Abstract

Among the four mathematical treatises that Avicenna takes care to place within his philosophical encyclopaedia, the one he devotes to arithmetic is undoubtedly the most singular. Contrary to the treatise on geometry, which differs little from its Euclidean model, the philosopher takes as his point of departure the treatise of Nicomachus of Gerase, but modifies its spirit to incorporate results from the many disciplines which were dealing with numbers: Euclidean Theory of numbers, Nicomachean Aritmāṭīqī, Indian reckoning, Ḥisāb, Algebra, etc. We would like to show how Avicenna, taking note of the changes in the mathematics of his time and led by a philosophical questioning about the nature of the disciplines, proposes here one of the very few texts that gives to Theory of numbers a synthetic image, gathering the themes of mathematical research for the next centuries.