This article was downloaded by: 10.3.98.104 On: 26 Sep 2021 Access details: subscription number Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK

The Renaissance World

John Jeffries Martin

Framing and Mirroring the World

Publication details https://www.routledgehandbooks.com/doi/10.4324/9780203401163.chTwo Lyle Massey Published online on: 24 Aug 2007

How to cite :- Lyle Massey. 24 Aug 2007, Framing and Mirroring the World from: The Renaissance World Routledge Accessed on: 26 Sep 2021 https://www.routledgehandbooks.com/doi/10.4324/9780203401163.chTwo

PLEASE SCROLL DOWN FOR DOCUMENT

Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms

This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo T way ofseeingtheworld,creatingarationalframeworkonwhichscientifi , andarchitecture,perspectivehasbeencreditedwithinauguratinganew tational realism.Essentiallytheapplicationofmedievalopticalgeometrytopainting, become indeliblyassociatedwithnotionsofepistemologicalprogressandrepresen- of nature.Inthe500yearssinceLeonardo’ pictures thatarebasedonopticalprinciplesconveyafundamentalunderstanding arid foundationofabanalacademic practicethatwasfirstchallengedbymodernist or innon-Europeancultures. Othershavepointedoutthatperspectivebecamethe and representation,suchasthose exhibitedinnorthernRenaissanceart,forinstance, bias inthedisciplinethatoverlooksmanyothercontemporaneous theoriesofoptics historianshaveargued thatthefocusonperspectivehascreatedanItalian-centric epistemological over-valuations ofsighttowhichperspectivehascontributed.Some the bodytoavisualapparatus.Theyquestionmind/body distinctionsand post-Cartesian philosophershavealsorejectedperspective’s apparentreductionof were alwaysalreadyencodedinthetechnique’s geometryandapplication.Some posited aneliteandliterateviewerwhoseclass,gender, andintellectualbackground for havingcreatedauniversal,humanistpointofview, inactualityperspective spective, albeitfordifferentreasons.Theypointoutthat whileithasbeenhailed point ofviewwouldsuggest.Socialtheoristshavealso criticizedone-pointper- more complexandmultifacetedphenomenonthanperspective’ perceptual theoristslongagorejectedthiscomparison,arguing that sightisafar directly analogoustoopticalvisionasitwasthenunderstood.Butcognitiveand century artistsandthinkers,forexample,believedthatpainters’geometrywas of theRenaissance,thistechnicalinventionhasalsohaditsdetractors.Mostfifteenth- itself. would cometodepend,anderectingananalyticscaffoldingforrepresentation .” signpost andgateway”withoutwhichnothing“canbedonewellinthematterof While manyhavecelebratedperspectiveasoneofthecrowningachievements of histime,LeonardodaVinci (1452–1519)saidthatperspectiveis “the than thatoflinearorpictorialperspective.Voicing themostadvanced ideas here isperhapsnoinventionmorecloselyassociatedwiththeRenaissance 1 For Leonardo,ratherthanmerelymirroringtheseenworld,perspectival FRAMING ANDMIRRORING THE WORLD CHAPTER TWO Lyle Massey 51 s death, thisgeometrictechniquehas s reliance onasingle c empiricism Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo the embodiedviewofboth artistandtheviewer, theidealprojectedviewpoint window. Thispictureshows usthatwhiletheconstructionofillusionsdependson and theapparatusinorder to markwherethestringcrossesthroughhinged various pointsonthelute.Theothersqueezesintosmall spacebetweenthepin One manholdsastringthatisfixed byapintobackwall,andheusesitmark between theoryandpractice.Two menareshownmanipulatingDürer’ rational applicationsofperspectiverevealbasicepistemological inconsistencies geometry andtoconnectrepresentationnatureinan unprecedented way. of machinewasalsounderstoodtodemonstratecertain truthsaboutvisionand the viewerinavisualgameof product wouldhavebeenillusionistic:e.g.,theresulting imagewouldhaveengaged alized three-dimensionalworldonatwo-dimensionalsurface. Themachine’ Euclidean opticaltheoryandgeometrytopainting,artists couldrecreatearation- This onecondensedimageassertsthatbyapplyingtherationalprinciplesof gence betweenalute,anintersectingplane,andhypothetical,idealviewpoint. Dürer (1471–1528)depictsadrawingmachineusedtotracethepointsofconver- proportion, science, butalsopartlyahallucinatoryaid. illusions, perspectivewasalwaysaparadox:thatis,itpartlyanexperimental also stoodapartfromotherformsofinquiry. Asatechniqueemployedtorender because itwasanexpressionofbothgeometricandrepresentationalideals, with butdidnotnecessarilydominatetheseotherstypesofinvestigation.However, various treatisesandinpractice,constitutedadiscourseonvisionthatintersected theories andadvanceknowledgeaboutvision.Perspective,asitwaspromulgatedin lens-based apparatuses,andotheropticalinstrumentsthatcoulddemonstratevarious increased, artists,engineers,andnaturalphilosophersconstructeddrawingmachines, what wesee.Asspeculationsabouttherelationshipbetweensensesandperception century. Understandinghowweseewasthoughttobeparamount understanding concern withvisionandopticalitythatspreadthroughEuropeinthesixteenth and humanknowledge. thus hasalwaysembodiedantitheticalstatementsaboutthenatureofoptics,reality, more sophisticatedillusionsintendedtodeceiveanddelightthesenses.Perspective of bothopticsandgeometry. Ontheother, itwasused intheserviceofincreasingly it encompassedcontrastingmodesofinquiry. Ontheonehand,itadvancedtheories used it.Perspectivebecameapowerfulmediumforexperimentationpreciselybecause know preciselywhatperspectivesignifiedinthemindsofthosewhoinventedand set oftheories,practices,andexpectations.Aftercenturiesdebatewestilldonot of rigidrepresentationalformalism. other withfalseideologies,pre-modernphilosophicalcomplacencies,andalegacy associated withthelastingingenuityandsagacityofRenaissanceon theoretical practice.Perspectiveisthereforeaconundrum.Ontheonehandit avant-garde movementsandthenirrevocablydeconstructedbypost-modernist It isnoteworthy In afamousillustration(Figure2.1)thatappearsattheendofhistreatiseon In manyrespects,thestudyofperspectivewasmerelyonesegmentabroader However, fromitsinceptionperspectivehasbeenacontestedandheterogeneous Underweysung derMessung , however , thatDürer’s imagealsoindicateshoweventhemost trompe l’oeil – Lyle Massey– (Nuremberg, 1525),theGermanartistAlbrecht 52 . But inthesixteenthcentury s , this kind machine. s end Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo word, fashioningitasamodern techniqueforviewing,measuring,and,aboveall, optical geometrywasknown