"[Hypotheses] 1. That the Moon receives its light from the sun. 2. That the earth is in the relation of a point and centre to the sphere in which the moon moves. 3. That, when the moon appears to us halved, the great circle which divides the dark and the bright portions of the moon is in the direction of our eye. 4. That, when the moon appears to us halved, its distance from the sun is then less than a quadrant by one-thirtieth of a quadrant. 5. That the breadth of the (earth's) shadow is (that) of two moons. 6. That the moon subtends one fifteenth part of a sign of the zodiac."
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Note: "is less than a quadrant..." is less than 90° by l/30th of 90° or 3°, and is therefore equal to 87°, i.e., Aristarchus assumes that at half-moon, the Moon's orbit around earth is 3° closer to the sun, rather than perpendicular to the line between centers of the sun and earth.]
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Aristarchus of Samos
Aristarchus of Samos (c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who devised the first known model envisioning the Earth in motion, orbiting around the Sun, or "central fire," at the center of the universe. He was influenced by Philolaus, and argued, like Anaxagoras before him, that the stars were entities similar to the sun. His astronomical ideas were in large rejected in favor the prevailing geocentric models of Aristotle and Ptolemy, until De revolutionibus orbium
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