Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/121

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Proposition VIII. Problem III.

If a body moves in the ſemi-circumference PQA; it is propoſed to find the law of the centripetal force tending to a point S, ſo remote, that all the lines PS, RS drawn thereto, may be taken for parallels. Pl. 3. Fig. 5.


Plate 3, Figure 5
Plate 3, Figure 5

From C the centre of the ſemi-circle, let the ſemidiameter CA be drawn, cutting the parallels at right angles in M and M and join CP. Becauſe of the ſimilar triangles CPM, PZT and RZQ we ſhall have to as to ; and from the nature of the circle, is equal to the rectangle , or the points P, Q coinciding, to the rectangle . Therefore is to as to ; and and that is, (neglecting the given ration reciprocally as . Q. E. I.

And the ſame thing is likewiſe eaſly inferred from the preceding Propoſition.