Quadrivium

In the classical world, both geometry and astronomy were considered to be part of the <a href="https://en.wikipedia.org/wiki/Quadrivium" title="Quadrivium">Quadrivium</a>, a subset of the seven <a href="https://en.wikipedia.org/wiki/Liberal_arts#History" class="mw-redirect" title="Liberal arts">liberal arts</a> considered essential for a free citizen to master.

The quadrivium (plural: quadrivia<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-JE-1">[1]</a>) are the four subjects, or arts, taught after teaching the <a href="https://en.wikipedia.org/wiki/Trivium_%28education%29" class="mw-redirect" title="Trivium (education)">trivium</a>.

The word is <a href="https://en.wikipedia.org/wiki/Latin" title="Latin">Latin</a>, meaning "the four ways" (or a "place where four roads meet"),<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-2">[2]</a> and its use for the four subjects has been attributed to <a href="https://en.wikipedia.org/wiki/Boethius" title="Boethius">Boethius</a> or <a href="https://en.wikipedia.org/wiki/Cassiodorus" title="Cassiodorus">Cassiodorus</a> in the 6th century.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-3">[3]</a><a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-4">[4]</a>

Together, the <a href="https://en.wikipedia.org/wiki/Trivium" title="Trivium">trivium</a> and the quadrivium comprised the seven <a href="https://en.wikipedia.org/wiki/Liberal_arts" class="mw-redirect" title="Liberal arts">liberal arts</a> (based on thinking skills),<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-nie-5">[5]</a> as opposed to the practical arts (such as <a href="https://en.wikipedia.org/wiki/Medicine" title="Medicine">medicine</a> and <a href="https://en.wikipedia.org/wiki/Architecture" title="Architecture">architecture</a>).

The quadrivium consisted of <a href="https://en.wikipedia.org/wiki/Arithmetic" title="Arithmetic">arithmetic</a>, <a href="https://en.wikipedia.org/wiki/Geometry" title="Geometry">geometry</a>, <a href="https://en.wikipedia.org/wiki/Music" title="Music">music</a> and <a href="https://en.wikipedia.org/wiki/Astronomy" title="Astronomy">astronomy</a>.

These followed the preparatory work of the trivium made up of <a href="https://en.wikipedia.org/wiki/Grammar" title="Grammar">grammar</a>, <a href="https://en.wikipedia.org/wiki/Logic" title="Logic">logic</a> and <a href="https://en.wikipedia.org/wiki/Rhetoric" title="Rhetoric">rhetoric</a>.

In turn, the quadrivium was considered preparatory work for the serious study of <a href="https://en.wikipedia.org/wiki/Philosophy" title="Philosophy">philosophy</a> (sometimes called the "liberal art par excellence")<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-6">[6]</a> and <a href="https://en.wikipedia.org/wiki/Theology" title="Theology">theology</a>.

<h2>Origins</h2>

These four studies compose the secondary part of the curriculum outlined by <a href="https://en.wikipedia.org/wiki/Plato" title="Plato">Plato</a> in <a href="https://en.wikipedia.org/wiki/The_Republic_%28Plato%29" class="mw-redirect" title="The Republic (Plato)">The Republic</a>, and are described in the seventh book of that work (in the order Arithmetic, Geometry, Astronomy, Music.) <a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-nie-5">[5]</a> The quadrivium is implicit in early <a href="https://en.wikipedia.org/wiki/Pythagoreanism" title="Pythagoreanism">Pythagorean</a> writings and in the De nuptiis of <a href="https://en.wikipedia.org/wiki/Martianus_Capella" title="Martianus Capella">Martianus Capella</a>, although the term "quadrivium" was not used until <a href="https://en.wikipedia.org/wiki/Boethius" title="Boethius">Boethius</a> early in the sixth century.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-7">[7]</a> As <a href="https://en.wikipedia.org/wiki/Proclus" title="Proclus">Proclus</a> 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.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-8">[8]</a>

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<h2>Medieval usage</h2>

At many medieval universities, this would have been the course leading to the degree of <a href="https://en.wikipedia.org/wiki/Master_of_Arts_%28Oxbridge_and_Dublin%29" title="Master of Arts (Oxbridge and Dublin)">Master of Arts</a> (after the <a href="https://en.wikipedia.org/wiki/Bachelor_of_Arts" title="Bachelor of Arts">BA</a>).

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 <a href="https://en.wikipedia.org/wiki/Bachelor_of_Philosophy" title="Bachelor of Philosophy">B.Phil</a> and <a href="https://en.wikipedia.org/wiki/British_degree_abbreviations" title="British degree abbreviations">B.Litt.</a> 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 <a href="https://en.wikipedia.org/wiki/Proclus" title="Proclus">Proclus</a> (412–485 AD), namely arithmetic and music on the one hand,<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-9">[9]</a> and geometry and cosmology on the other.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-10">[10]</a>

The subject of music within the quadrivium was originally the classical subject of <a href="https://en.wikipedia.org/wiki/Harmonic" title="Harmonic">harmonics</a>, in particular the study of the proportions between the music intervals created by the division of a <a href="https://en.wikipedia.org/wiki/Monochord" title="Monochord">monochord</a>.

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.

