Plato said, “geometry is the knowledge of that which always is, and not of a something which at some time comes into being and passes away…it tends to draw the soul to truth and is productive of a philosophical attitude of mind.” Geometry provides the student with a real experience of truth. At St. Gregory’s Academy we study demonstrative geometry in its purest form. The students learn and take turns demonstrating the whole of the first six books of Euclid’s Elements. The Elements is a classic example of scientific knowledge, which is a knowledge founded on the understanding of everything that comes prior to that knowledge. Such a mode of learning helps to ensure that the learning is genuine rather than the simple memorizing and manipulating of formulas. It also rigorously forms the mind to think clearly and logically, thus paving the way for philosophical and logical reasoning.
The geometry class at St. Gregory’s is much more than just a math class. Not only is the geometry better learned and grasped through Euclid’s organic method, but also the student receives a rigorous exercise in clear and organized thought and how to reproduce that mode of thought. Such an experience will profit a student interested in seeking the truth, no matter what its form. The geometry course is a difficult and demanding encounter with mathematics, truth, and beauty, therefore leaving lasting impressions on the students and also the teacher. We say that teaching is a species of friendship at St. Gregory’s. Friendship, however, implies some sort of common ground on which the friends might meet. When studying Euclid, both teacher and student stand humbly before the eternal truths manifested within his pages.
