第6章

1 ITremainstoconsiderthefollowingquestion。Wasthereeverabecomingofmotionbeforewhichithadnobeing，andisitperishingagainsoastoleavenothinginmotion?Orarewetosaythatitneverhadanybecomingandisnotperishing，butalwayswasandalwayswillbe?Isitinfactanimmortalnever-failingpropertyofthingsthatare，asortoflifeasitweretoallnaturallyconstitutedthings? Nowtheexistenceofmotionisassertedbyallwhohaveanythingtosayaboutnature，becausetheyallconcernthemselveswiththeconstructionoftheworldandstudythequestionofbecomingandperishing，whichprocessescouldnotcomeaboutwithouttheexistenceofmotion。Butthosewhosaythatthereisaninfinitenumberofworlds，someofwhichareinprocessofbecomingwhileothersareinprocessofperishing，assertthatthereisalwaysmotion(fortheseprocessesofbecomingandperishingoftheworldsnecessarilyinvolvemotion)，whereasthosewhoholdthatthereisonlyoneworld，whethereverlastingornot，makecorrespondingassumptionsinregardtomotion。Ifthenitispossiblethatatanytimenothingshouldbeinmotion，thismustcomeaboutinoneoftwoways:eitherinthemannerdescribedbyAnaxagoras，whosaysthatallthingsweretogetherandatrestforaninfiniteperiodoftime，andthatthenMindintroducedmotionandseparatedthem；orinthemannerdescribedbyEmpedocles，accordingtowhomtheuniverseisalternatelyinmotionandatrest-inmotion，whenLoveismakingtheoneoutofmany，orStrifeismakingmanyoutofone，andatrestintheintermediateperiodsoftime-hisaccountbeingasfollows: \'SinceOnehathlearnedtospringfromManifold，AndOnedisjoinedmakesmanifoldarise，ThustheyBecome，norstableistheirlife: Butsincetheirmotionmustalternatebe，ThushavetheyeverRestupontheirround\': forwemustsupposethathemeansbythisthattheyalternatefromtheonemotiontotheother。Wemustconsider，then，howthismatterstands，forthediscoveryofthetruthaboutitisofimportance，notonlyforthestudyofnature，butalsofortheinvestigationoftheFirstPrinciple。 LetustakeourstartfromwhatwehavealreadylaiddowninourcourseonPhysics。Motion，wesay，isthefulfilmentofthemovableinsofarasitismovable。Eachkindofmotion，therefore，necessarilyinvolvesthepresenceofthethingsthatarecapableofthatmotion。 Infact，evenapartfromthedefinitionofmotion，everyonewouldadmitthatineachkindofmotionitisthatwhichiscapableofthatmotionthatisinmotion:thusitisthatwhichiscapableofalterationthatisaltered，andthatwhichiscapableoflocalchangethatisinlocomotion:andsotheremustbesomethingcapableofbeingburnedbeforetherecanbeaprocessofbeingburned，andsomethingcapableofburningbeforetherecanbeaprocessofburning。 Moreover，thesethingsalsomusteitherhaveabeginningbeforewhichtheyhadnobeing，ortheymustbeeternal。Nowiftherewasabecomingofeverymovablething，itfollowsthatbeforethemotioninquestionanotherchangeormotionmusthavetakenplaceinwhichthatwhichwascapableofbeingmovedorofcausingmotionhaditsbecoming。Tosuppose，ontheotherhand，thatthesethingswereinbeingthroughoutallprevioustimewithouttherebeinganymotionappearsunreasonableonamoment\'sthought，andstillmoreunreasonable，weshallfind，onfurtherconsideration。Forifwearetosaythat，whilethereareontheonehandthingsthataremovable，andontheotherhandthingsthataremotive，thereisatimewhenthereisafirstmoventandafirstmoved，andanothertimewhenthereisnosuchthingbutonlysomethingthatisatrest，thenthisthingthatisatrestmustpreviouslyhavebeeninprocessofchange:fortheremusthavebeensomecauseofitsrest，restbeingtheprivationofmotion。Therefore，beforethisfirstchangetherewillbeapreviouschange。Forsomethingscausemotioninonlyoneway，whileotherscanproduceeitheroftwocontrarymotions:thusfirecausesheatingbutnotcooling，whereasitwouldseemthatknowledgemaybedirectedtotwocontraryendswhileremainingoneandthesame。Evenintheformerclass，however，thereseemstobesomethingsimilar，foracoldthinginasensecausesheatingbyturningawayandretiring，justasonepossessedofknowledgevoluntarilymakesanerrorwhenheuseshisknowledgeinthereverseway。Butatanyrateallthingsthatarecapablerespectivelyofaffectingandbeingaffected，orofcausingmotionandbeingmoved，arecapableofitnotunderallconditions，butonlywhentheyareinaparticularconditionandapproachoneanother:soitisontheapproachofonethingtoanotherthattheonecausesmotionandtheotherismoved，andwhentheyarepresentundersuchconditionsasrenderedtheonemotiveandtheothermovable。Soifthemotionwasnotalwaysinprocess，itisclearthattheymusthavebeeninaconditionnotsuchastorenderthemcapablerespectivelyofbeingmovedandofcausingmotion，andoneorotherofthemmusthavebeeninprocessofchange:forinwhatisrelativethisisanecessaryconsequence:e。g。ifonethingisdoubleanotherwhenbeforeitwasnotso，oneorotherofthem，ifnotboth，musthavebeeninprocessofchange。Itfollowsthen，thattherewillbeaprocessofchangeprevioustothefirst。 (Further，howcantherebeany\'before\'and\'after\'withouttheexistenceoftime?Orhowcantherebeanytimewithouttheexistenceofmotion?If，then，timeisthenumberofmotionoritselfakindofmotion，itfollowsthat，ifthereisalwaystime，motionmustalsobeeternal。Butsofarastimeisconcernedweseethatallwithoneexceptionareinagreementinsayingthatitisuncreated:infact，itisjustthisthatenablesDemocritustoshowthatallthingscannothavehadabecoming:fortime，hesays，isuncreated。Platoaloneassertsthecreationoftime，sayingthatithadabecomingtogetherwiththeuniverse，theuniverseaccordingtohimhavinghadabecoming。Nowsincetimecannotexistandisunthinkableapartfromthemoment，andthemomentakindofmiddle-point，unitingasitdoesinitselfbothabeginningandanend，abeginningoffuturetimeandanendofpasttime，itfollowsthattheremustalwaysbetime:fortheextremityofthelastperiodoftimethatwetakemustbefoundinsomemoment，sincetimecontainsnopointofcontactforusexceptthemoment。Therefore，sincethemomentisbothabeginningandanend，theremustalwaysbetimeonbothsidesofit。Butifthisistrueoftime，itisevidentthatitmustalsobetrueofmotion，timebeingakindofaffectionofmotion。) Thesamereasoningwillalsoservetoshowtheimperishabilityofmotion:justasabecomingofmotionwouldinvolve，aswesaw，theexistenceofaprocessofchangeprevioustothefirst，inthesamewayaperishingofmotionwouldinvolvetheexistenceofaprocessofchangesubsequenttothelast:forwhenathingceasestobemoved，itdoesnotthereforeatthesametimeceasetobemovable-e。g。thecessationoftheprocessofbeingburneddoesnotinvolvethecessationofthecapacityofbeingburned，sinceathingmaybecapableofbeingburnedwithoutbeinginprocessofbeingburned-nor，whenathingceasestobemovent，doesitthereforeatthesametimeceasetoabemotive。Again，thedestructiveagentwillhavetobedestroyed，afterwhatitdestroyshasbeendestroyed，andthenthatwhichhasthecapacityofdestroyingitwillhavetobedestroyedafterwards，(sothattherewillbeaprocessofchangesubsequenttothelast，)forbeingdestroyedalsoisakindofchange。If，then，viewwhichwearecriticizinginvolvestheseimpossibleconsequences，itisclearthatmotioniseternalandcannothaveexistedatonetimeandnotatanother:infactsuchaviewcanhardlybedescribedasanythlingelsethanfantastic。 Andmuchthesamemaybesaidoftheviewthatsuchistheordinanceofnatureandthatthismustberegardedasaprinciple，aswouldseemtobetheviewofEmpedocleswhenhesaysthattheconstitutionoftheworldisofnecessitysuchthatLoveandStrifealternatelypredominateandcausemotion，whileintheintermediateperiodoftimethereisastateofrest。ProbablyalsothosewholikelikeAnaxagoras，assertasingleprinciple(ofmotion)wouldholdthisview。Butthatwhichisproducedordirectedbynaturecanneverbeanythingdisorderly:fornatureiseverywherethecauseoforder。 Moreover，thereisnoratiointherelationoftheinfinitetotheinfinite，whereasorderalwaysmeansratio。Butifwesaythatthereisfirstastateofrestforaninfinitetime，andthenmotionisstartedatsomemoment，andthatthefactthatitisthisratherthanapreviousmomentisofnoimportance，andinvolvesnoorder，thenwecannolongersaythatitisnature\'swork:forifanythingisofacertaincharacternaturally，iteitherissoinvariablyandisnotsometimesofthisandsometimesofanothercharacter(e。g。fire，whichtravelsupwardsnaturally，doesnotsometimesdosoandsometimesnot)orthereisaratiointhevariation。Itwouldbebetter，therefore，tosaywithEmpedoclesandanyoneelsewhomayhavemaintainedsuchatheoryashisthattheuniverseisalternatelyatrestandinmotion:forinasystemofthiskindwehaveatonceacertainorder。Butevenheretheholderofthetheoryoughtnotonlytoassertthefact:heoughttoexplainthecauseofit:i。e。heshouldnotmakeanymereassumptionorlaydownanygratuitousaxiom，butshouldemployeitherinductiveordemonstrativereasoning。TheLoveandStrifepostulatedbyEmpedoclesarenotinthemselvescausesofthefactinquestion，norisitoftheessenceofeitherthatitshouldbeso，theessentialfunctionoftheformerbeingtounite，ofthelattertoseparate。Ifheistogoontoexplainthisalternatepredominance，heshouldadducecaseswheresuchastateofthingsexists，ashepointstothefactthatamongmankindwehavesomethingthatunitesmen，namelyLove，whileontheotherhandenemiesavoidoneanother:thusfromtheobservedfactthatthisoccursincertaincasescomestheassumptionthatitoccursalsointheuniverse。Then，again，someargumentisneededtoexplainwhythepredominanceofeachofthetwoforceslastsforanequalperiodoftime。Butitisawrongassumptiontosupposeuniversallythatwehaveanadequatefirstprincipleinvirtueofthefactthatsomethingalwaysissooralwayshappensso。ThusDemocritusreducesthecausesthatexplainnaturetothefactthatthingshappenedinthepastinthesamewayastheyhappennow:buthedoesnotthinkfittoseekforafirstprincipletoexplainthis\'always\':so，whilehistheoryisrightinsofarasitisappliedtocertainindividualcases，heiswronginmakingitofuniversalapplication。Thus，atrianglealwayshasitsanglesequaltotworightangles，butthereisneverthelessanulteriorcauseoftheeternityofthistruth，whereasfirstprinciplesareeternalandhavenoulteriorcause。Letthisconcludewhatwehavetosayinsupportofourcontentionthatthereneverwasatimewhentherewasnotmotion，andneverwillbeatimewhentherewillnotbemotion。 2 Theargumentsthatmaybeadvancedagainstthispositionarenotdifficulttodisposeof。Thechiefconsiderationsthatmightbethoughttoindicatethatmotionmayexistthoughatonetimeithadnotexistedatallarethefollowing: First，itmaybesaidthatnoprocessofchangeiseternal:forthenatureofallchangeissuchthatitproceedsfromsomethingtosomething，sothateveryprocessofchangemustbeboundedbythecontrariesthatmarkitscourse，andnomotioncangoontoinfinity。 Secondly，weseethatathingthatneitherisinmotionnorcontainsanymotionwithinitselfcanbesetinmotion；e。g。inanimatethingsthatare(whetherthewholeorsomepartisinquestion)notinmotionbutatrest，areatsomemomentsetinmotion:whereas，ifmotioncannothaveabecomingbeforewhichithadnobeing，thesethingsoughttobeeitheralwaysorneverinmotion。 Thirdly，thefactisevidentaboveallinthecaseofanimatebeings:foritsometimeshappensthatthereisnomotioninusandwearequitestill，andthatneverthelesswearethenatsomemomentsetinmotion，thatistosayitsometimeshappensthatweproduceabeginningofmotioninourselvesspontaneouslywithoutanythinghavingsetusinmotionfromwithout。Weseenothinglikethisinthecaseofinanimatethings，whicharealwayssetinmotionbysomethingelsefromwithout:theanimal，ontheotherhand，wesay，movesitself: therefore，ifananimaliseverinastateofabsoluterest，wehaveamotionlessthinginwhichmotioncanbeproducedfromthethingitself，andnotfromwithout。Nowifthiscanoccurinananimal，whyshouldnotthesamebetruealsooftheuniverseasawhole?Ifitcanoccurinasmallworlditcouldalsooccurinagreatone:andifitcanoccurintheworld，itcouldalsooccurintheinfinite； thatis，iftheinfinitecouldasawholepossiblybeinmotionoratrest。 