The Twofold Role of Diagrams in Euclid's Plane Geometry

Marco Panza (1)

1 REHSEIS (UMR_7596) - Recherches Epistémologiques et Historiques sur les Sciences Exactes et les Institutions Scientifiques

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid's geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it . My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid's plane geometry (EPG). Euclid's arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: i) To provide the conditions of identify of the objects of EPG is the same as to provide the identity conditions for the diagrams that represent them or—in the case of angles—of appropriate equivalence classes of diagrams that represent them; ii) The objects of EPG inherit some properties and relations from the diagrams.

Mots clés: Euclid; plane geometry; diagrams

Domaines: Philosophie

Marco Panza. The Twofold Role of Diagrams in Euclid's Plane Geometry. 2007. ⟨hal-00192165v1⟩