Word of the Day: QUADRIVIUM

QUADRIVIUM. The more advanced program in medieval liberal arts education (beyond the trivium), namely arithmetic, geometry, astronomy, and music. (Etym. Latin quatuor, four + viae, ways: quadrivium.)

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 (in the order Arithmetic, Geometry, Astronomy, Music).  The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term quadrivium was not used until Boethius, early in the sixth century. As Proclus, the 5th century neoplatonist, 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.

These followed the preparatory work of the trivium, consisting of grammar, logic, and rhetoric. In turn, the quadrivium was considered preparatory work for the study of philosophy (sometimes called the "liberal art par excellence") and theology.

The quadrivium may be considered to be the study of number and its relationship to space or time: arithmetic was pure number, geometry was number in space, music was number in time, and astronomy was number in space and time. 

Can you imagine modern seminarians studying all this to prepare themselves for philosophy!?