Not surprisingly, over the years this beautiful result has attracted the attentions
of many mathematicians, and there are several proofs known of
Fagnano himself apparently used differential calculus to prove it, though, by modern standards, it seems to me that this is far from being a routine exercise. Perhaps the
most appealing proofs of the theorem are those based on the Reflection Principle,
and two of these, in particular, due independently to L. Fej´er and H. A. Schwarz,
have made their appearance in several books aimed at general audiences