Planets all aſtronomers conſent. Therefore the centripetal forces of all the Planets are reciprocally as the ſquares of the diſtances from the centres of their orbits. If any ſhould object, that the apſides of the Planets, and eſpecially of the Moon, are not perfectly at reſt; but are carried with a ſlow kind of motion in conſequentia; one may give this anſwer, that though we ſhould grant this very ſlow motion to ariſe from hence, that the proportion of the centripetal force is a little different from the duplicate, yet that we are able to compute mathematically the quantity of that aberration, and find it perfectly inſenſible. For the ratio of the Lunar centripetal force it ſelf, which muſt be the moſt irregular of them all, will be indeed a little greater than the duplicate, but will be near ſixty times nearer to that than it is to the triplicate. But we may give a truer anſwer, by ſaying that this progreſion of the apſides ariſes not from an aberration from the duplicate proportion, but from a quite different cauſe, as is moſt admirably ſhewn in this philoſophy. It is certain then that the centripetal forces with which the primary Planets tend to the Sun, and the ſecondary to their primary, are accurately as the ſquares of the diſtances reciprocally.
From what has been hitherto ſaid, it is plain that the Planets are retained in their orbits by ſome force perpetually acting upon them; it is plain that that force is always directed towards the centres of their orbits; it is plain that its efficacy is augmented with the nearneſs to the centre, and diminiſhed with the ſame; and that it is augmented in the ſame proportion with which the ſquare of the
diſtance is diminiſhed, and diminiſhed in the ſame
