is　that　a　principle　is　great　rather　in　power　than　in　extent；　hence　that　which　was　small　at　the　start　turns　out　a　giant　at　the　end。　Now　the　conception　of　the　infinite　possesses　this　power　of　principles；　and　indeed　in　the　sphere　of　quantity　possesses　it　in　a　higher　degree　than　any　other　conception；　so　that　it　is　in　no　way　absurd　or　unreasonable　that　the　assumption　that　an　infinite　body　exists　should　be　of　peculiar　moment　to　our　inquiry。　The　infinite；　then；　we　must　now　discuss；　opening　the　whole　matter　from　the　beginning。　　　Every　body　is　necessarily　to　be　classed　either　as　simple　or　as　composite；　the　infinite　body；　therefore；　will　be　either　simple　or　composite。　　　But　it　is　clear；　further；　that　if　the　simple　bodies　are　finite；　the　composite　must　also　be　finite；　since　that　which　is　composed　of　bodies　finite　both　in　number　and　in　magnitude　is　itself　finite　in　respect　of　number　and　magnitude：　its　quantity　is　in　fact　the　same　as　that　of　the　bodies　which　compose　it。　What　remains　for　us　to　consider；　then；　is　whether　any　of　the　simple　bodies　can　be　infinite　in　magnitude；　or　whether　this　is　impossible。　Let　us　try　the　primary　body　first；　and　then　go　on　to　consider　the　others。　　　The　body　which　moves　in　a　circle　must　necessarily　be　finite　in　every　respect；　for　the　following　reasons。　（1）　If　the　body　so　moving　is　infinite；　the　radii　drawn　from　the　centre　will　be　infinite。　But　the　space　between　infinite　radii　is　infinite：　and　by　the　space　between　the　radii　I　mean　the　area　outside　which　no　magnitude　which　is　in　contact　with　the　two　lines　can　be　conceived　as　falling。　This；　I　say；　will　be　infinite：　first；　because　in　the　case　of　finite　radii　it　is　always　finite；　and　secondly；　because　in　it　one　can　always　go　on　to　a　width　greater　than　any　given　width；　thus　the　reasoning　which　forces　us　to　believe　in　infinite　number；　because　there　is　no　maximum；　applies　also　to　the　space　between　the　radii。　Now　the　infinite　cannot　be　traversed；　and　if　the　body　is　infinite　the　interval　between　the　radii　is　necessarily　infinite：　circular　motion　therefore　is　an　impossibility。　Yet　our　eyes　tell　us　that　the　heavens　revolve　in　a　circle；　and　by　argument　also　we　have　determined　that　there　is　something　to　which　circular　movement　belongs。　　　（2）　Again；　if　from　a　finite　time　a　finite　time　be　subtracted；　what　remains　must　be　finite　and　have　a　beginning。　And　if　the　time　of　a　journey　has　a　beginning；　there　must　be　a　beginning　also　of　the　movement；　and　consequently　also　of　the　distance　traversed。　This　applies　universally。　Take　a　line；　ACE；　infinite　in　one　direction；　E；　and　another　line；　BB；　infinite　in　both　directions。　Let　ACE　describe　a　circle；　revolving　upon　C　as　centre。　In　its　movement　it　will　cut　BB　continuously　for　a　certain　time。　This　will　be　a　finite　time；　since　the　total　time　is　finite　in　which　the　heavens　complete　their　circular　orbit；　and　consequently　the　time　subtracted　from　it；　during　which　the　one　line　in　its　motion　cuts　the　other；　is　also　finite。　Therefore　there　will　be　a　point　at　which　ACE　began　for　the　first　time　to　cut　BB。　This；　however；　is　impossible。　The　infinite；　then；　cannot　revolve　in　a　circle；　nor　could　the　world；　if　it　were　infinite。　　　（3）　That　the　infinite　cannot　move　may　also　be　shown　as　follows。　Let　A　be　a　finite　line　moving　past　the　finite　line；　B。　Of　necessity　A　will　pass　clear　of　B　and　B　of　A　at　the　same　moment；　for　each　overlaps　the　other　to　precisely　the　same　extent。　Now　if　the　two　were　both　moving；　and　moving　in　contrary　directions；　they　would　pass　clear　of　one　another　more　rapidly；　if　one　were　still　and　the　other　moving　past　it；　less　rapidly；　provided　that　the　speed　of　the　latter　were　the　same　in　both　cases。　This；　however；　is　clear：　that　it　is　impossible　to　traverse　an　infinite　line　in　a　finite　time。　Infinite　time；　then；　would　be　required。　（This　we　demonstrated　above　in　the　discussion　of　movement。）　And　it　makes　no　difference　whether　a　finite　is　passing　by　an　infinite　or　an　infinite　by　a　finite。　For　when　A　is　passing　B；　then　B　overlaps　A　and　it　makes　no　difference　whether　B　is　moved　or　unmoved；　except　that；　if　both　move；　they　pass　clear　of　one　another　more　quickly。　It　is；　however；　quite　possible　that　a　moving　line　should　in　certain　cases　pass　one　which　is　stationary　quicker　than　it　passes　one　moving　in　an　opposite　direction。　One　has　only　to　imagine　the　movement　to　be　slow　where　both　move　and　much　faster　where　one　is　stationary。　To　suppose　one　line　stationary；　then；　makes　no　difficulty　for　our　argument；　since　it　is　quite　possible　for　A　to　pass　B　at　a　slower　rate　when　both　are　moving　than　when　only　one　is。　