Renaissance Perspectives

8/12/2019 Renaissance Perspectives

http://slidepdf.com/reader/full/renaissance-perspectives 1/23

Renaissance PerspectivesAuthor(s): James ElkinsSource: Journal of the History of Ideas, Vol. 53, No. 2 (Apr. - Jun., 1992), pp. 209-230Published by: University of Pennsylvania Press

Stable URL: http://www.jstor.org/stable/2709871 .

Accessed: 01/06/2014 06:45

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

University of Pennsylvania Press is collaborating with JSTOR to digitize, preserve and extend access to

Journal of the History of Ideas.

http://www.jstor.org

This content downloaded from 62.204.192.85 on Sun, 1 Jun 2014 06:45:15 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=upenn

http://www.jstor.org/stable/2709871?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp





http://www.jstor.org/stable/2709871?origin=JSTOR-pdf

http://www.jstor.org/action/showPublisher?publisherCode=upenn



RenaissancePerspectives

JamesElkins

Erwin anofsky's924-25 ssay Die Perspektivels 'symbolischeForm,' still centralocumentnthe tudy fRenaissanceerspective,openswith quotationromiirer: 'Perspective'sa Latinword,mean-ing lookinghrough.'1AccordingoPanofsky'slaborationfDurer'sthought,perspective"ropers applied oan entire icture ot usttoindividualbjects n thepicture;tcreates "unity fpictorialpace.2Perspectives imagineds a methodhatmakes paquepanels nd can-vases quivalentowindows.ontemporarycholarshipollowsanofskyin this, o that hepredicateinperspective"s normallypplied o thesubjectpicture,"nd ngeneralntireaintingsnddrawingsrewhatare inperspective"henheyre orrectlyone nd notnperspective"whenheyvincenconsistencies,rrors,rnonperspectiveystems.herearemany ossibilitiesor uch ransgressions,ut ntheoryerspectivestaken obea thinghat overnsictures,atherhan n ornamentn omepreexistingictivepace.

Yet t s difficultofind onfirmationor his dea nRenaissanceextsandpaintings.here sgeometricvidencehat heperspectiveethodsthemselves eredesignedor hedepictionf ndividualbjects atherthan he stablishingf he infinite,sotropic,omogeneous"uclideanspacethatPanofsky entionss the a priori rganizingrincipleorcorrecterspective.ictorialvidence,oo,pointsnthisdirection;ndfifteenth-centurylorentineaintingsyDomenico eneziano,aoloUc-

1"Item Perspektivast in ateinischWort, edeutt in Durchsehung." anofsky,DiePerspektivels symbolische orm,'" Vortrageer bibliothekWarburg1924-25),258.(Henceforthanofsky). urer'sdefinitions from MS in theBritishMuseum. See K.Lange and F. Fuhse, DurersSchriftlicherachlass Halle, 1893). Panofsky's ssaywasreviewed yGunther ternn Logos 1928), 234-35;by H. Wieleitnern MitteilungenurGeschichte erMedizin und Natur,27 (1928), 3; and by G. Previtali n Paragone,91(1961), 52-58; and it has been translated nto Italian as La prospettivaome "formasimbolica" altri crittiMilan,1961), nd now ntoEnglish s Perspectives a SymbolicForm Cambridge, 992). See furtherhe bibliographynK. Veltman, Panofsky's er-spective:A Half Century ater," nM. D. Emiliani ed.), La Prospettivainascimentale(Florence, 980),565ff. ee further. Gioseffi,ncyclopedia fWorld rt, .v. "Perspec-tive,"XI, 189 Toronto,1969).

2 "Das ganze Bild"; "nichtnureinzelneObjekte."Panofsky,91.

209

Copyright1992 by JOURNALOF THE HISTORY OF IDEAS, INC.







210 JamesElkins

cello,Masaccio,Ghirlandaio,nd othersnclude erspectiveonstruc-tions hatdo notorder heentire paces f their aintings,ut nsteadplacecorrectlyrawn bjectswithin lessdeterminedpace.3

The dea that inear erspectiveropers a wayofunifyingicturesor pictorialpace, s thefirst f four omponentsfpost-Renaissancethinkingn perspectivehat ndowtwith greaternity han t had ntheRenaissance. second omponents the dentificationfperspectiveas a wholewith hemechanicalperspectiveindows" icturednthetreatises,nwhich rtistsnd pprenticesook hroughooden ramestobjects.4 ostRenaissanceuthors onot onnecterspectiveindows,eithereal r magined,othemainstreamfpicture aking.nsteadheyarerestrictedo pedagogicalraditionhat erves o ntroducehe real"perspectiveonewithtraightedgendcompass,ndtheyreassociatedwith pticalnstrumentsatherhan uthenticonstructions.

A thirdspect fourmodemonceptsthe deathat erspectiveada unifiedrigin,o that t wasdefinedn a single lace, t a single ime,andbya single roup fartists:nFlorence, eginningn1413,5 ytheexperimentsfBrunelleschi,hepaintingsfMasaccio, nd the reatisebyAlberti. hiseventwas notunderstoods such n theRenaissance,and whatwewould etemptedocall a lackofhistoricalnowledgenthepart f ater enaissance ritersadseveralmportantonsequences.Amonghemwas the dea that herewere everal enerallyompatibleperspectives,nd hat erspectiveasnot implydiscovered"llatonce.Perspectives,n theplural,wereunderstoodo havebeenadopted tdifferentimesndput odifferentses. his sthe multipleerspectives"ofmy itle;wewill onsiderts ppearancentextsswell s paintings.

A lastmodem deahelpfulnrecoveringheRenaissanceoncepts

I This thesis s defendednmyPoetics fPerspectiveIthaca,forthcoming).he quota-tion s from anofsky, 60 and passim.

I The term perspectivewindows" s a compromise ecause not all of them havewindowsor even intersectionshatare to be looked through. or the range of veli,i(n)strumenti,elari, nd so forth, ee M. Kemp, The ScienceofArt,OpticalThemes nWestern rt romBrunelleschioDesargues New Haven, 1990). See furtherW. Ivins,"On The Rationalization f Sight:with n Examination f Three RenaissanceTexts on

Perspective,"Metropolitan useum ofArt Paper, VIII (1938), 16. Ivins concludes-inaccurately,believe-thatAlberti xperimentedithperspectivesing uch a box withhinged ides.On the ubject fperspective indows er e, vins grees hey remarginal-and infacthe relegateshem o a footnote t the endofhistext ibid.,42,n. 2). For therelatedPerspectyftcasen,ee S. Koslow, "De wonderlijke erspectyfkas:n Aspect ofSeventeenth-CenturyutchPainting," ud Holland,82 (1967), 50ff. nd Elkins, 'DasNuissleineisset uf, hrKunstler ' urvilinear erspectivenSeventeenth entury utchPainting,"Oud Holland, 102 1989), 268ff.

