
Journal for Geometry and Graphics 20 (2016), No. 2, 243251 Copyright Heldermann Verlag 2016 Projective Proof and Generalization of Chasles's Theorem Along NonTorsal Lines Michal Zamboj Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic zamboj@karlin.mff.cuni.cz We prove Chasles's theorem for nondevelopable ruled surfaces, originally published in 1839, and generalize it to higherdimensional projective extensions of the real space for the first polars along nontorsal lines. We avoid the use of differential geometry and reprove 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 [ Fulltextpdf (5845 KB)] 