PTOLEMY

PTOLEMY

PTOLEMY (about ad 100-70), astronomer and mathematician, whose synthesis of the geocentric theory that the earth is the center of the universe dominated astronomical thought until the 17th century. He is also remembered for his contributions to the fields of mathematics, optics, and geography. Ptolemy was probably born in Greece, but his actual name, Claudius Ptolemaeus, reflects all that is really known of him: "Ptolemaeus" indicates that he was a resident of Egypt, and "Claudius" signifies Roman citizenship. In fact, ancient sources report that he lived and worked in Alexandria, Egypt, for the greater part of his life.

The Almagest

Ptolemy's earliest and most famous treatise, originally written in Greek, was translated into Arabic as al-Majisti (Great Work). In Europe, medieval Latin translations reproduced the title as Almagesti, and it has since become known simply as the Almagest. In this work, Ptolemy proposed a geometric theory to account mathematically for the apparent motions and positions of the planets, sun, and moon against the background of fixed stars. He began by accepting the generally held theory that the earth did not move but was at the center of the system. The planets and stars, moving eternally, were considered (for philosophical reasons) to move in perfectly circular orbits. He then elaborated on the theory in an attempt to account for such astronomical puzzles as the periodically retrograde (backward) motions of the planets and periodic variations in size or brightness of the moon and planets.

Ptolemy's abilities as an observational astronomer have been questioned, but his complex system seemed to account for celestial motions. Anomalies in a planet's motion were accounted for by the use of the epicycle, a circle centered on the circumference of a larger circle called the deferent. The planets, sun, and moon were regarded as located on the rims of rotating epicycles, and the earth itself was placed eccentrically to the center of the deferent. By adjusting the radii of the circles and their speeds of rotation, Ptolemy made the system fit most of the observed facts.

Ptolemy also had to introduce, however, another mathematical device known as the equant: an imaginary point halfway between the center of the deferent and the eccentric point representing the earth's position. Rather than maintain the constant, uniform motion of all circles in the system (deferents and epicycles), as had been required in all previous models of ancient astronomy, he assumed that the deferent moved uniformly with respect to the equant. (Thus the deferent's motion would not be uniform with respect to its own center.) This major departure from traditional assumptions was one reason the Polish astronomer Nicolaus Copernicus rejected Ptolemy's system in the 16th century and developed his own heliocentric world view of a sun-centered system. Even so, Copernicus retained an elaborate system of epicycles.

Other Works

Ptolemy also contributed substantially to mathematics by advancing the study of trigonometry, and he applied his theories to the construction of astrolabes and sundials. In his Tetrabiblos, he applied astronomy to astrology and the casting of horoscopes. Of considerable historical importance, despite considerable factual inaccuracies, is Ptolem's Geography, which charts the then-known world. This work, which employs a system of longitude and latitude, influenced mapmakers of the Renaissance, but it suffered from a lack of reliable information. Ptolemy also devoted a treatise, Harmonica, to music theory, and in Optics he explored the properties of light, especially refraction and reflection. This latter work, known only from an Arabic version, is of special interest for its combination of experiment and the construction of apparatus to promote the study of light and to develop a mathematical theory of its properties.