1. I have two calculus proofs on my page.
2. I have no patience with your link. He used calculus to argue that

F(x,y) ≥ 0

while it is obvious from the definition.

I am not wedded to the Pythagorean theorem or to its proofs. Sometimes I err in my selections, perhaps, even often so, but what I am on lookout for is elegance not a refutation of Elisha Loomis' opinions. So, no, this is not going to be proof #89.