Somethingsareonlyactually，somepotentially，some
potentiallyandactually，whattheyare，viz。inonecaseaparticular
reality，inanother，characterizedbyaparticularquantity，orthe
like。Thereisnomovementapartfromthings；forchangeisalways
accordingtothecategoriesofbeing，andthereisnothingcommonto
theseandinnoonecategory。Buteachofthecategoriesbelongsto
allitssubjectsineitheroftwoways(e。g。’this-ness’-forone
kindofitis’positiveform’，andtheotheris’privation’；andas
regardsqualityonekindis’white’andtheother’black’，andas
regardsquantityonekindis’complete’andtheother’incomplete’，
andasregardsspatialmovementoneis’upwards’andtheother
’downwards’，oronethingis’light’andanother’heavy’)；sothat
thereareasmanykindsofmovementandchangeasofbeing。There
beingadistinctionineachclassofthingsbetweenthepotential
andthecompletelyreal，Icalltheactualityofthepotentialas
such，movement。Thatwhatwesayistrue，isplainfromthe
followingfacts。Whenthe’buildable’，insofarasitiswhatwemean
by’buildable’，existsactually，itisbeingbuilt，andthisisthe
processofbuilding。Similarlywithlearning，healing，walking，
leaping，ageing，ripening。Movementtakeswhenthecompletereality
itselfexists，andneitherearliernorlater。Thecompletereality，
then，ofthatwhichexistspotentially，whenitiscompletelyrealand
actual，notquaitself，butquamovable，ismovement。ByquaImean
this:bronzeispotentiallyastatue；butyetitisnotthecomplete
realityofbronzequabronzethatismovement。Foritisnotthe
samethingtobebronzeandtobeacertainpotency。Ifitwere
absolutelythesameinitsdefinition，thecompleterealityof
bronzewouldhavebeenamovement。Butitisnotthesame。(Thisis
evidentinthecaseofcontraries；fortobecapableofbeingwelland
tobecapableofbeingillarenotthesame-foriftheywere，being
wellandbeingillwouldhavebeenthesame-itisthatwhichunderlies
andishealthyordiseased，whetheritismoistureorblood，thatis
oneandthesame。)Andsinceitisnot。thesame，ascolourandthe
visiblearenotthesame，itisthecompleterealityofthepotential，
andaspotential，thatismovement。Thatitisthis，andthatmovement
takesplacewhenthecompleterealityitselfexists，andneither
earliernorlater，isevident。Foreachthingiscapableofbeing
sometimesactual，sometimesnot，e。g。thebuildablequabuildable；and
theactualityofthebuildablequabuildableisbuilding。Forthe
actualityiseitherthis-theactofbuilding-orthehouse。Butwhen
thehouseexists，itisnolongerbuildable；thebuildableiswhat
isbeingbuilt。Theactuality，then，mustbetheactofbuilding，
andthisisamovement。Andthesameaccountappliestoallother
movements。
Thatwhatwehavesaidisrightisevidentfromwhatallothers
sayaboutmovement，andfromthefactthatitisnoteasytodefineit
otherwise。Forfirstlyonecannotputitinanyclass。Thisisevident
fromwhatpeoplesay。Somecallitothernessandinequalityandthe
unreal；noneofthese，however，isnecessarilymoved，andfurther，
changeisnoteithertotheseorfromtheseanymorethanfromtheir
opposites。Thereasonwhypeopleputmovementintheseclassesisthat
itisthoughttobesomethingindefinite，andtheprinciplesinoneof
thetwo’columnsofcontraries’areindefinitebecausetheyare
privative，fornoneofthemiseithera’this’ora’such’orinany
oftheothercategories。Andthereasonwhymovementisthoughtto
beindefiniteisthatitcannotbeclassedeitherwiththepotency
ofthingsorwiththeiractuality；forneitherthatwhichiscapable