5 This date has been advancedby G. Tanturli, Rapportidel Brunelleschi on gliambientietteratiiorentini,"n M. D. Emiliani ed.),La ProspettivainascimentaleFlor-ence, 1980),125-44, ndisnowwidely ccepted.The other elevant atesare Masaccio'sTrinityc. 1427-28) nd Alberti's e Pictura 1435).







Renaissance erspectives 211

thenotion hatperspectiveroper onsists f a collectionf essentialgeometricules nd that ndividual ethodsre nstancesf hose ules.I will uggesthat his oo wasunavailables such n theRenaissance:untilhe inal ears f he ixteenthentury,uthorsidnot ry oreducetheirechniqueso sets faxioms. aws,examples,nd rules fthumbcommingled,nd here as welterfmore-or-lessndependentethodsratherhan singlemathematicalet f xiomsnd logicallyntecedentsetof pplications.

Herewe will onsiderhe econd, hird,nd fourthfthesedeas-thosemost eadilylaborated ithouteometricnd pictorialdditionsto the rgument-andhen onsiderhe onsequencesfreturningo theRenaissanceoncept.

TheMarginal ositionfthePerspective indows

Whenhe describederspective,lbertipokemost ftenn terms fvisual ays nd n ntersection.6here reonly wopassagesnwhichheintersections saidtobe a window,ndboth remeant oaidthosewhomaynotbe ableto follow is rgument. hen ddressingyoung aint-ers"hesays he ntersections"like lass," ndheuses hewindowigureagain o set he tage orhis new onstruction:Let metellyouwhatdo when ampainting.irst f ll,onthe urfacen which amgoingtopaint,draw rectangle.. which regards anopenwindowhroughwhich heobject o be painted s seen... ."7 Bothpassages, s their on-texts ndrhetoricalodes f ddressndicate,remeantomake eomet-ricconceptslearer othe unlearned."fter hepassage uoted boveAlbertieginshe rickyiscussionf he o-calledostruzioneegittima,andthewindowiguresof ittle elp.

The "perspectiveindow"soneof class fpedagogicaligureshatgive he exts reaterlarityplate ).8 nthe ameway hat ecomparesthe ntersectionoa window, lbertiays circlesa garland,concavesurfaceneggshell,nd-in a particularlyelicitousmage-a surfacefdouble urvatureesemblesflutedolumn. hispractice assuggestedtohim y lassical hetoricalreatisesswell sby hemathematicalextshetook s models.9

6

"Erit .. picturantercisioyramidis isivae" nhis formulationn De pictura I.18;seealso ?I.12. See C. Graysoned.),LeonBattistaAlberti n Paintingnd On Sculpture:TheLatinTexts fDe Pictura ndDe StatuaeditedwithnglishTranslations,ntroduction,and Notes London,1972),48.

7Ibid.,?I.19, 55.8"Clarity"renders perspicuitas," orwhich ee especiallyD. Summers,Contrap-

posto:Style nd Meaning n RenaissanceArt,"TheArtBulletin, 9 (1977), 336-61.9As evidentia, lberti'smetaphorsnd similes ollowQuintilian'sdvicefor larity:

see Institutioratoria .2.64 and 6.2.32. See also Lousberg,Handbuchder literarischenRhetorikMunich,1960), ?810ff. n "vividrepresentation."or a general ccountof

sources, eeE. Wright,Alberti's e pictura:tsLiterarytructurendPurpose,"Journalofthe Warburgnd Courtauldnstitutes,7 (1984), 52-71.







212 JamesElkins

He was followednthis y Filareteca. 1465)whose oarsermagesreflectdisinclinationor bstracteasoning.ilareteomparedearningperspectiveo constructingbuilding,nd to assuage he readerwhoremainedoncernedbout he ifficultiesf he ubject, hichweremorewidely nownhanwhenAlberti rote, e coaxed: I think ouhaveunderstood,ven houghhissvery ifficulto understand.... he firsttime hewolf awthe ionhe seemed ery erribleohim.Then s hedrew little earer e did not eem o be so terrible.he closer egotthe ess erriblethe ion] ppeared. ead Aesop nGreek. hus t s witheverything."10ncomparisonoAlberti'solished oratian, iceronian,andArchimedeanropesndtoFilarete'sarablesndBoccaccianmeta-phors, hefiguressedbySerlio1540)sound ikefull-blownomericsimiles: e compareshewaythebase andcapital f a column omethreateninglyorwardn perspectiveo a river verflowingtsbanks,recallingheHomerickamandrosndthe imiles boutAjaxandotherheroes.

Like these imiles,hewindow igures clearlydentifieds a figureof peech. susual, ilarete asmore irectbout his hanAlberti:wefirst retend,"e says, to stand t a certain indow";nd ikeAlberti,

he didnot ry ousethewindowiguren hisensuingonstruction.2

Althougherspectiveindows ere istinctromhe ctual onstruc-tion fperspectiveictures,heywere sedtohelpproduce erspectiveviewswithoutnowledgefperspectiveules. lbertimay ave orrowedthe mage fa window rom is ownvelo, deviceheused to exhibitperspectiveffectso his friends.n Vasari'swords,Alberti sed hisinventiono make natural erspectives,13 and the erm natural"ug-

gests asari ssociated lberti'snvention ith imilar evicesmployed

10Filarete'sTreatise n Architecture,d. JohnR. Spencer New Haven, 1965),BookXXIII, fol.178r.The imageofthe house s a common igure nd is also usedbyAlbertiandL. Brion-Guerry,eanPelerinViator,a placedansl'histoiree la perspectiveParis,1962),ch. 2 of thetreatise.

"Iliad, 21. 211-382.12 Filarete'sTreatise, XII, fol.177r.Similarly, e saysorthogonalso the principal

pointare "an analogy" "asimilitudine") o visualrays ibid.,XXII.177v). Leonardo's

shorttreatise n perspectiveecently iscoveredn MS A (1492) uses the windowtointroducehe elements f perspectivend thencontinueswithgeometriconstructionsthatdo notdependon it.See Veltman, eonardoda Vinci nd the VisualDimensionsfScienceand Art Munich,1986),56ff.When Leonardosaid that"perspectives nothingother han ooking t a thing hrough transparentaneofglass" ". . . uno vetro ianoe ben'transparente,"S A lv), he was indicating wayof magining erspective,otoflearningts rulesor ofdrawingt. The functionf such passagesmaybe judgedmosteasilybya quickcountofRichter's election,where assagesutilizinghewindow igureare outnumberedeventy o twobythose thatdo not. See J.-P.Richter,The LiteraryWorks fLeonardoda VinciLondon,1970).