as as ithadbeendevelopedinGreek andArabicthought.IntheRenaissance, (1401–28) andFilippoBrunelleschi(1377–1446),Alberti drewonopticalgeometry fi of representationthathesawemerging beforehiminFlorence.Like manyother in 1436),Albertilinkedmedievalopticalgeometrydirectly tothenewpractices On Painting described theprinciplesonwhichDürer’s ideasandpictureswerebased.Inhiswork tive, itwastheItalianhumanistLeonBattistaAlberti (1404–72)whoinitially While Dürer’ mit demZirkelundRichtscheyt Figure 2.1 generic, universalparadigm,andtheotheracomplex,contingentvariable. and transcendent,theotherisheterogeneouscorporeal.Oneconstitutesa image presentsuswithaconflict betweentwokindsofviewpoint.Oneisarchetypal form toanidealscenario,buttheyalsostandoutsidethatscenario’s projection. The of perspectiveisabstract,disembodied,andmathematical.Dürer’s technicians give fteenth-century FlorentinessuchastheartistsDonatello (1386–1466), From AlbrechtDürer, (the firstversionwaswritteninLatin1435,andthesecond inItalian s was the firstprintedtreatisetodepictartistsactuallyusingperspec- – Framing andmirroringtheworld– A HISTOR . Nuremberg, 1525. AS APRACTICE perspectiva Draughtsmen withLute Y OFPERSPECTIVE 53 . Fifteenth-century artistsredefined , in hisUnderweysungderMessung medieval t h is Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo attached thepaintingtoanapparatuswithamirror Duomo, thecity’ a combination ofarchitecturalsurveyingtechniquesandworkshoppracticestoproduce foundations forthisnewartistictechnique.Around1413,Brunelleschiuseda from perspective: account providesaninsightintowhatfifteenth-centuryartistsandtheoristsexpected before 1489,AntonioManetti(1423–97)describedBrunelleschi’ philosopher whowroteextensivelyonoptics.InhisbiographyofBrunelleschiwritten that probablyderivedfromtheworkofAlhazen(965– convincing illusionbecauseitwasorganized aroundacentralvisual ray, aconcept out. With thisexperiment,Brunelleschisoughttoprovethattheimage achieveda would thenseereflectedboththepictureofbaptisteryandhisowneyepeeping of apublicspectacleinFlorenceatthistimewouldinvariablyhavebeenmale) look throughasmallholeinthebackofpaintingfromwhichhe(theviewer constitute interrelatedbranchesofknowledge. artificialis architect andsculptor, whoiscreditedwith havingproducedthemethodological to distinguishbetween representing angles ofvisiondiminishproportionally andthus“quantities”inthevisualfieldcan ray (the“princeofrays”)that providestheclearestfocusofsight.Within thepyramid, intersected byaplane.This “visual ,”heobserves,isanchoredbyacentral matical entitiessuchaslinesandpoints,Albertidefined visionasadoublepyramid written form.Beginninghistreatiseonpaintingwitha longdescriptionofmathe- that causedhimtoconnecthismethodthetheoryof the centralray? not basedontheoreticalideasaboutvision?Was itonly laterthathehadanepiphany vincing illusionofthebaptisteryusingmechanicalmethods thatthemselveswere out toproveacorrelationbetweenopticsandpainting? Ordidheproduceacon- or evenepistemologicalframeworkusedtoobtaintheimage. DidBrunelleschiset recreate thepanelexperimentexactlyasitwasortodetermine theprecisetechnique description. Whileinformative,Manetti’s accountlacksthenecessaryprecisionto never beenfoundandmostofwhatisknownaboutit comes onlyfromManetti’s But thedetailsofBrunelleschi’ Holy Trinity small, foreshortenedpaintingoftheFlorentinebaptisteryasifseenfrom whatever hasbeenaccomplishedsincehistimeinthatarea. distance inwhichtheyareshown.Heoriginatedtherulethatisessentialto every sortandlocation,withfigures andobjectsincorrectproportiontothe objects asperceivedbytheeyeofman:buildings,plains,mountains,places properly andrationallythereductionsenlargements ofnearanddistant since itformspartofthatsciencewhich,ineffect,consistssettingdown [Brunelleschi] propoundedandrealizedwhatpainterstodaycallperspective, While thepainterMasaccioproducedearliesttruepaintedperspective( The principlesofperspectivewerenotclarified untilAlbertiexpressedthemin (artificial orpainterlyperspective),butthetwofieldswereunderstoodto the world.EventuallyartistsandtheoristssuchasLeonardowouldcome in SantaMariaNovella,1426–27),itwasBrunelleschi,theFlorentine s cathedral.Hethensetupanow-famousexperimentinwhichhe perspectiva naturalis s – experiment remainmurky:thepaintingitselfhas Lyle Massey– 54 (the opticsofnaturalvision)and . Theviewerwasinvitedto c. 1039), anArabicnatural 2 s approach. His perspectiva The Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo education andademonstration oferuditioninfifteenth-centuryFlorence.Thus,by literature andphilosophythat hadincreasinglybecomethehallmarkofaclassical narratives drawnfromancient sources,emulatingtheGreco-Romanbodyof it customarilyhadbeenassociated.Inaddition,Alberti usesrhetoricaldevicesand distinguishing paintingfromtheartisanalpracticesormechanical artswithwhich (grammar literature todrawacorrelationbetweenthevisualarts andthesevenliberalarts of intellectratherthanlearnedskill.Alberti’s treatiseisoneofthefirstworks Representing paintinginthislight,Albertisuggeststhat itbeconsideredtheresult and heoffers Marquis ofMantua.Init,Albertialludestotheprince’ intellect. TheseconddedicationistoGianFrancescoGonzaga (1395–1444),the as someonewhosesuccessanengineerandarchitectwas dueingreatparttohis tically withlinesandcoloursonagivensurface,” given distance,withafixedcentreandcertainpositionoflights,representedartis- composition. Statingthatapaintingis“theintersectionofvisualpyramidat be of scholarand man oflearning”andintimatesthattherelationshipbetweentwomenis“one As AnthonyGraftonpointsout,indoingthis,Albertiidentifies Brunelleschi“asa concludes byaskingBrunelleschitoreviewthemanuscriptandoffercorrections. and RomewhowereknownthroughPliny’ Brunelleschi andotherFlorentineartistswiththoseoftheancientGreece of alettertoBrunelleschi,andinitAlbertifavorablycontraststheachievements Alberti’ The twodedicationstotheItalianversionofbookrevealagreatdealabout on equalfooting(althoughheisalsocarefultomaintainadistinctionbetweenthem). distance betweentheviewerandrecedingplanesofpicture. pictorial field.Thisperipheralpointmathematicallydeterminestheproportional a a be higheronthetwo-dimensionalsurfaceandshorterinwidth.ThusAlbertiinvents that thoseplanesareintendedtobeperceivedasfurtherfromtheviewershould field andprogressivelyshorterinlength.Transferred tothepictureplane,thismeans the