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(58.) Since by the quality of inertia a body can neither generate nor destroy motion, it follows that when two bodies act upon each other in any way whatever, the total quantity of motion in a given direction, after the action takes place, must be the same as before it, for otherwise some motion would be produced by the action of the bodies, which would contradict the principle that they are inert. The word “action” is here applied, perhaps improperly, but according to the usage of mechanical writers, to express a certain phenomenon or effect. It is, therefore, not to be understood as implying any active principle in the bodies to which it is attributed.

(59.) In the cases of collision of which we have spoken, one of the masses B was supposed to be quiescent before the impact. We shall now suppose it to be moving in the same direction as A, that is, towards C, but with a less velocity, so that A shall overtake it, and impinge upon it. After the impact, the two masses will move towards C with a common velocity, the amount of which we now propose to determine.