第4章

14

Thesedistinctionshavingbeendrawn，itisevidentthateverychangeandeverythingthatmovesisintime；forthedistinctionoffasterandslowerexistsinreferencetoallchange，sinceitisfoundineveryinstance。Inthephrase"movingfaster"Irefertothatwhichchangesbeforeanotherintotheconditioninquestion，whenitmovesoverthesameintervalandwitharegularmovement；e。g。inthecaseoflocomotion，ifboththingsmovealongthecircumferenceofacircle，orbothalongastraightline；andsimilarlyinallothercases。Butwhatisbeforeisintime；forwesay"before"and"after"withreferencetothedistancefromthe"now"，andthe"now"

istheboundaryofthepastandthefuture；sothatsince"nows"areintime，thebeforeandtheafterwillbeintimetoo；forinthatinwhichthe"now"is，thedistancefromthe"now"willalsobe。But"before"isusedcontrariwisewithreferencetopastandtofuturetime；forinthepastwecall"before"whatisfartherfromthe"now"，and"after"whatisnearer，butinthefuturewecallthenearer"before"andthefarther"after"。Sothatsincethe"before"isintime，andeverymovementinvolvesa"before"，evidentlyeverychangeandeverymovementisintime。

Itisalsoworthconsideringhowtimecanberelatedtothesoul；

andwhytimeisthoughttobeineverything，bothinearthandinseaandinheaven。Isbecauseitisanattribute，orstate，ormovement(sinceitisthenumberofmovement)andallthesethingsaremovable(fortheyareallinplace)，andtimeandmovementaretogether，bothinrespectofpotentialityandinrespectofactuality?

Whetherifsouldidnotexisttimewouldexistornot，isaquestionthatmayfairlybeasked；foriftherecannotbesomeonetocounttherecannotbeanythingthatcanbecounted，sothatevidentlytherecannotbenumber；fornumberiseitherwhathasbeen，orwhatcanbe，counted。Butifnothingbutsoul，orinsoulreason，isqualifiedtocount，therewouldnotbetimeunlessthereweresoul，butonlythatofwhichtimeisanattribute，i。e。ifmovementcanexistwithoutsoul，andthebeforeandafterareattributesofmovement，andtimeisthesequanumerable。

Onemightalsoraisethequestionwhatsortofmovementtimeisthenumberof。Mustwenotsay"ofanykind"?Forthingsbothcomeintobeingintimeandpassaway，andgrow，andarealteredintime，andaremovedlocally；thusitisofeachmovementquamovementthattimeisthenumber。Andsoitissimplythenumberofcontinuousmovement，notofanyparticularkindofit。

Butotherthingsaswellmayhavebeenmovednow，andtherewouldbeanumberofeachofthetwomovements。Isthereanothertime，then，andwilltherebetwoequaltimesatonce?Surelynot。Foratimethatisbothequalandsimultaneousisoneandthesametime，andeventhosethatarenotsimultaneousareoneinkind；forifthereweredogs，andhorses，andsevenofeach，itwouldbethesamenumber。

So，too，movementsthathavesimultaneouslimitshavethesametime，yettheonemayinfactbefastandtheothernot，andonemaybelocomotionandtheotheralteration；stillthetimeofthetwochangesisthesameiftheirnumberalsoisequalandsimultaneous；andforthisreason，whilethemovementsaredifferentandseparate，thetimeiseverywherethesame，becausethenumberofequalandsimultaneousmovementsiseverywhereoneandthesame。

Nowthereissuchathingaslocomotion，andinlocomotionthereisincludedcircularmovement，andeverythingismeasuredbysomeonethinghomogeneouswithit，unitsbyaunit，horsesbyahorse，andsimilarlytimesbysomedefinitetime，and，aswesaid，timeismeasuredbymotionaswellasmotionbytime(thisbeingsobecausebyamotiondefiniteintimethequantitybothofthemotionandofthetimeismeasured):if，then，whatisfirstisthemeasureofeverythinghomogeneouswithit，regularcircularmotionisaboveallelsethemeasure，becausethenumberofthisisthebestknown。Nowneitheralterationnorincreasenorcomingintobeingcanberegular，butlocomotioncanbe。Thisalsoiswhytimeisthoughttobethemovementofthesphere，viz。becausetheothermovementsaremeasuredbythis，andtimebythismovement。

Thisalsoexplainsthecommonsayingthathumanaffairsformacircle，andthatthereisacircleinallotherthingsthathaveanaturalmovementandcomingintobeingandpassingaway。Thisisbecauseallotherthingsarediscriminatedbytime，andendandbeginasthoughconformingtoacycle；foreventimeitselfisthoughttobeacircle。Andthisopinionagainisheldbecausetimeisthemeasureofthiskindoflocomotionandisitselfmeasuredbysuch。

Sothattosaythatthethingsthatcomeintobeingformacircleistosaythatthereisacircleoftime；andthisistosaythatitismeasuredbythecircularmovement；forapartfromthemeasurenothingelsetobemeasuredisobserved；thewholeisjustapluralityofmeasures。

Itissaidrightly，too，thatthenumberofthesheepandofthedogsisthesamenumberifthetwonumbersareequal，butnotthesamedecadorthesameten；justastheequilateralandthescalenearenotthesametriangle，yettheyarethesamefigure，becausetheyarebothtriangles。Forthingsarecalledthesameso-and-soiftheydonotdifferbyadifferentiaofthatthing，butnotiftheydo；e。g。

trianglediffersfromtrianglebyadifferentiaoftriangle，thereforetheyaredifferenttriangles；buttheydonotdifferbyadifferentiaoffigure，butareinoneandthesamedivisionofit。Forafigureoftheonekindisacircleandafigureofanotherkindoftriangle，andatriangleofonekindisequilateralandatriangleofanotherkindscalene。Theyarethesamefigure，then，that，triangle，butnotthesametriangle。Thereforethenumberoftwogroupsalso-isthesamenumber(fortheirnumberdoesnotdifferbyadifferentiaofnumber)，butitisnotthesamedecad；forthethingsofwhichitisasserteddiffer；onegrouparedogs，andtheotherhorses。

Wehavenowdiscussedtime-bothtimeitselfandthemattersappropriatetotheconsiderationofit。

BookV

1

EVERYTHINGwhichchangesdoessoinoneofthreesenses。Itmaychange(1)accidentally，asforinstancewhenwesaythatsomethingmusicalwalks，thatwhichwalksbeingsomethinginwhichaptitudeformusicisanaccident。Again(2)athingissaidwithoutqualificationtochangebecausesomethingbelongingtoitchanges，i。e。instatementswhichrefertopartofthethinginquestion:

thusthebodyisrestoredtohealthbecausetheeyeorthechest，thatistosayapartofthewholebody，isrestoredtohealth。Andaboveallthereis(3)thecaseofathingwhichisinmotionneitheraccidentallynorinrespectofsomethingelsebelongingtoit，butinvirtueofbeingitselfdirectlyinmotion。Herewehaveathingwhichisessentiallymovable:andthatwhichissoisadifferentthingaccordingtotheparticularvarietyofmotion:forinstanceitmaybeathingcapableofalteration:andwithinthesphereofalterationitisagainadifferentthingaccordingasitiscapableofbeingrestoredtohealthorcapableofbeingheated。Andtherearethesamedistinctionsinthecaseofthemover:(1)onethingcausesmotionaccidentally，(2)anotherpartially(becausesomethingbelongingtoitcausesmotion)，(3)anotherofitselfdirectly，as，forinstance，thephysicianheals，thehandstrikes。Wehave，then，thefollowingfactors:(a)ontheonehandthatwhichdirectlycausesmotion，and(b)ontheotherhandthatwhichisinmotion:

further，wehave(c)thatinwhichmotiontakesplace，namelytime，and(distinctfromthesethree)(d)thatfromwhichand(e)thattowhichitproceeds:foreverymotionproceedsfromsomethingandtosomething，thatwhichisdirectlyinmotionbeingdistinctfromthattowhichitisinmotionandthatfromwhichitisinmotion:forinstance，wemaytakethethreethings"wood"，"hot"，and"cold"，ofwhichthefirstisthatwhichisinmotion，thesecondisthattowhichthemotionproceeds，andthethirdisthatfromwhichitproceeds。Thisbeingso，itisclearthatthemotionisinthewood，notinitsform:forthemotionisneithercausednorexperiencedbytheformortheplaceorthequantity。Soweareleftwithamover，amoved，andagoalofmotion。Idonotincludethestarting-pointofmotion:foritisthegoalratherthanthestarting-pointofmotionthatgivesitsnametoaparticularprocessofchange。Thus"perishing"ischangetonot-being，thoughitisalsotruethatthatthatwhichperisheschangesfrombeing:and"becoming"ischangetobeing，thoughitisalsochangefromnot-being。

