127。Ithavingbeenshewnthattherearenoabstractideasoffigure，andthatitisimpossibleforusbyanyprecisionofthoughttoframeanideaofextensionseparatefromallothervisibleandtangiblequalitieswhichshallbecommonbothtosightandtouch：thequestionnowremainingis，whethertheparticularextensions，figures，andmotionsperceivedbysightbeofthesamekindwiththeparticularextensions，figures，andmotionsperceivedbytouch？InanswertowhichIshallventuretolaydownthefollowingproposition：Theextension，figures，andmotionsperceivedbysightarespecificallydistinctfromtheideasoftouchcalledbythesamenames，noristhereanysuchthingasoneideaorkindofideacommontobothsenses。Thispropositionmaywithoutmuchdifficultybecollectedfromwhathathbeensaidinseveralplacesofthisessay。
Butbecauseitseemssoremotefrom，andcontraryto，thereceivednotionsandsettledopinionofmankind，Ishallattempttodemonstrateitmoreparticularlyandatlargebythefollowingarguments。
128。WhenuponperceptionofanideaIrangeitunderthisorthatsort，itisbecauseitisperceivedafterthesamemanner，orbecauseithasalikenessorconformitywith，oraffectsmeinthesamewayas，theideasofthesortIrankitunder。Inshort，itmustnotbeentirelynew，buthavesomethinginitoldandalreadyperceivedbyme。Itmust，Isay，havesomuchatleastincommonwiththeideasIhavebeforeknownandnamedastomakemegiveitthesamenamewiththem。Butithasbeen，ifImistakenot，clearlymadeoutthatamanbornblindwouldnotatfirstreceptionofhissightthinkthethingshesawwereofthesamenaturewiththeobjectsoftouch，orhadanythingincommonwiththem；butthattheywereanewsetofideas，perceivedinanewmanner，andentirelydifferentfromallhehadeverperceivedbefore：sothathewouldnotcallthembythesamename，norreputethemtobeofthesamesortwithanythinghehadhithertoknown。
129。Secondly，lightandcoloursareallowedbyalltoconstituteasonorspeciesentirelydifferentfromtheideasoftouch：norwillanyman，Ipresume，saytheycanmakethemselvesperceivedbythatsense：butthereisnootherimmediateobjectofsightbesideslightandcolours。
Itisthereforeadirectconsequencethatthereisnoideacommontobothsenses。
130。Itisaprevailingopinion，evenamongstthosewhohavethoughtandwritmostaccuratelyconcerningourideasandthewayswherebytheyenterintotheunderstanding，thatsomethingmoreisperceivedbysightthanbarelylightandcolourswiththeirvariations。Mr。Locketermethsight，’Themostcomprehensiveofalloursenses，conveyingtoourmindstheideasoflightandcolours，whicharepeculiaronlytothatsense；
andalsothefardifferentideasofspace，figure，andmotion。EssayonHumanUnderstand。B。ii。C。9。S。9。Spaceordistance，wehaveshewn，isnototherwisetheobjectofsightthanofhearing。vid。sect。
46。Andasforfigureandextension，Ileaveittoanyonethatshallcalmlyattendtohisownclearanddistinctideastodecidewhetherhehadanyideaintromittedimmediatelyandproperlybysightsaveonlylightandcolours：orwhetheritDepossibleforhimtoframeinhismindadistinctabstractideaofvisibleextensionorfigureexclusiveofallcolour：andontheotherhand，whetherhecanconceivecolourwithoutvisibleextension？
Formyownpart，ImustconfessIamnotabletoattainsogreatanicetyofabstraction：inastrictsense，Iseenothingbutlightandcolours，withtheirseveralshadesandvariations。HewhobesidethesedothalsoperceivebysightideasfardifferentanddistinctfromthemhaththatfacultyinadegreemoreperfectandcomprehensivethanIcanpretendto。
Itmustbeownedthatbythemediationoflightandcoloursotherfardifferentideasaresuggestedtomymind：butsotheyarebyhearing，whichbesidesoundswhicharepeculiartothatsense，dothbytheirmediationsuggestnotonlyspace，figure，andmotion，butalsoallotherideaswhatsoeverthatcanbesignifiedbywords。
131。Thirdly，itis，Ithink，anaxiomuniversallyreceivedthatquantitiesofthesamekindmaybeaddedtogetherandmakeoneentiresum。
Mathematiciansaddlinestogether：buttheydonotaddalinetoasolid，orconceiveitasmakingonesumwithasurface：thesethreekindsofquantitybeingthoughtincapableofanysuchmutualaddition，andconsequentlyofbeingcomparedtogetherintheseveralwaysofproportion，arebythenesteemedentirelydisparateandheterogeneous。Nowletanyonetryinhisthoughtstoaddavisiblelineorsurfacetoatangiblelineorsurface，soastoconceivethemmakingonecontinuedsumorwhole。Hethatcandothismaythinkthemhomogeneous：buthethatcannot，mustbytheforegoingaxiomthinkthemheterogeneous。AblueandaredlineIcanconceiveaddedtogetherintoonesumandmakingonecontinuedline：buttomakeinmythoughtsonecontinuedlineofavisibleandtangiblelineaddedtogetheris，Ifind，ataskfarmoredifficult，andeveninsurmountable：andIleaveittothereflexionandexperienceofeveryparticularpersontodetermineforhimself。
