Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/473

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19 the joint force of its gravity to the Sun and Earth, thereby deſcribing an orbit, which inclofes not the Earth but the Sun, is yet conſidered as a compound motion, made from two motions, one about the Sun, and the other about the Earth; becauſe two ſuch motions are requiſite to anſwer the two forces of its gravity, if ſeparately conſidered: For the very ſame reaſon, the Moon's motion ought to be reſolved into a third motion of revolution, ſince there remains a third force to be ſatiſfied, and that is the force ariſing from the altes ration of the Moon's gravity to the Sun. And this when conſidered, will require a motion in a ſmall ellipſis, in the manner here deſcribed. T H E circle ADFH repreſents t.he Fig; orbit of the Moon about the Earth in the center if, as it would be at a mean diſtance, ' ſuppoſing the Moon had n'o gravity to any, other body but the Earth. The diameter AT F divides that part of the orbit which is towards the Sun, ſuppoſe ADF, from the part oppoſite to the Sun, ſuppoſe AH E The diameter at. right angles H ST D, is the line of the Moon's conjunction with or oppoſition to the Sun. The figure PQLK is an Ellipſis, whoſe cen-f ICI