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Ptolemy

PTOLEMY

PTOLEMY (c. 100170), Alexandrian astronomer, geographer, and mathematician. The last of the great astronomers of antiquity, Claudius Ptolemaeus (Ptolemy) compiled works that remained the standard astronomical textbooks until the Copernican revolution in astronomy in the sixteenth century. Almost nothing is known of the details of Ptolemy's life. His Hē mathēmatikē syntaxis (Mathematical Compilation) was written about 150 ce; the title by which this work is better known, the Almagest, is a medieval Latin derivation from an Arabic corruption of the Greek title under which the work came to be known in later antiquity, Ho megale syntaxis (The Great Compilation). The Almagest sums up the mathematical astronomy of the ancient world; it became the basis of Latin and Arabic astronomy.

Ptolemy's work follows in the Greek philosophical tradition, in which the sacred nature of the heavens is expressed by the incorruptibility of the celestial realm, the divinity of the heavenly bodies, and the perfection of their motions (uniformly circular, because the circle was considered the most perfect of figures and motion around a circle was eternal). The fact that the motions of the sun, moon, and planets are evidently not circular provided a formidable challenge to thinkers within this tradition; especially challenging were the planets' periodic reverses, or retrograde motions. Drawing upon the work of his Greek predecessors, Ptolemy was able to "save the appearances" of celestial motion by using circles in his geometry of the heavens. By employing Greek and Babylonian observational data, he was able to adjust his theoretical solutions to observed celestial positions and to predict them with a precision unmatched until the work of Johannes Kepler in the seventeenth century. The geometrical devices that Ptolemy usedthe eccentric, the epicycle, and the equantwere never thought to possess a physical reality, as he makes clear in the preface to the Almagest. But it was just for this reason that astronomy had a religious value. Astronomy developed the correspondence between the order of divine celestial things and the order of mathematical propositions.

Its science Aristotelian and its format Euclidean, the Almagest describes a stationary, spherical earth surrounded by concentric spheres carrying the sun, moon, planets, and stars. Motion is described geometrically by arrangements of several kinds of circles: (1) eccentrics, which are not centered on the earth; (2) epicycles, which orbit other circles that are centered on the earth; and (3) equants, in which the motion of the body on the circle is variable in relation to the center of the circle but uniform in relation to some noncentral point within the circle. The Almagest includes a star catalog and a table of observations later revised and expanded in Ptolemy's Prokheiroi kanones (Handy Tables).

Ptolemy's work on geometry, the Planisphaerium, of which only a distorted Greek title survives, Exaplōsis epiphaneias sphairas (Unfolding of a Spherical Surface), details the theory of the astrolabe, the chief astronomical instrument of antiquity and the Middle Ages. Ptolemy's Hypotheseis tōn planōmenon (Planetary Hypotheses) suggests that the spheres of the planets nestle within one another. The astrological complement to Ptolemy's astronomy is his Tetrabiblios. Ptolemy also wrote works on optics and music, as well as a Geography (Gr., Geographikē hyphēgēsis ), which gives directions on how to map the spherical earth on a flat surface and provides tables of longitude and latitude for generating maps. Because of a lack of precise longitude, Ptolemy's map of the known world was severely distorted, even where descriptive information abounded.

Ptolemy's works present an interrelated whole dominated by the successful application of mathematics to complex technical problems. For example, the determination of terrestrial latitude in the Geography is achieved through calculations based on astronomy. This in turn specifies the astrological character of the inhabitants of various parts of the earth. His cartography employs the mathematics of his optics and of the Planisphaerium. Ptolemy's authority in applied mathematics was undisputed for more than a millennium.