132。AfartherconfirmationofourtenetmaybedrawnfromthesolutionofMr。Molyneux’sproblem，publishedbyMr。LockeinhisEssay：whichIshallsetdownasittherelies，togetherwithMr。Locke’sopinionofit，’\"Supposeamanbornblind，andnowadult，andtaughtbyhistouchtodistinguishbetweenacubeandasphereofthesamemetal，andnighly[sic]ofthesamebigness，soastotell，whenhefeltoneandt’other，whichisthecubeandwhichthesphere。Supposethenthecubeandsphereplacedonatable，andtheblindmantobemadetosee：quaere，whetherbyhissight，beforehetouchedthem，hecouldnowdistinguishandtellwhichistheglobe，whichthecube？\"Towhichtheacuteandjudiciousproposeranswers：\"Not。Forthoughhehasobtainedtheexperienceofhowaglobe，howacube，affectshistouch，yethehasnotyetattainedtheexperiencethatwhataffectshistouchsoorsomustaffecthissightsoorso：orthataprotuberantangleinthecubethatpressedhishandunequallyshallappeartohiseyeasitdothinthecube。\"Iagreewiththisthinkinggentleman，whomIamproudtocallmyfriend，inhisanswertothishisproblem；andamofopinionthattheblindmanatfirstsightwouldnotbeablewithcertaintytosaywhichwastheglobe，whichthecube，whilstheonlysawthem。’（EssayonHumanUnderstanding，B。ii。C。9。S。8。）
133。Now，ifasquaresurfaceperceivedbytouchbeofthesamesortwithasquaresurfaceperceivedbysight，itiscertaintheblindmanherementionedmightknowasquaresurfaceassoonashesawit：itisnomorebutintroducingintohismindbyanewinletanideahehasbeenalreadywellacquaintedwith。Since，therefore，heissupposedtohaveknownbyhistouchthatacubeisabodyterminatedbysquaresurfaces，andthatasphereisnotterminatedbysquaresurfaces：uponthesuppositionthatavisibleandtangiblesquaredifferonlyinnumeroitfollowsthathemightknow，bytheunerringmarkofthesquaresurfaces，whichwasthecube，andwhichnot，whileheonlysawthem。Wemustthereforealloweitherthatvisibleextensionandfiguresarespecificallydistinctfromtangibleextensionandfigures，orelsethatthesolutionofthisproblemgivenbythosetwothoughtfulandingeniousmeniswrong。
134。MuchmoremightbelaidtogetherinproofofthepropositionI
haveadvanced：butwhathasbeensaidis，ifImistakenot，sufficienttoconvinceanyonethatshallyieldareasonableattention：andasforthosethatwillnotbeatthepainsofalittlethought，nomultiplicationofwordswilleversufficetomakethemunderstandthetruth，orrightlyconceivemymeaning。
135。Icannotletgotheabove—mentionedproblemwithoutsomereflexiononit。Ithathbeenevidentthatamanblindfromhisbirthwouldnot，atfirstsight，denominateanythinghesawbythenameshehadbeenusedtoappropriatetoideasoftouch，vid。sect。106。Cube，sphere，tablearewordshehasknownappliedtothingsperceivablebytouch，buttothingsperfectlyintangibleheneverknewthemapplied。Thosewordsintheirwontedapplicationalwaysmarkedouttohismindbodiesorsolidthingswhichwereperceivedbytheresistancetheygave：butthereisnosolidity，noresistanceorprotrusion，perceivedbysight。Inshort，theideasofsightareallnewperceptions，towhichtherebenonamesannexedinhismind：hecannotthereforeunderstandwhatissaidtohimconcerningthem：andtoaskofthetwobodieshesawplacedonthetable，whichwasthesphere，whichthecube？weretohimaquestiondownrightbanteringandunintelligible；nothingheseesbeingabletosuggesttohisthoughtstheideaofbody，distance，oringeneralofanythinghehadalreadyknown。
136。Itisamistaketothinkthesamethingaffectsbothsightandtouch。Ifthesameangleorsquarewhichistheobjectoftouchbealsotheobjectofvision，whatshouldhindertheblindmanatfirstsightfromknowingit？Forthoughthemannerwhereinitaffectsthesightbedifferentfromthatwhereinitaffectedhistouch，yet，therebeingbesidehismannerorcircumstance，whichisnewandunknown，theangleorfigure，whichisoldandknown，hecannotchoosebutdiscernit。
