They　must　also　accept　the　inference　that　the　mathematical　produce　heat　and　combustion；　since　they　too　possess　angles　and　contain　atomic　spheres　and　pyramids；　especially　if　there　are；　as　they　allege；　atomic　figures。　Anyhow　if　these　functions　belong　to　some　of　these　things　and　not　to　others；　they　should　explain　the　difference；　instead　of　speaking　in　quite　general　terms　as　they　do。　Again；　combustion　of　a　body　produces　fire；　and　fire　is　a　sphere　or　a　pyramid。　The　body；　then；　is　turned　into　spheres　or　pyramids。　Let　us　grant　that　these　figures　may　reasonably　be　supposed　to　cut　and　break　up　bodies　as　fire　does；　still　it　remains　quite　inexplicable　that　a　pyramid　must　needs　produce　pyramids　or　a　sphere　spheres。　One　might　as　well　postulate　that　a　knife　or　a　saw　divides　things　into　knives　or　saws。　It　is　also　ridiculous　to　think　only　of　division　when　allotting　fire　its　shape。　Fire　is　generally　thought　of　as　combining　and　connecting　rather　than　as　separating。　For　though　it　separates　bodies　different　in　kind；　it　combines　those　which　are　the　same；　and　the　combining　is　essential　to　it；　the　functions　of　connecting　and　uniting　being　a　mark　of　fire；　while　the　separating　is　incidental。　For　the　expulsion　of　the　foreign　body　is　an　incident　in　the　compacting　of　the　homogeneous。　In　choosing　the　shape；　then；　they　should　have　thought　either　of　both　functions　or　preferably　of　the　combining　function。　In　addition；　since　hot　and　cold　are　contrary　powers；　it　is　impossible　to　allot　any　shape　to　the　cold。　For　the　shape　given　must　be　the　contrary　of　that　given　to　the　hot；　but　there　is　no　contrariety　between　figures。　That　is　why　they　have　all　left　the　cold　out；　though　properly　either　all　or　none　should　have　their　distinguishing　figures。　Some　of　them；　however；　do　attempt　to　explain　this　power；　and　they　contradict　themselves。　A　body　of　large　particles；　they　say；　is　cold　because　instead　of　penetrating　through　the　passages　it　crushes。　Clearly；　then；　that　which　is　hot　is　that　which　penetrates　these　passages；　or　in　other　words　that　which　has　fine　particles。　It　results　that　hot　and　cold　are　distinguished　not　by　the　figure　but　by　the　size　of　the　particles。　Again；　if　the　pyramids　are　unequal　in　size；　the　large　ones　will　not　be　fire；　and　that　figure　will　produce　not　combustion　but　its　contrary。　　　From　what　has　been　said　it　is　clear　that　the　difference　of　the　elements　does　not　depend　upon　their　shape。　Now　their　most　important　differences　are　those　of　property；　function；　and　power；　for　every　natural　body　has；　we　maintain；　its　own　functions；　properties；　and　powers。　Our　first　business；　then；　will　be　to　speak　of　these；　and　that　inquiry　will　enable　us　to　explain　the　differences　of　each　from　each。
  Book　IV　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1
  WE　have　now　to　consider　the　terms　'heavy'　and　'light'。　We　must　ask　what　the　bodies　so　called　are；　how　they　are　constituted；　and　what　is　the　reason　of　their　possessing　these　powers。　The　consideration　of　these　questions　is　a　proper　part　of　the　theory　of　movement；　since　we　call　things　heavy　and　light　because　they　have　the　power　of　being　moved　naturally　in　a　certain　way。　The　activities　corresponding　to　these　powers　have　not　been　given　any　name；　unless　it　is　thought　that　'impetus'　is　such　a　name。　But　because　the　inquiry　into　nature　is　concerned　with　movement；　and　these　things　have　in　themselves　some　spark　（as　it　were）　of　movement；　all　inquirers　avail　themselves　of　these　powers；　though　in　all　but　a　few　cases　without　exact　discrimination。　We　must　then　first　look　at　whatever　others　have　said；　and　formulate　the　questions　which　require　settlement　in　the　interests　of　this　inquiry；　before　we　go　on　to　state　our　own　view　of　the　matter。　　　Language　recognizes　（a）　an　absolute；　（b）　a　relative　heavy　and　light。　Of　two　heavy　things；　such　as　wood　and　bronze；　we　say　that　the　one　is　relatively　light；　the　other　relatively　heavy。　Our　predecessors　have　not　dealt　at　all　with　the　absolute　use；　of　the　terms；　but　only　with　the　relative。　I　mean；　they　do　not　explain　what　the　heavy　is　or　what　the　light　is；　but　only　the　relative　heaviness　and　lightness　of　things　possessing　weight。　This　can　be　made　clearer　as　follows。　There　are　things　whose　constant　nature　it　is　to　move　away　from　the　centre；　while　others　move　constantly　towards　the　centre；　and　of　these　movements　that　which　is　away　from　the　centre　I　call　upward　movement　and　that　which　is　towards　it　I　call　downward　movement。　（The　view；　urged　by　some；　that　there　is　no　up　and　no　down　in　the　heaven；　is　absurd。　There　can　be；　they　say；　no　up　and　no　down；　since　the　universe　is　similar　every　way；　and　from　any　point　on　the　earth's　surface　a　man　by　advancing　far　enough　will　come　to　stand　foot　to　foot　with　himself。　