Didascalicon, Book II: the sciences, their parts and their discipline
Chapter VII. On the quadrivium
Since, then, as was said above, it properly pertains to mathematics to attend to abstract quantity, we must seek its species in the parts of quantity. “Abstract quantity is nothing else than a visible form impressed on the mind according to linear dimension, which consists in imagination”; its parts are two: one continuous, as a tree, a stone, which is called magnitude; the other discrete, as a flock, a people, which is called multitude. Again, of multitude, some is by itself, as three, four, or any other number; some is relative, as double, half, one and a half, one and a third, or anything of the sort. Of magnitude, some is movable, as the sphere of the world, some immovable, as the earth. Magnitude, then, that is by itself, arithmetic contemplates; that which is relative, music. Geometry professes the knowledge of immovable magnitude. The skill of the astronomical discipline claims for itself the science of the movable. Mathematics, therefore, is divided into arithmetic, music, geometry, astronomy.