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Proposition 17. The diameter of the earth is to the diameter of the moon in a ratio greater than [2.51] that which 108 has to 43, but less than [3.16… - Aristarchus of Samos
" "Proposition 17. The diameter of the earth is to the diameter of the moon in a ratio greater than [2.51] that which 108 has to 43, but less than [3.16] that which 60 has to 19.
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About 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 coelestium was published in 1543 by Copernicus, who was influenced by the work of Aristarchus through a close reading of Greek and Latin authors. The only known extant work by Aristarchus is "On the Dimensions and Distances of the Sun and Moon" which does not discuss his thesis on heliocentrism.
Also Known As
Native Name:
Ἀρίσταρχος ὁ Σάμιος
•
Αρίσταρχος ο Σάμιος
Alternative Names:
Aristarchos of Samos
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We are now in a position to prove the following propositions : —
1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon.
2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon.
3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one fifteenth part of a sign of the zodiac.
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