Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/474

ll 1° nr is carried round the Earth in the orbit ABDEFIL hav' its longer axis PL in length double Gfm§ lC ſhortcr aXi8 215, and lying always parallel to TD, the line joining the centers of the Earth and Sun. Whllit the ſaid figure is carried fromd to B, the Moon revolves the contrary Way from Qtr: N, ſo as to deſcribe equal areas in equal times about the centre of it; and to perform its revolution in the ſame time as the center of the ſaid Elliptic epicycle (if it may be ſo called,) performs its revolution; the Moon being always in the remoter extremity of its (hotter axis in Qand K when it is in the quarters, and in the neareſt of its longer axis at the time of the new and full Moon. T H E ſhorter ſemiaxis of this Ellipſis AQ is to the diſtance of its center from the Earth AT; in the duplicate proportion of the Moon's periodical time about the Earth to the Sun's periodical time: Which proportion, if there be 2 139 revolutions of the Moon to the Stars in 160 fydercal years, is that of 4.7 to 8400. T H E Fgure which is deſcribed by this compound motion of the Moon in the Elliptic epicycle, whilfi: the center of it is carried round the Earth, very nearly repreiknts the form of the Lunar orbit; ſuppoſing- it without eccentricity, and tltgt c