Examination of the treatises On the Section of a Cylinder and On the Section of a Cone of serenos of Antinoeia under the light of the Ancient Greek tradition on Optics

Abstract

Serenos of Antinoeia (III Century A.C.) was the author of two treatises On the Section of a Cylinder and On the Section of a Cone. In the second part of the treatise On the Section of a Cylinder, Serenos examines one definition by observation of parallel lines given by his friend the geometer Python. He bases his approach on a series of propositions (29-33). We are going to examine the way that Serenos defends this definition by observation with the tools of Euclidean geometrical optics and the tradition on conics of Apollonios. The terms and the notions Serenos uses were valid and legitimate for mathematicians working with the aid of the tools of Hellenistic mathematics. In our point of view, the nature of the properties in the treatise On the Section of a Cone is an open problem for historians. All of them agree on the fact that the goal is to do a comparative study on the sections produced in a cone by an intersection from a plan passing by its vertex. We are going to examine some propositions and throw light on a second aspect of this treatise which consists of basing geometrically optic properties.

Key words : Serenos of Antinoeia, section of a cylinder, section of a cone, ancient geometrical optic