Course

What does it mean to call geometry and arithmetic “liberal arts”?  In the vocabulary of the ancients, an “art” (ars in Latin, or techne in Greek), like a science, meant a carefully reasoned-out knowledge.  But more than that, it meant a knowledge of how to produce something.  Where there is no “product,” there is no “art.”  So it is possible for a form of knowledge to be a “science” but not an “art.”  For example, Aristotle considered the study of god to be a “science,” a body of knowledge rigorously reasoned out from self-evident principles, but not an “art,” because it did not teach us how to make gods, or how to do anything about god. . . .

Geometry, on the other hand, is both an “art” and a “science” according to the ancient senses of these terms.  It is a “science” because it begins from self-evident and necessary truths, and reasons forward to their logical consequences.  But it is also an “art” because it teaches us how to make certain things, certain constructions.  Although we form these in our minds, and need not draw them on paper or with a computer program (although that usually helps), these are nevertheless mental “products” of a sort.  The geometer, for example, can teach us how to put together circles and straight lines in such a way as to bisect a given angle.  And unlike the art of medicine, geometry makes use only of “abstract” materials.  No one regards a geometer as a failure if he is unable to produce a perfectly straight edge or a perfect circle made out of wood or paper or any other tangible material.  That type of production is irrelevant to his art.  Thanks to the abstract and mental quality of his materials, they enjoy a kind of uniformity and perfection which means that the statements about them will admit of no exceptions whatsoever.  So geometry is not only an art, but a “science” in the strictest (and ancient) sense of the term. . . .

-Michael Augros, Thomas Aquinas College

“1. It is said that the discipline of geometry was first discovered by the Egyptians, because, when the Nile River flooded and everyone’s possessions were covered with mud, the onset of dividing the earth by means of lines and measures gave a name to the skill. And thereupon, when it was greatly perfected by the acumen of wise men, the expanses of the sea, sky, and air were measured. 2. Stimulated by their zeal, these sages began, after they had measured the land, to inquire about the region of the sky, as to how far the moon is from the earth, and even the sun from the moon; and how great a distance there is to the pinnacle of the heavens. And so, using reasoning capable of being tested and proved, they determined the distances of the vault of heaven and the perimeter of the earth in terms of the number of stadia. 3. But because the discipline began with measuring the earth, it retained its name from its origin, for geometry (geometria) takes its name from ‘earth’ and ‘measure.’ In Greek, ‘earth’ is called ϒη and ‘measure’ is μετρα. The art of this discipline is concerned with lines, distances, sizes and shapes, and the dimensions and numbers found in shapes.” –St. Isidore of Seville (The Etymology of Isidore of Seville, III.x)

“Geometry is knowledge of what always is. Then it draws the soul towards truth and produces philosophic thought by directing upwards what we now wrongly direct downwards….[W]hen it comes to better understanding any subject, there is a world of a difference between someone who has grasped geometry and someone who hasn’t.” –Plato (The Republic VII, 527b-c)