Central Results from Newton’s Principia Mathematica

I. The Body of Least Resistance

Newton solves a variational problem about 10 years before the curve of quickest descent was found, a topic that is regarded to be the beginning of modern calculus of variations.

II. The Force of Attraction of a Spherical Body

First the geometrical proof of this theorem is analyzed; then it is indicated that this result demonstrates the definitive role of mathematics in modern natural philosophy.