Desargues and the "trait \`a preuves"

Summary. The 'trait {\`a} preuves' is a 17th century expression that refers to drawings rigorously justified by mathematics. This work is a reflection on the principle of purity of methods from a historical, mathematical and epistemological point of view. Our starting point is the problematic that arose in the 17th century on the occasion of a dispute between stonemasons and geometers who were theorists of stereotomy. Girard Desargues was involved in this controversy, and we can assume that Desargues' theorem was a key element in his argument. It clearly raises the question of the purity of methods. We will illustrate this with examples. And this leads us to David Hilbert's fundamental work on the subject.