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The trivium is implicit in the De nuptiis Philologiae et Mercurii ("On the Marriage of Philology and Mercury") by Martianus Capella, although the term was not used until the Carolingian Renaissance, when it was coined in imitation of the earlier quadrivium. Grammar, logic, and rhetoric were essential to a classical education, as explained in Plato's dialogues. The three subjects together were denoted by the word "trivium" during the Middle Ages, but the tradition was established in ancient Greece of first learning those three subjects. Contemporary iterations have taken various forms, including those found in certain British and American universities (some being part of the Classical education movement) and at the independent Oundle School in the United Kingdom.
Etymologically, the Latin word trivium means "the place where three roads meet" (tri + via); hence, the subjects of the trivium are the foundation for the quadrivium, the upper division of the medieval education in the liberal arts, which comprised arithmetic (number), geometry (number in space), music (number in time), and astronomy (number in space and time). Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts of classical antiquity.
Grammar teaches the mechanics of language to the student. This is the step where the student "comes to terms", i.e. defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.
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