me；　and　the　part　of　this　infinite；　E；　cannot　be　so　modified　in　the　same　time；　since　we　assume　that　a　less　quantity　makes　the　movement　in　a　less　time。　Let　E　then；　when　acted　upon　by　A；　complete　the　movement　in　the　time　D。　Then；　as　D　is　to　CD；　so　is　E　to　some　finite　part　of　B。　This　part　will　necessarily　be　moved　by　A　in　the　time　CD。　For　we　suppose　that　the　same　agent　produces　a　given　effect　on　a　greater　and　a　smaller　mass　in　longer　and　shorter　times；　the　times　and　masses　varying　proportionately。　There　is　thus　no　finite　time　in　which　infinites　can　move　one　another。　Is　their　time　then　infinite？　No；　for　infinite　time　has　no　end；　but　the　movement　communicated　has。　　　If　therefore　every　perceptible　body　possesses　the　power　of　acting　or　of　being　acted　upon；　or　both　of　these；　it　is　impossible　that　an　infinite　body　should　be　perceptible。　All　bodies；　however；　that　occupy　place　are　perceptible。　There　is　therefore　no　infinite　body　beyond　the　heaven。　Nor　again　is　there　anything　of　limited　extent　beyond　it。　And　so　beyond　the　heaven　there　is　no　body　at　all。　For　if　you　suppose　it　an　object　of　intelligence；　it　will　be　in　a　place…since　place　is　what　'within'　and　'beyond'　denote…and　therefore　an　object　of　perception。　But　nothing　that　is　not　in　a　place　is　perceptible。　　　The　question　may　also　be　examined　in　the　light　of　more　general　considerations　as　follows。　The　infinite；　considered　as　a　whole　of　similar　parts；　cannot；　on　the　one　hand；　move　in　a　circle。　For　there　is　no　centre　of　the　infinite；　and　that　which　moves　in　a　circle　moves　about　the　centre。　Nor　again　can　the　infinite　move　in　a　straight　line。　For　there　would　have　to　be　another　place　infinite　like　itself　to　be　the　goal　of　its　natural　movement　and　another；　equally　great；　for　the　goal　of　its　unnatural　movement。　Moreover；　whether　its　rectilinear　movement　is　natural　or　constrained；　in　either　case　the　force　which　causes　its　motion　will　have　to　be　infinite。　For　infinite　force　is　force　of　an　infinite　body；　and　of　an　infinite　body　the　force　is　infinite。　So　the　motive　body　also　will　be　infinite。　（The　proof　of　this　is　given　in　our　discussion　of　movement；　where　it　is　shown　that　no　finite　thing　possesses　infinite　power；　and　no　infinite　thing　finite　power。）　If　then　that　which　moves　naturally　can　also　move　unnaturally；　there　will　be　two　infinites；　one　which　causes；　and　another　which　exhibits　the　latter　motion。　Again；　what　is　it　that　moves　the　infinite？　If　it　moves　itself；　it　must　be　animate。　But　how　can　it　possibly　be　conceived　as　an　infinite　animal？　And　if　there　is　something　else　that　moves　it；　there　will　be　two　infinites；　that　which　moves　and　that　which　is　moved；　differing　in　their　form　and　power。　　　If　the　whole　is　not　continuous；　but　exists；　as　Democritus　and　Leucippus　think；　in　the　form　of　parts　separated　by　void；　there　must　necessarily　be　one　movement　of　all　the　multitude。　They　are　distinguished；　we　are　told；　from　one　another　by　their　figures；　but　their　nature　is　one；　like　many　pieces　of　gold　separated　from　one　another。　But　each　piece　must；　as　we　assert；　have　the　same　motion。　For　a　single　clod　moves　to　the　same　place　as　the　whole　mass　of　earth；　and　a　spark　to　the　same　place　as　the　whole　mass　of　fire。　So　that　if　it　be　weight　that　all　possess；　no　body　is；　strictly　speaking；　light：　and　if　lightness　be　universal；　none　is　heavy。　Moreover；　whatever　possesses　weight　or　lightness　will　have　its　place　either　at　one　of　the　extremes　or　in　the　middle　region。　But　this　is　impossible　while　the　world　is　conceived　as　infinite。　And；　generally；　that　which　has　no　centre　or　extreme　limit；　no　up　or　down；　gives　the　bodies　no　place　for　their　motion；　and　without　that　movement　is　impossible。　A　thing　must　move　either　naturally　or　unnaturally；　and　the　two　movements　are　determined　by　the　proper　and　alien　places。　Again；　a　place　in　which　a　thing　rests　or　to　which　it　moves　unnaturally；　must　be　the　natural　place　for　some　other　body；　as　experience　shows。　Necessarily；　therefore；　not　everything　possesses　weight　or　lightness；　but　some　things　do　and　some　do　not。　From　these　arguments　then　it　is　clear　that　the　body　of　the　universe　is　not　infinite。
  8
