To Prove the Evident: On the Inferential Role of Euclidean Diagrams

Abstract

Diagrams have been rightly acknowledged to license inferences in Euclid’s geometric practice. However, if on one hand purely visual proofs are to be found nowhere in the Elements, on the other, fully fledged proofs of diagrammatically evident statements are offered, as in El. I. 20: “In any triangle the sum of two sides is greater than the third.” In this paper I will explain, taking as a starting point Kenneth Manders’ analysis of Euclidean diagram, how exact and co-exact claims enter proposition I. 20. Then, I will ultimately argue that this proposition serves broader explanatory purposes, enhancing control on diagram appearance.