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

TL;DR

This paper offers a detailed analysis of the initial pages of Desargues' Brouillon Project to understand how the concept of involution was developed, comparing it with Jean de Beaugrand's interpretation.

Contribution

It provides a coherent thesis on the formation of the involution concept in Desargues' work through detailed textual analysis and comparison with contemporary critiques.

Findings

Clarifies Desargues' intention behind involution

Links involution to harmonic division concepts

Highlights differences with Jean de Beaugrand's reading

Abstract

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.