Oftheseobjections，then，thefirst-mentionedmotiontooppositesisnotalwaysthesameandnumericallyoneacorrectstatement；infact，thismaybesaidtobeanecessaryconclusion，providedthatitispossibleforthemotionofthatwhichisoneandthesametobenotalwaysoneandthesame。(Imeanthate。g。wemayquestionwhetherthenotegivenbyasinglestringisoneandthesame，orisdifferenteachtimethestringisstruck，althoughthestringisinthesameconditionandismovedinthesameway。)Butstill，howeverthismaybe，thereisnothingtopreventtherebeingamotionthatisthesameinvirtueofbeingcontinuousandeternal:weshallhavesomethingtosaylaterthatwillmakethispointclearer。 Asregardsthesecondobjection，noabsurdityisinvolvedinthefactthatsomethingnotinmotionmaybesetinmotion，thatwhichcausedthemotionfromwithoutbeingatonetimepresent，andatanotherabsent。Nevertheless，howthiscanbesoremainsmatterforinquiry；howitcomesabout，Imean，thatthesamemotiveforceatonetimecausesathingtobeinmotion，andatanotherdoesnotdoso: forthedifficultyraisedbyourobjectorreallyamountstothis-whyisitthatsomethingsarenotalwaysatrest，andtherestalwaysinmotion? Thethirdobjectionmaybethoughttopresentmoredifficultythantheothers，namely，thatwhichallegesthatmotionarisesinthingsinwhichitdidnotexistbefore，andadducesinproofthecaseofanimatethings:thusananimalisfirstatrestandafterwardswalks，nothavingbeensetinmotionapparentlybyanythingfromwithout。This，however，isfalse:forweobservethatthereisalwayssomepartoftheanimal\'sorganisminmotion，andthecauseofthemotionofthispartisnottheanimalitself，but，itmaybe，itsenvironment。Moreover，wesaythattheanimalitselforiginatesnotallofitsmotionsbutitslocomotion。Soitmaywellbethecase-orratherwemayperhapssaythatitmustnecessarilybethecase-thatmanymotionsareproducedinthebodybyitsenvironment，andsomeofthesesetinmotiontheintellectortheappetite，andthisagainthensetsthewholeanimalinmotion:thisiswhathappenswhenanimalsareasleep:thoughthereisthennoperceptivemotioninthem，thereissomemotionthatcausesthemtowakeupagain。Butwewillleavethispointalsotobeelucidatedatalaterstageinourdiscussion。 3 Ourenquirywillresolveitselfattheoutsetintoaconsiderationoftheabove-mentionedproblem-whatcanbethereasonwhysomethingsintheworldatonetimeareinmotionandatanotherareatrestagain?Nowoneofthreethingsmustbetrue:eitherallthingsarealwaysatrest，orallthingsarealwaysinmotion，orsomethingsareinmotionandothersatrest:andinthislastcaseagaineitherthethingsthatareinmotionarealwaysinmotionandthethingsthatareatrestarealwaysatrest，ortheyareallconstitutedsoastobecapablealikeofmotionandofrest；orthereisyetathirdpossibilityremaining-itmaybethatsomethingsintheworldarealwaysmotionless，othersalwaysinmotion，whileothersagainadmitofbothconditions。Thislastistheaccountofthematterthatwemustgive:forhereinliesthesolutionofallthedifficultiesraisedandtheconclusionoftheinvestigationuponwhichweareengaged。 Tomaintainthatallthingsareatrest，andtodisregardsense-perceptioninanattempttoshowthetheorytobereasonable，wouldbeaninstanceofintellectualweakness:itwouldcallinquestionawholesystem，notaparticulardetail:moreover，itwouldbeanattacknotonlyonthephysicistbutonalmostallsciencesandallreceivedopinions，sincemotionplaysapartinallofthem。 Further，justasinargumentsaboutmathematicsobjectionsthatinvolvefirstprinciplesdonotaffectthemathematician-andtheothersciencesareinsimilarcase-so，too，objectionsinvolvingthepointthatwehavejustraiseddonotaffectthephysicist:foritisafundamentalassumptionwithhimthatmotionisultimatelyreferabletonatureherself。 Theassertionthatallthingsareinmotionwemayfairlyregardasequallyfalse，thoughitislesssubversiveofphysicalscience: forthoughinourcourseonphysicsitwaslaiddownthatrestnolessthanmotionisultimatelyreferabletonatureherself，neverthelessmotionisthecharacteristicfactofnature:moreover，theviewisactuallyheldbysomethatnotmerelysomethingsbutallthingsintheworldareinmotionandalwaysinmotion，thoughwecannotapprehendthefactbysense-perception。Althoughthesupportersofthistheorydonotstateclearlywhatkindofmotiontheymean，orwhethertheymeanallkinds，itisnohardmattertoreplytothem: thuswemaypointoutthattherecannotbeacontinuousprocesseitherofincreaseorofdecrease:thatwhichcomesbetweenthetwohastobeincluded。Thetheoryresemblesthataboutthestonebeingwornawaybythedropofwaterorsplitbyplantsgrowingoutofit:ifsomuchhasbeenextrudedorremovedbythedrop，itdoesnotfollowthathalftheamounthaspreviouslybeenextrudedorremovedinhalfthetime:thecaseofthehauledshipisexactlycomparable:herewehavesomanydropssettingsomuchinmotion，butapartofthemwillnotsetasmuchinmotioninanyperiodoftime。Theamountremovedis，itistrue，divisibleintoanumberofparts，butnooneofthesewassetinmotionseparately:theywereallsetinmotiontogether。Itisevident，then，thatfromthefactthatthedecreaseisdivisibleintoaninfinitenumberofpartsitdoesnotfollowthatsomepartmustalwaysbepassingaway:itallpassesawayataparticularmoment。Similarly，too，inthecaseofanyalterationwhateverifthatwhichsuffersalterationisinfinitelydivisibleitdoesnotfollowfromthisthatthesameistrueofthealterationitself，whichoftenoccursallatonce，asinfreezing。Again，whenanyonehasfallenill，theremustfollowaperiodoftimeinwhichhisrestorationtohealthisinthefuture:theprocessofchangecannottakeplaceinaninstant:yetthechangecannotbeachangetoanythingelsebuthealth。Theassertion。therefore，thatalterationiscontinuousisanextravagantcallingintoquestionoftheobvious:foralterationisachangefromonecontrarytoanother。Moreover，wenoticethatastonebecomesneitherhardernorsofter。Again，inthematteroflocomotion，itwouldbeastrangethingifastonecouldbefallingorrestingonthegroundwithoutourbeingabletoperceivethefact。Further，itisalawofnaturethatearthandallotherbodiesshouldremainintheirproperplacesandbemovedfromthemonlybyviolence:fromthefactthenthatsomeofthemareintheirproperplacesitfollowsthatinrespectofplacealsoallthingscannotbeinmotion。Theseandothersimilararguments，then，shouldconvinceusthatitisimpossibleeitherthatallthingsarealwaysinmotionorthatallthingsarealwaysatrest。 Noragaincanitbethatsomethingsarealwaysatrest，othersalwaysinmotion，andnothingsometimesatrestandsometimesinmotion。Thistheorymustbepronouncedimpossibleonthesamegroundsasthosepreviouslymentioned:viz。thatweseetheabove-mentionedchangesoccurringinthecaseofthesamethings。Wemayfurtherpointoutthatthedefenderofthispositionisfightingagainsttheobvious，foronthistheorytherecanbenosuchthingasincrease:norcantherebeanysuchthingascompulsorymotion，ifitisimpossiblethatathingcanbeatrestbeforebeingsetinmotionunnaturally。Thistheory，then，doesawaywithbecomingandperishing。Moreover，motion，itwouldseem，isgenerallythoughttobeasortofbecomingandperishing，forthattowhichathingchangescomestobe，oroccupancyofitcomestobe，andthatfromwhichathingchangesceasestobe，orthereceasestobeoccupancyofit。 Itisclear，therefore，thattherearecasesofoccasionalmotionandoccasionalrest。 Wehavenowtotaketheassertionthatallthingsaresometimesatrestandsometimesinmotionandtoconfrontitwiththeargumentspreviouslyadvanced。Wemusttakeourstartasbeforefromthepossibilitiesthatwedistinguishedjustabove。Eitherallthingsareatrest，orallthingsareinmotion，orsomethingsareatrestandothersinmotion。Andifsomethingsareatrestandothersinmotion，thenitmustbethateitherallthingsaresometimesatrestandsometimesinmotion，orsomethingsarealwaysatrestandtheremainderalwaysinmotion，orsomeofthethingsarealwaysatrestandothersalwaysinmotionwhileothersagainaresometimesatrestandsometimesinmotion。Nowwehavesaidbeforethatitisimpossiblethatallthingsshouldbeatrest:neverthelesswemaynowrepeatthatassertion。Wemaypointoutthat，evenifitisreallythecase，ascertainpersonsassert，thattheexistentisinfiniteandmotionless，itcertainlydoesnotappeartobesoifwefollowsense-perception:manythingsthatexistappeartobeinmotion。Nowifthereissuchathingasfalseopinionoropinionatall，thereisalsomotion；andsimilarlyifthereissuchathingasimagination，orifitisthecasethatanythingseemstobedifferentatdifferenttimes:forimaginationandopinionarethoughttobemotionsofakind。Buttoinvestigatethisquestionatall-toseekareasonedjustificationofabeliefwithregardtowhichwearetoowellofftorequirereasonedjustification-impliesbadjudgementofwhatisbetterandwhatisworse，whatcommendsitselftobeliefandwhatdoesnot，whatisultimateandwhatisnot。Itislikewiseimpossiblethatallthingsshouldbeinmotionorthatsomethingsshouldbealwaysinmotionandtheremainderalwaysatrest。Wehavesufficientgroundforrejectingallthesetheoriesinthesinglefactthatweseesomethingsthataresometimesinmotionandsometimesatrest。Itisevident，therefore，thatitisnolessimpossiblethatsomethingsshouldbealwaysinmotionandtheremainderalwaysatrestthanthatallthingsshouldbeatrestorthatallthingsshouldbeinmotioncontinuously。Itremains，then，toconsiderwhetherallthingsaresoconstitutedastobecapablebothofbeinginmotionandofbeingatrest，orwhether，whilesomethingsaresoconstituted，somearealwaysatrestandsomearealwaysinmotion:foritisthislastviewthatwehavetoshowtobetrue。 4 Nowofthingsthatcausemotionorsuffermotion，tosomethemotionisaccidental，toothersessential:thusitisaccidentaltowhatmerelybelongstoorcontainsasapartathingthatcausesmotionorsuffersmotion，essentialtoathingthatcausesmotionorsuffersmotionnotmerelybybelongingtosuchathingorcontainingitasapart。 Ofthingstowhichthemotionisessentialsomederivetheirmotionfromthemselves，othersfromsomethingelse:andinsomecasestheirmotionisnatural，inothersviolentandunnatural。Thusinthingsthatderivetheirmotionfromthemselves，e。g。allanimals，themotionisnatural(forwhenananimalisinmotionitsmotionisderivedfromitself):andwheneverthesourceofthemotionofathingisinthethingitselfwesaythatthemotionofthatthingisnatural。Thereforetheanimalasawholemovesitselfnaturally:butthebodyoftheanimalmaybeinmotionunnaturallyaswellasnaturally:itdependsuponthekindofmotionthatitmaychancetobesufferingandthekindofelementofwhichitiscomposed。Andthemotionofthingsthatderivetheirmotionfromsomethingelseisinsomecasesnatural，inotherunnatural:e。g。 upwardmotionofearthythingsanddownwardmotionoffireareunnatural。Moreoverthepartsofanimalsareofteninmotioninanunnaturalway，theirpositionsandthecharacterofthemotionbeingabnormal。Thefactthatathingthatisinmotionderivesitsmotionfromsomethingismostevidentinthingsthatareinmotionunnaturally，becauseinsuchcasesitisclearthatthemotionisderivedfromsomethingotherthanthethingitself。Nexttothingsthatareinmotionunnaturallythosewhosemotionwhilenaturalisderivedfromthemselves-e。g。animals-makethisfactclear:forheretheuncertaintyisnotastowhetherthemotionisderivedfromsomethingbutastohowweoughttodistinguishinthethingbetweenthemoventandthemoved。Itwouldseemthatinanimals，justasinshipsandthingsnotnaturallyorganized，thatwhichcausesmotionisseparatefromthatwhichsuffersmotion，andthatitisonlyinthissensethattheanimalasawholecausesitsownmotion。 Thegreatestdifficulty，however，ispresentedbytheremainingcaseofthosethatwelastdistinguished。Wherethingsderivetheirmotionfromsomethingelsewedistinguishedthecasesinwhichthemotionisunnatural:weareleftwiththosethataretobecontrastedwiththeothersbyreasonofthefactthatthemotionisnatural。Itisinthesecasesthatdifficultywouldbeexperiencedindecidingwhencethemotionisderived，e。g。inthecaseoflightandheavythings。