Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/345



By a like reaoning if each of the bodies of the ytem A, B, C, D, &c. do ingly attract all the ret with accelerative forces, which are either reciprocally or directly in the ratio of any power whatever of the ditances from the attracting body; or which are defined by the diŧances from each of the attracting bodies according to any common law; it is plain that the abolute forces of thoe bodies are as the bodies themelves.

In a ytem of bodies whoe forces decreae in the duplicate ratio of the ditances, if the leer revolve about one very great one in ellipes, having their common focus in the centre of that great body, and of a figure exceeding accurate; and moreover by radiu drawn to that great body decribe area's proportional to the times exactly; the abolute forces of thoe bodies to each other will be either accurately or very nearly in the ratio of the bodies. And o on the contrary. This appears from cor. of prop. 68. compared with the firt corollary of this prop.

Thee propoitions naturally lead us to the analogy there is between centripetal forces, and the central bodies to which thoe forces ue to be directed. For it is reaonable to uppoe that forces which are directed to bodies hould depend upon the nature and quantity of thoe bodies, as we ee they do in magnetical experiments. And when uch caes occur, we are to compute the attractions of the bodies by aligning to each of their particles its proper force, and then collecting the um of