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。