Commentary on the First Book of Euclid's Elements

For it is agreed by everyone that everything which subsists from moving essences has a changeable existence. And how shall we add precision to precise and irrefutable forms from things that are not precise? For everything that is a cause of unchanging knowledge is itself such to a greater degree. Therefore, we must hypothesize the soul as the generator of mathematical forms and logoi. But if it subsists them while possessing their paradigms in its essence, and if these generations are projections of the forms pre-existing within it, then we will be in agreement with Plato in saying these things, and we will have discovered the true essence of mathematical subjects. If, however, it weaves such an immaterial order and generates such a theory without possessing or having pre-grasped the logoi, how can it distinguish the things generated, whether they happen to be fertile or whether they are anemiaia wind-eggs/void and images instead of truths? And by what rules does it measure the truth in these? And how, not possessing their essence, does it generate such a variety of logoi? For we would thus make their existence automatic and referable to no standard. If, therefore, mathematical forms are offspring of the soul, and it does not derive the logoi from sensible things, but rather the soul itself subsists them, and these are projected from those logoi, then the soul’s pangs and births are manifestations of enduring and eternal forms.

Secondly, therefore, if we collect the logoi of mathematical subjects from below and from sensible things,