In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project, is devoted to the last part of the text, in which Desargues puts his theory of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs.

在他关于圆锥曲线的Brouillon 计划的中间部分，Girard Desargues 发展了遍历理论，这一概念概括了阿波罗直径并允许对三种圆锥进行统一处理。我们在别处表明，它使德萨尔格得出了关于圆锥曲线的射影极性的完整理论。本文将结束我们对Brouillon 项目的研究，专门用于文本的最后一部分，其中 Desargues 通过对参数和焦点的经典理论进行非常优雅的处理，将他的遍历理论付诸实践。这将引导我们表明，只有当人们接受他在一个坚决的投影框架中进行推理时，才能理解 Desargues 的证明，在他的证明中将无限远的元素完全同化到有限距离的元素。