Newton's mature dynamics and the Principia: A simplified solution to the Kepler problem (Q1119554)

In three editions of Principia Newton gave variant proofs of the dynamical propositions concerning the motion of a body under a force directed to a fixed centre. (Propositions 6 and 11). The author examines these proofs and notes an approach that Newton might have used, but did not. This study of the details of the proof methods illustrates the flexible manner in which Newton used the `geometry-with-limits' technique which for him substituted for the calculus.