Carnot's theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France
The paper is devoted to a presentation and discussion of the achievements by Carnot, Servois and Brianchon, which brought a renewal of synthetic geometry in France. In particular, the author discusses 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. Brief biographical notes preceding the presentation of the works of Monge, Carnot, Servois and Brianchon are provided. These notes link some of their personal stories as politicians, or soldiers, to their mathematical work, and underline the role of the Ecole Polytechnique, and of military schools, in the process of renewal of geometry in France during the Napoleonic Era.
scientific article; zbMATH DE number 7461128
scientific article