Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/69

Rh

For Action and its oppoite Re-action are equal, by Law 3, and therefore, by Law 2, they produce in the motions equal changes towards oppoite parts. Therefore if the motions are directed towards the ame parts, whatever is added to the motion of the preceding body will be ubducted from the motion of that which follows; o that the um will be the ame 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 oppoite parts will remain the ame.

Thus if a pherical body A with two parts of velocity, is triple of a pherical body B which follows in the ame right line with ten parts of velocity, the motion of A will be to that of B as 6 to 10. Suppoe, then, their motions to be of 6 parts and of 10 parts, and the um will be 16 parts. Therefore, upon the meeting of the bodies, if A acquire 3, 4, or 5 parts of motion, B will loe as many; and therefore after reflexion A will proceed with 9, 10, or 11 parts, and B with 7, 6, or 5 parts; the um 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 Rh