THE CELESTIAL KINEMATICS OF IBN AL-HAYTHAM 1
After having reformulated optics, Ibn al-Haytham conceived of an analogous project for astronomy. This has just been revealed by an important book by the mathematician which has never been studied until now. Ibn al-Haytham's reform consists in excluding all cosmology, and in developing a systematic study of a celestial kinematics that has been completely geometrized. In turn, the realization of such a reform demanded innovative research in infinitesimal geometry. In this article, an attempt is made to present this new geometry, as well as the mathematical means invented to elaborate it.(Published Online February 12 2007)
1 This article is an English translation of a slightly modified version of the Introduction in my most recent book, Les mathématiques infinitésimales du IXe au XIe siècle. Vol. V: Ibn al-Haytham: Astronomie, géométrie sphérique et trigonométrie (London, 2006). I am grateful to J. V. Field for translating this article from French into English, and for making comments that led to improvements in the text. It goes without saying that I alone am responsible for any remaining errors.