L'Asymptote : Apollonius et ses lecteurs.

Abstract

In proposition 14 of the second book of his Conics, Apollonius proves that the asymptotes and the hyperbola approach one another indefinitely without meeting. This proposition appeals to the notion of infinity and of infinite construction of the sequences of distances between the curve and its asymptote. But this notion of 'infinity' was bound to create problems for both mathematicians and philosophers, since Geminus and Proclus. These problems were taken anew by al-Sijzī (second half of 10 th century) and his followers. In this article, the reader will find an outline of the history of this question, an analysis of the work of al-Qummī (a successor of al-Sijzī), as well as a critical edition and translation of new materials concerning the study of asymptotic behaviour.