Infinite Powers: The Story of Calculus - The Language of the Universe

by Steven H. Strogatz

By assuming his laws of motion and gravity as axioms and using his calculus as a deductive instrument, Newton proved that all three of Kepler’s laws followed as logical necessities. The same was true for Galileo’s law of inertia, the isochronism of pendulums, the odd-number rule for balls rolling down ramps, and the parabolic arcs of projectiles. Each of them was a corollary of the inverse-square law and F = ma. This appeal to deductive reasoning shocked Newton’s colleagues and disturbed them on philosophical grounds. Many of them were empiricists. They thought that logic applied only within mathematics itself. Nature had to be studied by experiment and observation. They were dumbfounded by the thought that nature had an inner mathematical core and that phenomena in nature could be deduced by logic from empirical axioms like the laws of gravity and motion.