Almagest

The Almagest is a book about the motion of the planets and the position of the stars written about AD 150 by Ptolemy (Claudius Ptolemaeus of Alexandria). It was the main astronomical manual for Islamic and European astronomers until the days of Kepler and Galileo around the turn of the 16th to the 17th century . Its original name was Syntaxis Mathematica (Mathematical Treatment); the work was referred to by Muslim scholars as Megale Syntaxis, Migisti, and finally Almagest. The first translation from the Greek was ordered by Harun al-Rashid (ca. 800), but this translation was lost. Via a translation from the Greek into Syrian it was translated into Arabic about 827 with the title Kitâb-al-Miğistî (the largest book); copies of this version are preserved until the present day. In 1175 Gerard of Cremona translated the book from Arabic into Latin and gave it the title Almagestum. Subsequently, the Greek text was recovered and circulated widely in Europe, although Cremona's translation continued to be more influential.

The Almagest is divided into 13 thoroughly mathematical books and astronomy and trigonometry are commingled. Book 1 is largely on spherical trigonometry and contains a trigonometry table that allowed Ptolemy in subsequent books to explain and predict the motions of the Sun, Moon, planets, and stars. In addition, Book 1 gives arguments for a geocentric, spherical cosmos. Book 2 uses the mathematics explained in Book 1 to discuss cartography and astronomical phenomena (such as the length of the longest day) characteristic of various localities. Book 3 deals with the motion of the Sun and how to predict its position in the zodiac at any given time, and Books 4 and 5 treat the more difficult problem of the Moon's motion. Book 5 also describes the construction of instruments to aid in these investigations. The theory developed to this point is applied to solar and lunar eclipses in Book 6.

Books 7 and 8 mainly concern the fixed stars, giving ecliptic coordinates and magnitudes for 1,022 stars. This star catalog relies heavily on that of Hipparchus (190 BC – ca. 120 BC), and in the majority of cases Ptolemy simply converted Hipparchus's description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. These two books also discuss the construction of a star globe that adjusts for precession. The remaining five books, the most original, set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time.

A predictive geocentric model for the planetary motion is by necessity very complicated, predictions would fail completely if the model would describe the planets as simply circling the Earth at a uniform speed. As was observed in Mesopotamia as early as 1900 BC, the planets do not move in the same direction at a uniform rate. Normally, the planets move eastward through the stellar constellation, but the normal motion of all planets, except the Sun and the Moon, is occasionally interrupted by brief intervals of westward (retrograde) motion.

To solve this problem two Greek astronomers and mathematicians, Apollonius (ca. 262 BC – ca. 190 BC) and Hipparchus assumed that the motion of the planets is on small circles, epicycles, which rotate uniformly about a central point. The central points, in turn, move on large circles, the deferents, that have the center of the earth as their midpoint. Ptolemy described this system in the Almagest and because his work replaced that of his predecessors and because all his successors modeled their work upon his, this theory is known as Ptolemaic astronomy.

References

• T. S. Kuhn, The Copernican Revolution, Harvard University Press (1957)
• M. Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press (1972).