the ethics(part ii)-第5章

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continue　its　motion；　and　the　angle　made　by　the　line　　of　motion　in



the　recoil　and　the　plane　of　the　body　at　rest；　whereon　the　moving



body　has　　impinged；　will　be　equal　to　the　angle　formed　by　the　line



of　motion　of　incidence　and　the　　same　plane。







So　far　we　have　been　speaking　only　of　the　most　simple　bodies；



which　are　only　distinguished　　one　from　the　other　by　motion　and



rest；　quickness　and　slowness。　　We　now　pass　on　to　　compound



bodies。







DefinitionWhen　any　given　bodies　of　the　same　or　different



magnitude　are　compelled　by　　other　bodies　to　remain　in　contact；　or



if　they　be　moved　at　the　same　or　different　rates　of　　speed；　so



that　their　mutual　movements　should　preserve　among　themselves　a



certain　fixed　　relation；　we　say　that　such　bodies　are　'in　union；'



and　that　together　they　compose　one　body　　or　individual；　which　is



distinguished　from　other　bodies　by　the　fact　of　this　union。







…Axiom　IIIIn　proportion　as　the　parts　of　an　individual；　or



a　compound　body；　are　in　　contact　over　a　greater　or　less



superficies；　they　will　with　greater　or　less　difficulty　admit　of　



being　moved　from　their　position；　consequently　the　individual



will；　with　greater　or　less　　difficulty；　be　brought　to　assume



another　form。　　Those　bodies；　whose　parts　are　in　contact　　over



large　superficies；　are　called　'hard；'　those；　whose　parts　are　in



contact　over　small　　superficies；　are　called　'soft；'　those；　whose



parts　are　in　motion　among　one　another；　are　　called　'fluid。'