  We　must　now　proceed　to　explain　why　there　cannot　be　more　than　one　heaven…the　further　question　mentioned　above。　For　it　may　be　thought　that　we　have　not　proved　universal　of　bodies　that　none　whatever　can　exist　outside　our　universe；　and　that　our　argument　applied　only　to　those　of　indeterminate　extent。　　　Now　all　things　rest　and　move　naturally　and　by　constraint。　A　thing　moves　naturally　to　a　place　in　which　it　rests　without　constraint；　and　rests　naturally　in　a　place　to　which　it　moves　without　constraint。　On　the　other　hand；　a　thing　moves　by　constraint　to　a　place　in　which　it　rests　by　constraint；　and　rests　by　constraint　in　a　place　to　which　it　moves　by　constraint。　Further；　if　a　given　movement　is　due　to　constraint；　its　contrary　is　natural。　If；　then；　it　is　by　constraint　that　earth　moves　from　a　certain　place　to　the　centre　here；　its　movement　from　here　to　there　will　be　natural；　and　if　earth　from　there　rests　here　without　constraint；　its　movement　hither　will　be　natural。　And　the　natural　movement　in　each　case　is　one。　Further；　these　worlds；　being　similar　in　nature　to　ours；　must　all　be　composed　of　the　same　bodies　as　it。　Moreover　each　of　the　bodies；　fire；　I　mean；　and　earth　and　their　intermediates；　must　have　the　same　power　as　in　our　world。　For　if　these　names　are　used　equivocally；　if　the　identity　of　name　does　not　rest　upon　an　identity　of　form　in　these　elements　and　ours；　then　the　whole　to　which　they　belong　can　only　be　called　a　world　by　equivocation。　Clearly；　then；　one　of　the　bodies　will　move　naturally　away　from　the　centre　and　another　towards　the　centre；　since　fire　must　be　identical　with　fire；　earth　with　earth；　and　so　on；　as　the　fragments　of　each　are　identical　in　this　world。　That　this　must　be　the　case　is　evident　from　the　principles　laid　down　in　our　discussion　of　the　movements；　for　these　are　limited　in　number；　and　the　distinction　of　the　elements　depends　upon　the　distinction　of　the　movements。　Therefore；　since　the　movements　are　the　same；　the　elements　must　also　be　the　same　everywhere。　The　particles　of　earth；　then；　in　another　world　move　naturally　also　to　our　centre　and　its　fire　to　our　circumference。　This；　however；　is　impossible；　since；　if　it　were　true；　earth　must；　in　its　own　world；　move　upwards；　and　fire　to　the　centre；　in　the　same　way　the　earth　of　our　world　must　move　naturally　away　from　the　centre　when　it　moves　towards　the　centre　of　another　universe。　This　follows　from　the　supposed　juxtaposition　of　the　worlds。　For　either　we　must　refuse　to　admit　the　identical　nature　of　the　simple　bodies　in　the　various　universes；　or；　admitting　this；　we　must　make　the　centre　and　the　extremity　one　as　suggested。　This　being　so；　it　follows　that　there　cannot　be　more　worlds　than　one。　　　To　postulate　a　difference　of　nature　in　the　simple　bodies　according　as　they　are　more　or　less　distant　from　their　proper　places　is　unreasonable。　For　what　difference　can　it　make　whether　we　say　that　a　thing　is　this　distance　away　or　that？　One　would　have　to　suppose　a　difference　proportionate　to　the　distance　and　increasing　with　it；　but　the　form　is　in　fact　the　same。　Moreover；　the　bodies　must　have　some　movement；　since　the　fact　that　they　move　is　quite　evident。　Are　we　to　say　then　that　all　their　movements；　even　those　which　are　mutually　contrary；　are　due　to　constraint？　No；　for　a　body　which　has　no　natural　movement　at　all　cannot　be　moved　by　constraint。　If　then　the　bodies　have　a　natural　movement；　the　movement　of　the　particular　instances　of　each　form　must　necessarily　have　for　goal　a　place　numerically　one；　i。e。　a　particular　centre　or　a　particular　extremity。　If　it　be　suggested　that　the　goal　in　each　case　is　one　in　form　but　numerically　more　than　one；　on　the　analogy　of　particulars　which　are　many　though　each　undifferentiated　in　form；　we　reply　that　the　variety　of　goal　cannot　be　limited　to　this　portion　or　that　but　must　extend　to　all　alike。　For　all　are　equally　undifferentiated　in　form；　but　any　one　is　different　numerically　from　any　other。　What　I　mean　is　this：　if　the　portions　in　this　world　behave　similarly　both　to　one　another　and　to　those　in　another　world；　then　the　portion　which　is　taken　hence　will　not　behave　differently　either　from　the　portions　in　another　world　or　from　those　in　the　same　world；　but　similarly　to　them；　since　in　form　no　portion　differs　from　another。　The　result　is　that　we　must　either　abandon　our　present　assumption　or　assert　that　the　centre　and　the　extremity　are　each　numerically　one。　But　this　being　so；　the　heaven；　by　the　same　evidence　and　the　same　necessary　inferences；　must　be　one　only　and　no　more。　　　A　consideration　of　the　other　kinds　of　movement　also　makes　it　plain　that　there　is　some　point　to　which　earth　and　fire　move　naturally。　For　in　general　that　which　is　moved　changes　from　something　into　something；　the　starting…point　and　the　goal　being　different　in　form；　and　always　it　is　a　finite　change。　For　instance；　to　recover　health　is　to　change　from　disease　to　health；　to　increase　is　to　change　from　smallness　to　greatness。　Locomotion　must　be　similar：　for　it　also　has　its　goal　and　starting…pointand　therefore　the　starting…point　and　the　goal　of　the　natural　movement　must　differ　in　form…just　as　the　movement　of　coming　to　health　does　not　take　any　direction　which　chance　or　the　wishes　of