Editing Quadrivium (section)

==Origins==
[[File:Boetius.png|thumb|upright|The Roman philosopher [[Boethius]], author of [[On the Consolation of Philosophy|''The Consolation of Philosophy'']]]]

These four studies compose the secondary part of the curriculum outlined by [[Plato]] in [[The Republic (Plato)|''The Republic'']] and are described in the seventh book of that work (in the order Arithmetic, Geometry, Astronomy, Music).<ref name="nie"/>
The quadrivium is implicit in early [[Pythagoreanism|Pythagorean]] writings and in the ''De nuptiis'' of [[Martianus Capella]], although the term ''quadrivium'' was not used until [[Boethius]], early in the sixth century.<ref>Marrou, Henri-Irénée (1969). "Les Arts Libéraux dans l'Antiquité Classique". pp. 6–27 in ''Arts Libéraux et Philosophie au Moyen Âge''. Paris: Vrin; Montréal: Institut d'Études Médiévales. pp. 18–19.</ref>  As [[Proclus]] wrote:

<blockquote>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 studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.<ref>Proclus. ''A Commentary on the First Book of Euclid's Elements'', xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. {{ISBN|0-691-02090-6}}.</ref></blockquote>