The book "On the Sizes and Distances of the Sun and Moon", which has long been ascribed to Aristarchus, says that he calculated the distance to the Sun to be between 18 and 20 times the distance to the Moon, whereas the true ratio is about . The latter estimate was based on the angle between the half-moon and the Sun, which he estimated as (the true value being close to ). Depending on the distance that Van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between and Earth radii. According to Eusebius of Caesarea in the "Praeparatio Evangelica" (Book XV, Chapter 53), Eratosthenes found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of "stadia" myriads 400 and ) but with the additional note that in the Greek text the grammatical agreement is between "myriads" (not "stadia") on the one hand and both "400" and "" on the other, as in Greek, unlike English, all three (or all four if one were to include "stadia") words are inflected. This has been translated either as "stadia" (1903 translation by Edwin Hamilton Gifford), or as "stadia" (edition of , dated 1974–1991). Using the Greek stadium of 185 to 190 metres, the former translation comes to to , which is far too low, whereas the second translation comes to 148.7 to 152.8 million kilometres (accurate within 2%). Hipparchus also gave an estimate of the distance of Earth from the Sun, quoted by Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of Noel Swerdlow and G. J. Toomer, this was derived from his assumption of a "least perceptible" solar parallax of . A Chinese mathematical treatise, the "Zhoubi Suanjing" (c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places li apart and the assumption that Earth is flat. In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as times Earth's radius.