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

 l H the plane was coincident with the plane of the ecliptic, and that the Sun cQntinu'd in the ame place during the Whole reV0lution of the Moon about the Earth. F no M the above contruction it:;}ppears, that the proportion between e mean ditance of the Moon and its greatet or leat: ditances, is eaily all iigned; being omething larger than that which is aigned by Sir War N efwtvfl in the Sth propoition of his third book. But as the cornputation there given, depends upon the olution of abipuadratig equation, affected with numera coeiiicif ents; which renders it impoible to compare the proportions with each other, o as to fee their agreement or diagreement, 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, unles the periods of the Sun and Moon hould be much nearer equal than they are. LetL be the periodical time of the Moon, S the period of the Sun, M the ynodical period of the Moon to the Sun, and D be the difference of the periodf 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.