impulſes. But theſe propoſitions are to be conſidered as purely mathematical; and therefore laying aſide all phyſical conſiderations, I make uſe of a familiar way of ſpeaking, to make my ſelf the more eaſily underſtood by a mathematical reader.
Proposition LVII. Theorem XX.
Two bodies attracting each other mutually, deſcribe ſimilar figures about their common centre of gravity, and about each other mutually.
For the diſtances 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 compoſition of ratio's, in a given ratio the whole diſtance between the bodies. Now theſe diſtances revolve about their common term with an equable angular motion, becauſe lying in the ſame 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, deſcribe upon planes, which either reſt with thoſe terms, or move with any motion not angular, figures entirely ſimilar round thoſe terms. Therefore the figures deſcribed by the revolution of theſe diſtances are ſimilar. Q. E. D.
