Sinceadefinitionisaformula，andeveryformulahasparts，
　　andastheformulaistothething，soisthepartoftheformulato
　　thepartofthething，thequestionisalreadybeingaskedwhetherthe
　　formulaofthepartsmustbepresentintheformulaofthewholeor
　　not。Forinsomecasestheformulaeofthepartsareseentobe
　　present，andinsomenot。Theformulaofthecircledoesnotinclude
　　thatofthesegments，butthatofthesyllableincludesthatofthe
　　letters；yetthecircleisdividedintosegmentsasthesyllableis
　　intoletters-Andfurtherifthepartsarepriortothewhole，andthe
　　acuteangleisapartoftherightangleandthefingerapartof
　　theanimal，theacuteanglewillbepriortotherightangleand
　　fingertotheman。Butthelatterarethoughttobeprior；forin
　　formulathepartsareexplainedbyreferencetothem，andinrespect
　　alsoofthepowerofexistingapartfromeachotherthewholesare
　　priortotheparts。
　　Perhapsweshouldrathersaythat’part’isusedinseveral
　　senses。Oneoftheseis’thatwhichmeasuresanotherthingin
　　respectofquantity’。Butletthissensebesetaside；letus
　　inquireaboutthepartsofwhichsubstanceconsists。Ifthenmatteris
　　onething，formanother，thecompoundoftheseathird，andboththe
　　matterandtheformandthecompoundaresubstanceeventhematter
　　isinasensecalledpartofathing，whileinasenseitisnot，
　　butonlytheelementsofwhichtheformulaoftheformconsists。
　　E。g。ofconcavityfleshforthisisthematterinwhichitis
　　producedisnotapart，butofsnubnessitisapart；andthe
　　bronzeisapartoftheconcretestatue，butnotofthestatuewhen
　　thisisspokenofinthesenseoftheform。Fortheform，orthe
　　thingashavingform，shouldbesaidtobethething，butthematerial
　　elementbyitselfmustneverbesaidtobeso。Andsotheformula
　　ofthecircledoesnotincludethatofthesegments，buttheformula
　　ofthesyllableincludesthatoftheletters；forthelettersare
　　partsoftheformulaoftheform，andnotmatter，butthesegmentsare
　　partsinthesenseofmatteronwhichtheformsupervenes；yetthey
　　arenearertheformthanthebronzeiswhenroundnessisproducedin
　　bronze。Butinasensenoteveneverykindofletterwillbepresent
　　intheformulaofthesyllable，e。g。particularwaxenlettersorthe
　　lettersasmovementsintheair；forinthesealsowehavealready
　　somethingthatispartofthesyllableonlyinthesensethatitis
　　itsperceptiblematter。Forevenifthelinewhendividedpasses
　　awayintoitshalves，orthemanintobonesandmusclesandflesh，
　　itdoesnotfollowthattheyarecomposedoftheseaspartsoftheir
　　essence，butratherasmatter；andthesearepartsoftheconcrete
　　thing，butnotalsooftheform，i。e。ofthattowhichtheformula
　　refers；whereforealsotheyarenotpresentintheformulae。Inone
　　kindofformula，then，theformulaofsuchpartswillbepresent，
　　butinanotheritmustnotbepresent，wheretheformuladoesnot
　　refertotheconcreteobject。Foritisforthisreasonthatsome
　　thingshaveastheirconstituentprinciplespartsintowhichtheypass
　　away，whilesomehavenot。Thosethingswhicharetheformandthe
　　mattertakentogether，e。g。thesnub，orthebronzecircle，pass
　　awayintothesematerials，andthematterisapartofthem；butthose
　　thingswhichdonotinvolvematterbutarewithoutmatter，andwhose
　　formulaeareformulaeoftheformonly，donotpassaway，-eithernot
　　atalloratanyratenotinthisway。Thereforethesematerialsare
　　principlesandpartsoftheconcretethings，whileoftheformthey
　　areneitherpartsnorprinciples。Andthereforetheclaystatueis
　　resolvedintoclayandtheballintobronzeandCalliasintofleshand
　　bones，andagainthecircleintoitssegments；forthereisasenseof
　　’circle’inwhichinvolvesmatter。For’circle’isusedambiguously，
　　meaningboththecircle，unqualified，andtheindividualcircle，
　　becausethereisnonamepeculiartotheindividuals。
　　Thetruthhasindeednowbeenstated，butstillletusstateit
　　yetmoreclearly，takingupthequestionagain。Thepartsofthe
　　formula，intowhichtheformulaisdivided，arepriortoit，either
