If the sides of a Triangle are divided in the ratios , , and , the Cevians form a central Triangle whose Area is
where is the Area of the original Triangle. For
For , 2, 3, ..., the areas are 0, 1/7, 4/13, 3/7, 16/31, 25/43, .... The Area of the Triangle formed by
connecting the division points on each side is
Routh's theorem gives Ceva's Theorem and Menelaus' Theorem as special cases.
See also Ceva's Theorem, Cevian, Menelaus' Theorem
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 211-212, 1969.
© 1996-9 Eric W. Weisstein