Ideal chords in Poncelet’s work, from Saratov to the Traité des propriétés projectives des figures - HAL-SHS - Sciences de l'Homme et de la Société
Chapitre D'ouvrage Année : 2024

Ideal chords in Poncelet’s work, from Saratov to the Traité des propriétés projectives des figures

Résumé

This article aims to clarify the nature of “ideal elements” that Jean-Victor Poncelet introduced into geometry, notably in his Traité des Propriétés Projectives des Figures (1822). Moreover, it argues that the notebooks that Poncelet wrote in Saratov, as a prisoner of war, between March 1813 and June 1814, shed light on the genesis of this concept and the part these elements played in Poncelet’s geometrical approach to geometry. In fact, the notebooks suggest that, as early as 1813-1814, Poncelet had shaped some of the key ideas that would turn the Traité into the foundation of projective geometry.
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Dates et versions

halshs-04380893 , version 1 (08-01-2024)

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Bruno Belhoste, Karine C.C. Chemla. Ideal chords in Poncelet’s work, from Saratov to the Traité des propriétés projectives des figures. Toke Lindegaard Knudsen; Jessica Carter. Episodes from the History of Mathematics: Essays in Honor of Jesper Lützen, De Gruyter, 2024, ⟨10.1515/9783110769968-004⟩. ⟨halshs-04380893⟩
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