Nowadefinitionofmotionhasbeengivenabove，fromwhichitwillbeseenthateverygoalofmotion，whetheritbeaform，anaffection，oraplace，isimmovable，as，forinstance，knowledgeandheat。Here，however，adifficultymayberaised。Affections，itmaybesaid，aremotions，andwhitenessisanaffection:thustheremaybechangetoamotion。Tothiswemayreplythatitisnotwhitenessbutwhiteningthatisamotion。Herealsothesamedistinctionsaretobeobserved:agoalofmotionmaybesoaccidentally，orpartiallyandwithreferencetosomethingotherthanitself，ordirectlyandwithnoreferencetoanythingelse:forinstance，athingwhichisbecomingwhitechangesaccidentallytoanobjectofthought，thecolourbeingonlyaccidentallytheobjectofthought；itchangestocolour，becausewhiteisapartofcolour，ortoEurope，becauseAthensisapartofEurope；butitchangesessentiallytowhitecolour。Itisnowclearinwhatsenseathingisinmotionessentially，accidentally，orinrespectofsomethingotherthanitself，andinwhatsensethephrase"itselfdirectly"isusedinthecasebothofthemoverandofthemoved:anditisalsoclearthatthemotionisnotintheformbutinthatwhichisinmotion，thatistosay"themovableinactivity"。Nowaccidentalchangewemayleaveoutofaccount:foritistobefoundineverything，atanytime，andinanyrespect。

Changewhichisnotaccidentalontheotherhandisnottobefoundineverything，butonlyincontraries，inthingsintermediatecontraries，andincontradictories，asmaybeprovedbyinduction。Anintermediatemaybeastarting-pointofchange，sinceforthepurposesofthechangeitservesascontrarytoeitheroftwocontraries:fortheintermediateisinasensetheextremes。Hencewespeakoftheintermediateasinasenseacontraryrelativelytotheextremesandofeitherextremeasacontraryrelativelytotheintermediate:forinstance，thecentralnoteislowrelatively-tothehighestandhighrelativelytothelowest，andgreyislightrelativelytoblackanddarkrelativelytowhite。

Andsinceeverychangeisfromsomethingtosomething-astheworditself(metabole)indicates，implyingsomething"after"(meta)

somethingelse，thatistosaysomethingearlierandsomethinglater-thatwhichchangesmustchangeinoneoffourways:fromsubjecttosubject，fromsubjecttononsubject，fromnon-subjecttosubject，orfromnon-subjecttonon-subject，whereby"subject"Imeanwhatisaffirmativelyexpressed。Soitfollowsnecessarilyfromwhathasbeensaidabovethatthereareonlythreekindsofchange，thatfromsubjecttosubject，thatfromsubjecttonon-subject，andthatfromnon-subjecttosubject:forthefourthconceivablekind，thatfromnon-subjecttononsubject，isnotchange，asinthatcasethereisnooppositioneitherofcontrariesorofcontradictories。

Nowchangefromnon-subjecttosubject，therelationbeingthatofcontradiction，is"comingtobe"-"unqualifiedcomingtobe"whenthechangetakesplaceinanunqualifiedway，"particularcomingtobe"

whenthechangeischangeinaparticularcharacter:forinstance，achangefromnot-whitetowhiteisacomingtobeoftheparticularthing，white，whilechangefromunqualifiednot-beingtobeingiscomingtobeinanunqualifiedway，inrespectofwhichwesaythatathing"comestobe"withoutqualification，notthatit"comestobe"

someparticularthing。Changefromsubjecttonon-subjectis"perishing"-"unqualifiedperishing"whenthechangeisfrombeingtonot-being，"particularperishing"whenthechangeistotheoppositenegation，thedistinctionbeingthesameasthatmadeinthecaseofcomingtobe。

Nowtheexpression"not-being"isusedinseveralsenses:andtherecanbemotionneitherofthatwhich"isnot"inrespectoftheaffirmationornegationofapredicate，norofthatwhich"isnot"

inthesensethatitonlypotentially"is"，thatistosaytheoppositeofthatwhichactually"is"inanunqualifiedsense:foralthoughthatwhichis"not-white"or"not-good"mayneverthelessheinmotionaccidentally(forexamplethatwhichis"not-white"mightbeaman)，yetthatwhichiswithoutqualification"not-so-and-so"cannotinanysensebeinmotion:thereforeitisimpossibleforthatwhichisnottobeinmotion。Thisbeingso，itfollowsthat"becoming"

cannotbeamotion:foritisthatwhich"isnot"that"becomes"。

Forhowevertrueitmaybethatitaccidentally"becomes"，itisneverthelesscorrecttosaythatitisthatwhich"isnot"thatinanunqualifiedsense"becomes"。Andsimilarlyitisimpossibleforthatwhich"isnot"tobeatrest。

Therearethesedifficulties，then，inthewayoftheassumptionthatthatwhich"isnot"canbeinmotion:anditmaybefurtherobjectedthat，whereaseverythingwhichisinmotionisinspace，thatwhich"isnot"isnotinspace:forthenitwouldbesomewhere。

So，too，"perishing"isnotamotion:foramotionhasforitscontraryeitheranothermotionorrest，whereas"perishing"isthecontraryof"becoming"。

Since，then，everymotionisakindofchange，andthereareonlythethreekindsofchangementionedabove，andsinceofthesethreethosewhichtaketheformof"becoming"and"perishing"，thatistosaythosewhichimplyarelationofcontradiction，arenotmotions:itnecessarilyfollowsthatonlychangefromsubjecttosubjectismotion。Andeverysuchsubjectiseitheracontraryoranintermediate(foraprivationmaybeallowedtorankasacontrary)andcanbeaffirmativelyexpressed，asnaked，toothless，orblack。If，then，thecategoriesareseverallydistinguishedasBeing，Quality，Place，Time，Relation，Quantity，andActivityorPassivity，itnecessarilyfollowsthattherearethreekindsofmotion-qualitative，quantitative，andlocal。

2

InrespectofSubstancethereisnomotion，becauseSubstancehasnocontraryamongthingsthatare。NoristheremotioninrespectofRelation:foritmayhappenthatwhenonecorrelativechanges，theother，althoughthisdoesnotitselfchange，isnolongerapplicable，sothatinthesecasesthemotionisaccidental。NoristheremotioninrespectofAgentandPatient-infacttherecanneverbemotionofmoverandmoved，becausetherecannotbemotionofmotionorbecomingofbecomingoringeneralchangeofchange。

Forinthefirstplacetherearetwosensesinwhichmotionofmotionisconceivable。(1)Themotionofwhichthereismotionmightbeconceivedassubject；e。g。amanisinmotionbecausehechangesfromfairtodark。Canitbethatinthissensemotiongrowshotorcold，orchangesplace，orincreasesordecreases?Impossible:forchangeisnotasubject。Or(2)cantherebemotionofmotioninthesensethatsomeothersubjectchangesfromachangetoanothermodeofbeing，ase。g。amanchangesfromfallingilltogettingwell?Eventhisispossibleonlyinanaccidentalsense。For，whateverthesubjectmaybe，movementischangefromoneformtoanother。(Andthesameholdsgoodofbecomingandperishing，exceptthatintheseprocesseswehaveachangetoaparticularkindofopposite，whiletheother，motion，isachangetoadifferentkind。)So，ifthereistobemotionofmotion，thatwhichischangingfromhealthtosicknessmustsimultaneouslybechangingfromthisverychangetoanother。Itisclear，then，thatbythetimethatithasbecomesick，itmustalsohavechangedtowhatevermaybetheotherchangeconcerned(forthatitshouldbeatrest，thoughlogicallypossible，isexcludedbythetheory)。Moreoverthisothercanneverbeanycasualchange，butmustbeachangefromsomethingdefinitetosomeotherdefinitething。

Sointhiscaseitmustbetheoppositechange，viz。convalescence。Itisonlyaccidentallythattherecanbechangeofchange，e。g。thereisachangefromrememberingtoforgettingonlybecausethesubjectofthischangechangesatonetimetoknowledge，atanothertoignorance。

Inthesecondplace，ifthereistobechangeofchangeandbecomingofbecoming，weshallhaveaninfiniteregress。Thusifoneofaseriesofchangesistobeachangeofchange，theprecedingchangemustalsobeso:e。g。ifsimplebecomingwaseverinprocessofbecoming，thenthatwhichwasbecomingsimplebecomingwasalsoinprocessofbecoming，sothatweshouldnotyethavearrivedatwhatwasinprocessofsimplebecomingbutonlyatwhatwasalreadyinprocessofbecominginprocessofbecoming。Andthisagainwassometimeinprocessofbecoming，sothateventhenweshouldnothavearrivedatwhatwasinprocessofsimplebecoming。Andsinceinaninfiniteseriesthereisnofirstterm，heretherewillbenofirststageandthereforenofollowingstageeither。Onthishypothesis，then，nothingcanbecomeorbemovedorchange。

Thirdly，ifathingiscapableofanyparticularmotion，itisalsocapableofthecorrespondingcontrarymotionorthecorrespondingcomingtorest，andathingthatiscapableofbecomingisalsocapableofperishing:consequently，iftherebebecomingofbecoming，thatwhichisinprocessofbecomingisinprocessofperishingattheverymomentwhenithasreachedthestageofbecoming:sinceitcannotbeinprocessofperishingwhenitisjustbeginningtobecomeorafterithasceasedtobecome:forthatwhichisinprocessofperishingmustbeinexistence。

