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

Bruno Belhoste (1) , Karine C.C. Chemla (2)

1 IHMC - Institut d'histoire moderne et contemporaine
2 SPHERE (UMR_7219) - Sciences, Philosophie, Histoire

This article aims at clarifying the nature of the “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 war prisoner, 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.

Keywords: Jean-Victor Poncelet; David Hilbert; Ernst Kummer; ideal element; ideal chords; ideal secant; projective geometry

Domains: History; History, Philosophy and Sociology of Sciences

Bruno Belhoste, Karine C.C. Chemla. Ideal chords in Poncelet’s work, from Saratov notebooks to the Traité des propriétés projectives des figures. Toke Lindegaard Knudsen, et Jessica Carter. Episodes from the History of Mathematics: Essays in Honor of Jesper Lützen, De Gruyter, In press. ⟨halshs-03931283⟩