De institutione musica II.5: Cur multiplicitas ceteris antecellat.
But in these it must be considered that the multiple kind of inequality seems far more ancient than the other two. For the arrangement of the natural number in multiples is compared with the unit, which is first; the superparticular, however, is not made by comparison with the unit but of the numbers themselves that are set after the unit, as three to two, four to three, and the rest after this manner. The formation of the superpartients lies far further back; it is compared not with consecutive numbers but with numbers passed over, and not always with an equal passing over, but now with one, now with two, now with three, now with four, and so it increases without limit. Further: the multiple begins from the unit, the superparticular from two, the superpartient proportion takes its beginning from three. But enough of these. Now it will be necessary to put first certain things which the Greeks call axioms, which we shall understand to what end they look only when we come to the demonstration of each matter.