Fourthly，theremustbeasubstrateunderlyingallprocessesofbecomingandchanging。Whatcanthisbeinthepresentcase?Itiseitherthebodyorthesoulthatundergoesalteration:whatisitthatcorrespondinglybecomesmotionorbecoming?Andagainwhatisthegoaloftheirmotion?Itmustbethemotionorbecomingofsomethingfromsomethingtosomethingelse。Butinwhatsensecanthisbeso?Forthebecomingoflearningcannotbelearning:soneithercanthebecomingofbecomingbebecoming，norcanthebecomingofanyprocessbethatprocess。

Finally，sincetherearethreekindsofmotion，thesubstratumandthegoalofmotionmustbeoneorotherofthese，e。g。locomotionwillhavetobealteredortobelocallymoved。

Tosumup，then，sinceeverythingthatismovedismovedinoneofthreeways，eitheraccidentally，orpartially，oressentially，changecanchangeonlyaccidentally，ase。g。whenamanwhoisbeingrestoredtohealthrunsorlearns:andaccidentalchangewehavelongagodecidedtoleaveoutofaccount。

Since，then，motioncanbelongneithertoBeingnortoRelationnortoAgentandPatient，itremainsthattherecanbemotiononlyinrespectofQuality，Quantity，andPlace:forwitheachofthesewehaveapairofcontraries。MotioninrespectofQualityletuscallalteration，ageneraldesignationthatisusedtoincludebothcontraries:andbyQualityIdonotheremeanapropertyofsubstance(inthatsensethatwhichconstitutesaspecificdistinctionisaquality)butapassivequalityinvirtueofwhichathingissaidtobeactedonortobeincapableofbeingactedon。MotioninrespectofQuantityhasnonamethatincludesbothcontraries，butitiscalledincreaseordecreaseaccordingasoneortheotherisdesignated:thatistosaymotioninthedirectionofcompletemagnitudeisincrease，motioninthecontrarydirectionisdecrease。

MotioninrespectofPlacehasnonameeithergeneralorparticular:

butwemaydesignateitbythegeneralnameoflocomotion，thoughstrictlytheterm"locomotion"isapplicabletothingsthatchangetheirplaceonlywhentheyhavenotthepowertocometoastand，andtothingsthatdonotmovethemselveslocally。

Changewithinthesamekindfromalessertoagreaterorfromagreatertoalesserdegreeisalteration:foritismotioneitherfromacontraryortoacontrary，whetherinanunqualifiedorinaqualifiedsense:forchangetoalesserdegreeofaqualitywillbecalledchangetothecontraryofthatquality，andchangetoagreaterdegreeofaqualitywillberegardedaschangefromthecontraryofthatqualitytothequalityitself。Itmakesnodifferencewhetherthechangebequalifiedorunqualified，exceptthatintheformercasethecontrarieswillhavetobecontrarytooneanotheronlyinaqualifiedsense:andathing"spossessingaqualityinagreaterorinalesserdegreemeansthepresenceorabsenceinitofmoreorlessoftheoppositequality。Itisnowclear，then，thatthereareonlythesethreekindsofmotion。

Theterm"immovable"weapplyinthefirstplacetothatwhichisabsolutelyincapableofbeingmoved(justaswecorrespondinglyapplytheterminvisibletosound)；inthesecondplacetothatwhichismovedwithdifficultyafteralongtimeorwhosemovementisslowatthestart-infact，whatwedescribeashardtomove；andinthethirdplacetothatwhichisnaturallydesignedforandcapableofmotion，butisnotinmotionwhen，where，andasitnaturallywouldbeso。ThislastistheonlykindofimmovablethingofwhichIusetheterm"beingatrest":forrestiscontrarytomotion，sothatrestwillbenegationofmotioninthatwhichiscapableofadmittingmotion。

Theforegoingremarksaresufficienttoexplaintheessentialnatureofmotionandrest，thenumberofkindsofchange，andthedifferentvarietiesofmotion。

3

Letusnowproceedtodefinetheterms"together"and"apart"，"incontact"，"between"，"insuccession"，"contiguous"，and"continuous"，andtoshowinwhatcircumstanceseachofthesetermsisnaturallyapplicable。

Thingsaresaidtobetogetherinplacewhentheyareinoneplace(inthestrictestsenseoftheword"place")andtobeapartwhentheyareindifferentplaces。

Thingsaresaidtobeincontactwhentheirextremitiesaretogether。

Thatwhichachangingthing，ifitchangescontinuouslyinanaturalmanner，naturallyreachesbeforeitreachesthattowhichitchangeslast，isbetween。Thus"between"impliesthepresenceofatleastthreethings:forinaprocessofchangeitisthecontrarythatis"last":andathingismovedcontinuouslyifitleavesnogaporonlythesmallestpossiblegapinthematerial-notinthetime(foragapinthetimedoesnotpreventthingshavinga"between"，while，ontheotherhand，thereisnothingtopreventthehighestnotesoundingimmediatelyafterthelowest)butinthematerialinwhichthemotiontakesplace。Thisismanifestlytruenotonlyinlocalchangesbutineveryotherkindaswell。(Noweverychangeimpliesapairofopposites，andoppositesmaybeeithercontrariesorcontradictories；sincethencontradictionadmitsofnomeanterm，itisobviousthat"between"mustimplyapairofcontraries)Thatislocallycontrarywhichismostdistantinastraightline:fortheshortestlineisdefinitelylimited，andthatwhichisdefinitelylimitedconstitutesameasure。

Athingis"insuccession"whenitisafterthebeginninginpositionorinformorinsomeotherrespectinwhichitisdefinitelysoregarded，andwhenfurtherthereisnothingofthesamekindasitselfbetweenitandthattowhichitisinsuccession，e。g。alineorlinesifitisaline，aunitorunitsifitisaunit，ahouseifitisahouse(thereisnothingtopreventsomethingofadifferentkindbeingbetween)。Forthatwhichisinsuccessionisinsuccessiontoaparticularthing，andissomethingposterior:foroneisnot"insuccession"totwo，noristhefirstdayofthemonthtobesecond:ineachcasethelatteris"insuccession"totheformer。

Athingthatisinsuccessionandtouchesis"contiguous"。The"continuous"isasubdivisionofthecontiguous:thingsarecalledcontinuouswhenthetouchinglimitsofeachbecomeoneandthesameandare，asthewordimplies，containedineachother:continuityisimpossibleiftheseextremitiesaretwo。Thisdefinitionmakesitplainthatcontinuitybelongstothingsthatnaturallyinvirtueoftheirmutualcontactformaunity。Andinwhateverwaythatwhichholdsthemtogetherisone，sotoowillthewholebeone，e。g。byarivetorglueorcontactororganicunion。

Itisobviousthatoftheseterms"insuccession"isfirstinorderofanalysis:forthatwhichtouchesisnecessarilyinsuccession，butnoteverythingthatisinsuccessiontouches:andsosuccessionisapropertyofthingspriorindefinition，e。g。

numbers，whilecontactisnot。Andifthereiscontinuitythereisnecessarilycontact，butifthereiscontact，thatalonedoesnotimplycontinuity:fortheextremitiesofthingsmaybe"together"

withoutnecessarilybeingone:buttheycannotbeonewithoutbeingnecessarilytogether。Sonaturaljunctionislastincomingtobe:fortheextremitiesmustnecessarilycomeintocontactiftheyaretobenaturallyjoined:butthingsthatareincontactarenotallnaturallyjoined，whilethereisnocontactclearlythereisnonaturaljunctioneither。Hence，ifassomesay"point"and"unit"haveanindependentexistenceoftheirown，itisimpossibleforthetwotobeidentical:forpointscantouchwhileunitscanonlybeinsuccession。

Moreover，therecanalwaysbesomethingbetweenpoints(foralllinesareintermediatebetweenpoints)，whereasitisnotnecessarythatthereshouldpossiblybeanythingbetweenunits:fortherecanbenothingbetweenthenumbersoneandtwo。

Wehavenowdefinedwhatismeantby"together"and"apart"，"contact"，"between"and"insuccession"，"contiguous"and"continuous":andwehaveshowninwhatcircumstanceseachofthesetermsisapplicable。

4

Therearemanysensesinwhichmotionissaidtobe"one":forweusetheterm"one"inmanysenses。

Motionisonegenericallyaccordingtothedifferentcategoriestowhichitmaybeassigned:thusanylocomotionisonegenericallywithanyotherlocomotion，whereasalterationisdifferentgenericallyfromlocomotion。

Motionisonespecificallywhenbesidesbeingonegenericallyitalsotakesplaceinaspeciesincapableofsubdivision:e。g。colourhasspecificdifferences:thereforeblackeningandwhiteningdifferspecifically；butatalleventseverywhiteningwillbespecificallythesamewitheveryotherwhiteningandeveryblackeningwitheveryotherblackening。Butwhiteisnotfurthersubdividedbyspecificdifferences:henceanywhiteningisspecificallyonewithanyotherwhitening。Whereithappensthatthegenusisatthesametimeaspecies，itisclearthatthemotionwilltheninasensebeonespecificallythoughnotinanunqualifiedsense:learningisanexampleofthis，knowledgebeingontheonehandaspeciesofapprehensionandontheotherhandagenusincludingthevariousknowledges。Adifficulty，however，mayberaisedastowhetheramotionisspecificallyonewhenthesamethingchangesfromthesametothesame，e。g。whenonepointchangesagainandagainfromaparticularplacetoaparticularplace:ifthismotionisspecificallyone，circularmotionwillbethesameasrectilinearmotion，androllingthesameaswalking。Butisnotthisdifficultyremovedbytheprinciplealreadylaiddownthatifthatinwhichthemotiontakesplaceisspecificallydifferent(asinthepresentinstancethecircularpathisspecificallydifferentfromthestraight)themotionitselfisalsodifferent?Wehaveexplained，then，whatismeantbysayingthatmotionisonegenericallyoronespecifically。