137。Visiblefigureandextensionhavingbeendemonstratedtobeofanatureentirelydifferentandheterogeneousfromtangiblefigureandextension，itremainsthatweinquireconcerning。Nowthatvisiblemotionisnotofthesamesortwithtangiblemotionseemstoneednofartherproof，itbeinganevidentcorollaryfromwhatwehaveshewnconcerningthedifferencethereisbetweenvisibleandtangibleextension：butforamorefullandexpressproofhereofweneedonlyobservethatonewhohadnotyetexperiencedvisionwouldnotatfirstsightknowmotion。Whenceitclearlyfollowsthatmotionperceivablebysightisofasortdistinctfrommotionperceivablebytouch。TheantecedentIprovethus：bytouchhecouldnotperceiveanymotionbutwhatwasupordown，totherightorleft，nearerorfartherfromhim；besidestheseandtheirseveralvarietiesorcomplications，itisimpossibleheshouldhaveanyideaofmotion。Hewouldnotthereforethinkanythingtobemotion，orgivethenamemotiontoanyideawhichhecouldnotrangeundersomeorotherofthoseparticularkindsthereof。
Butfromsect。95itisplainthatbythemereactofvisionhecouldnotknowmotionupwardsordownwards，totherightorleft，orinanyotherpossibledirection。FromwhichIconcludehewouldnotknowmotionatallatfirstsight。Asfortheideaofmotioninabstract，Ishallnotwastepaperaboutit，butleaveittomyreadertomakethebesthecanofit。
Tomeitisperfectlyunintelligible。
138。Theconsiderationofmotionmayfurnishanewfieldforinquiry：
butsincethemannerwhereinthemindapprehendsbysightthemotionoftangibleobjects，withthevariousdegreesthereof，maybeeasilycollectedfromwhathathbeensaidconcerningthemannerwhereinthatsensedothsuggesttheirvariousdistances，magnitudes，andsituations，Ishallnotenlargeanyfartheronthissubject，butproceedtoconsiderwhatmaybealleged，withgreatestappearanceofreason，againstthepropositionwehaveshewntobetrue。Forwherethereissomuchprejudicetobeencountered，abareandnakeddemonstrationofthetruthwillscarcesuffice。Wemustalsosatisfythescruplesthatmenmayraiseinfavouroftheirpreconceivednotions，shewwhencethemistakearises，howitcametospread，andcarefullydiscloseandrootoutthosefalsepersuasionsthatanearlyprejudicemighthaveimplantedinthemind。
139。First，therefore，itwillbedemandedhowvisibleextensionandfigurescometobecalledbythesamenamewithtangibleextensionandfigures，iftheyarenotofthesamekindwiththem？Itmustbesomethingmorethanhumouroraccidentthatcouldoccasionacustomsoconstantanduniversalasthis，whichhasobtainedinallagesandnationsoftheworld，andamongstallranksofmen，thelearnedaswellastheilliterate。
140。TowhichIanswer，wecannomoreargueavisibleandtangiblesquaretobeofthesamespeciesfromtheirbeingcalledbythesamename，thanwecanthatatangiblesquareandthemonosyllableconsistingofsixletterswherebyitismarkedareofthesamespeciesbecausetheyarebothcalledbythesamename。Itiscustomarytocallwrittenwordsandthethingstheysignifybythesamename：forwordsnotbeingregardedintheirownnature，orotherwisethanastheyaremarksofthings，ithadbeensuperfluous，andbesidethedesignoflanguage，tohavegiventhemnamesdistinctfromthoseofthethingsmarkedbythem。Thesamereasonholdsherealso。Visiblefiguresarethemarksoftangiblefigures，andfromsect。59itisplainthatinthemselvestheyarelittleregarded，oruponanyotherscorethanfortheirconnexionwithtangiblefigures，whichbynaturetheyareordainedtosignify。Andbecausethislanguageofnaturedothnotvaryindifferentagesornations，henceitisthatinalltimesandplacesvisiblefiguresarecalledbythesamenamesastherespectivetangiblefiguressuggestedbythem，andnotbecausetheyarealikeorofthesamesortwiththem。
141。But，sayyou，surelyatangiblesquareislikertoavisiblesquarethantoavisiblecircle：ithasfouranglesandasmanysides：soalsohasthevisiblesquare：butthevisiblecirclehasnosuchthing，beingboundedbyoneuniformcurvewithoutrightlinesorangles，whichmakesitunfittorepresentthetangiblesquarebutveryfittorepresentthetangiblecircle。Whenceitclearlyfollowsthatvisiblefiguresarepatternsof，orofthesamespecieswith，therespectivetangiblefiguresrepresentedbythem：thattheyarelikeuntothem，andoftheirownnaturefittedtorepresentthem，asbeingofthesamesort：andthattheyareinnorespectarbitrarysigns，aswords。
142。Ianswer，itmustbeacknowledgedthevisiblesquareisfitterthanthevisiblecircletorepresentthetangiblesquare，butthenitisnotbecauseitisliker，ormoreofaspecieswithit，butbecausethevisiblesquarecontainsinitseveraldistinctparts，wherebytomarktheseveraldistinctcorrespondingpartsofatangiblesquare，whereasthevisiblecircledothnot。Thesquareperceivedbytouchhathfourdistinct，equalsides，soalsohathitfourdistinctequalangles。Itisthereforenecessarythatthevisiblefigurewhichshallbemostpropertomarkitcontainfourdistinctequalpartscorrespondingtothefoursidesofthetangiblesquare，aslikewisefourotherdistinctandequalpartswherebytodenotethefourequalanglesofthetangiblesquare。Andaccordinglyweseethevisiblefigurescontaininthemdistinctvisibleparts，answeringtothedistincttangiblepartsofthefiguressignifiedorsuggestedbythem。
