Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/405

Rh to the line of the angle of emergence LIR is given. Q. E. D.

Let now the body pas ucceively through everal paces 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 eparetly, but different in the different paces; and by what was jut demontrated, the ine of the angle of incidence on the firt plane Aa is to the line of emergence from the econd plane Bb in a given ratio; and this line of incidence upon the econd plane Bb will be to the line of emergence from the third plane Cc in a given ratio; and this ine to the ine of emergence from the fourth plane Dd in a given ration; and o on in infinitum and by equality, the ine of incidence on the firt plane to the ine of emergence from the lat plane in a given ratio. Let now the intervals of the planes be diminihed, and their number be infinitely increaed, o that the action of attraction or impule, exerted according to any aigned law, may become continual, and the ratio of the line of incidence on the firt plane to the ine of emergence from the lat plane being all along given, will be given then alo. Q. E. D.

The ame things being uppoed, I ay that the velocity of the body before its incidence is to the veolocity after emergence as the ine of emergence to the ine of incidence.

Make AH and Id equal (PL. 25. Fig. 3.) and erect the perpendicualrs AG, dK meeting the lines