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FILEI= GA\R TA\ ME\N A)BOU/LHTA TW=N €SUMPIPTO/NTWN TAPEINOU=N, TA\ DE\ BOULHTA\ XAUNOU=N TA\S YUXA/S. €EI) DE\ [4MH\]4 TA\S A(RMONI/AS A)NAINO/MENOS EI)DE/NAI DIA\ TO\ TW=| €POLITIKW=| PROSH=KON LE/GEI TI PERI\ R(UQMW=N, TOU/TOU DH/POU €TH\N TOU= *GLAU/KWNOS AI)TIATE/ON A)/GNOIAN: TA\S ME\N GA\R A(RMO- @1NI/AS EI)DE/NAI KAI\ TA\ EI)/DH TA\ E)N AU)TAI=S, TOU\S DE\ R(UQMOU\S €A)GNOEI=N E)/FATO, KAI\ EI) KAI\ TOU/TWN EI)SI/ TINES E)PITH/DEIOI PRO\S €PAIDEI/AN. I(/N' OU)=N E)NDEI/CHTAI KAI\ TH=S TOU/TWN DUNA/MEWS PE/RI €KAI\ MH\ A)TELH\S O( LO/GOS AU)TW=| KATALEIFQH=| PERI\ TH=S O(/LHS €MOUSIKH=S KAI\ TH=S EI)S PAIDEI/AN AU)TH=S SUNTELEI/AS, BRAXE/A þï€´°³¶ÿï°°±ÿï‚éî Òÿ¡˜¸†PERI\ TW=N R(UQMW=N EI)KO/TWS EI)=PEN, E)FISTA\S PW=S E)STI KAI\ E)N €TOU/TOIS PAIDEUTIKO\N KAI\ FE/RON EI)S A)RETH/N: EI)=T' EU)QU\S TO\N €POLITIKO\N FULA/TTWN, A)LL' OU)K EI)S TO\N MOUSIKO\N METAPESEI=N €E)QE/LWN, KAI\ EI)S *DA/MWNA TH\N PERI\ TW=N R(UQMW=N A)POPE/MYAS €QEWRI/AN E(\N E)K PA/NTWN SULLOGI/ZETAI, XRH=NAI TO\N PAIDEUTIKO\N €EU)LOGI/AS STOXA/ZESQAI KAI\ EU)ARMOSTI/AS: KAI\ EU)RUQMI/AS, TA/XA €KA)N TOU/TOIS EI)S PA=SAN BLE/PWN TH\N YUXH/N. DIA\ ME\N GA\R €TH=S EU)LOGI/AS O( E)N H(MI=N TELEIOU=TAI LO/GOS, DIA\ DE\ TH=S EU)AR-€MOSTI/AS KAI\ EU)RUQMI/AS TO\ A)/LOGON KOSMEI=TAI: TH=S ME\N A)PO\ €TW=N DUNA/MEWN AU)TW=N A)RXOME/NHS [1A(RMO/ZONTAI GA\R E)KEI=NAI €PRO\ TW=N E)NERGEIW=N]1, TH=S DE\ E)N TAI=S E)NERGEI/AIS MO/NWS E)MFAINO-€ME/NHS: TA/TTONTAI GA\R AI( KINH/SEIS DIA\ TW=N R(UQMW=N, DIO/TI €KAI\ TOU/TWN E)STI\ TA/CIS O( R(UQMO/S, KAQ' O(/SON XRO/NW| METROU=N-€TAI KAI\ TO\ PRO/TERO/N E)STIN E)N AU)TAI=S KAI\ U(/STERON. €@*TOU/TWN ME\N OU)=N A(/DHN: TO\ DE\ E(PO/MENON SKOPW=MEN, TI/NA €EI)DE/NAI XRH\ KAT' AU)TO\N PERI\ MOUSIKH=S KAI\ POIHTIKH=S, PW=S €E)/XOUSI PRO\S A)LLH/LAS KAI\ PO/SAI TA/CEIS EI)SI\N MOUSIKH=S. €DO/CEIEN GA\R A)\N W(DI\ ME\N TH\N MOUSIKH\N SUNA/PTEIN PRO\S TH\N €POIHTIKH/N, O(/TAN LE/GH| TO\N POIHTH\N E)N TW=| TRI/PODI KAQH=SQAI €TH=S *MOU/SHS [&legg. IV p. 719b$] KAI\ O(/TAN TH\N A)PO\ *MOUSW=N €KATOKWXH\N