y　element　has　its　proper　movement；　and　a　simple　body　has　a　simple　movement；　and　the　number　of　simple　movements　is　not　infinite；　because　the　simple　motions　are　only　two　and　the　number　of　places　is　not　infinite；　on　these　grounds　also　we　should　have　to　deny　that　the　number　of　elements　is　infinite。
  5
  Since　the　number　of　the　elements　must　be　limited；　it　remains　to　inquire　whether　there　is　more　than　one　element。　Some　assume　one　only；　which　is　according　to　some　water；　to　others　air；　to　others　fire；　to　others　again　something　finer　than　water　and　denser　than　air；　an　infinite　body…so　they　say…bracing　all　the　heavens。　　　Now　those　who　decide　for　a　single　element；　which　is　either　water　or　air　or　a　body　finer　than　water　and　denser　than　air；　and　proceed　to　generate　other　things　out　of　it　by　use　of　the　attributes　density　and　rarity；　all　alike　fail　to　observe　the　fact　that　they　are　depriving　the　element　of　its　priority。　Generation　out　of　the　elements　is；　as　they　say；　synthesis；　and　generation　into　the　elements　is　analysis；　so　that　the　body　with　the　finer　parts　must　have　priority　in　the　order　of　nature。　But　they　say　that　fire　is　of　all　bodies　the　finest。　Hence　fire　will　be　first　in　the　natural　order。　And　whether　the　finest　body　is　fire　or　not　makes　no　difference；　anyhow　it　must　be　one　of　the　other　bodies　that　is　primary　and　not　that　which　is　intermediate。　Again；　density　and　rarity；　as　instruments　of　generation；　are　equivalent　to　fineness　and　coarseness；　since　the　fine　is　rare；　and　coarse　in　their　use　means　dense。　But　fineness　and　coarseness；　again；　are　equivalent　to　greatness　and　smallness；　since　a　thing　with　small　parts　is　fine　and　a　thing　with　large　parts　coarse。　For　that　which　spreads　itself　out　widely　is　fine；　and　a　thing　composed　of　small　parts　is　so　spread　out。　In　the　end；　then；　they　distinguish　the　various　other　substances　from　the　element　by　the　greatness　and　smallness　of　their　parts。　This　method　of　distinction　makes　all　judgement　relative。　There　will　be　no　absolute　distinction　between　fire；　water；　and　air；　but　one　and　the　same　body　will　be　relatively　to　this　fire；　relatively　to　something　else　air。　The　same　difficulty　is　involved　equally　in　the　view　elements　and　distinguishes　them　by　their　greatness　and　smallness。　The　principle　of　distinction　between　bodies　being　quantity；　the　various　sizes　will　be　in　a　definite　ratio；　and　whatever　bodies　are　in　this　ratio　to　one　another　must　be　air；　fire；　earth；　and　water　respectively。　For　the　ratios　of　smaller　bodies　may　be　repeated　among　greater　bodies。　　　Those　who　start　from　fire　as　the　single　element；　while　avoiding　this　difficulty；　involve　themselves　in　many　others。　Some　of　them　give　fire　a　particular　shape；　like　those　who　make　it　a　pyramid；　and　this　on　one　of　two　grounds。　The　reason　given　may　be…more　crudely…that　the　pyramid　is　the　most　piercing　of　figures　as　fire　is　of　bodies；　or…more　ingeniously…the　position　may　be　supported　by　the　following　argument。　As　all　bodies　are　composed　of　that　which　has　the　finest　parts；　so　all　solid　figures　are　composed　of　pryamids：　but　the　finest　body　is　fire；　while　among　figures　the　pyramid　is　primary　and　has　the　smallest　parts；　and　the　primary　body　must　have　the　primary　figure：　therefore　fire　will　be　a　pyramid。　Others；　again；　express　no　opinion　on　the　subject　of　its　figure；　but　simply　regard　it　as　the　of　the　finest　parts；　which　in　combination　will　form　other　bodies；　as　the　fusing　of　gold…dust　produces　solid　gold。　Both　of　these　views　involve　the　same　difficulties。　For　（1）　if；　on　the　one　hand；　they　make　the　primary　body　an　atom；　the　view　will　be　open　to　the　objections　already　advanced
  against　the　atomic　theory。　And　further　the　theory　is　inconsistent　with　a　regard　for　the　facts　of　nature。　For　if　all　bodies　are　quantitatively　commensurable；　and　the　relative　size　of　the　various　homoeomerous　masses　and　of　their　several　elements　are　in　the　same　ratio；　so　that　the　total　mass　of　water；　for　instance；　is　related　to　the　total　mass　of　air　as　the　elements　of　each　are　to　one　another；　and　so　on；　and　if　there　is　more　air　than　water　and；　generally；　more　of　the　finer　body　than　of　the　coarser；　obviously　the　element　of　water　will　be　smaller　than　that　of　air。　But　the　lesser　quantity　is　contained　in　the　greater。　Therefore　the　air　element　is　divisible。　And　the　same　could　be　shown　of　fire　and　of　all　bodies　whose　parts　are　relatively　fine。　（2）　If；　on　the　other　hand；　the　primary　body　is　divisible；　then　（a）　those　who　give　fire　a　special　shape　will　have　to　say　that　a　part　of　fire　is　not　fire；　because　a　pyramid　is　not　composed　of　pyramids；　and　also　that　not　every　body　is　either　an　element　or　composed　of　elements；　since　a　part　of　fire　will　be　neither　fire　nor　any　other　element。　