horizontalsegmentsthatarefarthestawaywillappearbothhigherinvisual eleventh propositioninthe receding planes.ThisadditionaldiagramappearstobedirectlybasedonEuclid’ d’aiuto center. To determinetheproportionalquantitiesof vision, Alberticreatesa and markapointinthemiddle.Thisrepresentsprinceofrayspiercing to drawasinglehorizontallinewithinthisrectangle(thepicture’s assumedhorizon) pass hypotheticallythroughthistwo-dimensionalplane.Hethendirectsthereader draw arectangleandimagineitastheintersection.Thevisualpyramidwouldthen which waswidelycirculatedinfifteenth-centuryItaly. mechanism knownasthe“distancepoint,”transposingEuclid’ formula forrationalizingthespatialrelationshipbetweenviewpointand measured bytriangulation.AlbertiprobablydrewthisnotionfromEuclid’s Establishing abaseinopticalgeometry, Albertithendescribeshowtobegina Throughout histreatise,Albertideliberatelyplacesopticalgeometryandpainting a , s motives formakingthiscomparison.Thefirstdedicationisintheform diagram designedtohelptheartistestablishproperdiminutionof , logic, rhetoric,arithmetic,geometry De pictura – .” Framing andmirroringtheworld– 5 as fodderfortheprince’s “customarypursuitofletters.” Alberti thereforerepresentsBrunelleschiasanequaland Optics , which statesthatthoseintersectionsrepresenting 55 s Natural History , music, andastronomy),thereby 4 Alberti instructsthereaderto 3 s pleasure intheliberalarts and othersources.He s propositioninto costruzione Optics s , Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo of original,detaileddiagrams. also addedsubstantialportionsonmathematicsandgeometry andprovidedaseries sometime intheearly1480s.Heextendedandclarified much ofAlberti’s text,but by Leonardo,bothofwhichwereillustrated.Pierocompleted treatises onpainting–onebyPierodellaFrancesca( was notpublisheduntil1847).Butthereweretwoother important fifteenth-century much later(theLatinversionwasfirstprintedinBasle 1540 andtheItalianversion no endofconsternationandspeculationamongarthistorians),norprinteduntil point illuminateAlberti’s otherwisesomewhat confusingexplanations).Nevertheless, useful forexplainingthenew technique(forinstance,hisdiagramsofthedistance eventually madeonbehalfof perspective,andhisdiagramswereamongthemost speculations wereparticularlyformativefortheepistemological claimsthatwere death, althougheventheninanabridgedanddubiously organized form.Leonardo’s tise unfinishedanditdidnotappearinprintuntilmore thanacenturyafterhis manuscript didnotappearinprintedformuntilmuchlater the principlesof is themostrationalofsenses,“princemathematics,”andpaintingsthatemploy of space.Alberti’ perspective werealsoconcernedwithissuesofvisualrepresentationandtheordering solids, andcartographicastronomicalprojections.Butmosttextsdealingwith matical fields: thetechniquefigured prominentlyindiscussionsofconics,thePlatonic relative meritsofthedifferentarts.EnthralledbyHorace’ thus ultimateevidenceofthehumanabilitytocommandknowledgeworld. its perfected,geometricunderstructureandidealizedviewpoint,perspectivewas painting couldbeseenasapropositionaboutvisionandtheorderofnature.W inquiry abouttheworldonaparwithotherformsofnaturalphilosophy. In claim thatacertainkindofnaturalisticrepresentationshouldbeseenasform as evidenceoftheartist’s intellect,Albertimadetheremarkableandhighlyoriginal and makesapersuasivecaseforelevatingthestatusofvisualart. employing variousstrategies,Albertialliespaintingtootherintellectualpursuits nature preciselybecauseofitsconnectiontotheeye. Painting isexceptionallyadeptatrenderingvisiblethemostelementaltruthsof primary meansbywhichthe treatise onpainting,heobservesthattheeyeiswindowofsouland“is and thiswasdueinparttothesheerforceofvision.Innotesforhisincomplete painting hadmorepowerthanpoetrytomakenaturepresentthemindofman to invokethepresenceofwhatwasabsent.Leonardo,forinstance,insistedthat ar “Ut picturapoesis”(“asispainting,sopoetry”),Renaissanceartistsandhumanists As Leonardohadmadeclear turn becameatheoryofopticsorratherpropositionabouthowandwhatwesee. the scienceofopticswastransformedintoatheorypainting,butpaintingin magnificently contemplatetheinfiniteworksofnature gued overthemeaningofimitationandpowerpaintingversuspoetry This characterizationofpaintinginformedRenaissancedebatesconcerningthe What wasthehistoricalimpactofAlberti’s strategy?Inpromotingperspective After Alberti,scholarsandartistsincorporatedperspectiveintovariousmathe perspectiva s text wasneitherillustratedwithdiagrams(afactthathascaused are adirectreflection oftheeye’ , theinventionofperspectiveheraldedanewerainwhich 8 Although finishedinthelatefifteenthcentury, Piero’s sensus communis – Lyle Massey– 56 of thebrainmaymostfullyand . c s similefromthe . s . singular reflective power. 1420–92) andtheother .” . 6 Leonardo lefthistrea- For Leonardo,theeye De prospectivapingendi Ars poetica De pictura ith - 7 , , Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo who lecturedatvariousuniversities throughoutItalyandthenwasinvitedtothe likely LucaPacioli(1445–1517), thecelebratedmathematicianandFranciscanfriar which someonethereiswilling toteachme.” I humanist Willibald Pirckheimer:“Ishallbefinished hereinanothertendays.Then for thistripisrecordedinaletterhewrotetohisclose friend,theNurembur him. DuringhissecondstayinItaly(1505–10/11)hetraveled toBologna.Hisreason Italian approaches,anditisclearthatperspectiveheld aparticularattractionfor book devotedtoproportion.Dürermadetwovisits Venice, whereheabsorbed suggestive avenueforthinkingaboutahostofproblems. voices andoftentoverydifferentends–revealshowthe topic becameavolubleand in oneformoranother. Theproliferationofprintedtexts–writteninmanydifferent points.” said thathepreferredtoconstructperspectives“withtwocenters,orrathervanishing of , GiovanBattistaCaporali( of thegreattheoristsperspectiveemployedsimilartechniques.Inhis1536edition with themoreintellectualizedtheoryofAlberti.Infact,mostartistsandevenmany thus hasfarmoreincommonwithlatemedievalworkshoppracticesthanitdoes lateral pointstoconstructtiledfloors andobliquelyangledbuildings.Hismethod expanded onthisbifocaltechnique.Inhistreatiseheemploysacentricandtwo (tiles) thatappearonthefloor. Usingamethodcalled intersecting gridcreatedbythesetwosetsoflineswasusedtoconstructthe there areincisedlinesfromtwolateralpointsoneithersideoftheframe.An in theSieneseartistPietroLorenzetti’s referred toasdualorbifocalconstructions.Afamousexampleofbifocalismappears make