<h2>Modern usage</h2>

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study of <a href="https://en.wikipedia.org/wiki/Number" title="Number">number</a> and its relationship to physical space or time: arithmetic was pure number, geometry was number in <a href="https://en.wikipedia.org/wiki/Space" title="Space">space</a>, music number in <a href="https://en.wikipedia.org/wiki/Time" title="Time">time</a>, and astronomy number in <a href="https://en.wikipedia.org/wiki/Spacetime" title="Spacetime">space and time</a>. <a href="https://en.wikipedia.org/wiki/Morris_Kline" title="Morris Kline">Morris Kline</a> classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-11">[11]</a>

This schema is sometimes referred to as "classical education" but it is more accurately a <a href="https://en.wikipedia.org/wiki/Renaissance_of_the_12th_century" title="Renaissance of the 12th century">development of the 12th and 13th centuries</a> Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the <a href="https://en.wikipedia.org/wiki/Classical_education_movement" title="Classical education movement">Classical education movement</a> and at the independent <a href="https://en.wikipedia.org/wiki/Oundle_School" title="Oundle School">Oundle School</a>, in the United Kingdom.<a href="https://en.wikipedia.org/wiki/Quadrivium#cite_note-12">[12]</a>

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<td class="mbox-text plainlist">Look up <a href="https://en.wiktionary.org/wiki/quadrivium" class="extiw" title="wiktionary:quadrivium">quadrivium</a> in Wiktionary, the free dictionary.</td>

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<ul>

<li><a href="https://en.wikipedia.org/wiki/Andreas_Capellanus" title="Andreas Capellanus">Andreas Capellanus</a></li>

<li><a href="https://en.wikipedia.org/wiki/Degrees_of_the_University_of_Oxford" title="Degrees of the University of Oxford">Degrees of the University of Oxford</a></li>

<li><a href="https://en.wikipedia.org/wiki/Trivium_%28education%29" class="mw-redirect" title="Trivium (education)">Trivium</a></li>

</ul>

<h2>References</h2>

</ol>

<ul>

<li id="cite_note-JE-1"><cite class="citation web">Kohler, Kaufmann. <a rel="nofollow" class="external text" href="http://www.jewishencyclopedia.com/articles/14950-wisdom">"Wisdom"</a>. <a href="https://en.wikipedia.org/wiki/Jewish_Encyclopedia" title="Jewish Encyclopedia">Jewish Encyclopedia</a>. Retrieved 2015-11-07.</cite></li>

<li id="cite_note-2">The word "quadrivium" indicates a 4-way intersection (as in a "4-way stop"), while "trivium" refers to a 3-way junction.</li>

<li id="cite_note-3">"Part I: The Age of Augustine", ND.edu, 2010, webpage: <a rel="nofollow" class="external text" href="http://maritain.nd.edu/jmc/etext/hwp205.htm">ND205</a>.</li>

<li id="cite_note-4">"quadrivium (education)", <a href="https://en.wikipedia.org/wiki/Britannica_Online" class="mw-redirect" title="Britannica Online">Britannica Online</a>, 2011, web: <a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/485943/quadrivium">EB</a>.</li>

<li id="cite_note-nie-5"><img src="/fa38c309-a14b-53e8-81d6-413d83d700ab.png"/> <cite class="citation encyclopaedia"><a href="https://en.wikipedia.org/wiki/Daniel_Coit_Gilman" title="Daniel Coit Gilman">Gilman, D. C.</a>; Thurston, H. T.; Colby, F. M., eds. (1905). "<a href="https://en.wikisource.org/wiki/The_New_International_Encyclop%C3%A6dia/Quadrivium" class="extiw" title="s:The New International Encyclopædia/Quadrivium">Quadrivium</a>". <a href="https://en.wikipedia.org/wiki/New_International_Encyclopedia" title="New International Encyclopedia">New International Encyclopedia</a> (1st ed.). New York: Dodd, Mead.</cite></li>

<li id="cite_note-6"><a href="https://en.wikipedia.org/wiki/Daniel_Coit_Gilman" title="Daniel Coit Gilman">Daniel Coit Gilman</a> et al. (1905) <a href="https://en.wikipedia.org/wiki/New_International_Encyclopedia" title="New International Encyclopedia">New International Encyclopedia</a>, lemma "Arts, Liberal"</li>

<li id="cite_note-7">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.</li>

<li id="cite_note-8">Proclus, A commentary on the first book of Euclid's Elements, xii, trans. Glenn Raymond Morrow (Princeton: Princeton University Press) 1992, pp. 29-30. <a href="https://en.wikipedia.org/wiki/Special:BookSources/0691020906" class="internal mw-magiclink-isbn">ISBN 0-691-02090-6</a>.</li>

<li id="cite_note-9">Craig Wright, The Maze and the Warrior - Symbols in Architecture, Theology, and Music, Harvard University Press 2001</li>

<li id="cite_note-10">Laura Ackerman Smoller, History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350-1420, Princeton University Press 1994</li>

<li id="cite_note-11">Morris Kline, "The Sine of G Major", Mathematics in Western Culture, Oxford University Press 1953</li>

<cite class="citation web"><a rel="nofollow" class="external text" href="http://www.boarding.org.uk/media/news/article/2352/Oundle-School-Improving-Intellectual-Challenge">"Oundle School - Improving Intellectual Challenge"</a>. The Boarding Schools' Association. 27 October 2014.</cite>

Each of these iterations have recently been discussed in a conference at <a href="https://en.wikipedia.org/wiki/King%27s_College_London" title="King's College London">King's College London</a> on "<a rel="nofollow" class="external text" href="http://www.kcl.ac.uk/artshums/depts/liberal/conference.aspx">The Future of Liberal Arts</a>" at schools and universities.</ul>