13Vasari,Vite, d.G. Milanesi Rome,1848), I, 540.VasarisaysAlberti'sstrumentoshowedhim"il mododi lucidare e prospettiveaturali."








by scholars n themedievalLatin traditionfperspectivaaturalis,uchas burning lasses nd curvedmirrors. ikemirrors nd lenses,Alberti'sinstrumentequired o trainingngeometry,ndwas thereforen opticalinstrumentather han a constructionroper o an artist.4

Diirer's definitionf perspective" 'perspectiva' s a Latin word,meaning looking hrough') is relevant gainherebecausehe repeatedthe connection etween hewindowfigurend optical,rather han per-spectival,methods.The opening entencen Diirer's manuscripts fol-lowedby fivedefinitions,akennot, s Panofsky'sontextmplies, romlinearperspective,ut from he Latinperspectivaaturalis:

Note:five hingsertaino this lookinghrough":Thefirsts the ye, hat ees.Next sthe hinghat s seen.Thirdsthe pacebetweenhem.Fourthis that] verythings seenby traightines,which rethe

shortestines.Fifths theparts fthe hinghat sseen.15

The intersection,crucial lement f inearperspectivehat s impliednthe firstentence,s not mentionednthe entiremanuscript, hichgoeson withpurely pticaltheorems. his is particularlynterestingecauseDurergotthe first art ofhis listfrom iero dellaFrancesca.16

Diirer's nstructionnMeasurement1525), a morecentral ext hantheonePanofskydduces, lsomakes he onnectionetweenhewindowfigurendperspectivaaturalis. iirer's fourmechanical evicesdo notinvolveknowledge fperspective,nd conversely emakesno use ofthewindowfigurenthe sections f Book IV thatdeal with ciography,he

artofperspectivalhadowprojection.ater heperspective indows ameto be placed at the endsoftreatises,partfrom he technicalmaterial.Daniele Barbaro'sPractice fPerspective1568) stresseshethings cam-eraobscura an do thatperspectiveannot: tcanshowbirds lying, atersparkling,nd it can imagebrilliant olors"unknown o geometry."7

The legitimateedagogical urpose fperspective indowshas beenaugmentedn moderncholarship ythe ssumptionhat hey ansignifyperspectives a whole.Yet despite heir ventual opularity,erspective

windows emained iedtoprefatoryontextsndto theperspectivaatu-

14 For thechangefromAlberti o Leonardo n the attitude o perspective indows,see Veltman, eonardoda Vinci, p. cit.,107?1 and p. 111.

15Lange und Fuchse,DurersSchriftlicherachlass,op. cit.,319: "thepartsof thething" enders die Theilungvoneinander."

16 This sshownn parallel olumnsn G. TenDoesschate, erspective:undamentals,Controversials,istoryNiewkoop,1964), 152,n. 2.

17Barbaro, a Praticadella perspettivaVenice,1568), 192:"Qui ui uederai e forme

nellacartacomesono,& le digradationi, i colori,& le ombre,& i mouimenti,e nubi,il tremolar elleacque,il uolarede gliuccelli,& tutto uello,che si puo uedere."







214 JamesElkins

ralis, ndwe havevirtuallyo evidence hat heywereused n seriouspaintingeforehe eventeenthentury.18

Multiple erspectivesnVasari nd ntheTreatises

There re at least four enses nwhichwe can speakof multipleperspectivesnstead f single erspective.hree re ncurrentsage:ncriticism,picture, building,ra gardenmayhave everal perspec-tives,"meaningprospects"rviewsndifferentirections;nmathemat-ics,therere several ifferentperspectives,"ncludingurvilinearer-spectivesndthe perspectivities"nd"projectivities"sed n projectivegeometry;nd nthehistoryfart, here re"perspectives"ssociatedwith articulareriods,uch s herringbonend vanishingxispseudo-perspectives.fourthensenwhich perspective" ay e plural ccursinRenaissanceexts hat peak f"perspectivesnpaintings."

Masaccio'sTrinitys an interestingxample fthis, ince t is theearliesticturerganizedccordingoa coherent,fnot ntirelyccurate,perspectivalchemaplate2). Althoughtsprecise onstructions stilldisputed,t s unifiedyperspective:ndeed,hat nityndtheforce fthefictivepace tconjuresrewhat ontinueo strike s about t. Theprimacyfthepicture'seometricnitysnot cknowledgedyVasari,however,hodoesnotmentionerspectivet alluntil ehaspraisedhefigures. hen e doesdescribeerspective,t s not heperspectivef hewhole,ut f single art: butwhat s most eautifuleside he igures,"he writes,is a barrel ault rawnnperspective."19he fact hatVasaridoesnotmentionerspectivettheoutsetmaymeanhewasbypassingthe bvious,ut venf hatsso,his ext emainsilentnwhatwe taketobe thepainting'salient eature.

Both he iguresndthebarrel ault rethingsn thepicturendnotthe argerrameworkewould all tsperspective.henwespeak bouttheTrinity,e tend o describehe iguresndthe rchitecturesthingsthatre rdered, ore r essunambiguously,y he erspectiveonstruc-tion. n Vasari's ext,hefiguresndthebarrel ault retwo eparate

18There is onlyone convincing onnection etween perspectivewindowand a

Renaissancework: picture f a sphereby Durerhas been shownto haveverydistantvanishing oints,ndicatingt was probably rawnwithStrabius's evice,whichDurerillustratesn hisbook.This is in contrastwith he widespread se ofthe windows ndsimilardevices n later centuries, y Bellotto,Canaletto,Vermeer,nd others.For thesphere eeJ.Harnest,Diirer ndPerspective,"nR. Strieber, lbrechturer NewYork,1982), 357, fig.454. The half-dozen eferenceso perspectivewindows re decisivelyoutnumberedytheforty-fourxtant reatises ublished efore1601and their everalthousand llustrations.ee furtheromazzo,Libro Quintodella Prospettiva,n Trattatodell'arte e la pitturaMilan, 1584);see the facsimile eprintHildesheim, 968),275 ff.

