Commentary on the First Book of Euclid's Elements

[it] establishes dianoia above doxa opinion, while it falls short of noēsis intellectual intuition. It remains for us to see what the essence of mathematical forms and genera should be called, and whether it should be conceded that it subsists from sensible things, either by way of aphaeresis abstraction, as people are accustomed to say, or by way of the collection of particular things into one common logos rational principle, or whether we should grant it an existence prior to these, as Plato claims and the progression of the whole demonstrates. First, therefore, if we say that mathematical forms subsist from sensible things, and that the soul forms the triangular or circular shape within itself in a secondary manner from the triangles or circles in matter, where do the precision and irrefutability of these logoi come from? For it is necessary that they come either from sensible things or from the soul. But it is impossible that they come from sensible things, for those would possess precision to a much greater degree. Therefore, they come from the soul, which adds perfection to the imperfect and precision to the imprecise. For where in sensible things is that which is partless, or widthless, or depthless? Where is the equality of lines drawn from the center, where the ever-standing logoi of the sides, or the rightness of angles? Do we not see how all sensible things are mixed with one another and how nothing in them is pure or free from its opposite, but all are divisible, extended, and moving? How, then, shall we attribute their permanent essence to unchanging logoi derived from things that are moving and existing in different ways at different times?