Allegory of Trivium and Quadrivium

Martianus Capella and the Seven Liberal Arts VOl.UM E 1

THE QUADRIVIUM OF MARTIANUS CAPELLA LATIN T ItADITlONS IN THE MATHEMATlCAL SCIENCES 50 .. C. - .. O.I 'SO

by WilIiam Harris Stahl WITH A STUDV

or THI.:

ALL EGORY

AND TIIE VER BAL DISCIPLINES

by RicharJJohnMnl wilh E. L

COLUMBIA UN TVERSITY PRESS N E W YORK AND L ON D ON '91'

The Allegory and lhe Trivium wbobIy d .... from .... 199- Mstti4nuo' poem ro .. ction "l _.u. a.ndlan'. p _ o"" "" • Se< abono PI'> '1"0. • Muriomu'

86

TJlE ALL[GORV ASD TIlE TRIVIUM

men lKu has an allegorica.l role: he is pn:scnter..-hMm, Vol. UI pt. ,¡'906) .

" "Mortionus Copell. CI Junbliq ...• R..... dt. I...u. Imnel, XXXVI ('9j8), 'Jj-j+

RELIGIOllS IDEAS

8,

,0-",

Dolpm ('0.' " '6), ar orber rimes rbe sun (: S, '9), ar orbers rbe syncrctization of a host of uligious figures ('9'·9'), and again the NeopLotouic Mind ('9,). This conversioo of the O lympians into dti· tics of orber, pmlosophictlly ba..d, uligions WIS frcqucnt io late antiquity." lo Muti3nus, howevcr, oo! ooly rbe Olympians are mus are similarly tuatcd, absorbed, rbe sacred figuru of anciem l rslic lArs Jives in me secood regioo of betw«n MIU"S aud Juno (,,6); Omsus io tcDm r.gion. ",itlt N.ptunc (54); VejovQ io tite fiftccoth, oen to Satum ($9) . "What weu "' onc time sepanttc and relatively hornogeneous currents of beli.cion ;nto a mystCTy, of salvaoon through divine interc=ion, such as Apuleius' Metamorpho,u reveals. lmmortality comes not from diwine gilt or perwnal hoUness bur from tite fame won by intcllectual achievement, aftee eifort 2nd saerifice. Aput fmm tIUs interpretation, the religious lore ;n Marri.og. U; of considerable interest to rhe hl,tori.tn of rdigion. The description of tite assembly of the gods (4'-6$) i.s one oi the tbree major ""orces for OUr pitifn1ly slight kuowledg.:: oi Eouscao w hich wu "" highJy regarded by the Roman •• Tm Marri.og. admirably the conflnence of rdigious mditions in tite late Ronun Empire and the role of rkc:ayed Ncoplatonism in bleuding the me3lIl5. Both W ein_ stock I1ld Turean ague rhat Ibis bleoding is OOt tite wock of Ml nianus, bur tlu.t be used the now-lost leaching of Cornelins [.aben, who had brought late Grcck .ud ¡",He religion and cosmology mro • synt.l=is. Martianns' particular achievcment wu ro combine th.Jlt religious syn_

'j.

" Uuno... p. "W.inorook. P.

'0"

THE ALLEGORY AND TI/ E TRIVIUM

I)Q

theas with lhe secular "religion of me seven am in m..t conren.

by placing bis creacise on

THE CURtllCULUM OF THE SEVEN LIBERAL AItTS

To

* "",dem, the curriculum of the ""ven am ot first appears ro

llave no principIe of unity; it ""ems lo be a nndom grouping oi subjcen in which any ""bstirutioo of one rOl another wouJd be !lO more significant Illan Ihe sub6titutiol1 of geography fOI Spanish io. rnodem pupil's COI1l'ge of study. H owe>'er, teachers of lhe eoorly Middle AgesOIssiodorus, Isidorc,Alcuin, lUbaouo Mmrus,john of Solj.bury,T1tierty of a..mu'..... regarded it:l.S an integrated curriculum widl ""ven cornponenl:l,.n mcessary, Thc otigins uf the curriculum wcre in clusical lt is well knowo thatthe IlNdy of rhetorle bcgon in the Greck world of thc fifth 8,'I>Iopt .. EPI"'''''''''''' do Thierty do: Outtr...• Mf P...,...u;O" i" 0 ...«, chop.., Satus Empiricus Ad".,._ n Dioge_ Loerti.. Liw. Df "" i. m 9- '5a nu. ¡, tIIe period In whlob 1'I0I0', 0."1/'" jo sere-

