The following theorem has been attributed to
Apollonius of Perga: 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
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Apollonius of Perga

Euclid's Elements 
Classical Theorems

Email  By Antonio Gutierrez
Aug 23, 2014
