{{Short description |Liberal arts of arithmetic, geometry, music and astronomy}}
{{for|the former art gallery in Sydney|Quadrivium (art gallery)}}
{{use dmy dates|date=May 2025}}
[[File:God the Geometer.jpg|thumb|upright=1.0|For most medieval scholars, who believed that God created the [[universe]] according to [[Musica universalis|geometric and harmonic principles]], [[science]]—particularly [[geometry]] and [[astronomy]]—was linked directly to [[divinity|the divine]]. To seek these principles, therefore, would be to seek God.<ref>{{Cite book |last=Hayes OFM |first=Fr. Zachary |title=S. Bonaventura, De Reductione Artium ad Theologiam |publisher=[[Franciscan Institute Publications]] |year=1996 |isbn=1-57659-043-7 |location=Ashland, Ohio |pages=11–34, 37–47 |language=Latin, English |trans-title=St. Bonaventure, On the Reduction of the Arts to Theology |oclc=835507484}}</ref>]]

The '''''quadrivium''''' (Latin for "four ways"<ref>"Quadrivium (education)". ''[[Britannica Online]]''. 2011. [http://www.britannica.com/EBchecked/topic/485943/quadrivium EB].
</ref>) is a [[pedagogy|pedogogical]] grouping of four historical mathematical arts—[[arithmetic]], [[geometry]], [[music]], and [[astronomy]]— which was first taught in [[classical antiquity]], and later revived in [[Middle Ages|medieval]] Europe. Together with the ''[[trivium]]'', they make up the seven classic disciplines of the [[liberal arts education]]. Beginning with [[Petrarch]] in the 14th century, [[humanitas#Revival|''studia humanitatis'']] and its subsequent offshoots gradually supplanted the ''trivium'' and ''quadrivium'' as curricular conventions. 

==History==
[[File:Boetius.png|thumb|upright|The Roman philosopher [[Boethius]], author of [[On the Consolation of Philosophy|''The Consolation of Philosophy'']]]]

The four mathematical arts compose the secondary part of the curriculum outlined by [[Plato]] in [[The Republic (Plato)|''The Republic'']] and are described in the seventh book of that work (in the order arithmetic, geometry, astronomy, music).<ref name="nie"/> The ''quadrivium'' is implicit in early [[Pythagoreanism|Pythagorean]] writings and in the ''De nuptiis'' of [[Martianus Capella]], although the term ''quadrivium'' was not used until [[Boethius]], early in the sixth century.<ref>Marrou, Henri-Irénée (1969). "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. pp. 18–19.</ref>  As [[Proclus]] wrote:

<blockquote>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 studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.<ref>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}}.</ref></blockquote>

The first use of ''quadrivium'' as a term has been attributed to [[Boethius]],{{Sfn|Fried|2015|p=2}} when he affirmed that the height of philosophy can be attained only following "a sort of fourfold path" (''quodam quasi quadruvio'').<ref>{{cite book | vauthors=((Stahl, W. H.)) | date=6 November 1978 | title=[[Roman Science: Origins, Development, and Influence to the Later Middle Ages]] | publisher=Praeger |  isbn=978-0-313-20473-9}}</ref>{{rp|199}} It was considered the foundation for the study of [[philosophy]] (sometimes called the "liberal art ''par excellence''")<ref>[[Daniel Coit Gilman|Gilman, Daniel Coit]], et al. (1905). ''[[New International Encyclopedia]]''. Lemma "Arts, Liberal".</ref> and [[theology]]. 

==Medieval usage==
[[File:Woman teaching geometry.jpg|thumb|''Woman Teaching How to Construct Geometric Shapes''. Illustration at the beginning of a medieval translation of Euclid's Elements ({{circa|1310}})]]

The medieval [[liberal arts education|liberal arts curriculum]] began with the ''[[trivium]]'', followed by the ''quadrivium''.<ref name="nie">{{Cite NIE |wstitle=Quadrivium |year=1905}}</ref> The seven liberal arts were considered "thinking skills" and were distinguished from practical arts, such as [[medicine]] and [[architecture]]. At many [[medieval universities]], the ''quadrivium'' would have been the course leading to the degree of [[Master of Arts]] (after the [[Bachelor of Arts|BA]]).{{Citation needed|date=October 2025}} 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 [[Bachelor of Philosophy|B.Phil]] and [[British degree abbreviations|B.Litt.]] degrees are examples in the field of philosophy). 

