(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.
(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.