Lemma　IV。　　If　from　a　body　or　individual；　compounded　of　several



bodies；　certain　bodies　be　　separated；　and　if；　at　the　same　time；



an　equal　number　of　other　bodies　of　the　same　nature　　take　their



place；　the　individual　will　preserve　its　nature　as　before；　without



any　change　in　its　　actuality　（forma）。







》》》》》ProofBodies　（Lemma　i。）　are　not　distinguished　in　respect　of



substance：　　that　which　　constitutes　the　actuality　（formam）　of　an



individual　consists　（by　the　last　Def。）　in　a　union　of　　bodies；　but



this　union；　although　there　is　a　continual　change　of　bodies；　will



（by　our　　hypothesis）　be　maintained；　the　individual；　therefore；



will　retain　its　nature　as　before；　both　in　　respect　of　substance



and　in　respect　of　mode。　　Q。E。D。







Lemma　V。　　If　the　parts　composing　an　individual　become　greater　or



less；　but　in　such　　proportion；　that　they　all　preserve　the　same



mutual　relations　of　motion　and　rest；　the　　individual　will　still



preserve　its　original　nature；　and　its　actuality　will　not　be



changed。







》》》》》ProofThe　same　as　for　the　last　Lemma。







Lemma　VI。　　If　certain　bodies　composing　an　individual　be　compelled



to　change　the　motion；　　which　they　have　in　one　direction；　for



motion　in　another　direction；　but　in　such　a　manner；　　that　they　be



able　to　continue　their　motions　and　their　mutual　communication　in



the　same　　relations　as　before；　the　individual　will　retain　its　own



nature　without　any　change　of　its　　actuality。







》》》》》ProofThis　proposition　is　self…evident；　for　the　individual



is　supposed　to　retain　all　　that；　which；　in　its　definition；　we



spoke　of　as　its　actual　being。







Lemma　VII。　　Furthermore；　the　individual　thus　composed　preserves



its　nature；　whether　it　　be；　as　a　whole；　in　motion　or　at　rest；



whether　it　be　moved　in　this　or　that　direction；　so　long　　as　each



part　retains　its　motion；　and　preserves　its　communication　with



other　parts　as　　before。







》》》》》ProofThis　proposition　is　evident　from　the　definition　of　an



individual　prefixed　to　　Lemma　iv。







*****NoteWe　thus　see；　how　a　composite　individual　may　be



affected　in　many　different　　ways；　and　preserve　its　nature



notwithstanding。　　Thus　far　we　have　conceived　an　individual　　as



composed　of　bodies　only　distinguished　one　from　the　other　in



respect　of　motion　and　　rest；　speed　and　slowness；　that　is；　of



bodies　of　the　most　simple　character。　　If；　however；　we　　now



conceive　another　individual　composed　of　several　individuals　of



diverse　natures；　we　　shall　find　that　the　number　of　ways　in　which



it　can　be　affected；　without　losing　its　nature；　will　　be　greatly



multiplied。　　Each　of　its　parts　would　consist　of　several　bodies；



and　therefore　（by　　Lemma　vi。）　each　part　would　admit；　without



change　to　its　nature；　of　quicker　or　slower　　motion；　and　would



consequently　be　able　to　transmit　its　motions　more　quickly　or　more



　slowly　to　the　remaining　parts。　　If　we　further　conceive　a　third



kind　of　individuals　composed　　of　individuals　of　this　second　kind；



we　shall　find　that　they　may　be　affected　in　a　still　greater　



number　of　ways　without　changing　their　actuality。　　We　may　easily



proceed　thus　to　infinity；　　and　conceive　the　whole　of　nature　as



one　individual；　whose　parts；　that　is；　all　bodies；　vary　in　



infinite　ways；　without　any　change　in　the　individual　as　a　whole。　



I　should　feel　bound　to　　explain　and　demonstrate　this　point　at



more　length；　if　I　were　writing　a　special　treatise　on　　body。　　But



I　have　already　said　that　such　is　not　my　object；　I　have　only



touched　on　the　　question；　because　it　enables　me　to　prove　easily



that　which　I　have　in　view。







POSTULATES　I。　　The　human　body　is　composed　of　a　number　of



individual　parts；　of　diverse　nature；　each　　one　of　which　is　in



itself　extremely　complex。







II。　　Of　the　individual　parts　composing　the　human　body　some　are



fluid；　some　soft；　some　　hard。







III。　　The　individual　parts　composing　the　human　body；　and



consequently　the　human　body　　itself；　are　affected　in　a　variety　of



ways　by　external　bodies。







IV。　　The　human　body　stands　in　need　for　its　preservation　of　a



number　of　other　bodies；　by　　which　it　is　continually；　so　to　speak；



regenerated。







V。　　When　the　fluid　part　of　the　human　body　is　determined　by　an



external　body　to　impinge　　often　on　another　soft　part；　it　changes



the　surface　of　the　latter；　and；　as　it　were；　leaves　the　



impression　thereupon　of　the　external　body　which　impels　it。







VI。　　The　human　body　can　move　external　bodies；　and　arrange　them　in



a　variety　of　ways。







PROPOSITIONS　XIV。　　The　human　mind　is　capable　of　perceiving　a



great　number　of　things；　and　is　so　in　　　proportion　as　its　body　is



capable　of　receiving　a　great　number　of　impressions。







》》》》》ProofThe　human　body　（by　Post。　iii。　and　vi。）　is　affected　in



very　many　ways　by　　external　bodies；　and　is　capable　in　very　many



ways　of　affecting　external　bodies。　　But　（II。xii。）　　the　human　mind



must　perceive　all　that　takes　place　in　the　human　body；　the　human



mind　is；　　therefore；　capable　of　perceiving　a　great　number　of



things；　and　is　so　in　proportion；　&c。　　　Q。E。D。







XV。　　The　idea；　which　constitutes　the　actual　being　of　the　human



mind；　is　not　simple；　but　　compounded　of　a　great　number　of　ideas。







》》》》》ProofThe　idea　constituting　the　actual　being　of　the　human



mind　is　the　idea　of　the　　body　（II。　xiii。）；　which　（Post。　i。）　is



composed　of　a　great　number　of　complex　individual　　parts。　　But



there　is　necessarily　in　God　the　idea　of　each　individual　part



whereof　the　body　is　　composed　（II。　viii。　Cor。）；　therefore　（II。



vii。）；　the　idea　of　the　human　body　is　composed　of　　each　of　these



numerous　ideas　of　its　component　parts。　　Q。E。D。







XVI。　　The　idea　of　every　mode；　in　which　the　human　body　is



affected　by　external　bodies；　　must　involve　the　nature　of　the



human　body；　and　also　the　nature　of　the　external　body。







》》》》》ProofAll　the　modes；　in　which　any　given　body　is　affected；



follow　from　the　nature　　of　the　body　affected；　and　also　from　the



nature　of　the　affecting　body　（by　Ax。　i。；　after　the　　Cor。　of　Lemma



iii。）；　wherefore　their　idea　is　also　necessarily　（by　I；　Ax。　iv。）