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Sir I s a a c Newto n’s Book I.

I y. This conclusion is not indeed absolutely true: for weshall find hereafter a , that the power of gravity is not of thefame strength at all distances from the center of the earth. Butnothing of this is in the least sensible in any distance, to whichwe can convey bodies. The weight of bodies is the very fameto sense upon the highest towers or mountains, as upon thelevel ground ; so that in all the observations we can make,the forementioned proportion between the velocity of a fall-ing body and the time, in which it has been descending, ob-tains without any the least perceptible difference.

16. From hence it follows, that the space, through whicha body falls, is not proportional to the time of the fall; forsince the body increases its velocity, a greater space will bepassed over in the fame portion of time at the latter part of thefall, than at the beginning. Suppose a body let fall from thepoint A (in fig. 8 .) were to descend from A to B in any por-tion of time ; then if in an equal portion of time it were toproceed from B to C; I fay, the space B C is greater than AB;so that the time of the fall from A to C being double the timeof the fall from A to B, AC shall be more than double of A B.

17. The geometers have proved, that the spaces, throughwhich bodies fall thus by their weight, are just in a duplicateor two-fold proportion of the times, in which the body hasbeen falling. That is, if we were to take the line D E in thefame proportion to A B, as the time, which the body has im-ployed in falling from A to C, bears to the time of the fall

* Book II. Chap. 5.

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