Commentary on Euclid's Elements

Whether similarity or dissimilarity is aptly predicated of our mathematical concepts, we speak of shapes as similar, and others we call dissimilar; likewise, we call some numbers similar and others dissimilar. Everything that follows from the powers of similarity belongs equally to all mathematical entities, Proclus is arguing that "similarity" is a universal mathematical property, not just a geometric or arithmetic one. with some acting as active powers and others being acted upon. Even Socrates in the Republic attributed to the Muses in their lofty speech A reference to the "Muses' Speech" in Plato's Republic (Book VIII, 546b), where Socrates discusses the "perfect number" that governs better and worse births. the task of encompassing the common principles of all mathematical ratios original: logōn within defined limits, setting them forth in numbers that are always known.
Clearly

What should we say then? Even the measures of harmony and symmetry appear to owe their existence to this [common science].
How these common things subsist.

Therefore, we must not think that these common principles exist directly within the many and distinct species [of mathematics], nor that they originate later from the many. Rather, they exist as entirely immaterial immaterial (aülous): existing apart from physical matter or specific examples., absolute, and precisely distinct entities. For this reason, the knowledge of them exists prior to the knowledge of specific things; it grants principles to those sciences, and many things subsist around them and are referred back to them.

For let the geometer say that, when four magnitudes are in proportion original: analogon, they will also be so alternately original: enallax. This refers to the property in Euclid's Elements where, if a:b = c:d, then a:c = b:d.; and indeed, he says this according to his own principles, which the one who truly knows would use. And if the arithmetician knows that when four numbers are in proportion, they will also be so alternately, he too would receive this from his own science. Who then is it that knows alternation in its own right—whether it occurs in magnitudes or in numbers—and knows the division...