Fundamentals of Arithmetic; Fundamentals of Music

We call those things "that which is," which neither grow by extension nor diminish by retraction, nor are changed by variations, but always guard themselves in their own power, resting upon the supports of their own nature. These things are qualities, quantities, forms, sizes, smallnesses, equalities, habits, acts, dispositions, places, times, and whatever is found joined in some way to bodies; these things themselves are indeed incorporeal by nature and flourish by the reason of an immutable substance, but they are changed by the participation of a body, and by the touch of a variable thing, they pass into a changeable inconstancy. Since these, therefore, as has been said, have obtained an immutable substance and power by nature, they are truly and properly said "to be." Wisdom, therefore, professes the knowledge of these things—that is, those which properly "are" and which are named "essences" by their own name. There are two parts of essence: one is continuous and joined to its own parts, and is not distributed by any boundaries, as are a tree, a stone, and all the bodies of this world, which are properly called magnitudes. Another is separated from itself and determined by parts, and as if gathered together into one assembly, as a flock, a people, a chorus, a heap, and whatever else whose parts are terminated by their own extremities and are distinct from the end of another. The proper name for these is "multitude." Again, some things of the multitude are "by themselves," as three or four or a tetragonus square number or any number that needs nothing to exist. But others do not exist by themselves, but are referred to something else, such as the double, the half, the sesqualter ratio of 3:2, or sesquitertium ratio of 4:3, and whatever is such that, if it were not related to another, it could not exist at all. Of magnitude, however, some things are remaining and lacking motion, while others are turned by a mobile rotation and do not rest at any time.