# Ptolemy (Claudius Ptolemaeus)

# PTOLEMY (CLAUDIUS PTOLEMAEUS)

Astronomer, mathematician, and geographer; author of the famous *Almagest* (Syntaxis mathematica), the standard work on astronomy from the 2d century until the 16th century. Ptolemy's biographical data are uncertain, except the fact that he lived and worked in Alexandria, Egypt. According to later sources, he was born probably at the end of the 1st century and died during the reign of Marcus Aurelius, i.e., between 161 and 180. Of Ptolemy's major writings mentioned here, the *Almagest* was by far his most influential work. It consists of 13 books that contain the main tenets of geocentric cosmology, and it gives a systematic summary of the achievements of Greek astronomy up to Ptolemy's time, including certain results of his own investigations. The first two books give mainly the geometrical theorems forming the basis of his mathematical astronomy and the basic assumptions of the geocentric hypothesis, i.e., the spherical shape of the earth and its state of rest in the center of the finite universe bounded by the sphere of the fixed stars. The third book deals with the movement of the sun, and the fourth and fifth with that of the moon. In these books, as well as in the other parts of his work, Ptolemy, in order to construct a consistent model accounting for the apparent motions of the celestial bodies, makes use of the theory of epicycles and eccentric circles. An epicycle is a small circle along whose circumference the star is carried while the center of the epicycle moves along the circumference of a larger circle round the earth. The center of this circle either coincides with that of the earth or, in the case of eccentric motion, is situated at some distance from the

earth. The next two books deal with the fixed stars and contain also a catalogue of more than a thousand stars with their positions and magnitudes. The last five books expound the theory of the five planets—the two inner planets Mercury and Venus, and the three outer ones Mars, Jupiter, and Saturn. Ptolemy also confirms Hipparchus's discovery of the precession of the equinoxes, giving, however, a slightly less accurate value than Hipparchus.

The *Almagest* was held in highest esteem during late antiquity and the Middle Ages until copernicus's *De revolutionibus* (1543). It was translated into Arabic and commented on by several Islamic astronomers from the 9th century on; and it was also the principal astronomic source book in the Western scholastic world, as can be seen by the numerous quotations in, e.g., thomas aquinas, john de sacrobosco, and roger bacon, and by various commentaries, for example, the *Epitome* (1496) of Regiomontanus.

In another astronomical work, "Hypotheses of the Planets," Ptolemy gives several improvements on the results of the *Almagest* and polemizes against attempts to return to the Aristotelian model of a single set of homocentric spheres; he reveals himself as a Platonist who believes that each planet is driven by a vital force emanating from its soul. His astrological work, *Tetrabiblos,* was one of the most famous of its kind during the Middle Ages. He is also the author of a geography, containing tables of the latitudes and longitudes of the main places of the inhabited world known at his time. His *Harmonics* is the last great systematic work of antiquity on musical harmony containing a theory of musical intervals and scales. In his *Optics* (extant only in a Latin translation), Ptolemy deduces mathematically, and verifies experimentally, several optical laws, e.g., the laws of reflection and refraction of light.

**Bibliography:** f. lammert, *Paulys Realenzyklopädie der klassischen Altertumswissenschaft,* ed. g. wissowa et al. (Stuttgart) 23.2 (1959) 1788–1859. j. l. e. dreyer, *A History of Astronomy from Thales to Kepler* (2d ed. Dover pa; New York 1953).

[s. sambursky]

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# Ptolemy (Claudius Ptolemaeus)

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