impossible。　And　the　same　argument　would　fit　the　case　of　lightness。　Again；　a　body　which　is　in　motion　but　has　neither　weight　nor　lightness；　must　be　moved　by　constraint；　and　must　continue　its　constrained　movement　infinitely。　For　there　will　be　a　force　which　moves　it；　and　the　smaller　and　lighter　a　body　is　the　further　will　a　given　force　move　it。　Now　let　A；　the　weightless　body；　be　moved　the　distance　CE；　and　B；　which　has　weight；　be　moved　in　the　same　time　the　distance　CD。　Dividing　the　heavy　body　in　the　proportion　CE：CD；　we　subtract　from　the　heavy　body　a　part　which　will　in　the　same　time　move　the　distance　CE；　since　the　whole　moved　CD：　for　the　relative　speeds　of　the　two　bodies　will　be　in　inverse　ratio　to　their　respective　sizes。　Thus　the　weightless　body　will　move　the　same　distance　as　the　heavy　in　the　same　time。　But　this　is　impossible。　Hence；　since　the　motion　of　the　weightless　body　will　cover　a　greater　distance　than　any　that　is　suggested；　it　will　continue　infinitely。　It　is　therefore　obvious　that　every　body　must　have　a　definite　weight　or　lightness。　But　since　'nature'　means　a　source　of　movement　within　the　thing　itself；　while　a　force　is　a　source　of　movement　in　something　other　than　it　or　in　itself　qua　other；　and　since　movement　is　always　due　either　to　nature　or　to　constraint；　movement　which　is　natural；　as　downward　movement　is　to　a　stone；　will　be　merely　accelerated　by　an　external　force；　while　an　unnatural　movement　will　be　due　to　the　force　alone。　In　either　case　the　air　is　as　it　were　instrumental　to　the　force。　For　air　is　both　light　and　heavy；　and　thus　qua　light　produces　upward　motion；　being　propelled　and　set　in　motion　by　the　force；　and　qua　heavy　produces　a　downward　motion。　In　either　case　the　force　transmits　the　movement　to　the　body　by　first；　as　it　were；　impregnating　the　air。　That　is　why　a　body　moved　by　constraint　continues　to　move　when　that　which　gave　the　impulse　ceases　to　accompany　it。　Otherwise；　i。e。　if　the　air　were　not　endowed　with　this　function；　constrained　movement　would　be　impossible。　And　the　natural　movement　of　a　body　may　be　helped　on　in　the　same　way。　This　discussion　suffices　to　show　（1）　that　all　bodies　are　either　light　or　heavy；　and　（2）　how　unnatural　movement　takes　place。　　　From　what　has　been　said　earlier　it　is　plain　that　there　cannot　be　generation　either　of　everything　or　in　an　absolute　sense　of　anything。　It　is　impossible　that　everything　should　be　generated；　unless　an　extra…corporeal　void　is　possible。　For；　assuming　generation；　the　place　which　is　to　be　occupied　by　that　which　is　coming　to　be；　must　have　been　previously　occupied　by　void　in　which　no　body　was。　Now　it　is　quite　possible　for　one　body　to　be　generated　out　of　another；　air　for　instance　out　of　fire；　but　in　the　absence　of　any　pre…existing　mass　generation　is　impossible。　That　which　is　potentially　a　certain　kind　of　body　may；　it　is　true；　become　such　in　actuality；　But　if　the　potential　body　was　not　already　in　actuality　some　other　kind　of　body；　the　existence　of　an　extra…corporeal　void　must　be　admitted。
  3
  It　remains　to　say　what　bodies　are　subject　to　generation；　and　why。　Since　in　every　case　knowledge　depends　on　what　is　primary；　and　the　elements　are　the　primary　constituents　of　bodies；　we　must　ask　which　of　such　bodies　are　elements；　and　why；　and　after　that　what　is　their　number　and　character。　The　answer　will　be　plain　if　we　first　explain　what　kind　of　substance　an　element　is。　An　element；　we　take　it；　is　a　body　into　which　other　bodies　may　be　analysed；　present　in　them　potentially　or　in　actuality　（which　of　these；　is　still　disputable）；　and　not　itself　divisible　into　bodies　different　in　form。　That；　or　something　like　it；　is　what　all　men　in　every　case　mean　by　element。　Now　if　what　we　have　described　is　an　element；　clearly　there　must　be　such　bodies。　For　flesh　and　wood　and　all　other　similar　bodies　contain　potentially　fire　and　earth；　since　one　sees　these　elements　exuded　from　them；　and；　on　the　other　hand；　neither　in　potentiality　nor　in　actuality　does　fire　contain　flesh　or　wood；　or　it　would　exude　them。　Similarly；　even　if　there　were　only　one　elementary　body；　it　would　not　contain　them。　For　though　it　will　be　either　flesh　or　bone　or　something　else；　that　does　not　at　once　show　that　it　contained　these　in　potentiality：　the　further　question　remains；　in　what　manner　it　becomes　them。　Now　Anaxagoras　opposes　Empedocles'　view　of　the　elements。　Empedocles　says　that　fire　and　earth　and　the　related　bodies　are　elementary　bodies　of　which　all　things　are　composed；　but　this　Anaxagoras　denies。　His　elements　are　the　homoeomerous　things；　viz。　flesh；　bone；　and　the　like。　Earth　and　fire　are　mixtures；　composed　of　them　and　all　the　other　seeds；　each　consisting　of　a　collection　of　all　the　homoeomerous　bodies；　separately　invisible；　and　that　explains　why　from　these　two　bodies　all　others　are　generated。　（To　him　fire　and　aither　are　the　same　thing。）　But　since　every　natural　body　has　it　proper　movement；　and　movements　are　either　simple　or　mixed；　mixed　in　mixed　bodies　and　simple　in　simple；　there　must　obviously　be　simple　bodies；　for　there　are　simple　movements。　It　is　plain；　then；　that　there　are　elements；　and　why。
