His supreme authority was of course Ptolemy. But it would only be by a rare chance that he could see the _Almagest_, even in a translation, and all the evidence that we can find in his own writings points to its being entirely unknown to him. On each of the three occasions that he quotes Ptolemy’s opinion on subjects dealt with in the _Almagest_ he is wrong: once it is Ptolemy’s view on the physical nature of the Galaxy,[91] as to which none had been expressed, although its appearance was carefully described; in another case he implies that Ptolemy discovered precession, and says that he added a ninth heaven to account for it,[92] and this double mistake was apparently copied from Albertus Magnus or Averroës.[93] As we know, it was Hipparchus who discovered precession, and Ptolemy gives him the credit for in the _Almagest_; it was the Arabian astronomers who added the ninth sphere. ------------------------------------------------------------------------ [91] _Conv._ II. xv. 73-77. [92] _Conv._ II. iii. 36-52, _V. N._ xxx. [93] Averroës, in his commentary on Aristotle’s _De Cœlo_, says that the ancients believed the eighth, or starry, heaven, to be the outermost, but that Ptolemy assumed a ninth, “because he said that he had discovered a slow motion along the signs of the zodiac in the fixed stars.” Albertus Magnus, in his _De Cœlo et Mundo_, Book II., says also that the ancients, including Aristotle, believed that there were only eight heavens, but that Ptolemy, so far as he can understand, believed in ten, on philosophical not mathematical grounds (compare _Conv._ II. iii. 40, 41). Albertus accepted the theory of “trepidation,” and thought this was the only movement which ought to be assigned to the star sphere; there remained, therefore, two motions, which affect all the planetary spheres and the star sphere, for which two more spheres must be assumed, a ninth sphere for precession, and a tenth, the primum mobile, for the diurnal motion. Outside all was the Empyrean. Dante never mentions trepidation, and evidently did not believe in it: he needed only nine moving spheres, therefore, but counts the Empyrean as a tenth heaven. ------------------------------------------------------------------------