Motionisoneinanunqualifiedsensewhenitisoneessentiallyornumerically:andthefollowingdistinctionswillmakeclearwhatthiskindofmotionis。Therearethreeclassesofthingsinconnexionwithwhichwespeakofmotion，the"thatwhich"，the"thatinwhich"，andthe"thatduringwhich"。Imeanthattheremusthesomethingthatisinmotion，e。g。amanorgold，anditmustbeinmotioninsomething，e。g。aplaceoranaffection，andduringsomething，forallmotiontakesplaceduringatime。Ofthesethreeitisthethinginwhichthemotiontakesplacethatmakesitonegenericallyorspecifically，itisthethingmovedthatmakesthemotiononeinsubject，anditisthetimethatmakesitconsecutive:

butitisthethreetogetherthatmakeitonewithoutqualification:

toeffectthis，thatinwhichthemotiontakesplace(thespecies)

mustbeoneandincapableofsubdivision，thatduringwhichittakesplace(thetime)mustbeoneandunintermittent，andthatwhichisinmotionmustbeone-notinanaccidentalsense(i。e。itmustbeoneasthewhitethatblackensisoneorCoriscuswhowalksisone，notintheaccidentalsenseinwhichCoriscusandwhitemaybeone)，normerelyinvirtueofcommunityofnature(fortheremightbeacaseoftwomenbeingrestoredtohealthatthesametimeinthesameway，e。g。frominflammationoftheeye，yetthismotionisnotreallyone，butonlyspecificallyone)。

Suppose，however，thatSocratesundergoesanalterationspecificallythesamebutatonetimeandagainatanother:inthiscaseifitispossibleforthatwhichceasedtobeagaintocomeintobeingandremainnumericallythesame，thenthismotiontoowillbeone:

otherwiseitwillbethesamebutnotone。Andakintothisdifficultythereisanother；viz。ishealthone?andgenerallyarethestatesandaffectionsinbodiesseverallyoneinessencealthough(asisclear)

thethingsthatcontainthemareobviouslyinmotionandinflux?Thusifaperson"shealthatdaybreakandatthepresentmomentisoneandthesame，whyshouldnotthishealthbenumericallyonewiththatwhichherecoversafteraninterval?Thesameargumentappliesineachcase。Thereis，however，wemayanswer，thisdifference:thatifthestatesaretwothenitfollowssimplyfromthisfactthattheactivitiesmustalsoinpointofnumberbetwo(foronlythatwhichisnumericallyonecangiverisetoanactivitythatisnumericallyone)，butifthestateisone，thisisnotinitselfenoughtomakeusregardtheactivityalsoasone:forwhenamanceaseswalking，thewalkingnolongeris，butitwillagainbeifhebeginstowalkagain。

But，bethisasitmay，ifintheaboveinstancethehealthisoneandthesame，thenitmustbepossibleforthatwhichisoneandthesametocometobeandtoceasetobemanytimes。However，thesedifficultieslieoutsideourpresentinquiry。

Sinceeverymotioniscontinuous，amotionthatisoneinanunqualifiedsensemust(sinceeverymotionisdivisible)becontinuous，andacontinuousmotionmustbeone。Therewillnotbecontinuitybetweenanymotionandanyotherindiscriminatelyanymorethanthereisbetweenanytwothingschosenatrandominanyothersphere:therecanbecontinuityonlywhentheextremitiesofthetwothingsareone。Nowsomethingshavenoextremitiesatall:andtheextremitiesofothersdifferspecificallyalthoughwegivethemthesamenameof"end":howshoulde。g。the"end"ofalineandthe"end"ofwalkingtouchorcometobeone?Motionsthatarenotthesameeitherspecificallyorgenericallymay，itistrue，beconsecutive(e。g。amanmayrunandthenatoncefallillofafever)，andagain，inthetorch-racewehaveconsecutivebutnotcontinuouslocomotion:foraccordingtoourdefinitiontherecanbecontinuityonlywhentheendsofthetwothingsareone。Hencemotionsmaybeconsecutiveorsuccessiveinvirtueofthetimebeingcontinuous，buttherecanbecontinuityonlyinvirtueofthemotionsthemselvesbeingcontinuous，thatiswhentheendofeachisonewiththeendoftheother。Motion，therefore，thatisinanunqualifiedsensecontinuousandonemustbespecificallythesame，ofonething，andinonetime。Unityisrequiredinrespectoftimeinorderthattheremaybenointervalofimmobility，forwherethereisintermissionofmotiontheremustberest，andamotionthatincludesintervalsofrestwillbenotonebutmany，sothatamotionthatisinterruptedbystationarinessisnotoneorcontinuous，anditissointerruptedifthereisanintervaloftime。Andthoughofamotionthatisnotspecificallyone(evenifthetimeisunintermittent)thetimeisone，themotionisspecificallydifferent，andsocannotreallybeone，formotionthatisonemustbespecificallyone，thoughmotionthatisspecificallyoneisnotnecessarilyoneinanunqualifiedsense。Wehavenowexplainedwhatwemeanwhenwecallamotiononewithoutqualification。

Further，amotionisalsosaidtobeonegenerically，specifically，oressentiallywhenitiscomplete，justasinothercasescompletenessandwholenessarecharacteristicsofwhatisone:

andsometimesamotionevenifincompleteissaidtobeone，providedonlythatitiscontinuous。

Andbesidesthecasesalreadymentionedthereisanotherinwhichamotionissaidtobeone，viz。whenitisregular:forinasenseamotionthatisirregularisnotregardedasone，thattitlebelongingrathertothatwhichisregular，asastraightlineisregular，theirregularbeingassuchdivisible。Butthedifferencewouldseemtobeoneofdegree。Ineverykindofmotionwemayhaveregularityorirregularity:thustheremayberegularalteration，andlocomotioninaregularpath，e。g。inacircleoronastraightline，anditisthesamewithregardtoincreaseanddecrease。Thedifferencethatmakesamotionirregularissometimestobefoundinitspath:thusamotioncannotberegularifitspathisanirregularmagnitude，e。g。abrokenline，aspiral，oranyothermagnitudethatisnotsuchthatanypartofittakenatrandomfitsontoanyotherthatmaybechosen。Sometimesitisfoundneitherintheplacenorinthetimenorinthegoalbutinthemannerofthemotion:forinsomecasesthemotionisdifferentiatedbyquicknessandslowness:thusifitsvelocityisuniformamotionisregular，ifnotitisirregular。Soquicknessandslownessarenotspeciesofmotionnordotheyconstitutespecificdifferencesofmotion，becausethisdistinctionoccursinconnexionwithallthedistinctspeciesofmotion。Thesameistrueofheavinessandlightnesswhentheyrefertothesamething:e。g。theydonotspecificallydistinguishearthfromitselforfirefromitself。Irregularmotion，therefore，whileinvirtueofbeingcontinuousitisone，issoinalesserdegree，asisthecasewithlocomotioninabrokenline:andalesserdegreeofsomethingalwaysmeansanadmixtureofitscontrary。Andsinceeverymotionthatisonecanbebothregularandirregular，motionsthatareconsecutivebutnotspecificallythesamecannotbeoneandcontinuous:forhowshouldamotioncomposedofalterationandlocomotionberegular?Ifamotionistoberegularitspartsoughttofitoneanother。

5

Wehavefurthertodeterminewhatmotionsarecontrarytoeachother，andtodeterminesimilarlyhowitiswithrest。Andwehavefirsttodecidewhethercontrarymotionsaremotionsrespectivelyfromandtothesamething，e。g。amotionfromhealthandamotiontohealth(wheretheopposition，itwouldseem，isofthesamekindasthatbetweencomingtobeandceasingtobe)；ormotionsrespectivelyfromcontraries，e。g。amotionfromhealthandamotionfromdisease；ormotionsrespectivelytocontraries，e。g。amotiontohealthandamotiontodisease；ormotionsrespectivelyfromacontraryandtotheoppositecontrary，e。g。amotionfromhealthandamotiontodisease；ormotionsrespectivelyfromacontrarytotheoppositecontraryandfromthelattertotheformer，e。g。amotionfromhealthtodiseaseandamotionfromdiseasetohealth:formotionsmustbecontrarytooneanotherinoneormoreoftheseways，asthereisnootherwayinwhichtheycanbeopposed。

