Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/119

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gent PR in Z; and laſtly, thro' the point Q draw LR parallel to SP, meeting the circle in L, and the tangent PZ in R. And, becauſe of the {{ls]]imilar triangles ZQR, ZTP, VPA, we ſhall have , that is, QRL, to , as to . And therefore is equal to . Multiply thoſe equals by and the points P and Q coinciding, for RL write PV; then we ſhall have . And therefore (by cor. 1. and 5. prop. 6.) the centripetal force is reciprocally as , that is (becauſe is given) reciprocally as the ſquare of the diſtance of altitude SP, and the cube of the chord PV conjunctly. Q. E. I.


The ſame otherwiſe

On the tangent PR produced, let fall the perpendicular ST: and (becauſe of the ſimilar triangles STP, VPA) we ſhall have AV to PV as SP to ST, and therefore , and , that is, (becauſe AV is given) reciprocally as . Q. E. I.