19Vasari,Vite, I, 291: "Ma quelloche vi e bellissimo, ltre lle figure, una voltaamezzabotte, irata nprospettiva."ee ibid., I, 672, for similar assageonCastagno'sScourgingfChrist.








accomplishments,ndno encompassingerspectives mentioned.ivenVasari'sManneristnclinationopraise ifficulta,e mayhave ingledout he ault npurpose.20etfor im, erspectiveas n embellishmentofpaintings,neof numberfpraiseworthyccomplishmentsnvolvingsomedegree f difficulta.s we know rom letter o Martino assi,Vasariwaswillingo forego erspectivalaturalismltogetheror star-tling r pleasingffect.21e hadnoconceptualierarchyor iscriticalterms uch sprospettiva,hiaroscuro,anner, race, nd composition:aesthetically,hey ere visual igures,"naloguesf he hetoricaliguresthat rnamentpeech; ntologically,hey ompeteds accomplishmentsworthyf praise.22iguresnd perspectivesere ftenmentionedo-gether,scomplements.onatello'sife f t.AnthonyntheHighAltarinSant'Antonio,adua 1446-50) stonishedllwho aw t, ccordingoVasari, nd theytood dmiringthebeautifulnd varied ompositions,full fextravagantiguresndforeshortenederspectiveiews."23

As in thecase of Masaccio'sTrinity,heperspectiveshat aughtVasari's ye endedobe solatedhowpiecesatherhan oherentpaces.On Ghiberti'soorshesingledut the round emple,onewith reatdifficultynperspective."24heopenwindown the ackgroundfGhir-landaio's irthf heVirginntheCappellaMaggiore,ta.MariaNovella,Florence1485-90)deceivedveryoneho aw t":again mittingen-tion fa spacethat s remarkableor tsharmoniousnity, hile igh-lightingn unobtrusiveetail mongmanythers. oVasari, oodpaint-ings ouldbe"full fperspectives":iero, or xample, aspraisedorchair, hallway,nd a horsenperspective,nd wassaid to be a greatmaster,as is shown yhisworks, hichrefull fperspectives."25

20 It would be easyto read too much ntothis, incebarrelvaultswereconsidereddifficultodrawwell nto he ixteenthentury;eefor xample erlio,I secondo ibro iperspettiva,. . mis en langue rancoise ar Iehan Martin Paris, 1545),ch. 3, fig. 23],which ontains similar onstructionnd a caution o avoidthe free nventionfdetailssuch as coffersn voussoirs. ignola, e dueregole ella prospettivaraticaRome,1583),preferredditionVignolaLondon,Archival acsimilesLimited,n Associationwith heBritishMuseum,M. Kemp,ed., 1988]), avesvaults or ast, nd goes cautiouslyhroughseveral asyexamples efore ackling he harder ases.

21 See MartinoBassi, Disparerin materiad'architettura,tperspettiva,onpareridi

eccelenti,tfamosiarchitettiPalladio, Vignola,Vasari,and Bertani), he 1i risoluono(Brescia,1572).Thetextsdiscussedn Panofsky,24-27, .68. A few ages retranslatedin R. Klein and H. Zerner, talianArt,1500-1600 EnglewoodCliffs, 966), 105-111.Panofskynvertedhefirst nd second xamplesPanofsky, bb. 35 and 36).Thetransla-tionof the title s fromKlein andZerner, 05.

22 For the origins fsomeofVasari'scritical ermsn classicalrhetoric,ee D. Sum-mers,Michelangelond theLanguageofArt Princeton, 982).

23 .. . ibelli variati omponimenti,ontanta opiadi stravagantiigureprospettivediminuiti." asari,Vite, I, 411.

24 . . tempio ondo,girattonprospettivaon unadifficultarande." bid., II, 241.25"... come nedi mostrano utte 'opere uepienedi prospettive."bid., II, 490-91.

The samepassageexemplifiesiero's paintings ythedepiction fa vase.







216 James lkins

Perspectivesn Vasari'sviewwere mallparts f paintings,atherthan ntire aintingsrways fmaking aintings.e never enied hatperspectiveight rganize ndunifyn entire icture,ndhis taste npicturesertainlyedhim wayfrom hat onclusion.26utthe bsenceof nymentionf uch purposeor erspective,oupledwith isdescrip-tions f solated assagesnpaintings,stelling.

Vasari'sdea of perspectiveaybe separatedrom everalmethod-ologicallyelatederms.edistinguishedprospettivaromwo ther ermsthat ave ough quivalentsnmodem nglish:iminuzione,hichs ikeour diminution,"nd corcioinRenaissancepelling,corta r corce),whichsa little urtherromur foreshortening."27nglishdiminution"

still arries he onnotationf n inexact runquantifiedecession,ndVasariusually nly equiredhat eople ecede etweenwovanishinglines.28iminutionndperspectiveere istinguishedrincipallyy heirdifferentpplications.he formerovernedhedepictionffigures,ndthe atter asreservedor rchitecturalndgeometricubjects.29ore-shortening,n theother and,was applied xclusivelyofigures;ndVasari's corcio,ike our"foreshortening,"as often sedto describelimbsrtorsosswell sentireigures.30oth oreshorteningnddiminu-

26 The closesthe comes to speaking f an entire aintings being in perspective"swhenhe mentions lberti's aintingf "una Vicen[z]ia nprospettiva SanMarco,"butthen tis clearhe meansthe city nd notthepainting.bid., II, 547.

27 A full tudy fthese nd other ermss needed; ee the exicographictudies yU.Scoti-Bertinelli,iorgioVasari crittorePisa, 1905), nd T. S. R. Boase, Vasari, heManand theBook 1979), 123ff.corciohas been tudied yR. Smith,Naturalversus cientificvision, heforeshortenedigurentheRenaissance,"Gazette esBeauxArts 1974),239-48.

28 Masaccio's lost painting ftheconsecrationf theCarmine,he reports, epicted"fiveor six people,whodiminishn proportionnd withgood udgment,heway they

would ook to theeye" ("che vanno diminuendoon proporzione guidizio, econda avedutadell'occhio").Likewise nUccello'sDeluge,the figuresweresaid to recede"ac-cording o the ines, nperspective,"he"lines" being he guiding rthogonalsndnear-orthogonalsf the two arks. See Vasari,Vite, I, 210 and 297.

29 AnexceptionccurswhenVasari praisesAlberti orwhatwewouldnow call aerialperspective:altreal disegnodelle lineeche e perfetto,o fecedi maniera on i colorisfuggire,hea pocoa pocoabbagliamentei perdedi vista:nel che mostro ssaid'intenderla prospettiva"ibid., I, 290). The association fperspectivend architecturalrawingis repeatedmany imes.Brunelleschi,ccording oVasari,taughtAlberti molti ermini

di prospettiva d'architettura."Ibid., II, 300). Vasari's description fAlberti'svelo,quoted bove, ontinues:ilmodo di ucidare eprospettiveaturali diminuiree figure."To Varchi,perspective as necessary orpainting othfiguresnd architecture.ee P.Barocchi,Trattati 'artedel Cinquecento,raManierismo Controriforma3 vols.;Bari,1960-62), , 39.

