Mathematical Disquisitions: The Booklet of Theses Immortalized by Galileo by Christopher M. Graney (review)

In Australia we can, almost daily, watch the sun slowly trace a circular arc across the sky. So it is counterintuitive to think that it is the sun, and not the earth, that is the centre of our existence. Increasing, and increasingly accurate, astronomical observations, enhanced by the invention of the telescope, accelerated the acceptance of Copernicus’s description of the solar system over the more convoluted Ptolemaic systems of epicycles (circles on circles). In the early seventeenth century, in addition to pre-Copernican views that had the authority of the Bible to back them up, there were also many common-sense observations that militated against the view of Copernicus. It was not just the earth going round the sun but also the earth spinning on its axis that caused consternation, and disbelief.

Enter Locher, or should we say Christoph Scheiner, Locher’s Jesuit mentor, since there was, and remains, controversy over who exactly wrote this book (for convenience I shall attribute it to Locher below). The debate on authorship is something for elsewhere and has already been taken up by one reviewer. Whatever the case, the book was published forty years before Newton, and what a difference Newton’s theories would make! This volume shows the sorts of attitudes that people would have to grapple with until the works of Newton arrived and became widely understood. In particular, the complexities of gravitation had yet to be worked out. Here we see the ideas of a lover of astronomy, ideas that are very largely quite sensible and/or comprehensible, being put forward in 1614 in opposition to those of the Copernicans (Copernicus’s book was published in 1543).

Graney’s translation, which takes certain liberties I shall mention later, takes us deep into contemporary thought and, for a very large part, the thought is perfectly acceptable: Locher follows common sense. He seems even more sensible when you remember there is no understanding of action at a distance, which was a key to Newton’s ideas. The translation helps us to see how Locher (and many contemporaries) thought.

Today, it is hard for us to realize how relatively quickly the vision of the solar system and the heavens changed in the century after Copernicus published his scheme. The sizes of stars and their distances were a revelation, while the use of the telescope, invented in 1608, led to obvious questions that could not be answered in Locher’s time (Disquisition XLII, p. 98). The author is aware of this and accepts part of Copernicus, for example, the view that Mercury and Venus go round the sun, while also accepting Tycho Brahe’s view that five planets go round the sun (pp. 59–60), but he is looking, and waiting, for further clarification: as he says on p. 58, it is easy to criticize, hard to get things right.

This is unashamedly ‘a student-friendly translation’ (p. ix). Nevertheless, students of the history, or perhaps better, of the development, of science will find many fascinating insights. A few examples. Unlike many in the seventeenth century, Locher is careful to distinguish astronomy and astrology (and has no interest in the latter) (p. 16). The argument on p. 19 against infinite multitudes held sway until George Cantor in the nineteenth century! (There is a similar argument in Disquisition XIX, pp. 51–52.) On the other hand, he argues there can be no slowest speed (p. 24), that distances are infinitely divisible (p. 49, item 5) but infinitesimals are impossible (p. 21). More surprising, perhaps, is his argument (against Aristotle in particular) on p. 22 that the universe cannot have always existed but must have had a beginning, but then the Bible’s authority is supreme (p. 31). Further, Graney adds commendable notes: note 100, re p. 43, on centripetal force, is outstanding, as is Locher’s insight.

On the negative side, the...