The universal law of gravitation

Abstract

Abstract After his Prolegomenon (Chapter 18), Newton proceeds to the deduction of his universal law of gravitation in the first 14 Propositions of Book III. We shall begin by listing the 19 propositions of Book I, the three propositions of Book II, and the Rules of Reasoning that will serve as the basis of Newton’s reasoning. An examination of this list is already of interest for revealing the priorities that Newton attaches to the various propositions; and in particular to Proposition XI (and XLI) in which he proved that a body will revolve in an elliptic orbit about its focus if acted upon by a centripetal force inversely as the square of the distance from the focus. It will be recalled that it was on hearing from Newton (in August, 1684) that he had proved this proposition ‘some years earlier’ and on receiving in the same year (November, 1684) De M otu Corporum in Gyrum in which the proposition is proved, that Halley persuaded Newton to embark on what was to become Philosophie naturalis Principia Mathematica. Nevertheless, Newton refers to Proposition XI only casually —almost as an afterthought¬ in the last but one of the 14 propositions that comprise this section. Newton’s priorities are clearly different.