continued force retained in thoſe curvilinear paths. Since then the Planets move in curvilinear orbits there muſt be ſome force operating, by whoſe repeated actions they are perpetually made to deflect from the tangents.
Now it is collected by mathematical reaſoning, and evidently demonſtrated, that all bodies that move in any curve line deſcribed in a plane, and which, by a radius drawn to any point, whether quieſcent, or any how moved, deſcribe areas about that point proportional to the times, are urged by forces directed towards that point. This muſt therefore be granted. Since then all aſtronomers agree that the primary Planets deſcribe about the Sun, and the ſecondary about the primary, areas proportional to the times; it follows that the forces by which they are perpetually turned aſide from the rectilinear tangents, and made to revolve in curvilinear orbits, are directed towards the bodies that are ſituate in the centres of the orbits. This force may therefore not improperly be called centripetal in reſpect of the revolving body, and in reſpect of the central body attractive; whatever cauſe it may be imagined to ariſe from.
But beſides, theſe things muſt be alſo granted, as being mathematically demonſtrated: If ſeveral bodies revolve with an equable motion in concentric circles, and the ſquares of the periodic times are as the cubes of the diſtances from the common centre; the centripetal forces will be reciprocally as the ſquares of the diſtances. Or, if bodies revolve in orbits that are very near to circles, and the apſides of the orbits reſt; the centripetal forces of the revolving bodies will be reciprocally as the ſquares of
diſtances. That both theſe caſes hold in all the