143。Butitwillnothencefollowthatanyvisiblefigureislikeunto，orofthesamespecieswith，itscorrespondingtangiblefigure，unlessitbealsoshewnthatnotonlythenumberbutalsothekindofthepartsbethesameinboth。Toillustratethis，Iobservethatvisiblefiguresrepresenttangiblefiguresmuchafterthesamemannerthatwrittenwordsdosounds。Now，inthisrespectwordsarenotarbitrary，itnotbeingindifferentwhatwrittenwordstandsforanysound：butitisrequisitethateachwordcontaininitsomanydistinctcharactersastherearevariationsinthesounditstandsfor。Thusthesingleletteraispropertomarkonesimpleuniformsound；andthewordadulteryisaccommodatedtorepresentthesoundannexedtoit，intheformationwhereoftherebeingeightdifferentcollisionsormodificationsoftheairbytheorgansofspeech，eachofwhichproducesadifferenceofsound，itwasfitthewordrepresentingitshouldconsistofasmanydistinctcharacters，therebytomarkeachparticulardifferenceorpartofthewholesound。Andyetnobody，Ipresume，willsaythesinglelettera，orthewordadultery，arelikeunto，orofthesamespecieswith，therespectivesoundsbythemrepresented。Itisindeedarbitrarythat，ingeneral，lettersofanylanguagerepresentsoundsatall：butwhenthatisonceagreed，itisnotarbitrarywhatcombinationoflettersshallrepresentthisorthatparticularsound。Ileavethiswiththereadertopursue，andapplyitinhisownthoughts。
144。Itmustbeconfessedthatwearenotsoapttoconfoundothersignswiththethingssignified，ortothinkthemofthesamespecies，aswearevisibleandtangibleideas。Butalittleconsiderationwillshewushowthismaybewithoutoursupposingthemofalikenature。Thesesignsareconstantanduniversal，theirconnexionwithtangibleideashasbeenlearntatourfirstentranceintotheworld；andeversince，almosteverymomentofourlives，ithasbeenoccurringtoourthoughts，andfasteningandstrikingdeeperonourminds。Whenweobservethatsignsarevariable，andofhumaninstitution；whenweremembertherewasatimetheywerenotconnectedinourmindswiththosethingstheynowsoreadilysuggest；butthattheirsignificationwaslearnedbytheslowstepsofexperience：thispreservesusfromconfoundingthem。Butwhenwefindthesamesignssuggestthesamethingsallovertheworld；whenweknowtheyarenotofhumaninstitution，andcannotrememberthatweeverlearnedtheirsignification，butthinkthatatfirstsighttheywouldhavesuggestedtousthesamethingstheydonow：allthispersuadesustheyareofthesamespeciesasthethingsrespectivelyrepresentedbythem，andthatitisbyanaturalresemblancetheysuggestthemtoourminds。
145。Addtothisthatwheneverwemakeanicesurveyofanyobject，successivelydirectingtheopticaxistoeachpointthereof，therearecertainlinesandfiguresdescribedbythemotionoftheheadoreye，whichbeingintruthperceivedbyfeeling，doneverthelesssomixthemselves，asitwere，withtheideasofsight，thatwecanscarcethinkbuttheyappertaintothatsense。Again，theideasofsightenterintothemindseveralatonce，moredistinctandunmingledthanisusualintheothersensesbesidethetouch。Sounds，forexample，perceivedatthesameinstant，areapttocoalesce，ifImaysosay，intoonesound：butwecanperceiveatthesametimegreatvarietyofvisibleobjects，veryseparateanddistinctfromeachother。Nowtangibleextensionbeingmadeupofseveraldistinctcoexistentparts，wemayhencegatheranotherreasonthatmaydisposeustoimaginealikenessorananalogybetweentheimmediateobjectsofsightandtouch。Butnothing，certainly，dothmorecontributetoblendandconfoundthemtogetherthanthestrictandcloseconnexiontheyhavewitheachother。
Wecannotopenoureyesbuttheideasofdistance，bodies，andtangiblefiguresaresuggestedbythem。Soswiftandsuddenandunperceivedisthetransitionfromvisibletotangibleideasthatwecanscarceforbearthinkingthemequallytheimmediateobjectofvision。
146。Theprejudicewhichisgroundedonthese，andwhateverothercausesmaybeassignedthereof，stickssofastthatitisimpossiblewithoutobstinatestrivingandlabourofthemindtogetentirelyclearofit。Butthenthereluctancywefindinrejectinganyopinioncanbenoargumentofitstruthtowhoeverconsiderswhathasbeenalreadyshewnwithregardtotheprejudicesweentertainconcerningthedistance，magnitude，andsituationofobjects；
