In this work, Tycho explained two problems posed for Copernicus by the absence of stellar parallax: 1. Due to the annual movement of the Earth around the Sun, one would expect to see stars appear to shift in position. This parallax evaded detection, even at Uraniborg. 2. Tycho reported precise measurements of the apparent widths of stars, which allowed him to quantify how large they must be as a function of their distance. If stars were far enough away to explain the absence of parallax, then the radius of even an ordinary star would have to be no less than the distance between the Earth and the Sun. In other words, if the Copernican system were true, then each star must be an incomparably immense body, altogether different than the Sun, breaking all analogy and proportion with the ordinary course of nature.