Nowmotionsrespectivelyfromacontraryandtotheoppositecontrary，e。g。amotionfromhealthandamotiontodisease，arenotcontrarymotions:fortheyareoneandthesame。(Yettheiressenceisnotthesame，justaschangingfromhealthisdifferentfromchangingtodisease。)Noraremotionrespectivelyfromacontraryandfromtheoppositecontrarycontrarymotions，foramotionfromacontraryisatthesametimeamotiontoacontraryortoanintermediate(ofthis，however，weshallspeaklater)，butchangingtoacontraryratherthanchangingfromacontrarywouldseemtobethecauseofthecontrarietyofmotions，thelatterbeingtheloss，theformerthegain，ofcontrariness。Moreover，eachseveralmotiontakesitsnameratherfromthegoalthanfromthestarting-pointofchange，e。g。motiontohealthwecallconvalescence，motiontodiseasesickening。Thusweareleftwithmotionsrespectivelytocontraries，andmotionsrespectivelytocontrariesfromtheoppositecontraries。

Nowitwouldseemthatmotionstocontrariesareatthesametimemotionsfromcontraries(thoughtheiressencemaynotbethesame；"tohealth"isdistinct，Imean，from"fromdisease"，and"fromhealth"

from"todisease")。

Sincethenchangediffersfrommotion(motionbeingchangefromaparticularsubjecttoaparticularsubject)，itfollowsthatcontrarymotionsaremotionsrespectivelyfromacontrarytotheoppositecontraryandfromthelattertotheformer，e。g。amotionfromhealthtodiseaseandamotionfromdiseasetohealth。

Moreover，theconsiderationofparticularexampleswillalsoshowwhatkindsofprocessesaregenerallyrecognizedascontrary:thusfallingillisregardedascontrarytorecoveringone"shealth，theseprocesseshavingcontrarygoals，andbeingtaughtascontrarytobeingledintoerrorbyanother，itbeingpossibletoacquireerror，likeknowledge，eitherbyone"sownagencyorbythatofanother。

Similarlywehaveupwardlocomotionanddownwardlocomotion，whicharecontrarylengthwise，locomotiontotherightandlocomotiontotheleft，whicharecontrarybreadthwise，andforwardlocomotionandbackwardlocomotion，whichtooarecontraries。Ontheotherhand，aprocesssimplytoacontrary，e。g。thatdenotedbytheexpression"becomingwhite"，wherenostarting-pointisspecified，isachangebutnotamotion。Andinallcasesofathingthathasnocontrarywehaveascontrarieschangefromandchangetothesamething。Thuscomingtobeiscontrarytoceasingtobe，andlosingtogaining。

Butthesearechangesandnotmotions。Andwhereverapairofcontrariesadmitofanintermediate，motionstothatintermediatemustbeheldtobeinasensemotionstooneorotherofthecontraries:

fortheintermediateservesasacontraryforthepurposesofthemotion，inwhicheverdirectionthechangemaybe，e。g。greyinamotionfromgreytowhitetakestheplaceofblackasstarting-point，inamotionfromwhitetogreyittakestheplaceofblackasgoal，andinamotionfromblacktogreyittakestheplaceofwhiteasgoal:forthemiddleisopposedinasensetoeitheroftheextremes，ashasbeensaidabove。Thusweseethattwomotionsarecontrarytoeachotheronlywhenoneisamotionfromacontrarytotheoppositecontraryandtheotherisamotionfromthelattertotheformer。

6

Butsinceamotionappearstohavecontrarytoitnotonlyanothermotionbutalsoastateofrest，wemustdeterminehowthisisso。A

motionhasforitscontraryinthestrictsenseofthetermanothermotion，butitalsohasforanoppositeastateofrest(forrestistheprivationofmotionandtheprivationofanythingmaybecalleditscontrary)，andmotionofonekindhasforitsoppositerestofthatkind，e。g。localmotionhaslocalrest。Thisstatement，however，needsfurtherqualification:thereremainsthequestion，istheoppositeofremainingataparticularplacemotionfromormotiontothatplace?Itissurelyclearthatsincetherearetwosubjectsbetweenwhichmotiontakesplace，motionfromoneofthese(A)toitscontrary(B)hasforitsoppositeremaininginAwhilethereversemotionhasforitsoppositeremaininginB。Atthesametimethesetwoarealsocontrarytoeachother:foritwouldbeabsurdtosupposethattherearecontrarymotionsandnotoppositestatesofrest。Statesofrestincontrariesareopposed。Totakeanexample，astateofrestinhealthis(1)contrarytoastateofrestindisease，and(2)themotiontowhichitiscontraryisthatfromhealthtodisease。For(2)itwouldbeabsurdthatitscontrarymotionshouldbethatfromdiseasetohealth，sincemotiontothatinwhichathingisatrestisratheracomingtorest，thecomingtorestbeingfoundtocomeintobeingsimultaneouslywiththemotion；andoneofthesetwomotionsitmustbe。And(1)restinwhitenessisofcoursenotcontrarytorestinhealth。

Ofallthingsthathavenocontrariesthereareoppositechanges(viz。changefromthethingandchangetothething，e。g。changefrombeingandchangetobeing)，butnomotion。So，too，ofsuchthingsthereisnoremainingthoughthereisabsenceofchange。Shouldtherebeaparticularsubject，absenceofchangeinitsbeingwillbecontrarytoabsenceofchangeinitsnot-being。Andhereadifficultymayberaised:ifnot-beingisnotaparticularsomething，whatisit，itmaybeasked，thatiscontrarytoabsenceofchangeinathing"sbeing?andisthisabsenceofchangeastateofrest?Ifitis，theneitheritisnottruethateverystateofrestiscontrarytoamotionorelsecomingtobeandceasingtobearemotion。Itisclearthenthat，sinceweexcludethesefromamongmotions，wemustnotsaythatthisabsenceofchangeisastateofrest:wemustsaythatitissimilartoastateofrestandcallitabsenceofchange。Anditwillhaveforitscontraryeithernothingorabsenceofchangeinthething"snot-being，ortheceasingtobeofthething:forsuchceasingtobeischangefromitandthething"scomingtobeischangetoit。

Again，afurtherdifficultymayberaised。Howisit，itmaybeasked，thatwhereasinlocalchangebothremainingandmovingmaybenaturalorunnatural，intheotherchangesthisisnotso?e。g。

alterationisnotnownaturalandnowunnatural，forconvalescenceisnomorenaturalorunnaturalthanfallingill，whiteningnomorenaturalorunnaturalthanblackening；so，too，withincreaseanddecrease:thesearenotcontrarytoeachotherinthesensethateitherofthemisnaturalwhiletheotherisunnatural，norisoneincreasecontrarytoanotherinthissense；andthesameaccountmaybegivenofbecomingandperishing:itisnottruethatbecomingisnaturalandperishingunnatural(forgrowingoldisnatural)，nordoweobserveonebecomingtobenaturalandanotherunnatural。Weanswerthatifwhathappensunderviolenceisunnatural，thenviolentperishingisunnaturalandassuchcontrarytonaturalperishing。

Aretherethenalsosomebecomingsthatareviolentandnottheresultofnaturalnecessity，andarethereforecontrarytonaturalbecomings，andviolentincreasesanddecreases，e。g。therapidgrowthtomaturityofprofligatesandtherapidripeningofseedsevenwhennotpackedcloseintheearth?Andhowisitwithalterations?Surelyjustthesame:wemaysaythatsomealterationsareviolentwhileothersarenatural，e。g。patientsalternaturallyorunnaturallyaccordingastheythrowofffeversonthecriticaldaysornot。But，itmaybeobjected，thenweshallhaveperishingscontrarytooneanother，nottobecoming。Certainly:andwhyshouldnotthisinasensebeso?Thusitissoifoneperishingispleasantandanotherpainful:andsooneperishingwillbecontrarytoanothernotinanunqualifiedsense，butinsofarasonehasthisqualityandtheotherthat。

Nowmotionsandstatesofrestuniversallyexhibitcontrarietyinthemannerdescribedabove，e。g。upwardmotionandrestabovearerespectivelycontrarytodownwardmotionandrestbelow，thesebeinginstancesoflocalcontrariety；andupwardlocomotionbelongsnaturallytofireanddownwardtoearth，i。e。thelocomotionsofthetwoarecontrarytoeachother。Andagain，firemovesupnaturallyanddownunnaturally:anditsnaturalmotioniscertainlycontrarytoitsunnaturalmotion。Similarlywithremaining:remainingaboveiscontrarytomotionfromabovedownwards，andtoearththisremainingcomesunnaturally，thismotionnaturally。Sotheunnaturalremainingofathingiscontrarytoitsnaturalmotion，justaswefindasimilarcontrarietyinthemotionofthesamething:oneofitsmotions，theupwardorthedownward，willbenatural，theotherunnatural。

Here，however，thequestionarises，haseverystateofrestthatisnotpermanentabecoming，andisthisbecomingacomingtoastandstill?Ifso，theremustbeabecomingofthatwhichisatrestunnaturally，e。g。ofearthatrestabove:andthereforethisearthduringthetimethatitwasbeingcarriedviolentlyupwardwascomingtoastandstill。Butwhereasthevelocityofthatwhichcomestoastandstillseemsalwaystoincrease，thevelocityofthatwhichiscarriedviolentlyseemsalwaystodecrease:soitwillheinastateofrestwithouthavingbecomeso。Moreover"comingtoastandstill"isgenerallyrecognizedtobeidenticaloratleastconcomitantwiththelocomotionofathingtoitsproperplace。