_01,

.. H .... Klink have coined tite word (or, in hi5 form, qu.o'¡ruvitnn) ¡ and lsidore of Seville, It once 10 offspring of aotiquity and a sin: of (he M¡dd!e Ages, !:reaes oí mem io the first three booIlure, ;IS wcll as rhe \llIe of Iogieal argument•• o thal ir is closely reJatcd ro irs sister ans, grammar "nd dialcctic. 11>e cementing of mis rclationship seems ro have beco prirn.riIy a Stoic contribution." Thc Stoics divided rhe fidd of philo$Ophy into c{hics, natunl philosophy. and Jogic; aOO rhis lut included al] aspects of vernal e:q¡lUIion, hmcc lhe wbole lrivium. &ndys Zcno himself and bis lilecessor in rhe school, Oetnthes, os antbo .. of worb OD gnrnmar" (Zeno'o wc!l·lecausc our $urviving LItio gnrnmatical tre:otises are rnainly of che fourm century A.D. Or bter,.nd che most one can do is compare Manianus wim each oí tItese and construct hypot:ltcKs ro aplain sUnibrities or differences.. There ue many pointo of correspondenc. between Manianus' third book .ud me work of Diomedes (dating from tite later fourth cenrury A.D.), which JUrgenoen apbins by supposmg tila! both borrowed fmm • comrnon ""urce. "I"his nu.y be true, but the source, ir :my, Iu.s pero ished. As Langbe.in points out, motcOver, there lre aIso many cotrCspondroccs lletwern Mattianus and Charisius, Muimus V1cturinns, Servius, and oc leur one anonymoWl Imllor; and they Canoot In be shown ro de"""nd froro one cOnnnon source . Funhermore, Martianus differs from Diomcdes in his definirlon oí • .¡yU.ble, in distinguishing lhe thrcc porto of • syJable, in distinguishing me foor gcner. of jwIc. and in details oí rile of including his UKnion

.. o.

C.ptU. " ....

""'De rutio> Mo.nioni Oo.peU .. b"bm," pbi/oJop .a,.. PI'-

c"""""", ••ú"."

p¡,;¡oIt!,H ",aL M

102

THE ALLEGORY ANO TKE TRIVIUM

chac a word can bear al! time tCf ,h. F.""k, ,. J' . .. Pp. '06. 'oS. "o, ",. "J.

GRAMMA R

"3

n')tcs certain similaritie5 betwcen 800k IR an0-9 (discussion of ending in thelmero S th.rough X, and oí voiees of verbo) 2nd 311-'1(eonjugarion of verb< idenriflCOtion of futtllor ".."...ml'" ¡" by J..., Pú ..... ''U Commcnulro do M...-cin de LooD ..... I"rtwiU. dLci di ManiaDo Ó7: .d."l"1Ioow. p. In. B. M..... s.m, Lo,;., p. J' . .. M..... p·SI .

"'9 phrutus appea .. ro hay. bcgun investigating atgII=nts "from hyD I AL I\CT IC

potbtsis"'" in wlUch a desi.rcd conclusion is tgree In otymological discussioo oí wrbum in Augustinus, coupled with his rejecrioo of etymologizing" 'iUW"'" not unir th •• h. had" VuroniJon work before mm bu. th •• he was n • • úog it crirically. SeCOIId, !he p=age (3H-60) which srands as an innoduction ro die ten CIllegOries (;n place of AtisrotIe's explanaúon of what is mU/l' by "homonyrnous," "synonymous," 2nd "patonymous") .Iso has affiniú., wilh Ihe logical w orles incJuded in lhe Augustinian corpus, The influent;al temtS lUqWWcum and wriwcum do nOI seem lo occur ;n extant authors befO:ni: Lom/>"oij¡

DIALECTIC

115

which are exp,msions of the material in Apuleill!, ,.. and other pesages'" wherc Apulcius expreases file thought not ooly moa clearly dlJn Mlrtianus bOl also more briefly. The possibititr of • common ArisrottlWt $Ource cannot be rouUy aclud«l. If, howcver, Apuleius is uuty M.rtimus· prinle ...urce, oue Cln only wish dIJe Martianus had plogiariud IJIOre whotcheane.nUl j96) IDd pro p.r, PI'- l , .. , l .

