the converse follows as a corollary. let "d", "e" and "f" be given on the lines "bc", "ac" and "ab" so that the equation holds. let "ad" and "be" meet at "o" and let "f"′ be the point where "co" crosses "ab". then by the theorem, the equation also holds for "d", "e" and "f"′. comparing the two,