
Journal for Geometry and Graphics 25 (2021), No. 2, 227230 Copyright Heldermann Verlag 2021 A Note on Some Generalizations of Monge's Theorem Marek Lassak University of Science and Technology, Bydgoszcz, Poland lassak@pbs.edu.pl We generalize Monge's theorem for n+1 pairwise homothetic sets (in particular convex bodies) in E^{n} in place of three disks in E^{2}. We also present a version for homotheties for pairs of vertices of a non degenerate simplex in E^{n}. It includes a reverse of Monge's theorem. Moreover, we give an analogon of Monge's theorem for the ndimensional sphere and hyperboloid model of the hyperbolic space. Keywords: Monge's theorem, Menelaus' theorem, Euclidean space, sphere, hyperbolic space. MSC: 52A20; 52A21, 52A55. [ Fulltextpdf (285 KB)] for subscribers only. 