l'oeuvre de Maimonide en arabe, en hebreu et en latin. Maimonides, a philosopher in the tradition of d'al-Farabi, was a physician, well-informed in mathematics, and a master of Talmudic literature. The goal of this book is to examine the links between philosophy and science in Maimonides' work, and also to situate it within its genuine historical context, between Cordoba and Cairo in the 12th century. The studies collected here explore several facets of this work: logic, mathematical knowledge and philosophy, medical writings, conception of free will and of the relations between nature and law, etc. They also examine the impact of Maimonides' work on Arabic, Hebrew, and Latin scientific and philosophical literature. (shrink)

Ibrāhīm Ibn Sinān was one of the most famous scientists of the tenth century. His specialities were geometry, logic and philosophy of mathematics. In this volume, the works of this scientist are thoroughly researched, and three new hypotheses presented.