Aristarchus (1), of Samos, Greek Astronomer, Mathematician, 3Rd Century BCE

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Aristarchus (1), of Samos, Greek astronomer, mathematician, 3rd century BCE Nathan Camillo Sidoli https://doi.org/10.1093/acrefore/9780199381135.013.737 Published online: 22 December 2015 This version: 28 June 2021

Subjects: Science, Technology, and Medicine

Updated in this version Article rewritten to reflect current scholarship.

Aristarchus, often called the “mathematician” in our sources, is dated through a summer solstice observation of 280 BCE attributed to him by Ptolemy (Alm. 3.1). He is said to have been a student of Straton of Lampsacus, who succeeded Theophrastus as the head of the Peripatetic school in 288/287 BCE (Stob. Ecl. 1.16.1); and he is most famous for having advanced the heliocentric hypothesis, although his only surviving work in mathematical astronomy assumes a geocentric cosmos.

According to Archimedes, Aristarchus hypothesized that the fixed stars and sun are unmoved, while the earth is carried around the sun on a circle, and that the sphere of the fixed stars is so large that the ratio of the circle about which the earth moves to the distance of the stars is that which a centre has to the surface of a sphere (Sand Reckoner, 4–5). We do not know how Aristarchus understood or utilized this hypothesis, which Archimedes claims is strictly impossible, but Archimedes himself reinterprets it to mean that the ratio of the diameter of the earth to the diameter of the earth’s orbit is the same as that of the diameter of the earth’s orbit to the diameter of the cosmos. Furthermore, Plutarch says that Aristarchus supposed that the earth rotates about its own axis (De fac. 923A, Quaest. Plat. 1006C). Philolaus of Croton and Heraclides Ponticus had previously put forward various claims about the mobility of the earth, but with the exception of Seleucus of Seleucia, the Chaldaean, there is little indication that anyone further developed these ideas after Aristarchus. In fact, Archimedes himself probably had no commitment to these ideas, because he puts them forward, not to advance any serious work in astronomy, but to have the hypothesis of a very large cosmos, which he can fill with sand in order to demonstrate a new system for working with large numbers that he had invented. On the other hand, the views of Aristarchus’s contemporary, Cleanthes of Assos, the head of the Stoic school, who wrote a treatise called Against Aristarchus and asserted that charges of impiety should be brought against him (Plut. De fac. 923A, Diog. Laert. 7.125), were probably also not held by many people.

Aristarchus’s only surviving work, On the Sizes and Distances of the Sun and the Moon, was an influential piece of mathematical reasoning that was included in collections of classic texts in the mathematical sciences in the late ancient and medieval periods. On Sizes assumes a geocentric configuration of the solar and lunar orbits, as shown by the description of the celestial bodies in On Sizes 6. The treatise begins with a series of six hypotheses, some of

Page 1 of 3 Printed from Oxford Classical Dictionary. Under the terms of the licence agreement, an individual user may print out a single article for personal use (for details see Privacy Policy and Legal Notice). Subscriber: OUP-Reference Gratis Access; date: 03 July 2021 which are purely geometrical, while others include numerical information and assert some ostensibly observational phenomena, although it is not certain what role observation actually played in their development. The treatise then proceeds through eighteen well-structured propositions, using elementary geometry, ratio manipulations, and proto-trignonometric lemmas asserting ratio inequalities between angles and sides in a right-angled triangle (see trigonometry). Through these means, Aristarchus shows that, among other things, the distance of the sun from the earth is between 18 and 20 times the distance of the moon from the earth (On Sizes 7), the ratio of the volume of the sun to that of the moon is between 5,832:1 and 8,000:1 (On Sizes 10), the ratio of the diameter of the sun to that of the earth is between 19:3 and 42:6 (On Sizes 15), the ratio of the volume of the sun to that of the earth is between 6,859:27 and 79,507:216 (On Sizes 16), the ratio of the diameter of the earth to that of the moon is between 108:43 and 60:19 (On Sizes 17), and the ratio of the volume of the earth to that of the moon is between 1,259,712:79,507 and 216,000:6,859 (On Sizes 18). (In Greek astronomical texts following Aristarchus it is also common to find celestial sizes and distances expressed as ratios.) The large discrepancies between these results and more accurate values are mostly due to certain geometric assumptions made in establishing the bounds, and to On Sizes Hypothesis 4, which asserts that the angular separation between the sun and the moon at half moon is ⅟30 of a right angle less than a right angle (= 87°). The numerical results that are derived are quite sensitive to this angle. On the other hand, On

Sizes Hypothesis 6, which states that the moon subtends ⅟15 of a zodiacal sign (= 2°), has a relatively small effect on the resulting numerical ratios. Hence, even if Aristarchus had replaced this by the much more accurate value of ⅟720 of the circle of the zodiac (= ½°), which Archimedes tells us that Aristarchus had elsewhere used (Archim., Sand Reckoner, 4), it would have made little difference in the final numbers. In the 4th century BCE, Pappus compared Aristarchus’s approach to this subject with Ptolemy’s in the Almagest, and provided some lemmas of use in reading On Sizes (Pappus, Collection 6.37–40).

Aristarchus is also associated with other work in the astral sciences. Vitruvius attributes to him a discussion of the causes of the phases of the moon as well as the invention of two types of sundial, hemispherical and flat-disc (De arch. 9.2.3–4, 9.8.1). Censorinus credits Aristarchus with a lunar and solar eclipse cycle that was a modification of Callippus’s cycle (DN 19.2), and he is reported to have written about the views of Thales on solar eclipses and perhaps of Heraclitus on the lunar cycle (POxy. 3710).

Bibliography

Berggren, J. Lennart, and Nathan Camillo Sidoli. “Aristarchus’s On the Sizes and Distances of the Sun and the Moon: Greek and Arabic texts.” Archive for History of Exact Sciences 61 (2007): 213–254.

Bowen, Alan C., and Bernard R. Goldstein. “Aristarchus, Thales, and Heraclitus on Solar Eclipses: An Astronomical Commentary on P. Oxy. 53.3710 Cols. 2.33–3.19.” Physics 31 (1994): 689–729.

Carman, Christián. “Two problems in Aristarchus’s Treatise On the Sizes and Distances of the Sun and the Moon.” Archive for History of Exact Sciences 68 (2014): 35–65.

Evans, James. The History and Practice of Ancient Astronomy. Oxford: Oxford University Press, 1998.

Page 2 of 3 Printed from Oxford Classical Dictionary. Under the terms of the licence agreement, an individual user may print out a single article for personal use (for details see Privacy Policy and Legal Notice). Subscriber: OUP-Reference Gratis Access; date: 03 July 2021 Heath, Thomas Little. Aristarchus of Samos: The Ancient Copernicus. Oxford: Clarendon Press, 1913.

Neugebauer, Otto. A History of Ancient Mathematical Astronomy. New York: Springer, 1975.

Noack, Beate. Aristarch von Samos: Untersuchungen zur Überlieferungsgeschichte der Schrift περὶ μεγεθῶν καὶ ἀποστημάτων ἡλίου καὶ σελήνης. Wiesbaden, Germany: Ludwig Reichert Verlag, 1992.

Wall, Byron Emerson. “Anatomy of a Precursor: The Historiography of Aristarchos of Samos.” Studies in History and Philosophy of Science 6 (1975): 201–228.

astronomical instruments

astronomy

Philolaus

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