Section 2 is physics rather than geometry; hopefully it will be an easier read.
Tuesday, July 19, 2016
Principia, Book 1, Section 1
This section is entirely geometric proofs of lemmas concerning either areas or ratios of lengths or areas in limiting cases as angles or lengths approach zero, or as the number of divisions becomes infinite. It's a hard slog, and I have to admit that I mostly read to get a sense of Newton's style rather than the details. I am proud of myself, though, for being able to deduce that Lemma 10 is a proof that dx=0.5*a(0)*dt^2 for small dt and v(0)=0 and that Lemma 11 is a proof that y~theta^2 for a pendulum set up such that y=0 when theta=0.