Whenthesethingsareinmotiontopositionsthereverseofthosetheywouldproperlyoccupy，theirmotionisviolent:whentheyareinmotiontotheirproperpositions-thelightthingupandtheheavythingdown-theirmotionisnatural；butinthislattercaseitisnolongerevident，asitiswhenthemotionisunnatural，whencetheirmotionisderived。Itisimpossibletosaythattheirmotionisderivedfromthemselves:thisisacharacteristicoflifeandpeculiartolivingthings。Further，ifitwere，itwouldhavebeenintheirpowertostopthemselves(Imeanthatife。g。athingcancauseitselftowalkitcanalsocauseitselfnottowalk)，andso，sinceonthissuppositionfireitselfpossessesthepowerofupwardlocomotion，itisclearthatitshouldalsopossessthepowerofdownwardlocomotion。Moreoverifthingsmovethemselves，itwouldbeunreasonabletosupposethatinonlyonekindofmotionistheirmotionderivedfromthemselves。Again，howcananythingofcontinuousandnaturallyconnectedsubstancemoveitself?Insofarasathingisoneandcontinuousnotmerelyinvirtueofcontact，itisimpassive:itisonlyinsofarasathingisdividedthatonepartofitisbynatureactiveandanotherpassive。 Thereforenoneofthethingsthatwearenowconsideringmovethemselves(fortheyareofnaturallyconnectedsubstance)，nordoesanythingelsethatiscontinuous:ineachcasethemoventmustbeseparatefromthemoved，asweseetobethecasewithinanimatethingswhenananimatethingmovesthem。Itisthefactthatthesethingsalsoalwaysderivetheirmotionfromsomething:whatitiswouldbecomeevidentifweweretodistinguishthedifferentkindsofcause。 Theabove-mentioneddistinctionscanalsobemadeinthecaseofthingsthatcausemotion:someofthemarecapableofcausingmotionunnaturally(e。g。theleverisnotnaturallycapableofmovingtheweight)，othersnaturally(e。g。whatisactuallyhotisnaturallycapableofmovingwhatispotentiallyhot):andsimilarlyinthecaseofallotherthingsofthiskind。 Inthesameway，too，whatispotentiallyofacertainqualityorofacertainquantityinacertainplaceisnaturallymovablewhenitcontainsthecorrespondingprincipleinitselfandnotaccidentally(forthesamethingmaybebothofacertainqualityandofacertainquantity，buttheoneisanaccidental，notanessentialpropertyoftheother)。Sowhenfireorearthismovedbysomethingthemotionisviolentwhenitisunnatural，andnaturalwhenitbringstoactualitytheproperactivitiesthattheypotentiallypossess。 Butthefactthattheterm\'potentially\'isusedinmorethanonesenseisthereasonwhyitisnotevidentwhencesuchmotionsastheupwardmotionoffireandthedownwardmotionofeartharederived。 Onewhoislearningasciencepotentiallyknowsitinadifferentsensefromonewhowhilealreadypossessingtheknowledgeisnotactuallyexercisingit。Whereverwehavesomethingcapableofactingandsomethingcapableofbeingcorrespondinglyactedon，intheeventofanysuchpairbeingincontactwhatispotentialbecomesattimesactual:e。g。thelearnerbecomesfromonepotentialsomethinganotherpotentialsomething:foronewhopossessesknowledgeofasciencebutisnotactuallyexercisingitknowsthesciencepotentiallyinasense，thoughnotinthesamesenseasheknewitpotentiallybeforehelearntit。Andwhenheisinthiscondition，ifsomethingdoesnotpreventhim，heactivelyexerciseshisknowledge:otherwisehewouldbeinthecontradictorystateofnotknowing。Inregardtonaturalbodiesalsothecaseissimilar。Thuswhatiscoldispotentiallyhot:thenachangetakesplaceanditisfire，anditburns，unlesssomethingpreventsandhindersit。So，too，withheavyandlight:lightisgeneratedfromheavy，e。g。airfromwater(forwateristhefirstthingthatispotentiallylight)，andairisactuallylight，andwillatoncerealizeitsproperactivityassuchunlesssomethingpreventsit。Theactivityoflightnessconsistsinthelightthingbeinginacertainsituation，namelyhighup:whenitisinthecontrarysituation，itisbeingpreventedfromrising。Thecaseissimilaralsoinregardtoquantityandquality。But，beitnoted，thisisthequestionwearetryingtoanswer-howcanweaccountforthemotionoflightthingsandheavythingstotheirpropersituations?Thereasonforitisthattheyhaveanaturaltendencyrespectivelytowardsacertainposition:andthisconstitutestheessenceoflightnessandheaviness，theformerbeingdeterminedbyanupward，thelatterbyadownward，tendency。Aswehavesaid，athingmaybepotentiallylightorheavyinmoresensesthanone。Thusnotonlywhenathingiswaterisitinasensepotentiallylight，butwhenithasbecomeairitmaybestillpotentiallylight:foritmaybethatthroughsomehindranceitdoesnotoccupyanupperposition，whereas，ifwhathindersitisremoved，itrealizesitsactivityandcontinuestorisehigher。Theprocesswherebywhatisofacertainqualitychangestoaconditionofactiveexistenceissimilar:thustheexerciseofknowledgefollowsatonceuponthepossessionofitunlesssomethingpreventsit。So，too，whatisofacertainquantityextendsitselfoveracertainspaceunlesssomethingpreventsit。Thethinginasenseisandinasenseisnotmovedbyonewhomoveswhatisobstructingandpreventingitsmotion(e。g。onewhopullsawayapillarfromunderarooforonewhoremovesastonefromawineskininthewateristheaccidentalcauseofmotion):andinthesamewaytherealcauseofthemotionofaballreboundingfromawallisnotthewallbutthethrower。Soitisclearthatinallthesecasesthethingdoesnotmoveitself，butitcontainswithinitselfthesourceofmotion-notofmovingsomethingorofcausingmotion，butofsufferingit。 Ifthenthemotionofallthingsthatareinmotioniseithernaturalorunnaturalandviolent，andallthingswhosemotionisviolentandunnaturalaremovedbysomething，andsomethingotherthanthemselves，andagainallthingswhosemotionisnaturalaremovedbysomething-boththosethataremovedbythemselvesandthosethatarenotmovedbythemselves(e。g。lightthingsandheavythings，whicharemovedeitherbythatwhichbroughtthethingintoexistenceassuchandmadeitlightandheavy，orbythatwhichreleasedwhatwashinderingandpreventingit)；thenallthingsthatareinmotionmustbemovedbysomething。 5 Nowthismaycomeaboutineitheroftwoways。Eitherthemoventisnotitselfresponsibleforthemotion，whichistobereferredtosomethingelsewhichmovesthemovent，orthemoventisitselfresponsibleforthemotion。Further，inthelattercase，eitherthemoventimmediatelyprecedesthelastthingintheseries，ortheremaybeoneormoreintermediatelinks:e。g。thestickmovesthestoneandismovedbythehand，whichagainismovedbytheman:intheman，however，wehavereachedamoventthatisnotsoinvirtueofbeingmovedbysomethingelse。Nowwesaythatthethingismovedbothbythelastandbythefirstmoventintheseries，butmorestrictlybythefirst，sincethefirstmoventmovesthelast，whereasthelastdoesnotmovethefirst，andthefirstwillmovethethingwithoutthelast，butthelastwillnotmoveitwithoutthefirst:e。g。thestickwillnotmoveanythingunlessitisitselfmovedbytheman。 Iftheneverythingthatisinmotionmustbemovedbysomething，andthemoventmusteitheritselfbemovedbysomethingelseornot，andintheformercasetheremustbesomefirstmoventthatisnotitselfmovedbyanythingelse，whileinthecaseoftheimmediatemoventbeingofthiskindthereisnoneedofanintermediatemoventthatisalsomoved(foritisimpossiblethatthereshouldbeaninfiniteseriesofmovents，eachofwhichisitselfmovedbysomethingelse，sinceinaninfiniteseriesthereisnofirstterm)-iftheneverythingthatisinmotionismovedbysomething，andthefirstmoventismovedbutnotbyanythingelse，itmuchbemovedbyitself。 Thissameargumentmayalsobestatedinanotherwayasfollows。 Everymoventmovessomethingandmovesitwithsomething，eitherwithitselforwithsomethingelse:e。g。amanmovesathingeitherhimselforwithastick，andathingisknockeddowneitherbythewinditselforbyastonepropelledbythewind。Butitisimpossibleforthatwithwhichathingismovedtomoveitwithoutbeingmovedbythatwhichimpartsmotionbyitsownagency:ontheotherhand，ifathingimpartsmotionbyitsownagency，itisnotnecessarythatthereshouldbeanythingelsewithwhichitimpartsmotion，whereasifthereisadifferentthingwithwhichitimpartsmotion，theremustbesomethingthatimpartsmotionnotwithsomethingelsebutwithitself，orelsetherewillbeaninfiniteseries。If，then，anythingisamoventwhilebeingitselfmoved，theseriesmuststopsomewhereandnotbeinfinite。Thus，ifthestickmovessomethinginvirtueofbeingmovedbythehand，thehandmovesthestick:andifsomethingelsemoveswiththehand，thehandalsoismovedbysomethingdifferentfromitself。Sowhenmotionbymeansofaninstrumentisateachstagecausedbysomethingdifferentfromtheinstrument，thismustalwaysbeprecededbysomethingelsewhichimpartsmotionwithitself。Therefore，ifthislastmoventisinmotionandthereisnothingelsethatmovesit，itmustmoveitself。 Sothisreasoningalsoshowsthatwhenathingismoved，ifitisnotmovedimmediatelybysomethingthatmovesitself，theseriesbringsusatsometimeorothertoamoventofthiskind。 AndifweconsiderthematterinyetathirdwaLyweshallgetthissameresultasfollows。Ifeverythingthatisinmotionismovedbysomethingthatisinmotion，etherthisbeinginmotionisanaccidentalattributeofthemoventsinquestion，sothateachofthemmovessomethingwhilebeingitselfinmotion，butnotalwaysbecauseitisitselfinmotion，oritisnotaccidentalbutanessentialattribute。Letusconsidertheformeralternative。Ifthenitisanaccidentalattribute，itisnotnecessarythatthatisinmotionshouldbeinmotion:andifthisissoitisclearthattheremaybeatimewhennothingthatexistsisinmotion，sincetheaccidentalisnotnecessarybutcontingent。Nowifweassumetheexistenceofapossibility，anyconclusionthatwetherebyreachwillnotbeanimpossibilitythoughitmaybecontrarytofact。Butthenonexistenceofmotionisanimpossibility:forwehaveshownabovethattheremustalwaysbemotion。 Moreover，theconclusiontowhichwehavebeenledisareasonableone。Fortheremustbethreethings-themoved，themovent，andtheinstrumentofmotion。Nowthemovedmustbeinmotion，butitneednotmoveanythingelse:theinstrumentofmotionmustbothmovesomethingelseandbeitselfinmotion(foritchangestogetherwiththemoved，withwhichitisincontactandcontinuous，asisclearinthecaseofthingsthatmoveotherthingslocally，inwhichcasethetwothingsmustuptoacertainpointbeincontact):andthemovent-thatistosay，thatwhichcausesmotioninsuchamannerthatitisnotmerelytheinstrumentofmotion-mustbeunmoved。Nowwehavevisualexperienceofthelastterminthisseries，namelythatwhichhasthecapacityofbeinginmotion，butdoesnotcontainamotiveprinciple，andalsoofthatwhichisinmotionbutismovedbyitselfandnotbyanythingelse:itisreasonable，therefore，nottosaynecessary，tosupposetheexistenceofthethirdtermalso，thatwhichcausesmotionbutisitselfunmoved。So，too，AnaxagorasisrightwhenhesaysthatMindisimpassiveandunmixed，sincehemakesittheprincipleofmotion:foritcouldcausemotioninthissenseonlybybeingitselfunmoved，andhavesupremecontrolonlybybeingunmixed。 Wewillnowtakethesecondalternative。Ifthemovementisnotaccidentallybutnecessarilyinmotion-sothat，ifitwerenotinmotion，itwouldnotmoveanything-thenthemovent，insofarasitisinmotion，mustbeinmotioninoneoftwoways:itismovedeitherasthatiswhichismovedwiththesamekindofmotion，orwithadifferentkind-eitherthatwhichisheating，Imean，isitselfinprocessofbecominghot，thatwhichismakinghealthyinprocessofbecominghealthy，andthatwhichiscausinglocomotioninprocessoflocomotion，orelsethatwhichismakinghealthyis，letussay，inprocessoflocomotion，andthatwhichiscausinglocomotioninprocessof，say，increase。Butitisevidentthatthisisimpossible。Forifweadoptthefirstassumptionwehavetomakeitapplywithineachoftheverylowestspeciesintowhichmotioncanbedivided:e。g。wemustsaythatifsomeoneisteachingsomelessoningeometry，heisalsoinprocessofbeingtaughtthatsamelessoningeometry，andthatifheisthrowingheisinprocessofbeingthrowninjustthesamemanner。Orifwerejectthisassumptionwemustsaythatonekindofmotionisderivedfromanother；e。g。thatthatwhichiscausinglocomotionisinprocessofincrease，thatwhichiscausingthisincreaseisinprocessofbeingalteredbysomethingelse，andthatwhichiscausingthisalterationisinprocessofsufferingsomedifferentkindofmotion。