ofbeingofacertainquantity，northatwhichisactuallyofa
certainquantity，isofnecessitymoved，andmovementisthoughttobe
anactuality，butincomplete；thereasonisthatthepotential，
whoseactualityitis，isincomplete。Andthereforeitishardto
graspwhatmovementis；foritmustbeclassedeitherunder
privationorunderpotencyorunderabsoluteactuality，but
evidentlynoneoftheseispossible。Thereforewhatremainsisthatit
mustbewhatwesaid-bothactualityandtheactualitywehave
described-whichishardtodetectbutcapableofexisting。
Andevidentlymovementisinthemovable；foritisthecomplete
realizationofthisbythatwhichiscapableofcausingmovement。
Andtheactualityofthatwhichiscapableofcausingmovementisno
otherthanthatofthemovable。Foritmustbethecompleterealityof
both。Forwhileathingiscapableofcausingmovementbecauseit
candothis，itisamoverbecauseitisactive；butitisonthe
movablethatitiscapableofacting，sothattheactualityofbothis
one，justasthereisthesameintervalfromonetotwoasfromtwoto
one，andasthesteepascentandthesteepdescentareone，butthe
beingofthemisnotone；thecaseofthemoverandthemovedis
similar。
Theinfiniteiseitherthatwhichisincapableofbeing
traversedbecauseitisnotitsnaturetobetraversed(this
correspondstothesenseinwhichthevoiceis’invisible’)，orthat
whichadmitsonlyofincompletetraverseorscarcelyadmitsof
traverse，orthatwhich，thoughitnaturallyadmitsoftraverse，is
nottraversedorlimited；further，athingmaybeinfinitein
respectofadditionorofsubtraction，orboth。Theinfinitecannotbe
aseparate，independentthing。Forifitisneitheraspatial
magnitudenoraplurality，butinfinityitselfisitssubstanceand
notanaccidentofit，itwillbeindivisible；forthedivisibleis
eithermagnitudeorplurality。Butifindivisible，itisnotinfinite，
exceptasthevoiceisinvisible；butpeopledonotmeanthis，norare
weexaminingthissortofinfinite，buttheinfiniteasuntraversable。
Further，howcananinfiniteexistbyitself，unlessnumberand
magnitudealsoexistbythemselvess-sinceinfinityisanattribute
ofthese？Further，iftheinfiniteisanaccidentofsomethingelse，
itcannotbequainfiniteanelementinthings，astheinvisibleis
notanelementinspeech，thoughthevoiceisinvisible。Andevidently
theinfinitecannotexistactually。Forthenanypartofitthatmight
betakenwouldbeinfinite(for’tobeinfinite’and’theinfinite’
arethesame，iftheinfiniteissubstanceandnotpredicatedofa
subject)。Thereforeitiseitherindivisible，orifitispartible，it
isdivisibleintoinfinites；butthesamethingcannotbemany
infinites(asapartofairisair，soapartoftheinfinitewouldbe
infinite，iftheinfiniteissubstanceandaprinciple)。Therefore
itmustbeimpartibleandindivisible。Buttheactuallyinfinite
cannotbeindivisible；foritmustbeofacertainquantity。Therefore
infinitybelongstoitssubjectincidentally。Butifso，then(aswe
havesaid)itcannotbeitthatisaprinciple，butthatofwhichit
isanaccident-theairortheevennumber。
Thisinquiryisuniversal；butthattheinfiniteisnotamong
sensiblethings，isevidentfromthefollowingargument。Ifthe
definitionofabodyis’thatwhichisboundedbyplanes’，there
cannotbeaninfinitebodyeithersensibleorintelligible；nora
separateandinfinitenumber，fornumberorthatwhichhasanumberis
numerable。Concretely，thetruthisevidentfromthefollowing
argument。Theinfinitecanneitherbecompositenorsimple。For(a)it
