The following theorem has been attributed to Apollonius: In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side. In other words, if BM is a median of a triangle ABC and if AB = c, BC = a, AC = b, and BM = m, prove that .
 
 

See also: Pythagoras Theorem, Euclid's Elements Book II Proposition 13, Stewart Theorem