Buttheseriesmuststopsomewhere，sincethekindsofmotionarelimited；andifwesaythattheprocessisreversible，andthatthatwhichiscausingalterationisinprocessoflocomotion，wedonomorethanifwehadsaidattheoutsetthatthatwhichiscausinglocomotionisinprocessoflocomotion，andthatonewhoisteachingisinprocessofbeingtaught:foritisclearthateverythingthatismovedismovedbythemoventthatisfurtherbackintheseriesaswellasbythatwhichimmediatelymovesit:infacttheearliermoventisthatwhichmorestrictlymovesit。Butthisisofcourseimpossible:foritinvolvestheconsequencethatonewhoisteachingisinprocessoflearningwhatheisteaching，whereasteachingnecessarilyimpliespossessingknowledge，andlearningnotpossessingit。Stillmoreunreasonableistheconsequenceinvolvedthat，sinceeverythingthatismovedismovedbysomethingthatisitselfmovedbysomethingelse，everythingthathasacapacityforcausingmotionhasassuchacorrespondingcapacityforbeingmoved: i。e。itwillhaveacapacityforbeingmovedinthesenseinwhichonemightsaythateverythingthathasacapacityformakinghealthy，andexercisesthatcapacity，hasassuchacapacityforbeingmadehealthy，andthatwhichhasacapacityforbuildinghasassuchacapacityforbeingbuilt。Itwillhavethecapacityforbeingthusmovedeitherimmediatelyorthroughoneormorelinks(asitwillif，whileeverythingthathasacapacityforcausingmotionhasassuchacapacityforbeingmovedbysomethingelse，themotionthatithasthecapacityforsufferingisnotthatwithwhichitaffectswhatisnexttoit，butamotionofadifferentkind；e。g。thatwhichhasacapacityformakinghealthymightassuchhaveacapacityforlearn。theseries，however，couldbetracedback，aswesaidbefore，untilatsometimeorotherwearrivedatthesamekindofmotion)。Nowthefirstalternativeisimpossible，andthesecondisfantastic:itisabsurdthatthatwhichhasacapacityforcausingalterationshouldassuchnecessarilyhaveacapacity，letussay，forincrease。Itisnotnecessary，therefore，thatthatwhichismovedshouldalwaysbemovedbysomethingelsethatisitselfmovedbysomethingelse:sotherewillbeanendtotheseries。Consequentlythefirstthingthatisinmotionwillderiveitsmotioneitherfromsomethingthatisatrestorfromitself。Butiftherewereanyneedtoconsiderwhichofthetwo，thatwhichmovesitselforthatwhichismovedbysomethingelse，isthecauseandprincipleofmotion，everyonewoulddecidetheformer:forthatwhichisitselfindependentlyacauseisalwayspriorasacausetothatwhichissoonlyinvirtueofbeingitselfdependentuponsomethingelsethatmakesitso。 Wemustthereforemakeafreshstartandconsiderthequestion；ifathingmovesitself，inwhatsenseandinwhatmannerdoesitdoso? Noweverythingthatisinmotionmustbeinfinitelydivisible，forithasbeenshownalreadyinourgeneralcourseonPhysics，thateverythingthatisessentiallyinmotioniscontinuous。Nowitisimpossiblethatthatwhichmovesitselfshouldinitsentiretymoveitself:forthen，whilebeingspecificallyoneandindivisible，itwouldasaWholebothundergoandcausethesamelocomotionoralteration:thusitwouldatthesametimebebothteachingandbeingtaught(thesamething)，orbothrestoringtoandbeingrestoredtothesamehealth。Moreover，wehaveestablishedthefactthatitisthemovablethatismoved；andthisispotentially，notactually，inmotion，butthepotentialisinprocesstoactuality，andmotionisanincompleteactualityofthemovable。Themoventontheotherhandisalreadyinactivity:e。g。itisthatwhichishotthatproducesheat:infact，thatwhichproducestheformisalwayssomethingthatpossessesit。Consequently(ifathingcanmoveitselfasawhole)，thesamethinginrespectofthesamethingmaybeatthesametimebothhotandnothot。So，too，ineveryothercasewherethemoventmustbedescribedbythesamenameinthesamesenseasthemoved。 Thereforewhenathingmovesitselfitisonepartofitthatisthemoventandanotherpartthatismoved。Butitisnotself-movinginthesensethateachofthetwopartsismovedbytheotherpart:thefollowingconsiderationsmakethisevident。Inthefirstplace，ifeachofthetwopartsistomovetheother，therewillbenofirstmovent。Ifathingismovedbyaseriesofmovents，thatwhichisearlierintheseriesismorethecauseofitsbeingmovedthanthatwhichcomesnext，andwillbemoretrulythemovent:forwefoundthattherearetwokindsofmovent，thatwhichisitselfmovedbysomethingelseandthatwhichderivesitsmotionfromitself:andthatwhichisfurtherfromthethingthatismovedisnearertotheprincipleofmotionthanthatwhichisintermediate。Inthesecondplace，thereisnonecessityforthemoventparttobemovedbyanythingbutitself:soitcanonlybeaccidentallythattheotherpartmovesitinreturn。Itakethenthepossiblecaseofitsnotmovingit:thentherewillbeapartthatismovedandapartthatisanunmovedmovent。Inthethirdplace，thereisnonecessityforthemoventtobemovedinreturn:onthecontrarythenecessitythatthereshouldalwaysbemotionmakesitnecessarythatthereshouldbesomemoventthatiseitherunmovedormovedbyitself。Inthefourthplaceweshouldthenhaveathingundergoingthesamemotionthatitiscausing-thatwhichisproducingheat，therefore，beingheated。Butasamatteroffactthatwhichprimarilymovesitselfcannotcontaineitherasinglepartthatmovesitselforanumberofpartseachofwhichmovesitself。For，ifthewholeismovedbyitself，itmustbemovedeitherbysomepartofitselforasawholebyitselfasawhole。If，then，itismovedinvirtueofsomepartofitbeingmovedbythatpartitself，itisthispartthatwillbetheprimaryself-movent，since，ifthispartisseparatedfromthewhole，thepartwillstillmoveitself，butthewholewilldosonolonger。Ifontheotherhandthewholeismovedbyitselfasawhole，itmustbeaccidentallythatthepartsmovethemselves:andtherefore，theirself-motionnotbeingnecessary，wemaytakethecaseoftheirnotbeingmovedbythemselves。Thereforeinthewholeofthethingwemaydistinguishthatwhichimpartsmotionwithoutitselfbeingmovedandthatwhichismoved:foronlyinthiswayisitpossibleforathingtobeself-moved。Further，ifthewholemovesitselfwemaydistinguishinitthatwhichimpartsthemotionandthatwhichismoved:sowhilewesaythatABismovedbyitself，wemayalsosaythatitismovedbyA。Andsincethatwhichimpartsmotionmaybeeitherathingthatismovedbysomethingelseorathingthatisunmoved，andthatwhichismovedmaybeeitherathingthatimpartsmotiontosomethingelseorathingthatdoesnot，thatwhichmovesitselfmustbecomposedofsomethingthatisunmovedbutimpartsmotionandalsoofsomethingthatismovedbutdoesnotnecessarilyimpartmotionbutmayormaynotdoso。ThusletAbesomethingthatimpartsmotionbutisunmoved，BsomethingthatismovedbyAandmovesG，GsomethingthatismovedbyBbutmovesnothing(grantedthatweeventuallyarriveatGwemaytakeitthatthereisonlyoneintermediateterm，thoughtheremaybemore)。ThenthewholeABGmovesitself。ButifItakeawayG，ABwillmoveitself，AimpartingmotionandBbeingmoved，whereasGwillnotmoveitselforinfactbemovedatall。NoragainwillBGmoveitselfapartfromA:forB impartsmotiononlythroughbeingmovedbysomethingelse，notthroughbeingmovedbyanypartofitself。SoonlyABmovesitself。Thatwhichmovesitself，therefore，mustcomprisesomethingthatimpartsmotionbutisunmovedandsomethingthatismovedbutdoesnotnecessarilymoveanythingelse:andeachofthesetwothings，oratanyrateoneofthem，mustbeincontactwiththeother。If，then，thatwhichimpartsmotionisacontinuoussubstance-thatwhichismovedmustofcoursebeso-itisclearthatitisnotthroughsomepartofthewholebeingofsuchanatureastobecapableofmovingitselfthatthewholemovesitself:itmovesitselfasawhole，bothbeingmovedandimpartingmotionthroughcontainingapartthatimpartsmotionandapartthatismoved。Itdoesnotimpartmotionasawholenorisitmovedasawhole:itisAalonethatimpartsmotionandBalonethatismoved。Itisnottrue，further，thatGismovedbyA，whichisimpossible。 Hereadifficultyarises:ifsomethingistakenawayfromA (supposingthatthatwhichimpartsmotionbutisunmovedisacontinuoussubstance)，orfromBthepartthatismoved，willtheremainderofAcontinuetoimpartmotionortheremainderofB continuetobemoved?Ifso，itwillnotbeABprimarilythatismovedbyitself，since，whensomethingistakenawayfromAB，theremainderofABwillstillcontinuetomoveitself。Perhapswemaystatethecasethus:thereisnothingtopreventeachofthetwoparts，oratanyrateoneofthem，thatwhichismoved，beingdivisiblethoughactuallyundivided，sothatifitisdivideditwillnotcontinueinthepossessionofthesamecapacity:andsothereisnothingtopreventself-motionresidingprimarilyinthingsthatarepotentiallydivisible。 Fromwhathasbeensaid，then，itisevidentthatthatwhichprimarilyimpartsmotionisunmoved:for，whethertheseriesisclosedatoncebythatwhichisinmotionbutmovedbysomethingelsederivingitsmotiondirectlyfromthefirstunmoved，orwhetherthemotionisderivedfromwhatisinmotionbutmovesitselfandstopsitsownmotion，onbothsuppositionswehavetheresultthatinallcasesofthingsbeinginmotionthatwhichprimarilyimpartsmotionisunmoved。 6 Sincetheremustalwaysbemotionwithoutintermission，theremustnecessarilybesomething，onethingoritmaybeaplurality，thatfirstimpartsmotion，andthisfirstmoventmustbeunmoved。Nowthequestionwhethereachofthethingsthatareunmovedbutimpartmotioniseternalisirrelevanttoourpresentargument:butthefollowingconsiderationswillmakeitclearthattheremustnecessarilybesomesuchthing，which，whileithasthecapacityofmovingsomethingelse，isitselfunmovedandexemptfromallchange，whichcanaffectitneitherinanunqualifiednorinanaccidentalsense。 Letussuppose，ifanyonelikes，thatinthecaseofcertainthingsitispossibleforthematdifferenttimestobeandnottobe，withoutanyprocessofbecomingandperishing(infactitwouldseemtobenecessary，ifathingthathasnotpartsatonetimeisandatanothertimeisnot，thatanysuchthingshouldwithoutundergoinganyprocessofchangeatonetimebeandatanothertimenotbe)。Andletusfurthersupposeitpossiblethatsomeprinciplesthatareunmovedbutcapableofimpartingmotionatonetimeareandatanothertimearenot。Evenso，thiscannotbetrueofallsuchprinciples，sincetheremustclearlybesomethingthatcausesthingsthatmovethemselvesatonetimetobeandatanothernottobe。For，sincenothingthathasnotpartscanbeinmotion，thatwhichmovesitselfmustasawholehavemagnitude，thoughnothingthatwehavesaidmakesthisnecessarilytrueofeverymovent。Sothefactthatsomethingsbecomeandothersperish，andthatthisissocontinuously，cannotbecausedbyanyoneofthosethingsthat，thoughtheyareunmoved，donotalwaysexist:noragaincanitbecausedbyanyofthosewhichmovecertainparticularthings，whileothersmoveotherthings。Theeternityandcontinuityoftheprocesscannotbecausedeitherbyanyoneofthemsinglyorbythesumofthem，becausethiscausalrelationmustbeeternalandnecessary，whereasthesumofthesemoventsisinfiniteandtheydonotallexisttogether。Itisclear，then，thatthoughtheremaybecountlessinstancesoftheperishingofsomeprinciplesthatareunmovedbutimpartmotion，andthoughmanythingsthatmovethemselvesperishandaresucceededbyothersthatcomeintobeing，andthoughonethingthatisunmovedmovesonethingwhileanothermovesanother，neverthelessthereissomethingthatcomprehendsthemall，andthatassomethingapartfromeachoneofthem，andthisitisthatisthecauseofthefactthatsomethingsareandothersarenotandofthecontinuousprocessofchange:andthiscausesthemotionoftheothermovents，whiletheyarethecausesofthemotionofotherthings。Motion，then，beingeternal，thefirstmovent，ifthereisbutone，willbeeternalalso:iftherearemorethanone，therewillbeapluralityofsucheternalmovents。Weought，however，tosupposethatthereisoneratherthanmany，andafiniteratherthananinfinitenumber。Whentheconsequencesofeitherassumptionarethesame，weshouldalwaysassumethatthingsarefiniteratherthaninfiniteinnumber，sinceinthingsconstitutedbynaturethatwhichisfiniteandthatwhichisbetterought，ifpossible，tobepresentratherthanthereverse: andhereitissufficienttoassumeonlyonemovent，thefirstofunmovedthings，whichbeingeternalwillbetheprincipleofmotiontoeverythingelse。 