Fundamentals of Arithmetic; Fundamentals of Music

and is led toward the more certain things of the intellect. For there are certain steps and fixed dimensions of progressions, by which one may ascend and advance, so that that eye of the mind—which, as Plato says, is deemed more worthy to be preserved than many bodily eyes, because by its light alone can truth be tracked or inspected—this eye, I say, once immersed and deprived of bodily senses, may be illuminated again by these disciplines. Which of these, therefore, is to be learned first, if not that which holds, as it were, the place of a principle and a mother to the others? This, however, is arithmetic. For this is prior to all, not only because God, the creator of this worldly mass, held it as the first exemplar of his reasoning and constituted all things according to it, whatever things the constructing reason found to have harmony through the numbers of an assigned order; but arithmetic is also declared to be prior for this reason: whatever things are prior by nature, when they are removed, the posterior things are simultaneously removed; but if the posterior things perish, nothing regarding the state of the prior substance is changed, just as an animal is prior to a human. For if you remove "animal," the nature of "human" would be immediately destroyed; if you remove "human," "animal" will not perish. And conversely, those things are always posterior which bring with them something else, and those are prior which, when spoken, bring nothing of the posterior things with them, as is also the case in the same human. For if you say "human," you will simultaneously name "animal," for the human is the same as the animal; if you say "animal," you have not simultaneously introduced the species "human," for "animal" is not the same as "human." The same thing seems to occur in geometry or arithmetic. For if you remove numbers, whence would come the triangle or the square or whatever moves within geometry, all of which are denominative of numbers?