La notion d'involution dans le Brouillon Project de Girard Desargues

In this article, we propose a coherent thesis for the formation of the notion of involution in Girard Desargues’ Brouillon Project. For this, we give a detailed analysis of the first 10 pages of the Brouillon, dealing in particular with various particular cases which help us to understand Desargues’ intention, which is to find a notion unifying the harmonic divisions considered in Apollonius’s theory of conics. We compare this analysis with the way Jean de Beaugrand read and criticised the Brouillon in his Advis Charitables.