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Journal for Geometry and Graphics 20 (2016), No. 2, 243--251
Copyright Heldermann Verlag 2016

Projective Proof and Generalization of Chasles's Theorem Along Non-Torsal Lines

Michal Zamboj
Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic

We prove Chasles's theorem for non-developable ruled surfaces, originally published in 1839, and generalize it to higher-dimensional projective extensions of the real space for the first polars along non-torsal lines. We avoid the use of differential geometry and re-prove the theorem strictly projectively, using only incidence properties for surfaces of higher degree.

Keywords: Chasles's theorem, ruled surface, projective methods, polar surface.

MSC: 51A05; 51N15, 51N35, 14J26

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