If；　therefore；　the　time　which　the　finite　moving　line　takes　to　pass　the　other　is　infinite；　then　necessarily　the　time　occupied　by　the　motion　of　the　infinite　past　the　finite　is　also　infinite。　For　the　infinite　to　move　at　all　is　thus　absolutely　impossible；　since　the　very　smallest　movement　conceivable　must　take　an　infinity　of　time。　Moreover　the　heavens　certainly　revolve；　and　they　complete　their　circular　orbit　in　a　finite　time；　so　that　they　pass　round　the　whole　extent　of　any　line　within　their　orbit；　such　as　the　finite　line　AB。　The　revolving　body；　therefore；　cannot　be　infinite。　　　（4）　Again；　as　a　line　which　has　a　limit　cannot　be　infinite；　or；　if　it　is　infinite；　is　so　only　in　length；　so　a　surface　cannot　be　infinite　in　that　respect　in　which　it　has　a　limit；　or；　indeed；　if　it　is　completely　determinate；　in　any　respect　whatever。　Whether　it　be　a　square　or　a　circle　or　a　sphere；　it　cannot　be　infinite；　any　more　than　a　foot…rule　can。　There　is　then　no　such　thing　as　an　infinite　sphere　or　square　or　circle；　and　where　there　is　no　circle　there　can　be　no　circular　movement；　and　similarly　where　there　is　no　infinite　at　all　there　can　be　no　infinite　movement；　and　from　this　it　follows　that；　an　infinite　circle　being　itself　an　impossibility；　there　can　be　no　circular　motion　of　an　infinite　body。　　　（5）　Again；　take　a　centre　C；　an　infinite　line；　AB；　another　infinite　line　at　right　angles　to　it；　E；　and　a　moving　radius；　CD。　CD　will　never　cease　contact　with　E；　but　the　position　will　always　be　something　like　CE；　CD　cutting　E　at　F。　The　infinite　line；　therefore；　refuses　to　complete　the　circle。　　　（6）　Again；　if　the　heaven　is　infinite　and　moves　in　a　circle；　we　shall　have　to　admit　that　in　a　finite　time　it　has　traversed　the　infinite。　For　suppose　the　fixed　heaven　infinite；　and　that　which　moves　within　it　equal　to　it。　It　results　that　when　the　infinite　body　has　completed　its　revolution；　it　has　traversed　an　infinite　equal　to　itself　in　a　finite　time。　But　that　we　know　to　be　impossible。　　　（7）　It　can　also　be　shown；　conversely；　that　if　the　time　of　revolution　is　finite；　the　area　traversed　must　also　be　finite；　but　the　area　traversed　was　equal　to　itself；　therefore；　it　is　itself　finite。　　　We　have　now　shown　that　the　body　which　moves　in　a　circle　is　not　endless　or　infinite；　but　has　its　limit。
  6
  Further；　neither　that　which　moves　towards　nor　that　which　moves　away　from　the　centre　can　be　infinite。　For　the　upward　and　downward　motions　are　contraries　and　are　therefore　motions　towards　contrary　places。　But　if　one　of　a　pair　of　contraries　is　determinate；　the　other　must　be　determinate　also。　Now　the　centre　is　determined；　for；　from　whatever　point　the　body　which　sinks　to　the　bottom　starts　its　downward　motion；　it　cannot　go　farther　than　the　centre。　The　centre；　therefore；　being　determinate；　the　upper　place　must　also　be　determinate。　But　if　these　two　places　are　determined　and　finite；　the　corresponding　bodies　must　also　be　finite。　Further；　if　up　and　down　are　determinate；　the　intermediate　place　is　also　necessarily　determinate。　For；　if　it　is　indeterminate；　the　movement　within　it　will　be　infinite；　and　that　we　have　already　shown　to　be　an　impossibility。　The　middle　region　then　is　determinate；　and　consequently　any　body　which　either　is　in　it；　or　might　be　in　it；　is　determinate。　But　the　bodies　which　move　up　and　down　may　be　in　it；　since　the　one　moves　naturally　away　from　the　centre　and　the　other　towards　it。　　　From　this　alone　it　is　clear　that　an　infinite　body　is　an　impossibility；　but　there　is　a　further　point。　If　there　is　no　such　thing　as　infinite　weight；　then　it　follows　that　none　of　these　bodies　can　be　infinite。　For　the　supposed　infinite　body　would　have　to　be　infinite　in　weight。　（The　same　argument　applies　to　lightness：　for　as　the　one　supposition　involves　infinite　weight；　so　the　infinity　of　the　body　which　rises　to　the　surface　involves　infinite　lightness。）　This　is　proved　as　follows。　Assume　the　weight　to　be　finite；　and　take　an　infinite　body；　AB；　of　the　weight　C。　Subtract　from　the　infinite　body　a　finite　mass；　BD；　the　weight　of　which　shall　be　E。　E　then　is　less　than　C；　since　it　is　the　weight　of　a　lesser　mass。　Suppose　then　that　the　smaller　goes　into　the　greater　a　certain　number　of　times；　and　take　BF　bearing　the　same　proportion　to　BD　which　the　greater　weight　bears　to　the　smaller。　For　you　may　subtract　as　much　as　you　please　from　an　infinite。　If　now　the　masses　are　proportionate　to　the　weights；　and　the　lesser　weight　is　that　of　the　lesser　mass；　the　greater　must　be　that　of　the　greater。　The　weights；　therefore；　of　the　finite　and　of　the　infinite　body　are　equal。　Again；　if　the　weight　of　a　greater　body　is　greater　than　that　of　a　less；　the　weight　of　GB　will　be　greater　than　that　of　FB；　and　thus　the　weight　of　the　finite　body　is　greater　than　that　of