And the Heaven of Jupiter can be compared to Geometry because of two properties.  The one is, that it moves between two Heavens, repugnant to its good tempering, namely, that of Mars and that of Saturn.  Hence Ptolemy says, in the book alluded to, that Jupiter is a star of a temperate complexion, midway between the cold of Saturn and the heat of Mars.  The other is, that amongst all the stars it appears white, as if silvered.  And these things are in the Science of Geometry.  Geometry moves between two things antagonistic to it; as between the point and the circle, and I term circle freely anything that is round, either a body or superfices; for, as Euclid says, the point is the beginning of Geometry, and, according to what he says, the circle is the most perfect figure in it, which must therefore have reason for its end; so that between the point and the circle, as between the beginning and the end, Geometry moves.  And these two are antagonistic to its certainty; for the point by its indivisibility is immeasurable, and the circle, on account of its arc, it is impossible to square perfectly, and therefore it is impossible to measure precisely.  And again, Geometry is most white, inasmuch as it is without spot of error, and it is most certain in itself, and by its handmaid, called Perspective.

And the Heaven of Saturn has two properties because of which it can be compared to Astrology.  One is the slowness of its movement through the twelve signs; for twenty-nine years and more, according to the writings of the Astrologers, is the time that it requires in its orbit.  The other is, that above all the other planets it is highest.  And these two properties are in Astrology, for in completing its circle, as in the acquirement of this Science, the greatest space of time is revolved, because its demonstrations are more than any other of the aforementioned Sciences, and long experience is requisite to those who would acquire good judgment in it.  And again, it is the highest of all the others, because, as Aristotle says in the commencement of his book on the Soul, the Science is high, because of its nobility, and because of the nobleness of its subject and its certainty.  And this Science more than any other of those mentioned above is noble and high, for noble and high is its subject, which is the movement of the Heavens; and high and noble, because of its certainty, which is without any defect, even as that which springs from the most perfect and most regular principle.  And if any one believe that there is defect in it, it is not on the part of the Science, but, as Ptolemy says, it is through our negligence, and to that it must be imputed.

CHAPTER XV.

After the comparisons which I have made of the seven first Heavens, we must now proceed to the others, which are three, as has been often stated.