30VasaripraisedMasaccio for his "nudes, and the foreshorteningsn his figures."Vasari, Vite, I, 290. M. Baxandall,Painting nd ExperiencenFifteenthenturytaly(Oxford, 972), 143-45, as called ttentiono the ocal nature f corci. ike a diminution,a foreshorteningouldalsobedone trictly,usingperspective,"lthoughhe ualificationwas unusual. See forexampleVasari, Vite, I, 206-7 on Uccello: "E non gli bastano

questovolleancomostraremaggiore ifficultanalcunecolonne he scortano erviadiprospettiva,"nd similarlyn p. 288. Scorta s appliedtoUccello'sperspectiverawing








tionwereometimesiven reer,on-perspectivalenses, utperspectiveswere lways hings one"by rules" nd with recision,nd theywerealmostxclusivelybjectsnpaintingsnstead f hings onepreparatorytoplacing bjects.

Foreshortenings,iminutions,erspectives,ndother ictorialeviceswere ometimesntentionallyrrayednManneristaintingss theywereinVasari's ext.At the opofBronzino's hristnLimbo, artly iddenin thegloom,s a tourdeforce fthree uchvisual igures:powerfulchiaroscuroetoff y thebright lag fChrist,hemenacing ellfires,andthegleamingyes f demon; particularlyepulsivecorciontheform f twisted,lmostcorchelyingemon;nd virtuosorospettivaof brokenrch een romelow, al di sotton tu. ronzino'suxtaposi-tion f hiaroscuro,corcio,ndprospettiva aywellhavebeen ntentional,a signaloknowingiewersfhismasteryplates and4). AsinVasari'sdescriptions,erspectiveoesnot rganizehristnLimbo ut rnamentsa cornerf t.

Theconcept fperspectives,n theplural, eingnpictures atherthan single erspectives a generatorf pictorialpace,may lso befoundn he reatises'llustrations.rawingsf bjectset gainstndeter-minate remptyackgrounds,s wasthepractice,ppear eady o beinsertednpaintingshereverpaintermight ant; nd sometimesecansee the ack of nterestntherelationetween heperspectivesfindividualbjects ndthe arger ictivepacesforwhich heywere n-tended.

Traces f hismedievalatternookmentalityay e found hereverobjectsnthe reatisesonot cknowledgerrequire specific ictorialsetting.hefancifuleometricolidsnJamnitzer'serspectivefRegular

Bodies1568)areplaced nplatformshat renot lways et na largerfictivepace plate ). Often he tands hathe drew s supportsorhispolyhedrare both onnectedo and cutbytheborder f thepicture.Withoutecedingineson theplatformsndwithno notation f theprincipalanishingoint rthepointsfdistance,eaders howishedostudy isdrawingsather han implyrace hemwouldhavehad toreconstructheir eometry-somethingewwouldhavebeen nterestedin doing.Perspective ethods ithout orizonines, uch as Piero's,

Alberti's,ilarete's,ndGauricus's,analsoproducerawingsf bjectsthat eem solated, eady o be copied nd used nother ompositions,whereheymightrmightot itwith pre-existingerspectivalcheme.

ThePerceivedluralityftheOriginsfPerspective

Thepluralityfperspectivesas historicalswell s theoreticalndpractical. asariwasunclearbout he riginsfperspective:ecredited

of a vase 490): ".... e fatto cortarel girare i tutti ueicircoli on molta razia."Infrequently,he ermsappliedoentireiguresr argerbjects,sonpp.195 ". . . di







218 JamesElkins

the second ge"ofmodernainting,nd speciallyrunelleschi,ccello,andAlberti, ith greater idelityo nature, nd said that he newsensitivityaused ainterstogive ule[s] o their erspectives,"gain nthe lural.3"odaywemight ant osay,more irmlynthe ingular,todiscover herules fperspective."asari'swas a loosephrase llowingfor ther ules nd other erspectives,nd hecreditedhediscoveryfperspectiveules o bothBrunelleschind Uccello.The passages avebeengivenwhatmaybe called"strong"nd "weak"readings.n thelatter asari sthoughtohave eenmistaken,speciallynthe arly ateshe gaveto Uccello,while n theformer,asari s said to have beenessentiallyorrect nd to have been mplyingccellohad an entirelydifferentind fperspectivehanBrunelleschi,eliberatelyonceivednoppositiono Brunelleschi's.

The passagesn BrunelleschindUccellomay e reconciled ithoutfallingackoneither fthesenterpretationsf he onceptf"perspec-tive" s oosenedlittlen ccordwithhe vidence ehave een onsider-ing.f perspectives"n he lural eed otmply eometricallyncompat-ible ystemsutonly ifferentspects f a single ctivity,henUccello,Brunelleschi,ndothersouldbe said to have"given ules" oseveral"perspectives."

In the LifeofUccello"we read: Paolo Uccello mployedimselfperpetually,ndwithoutny ntermissionhatever,nthe onsiderationofthemostdifficultuestionsonnected ith rt, o much o thathebroughthemethodfpreparinglans ndelevationsfbuildingsoperfection."32asarididnot laim hatUccellodiscoveredherules orallofperspectiver for llperspectives,nly hat eperfectedmethodinvolvinglans nd levations.hepassage n Brunelleschieads,npart:"Brunelleschiave onsiderablettentiono the tudyfperspective,herules orwhichwere hen erymperfectlynderstood,ndoftenalselyinterpreted;nd nthis eexpended uch ime,ntil t engthediscov-ered a perfectlyorrectmethod,hatoftakingheground lanandsectionsymeans f ntersectingines, trulyngenioushing,ndof

scortare e vedute di sotto n su"), 493 ("un angelo in scorto"),and 496 ("cavalli in

scorto").31 "Cosi cercanofar uelche vederano elnaturale, nonpiCu,cosi vennono d esser

piCuonsiderate meglio ndese e cose oro:e questodiede oroardimento imetter egolaalle prospettive; farle cortar ppuntocomefacevanodi rilievonaturali in propriaforme. ." (Vasari,Vite, II, 87). Vasari ncludedUccello npartbecausehe wasmistakenabout his dates, nd thought e was a contemporaryf Alberti nd Brunelleschi.or thissee the Vite, I, 217 n. 1. Assuming he newdatingforBrunelleschi's anels s correct,Uccello wouldhavebeenless than sixteenyearsold,mature nough o understand utprobably ot to collaborate.

