to the line of the angle of emergence LIR is given. Q. E. D.
Case 2. Let now the body paſs ſucceſſively through ſeveral ſpaces terminated with parallel planes, AabB, BbbC, &c. (Pl. 25. Fig. 2.) and let it be acted on by a force which is uniform in each of them ſeparetly, but different in the different ſpaces; and by what was juſt demonſtrated, the ſine of the angle of incidence on the firſt plane Aa is to the line of emergence from the ſecond plane Bb in a given ratio; and this line of incidence upon the ſecond plane Bb will be to the line of emergence from the third plane Cc in a given ratio; and this ſine to the ſine of emergence from the fourth plane Dd in a given ration; and ſo on in infinitum and by equality, the ſine of incidence on the firſt plane to the ſine of emergence from the laſt plane in a given ratio. Let now the intervals of the planes be diminiſhed, and their number be infinitely increaſed, ſo that the action of attraction or impulſe, exerted according to any aſſigned law, may become continual, and the ratio of the line of incidence on the firſt plane to the ſine of emergence from the laſt plane being all along given, will be given then alſo. Q. E. D.
Proposition XCV. Theorem XLIX.
The ſame things being ſuppoſed, I ſay that the velocity of the body before its incidence is to the veolocity after emergence as the ſine of emergence to the ſine of incidence.
Make AH and Id equal (PL. 25. Fig. 3.) and erect the perpendicualrs AG, dK meeting the lines