Thereisalsoanotherdifficultyinvolvedintheviewthatremaininginaparticularplaceiscontrarytomotionfromthatplace。Forwhenathingismovingfromordiscardingsomething，itstillappearstohavethatwhichisbeingdiscarded，sothatifastateofrestisitselfcontrarytothemotionfromthestateofresttoitscontrary，thecontrariesrestandmotionwillbesimultaneouslypredicableofthesamething。Maywenotsay，however，thatinsofarasthethingisstillstationaryitisinastateofrestinaqualifiedsense?For，infact，wheneverathingisinmotion，partofitisatthestarting-pointwhilepartisatthegoaltowhichitischanging:andconsequentlyamotionfindsitstruecontraryratherinanothermotionthaninastateofrest。

Withregardtomotionandrest，then，wehavenowexplainedinwhatsenseeachofthemisoneandunderwhatconditionstheyexhibitcontrariety。

[Withregardtocomingtoastandstillthequestionmayberaisedwhetherthereisanoppositestateofresttounnaturalaswellastonaturalmotions。Itwouldbeabsurdifthiswerenotthecase:

forathingmayremainstillmerelyunderviolence:thusweshallhaveathingbeinginanon-permanentstateofrestwithouthavingbecomeso。Butitisclearthatitmustbethecase:forjustasthereisunnaturalmotion，so，too，athingmaybeinanunnaturalstateofrest。Further，somethingshaveanaturalandanunnaturalmotion，e。g。firehasanaturalupwardmotionandanunnaturaldownwardmotion:isit，then，thisunnaturaldownwardmotionorisitthenaturaldownwardmotionofearththatiscontrarytothenaturalupwardmotion?Surelyitisclearthatbotharecontrarytoitthoughnotinthesamesense:thenaturalmotionofearthiscontraryinasmuchasthemotionoffireisalsonatural，whereastheupwardmotionoffireasbeingnaturaliscontrarytothedownwardmotionoffireasbeingunnatural。Thesameistrueofthecorrespondingcasesofremaining。Buttherewouldseemtobeasenseinwhichastateofrestandamotionareopposites。]

BookVI

1

Nowiftheterms"continuous"，"incontact"，and"insuccession"areunderstoodasdefinedabovethingsbeing"continuous"iftheirextremitiesareone，"incontact"iftheirextremitiesaretogether，and"insuccession"ifthereisnothingoftheirownkindintermediatebetweenthem-nothingthatiscontinuouscanbecomposed"ofindivisibles":e。g。alinecannotbecomposedofpoints，thelinebeingcontinuousandthepointindivisible。Fortheextremitiesoftwopointscanneitherbeone(sinceofanindivisibletherecanbenoextremityasdistinctfromsomeotherpart)nortogether(sincethatwhichhasnopartscanhavenoextremity，theextremityandthethingofwhichitistheextremitybeingdistinct)。

Moreover，ifthatwhichiscontinuousiscomposedofpoints，thesepointsmustbeeithercontinuousorincontactwithoneanother:andthesamereasoningappliesinthecaseofallindivisibles。Nowforthereasongivenabovetheycannotbecontinuous:andonethingcanbeincontactwithanotheronlyifwholeisincontactwithwholeorpartwithpartorpartwithwhole。Butsinceindivisibleshavenoparts，theymustbeincontactwithoneanotheraswholewithwhole。Andiftheyareincontactwithoneanotheraswholewithwhole，theywillnotbecontinuous:forthatwhichiscontinuoushasdistinctparts:

andthesepartsintowhichitisdivisiblearedifferentinthisway，i。e。spatiallyseparate。

Nor，again，canapointbeinsuccessiontoapointoramomenttoamomentinsuchawaythatlengthcanbecomposedofpointsortimeofmoments:forthingsareinsuccessionifthereisnothingoftheirownkindintermediatebetweenthem，whereasthatwhichisintermediatebetweenpointsisalwaysalineandthatwhichisintermediatebetweenmomentsisalwaysaperiodoftime。

Again，iflengthandtimecouldthusbecomposedofindivisibles，theycouldbedividedintoindivisibles，sinceeachisdivisibleintothepartsofwhichitiscomposed。But，aswesaw，nocontinuousthingisdivisibleintothingswithoutparts。Norcantherebeanythingofanyotherkindintermediatebetweenthepartsorbetweenthemoments:foriftherecouldbeanysuchthingitisclearthatitmustbeeitherindivisibleordivisible，andifitisdivisible，itmustbedivisibleeitherintoindivisiblesorintodivisiblesthatareinfinitelydivisible，inwhichcaseitiscontinuous。

Moreover，itisplainthateverythingcontinuousisdivisibleintodivisiblesthatareinfinitelydivisible:forifitweredivisibleintoindivisibles，weshouldhaveanindivisibleincontactwithanindivisible，sincetheextremitiesofthingsthatarecontinuouswithoneanotherareoneandareincontact。

Thesamereasoningappliesequallytomagnitude，totime，andtomotion:eitherallofthesearecomposedofindivisiblesandaredivisibleintoindivisibles，ornone。Thismaybemadeclearasfollows。Ifamagnitudeiscomposedofindivisibles，themotionoverthatmagnitudemustbecomposedofcorrespondingindivisiblemotions:e。g。ifthemagnitudeABGiscomposedoftheindivisiblesA，B，G，eachcorrespondingpartofthemotionDEZofOoverABGisindivisible。Therefore，sincewherethereismotiontheremustbesomethingthatisinmotion，andwherethereissomethinginmotiontheremustbemotion，thereforethebeing-movedwillalsobecomposedofindivisibles。SoOtraversedAwhenitsmotionwasD，B

whenitsmotionwasE，andGsimilarlywhenitsmotionwasZ。Nowathingthatisinmotionfromoneplacetoanothercannotatthemomentwhenitwasinmotionbothbeinmotionandatthesametimehavecompleteditsmotionattheplacetowhichitwasinmotion:e。g。ifamaniswalkingtoThebes，hecannotbewalkingtoThebesandatthesametimehavecompletedhiswalktoThebes:and，aswesaw，O

traversesathepartlesssectionAinvirtueofthepresenceofthemotionD。Consequently，ifOactuallypassedthroughAafterbeinginprocessofpassingthrough，themotionmustbedivisible:foratthetimewhenOwaspassingthrough，itneitherwasatrestnorhadcompleteditspassagebutwasinanintermediatestate:whileifitispassingthroughandhascompleteditspassageatthesamemoment，thenthatwhichiswalkingwillatthemomentwhenitiswalkinghavecompleteditswalkandwillbeintheplacetowhichitiswalking；

thatistosay，itwillhavecompleteditsmotionattheplacetowhichitisinmotion。AndifathingisinmotionoverthewholeKBGanditsmotionisthethreeD，E，andZ，andifitisnotinmotionatalloverthepartlesssectionAbuthascompleteditsmotionoverit，thenthemotionwillconsistnotofmotionsbutofstarts，andwilltakeplacebyathing"shavingcompletedamotionwithoutbeinginmotion:foronthisassumptionithascompleteditspassagethroughAwithoutpassingthroughit。Soitwillbepossibleforathingtohavecompletedawalkwithouteverwalking:foronthisassumptionithascompletedawalkoveraparticulardistancewithoutwalkingoverthatdistance。Since，then，everythingmustbeeitheratrestorinmotion，andOisthereforeatrestineachofthesectionsA，B，andG，itfollowsthatathingcanbecontinuouslyatrestandatthesametimeinmotion:for，aswesaw，OisinmotionoverthewholeABGandatrestinanypart(andconsequentlyinthewhole)ofit。Moreover，iftheindivisiblescomposingDEZaremotions，itwouldbepossibleforathinginspiteofthepresenceinitofmotiontobenotinmotionbutatrest，whileiftheyarenotmotions，itwouldbepossibleformotiontobecomposedofsomethingotherthanmotions。

Andiflengthandmotionarethusindivisible，itisneithermorenorlessnecessarythattimealsobesimilarlyindivisible，thatistosaybecomposedofindivisiblemoments:forifthewholedistanceisdivisibleandanequalvelocitywillcauseathingtopassthroughlessofitinlesstime，thetimemustalsobedivisible，andconversely，ifthetimeinwhichathingiscarriedoverthesectionA

isdivisible，thissectionAmustalsobedivisible。

2

Andsinceeverymagnitudeisdivisibleintomagnitudes-forwehaveshownthatitisimpossibleforanythingcontinuoustobecomposedofindivisibleparts，andeverymagnitudeiscontinuous-itnecessarilyfollowsthatthequickeroftwothingstraversesagreatermagnitudeinanequaltime，anequalmagnitudeinlesstime，andagreatermagnitudeinlesstime，inconformitywiththedefinitionsometimesgivenof"thequicker"。SupposethatAisquickerthanB。Nowsinceoftwothingsthatwhichchangessoonerisquicker，inthetimeZH，inwhichAhaschangedfromGtoD，BwillnotyethavearrivedatD

butwillbeshortofit:sothatinanequaltimethequickerwillpassoveragreatermagnitude。Morethanthis，itwillpassoveragreatermagnitudeinlesstime:forinthetimeinwhichAhasarrivedatD，Bbeingtheslowerhasarrived，letussay，atE。ThensinceA

hasoccupiedthewholetimeZHinarrivingatD，willhavearrivedatOinlesstimethanthis，sayZK。NowthemagnitudeGOthatAhaspassedoverisgreaterthanthemagnitudeGE，andthetimeZKislessthanthewholetimeZH:sothatthequickerwillpassoveragreatermagnitudeinlesstime。Andfromthisitisalsoclearthatthequickerwillpassoveranequalmagnitudeinlesstimethantheslower。Forsinceitpassesoverthegreatermagnitudeinlesstimethantheslower，and(regardedbyitself)passesoverLMthegreaterinmoretimethanLXthelesser，thetimePRhinwhichitpassesoverLMwillbemorethanthetimePS，whichitpassesoverLX:sothat，thetimePRhbeinglessthanthetimePChinwhichtheslowerpassesoverLX，thetimePSwillalsobelessthanthetimePX:foritislessthanthetimePRh，andthatwhichislessthansomethingelsethatislessthanathingisalsoitselflessthanthatthing。