32 66... tanta che ridusse perfezionel modo di tirare e prospettive alle piantede'casamenti da'profili egli difizi."Ibid., I, 204). The translations altered romheone inVasari,LivesofthePaintersNew York, 1902), I, 178.








great tility o the rtsofdesign."33 gain whatwas discoveredwas "onemethod": fVasariknew f a single orrect erspectiveoundntheearly1420s,he did notsayso.4 Other uthors lso spokeof"methods"nthe

plural, ollowingheusage oftheperspectivereatiseshemselves.35ilar-etecredited runelleschi ith thewayofmaking hisplane,"meaningAlberti's quaredpavement,utdid notmentionhediscoveryfperspec-tive n anymoregeneral ense.36ven Androuet u Cerceau 1576) andEgnazioDanti 1583),who poke t engthbout hehistoryfperspectivein their reatises, id not name a single riginator.37

In accordwith this ack of a clear understandingf the originofperspective, enaissance uthorsdisagreed n whoshould be namedas

perspective'sreatestuthority.everal eferredoPierodella Francesca38and a fewto Diirer,butmost,curiously nough, enttheirreaders oEuclidforfurthernformation.39he referenceso Euclid show that hewriters ad not considered xactlyhowperspectivemight avebeen de-rived, ven though heyknew twas importanthat t had a connectionto geometry.wo texts pitomize hisvagueness y referringeaders o

3"... trovoda se un modoche ella potessevenirgiusta perfetta." asari,Vite, I,332.The translations modified romVasari, 1902ed., loc.cit., , 249.

34 Cristoforoandinowasalso uncertainbouttheorigin fperspective.runelleschi,he says,"understood erspective ell,and somesay he was either he nventor r therediscovererf t." Quoted n Baxandall,Paintingnd Experience, 25.

35 "Modo" was an ubiquitous ategory,ndwas thestandardway of speaking boutgeometricmethodsn the treatises.Most of themethodswereknown s "modi."

36 ... il modo di fare uestopiano." See Filarete,Treatise, XII, fol.178r.37 For thepassage n Androuet u Cerceau,Leqonsdeperspectiveositive1576), see

Brion-Guerry,eanPMerin, 43. ForVignola's reatisend its istofperspectivistseeJ.Field,"GiovanniBattistaBenedetti n the Mathematicsf LinearPerspective," ournaloftheWarburgnd Courtauldnstitutes,8 (1985), 71-72.

38 Most famously aniele Barbaro,La Praticadella PerspettivaVenice,1568)whothought iero'sruleswere for diots," nd set outto make hem asier ndmore ccessi-ble. See Elkins, Piero dellaFrancesca ndtheRenaissance roof f LinearPerspective,"TheArtBulletin, 9 (1987),220-30, 21,n. 12;and Field,"GiovanniBattista enedetti,"op.cit., 6. BothPiero nd Durerwerenamed nthe apsulehistoryfperspectivereatisesgivenbyDanti. See ibid.,71-72.

39 See for xample irigatti,a Praticadi ProspettivaVenice,1596),text o chapter(n.p.):"Le ragioni i questi .. dico,quanto lla speculatione annodottamentessegnateprimaEuclide,di poi piu diffusamenteitellione ei loropropriiibridella prospettiva.Ma quantoa quella pratica . ." etc. Serlio, I SecondoLibrodella PerspettivaParis,1545), beginsby adducingEuclid,who he says "spokedarkly"of thefoundationsfperspective,nd includes eferenceso twoother uthorities:. . . benche i sono altrevie,comequella del telar, del portello,he vogliamodire, aqual e dimostrata a AlbertoDurero:ci e ancor quella della propriaforma, ia veramente uonissima, sicura: mamoltodifficile mostrarlaltrimenti. ." (book2, chapter , text ofig. 44]). The "viaveramente uonissima"s presumably variant fthevisualraymethod, irstxposited

byPiero. Jamnitzer,erspectivaorporumegulariumNuremberg, 568),facsimile e-print, d. A. Flocon (Paris, 1964),also mentions uclid.







220 JamesElkins

themedieval erspectivaaturalischolarWitelo,whosework hares nlythe name "perspective" with the new science.40

Paleotti'sDiscourse nSacred and Profane mages 1582) containslistofthings painterhould magine efore ebeginswork,ncluding"theoutlines,he urfaces fbodies, gracefulolor cheme," nd soforth,nd perspectivesburiednthemiddlefthe ist: thedivision flight ndshade, hemethodfperspective,heproportions."'41n thiscontextthemethodfperspective"s reminiscentfLeonardo's hreekinds fperspective,hich t various imesn his ifemeant ifferentthings;42ut Paleottimayalso have beenthinkingfVasari'sway ofspeakingboutmethodsr abouttheperspectivereatiseshemselves,which id the ame.At thetime aleottiwrote, herewerenumerousperspectivesnd severalwaysperspectivesouldbeplural.Mostofthesixteenthentury'swenty-odderspectiveethods ere nplace;Leo-nardo adcountedhree indsfperspectivend venmoremethods;ndVasari adwrittenbout perspectives"n he lural,sthingsnventedtdifferentimes.

Thingsncluded nder Perspective"

Ourfinal heme,heheterogeneityfperspectiveethods,smostrigorouslyreatedy nalyzinghemathematicalontentf hemethodsthemselves,oshowhow hey iffernprooftructure,xternalonnec-tions,ndframingarrationrom hemethodsxpositednRenaissancemathematicsexts.uckily,nanalogous ointmay e made y onsider-ing he reatises'onmathematicalontent.enaissanceerspectiverea-tises idnot onfinehemselvesoAlbertianavements,nd heirontentscontained wider ange f ubjectsnderherubricperspective"hanwe would ountenanceoday.

Althoughiirer's extwasnot ntendeds a book olely nperspec-tive,43hewayhe introducedhesectionsn perspectivendicates heboundariesf thediscipline ere essclearforhim han hey re now.The fourthook, ontainingwomethodsn shadow rojectionnd the

40The two are Sirigatti, a praticadi prospettiva,nd GiovanniBattista enedetti, e

rationibus perationumerspectivaeTurin, 1585).41 Barocchi,Trattati,I, 170.42 A table of Leonardo's vacillationss provided n Veltman, eonardoda Vinci, 7.

The three inds omprehended,t onepoint r another, ome thirteenategories. o thisit maybe added thatLeonardowasnot always uretherewere hreekinds o beginwith;see Elkins, Did LeonardoDevelopa Theory fCurvilinearerspective?-TogetherWithSome Remarkson the Angle' and 'Distance' Axioms,"Journal f the Warburg ndCourtauld nstitutes,1 (1988), 190-96.

