On Nicomachus's Introduction to Arithmetic

IAMBLICHUS

so precisely ordered by divine providence, certain sciences, having cut off and delimited what was encompassed by them from each, called the poson quantity from the multitude—which is already familiar—and the pēlikon magnitude/how-much from magnitude in the same way. And they subjected both of their genera to the sciences of their own knowledge: quantity to arithmetic, and magnitude to geometry. But since these were not of one form, and each admitted a more partial subdivision—for of the quantity, one part was considered in itself, removed from any relation to another, for example, the even and the odd, the perfect and the deficient, and the like; and the other part was considered as having a relation to something else (which is specifically called quantity in relation to something), such as the equal and the unequal, the multiple, the superparticular, the superpartient, and similar things. And again, of the magnitude, one part exists and is conceived as stationary, and the other as moving and carried. For this reason, it is reasonable that two other sciences followed and laid hold of the theory regarding the knowable of each alongside the two aforementioned sciences. For to arithmetic, which specifically obtained the study of quantity in itself, music shared in the technology of quantity in relation to something (for its harmonic aspect and its proclamation regarding concords is nothing other than articulating the relations and ratios of notes to one another, and the quantity of their excesses and deficiencies). And to geometry, which is engaged in the examination of stationary and standing magnitude, spherical science became a collaborator, having become the expert of moving magnitude—that is, clearly, of the most perfect, ordered, and uniform...