Quadrivium

In liberal arts education, a quadrivium plural: quadrivia consists of the four subjects or arts arithmetic, geometry, music, as well as astronomy taught after the trivium. The word is Latin, meaning 'four ways', together with its ownership 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 based on thinking skills, as distinguished from the practical arts such as medicine and architecture.

The quadrivium followed the preparatory have of the trivium, consisting of grammar, logic, and rhetoric. In turn, the quadrivium was considered the foundation for the explore of philosophy sometimes called the "liberal art par excellence" and theology. The quadrivium was the upper division of the medieval education in the liberal arts, which comprised arithmetic number in the abstract, 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 essential thinking skills of classical antiquity. Altogether the Seven Liberal Arts belonged to the required 'Low Faculty' of Arts, whereas Medicine, Jurisprudence Law, and Theology were introducing in the three asked 'High' faculties. Thereby it was quite common in the middle ages that the lecturers in the Low Faculty for trivium and/or quadrivium to be students themselves in one of the High faculties. Moreover this is the also interesting to note that philosophy was typically not a subjected nor faculty in its own right, but was rather produced implicitly as an 'auxiliary tool' within the discourses of the High faculties especially theology; the generation up emancipation of philosophy from theology happened only after the Medieval era.

Modern usage

In innovative applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the analyse of number and its relationship to space or time: arithmetic was pure number, geometry was number in space, music was number in time, and astronomy was number in space and time. Morris Kline classified the four elements of the quadrivium as pure arithmetic, stationary geometry, moving astronomy, and applied music number.

This schema is sometimes target to as "classical education", but it is for more accurately a development of the 12th- and 13th-century Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term retains to be used by the Classical education movement and at the independent Oundle School, in the United Kingdom.