prejudicessofamiliartoourminds，soconfirmedandinveterate，astheywillhardlygivewaytotheclearestdemonstration。
147。Uponthewhole，IthinkwemayfairlyconcludethattheproperobjectsofvisionconstituteanuniversallanguageoftheAuthorofNature，wherebyweareinstructedhowtoregulateouractionsinordertoattainthosethingsthatarenecessarytothepreservationandwell—beingofourbodies，asalsotoavoidwhatevermaybehurtfulanddestructiveofthem。
Itisbytheirinformationthatweareprincipallyguidedinallthetransactionsandconcernsoflife。Andthemannerwhereintheysignifyandmarkuntoustheobjectswhichareatadistanceisthesamewiththatoflanguagesandsignsofhumanappointment，whichdonotsuggestthethingssignifiedbyanylikenessoridentityofnature，butonlybyanhabitualconnexionthatexperiencehasmadeustoobservebetweenthem。
148。Supposeonewhohadalwayscontinuedblindbetoldbyhisguidethatafterhehasadvancedsomanystepsheshallcometothebrinkofaprecipice，orbestoppedbyawall；mustnotthistohimseemveryadmirableandsurprizing？Hecannotconceivehowitispossibleformortalstoframesuchpredictionsasthese，whichtohimwouldseemasstrangeandunaccountableasprophesydothtoothers。Eventheywhoareblessedwiththevisivefacultymay（thoughfamiliaritymakeitlessobserved）findthereinsufficientcauseofadmiration。Thewonderfulartandcontrivancewherewithitisadjustedtothoseendsandpurposesforwhichitwasapparentlydesigned，thevastextent，number，andvarietyofobjectsthatareatoncewithsomucheaseandquicknessandpleasuresuggestedbyit：alltheseaffordsubjectformuchandpleasingspeculation，andmay，ifanything，giveussomeglimmeringanalogouspræ；notionofthingswhichareplacedbeyondthecertaindiscoveryandcomprehensionofourpresentstate。
149。IdonotdesigntotroublemyselfwithdrawingcorollariesfromthedoctrineIhavehithertolaiddown。Ifitbearsthetestothersmay，sofarastheyshallthinkconvenient，employtheirthoughtsinextendingitfarther，andapplyingittowhateverpurposesitmaybesubservientto：only，Icannotforbearmakingsomeinquiryconcerningtheobjectofgeometry，whichthesubjectwehavebeenupondothnaturallyleadoneto。
Wehaveshewnthereisnosuchideaasthatofextensioninabstract，andthattherearetwokindsofsensibleextensionandfigureswhichareentirelydistinctandheterogeneousfromeachother。Now，itisnaturaltoinquirewhichoftheseistheobjectofgeometry。
150。Somethingstherearewhichatfirstsightinclineonetothinkgeometryconversantaboutvisibleextension。Theconstantuseoftheeyes，bothinthepracticalandspeculativepartsofthatscience，dothverymuchinduceusthereto。Itwould，withoutdoubt，seemoddtoamathematiciantogoabouttoconvincehimthediagramshesawuponpaperwerenotthefigures，oreventhelikenessofthefigures，whichmakethesubjectofthedemonstration。Thecontrarybeingheldanunquestionabletruth，notonlybymathematicians，butalsobythosewhoapplythemselvesmoreparticularlytothestudyoflogic；Imean，whoconsiderthenatureofscience，certainty，anddemonstration：itbeingbythemassignedasonereasonoftheextraordinaryclearnessandevidenceofgeometrythatinthissciencethereasoningsarefreefromthoseinconvenienceswhichattendtheuseofarbitrarysigns，theveryideasthemselvesbeingcopiedoutandexposedtoviewuponpaper。
But，bythebye，howwellthisagreeswithwhattheylikewiseassertofabstractideasbeingtheobjectofgeometricaldemonstrationIleavetobeconsidered。
151。Tocometoaresolutioninthispointweneedonlyobservewhathathbeensaidinsect。59，60，61，whereitisshewnthatvisibleextensionsinthemselvesarelittleregarded，andhavenosettleddeterminablegreatness，andthatmenmeasurealtogether，bytheapplicationoftangibleextensiontotangibleextension。Allwhichmakesitevidentthatvisibleextensionandfiguresarenottheobjectofgeometry。
152。Itisthereforeplainthatvisiblefigureareofthesameuseingeometrythatwordsare：andtheonemayaswellbeaccountedtheobjectofthatscienceastheother，neitherofthembeingotherwiseconcernedthereinthanastheyrepresentorsuggesttothemindtheparticulartangiblefiguresconnectedwiththem。Thereisindeedthisdifferencebetweenthesignificationoftangiblefiguresbyvisiblefigures，andofideasbywords：