apleatoelevatethestatusofart. anything likeAlberti’s mathematicalandphilosophicaljustification,nordoeshe method, barelycorrelatingittoopticsorgeometry. Inshort,hedoesnotoffer Piero, andLeonardo,Viator providesonlyarudimentaryrationalizationofhis these areaccompaniedbyonlyashortanduninformativetext.IncontrasttoAlberti, did notappearuntil1505.ItwastheworkofCanonToul, JeanPélerin( observations, andplagiarismsoflaterauthors. his ideas,buriedastheywereinnotebooks,onlyfilteredoutthroughthecomments, for artistsandscenedesigners,therearealsoafewgeometricdiagrams.Unfortunately of thetreatise’ 1435–1524), whopublishedunderhisLatinname,Viator (“voyager”).Whilemost proportion, ,geometry of workshoppracticesandtheoreticalmusings. commentators. Thusperspectivemayhavebeentheresultofacomplexinterweaving practices mayhaveevolvedintothetheoryofdistancepointelaboratedbylater multiple editions)wereprintedthroughoutEurope. numbers; between1500and1700roughly90booksonthesetopics(manywith shall ridetoBolognainorderlearnmoreaboutthe secretartofperspective, As mentioned,Dürerpublishedoneoftheearliesttreatments ofperspectiveina Instead Viator’s diagramsreflectcommonworkshopmethodsthatareoften The firstprintedtreatisedevotedentirelytoperspective, Following Viator, anumberoftreatisesonpaintingandrelatedsubjectssuchas 9 Although notbasedonanysuppositionsaboutvisionorgeometry s illustrationsdepictstage-likesettingsthatareprofferedastemplates – Framing andmirroringtheworld– , and scenedesignwerepublishedinincreasing Birth oftheVirgin 1476–c. c. 57 11 His contactinBolognawas most 1560) statesthatLeonardoonce tiers points 10 (1335–42). Inthispainting All dealtwithperspective De artificialisperspectiva (three point),Viator pavimenti , bifocal c g , . , Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo perspective geometry proportion andmathematics,similarassociationsmayhaveattimesadheredto provides techniquesformeasuring andforeshorteningcomplex,multi-sidedobjects, also marriescontemporarysolid geometrytopainterlyperspective.LikeDürerhe Hirschvogel (1503–53),LorenzStoer( complex bodies.From1543to1571Nuremberg producedworks by Augustin printing sitesfortreatisesdevotedtoproblemsofproportionandrepresenting Following thepublicationofDürer’s manual,Nuremberg becameoneofthemajor of humanfacultiesandthatitwasbasedonunequivocalintellectualfoundations. were similartothoseofAlberti.Heclaimedthatpaintingrequiredthehighest reasons forproducingatreatiseonproportionandembracingtheartofperspective of knowledge,whichmaybewhyDürerdeemedit“secret.” of myworktothepracticesuchabeautifulinvention.” to mebefoundedonperspective,[andthus]itseems reasonabletodevoteapart night skyorplanisphere.AccordingtoBarbaro,thePtolemaic planisphere“appears of hisperiod,BarbarowasfascinatedwithPtolemy’ Platonic solidsforPacioli’s and healsometLeonardoinMilan.Infact,providedillustrationsofthe Sforza courtinMilan.PacioliknewandplagiarizedtheworkofPierodellaFrancesca, a which wasbasedonasinglepointofvisualprojection, mayhaveevenprovided that Ptolemy’ direction. Fromearlyon,Italianwritersfor for literate,humanistaudiencesandbookcollectors. intricate andbeautifulillustrationsthatmadethebooksexpensiveobjectsintended perspective withgeometry on thevariedarticulationofregularandsemi-regularsolidsfirmlycorrelated and HansLencker(1523–85).ConceivedalongDürer’ Ptolemy’ mathematician EgnazioDanti(1536–86). (1507–73), whichwasedited,annotated,andprinted posthumouslybythe della prospettivapratica (V discourse withitsownlanguageandparadigms.Thesewere two otherworksprintedinthisperiodthatestablishedperspectiveasadistinct that wouldcometodefinearchitecturalpracticeforensuingcenturies.Butitwas Architecture (Paris, 1545).Serlio’ architecture andscenedesign.ThiswasSebastianoSerlio’ and mathematics.OneoftheearliestItalianworksonperspectivewasdevotedto of perspective.Pacioli’s treatiseunderscoredthe“divine”andmysticalnatureof mathematician whowasinturnconnectedtosomeofthegreatRenaissancemasters geometry andproportion.Dürerwasthereforeapprenticinghimselftoawell-known model forearlytheoristsofperspective suchasBrunelleschi. enice, 1569)bytheVenetian patricianDanieleBarbaro(1513–70)and Nevertheless, itwasnottoosecrettobepublishedinmanualsforpainters.Dürer’s In sixteenth-centuryItalythestudyofperspectiveevolvedinaslightlydifferent One ofBarbaro’ s astronomicalprojectionandperspective.Aswithmany mathematicians in thatheestablishedasetofsurveyingandrepresentationaltechniques s geographic systemfordepictingthe s most importantcontributionswastoshowtherelationbetween s . Italsoseemedtobeanesotericandeven text wastheRenaissanceanswertoV (, 1583)bythearchitectJacopoBarozzidaVignola . De divinaproportione At thesametime,theywerefilledwithincreasingly – Lyle Massey– c . 1540–1620), W 58 ged alinkbetweenpainting,architecture, (Venice, 1494),atreatiseonsolid mappa mundi s model,thesetreatisesfocused s systemofprojectionforthe 12 enzel Jamnitzer(1508–85), s In fact,ithasbeenar Il primolibrod’architettura La praticadellaperspettiva 13 itruvius’ But Barbaro’ slightly occultkind (map oftheearth), T Le dueregole en Bookson s treatise gued Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo are bestwhenthey“mirrorthegeometricalstructurebehindnaturalforms.” out, inequatingvisionandproportionBarbaroespousestheideathatworksofart how theeyedeterminesproportionanddiminution.AsMartinKemphaspointed and upside-downimageofwhatisoutside)butonlyinsofarasitdemonstrates construction. Danti,hiseditor demonstrate howtocorrelateanarchitecturalgroundplanadistancepoint vanishing point.Hisremarkablediagramsoftwoalternative“rules”forperspective explanations oftherelationbetweenviewer’ greatly onprojectivetheoriesofperspective,Vignola providedvividlyillustrated and wasaddressedequallytopainters,architects,mathematicians.Expanding of representationbasedongeometricalprojection. Barbaro thusfurnishesthereaderwithafull-fledgedjustificationforcertaintypes the Vision arbitratestheproportionsthatappearinnature.Barbarocomparessightto sight isthesensethatallowsforjudgment,andEuclid’s theoremsmakethisclear. but healsoconnectshisconstructionstoEuclideanprinciples.AccordingBarbaro, and projectivetechniquesforartistsarchitects. and ontheotheritbecameincorporatedintoaseriesof formulaicrepresentational as thebasisforamoreandsophisticatedabstracted geometryofprojection, of perspectivehadbeguntosplitintotwoareasinquiry painted