For Action and its oppoſite Re-action are equal, by Law 3, and therefore, by Law 2, they produce in the motions equal changes towards oppoſite parts. Therefore if the motions are directed towards the ſame parts, whatever is added to the motion of the preceding body will be ſubducted from the motion of that which follows; ſo that the ſum will be the ſame as before. If the bodies meet, with contrary motions, there will be an equal deduction from the motions of both; and therefore the difference of the motions directed towards oppoſite parts will remain the ſame.
Thus if a ſpherical body A with two parts of velocity, is triple of a ſpherical body B which follows in the ſame right line with ten parts of velocity, the motion of A will be to that of B as 6 to 10. Suppoſe, then, their motions to be of 6 parts and of 10 parts, and the ſum will be 16 parts. Therefore, upon the meeting of the bodies, if A acquire 3, 4, or 5 parts of motion, B will loſe as many; and therefore after reflexion A will proceed with 9, 10, or 11 parts, and B with 7, 6, or 5 parts; the ſum remaining always of 16 parts as before. If the body A acquire 9, 10, 11, or 12 parts of motion, and therefore after meeting proceed with 15, 16, 17, or 18 parts, the body