43 The titlemay be rendered nmodem terms s: InstructionnMeasurement,Withthe Compass nd Triangle, fTwoDimensional nd ThreeDimensional igures.. (Un-derweysungerMessung,mitdem zirckelundrichtscheyt,n Linien ebnenunndgantzencorporen .. ).








four erspective indows, eginswithmap projectionsnd geometricsolids. hepassage n shadows, hich iirermeant s hisown ontribu-tion o the ubject, ollows pagedevotedothemethods f enlargingandreducingictures.hisuxtaposition,hich iirermayhavegottenfromiero ellaFrancesca, oesnotmark he oundaryetweenerspec-tive ndan alliedmethod: athert ndicates,s itdoes nPiero's ext,that nlargingnd reducing ere aken obe ancillaryarts f inearperspective.

Johann I von Pfalz-Simmern's seful ittleBook of nstructionntheArtofMeasuringwith heCompass nd Straightedge1531), the nextGermanext fterhe irstditionfDiirer's ook1525), ivideserspec-tive nto even arts.44nly hefirst ourwould e consideredperspec-tive" oday plate 1). His shorthand ethod or onstructingacesbydrawingcross o ocate heprincipaleaturessnot perspective"nthemodemense,ll themoreobecause esays hedrawings ay emadefreely,nd "notaccordingoproportion."45onstructionsikehis areclosest o the ngularutomatonsucaCambiaso rew rthe wkwardblocked-outannequinsn Diirer's ook nhuman roportions.ohannII also included pageoftipsonhow to drawhelmetsndheraldry,anotherubject f nteresto Durer plate6). "Perspective" as hereconceived rimarilys "diminution"nVasari's ense that s,as theartofmaking onvincingecedingines nfiguresnd andscapes)ndsecondarilysa geometricidfor rawingaces, igures,eraldicnimals,armor,ndfor nlargingndreducing.46

The ection nopticsnJoachimortius'sucubrationes1541) s thescholarlyideofthisGerman redilection"lucubrationes"re iterally"studies one tnight").t containshe arliestuantifiednalysisf wo

point erspective,lthough ost fthe exts devoted o llustrationsfdiminutionnthemannerfPelerin. ther ectionsfFortius's ook

"They are how lines convergewhich s to say, the essentialrequirements or agood diminution),he quaring fpavements,heforeshorteningf nteriors, somewhatmuddled xplanation fdistancepoints, n evenmore mistaken ection n landscapes,one on placingfigures n pavements,nd one on enlarging nd reducing ictures. eeJohannI. von Pfalz-Simmern,yn schonnutzlich uchlin nd underwiesunger kunst

desMessensmitdemZirckel,RichtscheidtderLinial (Simmern, 531), ndthefacsimileedition, d. Trude Aldrian Graz, 1970).The authorwas misidentifieds HieronymusRodler; see H. Schiiling, heorien er malerischeninear-Perspektiveor1601 (GieBen,1973) for lternate ersions f theduke's name.

4 ... nitproportionirtentlizer";he normally laims his drawings re done "nachrechter unstder Perspectiua."JohannI, Eyn schonnutzlich uchlin, 5.

46 Seventy-sevenagesdescribe hefirst,ndeleven he secondtopic.Erhard ch6n'sInstructionn theProportionsnd Placement f Poses (1538) continued hisblurringfboundariesncludingwhatwe would call compositionplate 7). See Sch6n,Unnderweis-sungderproportzionnnd tellung erpossen .. (Nuremberg,538).Themodern ditionis: Unterweisunger Proportionnd Stellungder Possen,Nurnberg,542, ed. L. Baer(Frankfurtm Main, 1920).







222 JamesElkins

proferescriptionsf cientificnstruments;nda formidableiscellanyofnow-forgottenechanicalevices oundtsway nto erspectiverea-tises ate nthe ixteenthentury.encker'serspective,rieflyescribed(1596) and his unfinishedanuscriptitled erspectivec. 1600)47haveexhaustiveescriptionsfproportionalividers,uadrants,strolabes,andmore xoticnstruments,ll underhe ubricfperspective.erspecti-vistswere lso nvolvednthe nventionf he proportional"r "reduc-tion"compass.48eretherules fperspective,ncesecret utsimple,havebecome ecretndcomplex,ndthepresencef aux-hieroglyphsamong encker'sllustrationsswholly ppropriate.

In additionorules ornlargingrreducingnd hortcutsor rawingthingsike rmorndposes, ixteenthenturyexts lso ncludedeomet-ric solids s partof perspective.riginally,nPierodellaFrancesca'streatise,he olidswere sedonly ohelpconstructolygonalemples,baptismalonts,nd wells.When iero reatedhe olids er e,hedidso in a separate ook of theFiveRegularSolids.49Butbythetime fBarbaro'sPractice fPerspective1568), the olidsweremore hanusefultools or rawingrchitecturalormsrconvenientntroductionsocom-plicated echniques;heywere hemselvesart fthe ubjectmatternd

could ccupyubstantialortionsf treatise.hecentralmportancefgeometricolids o Barbaro s most pparentwhenhe offersut-outplansfor he argest,mostrregularolids, o that hey ouldbe easilyconstructedithoutnowledgef heperspectivee had ust akenuchpains oexposit.50

47 An earlier ook,PerspectivaiterariaNuremberg,567),contains xamples ftheletters f thealphabet n perspective;hethird xists n MS only Newberry ibrary,Chicago)and is unfinished.

48 Theywerealso called"geometricalompasses."See M. Kemp,ScienceofArt, p.cit.,and the same author'sGeometricalerspectiveromBrunelleschioDesargues:APictorialMeansofan Intellectual nd? (London,1984),114,for Guidubaldo's ector,"and further. L. Rose, "The Origins ftheProportional ompassfromMordente oGalileo,"Physis, 0 1968), 539-69.Galileowrote short reatise n thesubjectn 1606(forreference,ee Kemp,op. cit.,114,n. 3). According o Veltman, eonardoda Vinci,op. cit.,445,n. 7, "[i]t s likely hatLeonardodeveloped primitiveorm f thepropor-tional ompassbutnotthe ector."Veltmanspreparing full-lengthtudy nthehistoryof compasses nd sectors.

49For Pierodella Francesca, ibellusdequinque orporibusegularibuseeH. Mancini,(ed.), "L'opera 'De corporibus egularibus' i PietroFranceschidettoDella Francesca,usurpatada Fra' Luca Pacioli,"Memorie ellaR. Accademiadi Licei, Rome,s. 5,XIV,fasc.VIIB (1916), 441-580.For a general ccount,unfortunatelyotas technical s itmight e, see M. Daly Davis, Piero della Francesca'sMathematical reatisesRavenna,1977).

