Not as many people know that he was the father of calculus (along with Gottfried Leibniz who figured it out independently around the same time). That's really where all the heavy lifting was in elementary mechanics, where by using the laws as something of a base case (especially the 2nd, F=dP/dt), calculus could be used to project an objects future motion. So in a way, it was by calculus that the laws could be shown as accurate in the first place.

I think Kepler deserves some credit too, that dude basically figured out a specific application of calculus in the motion of orbitals before Newton's and Leibniz's general calculus even existed.