Procli Diadochi In Primum Euclidis Elementorum Librum Commentarii

dianoia having set itself above doxa opinion, while falling short of noēsis intellection. It is fitting for us to discern what we ought to call the essence of mathematical eide forms and genera, and whether it must be granted that it originates from sensible things—either through aphairesis abstraction, as they are accustomed to say, or through the aggregation of particulars into one common logos rational principle—or whether we must grant it existence prior to these, as Plato asserts and as the procession of all things demonstrates.

First, then, if we say that mathematical eide come into being from sensible things, with the soul forming the circular or triangular shape within itself after the fact from the triangles or circles in matter, from where does the precision and irrefutability of their logoi arise? It must arise either from sensible things or from the soul. But it is impossible from sensible things, for they would much rather possess precision. Therefore, it arises from the soul, which adds the perfect to the imperfect and the precise to the imprecise. For where in sensible things is the partless, the widthless, or the depthless? Where is the equality of lines drawn from the center, the ever-standing logoi of the sides, or the correctness of the angles? Do we not see how all sensible things are mixed within one another, and how there is nothing pure in them, nor free from its opposite, but all are divisible, extended, and moving? How, then, shall we assign their permanent essence to these unchanging logoi from things that are in motion and existing differently at different times?