Henceitfollowsthatthequickerwilltraverseanequalmagnitudeinlesstimethantheslower。Again，sincethemotionofanythingmustalwaysoccupyeitheranequaltimeorlessormoretimeincomparisonwiththatofanotherthing，andsince，whereasathingisslowerifitsmotionoccupiesmoretimeandofequalvelocityifitsmotionoccupiesanequaltime，thequickerisneitherofequalvelocitynorslower，itfollowsthatthemotionofthequickercanoccupyneitheranequaltimenormoretime。Itcanonlybe，then，thatitoccupieslesstime，andthuswegetthenecessaryconsequencethatthequickerwillpassoveranequalmagnitude(aswellasagreater)inlesstimethantheslower。

Andsinceeverymotionisintimeandamotionmayoccupyanytime，andthemotionofeverythingthatisinmotionmaybeeitherquickerorslower，bothquickermotionandslowermotionmayoccupyanytime:andthisbeingso，itnecessarilyfollowsthattimealsoiscontinuous。BycontinuousImeanthatwhichisdivisibleintodivisiblesthatareinfinitelydivisible:andifwetakethisasthedefinitionofcontinuous，itfollowsnecessarilythattimeiscontinuous。Forsinceithasbeenshownthatthequickerwillpassoveranequalmagnitudeinlesstimethantheslower，supposethatA

isquickerandBslower，andthattheslowerhastraversedthemagnitudeGDinthetimeZH。Nowitisclearthatthequickerwilltraversethesamemagnitudeinlesstimethanthis:letussayinthetimeZO。Again，sincethequickerhaspassedoverthewholeDinthetimeZO，theslowerwillinthesametimepassoverGK，say，whichislessthanGD。AndsinceB，theslower，haspassedoverGKinthetimeZO，thequickerwillpassoveritinlesstime:sothatthetimeZOwillagainbedivided。AndifthisisdividedthemagnitudeGK

willalsobedividedjustasGDwas:andagain，ifthemagnitudeisdivided，thetimewillalsobedivided。Andwecancarryonthisprocessforever，takingtheslowerafterthequickerandthequickerafterthesloweralternately，andusingwhathasbeendemonstratedateachstageasanewpointofdeparture:forthequickerwilldividethetimeandtheslowerwilldividethelength。

If，then，thisalternationalwaysholdsgood，andateveryturninvolvesadivision，itisevidentthatalltimemustbecontinuous。

Andatthesametimeitisclearthatallmagnitudeisalsocontinuous；forthedivisionsofwhichtimeandmagnituderespectivelyaresusceptiblearethesameandequal。

Moreover，thecurrentpopularargumentsmakeitplainthat，iftimeiscontinuous，magnitudeiscontinuousalso，inasmuchasathingassesoverhalfagivenmagnitudeinhalfthetimetakentocoverthewhole:infactwithoutqualificationitpassesoveralessmagnitudeinlesstime；forthedivisionsoftimeandofmagnitudewillbethesame。Andifeitherisinfinite，soistheother，andtheoneissointhesamewayastheother；i。e。iftimeisinfiniteinrespectofitsextremities，lengthisalsoinfiniteinrespectofitsextremities:iftimeisinfiniteinrespectofdivisibility，lengthisalsoinfiniteinrespectofdivisibility:andiftimeisinfiniteinbothrespects，magnitudeisalsoinfiniteinbothrespects。

HenceZeno"sargumentmakesafalseassumptioninassertingthatitisimpossibleforathingtopassoverorseverallytocomeincontactwithinfinitethingsinafinitetime。Fortherearetwosensesinwhichlengthandtimeandgenerallyanythingcontinuousarecalled"infinite":theyarecalledsoeitherinrespectofdivisibilityorinrespectoftheirextremities。Sowhileathinginafinitetimecannotcomeincontactwiththingsquantitativelyinfinite，itcancomeincontactwiththingsinfiniteinrespectofdivisibility:forinthissensethetimeitselfisalsoinfinite:

andsowefindthatthetimeoccupiedbythepassageovertheinfiniteisnotafinitebutaninfinitetime，andthecontactwiththeinfinitesismadebymeansofmomentsnotfinitebutinfiniteinnumber。

Thepassageovertheinfinite，then，cannotoccupyafinitetime，andthepassageoverthefinitecannotoccupyaninfinitetime:ifthetimeisinfinitethemagnitudemustbeinfinitealso，andifthemagnitudeisinfinite，soalsoisthetime。Thismaybeshownasfollows。LetABbeafinitemagnitude，andletussupposethatitistraversedininfinitetimeG，andletafiniteperiodGDofthetimebetaken。Nowinthisperiodthethinginmotionwillpassoveracertainsegmentofthemagnitude:letBEbethesegmentthatithasthuspassedover。(ThiswillbeeitheranexactmeasureofABorlessorgreaterthananexactmeasure:itmakesnodifferencewhichitis。)Then，sinceamagnitudeequaltoBEwillalwaysbepassedoverinanequaltime，andBEmeasuresthewholemagnitude，thewholetimeoccupiedinpassingoverABwillbefinite:foritwillbedivisibleintoperiodsequalinnumbertothesegmentsintowhichthemagnitudeisdivisible。Moreover，ifitisthecasethatinfinitetimeisnotoccupiedinpassingovereverymagnitude，butitispossibletoassoversomemagnitude，sayBE，inafinitetime，andifthisBE

measuresthewholeofwhichitisapart，andifanequalmagnitudeispassedoverinanequaltime，thenitfollowsthatthetimelikethemagnitudeisfinite。ThatinfinitetimewillnotbeoccupiedinpassingoverBEisevidentifthetimebetakenaslimitedinonedirection:forasthepartwillbepassedoverinlesstimethanthewhole，thetimeoccupiedintraversingthispartmustbefinite，thelimitinonedirectionbeinggiven。Thesamereasoningwillalsoshowthefalsityoftheassumptionthatinfinitelengthcanbetraversedinafinitetime。Itisevident，then，fromwhathasbeensaidthatneitheralinenorasurfacenorinfactanythingcontinuouscanbeindivisible。

Thisconclusionfollowsnotonlyfromthepresentargumentbutfromtheconsiderationthattheoppositeassumptionimpliesthedivisibilityoftheindivisible。Forsincethedistinctionofquickerandslowermayapplytomotionsoccupyinganyperiodoftimeandinanequaltimethequickerpassesoveragreaterlength，itmayhappenthatitwillpassoveralengthtwice，oroneandahalftimes，asgreatasthatpassedoverbytheslower:fortheirrespectivevelocitiesmaystandtooneanotherinthisproportion。

Suppose，then，thatthequickerhasinthesametimebeencarriedoveralengthoneandahalftimesasgreatasthattraversedbytheslower，andthattherespectivemagnitudesaredivided，thatofthequicker，themagnitudeABGD，intothreeindivisibles，andthatoftheslowerintothetwoindivisiblesEZ，ZH。Thenthetimemayalsobedividedintothreeindivisibles，foranequalmagnitudewillbepassedoverinanequaltime。SupposethenthatitisthusdividedintoKL，LM，MN。Again，sinceinthesametimetheslowerhasbeencarriedoverEZ，ZH，thetimemayalsobesimilarlydividedintotwo。Thustheindivisiblewillbedivisible，andthatwhichhasnopartswillbepassedovernotinanindivisiblebutinagreatertime。Itisevident，therefore，thatnothingcontinuousiswithoutparts。

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Thepresentalsoisnecessarilyindivisible-thepresent，thatis，notinthesenseinwhichthewordisappliedtoonethinginvirtueofanother，butinitsproperandprimarysense；inwhichsenseitisinherentinalltime。Forthepresentissomethingthatisanextremityofthepast(nopartofthefuturebeingonthissideofit)

andalsoofthefuture(nopartofthepastbeingontheothersideofit):itis，aswehavesaid，alimitofboth。Andifitisonceshownthatitisessentiallyofthischaracterandoneandthesame，itwillatoncebeevidentalsothatitisindivisible。

