This work of Johannes Kepler (whose title in English is *A New Astronomy*) introduces the first two laws that bear his name: the orbit of each planet is an ellipse with the sun at one focus, and planets sweep out equal areas of the ellipse in equal times. This was an amazing achievement. Universal gravitation was still unknown and his data consisted almost exclusively of Tycho Brahe’s observations of Mars. Kepler describes his struggles here as “warfare with Mars”.

Kepler’s writings are not well known. He wrote in Latin for technical specialists. By contrast, his contemporary Galileo wrote in the vernacular for a wider audience, so his work is much better known. It has taken a long time to bring Kepler’s work into English. The current book does this in quite an elegant way.

The book started out with the modest title of “Commentaries on Mars”. According to historical evidence, Kepler had completed most of the book before he hit on the idea of ellipses. It was then that the more subdued title became (not unjustly) the more grandiose one. Kepler had to go back and stitch his new ideas into the text, and he did so imperfectly.

Kepler uses all the rhetorical tools at his disposal to persuade the reader, step-by-step, that his approach is correct. He contends at every stage with the previous work of Ptolemy, Copernicus and Brahe. He regularly formulates proofs relating to the geometry of a planetary orbit according to each of their models. He does this to show their geometric equivalence, and thus that geometry itself cannot determine which one is correct.

Kepler was determined to base his work on physical principles and not on some predetermined geometrical hypotheses. Yet his physics was often wrong. He thought that the sun exerted a magnetic influence and interacted with the magnetic properties of the planets. He largely based his arguments on data and calculation, but the data too were imperfect.

Kepler’s struggles were intense. Again and again he calculates and re-calculates approximations for orbits of Mars, but he’s not satisfied with complex orbits that almost fit the data. He believes that the sun powers the planets’ motion, and argues that the power diminishes with distance from the sun. Verifying that would demand a great deal of calculation, so he makes a critical guess that is consistent with this: planets sweep out equal areas in equal time. He also argues that for this to be true, that orbits must be roughly oval. After more than forty failed attempts he gets to the notion of the ellipse, an idea he had rejected earlier because he thought it was too simple and would not have been overlooked by others.

It was quite an extraordinary piece of work. He lets us see his frustration, his aggravation at the huge number of false starts, and his sense of humor. At one point he writes, “… another hypothesis goes up in smoke”. As we read along, we can often imagine Kepler muttering to himself.

Usually a translator’s work stays well in the background unless something about it is bad. In this book the translation is remarkable. Kepler evidently wrote in a hurry. His style is not notable for its clarity and is further complicated both by the syntactic flexibility of Latin and his curious puns and allusions. The translator (William Donahue) built on earlier translations done in the 1960s at Harvard and produced a finished marvel. He was incredibly thorough. This is what he says about dealing with Kepler’s mathematical arguments: “… to test my comprehension, I repeated every computation in the book. Although this may seem an extreme measure, I have time and again found this precaution justified, both in fitting the translation to the argument and in gaining a perspective on the whole that could not be acquired any other way.”

As a gift to the reader, throughout the main text the translator unwraps Kepler’s convoluted syntax and breaks up his very long sentences into shorter ones. He does retain Kepler’s style for the Dedication to his sponsor, Rudolph II — perhaps just so readers can see what they’re missing in the rest of the book.

This is not bedtime reading. It may be of most interest now to historians, but it is surely worth dipping into for anyone interested in Kepler and his work. The book itself is physically attractive, similar in size to the original 1609 edition and retaining Kepler’s original marginal notes and full-scale diagrams.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.