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The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads". Together, the trivium and the quadrivium comprised the seven liberal arts.[1] The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.

## Contents

### Origins

These four studies compose the secondary part of the curriculum outlined by Plato in The Republic, and are described in the seventh book of that work.[1] The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term was not used until Boethius early in the sixth century.[2] As Proclus wrote:

The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving[3].

### Medieval usage

At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA the student could enter for Bachelor's degrees of the higher faculties, such as Medecine or Law. To this day some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy, and the B.Mus. remains a postgraduate qualification at Oxford and Cambridge universities).

The study was eidetic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus, namely arithmetic and music on the one hand,[4] and geometry and cosmology on the other.[5]