Enthymemathical proofs and canonical proofs in Euclid's plane geometry

Abel Lassalle-Casanave

Marco Panza

pp. 127-144

in: Hassan Tahiri (ed), The philosophers and mathematics, Berlin, Springer, 2018

Abstract

Since the application of Postulate I.2 in Euclid's Elements is not uniform, one could wonder in what way should it be applied in Euclid's plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.