  We show in this article how Girard Desargues, in his well known text on
conics, the \textit{Brouillon Project,} manages to use Menelaos' theorem with
some awesome virtuosity. To this end, we propose a detailed analysis of his
\textit{combinatorial} approach, which was already visible in the development
of his notion of involution. We shall study the proofs of two important
theorems of the \textit{Brouillon.} The first is the theorem of the "ram\'ee",
stating that the configuration of involution is invariant by perspective
projection, and the second is the great theorem of Desargues on pencils of
conics. We shall also study in the same spirit the first lemma (dealing with
the hexagram) of the \textit{Essay pour les coniques} by Pascal and the
\textit{Advis charitables} by de Beaugrand.

History and Overview