On Lemmas 1 and 2 to Proposition 39 of Book 3 of Newton's principia (Q5930178)

The author presents a clear and rigorous discussion on Lemmas 1 and 2 to Proposition 39 of Book 3 of Newton's Principles of Natural Philosophy, by using, where appropriate, modern mathematical notation. This proposition deals with the precession of the equinoxes and these lemmas are concerned with the turning moment exerted on the earth by tidal forces due to the gravitational attraction of the sun. The paper includes an interesting preliminary discussion of some physical ideas about the problem of computing the rate of precession of the equinoxes.