thatwhereasthelatterisvariableanduncertain，dependingaltogetheronthearbitraryappointmentofmen，theformerisfixedandimmutablythesameinalltimesandplaces。Avisiblesquare，forinstance，suggeststothemindthesametangiblefigureinEuropethatitdothinAmerica。
HenceitisthatthevoiceoftheAuthorof’Naturewhichspeakstooureyes，isnotliabletothatmisinterpretationandambiguitythatlanguagesofhumancontrivanceareunavoidablysubjectto。
153。Thoughwhathasbeensaidmaysufficetoshewwhatoughttobedeterminedwithrelationtotheobjectofgeometry，Ishallnevertheless，forthefullerillustrationthereof，considerthecaseofanintelligence，orunbodiedspirit，whichissupposedtoseeperfectlywell，i。e。tohaveaclearperceptionoftheproperandimmediateobjectsofsight，buttohavenosenseoftouch。WhethertherebeanysuchbeinginNatureornoisbesidemypurposetoinquire。Itsufficeththatthesuppositioncontainsnocontradictioninit。Letusnowexaminewhatproficiencysuchaonemaybeabletomakeingeometry。Whichspeculationwillleadusmoreclearlytoseewhethertheideasofsightcanpossiblybetheobjectofthatscience。
154。First，then，itiscertaintheaforesaidintelligencecouldhavenoideaofasolid，orquantityofthreedimensions，whichfollowethfromitsnothavinganyideaofdistance。Weindeedarepronetothinkthatwehavebysighttheideasofspaceandsolids，whicharisethfromourimaginingthatwedo，strictlyspeaking，seedistanceandsomepartsofanobjectatagreaterdistancethanothers；whichhathbeendemonstratedtobetheeffectoftheexperiencewehavehad，whatideasoftouchareconnectedwithsuchandsuchideasattendingvision：buttheintelligenceherespokenofissupposedtohavenoexperienceoftouch。Hewouldnot，therefore，judgeaswedo，norhaveanyideaofdistance，outness，orprofundity，norconsequentlyofspaceorbody，eitherimmediatelyorbysuggestion。
Whenceitisplainhecanhavenonotionofthosepartsofgeometrywhichrelatetothemensurationofsolidsandtheirconvexorconcavesurfaces，andcontemplatethepropertiesoflinesgeneratedbythesectionofasolid。
Theconceivingofanypartwhereofisbeyondthereachofhisfaculties。
155。Farther，hecannotcomprehendthemannerwhereingeometersdescribearightlineorcircle；theruleandcompasswiththeirusebeingthingsofwhichitisimpossibleheshouldhaveanynotion：norisitaneasiermatterforhimtoconceivetheplacingofoneplaneorangleonanother，inordertoprovetheirequality：sincethatsupposethsomeideaofdistanceorexternalspace。Allwhichmakesitevidentourpureintelligencecouldneverattaintoknowsomuchasthefirstelementsofplanegeometry。Andperhapsuponaniceinquiryitwillbefoundhecannotevenhaveanideaofplanefiguresanymorethanhecanofsolids；sincesomeideaofdistanceisnecessarytoformtheideaofageometricalplane，aswillappeartowhoevershallreflectalittleonit。
156。Allthatisproperlyperceivedbythevisivefacultyamountstonomorethancolours，withtheirvariationsanddifferentproportionsoflightandshade。Buttheperpetualmutabilityandfleetingnessofthoseimmediateobjectsofsightrenderthemincapableofbeingmanagedafterthemannerofgeometricalfigures；norisitinanydegreeusefulthattheyshould。Itistruetherearediversofthemperceivedatonce，andmoreofsomeandlessofothers：butaccuratelytocomputetheirmagnitudeandassignprecisedeterminateproportionsbetweenthingssovariableandinconstant，ifwesupposeitpossibletobedone，mustyetbeaverytriflingandinsignificantlabour。
157。Imustconfessmenaretemptedtothinkthatflatorplanefiguresareimmediateobjectsofsight，thoughtheyacknowledgesolidsarenot。
Andthisopinionisgroundedonwhatisobservedinpainting，wherein（itseems）theideasimmediatelyimprintedonthemindareonlyofplanesvariouslycoloured，whichbyasuddenactofthejudgmentarechangedintosolids。
Butwithalittleattentionweshallfindtheplanesherementionedastheimmediateobjectsofsightarenotvisiblebuttangibleplanes。Forwhenwesaythatpicturesareplanes，wemeantherebythattheyappeartothetouchsmoothanduniform。Butthenthissmoothnessanduniformity，or，inotherwords，thisplanenessofthepicture，isnotperceivedimmediatelybyvision：foritappearethtotheeyevariousandmultiform。