But　the　extremity　of　the　whole；　which　we　call　'above'；　is　in　position　above　and　in　nature　primary。　And　since　the　universe　has　an　extremity　and　a　centre；　it　must　clearly　have　an　up　and　down。　Common　usage　is　thus　correct；　though　inadequate。　And　the　reason　of　its　inadequacy　is　that　men　think　that　the　universe　is　not　similar　every　way。　They　recognize　only　the　hemisphere　which　is　over　us。　But　if　they　went　on　to　think　of　the　world　as　formed　on　this　pattern　all　round；　with　a　centre　identically　related　to　each　point　on　the　extremity；　they　would　have　to　admit　that　the　extremity　was　above　and　the　centre　below。）　By　absolutely　light；　then；　we　mean　that　which　moves　upward　or　to　the　extremity；　and　by　absolutely　heavy　that　which　moves　downward　or　to　the　centre。　By　lighter　or　relatively　light　we　mean　that　one；　of　two　bodies　endowed　with　weight　and　equal　in　bulk；　which　is　exceeded　by　the　other　in　the　speed　of　its　natural　downward　movement。
  2
  Those　of　our　predecessors　who　have　entered　upon　this　inquiry　have　for　the　most　part　spoken　of　light　and　heavy　things　only　in　the　sense　in　which　one　of　two　things　both　endowed　with　weight　is　said　to　be　the　lighter。　And　this　treatment　they　consider　a　sufficient　analysis　also　of　the　notions　of　absolute　heaviness；　to　which　their　account　does　not　apply。　This；　however；　will　become　clearer　as　we　advance。　One　use　of　the　terms　'lighter'　and　'heavier'　is　that　which　is　set　forth　in　writing　in　the　Timaeus；　that　the　body　which　is　composed　of　the　greater　number　of　identical　parts　is　relatively　heavy；　while　that　which　is　composed　of　a　smaller　number　is　relatively　light。　As　a　larger　quantity　of　lead　or　of　bronze　is　heavier　than　a　smaller…and　this　holds　good　of　all　homogeneous　masses；　the　superior　weight　always　depending　upon　a　numerical　superiority　of　equal　parts…in　precisely　the　same　way；　they　assert；　lead　is　heavier　than　wood。　For　all　bodies；　in　spite　of　the　general　opinion　to　the　contrary；　are　composed　of　identical　parts　and　of　a　single　material。　But　this　analysis　says　nothing　of　the　absolutely　heavy　and　light。　The　facts　are　that　fire　is　always　light　and　moves　upward；　while　earth　and　all　earthy　things　move　downwards　or　towards　the　centre。　It　cannot　then　be　the　fewness　of　the　triangles　（of　which；　in　their　view；　all　these　bodies　are　composed）　which　disposes　fire　to　move　upward。　If　it　were；　the　greater　the　quantity　of　fire　the　slower　it　would　move；　owing　to　the　increase　of　weight　due　to　the　increased　number　of　triangles。　But　the　palpable　fact；　on　the　contrary；　is　that　the　greater　the　quantity；　the　lighter　the　mass　is　and　the　quicker　its　upward　movement：　and；　similarly；　in　the　reverse　movement　from　above　downward；　the　small　mass　will　move　quicker　and　the　large　slower。　Further；　since　to　be　lighter　is　to　have　fewer　of　these　homogeneous　parts　and　to　be　heavier　is　to　have　more；　and　air；　water；　and　fire　are　composed　of　the　same　triangles；　the　only　difference　being　in　the　number　of　such　parts；　which　must　therefore　explain　any　distinction　of　relatively　light　and　heavy　between　these　bodies；　it　follows　that　there　must　be　a　certain　quantum　of　air　which　is　heavier　than　water。　But　the　facts　are　directly　opposed　to　this。　The　larger　the　quantity　of　air　the　more　readily　it　moves　upward；　and　any　portion　of　air　without　exception　will　rise　up　out　of　the　water。　　　So　much　for　one　view　of　the　distinction　between　light　and　heavy。　To　others　the　analysis　seems　insufficient；　and　their　views　on　the　subject；　though　they　belong　to　an　older　generation　than　ours；　have　an　air　of　novelty。　It　is　apparent　that　there　are　bodies　which；　when　smaller　in　bulk　than　others；　yet　exceed　them　in　weight。　It　is　therefore　obviously　insufficient　to　say　that　bodies　of　equal　weight　are　composed　of　an　equal　number　of　primary　parts：　for　that　would　give　equality　of　bulk。　Those　who　maintain　that　the　primary　or　atomic　parts；　of　which　bodies　endowed　with　weight　are　composed；　are　planes；　cannot　so　speak　without　absurdity；　but　those　who　regard　them　as　solids　are　in　a　better　position　to　assert　that　of　such　bodies　the　larger　is　the　heavier。　But　since　in　composite　bodies　the　weight　obviously　does　not　correspond　in　this　way　to　the　bulk；　the　lesser　bulk　being　often　superior　in　weight　（as；　for　instance；　if　one　be　wool　and　the　other　bronze）；　there　are　some　who　think　and　say　that　the　cause　is　to　be　found　elsewhere。　The　void；　they　say；　which　is　imprisoned　in　bodies；　lightens　them　and　sometimes　makes　the　larger　body　the　lighter。　The　reason　is　that　there　is　more　void。　And　this　would　also　account　for　the　fact　that　a　body　compos