Aristarchus of Samos

“Sir Thomas Heath, Aristarchus of Samos: The Ancient Copernicus containing translation of Aristarchus On the Sizes and Distances of the Sun and the Moon”

“John Louis Emil Dreyer, History of the planetary systems from Thales to Kepler (1906)”

“Apart from its [On the sizes and distances of the Sun and Moon] astronomical content, it is of the greatest interest for its geometry. Thoroughly classical in form and language, as befits the period between Euclid and Archimedes, it is the first extant specimen of pure geometry used with a trigonometrical object, and in this respect is a sort of forerunner of Archimedes' Measurement of a Circle.”

“There is... no reason to doubt the unanimous testimony of antiquity that Aristarchus was the real originator of the Copernican hypothesis.”

“Archimedes tells us that Aristarchus wrote a book of hypotheses, one of which was that the sun and the fixed stars remain unmoved and that the earth revolves round the sun in the circumference of a circle. Now Archimedes was a younger contemporary of Aristarchus; he must have seen the book of hypotheses in question, and we could have no better evidence for attributing to Aristarchus the first enunciation of the Copernican hypothesis.”

“Archimedes distinctly says in his Psammites or Sand-reckoner that Aristarchus was the first to discover that the apparent diameter of the sun is about 1/720th part of the complete circle described by it in the daily rotation, or, in other words, that the angular diameter is about 1/2°, which is very near the truth.”

“The hypothesis of Aristarchus included the rotation of the earth, as might be expected.”

“One of the persons in the dialogue, being called to account for turning the world upside down, says that he is quite content so long as he is not accused of impiety, "like as Kleanthes held that Aristarchus of Samos ought to be accused of impiety for moving the hearth of the world as the man in order to save the phenomena supposed that the heavens stand still and the earth moves in an oblique circle at the same time as it turns round its axis."”

“We have to depend on statements of subsequent writers when we endeavor to give Aristarchus his proper place in the history of cosmical systems.”

“[Aristarchus] is so obscure that Wallis was obliged to annotate him from one end to the other, in the effort to make him intelligible.”

“Copernicus, Kepler and Galileo were ‘revisionists’ in rejecting the geocentric system of Ptolemy (which held sway for some 1500 years) and, against an oppressive and repressive mainstream opinion (and officialdom), reinstated—with improvements—the heliocentric system of Aristarchos of Samos (3rd cent BCE).”

“Proposition 18. The earth is to the moon in a [volume] ratio greater than [15.8] that which 1259712 has to 79507, but less than [31.5] that which 216000 has to 6859.”

“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.”

“Proposition 16. The sun has to the earth a [volume] ratio greater than [254] that which 6859 has to 27, but less than [368] that which 79507 has to 216.”

“Proposition 15. The diameter of the sun has, to the diameter of the earth a ratio greater than [6.3] that which 19 has to 3, but less than [7.2] that which 43 has to 6.”

“Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.”

“Proposition 12. The diameter of the circle which divides the dark and the bright portions in the moon is less than the diameter of the moon, but has to it a ratio greater than [0.99] that which 89 has to 90.”

“Proposition 11. The diameter of the moon is less than 2/45ths [0.04], but greater than 1/30th [0.03] of the distance of the centre of the moon from our eye.”

“Proposition 10. The sun has to the moon a [volume] ratio greater than that which 5832 has to 1, but less than that which 8000 has to 1.”

“Proposition 9. The diameter of the sun is greater than 18 times, but less than 20 times, the diameter of the moon.”