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The quadrivium (plural: quadrivia) are the four subjects, or arts, taught after teaching the trivium. The word is Latin, meaning "the four ways" (or a "place where four roads meet"),〔 The word "quadrivium" indicates a 4-way intersection (as in a "4-way stop"), while "trivium" refers to a 3-way junction. 〕 and its use for the four subjects has been attributed to Boethius or Cassiodorus in the 6th century.〔 "Part I: The Age of Augustine", ND.edu, 2010, webpage: (ND205 ). 〕〔 "quadrivium (education)", ''Britannica Online'', 2011, web: (EB ). 〕 Together, the trivium and the quadrivium comprised the seven liberal arts (based on thinking skills), as opposed to the practical arts (such as medicine and architecture). The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic, and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy (sometimes called the "liberal art ''par excellence''")〔Daniel Coit Gilman et al. (1905) ''New International Encyclopedia'', lemma "Arts, Liberal"〕 and theology. ==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 (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.〔Henri-Irénée Marrou, "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), 1969, pp. 18-19.〕 As Proclus wrote:
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