Fundamentals of Arithmetic; Fundamentals of Music

Therefore, it is also established that the power of music precedes the courses of the stars in antiquity, which arithmetic does not doubt to surpass by nature, since it seems more ancient than the things that are prior to it. Yet, all courses of the stars and all astronomical reason are established by the very nature of numbers themselves. For thus we collect risings and settings, thus we guard the slownesses and velocities of the wandering stars planets, thus we recognize the eclipses and the manifold variations of the moon. Therefore, since it has become clear that the power of arithmetic is prior, let us take the beginning of our discussion from here.

On the substance of number.

II. All things that have been constructed by the primordial nature of things seem to be formed by the reason of numbers. For this was the principal exemplar in the mind of the creator. From this, the multitude of the four elements was borrowed; from this, the changes of the seasons; from this, the motions of the stars and the turning of the heavens. Since these things are so, and since the state of all things functions through the connection of numbers, it is necessary that number itself, always remaining in its own substance equally, should be composed not of diverse things—for what would join the substance of number, when its exemplar had joined all things?—but it seems to be composed of itself. Furthermore, nothing seems to be composed of like things, nor of those which are joined by no proportion of reason and are separated from one another by every substance and nature. It is established, therefore, since number is joined, that it is joined neither from like things nor from those which have no ratio of proportion toward one another.