Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/52

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8
Book I.
Mathematical Principles

the centre of the Magnetiſm, or the Earth in the centre of the gravitating force), or any thing elſe that does not yet appear. For I here deſign only to give a Mathematical notion of those forces, without conſidering their Phyſical cauſes and ſeats.

Wherefore the accelerative force will ſtand in the same relation to the motive, as celerity does to motion. For the quantity of motion ariſes from the celerity, drawn into the quantity of matter; and the motive force ariſses from the accelerative force multiplied by the ſame quantity of matter. For the ſum of the actions of the accelerative force, upon the ſeveral particles of the body, is the motive force of the whole. Hence it is, that near the ſuffice of the earth, where the accelerative gravity, or force productive of gravity, in all bodies is the ſame, the motive gravity or the weight is as the body; but if we ſhould ascend to higher regions, where the accelerative gravity is leſs, the weight would be equally diminiſhed, and would always be as the product of the body, by the accelerative gravity. So in those regions, where the accelerative gravity is diminiſhed into one-half, the weight of a body two or three times leſs, will be four or ſix times leſs.

I likewiſe call attractions and impulſes, in the ſame ſenſe, accelerative, and motive; and uſe the words attraction, impulſe, or propenſity of any ſort towards a centre, promiſcuouſly, and indifferently, one for another; conſidering thoſe forces not phyſically, but mathematically: wherefore the reader is not to imagine that by thoſe words I anywhere take upon me to define the kind, or the manner of any action, the cauſes or the physical reason thereof, or that I attribute forces, in a true and phyſical ſenſe, to certain centres (which are only mathematical points); when