Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/301

 impules. But thee propoitions are to be conidered as purely mathematical; and therefore laying aide all phyical coniderations, I make ue of a familiar way of peaking, to make my elf the more eaily undertood by a mathematical reader.

Two bodies attracting each other mutually, decribe imilar figures about their common centre of gravity, and about each other mutually.

For the ditances of the bodies from their common centre of gravity are reciprocally as the bodies; and therefore in a given ratio to each other; and thence by compoition of ratio's, in a given ratio the whole ditance between the bodies. Now thee ditances revolve about their common term with an equable angular motion, becaue lying in the ame right line they never change their inclination to each other mutually. But right lines that are in a given ratio to each other, and revolve about their terms with an equal angular motion, decribe upon planes, which either ret with thoe terms, or move with any motion not angular, figures entirely imilar round thoe terms. Therefore the figures decribed by the revolution of thee ditances are imilar. Q. E. D.