Ptolemy went to great lengths in his texts to provide procedures whereby his technical achievements could be reproduced. He thus laid the foundation for other civilizations to assimilate his work, become expert at it, and progress beyond it. Such cultural innovation is invariably associated with religious creativity, though not in a predictable fashion. For example, though Ptolemy's astronomy was used to corroborate the religious view that the earth was at the center of the universe, no one was ever convinced of this view because of the astronomy of eccentrics, epicycles, and equants. However, becoming technically expert in these devices did allow the accurate prediction of religious feasts. Although the Jewish philosopher Maimonides (Mosheh ben Maimon, 1135/81204) criticized Ptolemy, he did incorporate some of the astronomer's techniques for determining the date of Passover.

The translation of Ptolemy's work into Arabic in the ninth century was a catalyst for the flowering of Islamic culture. Refined astronomical tables were created, such as the Toledan Tables of al-Zarālla (c. 1080). This served as the basis for the Alfonsine Tables, which was compiled circa 1252 by some fifty astronomers assembled for that purpose by Alfonso X of Castile, and which predicted the dates of the Easter moon. New theories of optics were proposed by the Arab heritors of Ptolemy; new geographical values were established. The Islamic appropriation of Hellenistic natural philosophy inspired the Christian Middle Ages. A desire for the Almagest brought the greatest of medieval translators of Arabic, Gerard of Cremona (11141187), to Toledo. The merits of a true physical astronomy and of "saving the appearances" by geometry were argued in medieval universities, where Ptolemaic astronomy became part of the curriculum. Although the celestial bodies were no longer thought of as gods by medieval Europeans, their movement was believed to exhibit God's will (and their order his wisdom), and hence Ptolemy's astronomy continued to provide for the intellectual contemplation of the divine celestial order. Dante drew upon Ptolemy for the cosmology of his Commedia (1321).

When the Geography, with its techniques of projection, was first translated into Latin in fifteenth-century Florence, it contributed to the rediscovery of linear perspective and to the development of cartography during the voyages of exploration. Because the distortions of Ptolemy's map of the globe bore the prestige of his mathematics, Columbus and others were convinced that it would be quite easy to reach Asia by sailing west. When Renaissance astronomers finally became truly competent in Ptolemy's astronomy, their dissatisfaction with his accuracy and methods culminated in the Copernican revolution that established modern cosmology. The Jesuit mission to China in the seventeenth century used the predictive precision of Ptolemaic astronomy to enhance the value of their religious teaching at the emperor's court. Thus it was ironic that Ptolemy's science and technology were helping to introduce Christianity to the Far East at the same time that Copernican astronomy was making Ptolemaic astronomy obsolete in the West. And well after Ptolemy's cosmos was superseded by the physical universe as defined by Copernicus, Newton, and others, the Tetrabiblios remained an astrological standard. It was translated into English and published in 1701, the second edition in 1786.

Bibliography

A translation of Ptolemy's Almagest was done by R. Catesby Taliaferro in Ptolemy, Copernicus, Kepler, vol. 16 of the "Great Books of the Western World," edited by Robert Maynard Hutchins (Chicago, 1952). The inclusion of the De revolutionibus by Copernicus in the same text facilitates the comparison of these two all-important works in the history of astronomy. A scrupulous new translation of the Almagest is provided in G. J. Toomer's Ptolemy's Almagest (London, 1984). Frank E. Robbins translated the Tetrabiblios for the "Loeb Classical Library" (Cambridge, Mass., 1940). An English translation of the Latin Geographia is found in Edward Luther Stevenson's Geography of Claudius Ptolemy (New York, 1933). An exhaustive technical account of the Almagest and its historical antecedents is provided in Otto Neugebauer's A History of Ancient Mathematical Astronomy, vol. 1 (New York, 1975). G. J. Toomer, in his article "Ptolemy, Claudius," in the Dictionary of Scientific Biography (New York, 19701980), gives a concise description of Ptolemy's science with an up-to-date bibliography. A very readable discussion of the problems posed by observational astronomy and the Greek solutions to them, as well as of their cultural context, is provided in Thomas Kuhn's The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, rev. ed. (New York, 1959).

Michael A. Kerze (1987)

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