On the Principles of Arithmetic and On the Principles of Music

astronomy, while geometry is the teaching of immobile things; or because the very motion of the stars is celebrated through the modulations of harmony. Therefore, it is established that the power of numbers precedes the courses of the stars in antiquity, just as it is certain that arithmetic surpasses music in its nature, since it appears more ancient than those things which are prior to it Arithmetic is the "prior" thing upon which the "posterior" sciences of geometry and music depend.. Properly speaking, however, it is by the very nature of numbers that every course of the stars and the entire system of astronomy is 5 established. For it is thus that we calculate their risings and settings, thus we monitor the delays and speeds of the wandering stars original: errantium siderum, referring to the planets, which appear to "wander" against the fixed stars., 10 and thus we recognize the eclipses and the manifold variations of the moon. Therefore, since the power of arithmetic is prior, as has been made clear, let us take the beginning of our discussion from here.

On the substance of number.

II. All things whatsoever that have been constructed from the primeval nature 15 of things seem to have been formed by the logic of numbers. For this was the principal exemplar in the mind of the Creator original: conditoris. Boethius refers to the "Architect" or "Maker" of the universe who used number as a blueprint.. From here the multitude of the four elements was borrowed, from here the changes of the seasons, from here the motion of the stars and the turning of the heavens. Since these things are so, and 20 since the state of all things functions through the binding of numbers, it is necessary that that number, always holding itself equally in its own substance, remains permanent; and that it is composed not from diverse things—for what would join the substance of number itself, since its own exemplar had joined all other things together?—25 but it seems to be composed from itself. Furthermore, nothing seems to be composed of like things, nor of those things which are joined by no proportion of reason and are separate from one another in all substance and nature. It is established, therefore, that since number is joined together, it is neither joined from like things 30 nor from those things which are joined to one another by no proportion of reason—

The following are scholarly notes on manuscript variations found at the bottom of the original page:
1 geometrica in manuscripts c, d, f, r; in l the letter 'c' was deleted by an erasure. 4 procedere in manuscript a. 6 antiquior videatur in a, c, f, s. || in ipsa in f. 13 A second hand added the title in d. 20 rerum omnium in f, omnium rerum in s || numerum in c || collectione in r. 26 ex his omitted in l; added in the margin of d. 27 coniunguntur in f. 30 se ad in d. || rationi, with the 's' deleted by erasure, in c.