Thefollowingargumentalsomakesitevidentthatthefirstmoventmustbesomethingthatisoneandeternal。Wehaveshownthattheremustalwaysbemotion。Thatbeingso，motionmustalsobecontinuous，becausewhatisalwaysiscontinuous，whereaswhatismerelyinsuccessionisnotcontinuous。Butfurther，ifmotioniscontinuous，itisone:anditisoneonlyifthemoventandthemovedthatconstituteitareeachofthemone，sinceintheeventofathing\'sbeingmovednowbyonethingandnowbyanotherthewholemotionwillnotbecontinuousbutsuccessive。 Moreoveraconvictionthatthereisafirstunmovedsomethingmaybereachednotonlyfromtheforegoingarguments，butalsobyconsideringagaintheprinciplesoperativeinmovents。Nowitisevidentthatamongexistingthingstherearesomethataresometimesinmotionandsometimesatrest。Thisfacthasservedabovetomakeitclearthatitisnottrueeitherthatallthingsareinmotionorthatallthingsareatrestorthatsomethingsarealwaysatrestandtheremainderalwaysinmotion:onthismatterproofissuppliedbythingsthatfluctuatebetweenthetwoandhavethecapacityofbeingsometimesinmotionandsometimesatrest。Theexistenceofthingsofthiskindiscleartoall:butwewishtoexplainalsothenatureofeachoftheothertwokindsandshowthattherearesomethingsthatarealwaysunmovedandsomethingsthatarealwaysinmotion。 Inthecourseofourargumentdirectedtothisendweestablishedthefactthateverythingthatisinmotionismovedbysomething，andthatthemoventiseitherunmovedorinmotion，andthat，ifitisinmotion，itismovedeitherbyitselforbysomethingelseandsoonthroughouttheseries:andsoweproceededtothepositionthatthefirstprinciplethatdirectlycausesthingsthatareinmotiontobemovedisthatwhichmovesitself，andthefirstprincipleofthewholeseriesistheunmoved。Furtheritisevidentfromactualobservationthattherearethingsthathavethecharacteristicofmovingthemselves，e。g。theanimalkingdomandthewholeclassoflivingthings。Thisbeingso，then，theviewwassuggestedthatperhapsitmaybepossibleformotiontocometobeinathingwithouthavingbeeninexistenceatallbefore，becauseweseethisactuallyoccurringinanimals:theyareunmovedatonetimeandthenagaintheyareinmotion，asitseems。Wemustgraspthefact，therefore，thatanimalsmovethemselvesonlywithonekindofmotion，andthatthisisnotstrictlyoriginatedbythem。Thecauseofitisnotderivedfromtheanimalitself:itisconnectedwithothernaturalmotionsinanimals，whichtheydonotexperiencethroughtheirowninstrumentality，e。g。increase，decrease，andrespiration:theseareexperiencedbyeveryanimalwhileitisatrestandnotinmotioninrespectofthemotionsetupbyitsownagency:herethemotioniscausedbytheatmosphereandbymanythingsthatenterintotheanimal:thusinsomecasesthecauseisnourishment:whenitisbeingdigestedanimalssleep，andwhenitisbeingdistributedthroughthesystemtheyawakeandmovethemselves，thefirstprincipleofthismotionbeingthusoriginallyderivedfromoutside。Thereforeanimalsarenotalwaysincontinuousmotionbytheirownagency:itissomethingelsethatmovesthem，itselfbeinginmotionandchangingasitcomesintorelationwitheachseveralthingthatmovesitself。 (Moreoverinalltheseself-movingthingsthefirstmoventandcauseoftheirself-motionisitselfmovedbyitself，thoughinanaccidentalsense:thatistosay，thebodychangesitsplace，sothatthatwhichisinthebodychangesitsplacealsoandisaself-moventthroughitsexerciseofleverage。)Hencewemayconfidentlyconcludethatifathingbelongstotheclassofunmovedmoventsthatarealsothemselvesmovedaccidentally，itisimpossiblethatitshouldcausecontinuousmotion。Sothenecessitythatthereshouldbemotioncontinuouslyrequiresthatthereshouldbeafirstmoventthatisunmovedevenaccidentally，if，aswehavesaid，thereistobeintheworldofthingsanunceasingandundyingmotion，andtheworldistoremainpermanentlyself-containedandwithinthesamelimits:forifthefirstprincipleispermanent，theuniversemustalsobepermanent，sinceitiscontinuouswiththefirstprinciple。(Wemustdistinguish，however，betweenaccidentalmotionofathingbyitselfandsuchmotionbysomethingelse，theformerbeingconfinedtoperishablethings，whereasthelatterbelongsalsotocertainfirstprinciplesofheavenlybodies，ofallthose，thatistosay，thatexperiencemorethanonelocomotion。) Andfurther，ifthereisalwayssomethingofthisnature，amoventthatisitselfunmovedandeternal，thenthatwhichisfirstmovedbyitmustbeeternal。Indeedthisisclearalsofromtheconsiderationthattherewouldotherwisebenobecomingandperishingandnochangeofanykindinotherthings，whichrequiresomethingthatisinmotiontomovethem:forthemotionimpartedbytheunmovedwillalwaysbeimpartedinthesamewayandbeoneandthesame，sincetheunmoveddoesnotitselfchangeinrelationtothatwhichismovedbyit。Butthatwhichismovedbysomethingthat，thoughitisinmotion，ismoveddirectlybytheunmovedstandsinvaryingrelationstothethingsthatitmoves，sothatthemotionthatitcauseswillnotbealwaysthesame:byreasonofthefactthatitoccupiescontrarypositionsorassumescontraryformsatdifferenttimesitwillproducecontrarymotionsineachseveralthingthatitmovesandwillcauseittobeatonetimeatrestandatanothertimeinmotion。 Theforegoingargument，then，hasservedtoclearupthepointaboutwhichweraisedadifficultyattheoutset-whyisitthatinsteadofallthingsbeingeitherinmotionoratrest，orsomethingsbeingalwaysinmotionandtheremainderalwaysatrest，therearethingsthataresometimesinmotionandsometimesnot?Thecauseofthisisnowplain:itisbecause，whilesomethingsaremovedbyaneternalunmovedmoventandarethereforealwaysinmotion，otherthingsaremovedbyamoventthatisinmotionandchanging，sothattheytoomustchange。Buttheunmovedmovent，ashasbeensaid，sinceitremainspermanentlysimpleandunvaryingandinthesamestate，willcausemotionthatisoneandsimple。 7 Thismatterwillbemadeclearer，however，ifwestartafreshfromanotherpoint。Wemustconsiderwhetheritisorisnotpossiblethatthereshouldbeacontinuousmotion，and，ifitispossible，whichthismotionis，andwhichistheprimarymotion:foritisplainthatiftheremustalwaysbemotion，andaparticularmotionisprimaryandcontinuous，thenitisthismotionthatisimpartedbythefirstmovent，andsoitisnecessarilyoneandthesameandcontinuousandprimary。 Nowofthethreekindsofmotionthatthereare-motioninrespectofmagnitude，motioninrespectofaffection，andmotioninrespectofplace-itisthislast，whichwecalllocomotion，thatmustbeprimary。 Thismaybeshownasfollows。Itisimpossiblethatthereshouldbeincreasewithoutthepreviousoccurrenceofalteration:forthatwhichisincreased，althoughinasenseitisincreasedbywhatislikeitself，isinasenseincreasedbywhatisunlikeitself:thusitissaidthatcontraryisnourishmenttocontrary:butgrowthiseffectedonlybythingsbecomingliketolike。Theremustbealteration，then，inthatthereisthischangefromcontrarytocontrary。Butthefactthatathingisalteredrequiresthatthereshouldbesomethingthataltersit，somethinge。g。thatmakesthepotentiallyhotintotheactuallyhot:soitisplainthatthemoventdoesnotmaintainauniformrelationtoitbutisatonetimenearertoandatanotherfartherfromthatwhichisaltered:andwecannothavethiswithoutlocomotion。If，therefore，theremustalwaysbemotion，theremustalsoalwaysbelocomotionastheprimarymotion，and，ifthereisaprimaryasdistinguishedfromasecondaryformoflocomotion，itmustbetheprimaryform。Again，allaffectionshavetheiroriginincondensationandrarefaction:thusheavyandlight，softandhard，hotandcold，areconsideredtobeformsofdensityandrarity。Butcondensationandrarefactionarenothingmorethancombinationandseparation，processesinaccordancewithwhichsubstancesaresaidtobecomeandperish:andinbeingcombinedandseparatedthingsmustchangeinrespectofplace。 Andfurther，whenathingisincreasedordecreaseditsmagnitudechangesinrespectofplace。 Again，thereisanotherpointofviewfromwhichitwillbeclearlyseenthatlocomotionisprimary。Asinthecaseofotherthingssotoointhecaseofmotiontheword\'primary\'maybeusedinseveralsenses。Athingissaidtobepriortootherthingswhen，ifitdoesnotexist，theotherswillnotexist，whereasitcanexistwithouttheothers:andthereisalsopriorityintimeandpriorityinperfectionofexistence。Letusbegin，then，withthefirstsense。Nowtheremustbemotioncontinuously，andtheremaybecontinuouslyeithercontinuousmotionorsuccessivemotion，theformer，however，inahigherdegreethanthelatter:moreoveritisbetterthatitshouldbecontinuousratherthansuccessivemotion，andwealwaysassumethepresenceinnatureofthebetter，ifitbepossible:since，then，continuousmotionispossible(thiswillbeprovedlater:forthepresentletustakeitforgranted)，andnoothermotioncanbecontinuousexceptlocomotion，locomotionmustbeprimary。Forthereisnonecessityforthesubjectoflocomotiontobethesubjecteitherofincreaseorofalteration，norneeditbecomeorperish:ontheotherhandtherecannotbeanyoneoftheseprocesseswithouttheexistenceofthecontinuousmotionimpartedbythefirstmovent。 Secondly，locomotionmustbeprimaryintime:forthisistheonlymotionpossibleforthings。Itistrueindeedthat，inthecaseofanyindividualthingthathasabecoming，locomotionmustbethelastofitsmotions:forafteritsbecomingitfirstexperiencesalterationandincrease，andlocomotionisamotionthatbelongstosuchthingsonlywhentheyareperfected。Buttheremustpreviouslybesomethingelsethatisinprocessoflocomotiontobethecauseevenofthebecomingofthingsthatbecome，withoutitselfbeinginprocessofbecoming，ase。g。thebegottenisprecededbywhatbegotit:otherwisebecomingmightbethoughttobetheprimarymotiononthegroundthatthethingmustfirstbecome。Butthoughthisissointhecaseofanyindividualthingthatbecomes，neverthelessbeforeanythingbecomes，somethingelsemustbeinmotion，notitselfbecomingbutbeing，andbeforethistheremustagainbesomethingelse。Andsincebecomingcannotbeprimary-for，ifitwere，everythingthatisinmotionwouldbeperishable-itisplainthatnooneofthemotionsnextinordercanbepriortolocomotion。BythemotionsnextinorderI meanincreaseandthenalteration，decrease，andperishing。Alltheseareposteriortobecoming:consequently，ifnotevenbecomingispriortolocomotion，thennooneoftheotherprocessesofchangeissoeither。 Thirdly，thatwhichisinprocessofbecomingappearsuniversallyassomethingimperfectandproceedingtoafirstprinciple:andsowhatisposteriorintheorderofbecomingispriorintheorderofnature。 Nowallthingsthatgothroughtheprocessofbecomingacquirelocomotionlast。Itisthisthataccountsforthefactthatsomelivingthings，e。g。plantsandmanykindsofanimals，owingtolackoftherequisiteorgan，areentirelywithoutmotion，whereasothersacquireitinthecourseoftheirbeingperfected。Therefore，ifthedegreeinwhichthingspossesslocomotioncorrespondstothedegreeinwhichtheyhaverealizedtheirnaturaldevelopment，thenthismotionmustbepriortoallothersinrespectofperfectionofexistence:andnotonlyforthisreasonbutalsobecauseathingthatisinmotionlosesitsessentialcharacterlessintheprocessoflocomotionthaninanyotherkindofmotion:itistheonlymotionthatdoesnotinvolveachangeofbeinginthesenseinwhichthereisachangeinqualitywhenathingisalteredandachangeinquantitywhenathingisincreasedordecreased。Aboveallitisplainthatthismotion，motioninrespectofplace，iswhatisinthestrictestsenseproducedbythatwhichmovesitself；butitistheself-moventthatwedeclaretobethefirstprincipleofthingsthataremovedandimpartmotionandtheprimarysourcetowhichthingsthatareinmotionaretobereferred。 Itisclear，then，fromtheforegoingargumentsthatlocomotionistheprimarymotion。Wehavenowtoshowwhichkindoflocomotionisprimary。Thesameprocessofreasoningwillalsomakeclearatthesametimethetruthoftheassumptionwehavemadebothnowandatapreviousstagethatitispossiblethatthereshouldbeamotionthatiscontinuousandeternal。