the line D E with the velocity, which it had before in that line. Again I say, the second impulse in E is equal to the first. By what has been said on the second law of motion concerning the effect of oblique impulses[86], it will be understood, that the impulse in E, whereby the body was turned out of the line D E into the line E F, is of such strength, that if the body had been at rest, when this impulse had acted upon it, this impulse would have communicated so much motion to the body, as would have carried it through a length equal to H I, in the time wherein the body would have passed from E to H, or in the time wherein it passed from E to I. In the same manner, on the return of the body, the impulse in E, whereby the body is turned out of the line F E into E D, is of such strength, that if it had acted on the body at rest, it would have caused the body to move through a length equal to K L, in the same time, as the body would imploy in passing through E K with the velocity, wherewith it returns in the line F E. Therefore the second impulse, had it acted on the body at rest, would have caused it to move through a length equal to K L in the same space of time, as would be taken up by the body in passing through a length equal to H I, were the first impulse to act on the body when at rest. That is, the effects of the first and second impulse on the body when at rest would be the same; for K L and H I are equal: consequently the second impulse is equal to the first. 11. THUS if the body be returned through F E with the velocity, wherewith it moved forward; we have shewn how by the repetition of the impulse, which acted on it at E, the body will return again into the line D E with the velocity, which it had before in that line. By the same process of reasoning it may be proved, that, when the body is returned back to D, the impulse, which before acted on the body at that point, will throw the body into the line D C with the velocity, which it first had in that line; and the other impulses being successively repeated, the body will at length be brought back again into the line B A with the velocity, wherewith it set out in that line.