La théorie des courbes et des équations dans la Géométrie cartésienne : 1637-1661

Abstract : In this thesis, I study three central topics in the Cartesian Geometry: the Pappus' problem, the problem of tangents and normals, and a problem of gnomonic known under the name of Problema Astronomicum. By "Cartesian Geometry", I mean the corpus formed by the Geometry, published in 1637, as well as the Cartesian Correspondence and the two Latin editions directed by Frans van Schooten published respectively in 1649 and 1659-1661. I study the genesis of the Cartesian theory of geometrical curves defined by algebraic equations through the controversies in the Cartesian correspondence: the controversy with Roberval about the Pappus' problem, the controversy with Fermat about tangents, and the controversy with Stampioen about the Problema astronomicum. I show that the Geometry of the Correspondence constitutes a mean term between the Geometry of 1637 and the Latin editions of 1649 and 1659-1661, by pointing out issues about the concept of algebraic curve. Moreover, I study and compare Fermat's method of tangents and Descartes' method for normals by referring them to Apollonius' Conics.
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Submitted on : Tuesday, January 8, 2008 - 8:33:16 PM
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Sébastien Maronne. La théorie des courbes et des équations dans la Géométrie cartésienne : 1637-1661. Histoire et perspectives sur les mathématiques [math.HO]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00204125v2⟩

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