orbuiltillusions.Infact,bytheendofsixteenthcenturystudy subject toadifficultandabstrusemathematicsthatwentfarbeyondthedemandsof projections. Guidobaldo’ perspective asthebasisforexploringPtolemaicastronomical,conical,andorthographic 1558) and 75) andGuidobaldodelMonte(1545–1607).In of professionalandamateurmathematicianssuchasFederigoCommandino(1509– painting, butahybridofallthree:namely, perspective. a drawing machinesandtechniques.Inshort,Vignola andDantiidentified anddefined text, updatingthemathematics,interjectingnewdiscoveries,andillustrating in hand,contemplatingtheineffective instrumentsofinspirationthatsurroundher of bothRenaissancescienceandart.Dürer’ sixteenth century for analyticreappraisalsandself-reflexive critiques.Asearlyasthebeginningof perspectivewasacatalyst Even beforeitbegantosplitintodifferingareasofinquiry, toward projectivegeometry of thesaturnineartistictemperament, Dürer’ represents anascentexpression ofthesesentiments(Figure2.2).Asanembodiment mathematician GirardDesar new areaofinquirythatwasneithersolelymathematics,norarchitecture, On theotherhand,Vignola’s Ledueregole Later inthecentury, however, perspectivefellincreasinglyintothedomain Claudii Ptolomaeiliberdeanalemmate , perspective wasassociatedwiththevaingloriouspresumptiveness (an encloseddarkenedboxwithapinholethatprojectsreverse – Framing andmirroringtheworld– THE SELF-CRITIQUINGAR s Perspectivae librisex a , gues inthe1630s.Atthispoint,perspectivebecame , alsoprovidedarunningcommentaryonVignola’s field thatwouldbefullyrealizedbytheFrench 59 s wingedfemalefiguresitsglumly tied togetherallpreviousspeculations s famous print (Pesaro, 1600)movedperspective (Rome, 1563),Commandinoused s space,thepictureplane,and Ptolomaei planisphaerium . On T the onehanditserved Melencholia I (V (1514) enice, , chin 14 . Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo panel ofnumbers,thecompass, andothersymbols,thepolyhedronimbuesentire to adisjunctionbetweendivine andhumancreativity. Alongwiththemysterious can beinterpretedasasymbol ofgeometryandproportionthatneverthelessattests treatises. ButDürerpurposefullyrenderedthiscomplex objectincorrectly. Thusit One oftheseisashadedpolyhedron,thesortthatappeared regularlyinperspective Figure 2.2 Albrecht Dürer. Melencholia I – Lyle Massey– (1514). DavisonArtCenter,WesleyanUniversity. 60 Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo “anamorphic.” trick imagesoflessgravity. Sincetheseventeenthcentury, thesehavebeenlabeled textbook. AttestingtothetwoFrenchmen’ torquetum (usedtodeterminethemotionsofcelestialbodies),andamathematics flutes, aGermanhymnal,terrestrialandcelestialglobes,quadrants,sundials, hold musicalandscientifi altar it Mantegna’ (1431–1506) skewed views.PrecipitouslyforeshortenedworkssuchasAndreaMantegna’s it wasfirstinvented,artistsrecognizedthatperspectivecouldbeusedtocreatehighly became recognizablefromsidelongorhiddenviewpoints.Virtually fromthemoment of aformperspectivethatwasinitiallyusedtoproduce“secret”imagesonly their practice.Forinstance,fromthelatefifteenthcenturyon,artistswereaware artistic ingenuity. the contradictions,doubts,andinsecuritiesofRenaissancenaturalphilosophy engraving withasenseofmisapprehensionandinadequacy. to Thisimagetestifies included inHolbein’ life, theskullwasaconventionalsymbolof resolves intoaleeringskull. to thepaintedsurface.Ataviewpointalongpicture’s edge,thisamorphousshape recognizable onlywhenseenfromtherightsideofpainting andfromveryclose Neither fullypartofthepainting,norviewer’s space,theimagebecomes of thissolemnportraitisastrange,floatingobjectthatseems suspendedinmid-air. inlaid pavementalludestothelocation).Theyfl of HenryVIII,placesthemintheinteriorW inexpensive prints,called German printerErhardSchon(1491–1542),whowasastudentofDürer’s. These perspective curieuse (reverse perspective),whileJean-FrançoisNiceron(1613–46)coinedthephrase“ Gian PaoloLomazzo(1538–1600),forexample,usedtheterm“ of theeducatedupperclasses:geometry, astronomy, arithmetic,andmusic. of objectsrepresentsthemathematicalintereststhatwouldhavebeencharacteristic viewer ofthevanityandhubris ofhumanendeavors. of the richgreenfabricofacurtain. Scientifi small crucifi instruments betweenthetwomen.Thepointisunderscored bythepresenceofa Jean deDintevilleandGeor the Younger (1497/8–1543)paintedin1533(Figure2.3).Thisdouble portraitof in atleastone“highart”example: in somecases,eroticandscatologicalimages.Butanamorphosisalsofoundanoutlet seem asthoughChrist’s severelyrakedbodyisbeingoffered tothevieweronan divine revelation,andtheskull tipsthescalesagainstformerasitreminds But perspectivistsalsocametoincorporatethesedoubtsintotheveryfabricof In northernRenaissancepainting,particularlyinthedeveloping genreofstill A , otherartists,includingLeonardo,usedsimilarrakedperspectivestoproduce typical useofanamorphosiscanbefoundinengravingsproducedbythe s paintingunderscoresthedoctrineoftransubstantiationbymaking x Dead Christ 15 on theupperleftofpaintingthatisonlypartially concealed by .” Before this,otherlabelswereusedtoidentifythistypeofdistortion. – s Framing andmirroringtheworld– painting asanintentionalcontrasttothehighlydetailed of 1480–90felljustshyadisorientingdistortion.While c Vexierbilder instruments. Amongtheobjectsweseealute,caseof ges deSelve,twoFrenchambassadorstothecourt or “puzzlepictures,”concealedportraitsand, The FrenchAmbassadors c 61 knowledge isjuxtaposedagainst thetruth s varied intellectualpastimes,thisarray vanitas ank atablewithtwoshelvesthat estminster Abbey(theelaborate or memento mori by HansHolbein prospettiva inversa . It isprobably 16 In front la ” Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo through whichthisrealityisconveyed. to usgeometricallyandmathematically, butonlyinsofarasweembracetheillusions painting intentionallyrevealsperspective’ perspective isturnedonitselfinaprevaricatinggameof contravention.Holbein’s through mathematics.But,ofcourse,allthisisdoneon purpose.Inanamorphosis, the sametimeitchallengestwomen’s capacitytomeasureandrationalizespace technically virtuosic,foreshortenedpavementandthetable’ it subvertstheportrait’s seeminglylinear, rationalorganization. It contradictsthe Archive/The NationalGallery,London/EileenTweedy. Figure 2.3 But theskullisnotsimplyanothericonographicsymbol. Throughitsdistortion, Hans HolbeintheYounger(1497–1543). – Lyle Massey– 62 s paradoxical nature:theworldisavailable The Ambassadors