On the Sizes and Distances

On the Sizes and Distances (of the Sun and Moon) is widely accepted as the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310–230 BCE. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius. The book was presumably preserved by students of Pappus of Alexandria's course in mathematics, although there is no evidence of this. The editio princeps was published by John Wallis in 1688, using several medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also a 1572 Latin translation and commentary by Frederico Commandino. Symbols The work's method relied on several observations: The apparent size of the Sun and the Moon in the sky. The size of the Earth's shadow in relation to the Moon during a lunar eclipse The angle between the Sun and Moon during a half moon is 90°. The rest of the article details a reconstruction of Aristarchus' method and results. The reconstruction uses the following variables: