  Nous tentons dans cet article de proposer une th\`ese coh\'erente concernant
la formation de la notion d'involution dans le Brouillon Project de Desargues.
Pour cela, nous donnons une analyse d\'etaill\'ee des dix premi\`eres pages
dudit Brouillon, comprenant les d\'eveloppements de cas particuliers qui aident
\`a comprendre l'intention de Desargues. Nous mettons cette analyse en regard
de la lecture qu'en fait Jean de Beaugrand et que l'on trouve dans les Advis
Charitables.
  The purpose of this article is to propose a coherent thesis on how Girard
Desargues arrived at the notion of involution in his Brouillon Project of 1639.
To this purpose we give a detailed analysis of the ten first pages of the
Brouillon, including developments of particular cases which help to understand
the goal of Desargues, as well as to clarify the links between the notion of
involution and that of harmonic division. We compare the conclusions of this
analysis with the very critical reading Jean de Beaugrand made of the Brouillon
Project in the Advis Charitables of 1640.