　　allorsomeofthem。Theformulaoftherightangle，however，doesnot
　　includetheformulaoftheacute，buttheformulaoftheacute
　　includesthatoftherightangle；forhewhodefinestheacuteuses
　　therightangle；fortheacuteis’lessthanarightangle’。The
　　circleandthesemicirclealsoareinalikerelation；forthe
　　semicircleisdefinedbythecircle；andsoisthefingerbythewhole
　　body，forafingeris’suchandsuchapartofaman’。Thereforethe
　　partswhichareofthenatureofmatter，andintowhichasits
　　matterathingisdivided，areposterior；butthosewhichareofthe
　　natureofpartsoftheformula，andofthesubstanceaccordingto
　　itsformula，areprior，eitherallorsomeofthem。Andsincethesoul
　　ofanimalsforthisisthesubstanceofalivingbeingistheir
　　substanceaccordingtotheformula，i。e。theformandtheessenceofa
　　bodyofacertainkindatleastweshalldefineeachpart，ifwe
　　defineitwell，notwithoutreferencetoitsfunction，andthiscannot
　　belongtoitwithoutperception，sothatthepartsofsoulareprior，
　　eitherallorsomeofthem，totheconcrete’animal’，andsotoo
　　witheachindividualanimal；andthebodyandpartsareposteriorto
　　this，theessentialsubstance，anditisnotthesubstancebutthe
　　concretethingthatisdividedintothesepartsasitsmatter:-this
　　beingso，totheconcretethingtheseareinasenseprior，butina
　　sensetheyarenot。Fortheycannotevenexistifseveredfromthe
　　whole；foritisnotafingerinanyandeverystatethatisthe
　　fingerofalivingthing，butadeadfingerisafingeronlyin
　　name。Somepartsareneitherpriornorposteriortothewhole，i。e。
　　thosewhicharedominantandinwhichtheformula，i。e。the
　　essentialsubstance，isimmediatelypresent，e。g。perhapstheheartor
　　thebrain；foritdoesnotmatterintheleastwhichofthetwohas
　　thisquality。Butmanandhorseandtermswhicharethusappliedto
　　individuals，butuniversally，arenotsubstancebutsomethingcomposed
　　ofthisparticularformulaandthisparticularmattertreatedas
　　universal；andasregardstheindividual，Socratesalreadyincludesin
　　himultimateindividualmatter；andsimilarlyinallothercases。’A
　　part’maybeaparteitheroftheformi。e。oftheessence，orof
　　thecompoundoftheformandthematter，orofthematteritself。
　　Butonlythepartsoftheformarepartsoftheformula，andthe
　　formulaisoftheuniversal；for’beingacircle’isthesameasthe
　　circle，and’beingasoul’thesameasthesoul。Butwhenwecometo
　　theconcretething，e。g。thiscircle，i。e。oneoftheindividual
　　circles，whetherperceptibleorintelligibleImeanbyintelligible
　　circlesthemathematical，andbyperceptiblecirclesthoseofbronze
　　andofwood，-ofthesethereisnodefinition，buttheyareknownby
　　theaidofintuitivethinkingorofperception；andwhentheypassout
　　ofthiscompleterealizationitisnotclearwhethertheyexistor
　　not；buttheyarealwaysstatedandrecognizedbymeansofthe
　　universalformula。Butmatterisunknowableinitself。Andsomematter
　　isperceptibleandsomeintelligible，perceptiblematterbeingfor
　　instancebronzeandwoodandallmatterthatischangeable，and
　　intelligiblematterbeingthatwhichispresentinperceptible
　　thingsnotquaperceptible，i。e。theobjectsofmathematics。
　　Wehavestated，then，howmattersstandwithregardtowholeand
　　part，andtheirpriorityandposteriority。Butwhenanyoneasks
　　whethertherightangleandthecircleandtheanimalareprior，or
　　thethingsintowhichtheyaredividedandofwhichtheyconsist，i。e。
　　theparts，wemustmeettheinquirybysayingthatthequestioncannot
　　beansweredsimply。Forifevenbaresoulistheanimalorthe
　　livingthing，orthesoulofeachindividualistheindividualitself，
　　and’beingacircle’isthecircle，and’beingarightangle’and
　　theessenceoftherightangleistherightangle，thenthewholein
　　onesensemustbecalledposteriortotheartinonesense，i。e。to
　　thepartsincludedintheformulaandtothepartsoftheindividual
　　rightangleforboththematerialrightanglewhichismadeof
　　bronze，andthatwhichisformedbyindividuallines，areposteriorto
