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 ratios, in a given ratio to 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.