page_title: Quadrivium
section_title: Medieval usage
hierarchical_section_title: Quadrivium / Medieval usage
caption_attribution_description: English: Detail of a scene in the bowl of the letter 'P' with a woman with a set-square and dividers; using a compass to measure distances on a diagram. In her left hand she holds a square, an implement for testing or drawing right angles. She is watched by a group of students. In the Middle Ages, it is unusual to see women represented as teachers, in particular when the students appear to be monks. She is most likely the personification of Geometry, based on Martianus Capella's famous book De Nuptiis Philologiae et Mercurii, [5th c.] a standard source for allegorical imagery of the seven liberal arts. Illustration at the beginning of Euclid's Elementa, in the translation attributed to Adelard of Bath. Français&#160;: Détail d'une enluminure du XIVe siècle, contrepoinçon d'une lettre capitale P, au début des Éléments d'Euclide, dans une traduction attribuée à Adélar de Bath. Une femme porte une équerre d'une main et utilise un compas de l'autre pour mesurer des distances sur un diagramme. Un groupe de moines, apparemment ses étudiants, la regardent. Au Moyen Âge, la représentation d'une femme dans un rôle d'enseignant est inhabituelle. La femme représentée ici serait donc plutôt une personnification de la géométrie.
context_page_description: In liberal arts education, the quadrivium consists of the four subjects or arts, taught after teaching the trivium. The word is Latin, meaning four ways, and its use for the four subjects has been attributed to Boethius or Cassiodorus in the 6th century. Together, the trivium and the quadrivium comprised the seven liberal arts, as distinguished from the practical arts.
  The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium, consisting of grammar, logic, and rhetoric. In turn, the quadrivium was considered the foundation for the study of philosophy and theology. The quadrivium was the upper division of the medieval education in the liberal arts, which comprised arithmetic, geometry, music, and astronomy. Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts of classical antiquity.
context_section_description: At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA, the student could enter for bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day, some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy).
  The study was eclectic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus (AD 412–485), namely arithmetic and music on the one hand and geometry and cosmology on the other.
  The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the musical intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised in both European and Islamic cultures.
caption: Woman teaching geometry. Illustration at the beginning of a medieval translation of Euclid's Elements, (c. 1310)
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