Proclus was trained at Alexandria and then moved to Athens, where he devoted himself to Neo-Platonic philosophy, and became the head of that school:
Though he esteemed mathematics highly, it was only as a handmaid to philosophy. He quotes Plato's opinion to the effect that "mathematics, as making use of hypotheses, falls short of the non-hypothetical and perfect science." And again, while "mathematical science must be considered desirable in itself, though not with reference to the needs of daily life, if it is necessary to refer the benefit arising from it to something else, we must connect that benefit with intellectual knowledge, to which it leads the way and is a propaedeutic, clearing the eye of the soul and taking away the impediments which the senses place in the way of the knowledge of universals." We know that in the Neo-Platonic school the younger pupils learnt mathematics; and it is clear that Proclus taught this subject, and that this was the origin of the commentary.
Heath, The Thirteen Books of Euclid's Elements, 29-30"Propaedeutic" means a piece of learning that prepares you for something else. In Proclus' opinion, mathematics was a means to an end: an exercise to prepare young minds for the philosophical life. We all know that geometry has a multitude of practical applications, but to large degree it is still taught for the same reasons that Proclus had in mind: propaedeusis.
Geometry was apparently used as a propaedeutic even a few generations before Euclid. Dunham (28) quotes the often cited phrase that was supposedly inscribed over the door to Plato's Academy in Athens, "Let no man ignorant of geometry enter here." Dunham continues, "we might say that Plato regarded geometry as the ideal entrance requirement, the Scholastic Aptitude Test of his day."
 |
 |
 |
 |
 |
 |