Quadrivium

The “Quadrivium” is a set of four arts, which provide a student with the art and science of the four species of Quantity. Mathematics were introduced by Pythagoras as a means of ascending intellectually from the observation of sensible things to the contemplation of immaterial things, which is the ultimate aim of philosophy. The first art of the Quadrivium, and fourth of the seven classical liberal arts, is Arithmetic, through which we learn the art and science of absolute multitude or number. The ancient sources for this study are numerous, and we study them through a nineteenth-century text that collected the teachings of the ancients on Arithmetic. The second art of the Quadrivium, and sixth of the seven classical liberal arts, is Geometry, through which we learn the art and science of magnitudes at rest. This art is named “Geometry,” or the “measurement of the Earth,” because, throughout history, it was argued by the wise men that the earth (Ge in Greek) was a body at rest. The source for this study is the famous text of Euclid, The Elements, which has been studied for over 2,300 years. The third art of the Quadrivium, and fifth of the seven classical liberal arts, is Music, through which we learn the art and science of relative multitude, or ratio. Our source for this study is the sixth-century Catholic scholar Boethius, whose work on the art of music has been a standard text for 1,400 years. The fourth art of the Quadrivium, and last of the seven classical liberal arts, is Astronomy, through which we learn the art and science of magnitudes in motion. This art is named “Astronomy,” or “rule of the stars,” because it was the conviction of the ancients that the stars were bodies in motion about the earth. The sources for this study include Aristotle and Ptolemy, whose works have been studied for 2,000 years. Modern “Copernican” astronomy may also be studied, but it serves a different purpose.