Routh's, Menelaus' and Generalized Ceva's Theorems

  title={Routh's, Menelaus' and Generalized Ceva's Theorems},
  author={Boris A. Shminke},
  journal={Formalized Mathematics},
We use the following convention: A, B, C, A1, B1, C1, A2, B2, C2 are points of E2 T, l1, m1, n1 are real numbers, and X, Y , Z are subsets of E2 T. Let us consider X, Y . We introduce X is parallel to Y as a synonym of X misses Y . Let us consider X, Y , Z. We say that X, Y , Z are concurrent if and only if: (Def. 1) X is parallel to Y and Y is parallel to Z and Z is parallel to X or there exists A such that A ∈ X and A ∈ Y and A ∈ Z. One can prove the following propositions: (1) (A+B)1 = A1… CONTINUE READING