Proof #4 is the one that Frank & I were so impressed with; #1 is the one
that Nick (along with anyone who graduated St Johns) failed to reproduce; #5
is the one due to Pres. Garfield (an intelligent president! those were the
days...). And you can get an "extra-geometric" proof that relies on Newton's
2nd law at http://www.cut-the-knot.org/pythagoras/mech.shtml