Copernicus believed that his system actually accorded better than the older geocentric system with the way the universe ought to be. He believed he was describing the actual truths of an essentially mathematical universe. Heavenly motions must be perfect circles. In Copernicus’ time, all this reminds us, astronomy was still a branch of mathematics—in E. A. Burtt’s phrase “the geometry of the heavens.” Following Pythagorean and Neoplatonic doctrine, this carried implications too for mathematics itself, which, instead of being the deductive study of abstract constructs, purported to describe the
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