I guess it's possible that Archimedes invented the integral calculus a hundred generations before Newton and Leibniz because Syracuse was teeming with calculus-like ideas that didn't get written down, and things like the Antikythera Mechanism suggest that there were a lot of important intellectual achievements refined through broad communities of practice that didn't survive. But it seems just as likely to me that Archimedes was just that good.

(A tidbit about that Definition 5 there: I read in Russo that Galileo could not see the point of it. To him a ratio was a concrete thing, a number you got by dividing two other numbers. His civilization, says Russo, had lost the concept of freely invented axiomatic definitions and didn't really recover it till the 19th C.)

I like to think of Archimedes as the first mathematical physicist. Of course Euclidean geometry itself is a physical theory, so there's one ground to disagree.