158。Fromallwhichwemayconcludethatplanesarenomoretheimmediateobjectofsightthansolids。Whatwestrictlyseearenotsolids，noryetplanesvariouslycoloured：theyareonlydiversityofcolours。Andsomeofthesesuggesttothemindsolids，andotherplanefigures，justastheyhavebeenexperiencedtobeconnectedwiththeoneortheother：sothatweseeplanesinthesamewaythatweseesolids，bothbeingequallysuggestedbytheimmediateobjectsofsight，whichaccordinglyarethemselvesdenominatedplanesandsolids。Butthoughtheyarecalledbythesamenameswiththethingsmarkedbythem，theyareneverthelessofanatureentirelydifferent，ashathbeendemonstrated。
159。Whathathbeensaidis，ifImistakenot，sufficienttodecidethequestionweproposedtoexamine，concerningtheabilityofapurespirit，suchaswehavedescribed，toknowgeometry。Itis，indeed，noeasymatterforustoenterpreciselyintothethoughtsofsuchanintelligence，becausewecannotwithoutgreatpainscleverlyseparateanddisentangleinourthoughtstheproperobjectsofsightfromthoseoftouchwhichareconnectedwiththem。This，indeed，inacompletedegreeseemsscarcepossibletobeperformed：whichwillnotseemstrangetousifweconsiderhowharditisforanyonetohearthewordsofhisnativelanguagepronouncedinhisearswithoutunderstandingthem。Thoughheendeavourtodisunitethemeaningfromthesound，itwillneverthelessintrudeintohisthoughts，andheshallfinditextremedifficult，ifnotimpossible，toputhimselfexactlyinthepostureofaforeignerthatneverlearnedthelanguage，soastobeaffectedbarelywiththesoundsthemselves，andnotperceivethesignificationannexedtothem。Bythistime，Isuppose，itisclearthatneitherabstractnorvisibleextensionmakestheobjectofgeometry；
thenotdiscerningofwhichmayperhapshavecreatedsomedifficultyanduselesslabourinmathematics。Appendix[7]
Thecensureswhich，Iaminformed，havebeenmadeontheforegoingessayinclinedmetothinkIhadnotbeenclearandexpressenoughinsomepoints，andtopreventbeingmisunderstoodforthefuture，IwaswillingtomakeanynecessaryalterationsoradditionsinwhatIhadwritten。Butthatwasimpracticable，thepresenteditionhavingbeenalmostfinishedbeforeIreceivedthisinformation。WhereforeIthinkitpropertoconsiderinthisplacetheprincipalobjectionsthatarecometomynotice。
Inthefirstplaceit’sobjectedthatinthebeginningoftheessayIargueeitheragainstalluseoflinesandanglesinoptics，andthenwhatIsayisfalse；oragainstthosewritersonlywhowillhaveitthatwecanperceivebysensetheopticaxes，angles，etc。，andthenit’sinsignificant，thisbeinganabsurditywhichnooneeverheld。TowhichIanswerthatIargueonlyagainstthosewhoareofopinionthatweperceivethedistanceofobjectsbylinesandanglesor，astheytermit，byakindofinnategeometry。Andtoshewthatthisisnotfightingwithmyownshadow，IshallheresetdownapassagefromthecelebratedDescartes。
Distantiampraetereadiscimus，permutuamquandamconspirationemoculorum。UtenimcaecusnosterduobacillatenensAEetCE，dequorumlongitudineincercus，solumqueintervallummanuumAetC，cummagnitudineangulorumACE，etCAEexploratumhabens，inde，utexgeometriaquadamomnibusinnata，scirepotestubisitpunctumE。SicquumnostrioculiRSTetrstambo，vertunturadX，magnitudolineaeSs，etangulorumXSsetXsS，certosnosreduntubisitpunctumX。Etidemoperaalterutriuspossumusindagare，locoillummovendo，utsiversusXillumsemperdirigentes，primosistamusinpunctoS，etstatimpostinpunctos，hocsufficietutmagnitudolineaeSs，etduorumangulorumXSsetXsS
nostraeimaginationisimuloccurrant，etdistantiampunctiXnosedoceant；
idqueperactionemmentis，quaelicetsimplexjudiciumessevideatur，ratiocinationemtamenquandaminvolutamhabet，similemilli，quageometraeperduasstationesdiversas，locainaccessadimetiuntur。[8]Imightamasstogethercitationsfromseveralauthorstothesamepurpose，butthisbeingsoclearinthepoint，andfromanauthorofsogreatnote，Ishallnottroublethereaderwithanymore。WhatIhavesaidonthisheadwasnotforthesakeoffindingfaultwithothermen，butbecauseIjudgeditnecessarytodemonstrateinthefirstplacethatweneitherseedistanceimmediately，noryetperceiveitbythemediationofanythingthathath（aslinesandangles）anecessaryconnexionwithit。Foronthedemonstrationofthispointthewholetheorydepends。
