There have been many opinions regarding the number and the positions of the spheres, Dante says, but the truth about them has at length been found. The scheme which he expounds is that of Ptolemy, modified by the Arabs and adapted to the doctrines of the Church by Christian writers. In the _Vita Nuova_ he almost seems to imply that the nine moving spheres form an article of faith. “Secondo Tolommeo e secondo la Cristiana verità, nove siano li cieli che si muovono.”[574] ------------------------------------------------------------------------ [574] “According to Ptolemy and according to Christian Truth, nine is the number of the moving heavens.” _V. N._ xxx. 16-18. ------------------------------------------------------------------------ Quoting from Albertus Magnus, or Averroës, he apparently credits Ptolemy with the discovery of precession, for he says that it was Ptolemy who added a ninth sphere to the eight of Aristotle, because he perceived that otherwise the outer sphere would have a double movement, and so he felt obliged to assume a sphere beyond the star sphere which should have only the one simple motion of the diurnal east to west revolution. The period of this revolution (the sidereal day) Dante gives as 23 hours and ¹⁴/₁₅ths of an hour, “grossamente assegnando,”[575] _i.e._ 23 hours 56 minutes, which is the correct value ignoring the 4 seconds. We know that it was not Ptolemy in fact who thought it necessary to add a ninth sphere; he was not sufficiently interested in spheres, since to him they were only mathematical abstractions: but the Arabs of Baghdad noted that he had added another _movement_, the discovery of Hipparchus; and they, accepting the spheres as material instruments of celestial motions, felt obliged to assume the existence of the Primum Mobile or 9th sphere. That Dante should believe the spheres to exist as actual entities was inevitable, for his principal authorities, Greek, Arab, and Christian, all taught this. And there is abundant evidence that he did think of them thus. He calls them bodies:—“omnia corpora,”[576] “questi corpi grandi,”[577] “cerchi corporai,”[578] “il maggior corpo,”[579] etc. They are transparent, one sphere not obstructing the light from another;[580] and composed of æther, “questo etera tondo.”[581] They have a certain thickness, and would be visible if near enough, for Dante speaks of the inner margin of the Primum Mobile, and says that it was too far above him for him to have seen it yet, when he was in the Star Sphere.[582] ------------------------------------------------------------------------ [575] “Roughly speaking.” _Conv._ II. iii. 36-48. [576] “All bodies.” _Ep._ x. 445. [577] “These vast bodies.” _Par._ viii. 99. [578] “Material circles” (here compared with the Angels, who are purely spiritual). _Par._ xxviii. 64. [579] “The greatest body.” _Par._ xxx. 39. [580] _Purg._ iii. 29, 30. [581] “This rounded ether.” _Par._ xxii. 132.