Aristarchus of Samos (ca 280 – 270 BCE) was the first to put forward the heliocentric hypothesis; he explained that the size of the earth and even of the sphere containing the earth’s orbit was negligible as compared with the sphere of the fixed stars; he gave a method to measure the distances of the sun and moon. The only extant text by Aristarchus is his treatise on the measurement of the distances and sizes of the Sun and Moon, where the author uses a geocentric orientation, and that is therefore assumed to be an early work, antedating his heliocentric hypothesis.

The Greek text was translated into Arabic in the tenth century. The first Latin translation from Greek was done by Giorgio Valla (1447-1500) and published in Venice in 1488. The present text, published in Pesaro in 1572, is the first edition of the much more accurate translation by Federico Commandino (1509-1575), an Italian humanist and mathematician whose translations of Apollonius, Archimedes and Euclid lead the way to Galileo and in general to the rebirth of mathematical research in the sixteenth and seventeenth century. The Greek text was published only a century later in England.

The treatise is significant because of its scientific method of using both observational data (even though they were quite inaccurate) and mathematical theory, mainly trigonometry. In addition to the apparent or angular size of the Moon and Sun, Aristarchus measured the shadow of the Earth on the Moon during a lunar eclipse, treating the distances of the Moon and Sun as constant, as would most contemporary astronomers. The principal results were numerically precise (though observationally faulty) measurements of the distances and sizes of Sun and Moon and the Earth.

The figure here shows diagram illustrating proposition 13. From the bottom to the top, three circles represent the Sun, the Earth and the Moon during a total eclipse, with A, B and C standing for their respective centers; the text proceeds to derive precise ratios between their diameters and distances based on trigonometrical methods.

**Sources**

- J. L. Berggren, Nathan Sidoli, Aristarchus's On the Sizes and Distances of the Sun and the Moon: Greek and Arabic Texts, Archive for History of Exact Sciences, May 2007, Volume 61, Issue 3, pp 213-254
- Heath, Sir Thomas, Aristarchus of Samos, the ancient Copernicus; a history of Greek astronomy to Aristarchus, together with Aristarchus's Treatise on the sizes and distances of the sun and moon: a new Greek text with translation and notes. London: Oxford University Press, 1913, pp. 393-399
- Paul T Keyser and Georgia Irby-Massie (eds), The encyclopedia of ancient natural scientists : the Greek tradition and its many heirs, Milton Park, Abingdon, Oxon ; New York, NY : Routledge, 2008.
- Charles Coulston Gillispie; American Council of Learned Societies, Dictionary of scientific biography. New York C. Scribner 1970-1990, vol. 1, pp.246-48.
- George Sarton, Introduction to the history of science, Baltimore: Williams & Wilkins Co., 1927-1948, vol. 1, pp. 156-7.