Sir I s a a c Newt on’s Book II.

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found out from their causes, which this philosophy has broughtto light, and has shewn the dependence of these inequalitiesupon such causes in so perfect a manner, that we not only learnfrom thence in general, what those inequalities are, but areable to compute the degree of them. Of this Sir I s. N e w t o nhas given several specimens, and has moreover found meansto reduce the moon's motion so completely to rule, that hehas framed a theory, from which the place of that planetmay at all times be computed, very nearly or altogether as ex-actly, as the places of the primary planets themselves, which ismuch beyond what the greatest astronomers could ever effect.

1. T h e first thing demonstrated of these secondary planetsis, that they are drawn towards their respective primary in thefame manner as the primary planets are attracted by the fun.That each secondary planet is kept in its orbit by a powerpointed towards the center of the primary planet, aboutwhich the secondary revolves; and that the power, by whichthe secondaries of the fame primary are influenced, bears theseme relation to the distance from the primary, as the power,by which the primary planets are guided, does in regard tothe distance from the fun \ This is proved in the satellites ofJupiter and Saturn, because they move in circles, as far as wecan observe, about their respective primary with an equablecourse, the respective primary being the center of each or-bit : and by comparing the times, in which the different sa-tellites of the fame primary perform their periods, they are

1 .Newton. Princ. Lib. III. prop. 1.

found