Procli Diadochi In Primum Euclidis Elementorum Librum Commentarii

for everything that comes into existence from moving substances is agreed to have a changeable existence from them. And how shall we add precision to the precise and irrefutable eide forms from things that are not precise? For everything that is the cause of unchanging knowledge is itself such in a greater degree. Therefore, we must posit the soul as the generative principle of mathematical eide and logoi rational principles. But if it brings them into existence because it possesses the paradigms in its essence, and these generations are projections of the forms pre-existing within it, we will be in agreement with Plato and will have found the true essence of mathematical studies. But if it weaves such an immaterial order and engenders such theory without possessing or having previously grasped these logoi, how can it distinguish what is produced—whether they happen to be fertile or wind-eggs and images instead of realities—and what rules does it use to measure the truth in these things? And how, not possessing their essence, does it engender such a variety of logoi? For we would be making their existence automatic and referred to no standard. If, therefore, mathematical eide are offspring of the soul and do not have the logoi—which the soul brings into existence—from sensible things, then they are projected from the former, and its labor pains and births are the manifestation of remaining and eternal eide.

Second, therefore, if we collect the logoi of mathematics from below and from sensible things...