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Astronomy Explained Upon Sir Isaac Newton's Principles

Note 30 — CHAP. VII. The physical Causes of the Motions of the Planets. The Excentricities of their Orbits. The Times in which the Action of Gravity would bring them to the Sun. Archimedes’s ideal Problem for moving the Earth. The World not eternal.

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To make the projectile force balance the gravitating power so exactly as that the body may move in a Circle, the projectile velocity of the body must be such as it would have acquired by gravity alone in falling through half the radius.

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