50The inclusionof geometric olids, and the accompanyingnterest n (non-perspectival)nstruments,ere aterpurgedfrom perspective" roper n texts uchasBenedetti's iversarumpeculationum,nd GuidubaldodelMonte'sPerspectivaeibri ex(Pesaro,1600). cannot greewithM. Daly Davis,Pierodella Francesca'sMathematical

Treatises,p. cit.,93,when he writes hat"[d]rawing egular odies nperspective asevidently,orBarbaro, nexercisen earning ow to render uildings." arbaro'snterest








The arcana f olidgeometrynd nstrumentationere ropped,utthebroad nderstandingf perspective"etained,n texts hat ocussedon architecturalrawing.erlio's erspective1540)presentedimplifiedand partlymistaken ethodsdequate orpracticingrchitects.therwriters adeperspectivevenmore tilitariannd ungeometric.ietroCataneo's FourBooksofArchitecture1554) has plates aid to be "drawnbytherules fperspective" hich urn ut to be nothingmore hanelevations ithhints fforeshortening.5"is perspectivesnd those fAndrouet u Cerceau re slightlyetrogradeestatementsfexistingmethods. ased on thesurvivingreatises,ixteenthenturyrchitectswould aveknownperspective"s a numberfrules f humb,ome fthem naccuratepproximationso egitimateonstructions.

SomeConclusions

Nopressingeedwasfelt o defineerspectiveproper":heRenais-sance uthors idnotfeel hepull hatmodern ritersotoward morepure ressential athematicalore fmeaning.ach of he hree hemeswe have onsidered ayberecast s a modem ogma, unitymposedon theRenaissancematerial:herewould hen e a "unityfpictorialspace," "unityf he rigin"fperspective,nda "geometricnity"operspectives a whole. he"unityfpictorialpace"wasnotmentionedbyVasari,whowrotensteadboutwhatwe call"passages," ortionsfpaintingshat speciallytruck im.To Vasaripictures ere ometimes"full" fperspectives,ith picture" eing he ncompassingerm nd"perspective"he nscribederm,nstead ftheotherway round. he"unityf theorigin" fperspectiveasnotperceiveds such; nstead

Piero,Filarete, auricus, eonardo, anti,Vasari,Du Cerceau, ndothers eferredheir eaderso ists fearlieruthors,r even o EuclidandWitelo, or heoriginsfperspective.he "geometricalnity fperspective"as likewise nformulated:enaissanceuthorspokeofindividual ethodsoodfor pecificsesand ncludedmany hingsntheir erspectivereatiseshatwe wouldnowexclude. hecategoryf"perspective"asmultiple:t hadmultiplerigins,mbracedmultipletechniques,ndoccurredmultiplyithinaintings.

Theresult,or urreadingsf the Renaissanceicturesndtexts,mighte a cautiouswarenessfa certainackofconceptual recisionandholism. aintersuch sGhiberti,ccello, iero ellaFrancesca,ndLeonardo, hohavebeen harged ith evelopingheirwn chismatic

went arbeyond hat, s evidenced ythe laborationfhis solids s compared oPiero's,which lways uggest aptismal onts, ozzi,and the ike.

51". . . tirataperordinedi Prospettiva." notherkindofexpositions found nDuCerceau'sTrois ivres 'architectureParis,1559).Du Cerceaudoesnotdistinguishetweenelevations nd perspectiverawings,hereby ubsuming widerrangeofarchitecturaldrawing nder perspective."







224 James lkins

non-perspectivalariants, ight e reassessedn the ight f he bsenceof any mention f heretical erspectivesnRenaissance ocumentsswell as bythe ooserRenaissance wareness fmultiple modi" and"prospettive,"ot nconflict ith ne another,ut s practicallterna-tives. urreadingsf he aintings,oo,mighte-emphasizehe xpressivedisunitieshat rebroughtbout n paintingsy Uccello,PierodellaFrancesca, hirlandaio,nd n ntarsia ecorationsnUrbinondGub-bio, bytheuseofmultiple,eometricallyncommensurateethodsnonepicture. ndfinally,urnatural rthistoricalendencyospeak f"pictorialpace" might e softenedo take nto ccount hefact hatRenaissanceistorians,ritics,ndgeometersenerallyidnot peak fpictorialpace, r evenofa unifiedpacewithin picture,ut oftheobjectshatwent nto hepictures.

School ftheArt nstitutefChicago.

I would ike to thankE. E. Rosenthal nd David Summers or heir omments ndsuggestions.







RenaissancePerspectives 225

Plate 1: "Und so du Landschafftenurch eyn fenster bconterfectenill...," fromJohannI. vonPfalz-Simmeren,ynschonnutzlich uchlin ndunderwiesunger kunstdes MessensmitdemZirckel,RichtscheidtderLinial (Simmern, 531);facsimile dition,

editedbyTrude Aldrian Graz, 1970).







226 JamesElkins

, I

t~~~~~~~~~~~~~~~~~f

Plate'M scI o,Tiiy 47o 48 lrne t.M raNvla ht:Aiai








' kf< >

C.r)

41

N ' f i '\ s X ' b ';; 0 g f X

,, . . x i .: A >. X~~~~~~~~' ::t-'t*9EtxS t>Fve<?,<'*?A,t,,0

4. . ....... ; <'? ' S, ? fi ' o-~~~~

58t 72> f5*^<' * vAO'.'.''^ $? ?,,' 2~~~~~~~~~~~~~~~~? ;iS S We . XAS ̂ -x/-.Si,, ~~~~~

t ^,g, w.R,, :.S:~~

:>:{ X',''^':9Df7<.4<' v ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ "

:'B'i"s': w;'s. 7\i'0gat<g :C~ ~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~~L

^ | r #~~~~~wi,A~~~~~,b 3 S D7, s~~~~~

_= 'w~~~

?~~~~~~~~~~~~







228 JamesElkins

-- 4.X: ,-. ., , @e ,

0

0-

7~~~~Z








Plate 5: Geometric olids fromWentzelJamnitzer,erspectivaorporum egularium..(Nuremberg,568);facsimile eprint,d. A. Flocon (Paris, 1964).

Plate6: Schemata ordrawing elmets. rom ohannI. von Pfalz-Simmeren,ny schonnutzlich uchlin ndunderwiesungerkunst es Messensmitdem Zirekel,RichtscheidtoderLinial (Simmern, 531); facsimile dition, ditedby TrudeAldrian Graz, 1970).







230 James lkins

NiCCb.*fIt Ura5ttot*i,,tv*fe0otrd#grce*'b<u

tnitfFugn -nbtmgvnwrimtW)ba op ait dtwqtSj tlbnt

Mbn bw V1 Xrlpolgfif$genfid

.~ ~ ~~~ ~(rnfr a. M. 1920__

Documents

Renaissance Perspectives