Nowitisclearfromthefollowingconsiderationsthatnootherthanlocomotioncanbecontinuous。 Everyothermotionandchangeisfromanoppositetoanopposite:thusfortheprocessesofbecomingandperishingthelimitsaretheexistentandthenon-existent，foralterationthevariouspairsofcontraryaffections，andforincreaseanddecreaseeithergreatnessandsmallnessorperfectionandimperfectionofmagnitude:andchangestotherespectivecontrariesarecontrarychanges。Nowathingthatisundergoinganyparticularkindofmotion，butthoughpreviouslyexistenthasnotalwaysundergoneit，mustpreviouslyhavebeenatrestsofarasthatmotionisconcerned。Itisclear，then，thatforthechangingthingthecontrarieswillbestatesofrest。Andwehaveasimilarresultinthecaseofchangesthatarenotmotions:forbecomingandperishing，whetherregardedsimplyassuchwithoutqualificationorasaffectingsomethinginparticular，areopposites:thereforeprovideditisimpossibleforathingtoundergooppositechangesatthesametime，thechangewillnotbecontinuous，butaperiodoftimewillintervenebetweentheoppositeprocesses。Thequestionwhetherthesecontradictorychangesarecontrariesornotmakesnodifference，providedonlyitisimpossibleforthembothtobepresenttothesamethingatthesametime:thepointisofnoimportancetotheargument。Nordoesitmatterifthethingneednotrestinthecontradictorystate，orifthereisnostateofrestasacontrarytotheprocessofchange:itmaybetruethatthenon-existentisnotatrest，andthatperishingisaprocesstothenon-existent。Allthatmattersistheinterventionofatime:itisthisthatpreventsthechangefrombeingcontinuous:so，too，inourpreviousinstancestheimportantthingwasnottherelationofcontrarietybuttheimpossibilityofthetwoprocessesbeingpresenttoathingatthesametime。Andthereisnoneedtobedisturbedbythefactthatonthisshowingtheremaybemorethanonecontrarytothesamething，thataparticularmotionwillbecontrarybothtorestandtomotioninthecontrarydirection。 Wehaveonlytograspthefactthataparticularmotionisinasensetheoppositebothofastateofrestandofthecontrarymotion，inthesamewayasthatwhichisofequalorstandardmeasureistheoppositebothofthatwhichsurpassesitandofthatwhichitsurpasses，andthatitisimpossiblefortheoppositemotionsorchangestobepresenttoathingatthesametime。Furthermore，inthecaseofbecomingandperishingitwouldseemtobeanutterlyabsurdthingifassoonasanythinghasbecomeitmustnecessarilyperishandcannotcontinuetoexistforanytime:and，ifthisistrueofbecomingandperishing，wehavefairgroundsforinferringthesametobetrueoftheotherkindsofchange，sinceitwouldbeinthenaturalorderofthingsthattheyshouldbeuniforminthisrespect。 8 Letusnowproceedtomaintainthatitispossiblethatthereshouldbeaninfinitemotionthatissingleandcontinuous，andthatthismotionisrotatorymotion。Themotionofeverythingthatisinprocessoflocomotioniseitherrotatoryorrectilinearoracompoundofthetwo:consequently，ifoneoftheformertwoisnotcontinuous，thatwhichiscomposedofthembothcannotbecontinuouseither。Nowitisplainthatifthelocomotionofathingisrectilinearandfiniteitisnotcontinuouslocomotion:forthethingmustturnback，andthatwhichturnsbackinastraightlineundergoestwocontrarylocomotions，since，sofarasmotioninrespectofplaceisconcerned，upwardmotionisthecontraryofdownwardmotion，forwardmotionofbackwardmotion，andmotiontotheleftofmotiontotheright，thesebeingthepairsofcontrariesinthesphereofplace。Butwehavealreadydefinedsingleandcontinuousmotiontobemotionofasinglethinginasingleperiodoftimeandoperatingwithinasphereadmittingofnofurtherspecificdifferentiation(forwehavethreethingstoconsider，firstthatwhichisinmotion，e。g。amanoragod，secondlythe\'when\'ofthemotion，thatistosay，thetime，andthirdlythespherewithinwhichitoperates，whichmaybeeitherplaceoraffectionoressentialformormagnitude):andcontrariesarespecificallynotoneandthesamebutdistinct:andwithinthesphereofplacewehavetheabove-mentioneddistinctions。MoreoverwehaveanindicationthatmotionfromAtoBisthecontraryofmotionfromBtoAinthefactthat，iftheyoccuratthesametime，theyarrestandstopeachother。Andthesameistrueinthecaseofacircle:themotionfromAtowardsBisthecontraryofthemotionfromAtowardsG:foreveniftheyarecontinuousandthereisnoturningbacktheyarresteachother，becausecontrariesannihilateorobstructoneanother。Ontheotherhandlateralmotionisnotthecontraryofupwardmotion。Butwhatshowsmostclearlythatrectilinearmotioncannotbecontinuousisthefactthatturningbacknecessarilyimpliescomingtoastand，notonlywhenitisastraightlinethatistraversed，butalsointhecaseoflocomotioninacircle(whichisnotthesamethingasrotatorylocomotion:for，whenathingmerelytraversesacircle，itmayeitherproceedonitscoursewithoutabreakorturnbackagainwhenithasreachedthesamepointfromwhichitstarted)。Wemayassureourselvesofthenecessityofthiscomingtoastandnotonlyonthestrengthofobservation，butalsoontheoreticalgrounds。Wemaystartasfollows:wehavethreepoints，starting-point，middle-point，andfinishing-point，ofwhichthemiddle-pointinvirtueoftherelationsinwhichitstandsseverallytotheothertwoisbothastarting-pointandafinishing-point，andthoughnumericallyoneistheoreticallytwo。Wehavefurtherthedistinctionbetweenthepotentialandtheactual。Sointhestraightlineinquestionanyoneofthepointslyingbetweenthetwoextremesispotentiallyamiddle-point:butitisnotactuallysounlessthatwhichisinmotiondividesthelinebycomingtoastandatthatpointandbeginningitsmotionagain:thusthemiddle-pointbecomesbothastarting-pointandagoal，thestarting-pointofthelatterpartandthefinishing-pointofthefirstpartofthemotion。 Thisisthecasee。g。whenAinthecourseofitslocomotioncomestoastandatBandstartsagaintowardsG:butwhenitsmotioniscontinuousAcannoteitherhavecometobeorhaveceasedtobeatthepointB:itcanonlyhavebeenthereatthemomentofpassing，itspassagenotbeingcontainedwithinanyperiodoftimeexceptthewholeofwhichtheparticularmomentisadividing-point。TomaintainthatithascometobeandceasedtobetherewillinvolvetheconsequencethatAinthecourseofitslocomotionwillalwaysbecomingtoastand:foritisimpossiblethatAshouldsimultaneouslyhavecometobeatBandceasedtobethere，sothatthetwothingsmusthavehappenedatdifferentpointsoftime，andthereforetherewillbetheinterveningperiodoftime:consequentlyAwillbeinastateofrestatB，andsimilarlyatallotherpoints，sincethesamereasoningholdsgoodineverycase。WhentoA，thatwhichisinprocessoflocomotion，B，themiddle-point，servesbothasafinishing-pointandasastarting-pointforitsmotion，AmustcometoastandatB，becauseitmakesittwojustasonemightdointhought。 However，thepointAistherealstarting-pointatwhichthemovingbodyhasceasedtobe，anditisatGthatithasreallycometobewhenitscourseisfinishedanditcomestoastand。Sothisishowwemustmeetthedifficultythatthenarises，whichisasfollows。 SupposethelineEisequaltothelineZ，thatAproceedsincontinuouslocomotionfromtheextremepointofEtoG，andthat，atthemomentwhenAisatthepointB，DisproceedinginuniformlocomotionandwiththesamevelocityasAfromtheextremityofZ toH:then，saystheargument，DwillhavereachedHbeforeAhasreachedGforthatwhichmakesanearlierstartanddeparturemustmakeanearlierarrival:thereason，then，forthelatearrivalofA isthatithasnotsimultaneouslycometobeandceasedtobeatB: otherwiseitwillnotarrivelater:forthistohappenitwillbenecessarythatitshouldcometoastandthere。ThereforewemustnotholdthattherewasamomentwhenAcametobeatBandthatatthesamemomentDwasinmotionfromtheextremityofZ:forthefactofA\'shavingcometobeatBwillinvolvethefactofitsalsoceasingtobethere，andthetwoeventswillnotbesimultaneous，whereasthetruthisthatAisatBatasectionalpointoftimeanddoesnotoccupytimethere。Inthiscase，therefore，wherethemotionofathingiscontinuous，itisimpossibletousethisformofexpression。Ontheotherhandinthecaseofathingthatturnsbackinitscoursewemustdoso。ForsupposeHinthecourseofitslocomotionproceedstoDandthenturnsbackandproceedsdownwardsagain:thentheextremepointDhasservedasfinishing-pointandasstarting-pointforit，onepointthusservingastwo:thereforeHmusthavecometoastandthere:itcannothavecometobeatDanddepartedfromDsimultaneously，forinthatcaseitwouldsimultaneouslybethereandnotbethereatthesamemoment。Andherewecannotapplytheargumentusedtosolvethedifficultystatedabove:wecannotarguethatHisatDatasectionalpointoftimeandhasnotcometobeorceasedtobethere。Forherethegoalthatisreachedisnecessarilyonethatisactually，notpotentially，existent。Nowthepointinthemiddleispotential:butthisoneisactual，andregardedfrombelowitisafinishing-point，whileregardedfromaboveitisastarting-point，sothatitstandsinthesesametworespectiverelationstothetwomotions。Thereforethatwhichturnsbackintraversingarectilinearcoursemustinsodoingcometoastand。Consequentlytherecannotbeacontinuousrectilinearmotionthatiseternal。 Thesamemethodshouldalsobeadoptedinreplyingtothosewhoask，inthetermsofZeno\'sargument，whetherweadmitthatbeforeanydistancecanbetraversedhalfthedistancemustbetraversed，thatthesehalf-distancesareinfiniteinnumber，andthatitisimpossibletotraversedistancesinfiniteinnumber-orsomeonthelinesofthissameargumentputthequestionsinanotherform，andwouldhaveusgrantthatinthetimeduringwhichamotionisinprogressitshouldbepossibletoreckonahalf-motionbeforethewholeforeveryhalf-distancethatweget，sothatwehavetheresultthatwhenthewholedistanceistraversedwehavereckonedaninfinitenumber，whichisadmittedlyimpossible。Nowwhenwefirstdiscussedthequestionofmotionweputforwardasolutionofthisdifficultyturningonthefactthattheperiodoftimeoccupiedintraversingthedistancecontainswithinitselfaninfinitenumberofunits:thereisnoabsurdity，wesaid，insupposingthetraversingofinfinitedistancesininfinitetime，andtheelementofinfinityispresentinthetimenolessthaninthedistance。But，althoughthissolutionisadequateasareplytothequestioner(thequestionaskedbeingwhetheritispossibleinafinitetimetotraverseorreckonaninfinitenumberofunits)，neverthelessasanaccountofthefactandexplanationofitstruenatureitisinadequate。Forsupposethedistancetobeleftoutofaccountandthequestionaskedtobenolongerwhetheritispossibleinafinitetimetotraverseaninfinitenumberofdistances，andsupposethattheinquiryismadetorefertothetimetakenbyitself(forthetimecontainsaninfinitenumberofdivisions):thenthissolutionwillnolongerbeadequate，andwemustapplythetruththatweenunciatedinourrecentdiscussion，statingitinthefollowingway。Intheactofdividingthecontinuousdistanceintotwohalvesonepointistreatedastwo，sincewemakeitastarting-pointandafinishing-point:andthissameresultisalsoproducedbytheactofreckoninghalvesaswellasbytheactofdividingintohalves。Butifdivisionsaremadeinthisway，neitherthedistancenorthemotionwillbecontinuous:formotionifitistobecontinuousmustrelatetowhatiscontinuous: andthoughwhatiscontinuouscontainsaninfinitenumberofhalves，theyarenotactualbutpotentialhalves。Ifthehalvesaremadeactual，weshallgetnotacontinuousbutanintermittentmotion。Inthecaseofreckoningthehalves，itisclearthatthisresultfollows:forthenonepointmustbereckonedastwo:itwillbethefinishing-pointoftheonehalfandthestarting-pointoftheother，ifwereckonnottheonecontinuouswholebutthetwohalves。 Thereforetothequestionwhetheritispossibletopassthroughaninfinitenumberofunitseitheroftimeorofdistancewemustreplythatinasenseitisandinasenseitisnot。Iftheunitsareactual，itisnotpossible:iftheyarepotential，itispossible。Forinthecourseofacontinuousmotionthetravellerhastraversedaninfinitenumberofunitsinanaccidentalsensebutnotinanunqualifiedsense:forthoughitisanaccidentalcharacteristicofthedistancetobeaninfinitenumberofhalf-distances，thisisnotitsrealandessentialcharacter。