Menelaus' Thm

 Menelaus's Theorem is very similar to Ceva's Theorem.  The theorem states that if a straight line intersects all three sides of a triangle (one or all three intersections may be on the extended legs) then the sides must be cut into proportions that multiply to make one.  Using the figure, triangle ABC is cut by the line at A', B', and C' on the opposite sides of the trinangle and so . The theorem is also written in the equivalent form, .
The theorem is named for Menelaus of Alexandria, who lived around the end of the first century.  You can find more about his life at the St Andrews University web site.
  Menelaus also proved a spherical version of the same theorem.  If the triangle and the cutting line are all formed by great circle arcs on a sphere, then the formula states that .


Almost 1900 years after Menelaus (1995) a mathematician named Hoehn published a similar looking theorem about Pentagons in Mathematics Magazine.  In it he stated that the product of all the red segments equals the product of all the blue segments.