Jean-Victor Poncelet: das funções do método projetivo à patrimonialização de um personagem

Abstract

This work has as its central theme the contribution of Jean-Victor Poncelet to the development of a new area of geometry that would later be called projective geometry. In the early 19th century, there arose the need to give synthetic geometry the same scope as analytic geometry, and for this purpose, the new concepts of projectivity and continuity had a decisive and restorative force in geometry, with the figure as a central element, even if composed of some imaginary elements. This new line of thought was made possible thanks to a combination of factors that emerged in the late 18th century, such as the newly created École Polytechnique, Monge’s Descriptive Geometry discipline, Carnot’s Geometry of Position, the works of Brianchon and Servois, among others, and Gergonne’s journal, the Annales de Mathématiques Pures et Appliquées, which, by disseminating the new concepts more widely, had a strong influence on geometric thinking. The aim of this work is to study how Poncelet developed his methods and how the content of Poncelet’s work was received and appropriated by the French mathematical community, to finally be introduced into French textbooks. The publication of Poncelet’s complete geometric works from 1862 to 1866 inaugurates a new stage, which we call "patrimonialization"after Poncelet’s death, where Poncelet’s work is considered as a whole, a landmark of the beginning of modern geometry and, in a way, "enshrined"in the heritage of mathematicians in the late 19th century.