B, loſing ſo many parts as A has got, will either proceed with one part, having loſt 9, or ſtop and remain at reſt, as having loſt its whole progreſſive motion of 10 parts: or it will go back with 1 part, having not only loſt its whole motion, but (if I may ſo ſay) one part more; or it will go back with 2 parts, becauſe a progreſſive motion of 12 parts is taken off. And ſo the ſums of the conſpiring 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 alſo known, by taking the velocity after to the velocity before reflexion, as the motion after is to the motion before. As in the laſt caſe, 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 ſaying, as the 6 parts of motion, before to 18 parts after, ſo are 2 parts of velocity before reflexion to 6 parts after.
But if the bodies are either not ſpherical, or, moving in different right lines, impinge obliquely one upon the other, and their motions after reflexion are required, in thoſe caſes we are firſt to determine the poſition of the plane that touches the concurring bodies in the point of concourſe; then the motion of each body (by Corol. 2) is to be reſolved into two, one perpendicular to that plane, and the other parallel to it. This done, becauſe the bodies act upon each other in the direction of a line perpendicular to this plane, the parallel motions are to be retained the ſame after reflexion as before; and to the perpendicular motions we are to aſſign equal changes towards the contrary parts; in
