This book provides a fascinating look at the night sky and the techniques that early civilizations, particularly Babylonian and Greek, used to model planetary motions. Although it assumes only high school mathematics (especially a solid foundation in geometry), the exposition can be dense at points, and students new to the subject should be forewarned that a good bit of thought and reflection will be required to comprehend several of the concepts. That having been said, Aaboe does a masterful job of covering a wide array of intriguing topics in a relatively short book, and any effort expended on reading it will be well rewarded.
A good example of the somewhat difficult, yet very worthwhile, content of this book is found in "Chapter 0: What to Know about Naked-Eye Astronomy". Because ancient peoples built their models on observations of the sky, the natural viewpoint for a discussion of their techniques is that of an observer on the earth. However, as Aaboe recognizes in the Preface, people today are often "ignorant of what you can expect to see when you look at the night sky with the naked eye," and so it is necessary to provide a primer on how heavenly bodies appear to move relative to the earth. Chapter 0 starts from scratch and develops the needed background in everything from celestial coordinate systems to the details of apparent planetary motion (appearance and disappearance from visibility, retrograde motion, etc.).
Although Chapter 0 is entirely self-contained, it may still be a challenging read for those not previously acquainted with such topics. Indeed, Aaboe proceeds in a wholly descriptive manner, intentionally avoiding any references to a heliocentric model of the solar system. He justifies this in the Preface, explaining that it would be even more difficult to do otherwise. However, for students familiar with the backdrop of Copernican theory (and unfamiliar with apparent motion of planets in the night sky), this purely descriptive crash course can be rather hard to internalize and digest. Despite this complaint, the chapter is manageable, with the proper investment of time and care, and careful study will yield a solid comprehension of how heavenly bodies appear to move through the sky.
After Chapter 0, Aaboe moves on to the main part of the book, explaining ancient methods for predicting and modeling celestial events. He begins Chapter 1 with a several page description of the archaeology and research that have allowed us to learn what we know today about Babylonian methods. Such historical interludes occur throughout and may seem unwanted digressions to some readers. If that is the case, these portions can easily be skimmed and focus can be concentrated primarily on the computations and models (though a certain amount of context is of course indispensable). However, if one has a taste for these topics, Aaboe's interweaving of historical and archaeological context is thoroughly enjoyable and enriching.
Historical development aside, the book of course focuses on descriptions of the predictive and modeling systems that were used in Babylonian and Greek civilizations. Aaboe explains how and why the systems worked (and how we learned about them and to whom we believe them to be attributable). His exposition is fascinating and very readable, though, once again, for those not accustomed to the basics of naked-eye astronomy, it can be a little rough going. The main difficulty is that without intuition for how heavenly bodies generally appear to move, it can be doubly hard to understand a system designed to predict exactly these motions. A lack of internalization of these concepts makes the reading at points somewhat dense, but, as is true throughout the book, the treatment is self-contained, and a bit of thought and reflection at the necessary points will resolve the difficulties (and lead to a much better understanding of observational astronomy in the process).
Most likely this book would not be used as the primary text for a course. It can be relatively dense and would probably serve better as a source for supplemental reading. In addition, it would probably be a great book for independent reading for a motivated student who has a strong grasp of geometry and an interest in observational astronomy and its history. In particular, talented students at the high school age and college students who are interested in these topics would likely find this book very enjoyable and enriching.
Overall, the book is fascinating to read for several reasons, including its observational astronomical viewpoint, its rich historical and cultural content, and, of course, its exposition and explanation of ancient techniques of celestial predictions and modeling. Potential readers, especially those unfamiliar with naked eye astronomy, must be warned, though, that the style can make it a bit challenging to internalize the necessary concepts. However, anyone with an interest in ancient astronomy will deem any effort expended on this book well spent.
Tom Brennan's primary mathematical interests include harmonic analysis, Fourier analysis and analytic number theory. He is currently working as an attorney at Cravath, Swaine & Moore, but he continues to pursue his mathematical research.
Chapter 0: What Every Young Person Ought To Know About Naked-Eye Astronomy; Chapter 1: Babylonian Arithmetical Astronomy; Chapter 2: Greek Geometrical Planetary Models; Chapter 3: Ptolymy's Cosmology; Chapter 4: Kepler Motion Viewed From Either Focus; Selected Bibliography