Likewise the mathematicians have concluded that there were a definite number of spheres, not that it is necessary to be so, but because one can not teach anything definitely about such things unless one distinguishes the spheres thus, on account of the variety of their motions, about which one can teach nothing without such imagination, if I may so name it. For teachers and professors of these sciences or theories say: We give examples, not because they are in every detail correct, but in order that no one may teach differently concerning those subjects. Therefore it would be the height of folly to despise and ridicule such things as some do, because it is not so sure that it could not be different, for they serve to the end that good arts and sciences may be taught, and that is sufficient. The philosophers in general teach such things, to which the more modern theologians agree and add to these eight spheres two more,--the crystalline, glacial or aqueous heaven, and then the empyreal or fiery heaven. The Greeks however have discussed these themes much more elegantly and prudently than our scholars. For Ambrose and Augustine have had very childish thoughts. Therefore I praise Jerome because he simply passed over them in silence. There are some who hold that the crystalline heaven is watery, because they think it is the waters of which Moses here speaks, and there the firmament or eighth sphere is added so that they be not consumed by their rapid and constant motion. But these are puerile thoughts, and I will rather confess that I do not understand Moses in this passage than that I should approve such illiterate thoughts. The seventh heaven they call empyreal; not because it is fiery or burning, but from the light which is lucid and splendid. This heaven in the home of God and of the blessed, because it was filled immediately after creation with angels, and Lucifer, as they affirm, fell from this heaven. These are about all the ideas that theologians have added to the opinions of philosophers. However, our scientists, who have studied astronomy, teach that there are still more spheres; namely, twelve, and three motions in the eight spheres; as, the _motum raptum_, _motum proprium_, _motum trepidationis_, a rending motion, a characteristic motion, and a trembling motion. For of such things indeed one cannot speak, unless he give each motion its own sphere.