... Ef:. tbe

divioioo of rboro,;" inro th= (oruI onIy rhree.l 'J'P'I" balevtlc. lo""';'" cpi"'idic; tbo dirioioo of!be dwioo el tbo ..,dieoeo (Rbnorl& ,. J. ,_¡l. For die toploal. o. spocificolly Atbrn; .... b1Is of che - . ...,. l. ,. i'"S • •"-

... Rb#orl&."¡ 11 •• "" ....... • do Capbn. PO.ü. bnt ... A. E. DougIo=! by M.m.nllS (909) . . . "Io{ry figure ...boto ..... odiouo beod wu odomrd ",id> omuneo" af glitteling JOld" lIId . . . maideo ",bo "moved _ • ¡¡roce ..... her motbtr cQUld hardly nu.td>," • Abot",: • tray. rovf the Uf in Latin, • nn: oc:cum:nce for thls $Uhicct. die ave .... ' Amidlt tite resplendem sening of me Cl'lesñal f huw VIl.O tl'CItcd gtOfTlCtlJ in (he funrth book of tusl"" BI.>I.>b of 1M DiseipJjntl. 1I ouc elrlicr surmisotll are: eQrrect," that V....... •• 0001< cnmprised I modicum of geomttty and !he ciernen!! oí Il1lVeying. Mutianus lll\ISl han bcen largcly indtpendtnr of Vlrro in eQmposlng tus De I",,,,,n;'. MartitnuI· book makcs 00 n1ClIllon of su,,",ying, and ir ÍIi deu W! V .......'. book did . - doaI ",¡,h rqu-I gcogrophy. W. IIJ... lOI1\C san! knowlcdge ahou. Lotin SlUdits of gcomeuy in me period jua. ""d jllSt .fur tbe of me W$tm Emplee. AH qUldrmum srudi.. languished in me ..... tin world. .00 gwrnouy ,.".. tht mosr negJecud subjca in tbe four." Augustine, w ho, prior ro ManiuluJ, had been engogef a De ..... ric•. " How

Dona bu,

(O ,

,.JI

...,...,.

, s...dom f'/O'1'OJ ... dntcd .., &cOfnphy¡ kCrions

, 7mpilen '" off .. _

9'l6l. Go, .......... tbo " .._ iD iho fol•• " ._., 0Dd boüono ..... tho)I1>tIoGi 10"'11 m ' ... ... 11 ttIio tIoooio jo - ..... ;, _ d indO , . . truo... """'" _ (1' l1000 .... _ . . ...,.,...... _ _ he ii0" Do ,;¡u ""bit) from Solinus, is • nluablc fO tite delCrionlio:t of cluoiclll writings "' tht Iund. of Intd;....] ct pr""f. wcrc rcquircd ro dcmonsuate the .doqnacy of coast:al surveY' ro cncomp'" remoce r.:gions. Lltin ",ritul eustonwily inaodu=! proofs of • COntinUOllll oceau-Ñbulous circum-

navigations of the nortbcm and southem eontineuts. Pliny's proofs are gublcd by Maniaous. Pliny (l. '70), 011 the IUthority of Corndius u a prneru froro the lring Nepos. say' tbat MeteUus Cele! of the Sw1tbi2m some Indians wbo liad beco driveo from thcir coorse, by stOml!, o.Il the w:ay ro Germany¡ MartWws (6u) has it that Coroelius, alter aking sorne ludians captive, sailcd post Germany. Marrdoer mon u';"bIe dota .bout tbeir own region from boob ., ...... by oudIott '"'" 111ft depeods "1"'" Solin.. ....t PIiI>y ond sino "" Infotmstion oborn: B.. trio ..,d Suony. Se. Di&tJi/1 U/nr J. """"". ",bU urr.., od. G. Potthoy, PI' 4N1.