Nowthepresentthatistheextremityofbothtimesmustbeoneandthesame:forifeachextremityweredifferent，theonecouldnotbeinsuccessiontotheother，becausenothingcontinuouscanbecomposedofthingshavingnoparts:andiftheoneisapartfromtheother，therewillbetimeintermediatebetweenthem，becauseeverythingcontinuousissuchthatthereissomethingintermediatebetweenitslimitsanddescribedbythesamenameasitself。Butiftheintermediatethingistime，itwillbedivisible:foralltimehasbeenshowntobedivisible。Thusonthisassumptionthepresentisdivisible。Butifthepresentisdivisible，therewillbepartofthepastinthefutureandpartofthefutureinthepast:forpasttimewillbemarkedofffromfuturetimeattheactualpointofdivision。Alsothepresentwillbeapresentnotinthepropersensebutinvirtueofsomethingelse:forthedivisionwhichyieldsitwillnotbeadivisionproper。Furthermore，therewillbeapartofthepresentthatispastandapartthatisfuture，anditwillnotalwaysbethesamepartthatispastorfuture:infactoneandthesamepresentwillnotbesimultaneous:forthetimemaybedividedatmanypoints。If，therefore，thepresentcannotpossiblyhavethesecharacteristics，itfollowsthatitmustbethesamepresentthatbelongstoeachofthetwotimes。Butifthisissoitisevidentthatthepresentisalsoindivisible:forifitisdivisibleitwillbeinvolvedinthesameimplicationsasbefore。Itisclear，then，fromwhathasbeensaidthattimecontainssomethingindivisible，andthisiswhatwecallapresent。

Wewillnowshowthatnothingcanbeinmotioninapresent。Forifthisispossible，therecanbebothquickerandslowermotioninthepresent。SupposethenthatinthepresentNthequickerhastraversedthedistanceAB。Thatbeingso，theslowerwillinthesamepresenttraverseadistancelessthanAB，sayAG。ButsincetheslowerwillhaveoccupiedthewholepresentintraversingAG，thequickerwilloccupylessthanthisintraversingit。Thusweshallhaveadivisionofthepresent，whereaswefoundittobeindivisible。

Itisimpossible，therefore，foranythingtobeinmotioninapresent。

Norcananythingbeatrestinapresent:for，asweweresaying，onlycanbeatrestwhichisnaturallydesignedtobeinmotionbutisnotinmotionwhen，where，orasitwouldnaturallybeso:since，therefore，nothingisnaturallydesignedtobeinmotioninapresent，itisclearthatnothingcanbeatrestinapresenteither。

Moreover，inasmuchasitisthesamepresentthatbelongstoboththetimes，anditispossibleforathingtobeinmotionthroughoutonetimeandtobeatrestthroughouttheother，andthatwhichisinmotionoratrestforthewholeofatimewillbeinmotionoratrestasthecasemaybeinanypartofitinwhichitisnaturallydesignedtobeinmotionoratrest:thisbeingso，theassumptionthattherecanbemotionorrestinapresentwillcarrywithittheimplicationthatthesamethingcanatthesametimebeatrestandinmotion:forboththetimeshavethesameextremity，viz。thepresent。

Again，whenwesaythatathingisatrest，weimplythatitsconditioninwholeandinpartisatthetimeofspeakinguniformwithwhatitwaspreviously:butthepresentcontainsno"previously":

consequently，therecanbenorestinit。

Itfollowsthenthatthemotionofthatwhichisinmotionandtherestofthatwhichisatrestmustoccupytime。

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Further，everythingthatchangesmustbedivisible。Forsinceeverychangeisfromsomethingtosomething，andwhenathingisatthegoalofitschangeitisnolongerchanging，andwhenbothititselfandallitspartsareatthestarting-pointofitschangeitisnotchanging(forthatwhichisinwholeandinpartinanunvaryingconditionisnotinastateofchange)；itfollows，therefore，thatpartofthatwhichischangingmustbeatthestarting-pointandpartatthegoal:forasawholeitcannotbeinbothorinneither。

(Hereby"goalofchange"Imeanthatwhichcomesfirstintheprocessofchange:e。g。inaprocessofchangefromwhitethegoalinquestionwillbegrey，notblack:foritisnotnecessarythatthatthatwhichischangingshouldbeateitheroftheextremes。)Itisevident，therefore，thateverythingthatchangesmustbedivisible。

Nowmotionisdivisibleintwosenses。Inthefirstplaceitisdivisibleinvirtueofthetimethatitoccupies。Inthesecondplaceitisdivisibleaccordingtothemotionsoftheseveralpartsofthatwhichisinmotion:e。g。ifthewholeAGisinmotion，therewillbeamotionofABandamotionofBG。Thatbeingso，letDEbethemotionofthepartABandEZthemotionofthepartBG。ThenthewholeDZmustbethemotionofAG:forDZmustconstitutethemotionofAG

inasmuchasDEandEZseverallyconstitutethemotionsofeachofitsparts。Butthemotionofathingcanneverbeconstitutedbythemotionofsomethingelse:consequentlythewholemotionisthemotionofthewholemagnitude。

Again，sinceeverymotionisamotionofsomething，andthewholemotionDZisnotthemotionofeitheroftheparts(foreachofthepartsDE，EZisthemotionofoneofthepartsAB，BG)orofanythingelse(for，thewholemotionbeingthemotionofawhole，thepartsofthemotionarethemotionsofthepartsofthatwhole:

andthepartsofDZarethemotionsofAB，BGandofnothingelse:

for，aswesaw，amotionthatisonecannotbethemotionofmorethingsthanone):sincethisisso，thewholemotionwillbethemotionofthemagnitudeABG。

Again，ifthereisamotionofthewholeotherthanDZ，saythetheofeachoftheartsmaybesubtractedfromit:andthesemotionswillbeequaltoDE，EZrespectively:forthemotionofthatwhichisonemustbeone。SoifthewholemotionOImaybedividedintothemotionsoftheparts，OIwillbeequaltoDZ:ifontheotherhandthereisanyremainder，sayKI，thiswillbeamotionofnothing:

foritcanbethemotionneitherofthewholenoroftheparts(asthemotionofthatwhichisonemustbeone)norofanythingelse:foramotionthatiscontinuousmustbethemotionofthingsthatarecontinuous。AndthesameresultfollowsifthedivisionofOI

revealsasurplusonthesideofthemotionsoftheparts。

Consequently，ifthisisimpossible，thewholemotionmustbethesameasandequaltoDZ。

Thistheniswhatismeantbythedivisionofmotionaccordingtothemotionsoftheparts:anditmustbeapplicabletoeverythingthatisdivisibleintoparts。

Motionisalsosusceptibleofanotherkindofdivision，thataccordingtotime。Forsinceallmotionisintimeandalltimeisdivisible，andinlesstimethemotionisless，itfollowsthateverymotionmustbedivisibleaccordingtotime。Andsinceeverythingthatisinmotionisinmotioninacertainsphereandforacertaintimeandhasamotionbelongingtoit，itfollowsthatthetime，themotion，thebeing-in-motion，thethingthatisinmotion，andthesphereofthemotionmustallbesusceptibleofthesamedivisions(thoughspheresofmotionarenotalldivisibleinalikemanner:thusquantityisessentially，qualityaccidentallydivisible)。ForsupposethatAisthetimeoccupiedbythemotionB。Thenifallthetimehasbeenoccupiedbythewholemotion，itwilltakelessofthemotiontooccupyhalfthetime，lessagaintooccupyafurthersubdivisionofthetime，andsoontoinfinity。Again，thetimewillbedivisiblesimilarlytothemotion:forifthewholemotionoccupiesallthetimehalfthemotionwilloccupyhalfthetime，andlessofthemotionagainwilloccupylessofthetime。

Inthesamewaythebeing-in-motionwillalsobedivisible。ForletGbethewholebeing-in-motion。Thenthebeing-in-motionthatcorrespondstohalfthemotionwillbelessthanthewholebeing-in-motion，thatwhichcorrespondstoaquarterofthemotionwillbelessagain，andsoontoinfinity。Moreoverbysettingoutsuccessivelythebeing-in-motioncorrespondingtoeachofthetwomotionsDG(say)andGE，wemayarguethatthewholebeing-in-motionwillcorrespondtothewholemotion(forifitweresomeotherbeing-in-motionthatcorrespondedtothewholemotion，therewouldbemorethanonebeing-inmotioncorrespondingtothesamemotion)，theargumentbeingthesameasthatwherebyweshowedthatthemotionofathingisdivisibleintothemotionsofthepartsofthething:forifwetakeseparatelythebeing-inmotioncorrespondingtoeachofthetwomotions，weshallseethatthewholebeing-inmotioniscontinuous。

Thesamereasoningwillshowthedivisibilityofthelength，andinfactofeverythingthatformsasphereofchange(thoughsomeoftheseareonlyaccidentallydivisiblebecausethatwhichchangesisso):forthedivisionofonetermwillinvolvethedivisionofall。

So，too，inthematteroftheirbeingfiniteorinfinite，theywillallalikebeeithertheoneortheother。Andwenowseethatinmostcasesthefactthatallthetermsaredivisibleorinfiniteisadirectconsequenceofthefactthatthethingthatchangesisdivisibleorinfinite:fortheattributes"divisible"and"infinite"

belonginthefirstinstancetothethingthatchanges。Thatdivisibilitydoessowehavealreadyshown:thatinfinitydoessowillbemadeclearinwhatfollows?