Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/24

Rh decribe equal paces in equal times; and this is yet more accurately proved by the experiments of pendulums.

The attractive forces of bodies at equal ditances, are as the quantities of matter in the bodies. For ince bodies gravitate towards the Earth, and the Earth again towards bodies with equal moments; the weight of the Earth towards every body, or the force with which the body attracts the Earth, will be equal to the weight of the ame body towards the Earth. But this weight was hewn to be as the quantity of matter in the body; and therefore the force with which every body attracts the Earth, or the abolute force of the body, will be as the ame quantity of matter.

Thefore the attractive force of the entire bodies aries from, and is compounded of, the attractive forces of the parts, becaue as was jut hewn, if the bulk of the matter be augmented or diminihed, its virtue is proportionably augmented or diminihed. We mut therefore conclude that the action of the Earth is compounded of the united actions of its parts; and therefore that all terretrial bodies mut attract each other mutually, with abolute forces that are as the matter attracting. This is the nature of gravity upon Earth; let us now ee what it is in the Heavens.

That every body pereveres in its tate either of ret, or of moving uniformly in a right line, unles in o far as it is compelled to change that tate by forces impreed, is a law of nature univerally received by all philoophers. But from thence it follows that bodies which move in curve lines, and are therefore continually going off from the right lines that are tangents to their orbits, are by ome Rh