Reviewed by:

• Mathematical Disquisitions: The Booklet of Theses Immortalized by Galileo by Christopher M. Graney
• John N. Crossley

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 [End Page 212] 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...

审核人：

• 数学专题：克里斯托弗·M·格兰尼（Christopher M. Graney）的伽利略（Galileo）永垂不朽的论文手册
• 约翰·N·克罗斯利

在澳大利亚，几乎每天，我们都可以看着太阳慢慢在天空上划出一个圆弧。因此认为是太阳而不是地球是我们生存的中心是违反直觉的。望远镜的发明增强了越来越多，越来越准确的天文观测，从而加速了哥白尼关于太阳系的描述的接受，而不是更复杂的上轮式托勒密系统（圆圈）。在十七世纪初期，除了哥白尼时代以前的观点具有圣经的权威来支持它们之外，还有许多常识性的观点与哥白尼的观点背道而驰。不仅是地球绕着太阳转，而且地球在其轴上旋转也引起惊and和难以置信。

请进入Locher，或者我们应该说Locher的耶稣会士导师Christoph Scheiner，因为关于谁确切地写这本书一直存在并且仍然存在争议（为方便起见，我将其归因于下面的Locher）。关于作者身份的辩论在其他地方也有涉及，并且已经由一位审阅者进行了讨论。无论如何，这本书在牛顿之前出版了四十年，这对牛顿的理论有何影响！这本书显示了人们在牛顿的作品到来并被广泛理解之前必须应对的各种态度。特别是引力的复杂性尚未解决。在这里，我们看到了天文学爱好者的想法，这些想法在很大程度上非常明智和/或易于理解，

Graney的翻译具有一定的自由性，我将在后面提到，它带我们深入了解当代思想，并且在很大程度上，该思想是完全可以接受的：Locher遵循常识。当您记得远距离了解动作时，他显得更加明智，这是牛顿思想的关键。翻译帮助我们了解了Locher（以及许多同时代人）的想法。

今天，我们很难意识到哥白尼发表了他的计划后，太阳系和天体的视野在一个世纪中相对迅速地发生了变化。恒星的大小和它们的距离是一个启示，而1608年发明的望远镜的使用导致了明显的问题，这些问题在Locher的时代无法回答（Disquisition XLII，第98页）。作者意识到了这一点[第212页]，并接受了哥白尼的一部分，例如，水星和金星绕着太阳转的观点，同时也接受了第谷·布拉赫关于五颗行星绕着太阳转的观点（第59–60页） ），但他正在寻找并等待进一步的澄清：正如他在p。上所说。58，很容易受到批评，很难把事情弄对。

这无疑是“对学生友好的翻译”（第ix页）。尽管如此，学习科学的历史，或者也许是发展的更好的学生，将会发现许多有趣的见解。一些例子。与17世纪的许多人不同，Locher小心翼翼地区分天文学和占星术（对后者没有兴趣）（第16页）。关于p的论点。19世纪反对无数群众的统治一直持续到19世纪的乔治·坎托！（《Disquisition XIX》中有类似的论点，第51-52页。）另一方面，他认为不可能有最慢的速度（第24页），距离是无限可分的（第49页，第5项），但是不可能有最小的距离（第21页）。也许更令人惊讶的是他关于p的论点（尤其是针对亚里斯多德的论点）。22宇宙不可能永远存在，而必须有一个开始，但是圣经的权威才是至高无上的（第31页）。此外，Graney还添加了值得称赞的注释：注释100，第13页。43，向心力方面非常出色，Locher的见识也很出色。

不利的一面是...