Fundamentals of Arithmetic; Fundamentals of Music

Arithmetic speculates upon that multitude which is "by itself," while the temperaments of musical modulation understand that which is "related to something." Geometry promises the knowledge of immobile magnitude, and the skill of the astronomical discipline claims the science of mobile magnitude. If an inquirer lacks these four parts, he cannot find the truth, and without this speculation of truth, no one can be truly wise. For wisdom is the knowledge and integral comprehension of those things which truly are. To him who scorns this—that is, these paths of wisdom—I declare that he is not philosophizing correctly, if indeed philosophy is the "love of wisdom," which he would have already despised in scorning these things. I think it should also be added that the whole force of the multitude, having progressed from a single starting point, grows to infinite increases of progression. Magnitude, however, beginning from a finite quantity, does not receive a limit in division; it undergoes the most infinite sections of its own body. Philosophy, therefore, voluntarily rejects this infinity of nature and indeterminate power. For nothing that is infinite can be gathered by science or comprehended by the mind; but from here, reason has taken for itself that in which it can exercise the skill of searching for truth. For it has chosen from the infinite plurality of the multitude the limit of a finite quantity, and having rejected the section of interminable magnitude, it has demanded for itself defined spaces for cognition. Therefore, it is clear that whoever has passed over these things has lost all learning of philosophy. This, therefore, is that quadrivium fourfold path by which those must travel for whom a more excellent soul as opposed to mere animals or lower beings is intended from the senses born with us.