Itisalsoplainthatunlessweholdthatthepointoftimethatdividesearlierfromlateralwaysbelongsonlytothelatersofarasthethingisconcerned，weshallbeinvolvedintheconsequencethatthesamethingisatthesamemomentexistentandnotexistent，andthatathingisnotexistentatthemomentwhenithasbecome。Itistruethatthepointiscommontobothtimes，theearlieraswellasthelater，andthat，whilenumericallyoneandthesame，itistheoreticallynotso，beingthefinishing-pointoftheoneandthestarting-pointoftheother:butsofarasthethingisconcerneditbelongstothelaterstageofwhathappenstoit。LetussupposeatimeABGandathingD，DbeingwhiteinthetimeAandnot-whiteinthetimeB。ThenD isatthemomentGwhiteandnot-white:forifwewererightinsayingthatitiswhiteduringthewholetimeA，itistruetocallitwhiteatanymomentofA，andnot-whiteinB，andGisinbothAandB。Wemustnotallow，therefore，thatitiswhiteinthewholeofA，butmustsaythatitissoinallofitexceptthelastmomentG。G belongsalreadytothelaterperiod，andifinthewholeofA not-whitewasinprocessofbecomingandwhiteofperishing，atG theprocessiscomplete。AndsoGisthefirstmomentatwhichitistruetocallthethingwhiteornotwhiterespectively。Otherwiseathingmaybenon-existentatthemomentwhenithasbecomeandexistentatthemomentwhenithasperished:orelseitmustbepossibleforathingatthesametimetobewhiteandnotwhiteandinfacttobeexistentandnon-existent。Further，ifanythingthatexistsafterhavingbeenpreviouslynon-existentmustbecomeexistentanddoesnotexistwhenitisbecoming，timecannotbedivisibleintotime-atoms。ForsupposethatDwasbecomingwhiteinthetimeAandthatatanothertimeB，atime-atomconsecutivewiththelastatomofA，Dhasalreadybecomewhiteandsoiswhiteatthatmoment:then，inasmuchasinthetimeAitwasbecomingwhiteandsowasnotwhiteandatthemomentBitiswhite，theremusthavebeenabecomingbetweenAandBandthereforealsoatimeinwhichthebecomingtookplace。Ontheotherhand，thosewhodenyatomsoftime(aswedo) arenotaffectedbythisargument:accordingtothemDhasbecomeandsoiswhiteatthelastpointoftheactualtimeinwhichitwasbecomingwhite:andthispointhasnootherpointconsecutivewithorinsuccessiontoit，whereastime-atomsareconceivedassuccessive。MoreoveritisclearthatifDwasbecomingwhiteinthewholetimeA，thetimeoccupiedbyitinhavingbecomewhiteinadditiontohavingbeeninprocessofbecomingwhiteisnomorethanallthatitoccupiedinthemereprocessofbecomingwhite。 Theseandsuch-like，then，aretheargumentsforourconclusionthatderivecogencyfromthefactthattheyhaveaspecialbearingonthepointatissue。Ifwelookatthequestionfromthepointofviewofgeneraltheory，thesameresultwouldalsoappeartobeindicatedbythefollowingarguments。Everythingwhosemotioniscontinuousmust，onarrivingatanypointinthecourseofitslocomotion，havebeenpreviouslyalsoinprocessoflocomotiontothatpoint，ifitisnotforcedoutofitspathbyanything:e。g。onarrivingatBathingmustalsohavebeeninprocessoflocomotiontoB，andthatnotmerelywhenitwasneartoB，butfromthemomentofitsstartingonitscourse，sincetherecanbe，noreasonforitsbeingsoatanyparticularstageratherthanatanearlierone。So，too，inthecaseoftheotherkindsofmotion。NowwearetosupposethatathingproceedsinlocomotionfromAtoGandthatatthemomentofitsarrivalatGthecontinuityofitsmotionisunbrokenandwillremainsountilithasarrivedbackatA。ThenwhenitisundergoinglocomotionfromAtoG itisatthesametimeundergoingalsoitslocomotiontoAfromG: consequentlyitissimultaneouslyundergoingtwocontrarymotions，sincethetwomotionsthatfollowthesamestraightlinearecontrarytoeachother。Withthisconsequencetherealsofollowsanother:wehaveathingthatisinprocessofchangefromapositioninwhichithasnotyetbeen:so，inasmuchasthisisimpossible，thethingmustcometoastandatG。Thereforethemotionisnotasinglemotion，sincemotionthatisinterruptedbystationarinessisnotsingle。 Further，thefollowingargumentwillservebettertomakethispointclearuniversallyinrespectofeverykindofmotion。Ifthemotionundergonebythatwhichisinmotionisalwaysoneofthosealreadyenumerated，andthestateofrestthatitundergoesisoneofthosethataretheoppositesofthemotions(forwefoundthattherecouldbenootherbesidesthese)，andmoreoverthatwhichisundergoingbutdoesnotalwaysundergoaparticularmotion(bythisImeanoneofthevariousspecificallydistinctmotions，notsomeparticularpartofthewholemotion)musthavebeenpreviouslyundergoingthestateofrestthatistheoppositeofthemotion，thestateofrestbeingprivationofmotion；then，inasmuchasthetwomotionsthatfollowthesamestraightlinearecontrarymotions，anditisimpossibleforathingtoundergosimultaneouslytwocontrarymotions，thatwhichisundergoinglocomotionfromAtoGcannotalsosimultaneouslybeundergoinglocomotionfromGtoA:andsincethelatterlocomotionisnotsimultaneouswiththeformerbutisstilltobeundergone，beforeitisundergonetheremustoccurastateofrestatG:forthis，aswefound，isthestateofrestthatistheoppositeofthemotionfromG。Theforegoingargument，then，makesitplainthatthemotioninquestionisnotcontinuous。 Ournextargumenthasamorespecialbearingthantheforegoingonthepointatissue。Wewillsupposethattherehasoccurredinsomethingsimultaneouslyaperishingofnot-whiteandabecomingofwhite。Thenifthealterationtowhiteandfromwhiteisacontinuousprocessandthewhitedoesnotremainanytime，theremusthaveoccurredsimultaneouslyaperishingofnot-white，abecomingofwhite，andabecomingofnot-white:forthetimeofthethreewillbethesame。 Again，fromthecontinuityofthetimeinwhichthemotiontakesplacewecannotinfercontinuityinthemotion，butonlysuccessiveness:infact，howcouldcontraries，e。g。whitenessandblackness，meetinthesameextremepoint? Ontheotherhand，inmotiononacircularlineweshallfindsinglenessandcontinuity:forherewearemetbynoimpossibleconsequence:thatwhichisinmotionfromAwillinvirtueofthesamedirectionofenergybesimultaneouslyinmotiontoA(sinceitisinmotiontothepointatwhichitwillfinallyarrive)，andyetwillnotbeundergoingtwocontraryoroppositemotions:foramotiontoapointandamotionfromthatpointarenotalwayscontrariesoropposites:theyarecontrariesonlyiftheyareonthesamestraightline(forthentheyarecontrarytooneanotherinrespectofplace，ase。g。thetwomotionsalongthediameterofthecircle，sincetheendsofthisareatthegreatestpossibledistancefromoneanother)，andtheyareoppositesonlyiftheyarealongthesameline。 Thereforeinthecasewearenowconsideringthereisnothingtopreventthemotionbeingcontinuousandfreefromallintermission: forrotatorymotionismotionofathingfromitsplacetoitsplace，whereasrectilinearmotionismotionfromitsplacetoanotherplace。 Moreovertheprogressofrotatorymotionisneverlocalizedwithincertainfixedlimits，whereasthatofrectilinearmotionrepeatedlyisso。Nowamotionthatisalwaysshiftingitsgroundfrommomenttomomentcanbecontinuous:butamotionthatisrepeatedlylocalizedwithincertainfixedlimitscannotbeso，sincethenthesamethingwouldhavetoundergosimultaneouslytwooppositemotions。So，too，therecannotbecontinuousmotioninasemicircleorinanyotherarcofacircle，sinceherealsothesamegroundmustbetraversedrepeatedlyandtwocontraryprocessesofchangemustoccur。Thereasonisthatinthesemotionsthestarting-pointandtheterminationdonotcoincide，whereasinmotionoveracircletheydocoincide，andsothisistheonlyperfectmotion。 Thisdifferentiationalsoprovidesanothermeansofshowingthattheotherkindsofmotioncannotbecontinuouseither:forinallofthemwefindthatthereisthesamegroundtobetraversedrepeatedly； thusinalterationtherearetheintermediatestagesoftheprocess，andinquantitativechangetherearetheinterveningdegreesofmagnitude:andinbecomingandperishingthesamethingistrue。Itmakesnodifferencewhetherwetaketheintermediatestagesoftheprocesstobefewormany，orwhetherweaddorsubtractone:forineithercasewefindthatthereisstillthesamegroundtobetraversedrepeatedly。Moreoveritisplainfromwhathasbeensaidthatthosephysicistswhoassertthatallsensiblethingsarealwaysinmotionarewrong:fortheirmotionmustbeoneorotherofthemotionsjustmentioned:infacttheymostlyconceiveitasalteration(thingsarealwaysinfluxanddecay，theysay)，andtheygosofarastospeakevenofbecomingandperishingasaprocessofalteration。Ontheotherhand，ourargumenthasenabledustoassertthefact，applyinguniversallytoallmotions，thatnomotionadmitsofcontinuityexceptrotatorymotion:consequentlyneitheralterationnorincreaseadmitsofcontinuity。Weneednowsaynomoreinsupportofthepositionthatthereisnoprocessofchangethatadmitsofinfinityorcontinuityexceptrotatorylocomotion。 9 Itcannowbeshownplainlythatrotationistheprimarylocomotion。 Everylocomotion，aswesaidbefore，iseitherrotatoryorrectilinearoracompoundofthetwo:andthetwoformermustbepriortothelast，sincetheyaretheelementsofwhichthelatterconsists。 Moreoverrotatorylocomotionispriortorectilinearlocomotion，becauseitismoresimpleandcomplete，whichmaybeshownasfollows。 Thestraightlinetraversedinrectilinearmotioncannotbeinfinite:forthereisnosuchthingasaninfinitestraightline；andeveniftherewere，itwouldnotbetraversedbyanythinginmotion: fortheimpossibledoesnothappenanditisimpossibletotraverseaninfinitedistance。Ontheotherhandrectilinearmotiononafinitestraightlineisifitturnsbackacompositemotion，infacttwomotions，whileifitdoesnotturnbackitisincompleteandperishable:andintheorderofnature，ofdefinition，andoftimealikethecompleteispriortotheincompleteandtheimperishabletotheperishable。Again，amotionthatadmitsofbeingeternalispriortoonethatdoesnot。Nowrotatorymotioncanbeeternal:butnoothermotion，whetherlocomotionormotionofanyotherkind，canbeso，sinceinallofthemrestmustoccurandwiththeoccurrenceofrestthemotionhasperished。Moreovertheresultatwhichwehavearrived，thatrotatorymotionissingleandcontinuous，andrectilinearmotionisnot，isareasonableone。Inrectilinearmotionwehaveadefinitestarting-point，finishing-point，middle-point，whichallhavetheirplaceinitinsuchawaythatthereisapointfromwhichthatwhichisinmotioncanbesaidtostartandapointatwhichitcanbesaidtofinishitscourse(forwhenanythingisatthelimitsofitscourse，whetheratthestarting-pointoratthefinishing-point，itmustbeinastateofrest)。Ontheotherhandincircularmotiontherearenosuchdefinitepoints:forwhyshouldanyonepointonthelinebealimitratherthananyother?Anyonepointasmuchasanyotherisalikestarting-point，middle-point，andfinishing-point，sothatwecansayofcertainthingsboththattheyarealwaysandthattheyneverareatastarting-pointandatafinishing-point(sothatarevolvingsphere，whileitisinmotion，isalsoinasenseatrest，foritcontinuestooccupythesameplace)。Thereasonofthisisthatinthiscaseallthesecharacteristicsbelongtothecentre:thatistosay，thecentreisalikestarting-point，middle-point，andfinishing-pointofthespacetraversed；consequentlysincethispointisnotapointonthecircularline，thereisnopointatwhichthatwhichisinprocessoflocomotioncanbeinastateofrestashavingtraverseditscourse，becauseinitslocomotionitisproceedingalwaysaboutacentralpointandnottoanextremepoint: thereforeitremainsstill，andthewholeisinasensealwaysatrestaswellascontinuouslyinmotion。Ournextpointgivesaconvertibleresult:ontheonehand，becauserotationisthemeasureofmotionsitmustbetheprimarymotion(forallthingsaremeasuredbywhatisprimary):ontheotherhand，becauserotationistheprimarymotionitisthemeasureofallothermotions。Again，rotatorymotionisalsotheonlymotionthatadmitsofbeingregular。