In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the applications that Brianchon made of them to the theory of conic sections. The contributions of these authors brought the long-forgotten theorems of Desargues and Pascal fully to light, renewed the interest in synthetic geometry in France, and prepared the ground from which projective geometry later developed.

中文翻译：

---

卡诺的横截面理论及其 Servois 和 Brianchon 的应用：法国综合几何的觉醒

在本文中，我们深入讨论了与卡诺横截面理论相关的主要定理、它们最初被 Servois 所接受，以及 Brianchon 将它们应用到圆锥曲线理论中。这些作者的贡献使长期被遗忘的笛沙格和帕斯卡定理得以全面曝光，重燃了法国人对合成几何的兴趣，并为后来射影几何的发展奠定了基础。