On the Principles of Arithmetic and On the Principles of Music

PRINCIPLES OF ARITHMETIC I, 1.

...are known. Of these, therefore, the integrity of arithmetic contemplates that multitude which exists by itself, while the harmonies of musical melody come to know that multitude which is relative to something else original: "ad aliquid". The knowledge of immobile magnitude, moreover, geometry prom-
5ises, while the skill of the astronomical discipline claims the science of mobile magnitude. If an inquirer lacks these four parts, they cannot find the truth, and indeed without this contemplation of truth, no one can think rightly. For wisdom is the knowledge and complete understanding of those things which truly exist. I declare to
10the one who scorns these—that is, these paths of wisdom—that they are not philosophizing correctly, since philosophy is the "love of wisdom," which they have previously despised by scorning these paths. I also think this should be added: that the whole power of multitude, proceeding from
15the starting point of "one," grows toward the infinite increases of progression. Magnitude, however, beginning from a finite quantity, does not accept a limit in its division; for it admits the most infinite sections of its own body. Therefore, philosophy spontaneously repudiates this
20infinity of nature and its indeterminate power. For nothing that is infinite can be gathered by science or comprehended by the mind; but from this, reason itself has taken for itself the things in which it might exercise its skill as a seeker of truth. For it has chosen a limit of finite quantity from the plurality
25of infinite multitude, and, having rejected the sectioning of interminable magnitude, it demanded for itself defined spaces for knowledge. It is established, therefore, that whoever overlooks these things has lost the entire teaching of philosophy. This, then, is that quadrivium Latin: "quadruvium," meaning a "fourfold path" or "place where four roads meet." by which those must travel whose more excellent mind is drawn away from the senses born with us...

Critical notes on variant readings:
3. after "relative to something": manuscript r adds "is"; manuscript b adds "is" above the line. || "of musical melody": manuscript s reads "of musical modulation." || "come to know": manuscripts a, f, r, s read "know beforehand."
4. "geometry": manuscripts a, c, d, f, r read "geometrical."
5. "moreover": omitted in a, d, f, l, r. || "astronomical": manuscript c reads "of astronomy."
6. "claims": manuscript l reads "vindicates"; a, b, c, d, r read "has claimed." || "four": manuscript c uses Roman numeral IIII.
7. "can": manuscripts b, c read "will be able to"; f reads "is able"; r contains a subnote indicating "could."
9. "truly": manuscripts c, d, l use a variant spelling for "true."
11. "paths of wisdom": manuscript c reads "sentences of wisdom." || "to be": omitted in c, d, f, l, r, s.
18. "of its own body": manuscript f transposes to "receives of its own body." || "nature's infinity": manuscripts d, l reverse the word order.
22. "reason itself": manuscript f reverses the order; s reads "that reason itself." || "might": manuscripts d, f, l read "could."
23. "infinite": manuscript c and an erasure in r read "infinite." || "infinitely": manuscript f.
24. "finite": manuscript f.
26. "demanded": manuscripts a, c, d, r, s use a slightly different verb form.