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A Survey of the Almagest

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Ptolemy's Almagest is one of the great books of mathematics, one of the best examples of effective mathematical modeling. Ptolemy sets out to create a mathematical description of the planets and their motions. Based on vast amounts of empirical data, Eucldean geometry, and trigonometry, he produces a model that allows him to predict the future motions of the planets with a fair amount of accuracy.

Of course, today Ptolemy is mostly known as the one who established a geocentric model of the universe. In this, he is the victim of his success: precisely because his model is so good at predicting planetary motion, it was easy to conclude that the model was the reality. Since today everyone knows that the Earth is not at the center of the universe, Ptolemy was wrong. Similarly, Ptolemy argued that it was impossible for the Earth to be rotating quickly enough to account for the daily rotation of the heavens. We all know this was a mistake, though many of my students find it hard to figure out why Ptolemy's argument against the Earth's motion is wrong.

Of course, most of the people who talk about the Almagest have never read it, even though there exists an excellent English translation by G. J. Toomer. After all, the Almagest is a notoriously difficult book. Already in late antiquity there were several commentaries that stepped the student through Ptolemy's arguments. Modern readers need a guide as well. Olaf Pederson's Survey, first published in 1974 (so ten years before Toomer's translation), is precisely such a guide. It has served many readers since 1974; in fact, in his (new) introduction Alexander Jones describes it as "the first book one puts in the hands of a student approaching the Almagest."

Besides writing an introduction for the new edition, Jones has added extensive annotations. Presumably in order to keep the production costs down, these have been added in the back of the book. So the core of this book is a photographic reproduction of Pedersen's text. Black bars in the margins indicate sections where new scholarship requires some correction and/or addition be made, and the corresponding notes need to be looked for in the added pages at the end. One must, then, read with a finger in each part, flipping back and forth. Not ideal, but an acceptable compromise.

Pedersen locates the sections he is discussing by citing pages in Heiberg's Greek edition; Toomer's translation gives these in the margin, making it easy to use the two books together, which is certainly what any serious student must do. Toomer refers frequently to Pedersen, and of course Jones's notes refer frequently to Toomer.

Jones may be a little too optimistic when he says that modern students "no longer expect to be led by the hand"; reading Ptolemy, even with Pedersen's help, will be hard work. But reading it without such help would be almost impossible.


G. J. Toomer, Ptolemy's Almagest. Princeton University Press, 1998. (Originally published by Duckworth, 1984)


Fernando Q. Gouvêa is Cartar Professor of Mathematics at Colby College in Waterville, ME. He loves reading old books.

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Monday, December 6, 2010
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Olaf Pedersen
Sources and Studies in the History of Mathematics and Physical Sciences
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Fernando Q. Gouvêa
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- Forward to the revised edition.- Preface.- The almagest through the ages.- Physics and philosophy in the almagest.- Ptolemy as a mathematician.- Spherical astronomy in the almagest.- The motion of the sun.- The theories of the moon.- Parallaxes and eclipses.- The fixed stars.- The superior planets.- The inferior planets.- Retrograde motions and maximum elongations.- Latitudes and visibility periods.- Epilogue-the other ptolemy.- Apendix A: dated observations.- Appendix B: numerical parameters.- Bibliography.- Index of names.- Index of subjects.- Supplementary notes.- Supplementary bibliography.

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Wednesday, May 4, 2011