Secondly，itisobjectedthattheexplicationIgiveoftheappearanceofthehorizontalmoon（whichmayalsobeappliedtothesun）isthesamethatGassendushadgivenbefore。Ianswer，thereisindeedmentionmadeofthegrossnessoftheatmosphereinboth，butthenthemethodswhereinitisappliedtosolvethe：phenomenonarewidelydifferent，aswillbeevidenttowhoever，shallcomparewhatIhavesaidonthissubjectwiththefollowingwordsofGassendus。Heincdicipossevidetur：solemhumilemoculospeaatumideoappareremajorem，quamdumaltiusegreditur，quiadumvicinusesthorizontiprolixaestsenesvaporum，atqueadeocorpusculorumquaesolisradiositaretundunt，utoculusminusconniveat，etpupillaquasiumbrefactalongemagisamplificetur，quamdumsolemultumelatorarivaporesintercipiuntur，solqueipseitasplendescit，utpupillainipsumspeaanscontractissimaefficiatur。Nempeexhocessevidetur，curvisibilisspeciesexsoleprocedens，etperpupillamamplificatamintromissainretinam，amplioreminillasedemoccupet，majoremqueproindecreetsolisapparentiam，quamdumperconttactampupillameodemintromissacontendit（vid。Epist。IdeapparenteMagnitudinesolishumilisetsublimis，page6）。[9]ThissolutionofGassendusproceedsonafalseprinciple，viz。，thatthepupil’sbeingenlargedaugmentsthespeciesorimageonthefundoftheeye。
Thirdly，againstwhatissaidinsect。80，itisobjectedthatthemethingwhichissosmallasscarcetobediscernedbyamanmayappearlikeamountaintosomesmallinsect；fromwhichitfollowthattheminimumvisibileisnotequalinrespectofallcreatures。Ianswer，ifthisobjectionbesoundedtothebottomitwillbefoundtomeannomorethanthatthesameparticleofmatter，whichismarkedtoamanbyoneminimumvisibile，exhibitstoaninsectagreatnumberofminimavisibilia。
Butthisdoesnotprovethatoneminimumvisibileoftheinsectisnotequaltooneminimumvisibileoftheman。Thenotdistinguishingbetweenthemediateandimmediateobjectsofsightis，Isuspect，acauseofmisapprehensioninthismatter。
Someothermisinterpretationsanddifficultieshavebeenmade，butinthepointstheyreferto1haveendeavouredtobesoveryplainthatI
knownothowtoexpressmyselfmoreclearly。AllIshalladdisthatiftheywhoarepleasedtocriticiseonmyessaywouldbutreadthewholeoverwithsomeattention，theymightbethebetterabletocomprehendmymeaningandconsequentlytojudgeofmymistakes。
Iaminformedthat，soonafterthefirsteditionofthistreatiseamansomewherenearLondonwasmadetosee，whohadbeenbornblind，andcontinuedsoforabouttwentyyears。Suchaonemaybesupposedaproperjudgetodecidehowfarsometenetslaiddowninseveralplacesoftheforegoingessayareagreeabletotruth，andifanycuriouspersonhaththeopportunityofmakingproperinterrogatoriestohimthereon，Ishouldgladlyseemynotionseitheramendedorconfirmedbyexperience。
Footnotes[1]SeewhatDecartesandothershavewrittenonthissubject。
[2]Par。I。Prop。31，Sect。9。
[3]MolyneuxDioptr。，Par。I。Prop。5。
[4]Phil。Trans。Num。187。p。314
[5]Numb。187。P。323
[6]Diopt。par。2。c。7。P。289。
[7]ClassicsEditor’snote：Thisappendixappearedinthe2ndeditiononly（1709）。
[8]Weapprehenddistance，moreover，throughasortofjointactivityoftheeyes。Forinthesamewayasourblindman，holdingtwosticksofindeterminatelength，AEandCE，andknowingonlythedistancebetweenhishands，AandC，togetherwiththesizeoftheanglesACEandCAE，canthencedeterminethepositionofEbyasortofinnategeometricalknowledgesharedbyallmen，so，whenbothoureyes，RSTandrst，arefocusedonX，thelengthofthelineSsandthesizeoftheanglesXSsandXsSletusknowthepositionofthepointX。Wecanalsodiscoverthatpositionbymeansofeitheroneofoureyesalone，bychangingitslocation。IfwekeeptheeyefixedonXandholditfirstatpointSandthenimmediatelyafterwardsatpoints，thatwillbeenoughforthelengthofthelineSsandthesizeoftheanglesXSsandXsStobepresenttogetherintheimaginationandthustoinformusofthedistanceofthepointX。Theydosoinvirtueofanactofthemindwhich，whileitmayseemtobeasimplejudgment，neverthelessincludeswithinitselfacertainreasoningprocesslikethatbywhichgeometerscalculateinaccessiblepositionsfromtwoseparategivenpoints。[FromDescartes’Dioptrics，VI，13。]
[9]Thetruth，then，seemstobeasfollows：thereasonwhythesun，whenitislow，appearstotheeyetobelargerthanwhenithasclimbedhigherisbecause，aslongasitisneartothehorizon，the[interveningllayerofvapourisdeeper，andtheatomssodullthebrightnessofthesun’sraysthattheeyeblinksless。Forthepupilisasifshadedandisfarmoredilatedthanwhenthesunishighinthesky：
thenathinnerlayerofvapourintervenesandthesunitselfshinessobrightlythat，inlookingtowardsit，thepupilclosesupandbecomeshighlycontracted。Doubtlessthisistheexplanationwhythevisiblespeciescomingfromthesun，whenitreachestheretinathroughadilatedpupil，occupiesalargerplaceonitandsocreatestheappearanceofalargersunthanwhenitstrikestheretinaafterenteringbythesameroutebutthroughacontractededpupil。