cannotbeacompositebody，sincetheelementsarelimitedin
multitude。Forthecontrariesmustbeequalandnooneofthemmustbe
infinite；forifoneofthetwobodiesfallsatallshortoftheother
inpotency，thefinitewillbedestroyedbytheinfinite。Andthat
eachshouldbeinfiniteisimpossible。Forbodyisthatwhichhas
extensioninalldirections，andtheinfiniteistheboundlessly
extended，sothatiftheinfiniteisabodyitwillbeinfinitein
everydirection。Nor(b)cantheinfinitebodybeoneand
simple-neither，assomesay，somethingapartfromtheelements，from
whichtheygeneratethese(forthereisnosuchbodyapartfromthe
elements；foreverythingcanberesolvedintothatofwhichit
consists，butnosuchproductofanalysisisobservedexceptthe
simplebodies)，norfirenoranyotheroftheelements。Forapartfrom
thequestionhowanyofthemcouldbeinfinite，theAll，evenifitis
finite，cannoteitherbeorbecomeanyoneofthem，asHeraclitussays
allthingssometimebecomefire。Thesameargumentappliestothis
astotheOnewhichthenaturalphilosopherspositbesidesthe
elements。Foreverythingchangesfromcontrarytocontrary，e。g。
fromhottocold。
Further，asensiblebodyissomewhere，andwholeandparthavethe
sameproperplace，e。g。thewholeearthandpartoftheearth。
Thereforeif(a)theinfinitebodyishomogeneous，itwillbe
unmovableoritwillbealwaysmoving。Butthisisimpossible；forwhy
shoulditratherrest，ormove，down，up，oranywhere，ratherthan
anywhereelse？E。g。iftherewereaclodwhichwerepartofan
infinitebody，wherewillthismoveorrest？Theproperplaceofthe
bodywhichishomogeneouswithitisinfinite。Willtheclodoccupy
thewholeplace，then？Andhow？(Thisisimpossible。)Whatthenisits
restoritsmovement？Itwilleitherresteverywhere，andthenit
cannotmove；oritwillmoveeverywhere，andthenitcannotbe
still。But(b)iftheAllhasunlikeparts，theproperplacesofthe
partsareunlikealso，and，firstly，thebodyoftheAllisnotone
exceptbycontact，and，secondly，thepartswillbeeitherfiniteor
infiniteinvarietyofkind。Finitetheycannotbe；forthenthose
ofonekindwillbeinfiniteinquantityandthoseofanotherwillnot
(iftheAllisinfinite)，e。g。fireorwaterwouldbeinfinite，but
suchaninfiniteelementwouldbedestructiontothecontrary
elements。Butifthepartsareinfiniteandsimple，theirplaces
alsoareinfiniteandtherewillbeaninfinitenumberofelements；
andifthisisimpossible，andtheplacesarefinite，theAllalso
mustbelimited。
Ingeneral，therecannotbeaninfinitebodyandalsoaproper
placeforbodies，ifeverysensiblebodyhaseitherweightor
lightness。Foritmustmoveeithertowardsthemiddleorupwards，
andtheinfiniteeitherthewholeorthehalfofit-cannotdo
either；forhowwillyoudivideit？Orhowwillpartoftheinfinite
bedownandpartup，orpartextremeandpartmiddle？Further，every
sensiblebodyisinaplace，andtherearesixkindsofplace，but
thesecannotexistinaninfinitebody。Ingeneral，iftherecannotbe
aninfiniteplace，therecannotbeaninfinitebody；(andtherecannot
beaninfiniteplace，)forthatwhichisinaplaceissomewhere，
andthismeanseitherupordownorinoneoftheotherdirections，
andeachoftheseisalimit。
Theinfiniteisnotthesameinthesensethatitisasingle
thingwhetherexhibitedindistanceorinmovementorintime，butthe
posterioramongtheseiscalledinfiniteinvirtueofitsrelation
totheprior；i。e。amovementiscalledinfiniteinvirtueofthe
distancecoveredbythespatialmovementoralterationorgrowth，
andatimeiscalledinfinitebecauseofthemovementwhichoccupies
it。