Inrectilinearlocomotionthemotionofthingsinleavingthestarting-pointisnotuniformwiththeirmotioninapproachingthefinishing-point，sincethevelocityofathingalwaysincreasesproportionatelyasitremovesitselffartherfromitspositionofrest:ontheotherhandrotatorymotionistheonlymotionwhosecourseisnaturallysuchthatithasnostarting-pointorfinishing-pointinitselfbutisdeterminedfromelsewhere。 Astolocomotionbeingtheprimarymotion，thisisatruththatisattestedbyallwhohaveevermadementionofmotionintheirtheories:theyallassigntheirfirstprinciplesofmotiontothingsthatimpartmotionofthiskind。Thus\'separation\'and\'combination\' aremotionsinrespectofplace，andthemotionimpartedby\'Love\'and\'Strife\'takestheseforms，thelatter\'separating\'andtheformer\'combining\'。Anaxagoras，too，saysthat\'Mind\'，hisfirstmovent，\'separates\'。Similarlythosewhoassertnocauseofthiskindbutsaythat\'void\'accountsformotion-theyalsoholdthatthemotionofnaturalsubstanceismotioninrespectofplace:fortheirmotionthatisaccountedforby\'void\'islocomotion，anditssphereofoperationmaybesaidtobeplace。Moreovertheyareofopinionthattheprimarysubstancesarenotsubjecttoanyoftheothermotions，thoughthethingsthatarecompoundsofthesesubstancesaresosubject:theprocessesofincreaseanddecreaseandalteration，theysay，areeffectsofthe\'combination\'and\'separation\'ofatoms。Itisthesame，too，withthosewhomakeoutthatthebecomingorperishingofathingisaccountedforby\'density\'or\'rarity\':foritisby\'combination\'and\'separation\'thattheplaceofthesethingsintheirsystemsisdetermined。MoreovertothesewemayaddthosewhomakeSoulthecauseofmotion:fortheysaythatthingsthatundergomotionhaveastheirfirstprinciple\'thatwhichmovesitself\':andwhenanimalsandalllivingthingsmovethemselves，themotionismotioninrespectofplace。Finallyitistobenotedthatwesaythatathing\'isinmotion\'inthestrictsenseofthetermonlywhenitsmotionismotioninrespectofplace:ifathingisinprocessofincreaseordecreaseorisundergoingsomealterationwhileremainingatrestinthesameplace，wesaythatitisinmotioninsomeparticularrespect:wedonotsaythatit\'isinmotion\' withoutqualification。 Ourpresentposition，then，isthis:Wehavearguedthattherealwayswasmotionandalwayswillbemotionthroughoutalltime，andwehaveexplainedwhatisthefirstprincipleofthiseternalmotion:wehaveexplainedfurtherwhichistheprimarymotionandwhichistheonlymotionthatcanbeeternal:andwehavepronouncedthefirstmoventtobeunmoved。 10 Wehavenowtoassertthatthefirstmoventmustbewithoutpartsandwithoutmagnitude，beginningwiththeestablishmentofthepremissesonwhichthisconclusiondepends。 Oneofthesepremissesisthatnothingfinitecancausemotionduringaninfinitetime。Wehavethreethings，themovent，themoved，andthirdlythatinwhichthemotiontakesplace，namelythetime:andtheseareeitherallinfiniteorallfiniteorpartly-thatistosaytwoofthemoroneofthem-finiteandpartlyinfinite。LetA bethemovement，Bthemoved，andGtheinfinitetime。NowletussupposethatDmovesE，apartofB。ThenthetimeoccupiedbythismotioncannotbeequaltoG:forthegreatertheamountmoved，thelongerthetimeoccupied。ItfollowsthatthetimeZisnotinfinite。NowweseethatbycontinuingtoaddtoD，IshalluseupAandbycontinuingtoaddtoE，IshalluseupB:butIshallnotuseupthetimebycontinuallysubtractingacorrespondingamountfromit，becauseitisinfinite。ConsequentlythedurationofthepartofG whichisoccupiedbyallAinmovingthewholeofB，willbefinite。 Thereforeafinitethingcannotimparttoanythinganinfinitemotion。 Itisclear，then，thatitisimpossibleforthefinitetocausemotionduringaninfinitetime。 Ithasnowtobeshownthatinnocaseisitpossibleforaninfiniteforcetoresideinafinitemagnitude。Thiscanbeshownasfollows:wetakeitforgrantedthatthegreaterforceisalwaysthatwhichinlesstimethananotherdoesanequalamountofworkwhenengagedinanyactivity-inheating，forexample，orsweeteningorthrowing；infact，incausinganykindofmotion。Thenthatonwhichtheforcesactmustbeaffectedtosomeextentbyoursupposedfinitemagnitudepossessinganinfiniteforceaswellasbyanythingelse，infacttoagreaterextentthanbyanythingelse，sincetheinfiniteforceisgreaterthananyother。Butthentherecannotbeanytimeinwhichitsactioncouldtakeplace。SupposethatAisthetimeoccupiedbytheinfinitepowerintheperformanceofanactofheatingorpushing，andthatABisthetimeoccupiedbyafinitepowerintheperformanceofthesameact:thenbyaddingtothelatteranotherfinitepowerandcontinuallyincreasingthemagnitudeofthepowersoaddedIshallatsometimeorotherreachapointatwhichthefinitepowerhascompletedthemotiveactinthetimeA:forbycontinualadditiontoafinitemagnitudeImustarriveatamagnitudethatexceedsanyassignedlimit，andinthesamewaybycontinualsubtractionImustarriveatonethatfallsshortofanyassignedlimit。Sowegettheresultthatthefiniteforcewilloccupythesameamountoftimeinperformingthemotiveactastheinfiniteforce。Butthisisimpossible。Thereforenothingfinitecanpossessaninfiniteforce。Soitisalsoimpossibleforafiniteforcetoresideinaninfinitemagnitude。Itistruethatagreaterforcecanresideinalessermagnitude:butthesuperiorityofanysuchgreaterforcecanbestillgreaterifthemagnitudeinwhichitresidesisgreater。NowletABbeaninfinitemagnitude。ThenBG possessesacertainforcethatoccupiesacertaintime，letussaythetimeZinmovingD。NowifItakeamagnitudetwiceasgreatatBG，thetimeoccupiedbythismagnitudeinmovingDwillbehalfofEZ (assumingthistobetheproportion):sowemaycallthistimeZH。 Thatbeingso，bycontinuallytakingagreatermagnitudeinthiswayI shallneverarriveatthefullAB，whereasIshallalwaysbegettingalesserfractionofthetimegiven。Thereforetheforcemustbeinfinite，sinceitexceedsanyfiniteforce。Moreoverthetimeoccupiedbytheactionofanyfiniteforcemustalsobefinite:forifagivenforcemovessomethinginacertaintime，agreaterforcewilldosoinalessertime，butstilladefinitetime，ininverseproportion。Butaforcemustalwaysbeinfinite-justasanumberoramagnitudeis-ifitexceedsalldefinitelimits。Thispointmayalsobeprovedinanotherway-bytakingafinitemagnitudeinwhichthereresidesaforcethesameinkindasthatwhichresidesintheinfinitemagnitude，sothatthisforcewillbeameasureofthefiniteforceresidingintheinfinitemagnitude。 Itisplain，then，fromtheforegoingargumentsthatitisimpossibleforaninfiniteforcetoresideinafinitemagnitudeorforafiniteforcetoresideinaninfinitemagnitude。Butbeforeproceedingtoourconclusionitwillbewelltodiscussadifficultythatarisesinconnexionwithlocomotion。Ifeverythingthatisinmotionwiththeexceptionofthingsthatmovethemselvesismovedbysomethingelse，howisitthatsomethings，e。g。thingsthrown，continuetobeinmotionwhentheirmoventisnolongerincontactwiththem?Ifwesaythatthemoventinsuchcasesmovessomethingelseatthesametime，thatthethrowere。g。alsomovestheair，andthatthisinbeingmovedisalsoamovent，thenitwouldbenomorepossibleforthissecondthingthanfortheoriginalthingtobeinmotionwhentheoriginalmoventisnotincontactwithitormovingit:allthethingsmovedwouldhavetobeinmotionsimultaneouslyandalsotohaveceasedsimultaneouslytobeinmotionwhentheoriginalmoventceasestomovethem，evenif，likethemagnet，itmakesthatwhichithasmovedcapableofbeingamovent。Therefore，whilewemustacceptthisexplanationtotheextentofsayingthattheoriginalmoventgivesthepowerofbeingamoventeithertoairortowaterortosomethingelseofthekind，naturallyadaptedforimpartingandundergoingmotion，wemustsayfurtherthatthisthingdoesnotceasesimultaneouslytoimpartmotionandtoundergomotion:itceasestobeinmotionatthemomentwhenitsmoventceasestomoveit，butitstillremainsamovent，andsoitcausessomethingelseconsecutivewithittobeinmotion，andofthisagainthesamemaybesaid。Themotionbeginstoceasewhenthemotiveforceproducedinonememberoftheconsecutiveseriesisateachstagelessthanthatpossessedbytheprecedingmember，anditfinallyceaseswhenonemembernolongercausesthenextmembertobeamoventbutonlycausesittobeinmotion。Themotionoftheselasttwo-oftheoneasmoventandoftheotherasmoved-mustceasesimultaneously，andwiththisthewholemotionceases。Nowthethingsinwhichthismotionisproducedarethingsthatadmitofbeingsometimesinmotionandsometimesatrest，andthemotionisnotcontinuousbutonlyappearsso:foritismotionofthingsthatareeithersuccessiveorincontact，therebeingnotonemoventbutanumberofmoventsconsecutivewithoneanother:andsomotionofthiskindtakesplaceinairandwater。Somesaythatitis\'mutualreplacement\':butwemustrecognizethatthedifficultyraisedcannotbesolvedotherwisethaninthewaywehavedescribed。Sofarastheyareaffectedby\'mutualreplacement\'，allthemembersoftheseriesaremovedandimpartmotionsimultaneously，sothattheirmotionsalsoceasesimultaneously:butourpresentproblemconcernstheappearanceofcontinuousmotioninasinglething，andtherefore，sinceitcannotbemovedthroughoutitsmotionbythesamemovent，thequestionis，whatmovesit? Resumingourmainargument，weproceedfromthepositionsthattheremustbecontinuousmotionintheworldofthings，thatthisisasinglemotion，thatasinglemotionmustbeamotionofamagnitude(forthatwhichiswithoutmagnitudecannotbeinmotion)，andthatthemagnitudemustbeasinglemagnitudemovedbyasinglemovent(forotherwisetherewillnotbecontinuousmotionbutaconsecutiveseriesofseparatemotions)，andthatifthemovementisasinglething，itiseitheritselfinmotionoritselfunmoved:if，then，itisinmotion，itwillhavetobesubjecttothesameconditionsasthatwhichitmoves，thatistosayitwillitselfbeinprocessofchangeandinbeingsowillalsohavetobemovedbysomething:sowehaveaseriesthatmustcometoanend，andapointwillbereachedatwhichmotionisimpartedbysomethingthatisunmoved。Thuswehaveamoventthathasnoneedtochangealongwiththatwhichitmovesbutwillbeabletocausemotionalways(forthecausingofmotionundertheseconditionsinvolvesnoeffort):andthismotionaloneisregular，oratleastitissoinahigherdegreethananyother，sincethemoventisneversubjecttoanychange。So，too，inorderthatthemotionmaycontinuetobeofthesamecharacter，themovedmustnotbesubjecttochangeinrespectofitsrelationtothemovent。 Moreoverthemoventmustoccupyeitherthecentreorthecircumference，sincethesearethefirstprinciplesfromwhichasphereisderived。Butthethingsnearestthemoventarethosewhosemotionisquickest，andinthiscaseitisthemotionofthecircumferencethatisthequickest:thereforethemoventoccupiesthecircumference。 Thereisafurtherdifficultyinsupposingittobepossibleforanythingthatisinmotiontocausemotioncontinuouslyandnotmerelyinthewayinwhichitiscausedbysomethingrepeatedlypushing(inwhichcasethecontinuityamountstonomorethansuccessiveness)。 Suchamoventmusteitheritselfcontinuetopushorpullorperformboththeseactions，orelsetheactionmustbetakenupbysomethingelseandbepassedonfromonemoventtoanother(theprocessthatwedescribedbeforeasoccurringinthecaseofthingsthrown，sincetheairorthewater，beingdivisible，isamoventonlyinvirtueofthefactthatdifferentpartsoftheairaremovedoneafteranother): andineithercasethemotioncannotbeasinglemotion，butonlyaconsecutiveseriesofmotions。Theonlycontinuousmotion，then，isthatwhichiscausedbytheunmovedmovent:andthismotioniscontinuousbecausethemoventremainsalwaysinvariable，sothatitsrelationtothatwhichitmovesremainsalsoinvariableandcontinuous。 Nowthatthesepointsaresettled，itisclearthatthefirstunmovedmoventcannothaveanymagnitude。Forifithasmagnitude，thismustbeeitherafiniteoraninfinitemagnitude。Nowwehavealready\'provedinourcourseonPhysicsthattherecannotbeaninfinitemagnitude:andwehavenowprovedthatitisimpossibleforafinitemagnitudetohaveaninfiniteforce，andalsothatitisimpossibleforathingtobemovedbyafinitemagnitudeduringaninfinitetime。Butthefirstmoventcausesamotionthatiseternalanddoescauseitduringaninfinitetime。Itisclear，therefore，thatthefirstmoventisindivisibleandiswithoutpartsandwithoutmagnitude- THEEND-