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.
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.