Ceva, Menelaus, and selftransversality
The theorems of Ceva and Menelaus are well-known results in the elementary geometry of triangles. Since the early 19th century they have been generalized to polygons with more sides and in various other directions. The purpose of this paper is to formulate and prove a Ceva-Menelaus-selftransversality theorem. This theorem makes assertions not only about the ratios of lengths of line segments, but also about ratios of areas and volumes of triangles and simplices defined by the vertices of the \(n\)-gon and by transversals of appropriate dimension. A number of examples is given.
\(n-\)acrons (generalizations of \(n-\)gons)
elementary problems in Euclidean geometries
scientific article; zbMATH DE number 1019776