of the line of incidence GH to the firſt plane Aa be ſuch, that the ſine of incidence may be to the radius of the circle whoſe ſine it is, in the ſame ratio which the ſame ſine of incidence hath to the ſine of emergence from the plane Dd into the ſpace DdeE; and becauſe the ſine 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 becauſe the line of emergence coincides with that plane it is manifeſt that the body can proceed no farther towards the plane Ee. But neither can it proceed in the line of emergence Rd; becauſe it is perpetually attracted or impelled towards the medium of incidence. It will return therefore between the planes Cc, Dd, deſcribing an arc of a parabola QRq; whoſe principal vertex (by what Galileo has demonſtrated) is in R, Cutting the plane Ce in the ſame angle at q, that it did before at Q; then going on in the parabolic arcs qp, ph, &c. ſimilar and equal to the former arcs QP, PH &c. it will cut the reſt of the planes in the ſame p, h &c. as it did before in P, H, &c. will emerge at laſt with the ſame obliquity at h, with which it firſt impinged on that plane at H. Conceive now the intervals of the planes Aa, Bb, Cc, Dd, Ee, &c. to be infinitely diminiſhed, and the number infinitely increaſed, ſo that the action of attraction or impulſe, exerted according to any aſſigned law, may become continual; and the angle of emergence remaining all along equal to the angle of incidence will be equal to the ſame alſo at laſt. Q. E. D.
