difference　whether　we　apply　this　to　a　clod　or　common　fragment　of　earth　or　to　the　earth　as　a　whole。　The　fact　indicated　does　not　depend　upon　degrees　of　size　but　applies　universally　to　everything　that　has　the　centripetal　impulse。　Therefore　earth　in　motion；　whether　in　a　mass　or　in　fragments；　necessarily　continues　to　move　until　it　occupies　the　centre　equally　every　way；　the　less　being　forced　to　equalize　itself　by　the　greater　owing　to　the　forward　drive　of　the　impulse。　　　If　the　earth　was　generated；　then；　it　must　have　been　formed　in　this　way；　and　so　clearly　its　generation　was　spherical；　and　if　it　is　ungenerated　and　has　remained　so　always；　its　character　must　be　that　which　the　initial　generation；　if　it　had　occurred；　would　have　given　it。　But　the　spherical　shape；　necessitated　by　this　argument；　follows　also　from　the　fact　that　the　motions　of　heavy　bodies　always　make　equal　angles；　and　are　not　parallel。　This　would　be　the　natural　form　of　movement　towards　what　is　naturally　spherical。　Either　then　the　earth　is　spherical　or　it　is　at　least　naturally　spherical。　And　it　is　right　to　call　anything　that　which　nature　intends　it　to　be；　and　which　belongs　to　it；　rather　than　that　which　it　is　by　constraint　and　contrary　to　nature。　The　evidence　of　the　senses　further　corroborates　this。　How　else　would　eclipses　of　the　moon　show　segments　shaped　as　we　see　them？　As　it　is；　the　shapes　which　the　moon　itself　each　month　shows　are　of　every　kind　straight；　gibbous；　and　concave…but　in　eclipses　the　outline　is　always　curved：　and；　since　it　is　the　interposition　of　the　earth　that　makes　the　eclipse；　the　form　of　this　line　will　be　caused　by　the　form　of　the　earth's　surface；　which　is　therefore　spherical。　Again；　our　observations　of　the　stars　make　it　evident；　not　only　that　the　earth　is　circular；　but　also　that　it　is　a　circle　of　no　great　size。　For　quite　a　small　change　of　position　to　south　or　north　causes　a　manifest　alteration　of　the　horizon。　There　is　much　change；　I　mean；　in　the　stars　which　are　overhead；　and　the　stars　seen　are　different；　as　one　moves　northward　or　southward。　Indeed　there　are　some　stars　seen　in　Egypt　and　in　the　neighbourhood　of　Cyprus　which　are　not　seen　in　the　northerly　regions；　and　stars；　which　in　the　north　are　never　beyond　the　range　of　observation；　in　those　regions　rise　and　set。　All　of　which　goes　to　show　not　only　that　the　earth　is　circular　in　shape；　but　also　that　it　is　a　sphere　of　no　great　size：　for　otherwise　the　effect　of　so　slight　a　change　of　place　would　not　be　quickly　apparent。　Hence　one　should　not　be　too　sure　of　the　incredibility　of　the　view　of　those　who　conceive　that　there　is　continuity　between　the　parts　about　the　pillars　of　Hercules　and　the　parts　about　India；　and　that　in　this　way　the　ocean　is　one。　As　further　evidence　in　favour　of　this　they　quote　the　case　of　elephants；　a　species　occurring　in　each　of　these　extreme　regions；　suggesting　that　the　common　characteristic　of　these　extremes　is　explained　by　their　continuity。　Also；　those　mathematicians　who　try　to　calculate　the　size　of　the　earth's　circumference　arrive　at　the　figure　400；000　stades。　This　indicates　not　only　that　the　earth's　mass　is　spherical　in　shape；　but　also　that　as　compared　with　the　stars　it　is　not　of　great　size。
  Book　III　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1
  WE　have　already　discussed　the　first　heaven　and　its　parts；　the　moving　stars　within　it；　the　matter　of　which　these　are　composed　and　their　bodily　constitution；　and　we　have　also　shown　that　they　are　ungenerated　and　indestructible。　Now　things　that　we　call　natural　are　either　substances　or　functions　and　attributes　of　substances。　As　substances　I　class　the　simple　bodies…fire；　earth；　and　the　other　terms　of　the　series…and　all　things　composed　of　them；　for　example；　the　heaven　as　a　whole　and　its　parts；　animals；　again；　and　plants　and　their　parts。　By　attributes　and　functions　I　mean　the　movements　of　these　and　of　all　other　things　in　which　they　have　power　in　themselves　to　cause　movement；　and　also　their　alterations　and　reciprocal　transformations。　It　is　obvious；　then；　that　the　greater　part　of　the　inquiry　into　nature　concerns　bodies：　for　a　natural　substance　is　either　a　body　or　a　thing　which　cannot　come　into　existence　without　body　and　magnitude。　This　appears　plainly　from　an　analysis　of　the　character　of　natural　things；　and　equally　from　an　inspection　of　the　instances　of　inquiry　into　nature。　Since；　then；　we　have　spoken　of　the　primary　element；　of　its　bodily　constitution；　and　of　its　freedom　from　destruction　and　generation；　it　remains　to　speak　of　the　other　two。　In　speaking　of　them　we　shall　be　obliged　also　to　inquire　into　generation　and　destruction。　For　if　there　is　generation　anywhere；　it　must　be　in　these　elements　and　things　composed　of　them。　　　