Butthisisquitecomprehensibleassoonasbothcountfornothingmorethanformalconditionsofoursensibility，whiletheobjectscountmerelyasphenomena;forthentheformofthephenomenon，i。e。，pureintuition，canbyallmeansberepresentedasproceedingfromourselves，thatis，apriori。Sect。12。Inordertoaddsomethingbywayofillustrationandconfirmation，weneedonlywatchtheordinaryandnecessaryprocedureofgeometers。Allproofsofthecompletecongruenceoftwogivenfigures（wheretheonecanineveryrespectbesubstitutedfortheother）comeultimatelytothisthattheymaybemadetocoincide;whichisevidentlynothingelsethanasyntheticalpropositionrestinguponimmediateintuition，andthisintuitionmustbepure，orgivenapriori，otherwisethepropositioncouldnotrankasapodicticallycertain，butwouldhaveempiricalcertaintyonly。
Inthatcase，itcouldonlybesaidthatitisalwaysfoundtobeso，andholdsgoodonlyasfarasourperceptionreaches。Thateverywherespace（which（initsentirety]isitselfnolongertheboundaryofanotherspace）
hasthreedimensions，andthatspacecannotinanywayhavemore，isbasedonthepropositionthatnotmorethanthreelinescanintersectatrightanglesinonepoint;butthispropositioncannotbyanymeansbeshownfromconcepts，butrestsimmediatelyonintuition，andindeedonpureandaprioriintuition，becauseitisapodicticallycertain。Thatwecanrequirealinetobedrawntoinfinity（inindefinitum），orthataseriesofchanges（forexample，spacestraversedbymotion）shallbeinfinitelycontinued，presupposesarepresentationofspaceandtime，whichcanonlyattachtointuition，namely，sofarasitinitselfisboundedbynothing，forfromconceptsitcouldneverbeinferred。Consequently，thebasisofmathematicsactuallyarepureintuitions，whichmakeitssyntheticalandapodicticallyvalidpropositionspossible。Henceourtranscendentaldeductionofthenotionsofspaceandoftimeexplainsatthesametimethepossibilityofpuremathematics。Withoutsomesuchdeductionitstruthmaybegranted，butitsexistencecouldbynomeansbeunderstood，andwemustassumeII
thateverythingwhichcanbegiventooursenses（totheexternalsensesinspace，totheinternaloneintime）isintuitdbyusasitappearstous，notasitisinitself。\"Sect。13。Thosewhocannotyetridthemselvesofthenotionthatspaceandtimeareactualqualitiesinheringinthingsinthemselves，mayexercisetheiracumenonthefollowingparadox。Whentheyhaveinvainattempteditssolution，andarefreefromprejudicesatleastforafewmoments，theywillsuspectthatthedegradationofspaceandoftimetomereformsof@ursensuousintuitionmayperhapsbewellfounded，Iftwothingsarequiteequalinallrespectsaskmuchascanbeascertainedbyallmeanspossible，quantitativelyandqualitatively，itmustfollow，thattheonecaninallcasesandunderallcircumstancesreplacetheother，andthissubstitutionwouldnotoccasiontheleastperceptibledifference。
Thisinfactistrueofplanefiguresingeometry;butsomesphericalfiguresexhibit，notwithstandingacompleteinternalagreement，suchacontrastintheirexternalrelation，thattheonefigurecannotpossiblybeputintheplaceoftheother。Forinstance，twosphericaltrianglesonoppositehemispheres，whichhaveanarcoftheequatorastheircommonbase，maybequiteequal，bothasregardssidesandangles，sothatnothingistobefoundineither，ifitbedescribedforitselfaloneandcompleted，thatwouldnotequallybeapplicabletoboth;andyettheonecannotbeputintheplaceoftheother（beingsituatedupontheoppositehemisphere）。