Book One

[...acting] as a guide, and by its uniform embrace and contact with being, it surpasses other forms of knowledge. To those forms of knowledge which have been allotted a divisible and lowest nature, and which are found among all such material things, it [the highest intellection] is not at all established, being grasped in a divided way. But those things in the middle, such as the objects of mathematics original: mathēmatikon eidē, fall short of the stable nature [of the Intellect] but are elevated above divisible things by the discursive reason original: dianoia. Proclus distinguishes between Nous (direct, immediate spiritual intuition) and Dianoia (the step-by-step logic used in math).. Indeed, for this reason, mathematics is secondary to the Intellect and the highest science, but it is more perfect, clearer, and purer than opinion original: doxa.

For mathematics is an unfolding and development of the Intellect original: Nous, which encompasses that which is indivisible and unified in its intellectual applications; yet it [discursive reason] also brings together again what has been divided and refers it back to the Intellect. Just as these modes of knowledge differ from one another, so too are the objects of knowledge distinguished by their nature. The intelligible objects original: noēta are spread out above all things in their uniform existences, while the objects of sense original: aisthēta fall short of the primary substances in every way.

But mathematical objects, and generally those perceived by discursive reason original: dianoēta, have been allotted a middle rank. They exceed the former [the intelligibles] in their degree of division, but they surpass the latter [sensible objects] in their immateriality. While they fall short of the former in their simplicity, they take the lead over the latter in their clarity. They possess clearer manifestations original: emphaseis of the intelligible substance than sensible things do, but they are nonetheless images, imitating the uniform paradigms of being by making many copies of what is indivisible and diversifying what is simple. To speak summarily, they are stationed at the thresholds original: prothyrois — literally the "front porches" or vestibules of the primary forms, revealing that which is hidden, indivisible, and uniform...