And　（b）　those　whose　ground　of　distinction　is　size　will　have　to　recognize　an　element　prior　to　the　element；　a　regress　which　continues　infinitely；　since　every　body　is　divisible　and　that　which　has　the　smallest　parts　is　the　element。　Further；　they　too　will　have　to　say　that　the　same　body　is　relatively　to　this　fire　and　relatively　to　that　air；　to　others　again　water　and　earth。　　　　　The　common　error　of　all　views　which　assume　a　single　element　is　that　they　allow　only　one　natural　movement；　which　is　the　same　for　every　body。　For　it　is　a　matter　of　observation　that　a　natural　body　possesses　a　principle　of　movement。　If　then　all　bodies　are　one；　all　will　have　one　movement。　With　this　motion　the　greater　their　quantity　the　more　they　will　move；　just　as　fire；　in　proportion　as　its　quantity　is　greater；　moves　faster　with　the　upward　motion　which　belongs　to　it。　But　the　fact　is　that　increase　of　quantity　makes　many　things　move　the　faster　downward。　For　these　reasons；　then；　as　well　as　from　the　distinction　already　established　of　a　plurality　of　natural　movements；　it　is　impossible　that　there　should　be　only　one　element。　But　if　the　elements　are　not　an　infinity　and　not　reducible　to　one；　they　must　be　several　and　finite　in　number。
  6
  First　we　must　inquire　whether　the　elements　are　eternal　or　subject　to　generation　and　destruction；　for　when　this　question　has　been　answered　their　number　and　character　will　be　manifest。　In　the　first　place；　they　cannot　be　eternal。　It　is　a　matter　of　observation　that　fire；　water；　and　every　simple　body　undergo　a　process　of　analysis；　which　must　either　continue　infinitely　or　stop　somewhere。　（1）　Suppose　it　infinite。　Then　the　time　occupied　by　the　process　will　be　infinite；　and　also　that　occupied　by　the　reverse　process　of　synthesis。　For　the　processes　of　analysis　and　synthesis　succeed　one　another　in　the　various　parts。　It　will　follow　that　there　are　two　infinite　times　which　are　mutually　exclusive；　the　time　occupied　by　the　synthesis；　which　is　infinite；　being　preceded　by　the　period　of　analysis。　There　are　thus　two　mutually　exclusive　infinites；　which　is　impossible。　（2）　Suppose；　on　the　other　hand；　that　the　analysis　stops　somewhere。　Then　the　body　at　which　it　stops　will　be　either　atomic　or；　as　Empedocles　seems　to　have　intended；　a　divisible　body　which　will　yet　never　be　divided。　The　foregoing　arguments　show　that　it　cannot　be　an　atom；　but　neither　can　it　be　a　divisible　body　which　analysis　will　never　reach。　For　a　smaller　body　is　more　easily　destroyed　than　a　larger；　and　a　destructive　process　which　succeeds　in　destroying；　that　is；　in　resolving　into　smaller　bodies；　a　body　of　some　size；　cannot　reasonably　be　expected　to　fail　with　the　smaller　body。　Now　in　fire　we　observe　a　destruction　of　two　kinds：　it　is　destroyed　by　its　contrary　when　it　is　quenched；　and　by　itself　when　it　dies　out。　But　the　effect　is　produced　by　a　greater　quantity　upon　a　lesser；　and　the　more　quickly　the　smaller　it　is。　The　elements　of　bodies　must　therefore　be　subject　to　destruction　and　generation。　　　Since　they　are　generated；　they　must　be　generated　either　from　something　incorporeal　or　from　a　body；　and　if　from　a　body；　either　from　one　another　or　from　something　else。　The　theory　which　generates　them　from　something　incorporeal　requires　an　extra…corporeal　void。　For　everything　that　comes　to　be　comes　to　be　in　something；　and　that　in　which　the　generation　takes　place　must　either　be　incorporeal　or　possess　body；　and　if　it　has　body；　there　will　be　two　bodies　in　the　same　place　at　the　same　time；　viz。　that　which　is　coming　to　be　and　that　which　was　previously　there；　while　if　it　is　incorporeal；　there　must　be　an　extra…corporeal　void。　But　we　have　already　shown　that　this　is　impossible。　But；　on　the　other　hand；　it　is　equally　impossible　that　the　elements　should　be　generated　from　some　kind　of　body。　That　would　involve　a　body　distinct　from　the　elements　and　prior　to　them。　But　if　this　body　possesses　weight　or　lightness；　it　will　be　one　of　the　elements；　and　if　it　has　no　tendency　to　movement；　it　will　be　an　immovable　or　mathematical　entity；　and　therefore　not　in　a　place　at　all。　A　place　in　which　a　thing　is　at　rest　is　a　place　in　which　it　might　move；　either　by　constraint；　i。e。　unnaturally；　or　in　the　absence　of　constraint；　i。e。　naturally。　If；　then；　it　is　in　a　place　and　somewhere；　it　will　be　one　of　the　elements；　and　if　it　is　not　in　a　place；　nothing　can　come　from　it；　since　that　which　comes　into　being　and　that　out　of　which　it　comes　must　needs　be　together。　The　elements　therefore　cannot　be　generated　from　something　incorporeal　nor　from　a　body　which　is　not　an　element；　and　the　only　r