GEOMETRY

'37

ser the foan and content of world geognphy (oc ova a thoU3llJld

Y" • .

Pliny'. place narncs along the mainland come in helte.r-skdter profu_ ruon. To aUeviate the tedium of readen he shows inrere.t and 9O[IIetimes emotion when writing grtat rivert lil«: the Po and Danuhe OC about places with litcnry or mythologica1 mociatioRS; fmm time lO time he n:tnccs rus coursc to rcmark about off$hon: isIands, iucluding tiny ones, in sorne dcta.il: and he delighu in occasionaUy in_ serting in inctedib!e tlIle about sorne place. These divertissements hsd a bettcr manee of survi",r in Pliny's SUC ... Copoll .. M_'7"O .......di • imocunte. ro< • deu f·""';ma· oí tbo ""'P le< V"....".., Iúmol. MD",.,,.,,,,. Afriul .. m, m . • "IlI...,...;."u • gi""" la UD codico di Mutllno Copdlo.." BodUtthJo dtII'b-

a out dre diff'.:uItieo, i/ noc tho impood>iity. oí obainIng rn ..""..... ..hre fu< dre ... dium.

'.' and Roman miles (u ,5oo)' We

GEOMETIlY

rny's estimatt ia both stadia (180,000) may be surm some RDnw> inttrmediory and nDl from Ptolcmy'. Gtoguph), (l . 11 . 1), as h2s beca comnllmly stIppSCd." Thc kmgitudiml distancc from che eastem cnrcmity of India t Cídiz is 8.578 miles (611-11), aceording to Ártcmid!>nlS. Mmi' nn. golt the figure and from Pliny (,. , ..,). Tbc figures of Pliay, as given in che IlWlUSCript!, are in R DIlIII!I numcNIs, which are fr«¡uendy inconectly copied by scribes. Mamanus' quamitics are wrimn OUt in brin, alld. since !le WllS using older mll!lU5CTipu of Pliny "ud SoUno. tlun those wc p"" • ir is obvino. 1M. Martimus' ten must be included in any con.tion of n13nuscripts for Pliny'. gcographicil books." Martimus then .tates (6 1,) tlul! rhe distancc as cecorded by lsidore" is 9.8'8 miles, tnei, in anempting to reconcile the discrepant !le points OUt thar Arcemidorus mean! to add to !ús (igure the distancc from Cldiz Cope Finistcrre, 99' mil ... l'hi$ too wu obuined from

.0

.. """"....,. Mat ond Solinuo we ;, motted by ""deo. miottbt, m.u..'¡OÓOlII, tod miOOQ "1'1"'"'" k O"eh< '" clear "1' mIIIy ol ti>< f • • hy ,.tdiog> ot Pliny" 00 rbc problomo ollDln\Jlcript tronrm¡""- oí Pliny', n""","'" seo BeaujOll. pp. '44"f6. p Joidou of Cho.ru. Ollt ot .._ wotb 00 .... rl""d TIu r.tM.too S,m.", (c. UI. ' I¡, Iw ..,,,,I...d. n.o G_k y'. ( •. '.1) toW ....hlob is OfDt oI.ip< weight in quesrions oi tho """..ricny oi E1IClid.. «no Seo TIH Tbirt_ 01 lWdorinfI:." s.. io e.. 1".. in Toanery, Sri_., eZlWtpIion ;, _ he .... follo>ring & lAciB Enclideoo troditioo whiclt tbo Gnoek .."'" ond ... hicl\ m-r ha ... origimted iD 80010: IV al VottO'. Nin< of ,b, Disci/'IiMI. Vomo ¡" len"...,. fto& 'f"'X"" tely recognize cbat sbe ¡,

.bou.

prel"'ring

tQ

work Out the construetion (or .he ¡In< proposiaon oí

Eudid and rhey bre3k joto acclaUn oI Euclid. Geomeuy, pleoscd with this 'pprobation oi her disciple, sn,uches fmm his Itmd rus preciOIlS bookl-which undoubtedly contain me proof. oI all tite propositions in the Ihineen boob oI the Elm1nIlJ*_ and gives dtem ro Jupiter .. a tel[tbook for che flll'thcr instruction oI the heavenly eompany •

.. Primuy -dio¡ ti> Pbto Tm... ... H 1>-.

