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Rh with regard to the ecliptic and the equator are computed from its distance from the other stars in Cassiopea and the places of these stars as observed at Hveen. Seven different combinations give results of which the extremes differ only about half a minute. Tycho also gives the places of the twelve comparison stars according to Alphonso and Copernicus (i.e., Ptolemy), which differ in many cases upwards of a degree from his own. He then turns in the sixth chapter to the question as to where the star was situated in space, and proves in four ways that it was far beyond the planets, "in the eighth sphere." First, the shape, light, continual twinkling, immovability, daily revolution like the fixed stars, and its having lasted more than a year, prove that it was not a comet. Secondly, it had no parallax, as the distance from the pole and from neighbouring stars remained unaltered during the daily revolution, while the polar distance would have varied 1° 5′ if the star had been as near as the moon, 2′ 52″ if as near as the sun, and 16″ if at the distance of Saturn, with smaller variations in the distances from the other stars. Here he not only gives this indication of his idea of the distance of the planets, but also shortly alludes to his system of the world. He remarks that if the star was situated in the sphere of Saturn, and if we adopt the annual motion of the earth according to Copernicus, the star would in a year appear to move backwards and forwards (i.e., have an annual parallax) to the extent of about ten degrees, so that even followers of Copernicus must admit that the star was far beyond Saturn. The third proof of the great distance of the star is, that the meridian