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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 (or "further") division of the medieval education in the liberal arts, which consists of arithmetic (numbers as abstract concepts), geometry (numbers in space), music (numbers in time), and astronomy (numbers in space ...
From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia [2]) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric.
Since Cassiodorus's educational program, the standard curriculum incorporated religious studies, the Trivium, and the Quadrivium. In some places monastic schools evolved into medieval universities which eventually largely superseded both institutions as centers of higher learning. [2]
The curriculum at medieval universities was heavily influenced by classical education, particularly the study of the liberal arts, which were divided into the trivium (grammar, rhetoric, and logic) and the quadrivium (arithmetic, geometry, music, and astronomy). These subjects provided the foundation for more advanced studies in theology, law ...
[1] [2] Mob Quad, late medieval quarters of Merton College, University of Oxford. The list of medieval universities comprises universities (more precisely, studia generalia) which existed in Europe during the Middle Ages. [3] It also includes short-lived foundations and European educational institutions whose university status is a matter of ...
As with most monastic and cathedral schools, the school's teaching was based on the traditional seven liberal arts, grouped into the trivium (study of logic, grammar and rhetoric) and into the quadrivium (arithmetic, geometry, music, and astronomy). There were, however, differences among the schools on the emphasis given to each subject.
The seven subjects in the ancient and medieval meaning came to be divided into the trivium of rhetoric, grammar, and logic, and the quadrivium of astronomy, arithmetic, geometry, and music. Since the late 1990s, major universities have gradually dropped the term liberal arts from their curriculum or created schools for liberal art disciplines ...
Book III covers the medieval Quadrivium, the four subjects that supplemented the Trivium being arithmetic, geometry, music, and astronomy. [b] He argues that there are infinitely many numbers, as you can always add one (or any other number) to whatever number you think is the limit. [16]