And the Heaven of the Sun may be compared to Arithmetic because of two properties: the one is, that with his light all the other stars are informed; the other is that the eye cannot gaze at it. And these two properties are in Arithmetic, which with its light illuminates all its Sciences: for their subjects are all considered under some Number, and with Number one always proceeds in the consideration of these; as in Natural Science the movable body is the subject, which movable body has in itself three reasons of continuity, and this has in itself reason of infinite number. And of Natural Science its first and chiefest consideration is to consider the principles of natural objects, which are three, that is, matter, privation, and form; in which this Number is seen, and not only in all together, but again in each one, as he who considers subtly may perceive. Wherefore, Pythagoras, according to what Aristotle says in the first book of the Physics, established as the principles of natural things, the equal and the unequal; considering all things to be Number. The other property of the Sun is again seen in Number, of which Number is the Science of Arithmetic, that the eye of the intellect cannot gaze at it. For Number, inasmuch as it is considered in itself, is infinite; and this we cannot, understand.
And the Heaven of Mars may be compared to Music because of two properties. One is its most beautiful relative position; for, when enumerating the movable Heavens, from which one soever you may begin, either from the lowest or from the highest, this Heaven of Mars is the fifth; it is the central one of all, that is, of the first, of the second, of the third, and of the fourth. The other is, that this Mars dries up and burns things, because his heat is like to that of fire; and this is why it appears flaming in colour, sometimes more and sometimes less, according to the density and rarity of the vapours which follow it, which of themselves are often kindled, as is determined in the first book on Meteors. And, therefore, Albumassar says that the kindling of these vapours signifies the death of Kings and the change of Kingdoms; for they are the effects of the dominion of Mars. And, therefore, Seneca says that, on the death of Augustus, he beheld on high a ball of fire. And in Florence, at the beginning of its destruction, there was seen in the air, in the form of a cross, a great quantity of these vapours following the planet Mars. And these two properties are in Music, which is all relative, as is seen in harmonized words and in songs, from which the sweeter harmony results in proportion as the relation is more beautiful, which in this Science is especially beautiful, because there is in it a special harmony. Again, Music attracts to itself human spirits, which are as it were chiefly vapours from the heart, so that they almost cease from all labour; so is the whole soul when it hears it, and the power of all those spirits flies as it were to the spirit of sense, which receives the sound.