,o¡,." .

EI_,,....

• Whether • """,pi«< ol!llt .,..;loN. in tb< W ... die twdhb cenwry- tht baic quertion lar 011 in...,..;g.tn 01 r.;., geom=y-hss -)'t'I b!odon of do. EItmMu inro Lotin befo« lo: veniono t>e< ..... 10"", ro th< Wm ¡., tbt twcUth «ni", """".. optt• .. ..."., oIxHJSt < Greeks ...... lDlown .. H A. P X H IThe 1le¡inniI>¡1. nlllllOric:oJ ni.... of the Gredt: Jettu. ...., H=Ii; k:.; P= .oo; X=-. H=tl l af arúh_ mology, iDduding _ boo'" devoKj«', tlu. • ......rr.d ¡., mote .". k .. formo N".:omochos· I-w.U&tioN '" Aritb.....ir dw. only with orithmedc pI"OpUIIlb. ...-ltirop 01 Moniuuo, c...iodonJs, toidon, ... d Bedo. .. f",. ...c.... DCeS 0Jl dUo suhject ... "'" o.rdclo lo TI><

Or{Of"d Chslle. F",. Noopyth.gor.....", iq Vano\ Leonudo F=ero, Ss ..... dtI "uqor/Jm., PI'- JI ....;+

writine> ...

ARITHMETIC

' ss

among quadrivium I:tUdies in me curriculum," fiOOing its pnletieal .ppijcation in eomputing the dttes of Euter and other feasa. Computus tabla l OO tteatiscs tum up wilh frequener in medieval Cm«ry. Friedmu K6"" ..... -.1 toeh· b&1"", ;" 4 .. Anrih, PI" S....,." ditcUJOCS ch. ordot ond m."g oo. dup. X of w copltd .........hetype. WK re'PO"''''' rOl ben iD fogu«> ... Nlcom.chu. , . 17. 6 (.... O'Oop. PI" ,¡6-J1). " Tho 1u¡cr "umbet lo tbto coIIed • ·"""tiplo" (pnJ'/¡Jik_). O . Niwmochw. l. ,8. 1 ( .... trOo,e. P. .. R.tit> .... "'..., ..... "Tbe Iotger nwnber k dIcn coIIed by hiaDrWu DI _ motioo .....pupsttieulor.". "'"" gr. ... currmcy by Boethius, iD bis tnmlorioD oi N"JCOJD2Chus. 1, co""'¡'" widWr. ll: < ""'" forms, bi< ".."...tioo of di< '"""" bacI! iDro G=k. P. TIUIOUY, "Ad M. Ülpl. M.tnWtuo' OOSib1o ..pJanonlona. MllfIluuo bao iD miod oqUM< (pi • .,.) nnmben orisinotig fMm tbe DlODad (. poi other ( j. "J. Any nwnber" either prime and incomposite or, if it is composite in rclation ro itself, is measured by some prime number (¡. )'.)1)," Nen cornes (¡85--J ..... ond '"' < rnditioD .,.¡gnlng tu HiPl"rclu" tbe Ioe";"n of tbe nnW poi", or Aries" moy \leen 0 = Ono Ncu¡¡doaI¡or, n . &... Scient:< .... p. ,18, po .... out eus, die (tont p2ws of Ursa Malor, and back to Oraco's Ilead,N (8'7) The [I...ocal G=k astronomers unclerstood th.at the locatioo of the arcric circlc: would vary with d.e latitude of tite observer; Gemioo' poims out tIlat a arele tflIced tluough me front paW5 of Ursa Mojor .pplie:s to ot.;erve.. on the islmd of Rhodes," Again sen:ing I compass point on me polc:st.r .he Iw traced the .ulTIme! tropic tbrough rhe cighth dcgree of Cancer, me cllest and bc:lly oí Leo, the .houlden oí Serpentllrius, the IIe:Id of Cygnus, the hoofs of Equus, rhe right h.nd oí Andromeda, die left .hin and Jeft .houlder of Perseus, the knees of Auriga, the head of Gemini and bid: tu me cighth degn:e of Cancel." (h8) The cdcsrial eqoatol', equidistant from me pule:!, is tr2CCd from the eighm deg= of Ams, ro {he mracced IIoof of Tauros, tbence ro tite helr of Orioo, through cM dented coil of Hydra, tllrough Cnter and Corvus ro me eigllth do:g= of Libn; rilen it puses ro me lmces of •• do "'" a¡;«< ;. lbek lliu of cdatisl ci,clos.. Somo coum ti.",," ... ..",.., _ "nJ ..".". r..... Ibao ..... Theoll. ""d O their celootW globes. .. Gem.in... O' 6J), ¡., remukio¡ upon thlo difftcUhy, _ . a tbat thc botI>4a can be "'1'" .. ,.,.¡ by thc cond ",hio:h "'1'1"'"" • JIobe.

