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The quadrivium (plural: quadrivia[1]) 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"),[2] and its use for the four subjects has been attributed to Boethius or Cassiodorus in the 6th century.[3][4] Together, the trivium and the quadrivium comprised the seven liberal arts (based on thinking skills),[5] 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")[citation needed] and theology.


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.[5] 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.[6] As Proclus wrote:

The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.[7]

Medieval usage[edit]

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 (412–485 AD), namely arithmetic and music on the one hand,[8] and geometry and cosmology on the other.[9]

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music 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 both in European and Islamic cultures.

Modern usage[edit]

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study of number and its relationship to physical space or time: arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.[10]

This schema is sometimes referred to as "classical education" but it is more accurately a development of the 12th and 13th centuries with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the classical education movement.

See also[edit]


  1. ^ "JewishEncyclopedia.com - WISDOM" (includes term "trivia"), web: JE210.
  2. ^ The word "quadrivium" indicates a 4-way intersection (as in a "4-way stop"), while "trivium" refers to a 3-way junction.
  3. ^ "Part I: The Age of Augustine", ND.edu, 2010, webpage: ND205.
  4. ^ "quadrivium (education)", Britannica Online, 2011, web: EB.
  5. ^ a b Wikisource-logo.svg "Quadrivium". New International Encyclopedia. 1905. 
  6. ^ 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.
  7. ^ Proclus, A commentary on the first book of Euclid's Elements, xii, trans. Glenn Raymond Morrow (Princeton: Princeton University Press) 1992, pp. 29-30. ISBN 0-691-02090-6.
  8. ^ Craig Wright, The Maze and the Warrior - Symbols in Architecture, Theology, and Music, Harvard University Press 2001
  9. ^ Laura Ackerman Smoller, History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350-1420, Princeton University Press 1994
  10. ^ Morris Kline, "The Sine of G Major", Mathematics in Western Culture, Oxford University Press 1953

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20 news items

Oxford Student

Oxford Student
Thu, 03 Jul 2014 11:00:00 -0700

OxStu Fashion: I think it's really interesting and innovative that part of your inspiration is drawn from a mathematical/science source, the quadrivium. There is always a lot of mentioning of the overlapping between fashion and the fine arts, but ...

Christian Science Monitor

Christian Science Monitor
Thu, 24 Jul 2014 02:56:15 -0700

Down the road, so to speak, lay the quadrivium: arithmetic, geometry, music, and astronomy. These seven “liberal arts,” artes liberales, were of no immediate practical purpose and thus deemed worthy of “free men” – liberal meaning “free.” Parents of ...

The Hindu

The Hindu
Thu, 24 Jul 2014 07:07:43 -0700

According to Quadrivium managing director K. Dinesh, live streaming of video to the control station is done using the software. Besides, silent call from the mobile to transmit the audio to the control station is also part of the system. The ...
The New Indian Express
Wed, 23 Jul 2014 20:33:39 -0700

Stanpower Company of Hyderabad provided technology for the RUPSS and Quadrivium developed technology for the women distress assistance system. Later, Chinarajappa underlined the need to make use of new technology in the police department.
Sat, 19 Jul 2014 21:41:15 -0700

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology,” edited by Miranda Lundy. 4. “The Monk of Mount Athos: Staretz Silouan, 1866-1938” by Sophrony Sakharov. 5. “The Wichita Reader: A Collection of Writing About a ...
The New Indian Express
Sun, 13 Jul 2014 19:48:45 -0700

Quadrivium Software Private Limited created a special software which can be uploaded in the mobile phones. The officials can know the movements of the beat constables through mobile phone. Each step of the beat duty staff can be perceived through the ...


Mon, 28 Jul 2014 08:56:15 -0700

Latin Jazz, Soul-Jazz, Enclave Maestoso, Home Trío, Mallén Trío y Quadrivium Trío tocaron en Diverxa, La Cuba, Brunchies, Hel-Arte, Koyote, y El Templo del Café respectivamente. La XII edición del Festival, que se consolida como uno de los referentes ...


Sun, 27 Jul 2014 12:52:30 -0700

ఆండ్రాయిడ్ ఫోన్‌లలో కాడ్రివియమ్ సాఫ్ట్‌వేర్ సంస్థ ద్వారా రూపొందించిన ప్రత్యేక జీపీఎస్ విధానాన్ని అప్‌లోడ్ చేస్తారు. ఈ సెల్‌ఫోన్లను ప్రతి స్టేషన్‌కు అందజేస్తారు. ఆయా ప్రాంతాల ...

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