The Definitions of Fundamental Geometric Entities Contained in Book I of Euclids Elements

Abstract

OElig;he thesis is sustained that the definitions of fundamental geometric entities which open Euclids Elements actually are excerpts from the Definitions by Heron of Alexandria, interpolated in late antiquity into Euclids treatise. As a consequence, one of the main bases of the traditional Platonist interpretation of Euclid is refuted. Arguments about the constructivist nature of Euclids mathematical philosophy are given.