of the Earth, as the ſquare of the ſemi-diameter of the Earth to the ſquare of the ſemi-diameter of the orbit. But by what was ſhewn before the very ſame ratio holds between the centripetal force of the Moon revolving in its orbit, and the centripetal force of the Moon near the ſurface of the Earth. Therefore the centripetal force near the ſurface of the Earth is equal to the force of gravity. Therefore theſe are not two different forces, but one and the ſame; for if they were different, theſe forces united would cauſe bodies to deſcend to the Earth with twice the velocity they would fall with by the force of gravity alone. Therefore it is plain that the centripetal force, by which the Moon is perpetually, either impelled or attracted out of the tangent and retained in its orbit, is the very force of terreſtrial gravity reaching up to the Moon. And it is very reaſonable to believe that virtue ſhould extend it ſelf to vaſt diſtances, ſince upon the tops of the higheſt mountains we find no ſenſible diminution of it. Therefore the Moon gravitates towards the Earth; but on the other hand, the Earth by a mutual action equally gravitates towards the Moon; which is alſo abundantly confirmed in this philoſophy, where the Tides in the Sea and the Præceſſon of the Æquinoxes are treated of; which ariſe from the action both of the Moon and of the Sun upon the Earth. Hence laſtly, we diſcover by what law the force of gravity decreaſes at great diſtances from the Earth. For ſince gravity is no ways different from the Moon's centripetal force, and this is reciprocally proportional to the ſquare of the diſtance; it follows that it is in
that ratio that the force of gravity decreaſes.
