Chap. 2. PHILOSOPHY.

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are thus found. Suppofe A and B two numbers, and it berequired to find C the firft, and D the fecond ofthe two mean proportionals between them. Firft A Gmultiply A by it felf, and the product multiply £ dby b ; then C will be the number which in arith-metic is called the cubic root of this laft produd; that is,the number C being multiplied by it felf, and the productagain multiplied by the fame number C, will produce theprodud above mentioned. In like manner D is the cubicroot of the produd of B multiplied by it felf, and the pro-duce of that multiplication multiplied again by A.

10. It will be asked, perhaps, how this corredion can beadmitted, when the caufe of the motions of the planets wasbefore found by fuppofing the fim the center of the power,which aded upon them: for according to the prefent correc-tion this power appears rather to be direded to their commoncenter of gravity. But whereas the fim was at firft conclu-ded to be the center, to which the power ading on the planetsWas direded, becaufe the {paces deferibed round the fim inequal times were found to be equal; fo Sir I s a a c Newtonproves, that if the fim and planet move round their commoncenter of gravity, yet to an eye placed in the planet, the {pa-ces, which will appear to be deferibed about the fun, will havethe fame relation to the times of their defeription, as the realfpaces would have, if the fun were at reft a . I farther afterted,that, fuppofing the planets to move round the fun at reft,

a Princ. phiJof. Lib. I. prop. ;8. coroll. 3,

A a x