Newton tip

This comes from Cameron, who’s one of the more encylopedically educated people I know:

“Saw your post on Newton. I can’t say I’ve surveyed the many bios available, but Never At Rest, by Richard Westfall is well regarded.

If you’re ambitious and want to give your math-processing skills a workout, a look at Newton’s Principia for the Common Reader by S. Chandrasekhar (he of the limit) is well worth looking at – ‘common reader’ is a bit of a misnomer – at least a year of calculus and a solid grounding in physics would be needed to digest the material. It’s rather expensive, but if you can find a library copy, do give it a look.

I saw Chandrasekhar give a lecture back in the early 90s, when he was reading Newton, and preparing this book. Fascinating stuff. The common folklore has it that Newton developed his results using calculus, but presented them geometrically in the Principia to keep his methods secret. Chandrasekhar went through the original demonstrations, and reproduced them using modern calculus notation, but he found that the proofs are generally more compact and elegant in Newton’s geometrical style. This suggests that the common folklore has it wrong and that the work has its origin in the geometrical approach used in the original publication. This was in my Leibniz-scholar days, and I spoke with Chandrasekhar after the lecture about how difficult I was finding it to read Leibniz’s mathematical works, because of its heavily geometrical, rather than algebraic, approach. We learn, and think of, calculus as dealing with functions, but Leibniz and his contemporaries were very clearly dealing primarily with curves – and all their intuitions were based on a level of comfort with geometry that is pretty much an arcane lost art today. Chandrasekhar found pretty much the same to be the case with Newton – he was a geometer on a level that no-one can be said to be a geometer today.”