,8,

THl': QUADR I VIUM

oS interVaJs bclow that, 2nd the cquator i inttrvals bdow the rropic, wilh corrcsponding int«vals IIII.rking tbe Iocation uf tbe wrrc:sponding parillels in che southem Ilemisphen."

Ir oow time for AstrOtlomy ro ca!llJoguc of the constellations. Th= famili", in addition to muldng the location QÍ tIle cde:;tW cin:lcs, serve as reí.unce point:s fOI ubsaving plane-

tary motions. According

to cusrom, Marcianu. divides me constdL>_ tions ¡neo the zodiacal con.ru:llatioll5 and those Iying to me non" or $Outh of me zodiaco H. does uot se. fit ro Iist the sigo< uf the zodiac --me.e Ire too Imown ro need enumention-but he don say mat

",en

altllough mere are twdvc tqU41 zodiacal divisions, OI sigm, tbere are only eleven zodiac:tI constelbtioru. Scorpio occupies ir. own space witl! ¡", body ""d the opace of Libra with jo. claws. The sign mat the Rornans can "Libr:a" (!.he Bahncc) Greek wmers refer ro lIS ''the Oaws". (839) (Aitrooomy's IISt .a,ccment H Jargdy bUI not Ilcogethtr (:()r=") ¡\.brtianus Cflunts '9 consttlbtions nonh of the zodigc: Ursa MajO!', Ur.. Minor, DuCW, Perscus, Triangulum, Aurig2. Androrncda, Pcgo.NS, Serpentarius, Ddphinus, Aquila, 2nd Sogita. The .. are che con-

I'J_, ..... ...

.. A m'It, wlddy odopted..,heme, "'. "" . ... d by igned 60 inurnls ro u.. .......

JI« '"

bo upect of ,h. ¡;"",rlop.uJio B,¡,nmk. presrnn o cooun, of . .. Aruuo lisa " ..",rh; of time are required for the ri" , 7S) brid 0000IU>f oi dolo procedun .. -....I tito .ppu= diw-. ol tito be "",,00... tito onubod to tbe E'¡ypdoce "" .ppr=io>otion jO) tnnSit tv but 11. in coming lrom !he nonh. it do>ó&p). 1I ir """"" 1 coofuoion obottt rhe ner¡, like die moon, to asr ••lw:low'" and rhe only une ro tinger for. long time before yielding to the sun', brilliance. In moming risings it frequently arriu lor (our month$, bur in WtSt never lUore thm 10 da}'$-" II:!¡ rising:s and bst v;,ib,litics recur in mn... to ten-month cyelcs. (88!-83) Marslw;[$ own ",hit. the SilO', and .bont che earth. whieh ;. eccenttic ro ormr. Mus complete, a revolution in appro%irnately two ye.IS. Ir ha •• motien in brirud. of S' . Like the two plane'" heyond ;t, ir experiences starions and retrogradations, buc ir has ir. own apogeC< ;. Ihorn: ¡6 doY' p«< "poci", (C. ,,",,",a ..., •. lO. • • ¡) opeob o/ the 1"''''" llJId inlluooc:< lo det