Educationally, the ''trivium'' and the ''quadrivium'' imparted to the student the seven essential thinking skills of [[classical antiquity]].<ref>Onions, C.T., ed. (1991). The Oxford Dictionary of English Etymology. p. 944.</ref> Altogether the Seven Liberal Arts belonged to the so-called 'lower faculty' (of Arts), whereas Medicine, Jurisprudence (Law), and Theology were established in the three so-called 'higher' faculties.<ref>By way of example, until well into the 1970s, the faculty of Medicine of the University of Würzburg (Germany) was still officially referenced as a 'Hohe Fakultät' by its doctoral students in their written doctoral dissertations.</ref> It was therefore quite common in the middle ages for lecturers in the lower ''trivium'' and/or ''quadrivium'' faculty to be students themselves in one of the higher faculties. Philosophy was typically ''neither'' a subject ''nor'' a faculty in its own right, but was rather present ''implicitly'' as an 'auxiliary tool' within the discourses of the higher faculties, especially theology;<ref>'Philosophia ancilla theologiae'</ref> the separation of philosophy from theology and its elevation to an autonomous academic discipline were post-medieval developments.<ref>This separation is partly attributable to topical developments within philosophy itself, and due in part to Martin Luther's rejection of philosophy as 'useless for theology' as the Protestant Reformation evolved.</ref> 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<ref>Wright, Craig (2001). ''The Maze and the Warrior: Symbols in Architecture, Theology, and Music''. Cambridge, Massachusetts: Harvard University Press.</ref> and geometry and cosmology on the other.<ref>Smoller, Laura Ackerman (1994). ''History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350–1420''. Princeton: Princeton University Press.</ref>

The art of music within the ''quadrivium'' was originally the classical subject of [[harmonic]]s, 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.

===Decline===
Displacement of the ''quadrivium'' by other curricular approaches from the time of Petrarch gained momentum with the subsequent [[Renaissance]] emphasis on what became the modern [[humanities]], one of four liberal arts of the modern era, alongside [[natural science]] (where much of the actual subject matter of the original ''quadrivium'' now resides), [[social science]], and [[the arts]]; though it may appear that music in the ''quadrivium'' would be a modern branch of [[performing arts]], it was then an abstract system of proportions that was carefully studied at a distance from actual musical practice, and effectively a branch of [[music theory]] more tightly bound to arithmetic than to musical expression.{{Citation needed|date=December 2022}}

==Modern usage==
In modern applications of the liberal arts as curriculum in colleges or universities, the ''quadrivium'' has been considered by many to be the study of [[number]] and its relationship to space or time: arithmetic being pure number, geometry number in [[space]], music number in [[time]], and astronomy number in [[spacetime|space and time]].{{Citation needed|date=October 2025}} [[Morris Kline]] classified the four elements of the ''quadrivium'' as pure (arithmetic), stationary (geometry), moving (astronomy), and applied (music) number.<ref>Kline, Morris (1953). "The Sine of G Major". In ''Mathematics in Western Culture''. Oxford University Press.</ref>

The term continues to be used by the [[classical education movement]], and explicitly at the independent [[Oundle School]], in the United Kingdom.<ref>{{cite web |url=http://www.boarding.org.uk/media/news/article/2352/Oundle-School-Improving-Intellectual-Challenge |title=Oundle School – Improving Intellectual Challenge |date=27 October 2014 |website=The Boarding Schools' Association |access-date=10 December 2015 |archive-date=15 August 2020 |archive-url=https://web.archive.org/web/20200815195502/http://www.boarding.org.uk/media/news/article/2352/Oundle-School-Improving-Intellectual-Challenge |url-status=dead }}<br />Each of these iterations was discussed in a conference at [[King's College London]] on "[http://www.kcl.ac.uk/artshums/depts/liberal/conference.aspx The Future of Liberal Arts] {{Webarchive|url=https://web.archive.org/web/20160525204125/http://www.kcl.ac.uk/artshums/depts/liberal/conference.aspx |date=2016-05-25 }}" at schools and universities.</ref>

==See also==
* [[Andreas Capellanus]]
* [[Vedanga]]
* [[Degrees of the University of Oxford]]
* [[Four arts]]
* [[Martianus Capella]]
* [[Trivium]]

==References==
{{Reflist|30em}}

=== Book sources ===
* {{Cite book |last=Fried |first=Johannes |year=2015 |title=The Middle Ages |edition=3rd |location=Cambridge, MA |publisher=Harvard University Press |isbn=978-0-67405-562-9}}

== External links ==
* {{Wiktionary inline|quadrivium}}

{{Humanities}}
{{Classical education|state=collapsed}}
{{Authority control}}

[[Category:4 (number)]]
[[Category:Cultural lists]]
[[Category:Liberal arts education]]
[[Category:Medieval European education]]

[[es:Artes liberales#Las siete artes: Trivium et Quadrivium]]