Geodesic
A Note on Some Generalizations of Monge's Theorem
Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 227-23
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We generalize Monge's theorem for n+1 pairwise homothetic sets (in particular convex bodies) in En in place of three disks in E2. We also present a version for homotheties for pairs of vertices of a non degenerate simplex in En. It includes a reverse of Monge's theorem. Moreover, we give an analogon of Monge's theorem for the n-dimensional sphere and hyperboloid model of the hyperbolic space.
Classification : 52A20, 52A21, 52A55
Mots-clés : Monge's theorem, Menelaus' theorem, Euclidean space, sphere, hyperbolic space 
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     author = {M. Lassak},
     title = {A {Note} on {Some} {Generalizations} of {Monge's} {Theorem}},
     journal = {Journal for geometry and graphics},
     pages = {227--23},
     year = {2021},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a5/}
}
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M. Lassak. A Note on Some Generalizations of Monge's Theorem. Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 227-23. http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a5/