Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/23

From Wikisource
Jump to navigation Jump to search
This page has been validated.
Mr. Cotes's Preface,

ſafely when we come to conſider it in the heavenly bodies, that lie at ſo vaſt a diſtance from us. It is now agreed by all philoſophers that all circumterreſtrial bodies gravitate towards the Earth. That no bodies really light are to be found, is now confirmed by manifold experience. That which is relative levity, is not true levity, but apparent only; and ariſes from the preponderating gravity of the contiguous bodies.

Moreover, as all bodies gravitate towards the Earth, ſo does the Earth again towards bodies. That the action of gravity is mutual, and equal on both ſides, is thus proved. Let the maſs of the Earth be diſtinguiſhed into any two parts whatever, either equal, or any how unequal; now if the weights of the parts towards each other were not mutually equal, the leſſer weight would give way to the greater, and the two parts joined together would move on ad infinitum in a right line towards that part to which the greater weight tends; altogether againſt experience. Therefore we muſt ſay that the weights of the parts are conſtituted in equilibrio; that is, that the action of gravity is mutual and equal on both ſides.

The weights of bodies, at equal diſtances from the centre of the Earth, are as the quantities of matter in the bodies. This is collected from the equal acceleration of all bodies that fall from a ſtate of reſt by the force of their weights; for the forces by which unequal bodies are equally accelerated muſt be proportional to the quantities of the matter to be moved. Now that all bodies are in falling equally accelerated appears from hence, that

when the reſiſtance of the air is taken away, as it is under an exhauſted receiver, bodies falling de-

ſcribe