　　theirparts；whiletheimmaterialrightangleisposteriortothe
　　partsincludedintheformula，butpriortothoseincludedinthe
　　particularinstance，andthequestionmustnotbeansweredsimply。If，
　　however，thesoulissomethingdifferentandisnotidenticalwiththe
　　animal，evensosomepartsmust，aswehavemaintained，becalled
　　priorandothersmustnot。
　　Anotherquestionisnaturallyraised，viz。whatsortofparts
　　belongtotheformandwhatsortnottotheform，buttothe
　　concretething。Yetifthisisnotplainitisnotpossibleto
　　defineanything；fordefinitionisoftheuniversalandofthe
　　form。Ifthenitisnotevidentwhatsortofpartsareofthenature
　　ofmatterandwhatsortarenot，neitherwilltheformulaofthething
　　beevident。Inthecaseofthingswhicharefoundtooccurin
　　specificallydifferentmaterials，asacirclemayexistinbronzeor
　　stoneorwood，itseemsplainthatthese，thebronzeorthestone，are
　　nopartoftheessenceofthecircle，sinceitisfoundapartfrom
　　them。Ofthingswhicharenotseentoexistapart，thereisno
　　reasonwhythesamemaynotbetrue，justasifallcirclesthathad
　　everbeenseenwereofbronze；fornonethelessthebronzewouldbe
　　nopartoftheform；butitishardtoeliminateitinthought。E。g。
　　theformofmanisalwaysfoundinfleshandbonesandpartsofthis
　　kind；arethesethenalsopartsoftheformandtheformula？No，
　　theyarematter；butbecausemanisnotfoundalsoinothermatterswe
　　areunabletoperformtheabstraction。
　　Sincethisisthoughttobepossible，butitisnotclearwhen
　　itisthecase，somepeoplealreadyraisethequestioneveninthe
　　caseofthecircleandthetriangle，thinkingthatitisnotright
　　todefinethesebyreferencetolinesandtothecontinuous，but
　　thatallthesearetothecircleorthetriangleasfleshandbones
　　aretoman，andbronzeorstonetothestatue；andtheyreduceall
　　thingstonumbers，andtheysaytheformulaof’line’isthatof
　　’two’。AndofthosewhoasserttheIdeassomemake’two’the
　　line-itself，andothersmakeittheFormoftheline；forinsome
　　casestheysaytheFormandthatofwhichitistheFormarethesame，
　　e。g。’two’andtheFormoftwo；butinthecaseof’line’theysay
　　thisisnolongerso。
　　ItfollowsthenthatthereisoneFormformanythingswhose
　　formisevidentlydifferentaconclusionwhichconfrontedthe
　　Pythagoreansalso；anditispossibletomakeonethingthe
　　Form-itselfofall，andtoholdthattheothersarenotForms；but
　　thusallthingswillbeone。
　　Wehavepointedout，then，thatthequestionofdefinitions
　　containssomedifficulty，andwhythisisso。Andsotoreduceall
　　thingsthustoFormsandtoeliminatethematterisuselesslabour；
　　forsomethingssurelyareaparticularforminaparticularmatter，
　　orparticularthingsinaparticularstate。Andthecomparisonwhich
　　Socratestheyoungerusedtomakeinthecaseof’animal’isnot
　　sound；foritleadsawayfromthetruth，andmakesonesupposethat
　　mancanpossiblyexistwithouthisparts，asthecirclecanwithout
　　thebronze。Butthecaseisnotsimilar；forananimalissomething
　　perceptible，anditisnotpossibletodefineitwithoutreference
　　tomovement-nor，therefore，withoutreferencetotheparts’beingina
　　certainstate。Foritisnotahandinanyandeverystatethatisa
　　partofman，butonlywhenitcanfulfilitswork，andtherefore
　　onlywhenitisalive；ifitisnotaliveitisnotapart。
　　Regardingtheobjectsofmathematics，whyaretheformulaeof
　　thepartsnotpartsoftheformulaeofthewholes；e。g。whyarenot
　　thesemicirclesincludedintheformulaofthecircle？Itcannotbe
　　said，’becausethesepartsareperceptiblethings’；fortheyare
　　not。Butperhapsthismakesnodifference；forevensomethings
　　whicharenotperceptiblemusthavematter；indeedthereissome
　　matterineverythingwhichisnotanessenceandabareformbuta
　　’this’。Thesemicircles，then，willnotbepartsoftheuniversal
　　circle，butwillbepartsoftheindividualcircles，ashasbeen
　　saidbefore；forwhileonekindofmatterisperceptible，thereis
　　anotherwhichisintelligible。