  4
  The　next　question　to　consider　is　whether　the　elements　are　finite　or　infinite　in　number；　and；　if　finite；　what　their　number　is。　Let　us　first　show　reason　or　denying　that　their　number　is　infinite；　as　some　suppose。　We　begin　with　the　view　of　Anaxagoras　that　all　the　homoeomerous　bodies　are　elements。　Any　one　who　adopts　this　view　misapprehends　the　meaning　of　element。　Observation　shows　that　even　mixed　bodies　are　often　divisible　into　homoeomerous　parts；　examples　are　flesh；　bone；　wood；　and　stone。　Since　then　the　composite　cannot　be　an　element；　not　every　homoeomerous　body　can　be　an　element；　only；　as　we　said　before；　that　which　is　not　divisible　into　bodies　different　in　form。　But　even　taking　'element'　as　they　do；　they　need　not　assert　an　infinity　of　elements；　since　the　hypothesis　of　a　finite　number　will　give　identical　results。　Indeed　even　two　or　three　such　bodies　serve　the　purpose　as　well；　as　Empedocles'　attempt　shows。　Again；　even　on　their　view　it　turns　out　that　all　things　are　not　composed　of　homocomerous　bodies。　They　do　not　pretend　that　a　face　is　composed　of　faces；　or　that　any　other　natural　conformation　is　composed　of　parts　like　itself。　Obviously　then　it　would　be　better　to　assume　a　finite　number　of　principles。　They　should；　in　fact；　be　as　few　as　possible；　consistently　with　proving　what　has　to　be　proved。　This　is　the　common　demand　of　mathematicians；　who　always　assume　as　principles　things　finite　either　in　kind　or　in　number。　Again；　if　body　is　distinguished　from　body　by　the　appropriate　qualitative　difference；　and　there　is　a　limit　to　the　number　of　differences　（for　the　difference　lies　in　qualities　apprehended　by　sense；　which　are　in　fact　finite　in　number；　though　this　requires　proof）；　then　manifestly　there　is　necessarily　a　limit　to　the　number　of　elements。　　　There　is；　further；　another　view…that　of　Leucippus　and　Democritus　of　Abdera…the　implications　of　which　are　also　unacceptable。　The　primary　masses；　according　to　them；　are　infinite　in　number　and　indivisible　in　mass：　one　cannot　turn　into　many　nor　many　into　one；　and　all　things　are　generated　by　their　combination　and　involution。　Now　this　view　in　a　sense　makes　things　out　to　be　numbers　or　composed　of　numbers。　The　exposition　is　not　clear；　but　this　is　its　real　meaning。　And　further；　they　say　that　since　the　atomic　bodies　differ　in　shape；　and　there　is　an　infinity　of　shapes；　there　is　an　infinity　of　simple　bodies。　But　they　have　never　explained　in　detail　the　shapes　of　the　various　elements；　except　so　far　to　allot　the　sphere　to　fire。　Air；　water；　and　the　rest　they　distinguished　by　the　relative　size　of　the　atom；　assuming　that　the　atomic　substance　was　a　sort　of　master…seed　for　each　and　every　element。　Now；　in　the　first　place；　they　make　the　mistake　already　noticed。　The　principles　which　they　assume　are　not　limited　in　number；　though　such　limitation　would　necessitate　no　other　alteration　in　their　theory。　Further；　if　the　differences　of　bodies　are　not　infinite；　plainly　the　elements　will　not　be　an　infinity。　Besides；　a　view　which　asserts　atomic　bodies　must　needs　come　into　conflict　with　the　mathematical　sciences；　in　addition　to　invalidating　many　common　opinions　and　apparent　data　of　sense　perception。　But　of　these　things　we　have　already　spoken　in　our　discussion　of　time　and　movement。　They　are　also　bound　to　contradict　themselves。　For　if　the　elements　are　atomic；　air；　earth；　and　water　cannot　be　differentiated　by　the　relative　sizes　of　their　atoms；　since　then　they　could　not　be　generated　out　of　one　another。　The　extrusion　of　the　largest　atoms　is　a　process　that　will　in　time　exhaust　the　supply；　and　it　is　by　such　a　process　that　they　account　for　the　generation　of　water；　air；　and　earth　from　one　another。　Again；　even　on　their　own　presuppositions　it　does　not　seem　as　if　the　clements　would　be　infinite　in　number。　The　atoms　differ　in　figure；　and　all　figures　are　composed　of　pyramids；　rectilinear　the　case　of　rectilinear　figures；　while　the　sphere　has　eight　pyramidal　parts。　The　figures　must　have　their　principles；　and；　whether　these　are　one　or　two　or　more；　the　simple　bodies　must　be　the　same　in　number　as　they。　Again；　if　every　element　has　its　proper　movement；　and　a　simple　body　has　a　simple　movement；　and　the　number　of　simple