Two biographies of Vera Rubin

paper instrument for the motion of the Moon from Reinhold (1542). The book concludes with exhaustive lists of known manuscripts, known printed editions, and commentaries. There is a bibliography of primary and secondary sources, an index of names, and a usefully detailed table of contents. In this book Malpangotto has little to say about the equant, the announced motivation for Copernicus’s reform of astronomy. But elsewhere she has traced the problem from Peurbach to Copernicus through the commentary of Brudzewo (see esp. Archive for the History of Exact Science, 70 (2016): 36–411 and cf. Barker, this journal, 70 (2013): 125–48). Beyond context, then, Peurbach’s book and its commentaries contributed to astronomy in ways that have not yet been sufficiently studied or appreciated. Malpangotto argues vigorously that theorica orbs were accepted as real physical objects. This has consequences for both the content and the methods of astronomy. First we need to acknowledge that, for most astronomers from Peurbach through the time of Copernicus and until the general abandonment of celestial orbs following Tycho Brahe, the largest physical objects in the universe were the material orbs described in the Theoricae novae. Second, at the level of method, we need to recognize that, from at least the time of Peurbach, the principle that astronomical theories ought to correspond to the real world was adopted by astronomers in the Christian West (both ideas were already universally accepted in the Islamic East). These two changes are quite sufficient to support Malpangotto’s claim that the appearance of Peurbach’s book created a revolution in 15th-century astronomy that prepared the way for Copernicus’s 16th-century revolution.