The ſame otherwiſe
The perpendicular ST let fall upon the tangent and the chord PV of the circle concentrically cutting the ſpiral are in given ratio's to the height SP; and therefore is as , that is (by corol. 3. and 5. prop. 6.) reciprocally as the centripetal force.
Lemma 12.
All parallelograms circmſcribed about any conjugate diameters of a given ellipſis or hyperbola are equal among themſelves.
This is demonſtrated by the writers on the conic ſections.
Proposition X. Problem V.
If a body revolve: in an ellipſis: it is propoſed to find the law of the centripetal force tending to the centre of the ellipſus. Pl. 4. Fig. 1.
Suppoſe CA, CB to be ſemi-axes of the ellippſe; GP, DK conjugate diameters; PF, Qf perpendiculars to thoſe diameters; Qv an ordinate to the diameter GP; and if the parallelogram QvPR be compleated; then (by the properties of the conic ſections) the rectangle PvG will be to as to to , and (becauſe of the ſimilar triangles QvT, PCF) to as to ; and by compoſition, the ration of PvG to is compounded of