Geodesic
Projective Proof and Generalization of Chasles's Theorem Along Non-Torsal Lines
Journal for geometry and graphics, Tome 20 (2016) no. 2, pp. 243-251 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51A05, 51N15, 51N35, 14J26
Mots-clés : Chasles's theorem, ruled surface, projective methods, polar surface 
@article{JGG_2016_20_2_JGG_2016_20_2_a6,
     author = {M. Zamboj },
     title = {Projective {Proof} and {Generalization} of {Chasles's} {Theorem} {Along} {Non-Torsal} {Lines}},
     journal = {Journal for geometry and graphics},
     pages = {243--251},
     year = {2016},
     volume = {20},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2016_20_2_JGG_2016_20_2_a6/}
}
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M. Zamboj . Projective Proof and Generalization of Chasles's Theorem Along Non-Torsal Lines. Journal for geometry and graphics, Tome 20 (2016) no. 2, pp. 243-251. http://geodesic.mathdoc.fr/item/JGG_2016_20_2_JGG_2016_20_2_a6/