s perfect diminution.At , 1533. TheArt Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo eada noe idwtruhwihtesbett epitdi en. regard asanopenwindowthroughwhichthesubjecttobepaintedisseen on whichIamgoingtopaint,drawarectangleofwhateversizewant, a as picture.” asserted that“thefundamentaleventofthemodernageisconquestworld In alecturegivenin1938,theGermanphilosopherMartinHeidegger(1889–1976) knowing. and thusitsustainedaninherentlyfallaciousassociationbetweenseeing ignored other(phenomenological)aspectsofwhathecalled“being-in-the-world” image ofthewindow Renaissance notionsof “window” asaworld-picture.ButarthistorianJamesElkins haspointedout,while that distinguishedthemodernagefromallthoseprecededit. picture” gavewaytoa“modern”one),itwastheveryideaof“world one agetoanother(forexample,theoften-repeatedtropethatamedieval“world against thisnotion.Heinsistedthatratherthansimplyshiftinginkindfrom a – While wemightassumethattheideaofaworld-pictureorworld-viewisuniversal vision? historical interpretationofperspective asanobjectiveportraitofrealityandhuman similitude ofnatureinanempirical sense,thenhowdoweexplainthepersistent But ifthegoalofperspectiveinpaintingwasnotnecessarily toprovideanexact Cartesian consume thesepicturesfromasingularandirreduciblevantagepoint(thatofthe by andinourmentalpicturesofitwe,asself-understandinghumanbeings, Cartesian thought. neous legacyoftheEuropeanEnlightenment,particularlyasdemonstratedin the “worldpicture”didnotcarrypositiveconnotations.Instead,hesawitaserro- native painting wasastagesetintendedtoserveasanappropriate backdroptotheimagi- transparency ofthepictureplaneitself.AndyetforAlberti, theenclosureof has beenconsistentlymisconstruedasatechnicalimage intendedtoimplythe the outsideworld;ratheritneededtocreateawholenew worldwithintheframe. completely fromanytypeofopticalframing. vision toenlightenment. picture’ and representssightasthelocusofknowledge.Onemightsaythat“perspective” with arationalized,centralpointofview The perspectivepictureseemstopositahomogeneous,infinite,andoccurrentspace artistic theoryprovidedamodelforhowthisideaofmindandsightmightwork. clear allofourotherperceptions.Fifteenth-andsixteenth-centurypainting the sensethatconnectsourinnerbeingwithworldoutside.Itsortsoutandmakes metaphor firstemployedbyAlbertiin Heidegger’s is oneofthemostpowerfulphilosophicalcritiquesperspective René Descarteshadpostulatedthatourunderstandingoftheworldisconstituted foundational characteristicofanyhistoricalageorplace–Heideggerargued istoria s conver 21 cogito 17 or narrativeconstructedbytheartist.Apaintingdidnot needtorefl The imagethatepitomizesHeidegger’s “worldpicture”isthewindow, gence withCartesianismproduceda“wayofseeing”thatunited or subject).Becauseofitsinherentrelationtothemind,sightis – , THE LEGACYOFPERSPECTIVE in practice,the Framing andmirroringtheworld– perspectiva naturalis 20 The problemforHeideggerwasthatthis“wayofseeing” geometry 63 . On Painting It reducestheworldtoextendedmatter were metaphoricallyunifiedaroundthe 22 of perspectivewasdisassociatedalmost Over time,theideaof“window” : “First ofall,onthesurface 19 For Heidegger, . .” ect 18 23 Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo distortions thatoccurinregularvision).T “curvilinear” debateconcerningwhetherperspectiveshouldreflectthelateral was contestedeveninthefifteenthcentury(oneofmostfamousexamplesis with thisidea,nottheleastofwhichisthat“realism”attributedtoperspective was aresultofthiscomparativetesting.Ofcourse,therearenumberproblems old visualschemaswithnewerandmoresalientversions.Perspective,heobserves, That is,theyconsistentlymatchedwhatsawtorepresented,replacing Fifteenth-century artistsandviewersemployedaformofvisualtestingreality. result ofaseriesexperimentsinperception:whathecalled“schema-matching.” Gombrich (1909–2001)argued inArtandIllusion ordering andmanagementofFlorence’ concurrently withasetofskillsthatthemselvesweredeemed necessarytothesmooth that theonedefinedorcausedother solids andnumericallydeterminablerelationshipsofdistance. Hedoesnotar it wasarepresentationalpracticebuiltontheevocationof geometricandvolumetric suggests thatonereasonperspectivemeldedwiththeseinterests ispreciselybecause production, trade,monetarylending,andthecalculation ofinterest.Baxandall measuring, weighing,andgaugingwereallnecessaryto aneconomybasedoncloth and geometrywerefundamentalratherthanextraneous adaptiveskills.Counting, over othersatanygivenplaceintime. matching couldneveraccountforwhycertainversionsofpictorialrealitytookhold “natural” inanygivencultureortimeperiod.Nevertheless,thenotionofschema- debate aboutthecontingentandcontextualnatureofwhatisperceivedas“real”or matching istheunderlyingmechanismatwork.Gombrichopenedupanimportant representation doesnotnecessarilyhavetobethesameasanother’s, even ifschema- are not.Thus,onesocietyorculture’s versionofamatchbetween realityand that whilesomemightviewthetendencytotestasuniversal,resultingpictures moment intime,butnotatothers.To befair, Gombrichtooksomepainstoargue account forwhyagivenpictureofrealityisacceptableinsomeinstancesorat sentations ofitmaybeahumanphysiologicalandpsychologicaltrait,butcannot skills onehappenstopossess, thecategories,modelpatternsandhabitsof evaluation ofanimageduring anyhistoricalperioddependsonthe“interpreting reading andrecognizingparticular patterns.AsBaxandallpointsout,thesuccessful or weightby“eye”),andperspectivereliedonthisother conventionalskillsfor was highlyprizedinFlorentineculture(theabilityto gaugeorassessavolume that thecity’ shared bytheliterateandpoliticalclassesinfifteenth-centuryFlorence.Given “The PeriodEye,”Baxandalloutlinedaseriesofskillsandexpectationsthatwere mathematics withcertainconventionsofrepresentation.Inachapterfamouslytitled and diddevelopasharedvisuallanguagethatcombinedelementsofgeometry how agivengroupofpeoplewithsimilareconomicandsocialinterestscould . Ratherthanfocusonthereceptionofmedievaloptics,Baxandallexplores perspective tookholdasthepreferredmethodofrepresentingrealityinRenaissance Michael Baxandalloffersoneofthemostimpressiveattemptstoexplainwhy Grappling withtwentieth-centuryperceptualpsychology, thearthistorianE.H. In contrast,in s economy wasbasedonbankingandmercantileinterests,arithmetic Painting andExperienceinFifteenthCenturyItaly – Lyle Massey– s 64 , butratherthatFlorentineartdeveloped fortunes. Thetalentforvisualjudgment esting perceivedreal (1960) thatperspectivewasthe ity againstourrepre- , the arthistorian gue Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo perspective isartificial: itisgeometric,static,andideal.ForPanofsky space. Humansexperiencespaceasalivedphenomenon,butthepositedby or asitisseen.Norcanbesaidtoa“correct”evocation,inpictorialterms,of not anexerciseinverisimilitude:itisn’t isomorphicwitheithertheworldasitexists is pictorial.” perspective grid,onceitwasgrantedauthority, implied“thenotionthatrealityitself still exertsapullonhumanimaginativefaculties.As Patrick Heelanargues, the engendered oneofthemostpowerfullyconsistentways seeingtheworld,onethat matical andgeometricterms.Hereinliesitsclaimonour imagination.Perspective extensions. Inshort,perspectiveallowshumanstoconceive ofinfinityinmathe- is anexpressionofspacethatevokesmathematicallyconsistentcontinuitiesand us howwealreadyseebutrathershowstosee.Andinthiscase,what symbolizes aparticularwayofthinkingaboutspace.Perspectivedoesnotshow must insteadbeunderstoodasamythicalandconventionalstructure,onethat science andconvention,holding togetherunstableandoftenincommensurableideas operations ofvisionitself.Perspective wasexpectedtotreadafinelinebetween any attemptstocorrelateit strictly withobjectivity spective hasneverneatlyfittedwithanyparticularmodel ofinterpretationnorwith historical complexityanditsmanyphilosophical culturalassociations,per- and weredebatedthroughouttheRenaissancebyartists themselves.Becauseofits yet, questionsaboutthenatureandmeaningofperspective werepresentatitsbirth of humancreativity.” the sourceofthinkingaboutworldbutis,instead,arepresentationprocess As Rather theyareimaginativerepresentationsofhumanencounterswithreality. their encounterswiththegivenworld.Symbolicformsarenotimitationsofreality. other formsofrepresentationaresymbolicthroughwhichhumansmediate of theworld.Cassirerendorsednotionthatart,literature,geometricproofs,and must beseenasapeculiarformofsymbolicthinkingabouthumaninterpretations Indebted tothephilosophyofErnstCassirer, Panofskyargued thatperspective inference andanalogy.” with thisprobleminhisseminalessayof1927,“PerspectiveasSymbolicForm.” tenacious powerofthegeometricview. ThearthistorianErwinPanofskycontended to critiquetheperspectival“worldpicture”aslate1938istestament some versionofvisual“reality”dismantled.ThatHeideggerwouldfeelcompelled inquiry evenafteritscentralaxiomshadlongbeenabandonedandconnectionto perspective continuedtobeaprimarytropeforhumanunderstandingandempirical of timeinaparticularplace.Buthisanalysisdoesnotaccountforhowandwhy for perspectivetobeacceptedasanexpressionofpictorialrealityatagivenmoment pictorial form–thataparticularstyleofseeingcoulditselfbemadevisible. only tomeetthisrequirementbutalsodemonstratedthatacuitycouldbegiven on visualacuitytoascertainwhatwas“true”or“honest.”Perspectiveseemednot transparency intransactions.Florentinesadaptedasetofinterpretiveskillsthatrelied of diagramsandgeometricfiguresfulfilledaparticulardemandforcertaintype Of course,itispreciselythisviewofperspectivethatHeidegger rejected.And Baxandall explainsthesocialandeconomicconditionsthatmadeitpossible Michael AnnHollyputsit,forCassirera“symbolicformisneithertheworldnor 27 – 26 Framing andmirroringtheworld– 24 For Panofsky, operatesalongtheselines.Itis perspective Thus inRenaissanceFlorencethenewvisuallanguage 65 , naturalism, orevenwiththe , perspective 25 Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo 0Foracomprehensivebibliographyofthesebooksandtheirrespectiveeditions,seeLuigi 10 12 11 more fascinatingtoaRenaissanceaudience. about illusion,geometry, andvision.Thatitrepeatedlyfailedtodosoonlymade AntoniodiTucciManetti, 2 “[I]inourtimeLeonardodaVinciofFlorence,withwhomwehavespoken aboutthis 9 8 LeonardodaVinci, 1 7 LeonardodaVinci, 6 5 LeonBattistaAlberti, 4 DavidLindbergsuggeststhatAlbertiwouldhavebeenfamiliarwithEuclidthrougha 3 Margaret Walker(NewHaven:YaleUniversityPress,1989),p.52. perspective, Press, 1997). The InventionofInfinity: MathematicsandArtintheRenaissance corporibus regularibus mathematics; the he wasalsoahighlyaccomplishedmathematicianwhowrotetwotextbookson Piero isaninterestingcasepreciselybecausenotonlywasheapainterofgreatnote,but Perspective the Renaissance,seechapter5,“CurvedFoundations,”inJamesElkins, discussion oftheproblemsandmythssurroundingissuecurvilinearperspectivein that acurvedsurfacemorecloselyapproximatedtheconditionsofactualvision.For point perspective,andalsoarguedattimesinfavorofcurvilinearperspectiveonthebasis On theotherhand,Leonardorejectedmonocularmodelofvisionpositedbyone- Vanetti, et Renaissance quoted inCarloPedretti,“LeonardoonCurvilinearPerspective,” vanishing points.”Presumablythisisareferencetobifocal construction. Caporalias Daniele Barbaro, L. Strauss(NewYork:AbarisBooks, 1977),p.7. provided inAlbrechtDürer, The letteritselfisdatedtoOctober13,1506.Citationofthe letterwithtranslationis and Dutchauthorscontributingtothediscourse. the sixteenthcenturywitnesseditsspreadthroughoutEurope, withGerman,French, (Florence, 1979).Althoughinterestinperspectivewasborn in fifteenth-centuryItaly, nei suoisviluppidaEuclideaGaspardMonge recherché destoriadellaprospettva;contributoallfomazioneconoscenza deun’idearazionale, & Anthony Grafton, Penguin Press,1972),p.49. De Statua Chicago Press,1976),p.152,n.23. Lindberg, Latin versionofthe Kemp, Catherine Enggass(UniversityPark:PennStateUniversityPress,1970),p.42. Wang, 2000),p.76. The ScienceofArt De naturalietartificialiperspective–bibliografiaragionatadellefonti teoricheedelle , (Ithaca: CornellUniversityPress,1994). Theories ofVisionfromAl-KinditoKepler edited withtranslation,introductionandnotesbyCecilGrayson(London, . 25 (1963),p.70. affirmsthathedoesit,morethantheotherswithtwocentres,or rather . . La Praticadellaperspettiva Trattao d’abaco Leon BattistaAlberti:MasterBuilderoftheRenaissance Optics Leonardo onPainting Leonardo onPainting (a treatiseonthefiveregularbodiesofgeometry).SeeJ.V.Field, On PaintingandSculpture.TheLatinTextsofDePictura (New Haven:YaleUniversityPress, 1990),p.76. that waswidelycirculatedintheearlyfifteenthcentury.David The LifeofBrunelleschi The Painter’sManual – (a treatiseoncalculation)andthe Lyle Massey– NOTES , , 66 ed. MartinKempandtrans. p. 20. (Venice, 1569),p.163,astrans. byMartin , Studi edocumentidearchitettura9–10 , trans. andwithcommentaryby Walter , (Chicago andLondon:Universityof ed. andtrans.HowardSaalman (Oxford: OxfordUniversity Bibliothèque d’Humanisme Libellus dequinque (New York:Hill The Poeticsof Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo 2 18 22 2 0Thisphrase“waysofseeing”wascoinedbytheBritishculturaltheoristJohnBergerin 20 Heidgger,“TheAgeoftheWorldPicture,”p. 130. 