Sir Isaac Newton’s Book!.

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changed into a continual centripetal force. But as the explain-ing this method of reasoning is foreign to my present design;so I hope my readers, after what has been said, will find nodifficulty in receiving the proposition laid down above: that, ifthe body, which has moved through the curve line B HI (in fig.74..) from B to I, when it is come to I, be thrown directly backwith the fame velocity as that, wherewith it proceeded forward,the centripetal force, by acting over again all its operation onthe body, shall bring the body back again in the line IH B:and as the motion of the body in its course from B to I was eve-ry where in such a manner oblique to the line drawn from thecenter to the body, that the centripetal power acted in somedegree against the body’s motion, and gradually diminiffied it;so in the return of the body, the centripetal power will everywhere draw the body forward, and accelerate its motion bythe fame degrees, as before it retarded it.

13. This being agreed, suppose the body in X to have theline A K no longer obliquely inclined to its motion. In this cafe,if the body be turned back, in the manner we have been con-sidering, it must be directed back perpendicularly to AK.But if it had proceeded forward, it would likewise have mov-ed in a direction perpendicular to AX ; consequently, whe-ther it move from this point K backward or forward, it mustdescribe the same kind of course. Therefore since by beingturned back it will go over again the line KIH B; if it be per-mitted to go forward, the sine X L, which it shall describe,will be altogether similar to the line X H B.

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