Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/70

26 B, loing o many parts as A has got, will either proceed with one part, having lot 9, or top and remain at ret, as having lot its whole progreive motion of 10 parts: or it will go back with 1 part, having not only lot its whole motion, but (if I may o ay) one part more; or it will go back with 2 parts, becaue a progreive motion of 12 parts is taken off. And o the ums of the conpiring motions 15+1, or 16+0, and the differences of the contrary motions 17-1 and 18-2, will always be equal to 16 parts, as they were before the meeting and reflexion of the bodies. But the motions being known with which the bodies proceed after reflexion, the velocity of either will be alo known, by taking the velocity after to the velocity before reflexion, as the motion after is to the motion before. As in the lat cae, where the motion of the body A was of 6 parts before reflexion and of 18 parts after, and the velocity was of 2 parts before reflexion, the velocity thereof after reflexion will be found to be of 6 parts; by aying, as the 6 parts of motion, before to 18 parts after, o are 2 parts of velocity before reflexion to 6 parts after.

But if the bodies are either not pherical, or, moving in different right lines, impinge obliquely one upon the other, and their motions after reflexion are required, in thoe caes we are firt to determine the poition of the plane that touches the concurring bodies in the point of concoure; then the motion of each body (by Corol. 2) is to be reolved into two, one perpendicular to that plane, and the other parallel to it. This done, becaue the bodies act upon each other in the direction of a line perpendicular to this plane, the parallel motions are to be retained the ame after reflexion as before; and to the perpendicular motions we are to aign equal changes towards the contrary parts; in Rh