The trivium is followed, in the classical order of the liberal arts, by the quadrivium, the four arts of quantity. Contemporary higher studies often begin with number and measurement, as if they were the first language of knowledge. But mathematics and science must employ words and define them and reason correctly from them; and that is the place of the trivium. The trivium therefore does not delay or replace mathematics; it lays the most general foundations for all reasoning, including quantitative and mathematical reasoning.
The quadrivium is the study of quantity and of quantity as it is found in real things. Classically there are four arts. Arithmetic treats number, that is, discrete quantity. Geometry treats magnitude, that is, continuous quantity: the line and the figure. Music treats number as it is found in sound. Astronomy treats magnitude as it is found in the motions of the heavens.
Studium Institute will provide an introduction to the quadrivium on the same pattern as this introduction to the trivium. Interactive courses in some of the arts of the quadrivium are already available (see below).
Continue to Sources.