On the Routh-Steiner theorem and some generalisations

摘要

1. Introduction Coxeter in his book [1, p. 211], considered the following theorem of affine geometry; Theorem 1: If the sides BC, CA, AB of a triangle ABC are divided at L, M, N in the respective ratios λ: 1, μ: 1, v: 1, the cevians AL, BM, CN form a triangle whose area is times that of ABC.