  Save for the short opening sections, “Regulae Philosophandi” and “Phenomena,” Book 3, in contrast to Books 1 and 2, is not marked off into sections. Nevertheless, the main body of it does consist of four clearly separate parts: (1) the derivation of the law of gravity (Props. 1-8); (2) implications of this law for orbital and rotating bodies (from the corollaries to Prop. 8 through Prop. 24); (3) a quantitative derivation of select lunar inequalities and the precession of the equinoxes from the law of gravity (Props. 25-39); and (4) a solution for comet trajectories, with examples and comments (Props. 40-42). These parts will be discussed in sequence below.