19 4Kemp,TheScienceofArt 14 SamuelEdgerton, 13 5Theterm“”wasderivedfromtheGreek 15 17 23 24 6J.V.FieldandF.A.L.James, 16 AccordingtoHeidegger,“Wecallitthe‘perspective,’trackofforesight. Thus 1 ErwinPanofsky, 5 BBC andPenguinBooks,1972). German in was firstdeliveredonJune9,1938,atFreibrugimBreisgauandthenpublishedin . the determinateunderstandingofbeingmovesinacertainpre-determinedperspective we shallseenotonlythatbeingisunderstoodinanindeterminateway,but Elkins, asking whywesee). an epistemologicalsolutiontoontologicalquestion(ittellsushowweseewithout entirely inadequatemetaphorforeitherbeingorunderstandingpreciselybecauseitposits rogation. Thus,theperspectivalpicturewithitsCartesian“pointofview”wouldbean being, andforHeideggerthisconstitutedaperversionofthecorrectorderinter- how orinwhatwaywecometobetheworld.Knowledge,forDescartes,preceded view, Descartesandthosewhofollowedhimavoidedthemostimportantquestionof Metaphysics which sustainsandguidesourunderstandingofbeing.”Heidegger, (Leipzig andBerlin:Teubner,1927). Perspektive alssymbolischeForm,” inthe (New York:ZoneBooks,1991). Panofsky’stextwasoriginallypublishedas“Die University Press,1972),pp.29–30. Michael Baxandall, a Revolution and ex quahistoriacontueatur quadrangulum recoremanguloruminscribo,quodquidemmihiproapertafinestraest The Latintextisasfollows:“Principioinsuperficiepingendaquamamplumlebeat Other Essays Heidegger, “TheAgeoftheWorldPicture,”in no. 11(StanfordintheVale,1997). the HistoryofScienceandTechnology trope, andasignaloftheessentiallyfi According toJosephMasheck,thewindowhadonlyeverbeen intendedbyAlbertias“a it innowayconveyedtheactualpracticesofperspective. training necessarytoconstructperspective.Whilethewindow wasanadeptmetaphor, adopted byRenaissancewriterslikeAlbertiand,ontheother hand,thegeometric hand, whathecalls“optical”metaphorsassociatedwiththeclassical rhetoricaltradition spring 1991,p.35. ‘Window’: Art-historiographicNotesonanAntimodernist Misprision,” Magia universalis Barbaro andDantidiscussit).SeeBookIII“Magiaanamorphotica”ofGasparSchott’s 1657, morethanacenturyafteritwasinitiallyillustratedinperspectivetreatises(both . television seriespresentedbytheBBCin1972.SeeJohnBerger, Wehavebecomeimmersed(nottosaylost)inthisperspective, thislineofsight . morphe The PoeticsofPerspective (Ithaca: CornellUniversityPress,1991).Seeespeciallychapter5. , meaning “form,”andwascoinedbytheJesuitGasparSchott(1608–1666)in , Holzwege trans. WilliamLovitt(NewYork:Harper&Row,1977),p.134.Thelecture trans. R.Manheim(NewYork:Doubleday,1961),p.99.InHeidegger’s Perspective asSymbolicForm (Wurzburg, 1657),pp.101–69. – The HeritageofGiotto’sGeometry:ArtandScienceontheEveScientific Framing andmirroringtheworld– Painting andExperienceinFifteenthCenturyItaly (Frankfurt: VittorioKlostermann,1952). , p. 78. .”,inAlberti, . . , Science inArt:WorkstheNationalGallerythatIllustrate pp. 46–52.Elkinsdistinguishesbetween,ontheone , British SocietyfortheHistoryofScienceMonograph, ctive poeticsofpainting.”SeeMascheck,“Alberti’s 67 , trans. andintroductionbyChristopher Wood On PaintingandSculpture Vorträge derBibliothekWarburg The QuestionConcerningTechnologyand ana meaning “again”or“back” Ways ofSeeing An Introductionto (Oxford: Oxford p.55. , Art Journal 1924–25 (London: , Downloaded By: 10.3.98.104 At: 16:46 26 Sep 2021; For: 9780203401163, chapterTwo, 10.4324/9780203401163.chTwo Kemp, MartinandMargaretWalker,eds. Panofsky, Erwin. Lindbergh, David.TheoriesofVisionfromAl-Kindi to Kepler Heidegger, Martin.“TheAgeoftheWorldPicture,”in Baxandall, Michael. Baltrusaitis, Jurgis. Berger, John. Grootenboer, Hanneke. Grafton, Anthony. Gombrich, E.H. Frangenberg, Thomas.“TheImageandtheMovingEye:JeanPélerin(Viator)toGuidobaldo Edgerton, SamuelY. Damisch, Hubert.TheOriginofPerspective, Dürer, Albrecht. Foister, Susan,AshokRoy,andMartinWyld. Field, JudithV.TheInventionofInfinity: MathematicsandArtintheRenaissance Elkins, James. Kemp, Martin. Alpers, Svetlana. Alberti, LeonBattista. MichaelAnnHolly, 26 7PatrickA.Heelan, 27 New York:AbarisBooks,1977. Leonardo daVinciwithaSelectionofDocumentsRelatingtohisCareer asanArtist Haven: YaleUniversityPress,1989. Press, 1976. Yale UniversityPress,1989. and OtherEssays of ChicagoPress,1983. Dutch Still-lifePainting Hill &Wang,2000. Princeton UniversityPress,1960. del Monte.” London: NationalGalleryPublications,Ltd,1997. Revolution Press, 1994. University Press,1988. Phaidon, 1972. New York:OxfordUniversityPress,1997. Books, 1991. Statua California Press,1983),p.102. Press, 1984),pp.121–2. , edited withtranslation,introduction,andnotesbyCecilGrayson.London: . Ithaca andLondon:CornellUniversityPress,1991. Ways ofSeeing The PoeticsofPerspective The ScienceofArt:OpticalThemesinWesternArtfromBrunelleschi toSeurat Journal oftheWarburgandCourtauldInstitutes SUGGESTIONS FORFURTHER READING The ArtofDescribing:DutchintheSeventeenthCentury Art andIllusion:AStudyinthePsychologyofPictorialRepresentation The Painter’sManual , Perspective asSymbolicForm trans. andintroductionWilliamLovitt.NewYork:Harper&Row, 1977. Leon BattistaAlberti:MasterBuilderoftheItalianRenaissance Anamorphosis Painting andExperienceinFifteenth-centuryItaly The HeritageofGiotto’sGeometry:ArtandScienceontheEveScientific Space- andthePhilosophyofScience On PaintingandSculpture.TheLatinTextsofDePictura The RhetoricofPerspective:RealismandIllusionisminSeventeenth-century Panofsky andtheFoundationsofArtHistory . Chicago: UniversityofChicagoPress,2005. . London: BBCandPenguinBooks,1972. , trans. W.J.Strachan.NewYork:HarryN.Abrams,1977. Secondary sources – Primary sources . Lyle Massey– , Ithaca: CornellUniversityPress,1994. trans. andwithcommentarybyWalterL.Strauss. Leonardo onPainting:AnAnthologyofWritingsby trans. JohnGoodman.Cambridge,Mass.:MIT 68 , trans. ChristopherWood.New York:Zone Making andMeaning:Holbein’sAmbassadors The QuestionConcerningTechnology . Chicago: UniversityofChicago 49 (1986):150–71. (Ithaca: CornellUniversity , 2nd edn.Oxford:Oxford (Berkeley: Universityof . Chicago: University . . . New Haven: Oxford and . New York: Princeton: . New .