Neil DeGrasse Tyson's Cosmos

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1. A Gem From Newton’s Principia

Well worth reading. No calculus required.

Isaac Newton’s Mathematica Principia (1687) has been described as the most important, but also the least read, scientific book ever written. It has been little read mostly because it has been little comprehended. The book is filled with complex geometric diagrams, and Newton’s explanations are brief, the assumption being that the reader’s mathematical knowledge and ability is very high. Indeed, Newton later admitted that he had made the book difficult, so that he would, as he put it, “avoid being baited by little smatterers in mathematicks”. The great physicist Richard Feynman once tried to read the section on the elliptical orbits of the planets, and eventually gave up, saying that Newton’s use of obscure properties of ellipses made the going too difficult. (Feynman’s response was to do what few others could have done: he created his own geometric proof. This proof is described in the book “Feynman’s Lost Lecture”).

However, there is at least one result that Newton derived in the Principia that is fairly easy to understand, and I will describe it in this post. It also happens to be one of the important theorems in the Principia: a proof that Kepler’s Second Law is a consequence of mechanics.

Read more: http://brightstartutors.com/blog/2011/a-gem-from-newtons-principia/