"Aristarchus... was a contemporary of Euclid. His fame rests on his heliocentric theory... Perhaps "theory" is too strong a word, for his proofs were weak; yet it was a great idea, an idea redeveloped centuries later by Copernicus. ...an observer on Earth sees a half-moon only when ∠EMS [the angle between the Earth and Sun, from the persective of the Moon] is a right angle. ...sometimes both Sun and Moon are visible when the phase of the Moon is half-moon. So? Measure ∠MES [the angle between the Moon and Sun, from the persective of earth]... This is what Aristarchus did. ...the third angle is determined [since the sum of the three angles of any triangle is 180º], so the shape but not the size of ⃤ EMS [triangle formed by Earth-Moon-Sun] is known. Consequently, although the actual length of any side is not determinate, the ratio of any pair is. ...[Moon-Earth distance/Sun-Earth distance] ME/SE = cos α [where ∠MES = α]."
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George Pólya, Mathematical Methods in Science (1977)
https://en.wikiquote.org/wiki/Aristarchus_of_Samos
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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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