Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/475

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l H the plane was coincident with the plane of the ecliptic, and that the Sun cQntinu'd in the ſame place during the Whole reV0lution of the Moon about the Earth. F no M the above conſtruction it:;}ppears, that the proportion between e mean diſtance of the Moon and its greateſt or leaſt: diſtances, is eaſily all iigned; being ſomething larger than that which is aſſigned by Sir War N efwtvfl in the Sth propoſition of his third book. But as the cornputation there given, depends upon the ſolution of abipuadratig equation, affected with numera coeiiicif ents; which renders it impoſſible to compare the proportions with each other, ſo as to fee their agreement or diſagreement, except in a particular application to numbers; I (hall therefore fet down a rule, in general terms, derived from his method, which will be exact: enough, unleſs the periods of the Sun and Moon ſhould be much nearer equal than they are. LetL be the periodical time of the Moon, S the period of the Sun, M the ſynodical period of the Moon to the Sun, and D be the difference of the periodſf of the Sun and Moon; then, accordin to Sir Muze Ne=wton's method, the difference of the two axes of the Moon's elliptic orbit, as it is contracted by the aéliion I.