The Almagest

The Almagest, like Euclid's Elements, is so masterly and comprehensive a treatment of its subject that it eclipsed nearly all of its predecessors. In a massive series of thirteen books, Ptolemy shows how every detail of the motions of the sun, moon, planets, and stars can be expressed through geometrical models that can be used to compute celestial positions with remarkable accuracy. In the course of this impressive achievement, he develops the foundations of trigonometry, devises and describes astronomical instruments, shows how select observations may be used to determine the parameters of planetary models, and invents a remarkable method of iterative approximations to solve mathematical problems. His tables contain the earliest surviving examples of the use of zero as an independent number rather than as a place-holder (as in Babylonian mathematics). The present selection covers all the essential features of Ptolemy's treatment of the heavens, omitting only more difficult and abstruse matters such as the moon's motion and the calculation of eclipses. In the interest of conciseness, development of planetary theories is restricted to two planets, one inferior (Venus) and one superior (Mars). Nevertheless, Ptolemy's tables for computing positions for all five planets are included, together with instructions for their use. Ptolemy's text is accompanied by extensive notes and introductions that are aimed at making the book accessible to students encountering Ptolemy for the first time. The Preliminaries describe the basic phenomena of the heavens, such as the motions of the fixed stars and the observations that allow the sun's path in the heavens to be discerned. Brief accounts of astronomical instruments and of sexagesimal computations follow, along with necessary terminology and instructions for using Ptolemy's chronology. As the work progresses, many of Ptolemy's Books are introduced with their own Preliminaries, supplying readers with the information necessary to understand and work with the matters specific to those sections. Appendices provide a summary of trigonometry, showing how Ptolemy's tables relate to modern mathematical functions; a day calculator; and other aids. Book jacket.