Procli Diadochi In Primum Euclidis Elementorum Librum Commentarii

For eikasia knows the images of sensible things, which are seen in waters and other mirrors, having the lowest rank among forms and having become, in truth, images of images. And dianoia contemplates the images of the intelligible things, which have descended from the primary, simple, and partless eide forms into multiplicity and division. For this reason, the knowledge of this [dianoia] is suspended from other, older hypotheses, whereas noēsis ascends to the unhypothetical principle itself. If, therefore, mathematical things have attained neither a partless substance, separated from all division and multiplicity, nor one known by sense-perception, which is highly changeable and divisible in every way, it is manifest to everyone that they are dianoēta discursive objects according to their essence. And dianoia stands over them as a criterion, just as sense-perception does for sensible things, and eikasia for the objects of imagination. Hence, Socrates also determines that the knowledge of these [mathematical objects] is dimmer than the primary science, but clearer than the apprehension of doxa opinion. For they have an unfolding and discursive element of theory that exceeds noēsis, while the permanence and irrefutability of their logoi rational principles surpasses doxa. And they have received, by their descent, an initiation from hypothesis that is lower than the primary science, yet they exist in immaterial eide forms in a way more perfect than the knowledge of sensible things.