This　is　indeed　the　first　question　we　have　to　ask：　is　generation　a　fact　or　not？　Earlier　speculation　was　at　variance　both　with　itself　and　with　the　views　here　put　forward　as　to　the　true　answer　to　this　question。　Some　removed　generation　and　destruction　from　the　world　altogether。　Nothing　that　is；　they　said；　is　generated　or　destroyed；　and　our　conviction　to　the　contrary　is　an　illusion。　So　maintained　the　school　of　Melissus　and　Parmenides。　But　however　excellent　their　theories　may　otherwise　be；　anyhow　they　cannot　be　held　to　speak　as　students　of　nature。　There　may　be　things　not　subject　to　generation　or　any　kind　of　movement；　but　if　so　they　belong　to　another　and　a　higher　inquiry　than　the　study　of　nature。　They；　however；　had　no　idea　of　any　form　of　being　other　than　the　substance　of　things　perceived；　and　when　they　saw；　what　no　one　previously　had　seen；　that　there　could　be　no　knowledge　or　wisdom　without　some　such　unchanging　entities；　they　naturally　transferred　what　was　true　of　them　to　things　perceived。　Others；　perhaps　intentionally；　maintain　precisely　the　contrary　opinion　to　this。　It　has　been　asserted　that　everything　in　the　world　was　subject　to　generation　and　nothing　was　ungenerated；　but　that　after　being　generated　some　things　remained　indestructible　while　the　rest　were　again　destroyed。　This　had　been　asserted　in　the　first　instance　by　Hesiod　and　his　followers；　but　afterwards　outside　his　circle　by　the　earliest　natural　philosophers。　But　what　these　thinkers　maintained　was　that　all　else　has　been　generated　and；　as　they　said；　'is　flowing　away；　nothing　having　any　solidity；　except　one　single　thing　which　persists　as　the　basis　of　all　these　transformations。　So　we　may　interpret　the　statements　of　Heraclitus　of　Ephesus　and　many　others。　And　some　subject　all　bodies　whatever　to　generation；　by　means　of　the　composition　and　separation　of　planes。　　　Discussion　of　the　other　views　may　be　postponed。　But　this　last　theory　which　composes　every　body　of　planes　is；　as　the　most　superficial　observation　shows；　in　many　respects　in　plain　contradiction　with　mathematics。　It　is；　however；　wrong　to　remove　the　foundations　of　a　science　unless　you　can　replace　them　with　others　more　convincing。　And；　secondly；　the　same　theory　which　composes　solids　of　planes　clearly　composes　planes　of　lines　and　lines　of　points；　so　that　a　part　of　a　line　need　not　be　a　line。　This　matter　has　been　already　considered　in　our　discussion　of　movement；　where　we　have　shown　that　an　indivisible　length　is　impossible。　But　with　respect　to　natural　bodies　there　are　impossibilities　involved　in　the　view　which　asserts　indivisible　lines；　which　we　may　briefly　consider　at　this　point。　For　the　impossible　consequences　which　result　from　this　view　in　the　mathematical　sphere　will　reproduce　themselves　when　it　is　applied　to　physical　bodies；　but　there　will　be　difficulties　in　physics　which　are　not　present　in　mathematics；　for　mathematics　deals　with　an　abstract　and　physics　with　a　more　concrete　object。　There　are　many　attributes　necessarily　present　in　physical　bodies　which　are　necessarily　excluded　by　indivisibility；　all　attributes；　in　fact；　which　are　divisible。　There　can　be　nothing　divisible　in　an　indivisible　thing；　but　the　attributes　of　bodies　are　all　divisible　in　one　of　two　ways。　They　are　divisible　into　kinds；　as　colour　is　divided　into　white　and　black；　and　they　are　divisible　per　accidens　when　that　which　has　them　is　divisible。　In　this　latter　sense　attributes　which　are　simple　are　nevertheless　divisible。　Attributes　of　this　kind　will　serve；　therefore；　to　illustrate　the　impossibility　of　the　view。　It　is　impossible；　if　two　parts　of　a　thing　have　no　weight；　that　the　two　together　should　have　weight。　But　either　all　perceptible　bodies　or　some；　such　as　earth　and　water；　have　weight；　as　these　thinkers　would　themselves　admit。　Now　if　the　point　has　no　weight；　clearly　the　lines　have　not　either；　and；　if　they　have　not；　neither　have　the　planes。　Therefore　no　body　has　weight。　It　is；　further；　manifest　that　their　point　cannot　have　weight。　For　while　a　heavy　thing　may　always　be　heavier　than　something　and　a　light　thing　lighter　than　something；　a　thing　which　is　heavier　or　lighter　than　something　need　not　be　itself　heavy　or　light；　just　as　a　large　thing　is　larger　than　others；　but　what　is　larger　is　not　always　large。　A　thing　which；　judged　absolutely；　is　small　may　none　the　less　be　larger　than　other　things。　Whatever；　then；　is　heavy　and　also　heavier　than　something　else；　must　exceed　this　by　something　which　is　heavy。　A　heavy　thing　therefore　is　always　divisible。　But　it　is　common　ground　that　a　point　is　indivisible。　Again；　suppose　that　what　is　heavy　or　weight　is　a　dense　body；　and　what　is　light　r