Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/407

Rh of the line of incidence GH to the firt plane Aa be uch, that the ine of incidence may be to the radius of the circle whoe ine it is, in the ame ratio which the ame ine of incidence hath to the ine of emergence from the plane Dd into the pace DdeE; and becaue the ine of emergence is now become equal to radius, the angle of emergence will be a right one, and therefore the line of emergence will coincide with the plane Dd. Let the body come to this plane in the point R; and becaue the line of emergence coincides with that plane it is manifet that the body can proceed no farther towards the plane Ee. But neither can it proceed in the line of emergence Rd; becaue it is perpetually attracted or impelled towards the medium of incidence. It will return therefore between the planes Cc, Dd, decribing an arc of a parabola QRq; whoe principal vertex (by what Galileo has demontrated) is in R, Cutting the plane Ce in the ame angle at q, that it did before at Q; then going on in the parabolic arcs qp, ph, &c. imilar and equal to the former arcs QP, PH &c. it will cut the ret of the planes in the ame p, h &c. as it did before in P, H, &c. will emerge at lat with the ame obliquity at h, with which it firt impinged on that plane at H. Conceive now the intervals of the planes Aa, Bb, Cc, Dd, Ee, &c. to be infinitely diminihed, and the number infinitely increaed, o that the action of attraction or impule, exerted according to any aigned law, may become continual; and the angle of emergence remaining all along equal to the angle of incidence will be equal to the ame alo at lat. Q. E. D.