The status of the diagram in Euclid’s Elements

Abstract

This work is the beginning of a study of the role of the diagram in Greek mathematics. We discuss the status of the diagram in Euclid‘s Elements trying to situate it in the cultural and philosophical context, using in particular the texts of Plato and Aristotle that stressed the relevant relationship between vision and thought. In a first time, we tried to define the semiotic and linguistic character of the Euclid’s diagram, helping us of Peirce‘s approach. In a second time, we analyze how the diagrams have their own syntactic rules related to meanings that these incorporate, giving them an ideogramatic function. Finally, we emphasize the importance of the diagram in the so-called formular character of Greek mathematics and even the style of propositions.