LABOU=SAN A(PALH\N KAI\ A)/BATON YUXH\N A)NEGEI/REIN €KAI\ E)KBAKXEU/EIN KATA/ TE W)|DA\S KAI\ TH\N A)/LLHN POI/HSIN [&Phaedr. €&p. 245a$], W(DI\ DE\ DII+STA/NEIN AU)TA\S A)LLH/LWN, W(/SPER O(/TAN €TOU\S BI/OUS DIORI/ZWN TO\N ME\N MOUSIKO\N EI)S TO\N PRW=TON FE/- @1RWN KATATA/TTH|, KAQA/PER KAI\ PA/NTA TO\N FILO/KALON, TO\N DE\ €POIHTIKO\N EI)S TO\N E(/KTON, KAQA/PER KAI\ PA/NTA TO\N MIMHTIKO/N €[&Phaedr. p. 248d$]. E)/OIKEN DH\ OU)=N POLLA\ TH=S MOUSIKH=S €EI)/DH QEASA/MENOS PA=N ME\N TO\ POIHTIKO\N GE/NOS U(PO\ TH\N MOU-€SIKH\N A)NAPE/MPEIN, OU) PA=N DE\ TO\ MOUSIKO\N EI)S TH\N POIH-€TIKH\N KATAKLEI/EIN. TI/NA OU)=N MOUSIKH\N A)\N FAI/H POIHTIKH/N, €A)/CION H(MA=S LE/GEIN DIORISAME/NOUS PRW=TON TA\ EI)/DH PA/NTA TH=S €MOUSIKH=S. LE/GOMEN OU)=N KAI\ TH\N FILOSOFI/AN AU)TH\N MEGI/STHN €EI)=NAI MOUSIKH/N, W(/SPER KAI\ E)RWTIKH\N EI) BOU/LEI FA/NAI TH\N €E)RWTIKWTA/THN A(RMOSAME/NHN OU) LU/RAN, A)LL' AU)TH\N TH\N YUXH\N €TH\N A)RI/STHN A(RMONI/AN, DI' H(\N H( YUXH\ TA/ TE A)NQRW/PINA €PA/NTA DUNATO\N KOSMEI=N KAI\ TA\ QEI=A TELE/WS U(MNW|DEI=N, AU)TO\N €MIMOUME/NH TO\N MOUSHGE/THN, O(\S U(MNEI= ME\N TO\N PATE/RA TAI=S €NOERAI=S W)|DAI=S, SUNE/XEI DE\ TO\N O(/LON KO/SMON TOI=S A)LU/TOIS €DESMOI=S O(MOPOLW=N PA/NTA, KAQA/PER O( E)N TW=| <20*KRATU/LW|>20 LE/GEI €*SWKRA/THS [&p. 405c$]. 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LE/GEI DE\ KAI\ TH\N E)K *MOUSW=N KATO-€KWXH\N MOUSIKH\N TRO/PON A)/LLON W(S E)CORMW=SAN KAI\ KINOU=SAN €EI)S TH\N E)/NQEON POIHTIKH\N TA\S YUXA/S: <20O(\S>20 GA\R A)/N, FHSI/N, €<20A)/NEU *MOUSW=N MANI/AS E)PI\ POIHTIKH=S QU/RAS A)FI/KH-€TAI, KAI\ AU)TO\S A)TELH/S E)STI POIHTH\S KAI\ H( POI/HSIS €AU)TOU= U(PO\ TH=S TW=N MAINOME/NWN H( TOU= SWFRONOU=N-€TOS H)FANI/SQH>20 [&Phaedr. p. 245a$]: KA)NTAU=QA TO\ MOUSIKO\N @1 EI)S TAU)TO\N H(/KEI KAI\ TO\ POIHTIKO/N, TH=S E)NQE/OU MOUSIKH=S TO\N €E)/NQEON A)POTELOU/SHS POIHTH/N: OU) GA\R EI)S A)/LLO TI/ FHSIN TO\N €E)K *MOUSW=N KA/TOXON E)NQEA/ZEIN H)\ EI)S TO\ POIHTH\N GENE/SQAI, €TW=N ME\N E)/MPROSQEN GEGONO/TWN E)/RGWN A)GAQW=N U(MNW|DO/N, EI)S €ZH=LON DE\ A)NEGEI/RONTA PAIDEI/AS DIA\ TOU/TWN TOU\S E)PIGINO-€ME/NOUS. O(/POU DH\ KAI\ TO\ E)/RGON MA/LISTA TH=S POIHTIKH=S O(/SON €E)STI\N EI)S PAIDEI/AN A)NH=KON E)CE/FHNEN KAI\ OI(=ON, KAI\ W(S OU) €NOMOQETIKO/N E)STIN, A)LL' O)/NTWS TRI/TON A)PO\ TH=S A)LHQEI/AS, €DIA\ TW=N EI)S TOU\S A)GAQOU\S GEGONO/TAS E)GKWMI/WN PAIDEU=ON €TOU\S ZHLOU=NTAS TA\ TW=N A)GAQW=N E)PITHDEU/MATA. 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LE/GEI DE\ A)/RA KAI\ TO\ TRI/TON MOUSIKH=S EI)=DOS, €OU)KE/TI TOU=TO KAQA/PER TO\ PRORRHQE\N E)NQEASTIKO/N, A)NAGW-€GO\N DE\ O(/MWS A)PO\ TW=N FAINOME/NWN A(RMONIW=N EI)S TO\ A)FANE\S @1 TH=S QEI/AS A(RMONI/AS KA/LLOS: FILO/KALOS GA\R KAI\ O( TOIOU=TOS €MOUSIKO/S, W(/SPER KAI\ O( E)RWTIKO/S, EI) KAI\ O(\ ME\N DI' O)/YEWS, €O(\ DE\ DI' A)KOH=S A)NAMIMNH/SKETAI TOU= KALOU=. 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E)/TI DE/, TI/NES OI( O(MOIOU=NTES SXHMA-€TISMOI\ KAI\ TI/NES OI( A)NOMOIOU=NTES: KAI\ GA\R TW=N SXHMA/TWN €TA\ ME/N E)STIN SU/MFWNA KAI\ DIA\ TOU=TO O(MOIOU=NTA KALEI=TAI, €TA\ DE\ A)SU/MFWNA KAI\ DIA\ TOU=TO A)NOMOIOU=NTA: TA\ ME\N GA\R €TRI/GWNA SU/MFWNA, TA\ DE\ TETRA/GWNA A)SU/MFWNA. DEI= TOI/NUN €TA\ O(MOIOU=NTA TW=N A)GAQOPOIW=N E)KLE/GESQAI PRO/S TE TH\N SPO-€RI/MHN W(/RAN KAI\ PRO\S A)LLH/LOUS. 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KAI\ €OU) TOU=TO MO/NON, A)LLA\ KAI\ TW=N H(MIKUKLI/WN TOU= ZW|OFO/ROU €KU/KLOU DEI= TA\S DIAFORA\S O(RA=N KAI\ W(S TO\ ME\N AU)CHTIKO/N €E)STI TH=S GENE/SEWS, TO\ A)PO\ AI)GO/KERW, TO\ DE\ MEIWTIKO/N, TO\ €A)PO\ KARKI/NOU: KAI\ GA\R E)N E)KEI/NW| ME\N E)PIDI/DWSI TO\ FW=S, €E)N TOU/TW| DE\ E)LASSOU=TAI. 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EI) DE\ TOU=T' A)LHQE/S, €EI)DO/TAS TH\N SPORI/MHN SELH/NHN DUNATO\N GIGNW/SKEIN KAI\ TH\N €W(/RAN TH=S A)POKUH/SEWS KAI\ E)/MPALIN: TAU=TA DE\ GIGNW/SKONTAS €XRH\ SKOPEI=N, EI) E(PTA/MHNON TO\ TEXQHSO/MENON H)\ E)NNEA/MHNON, €KAI\ POSAXW=S KAI\ PW=S E(KA/TERA TI/KTETAI, KAI\ OU(/TWS PROSEN-€NOEI=N TA\S GENE/SEIS TW=N SPEIROME/NWN. E)PI\ ME\N OU)=N TW=N €E)NNEAMH/NWN GI/GNONTAI AI( SPORAI\ E)N TW=| EU)WNU/MW| TETRAGW/NW| €TOU= TH=S A)POKUH/SEWS H(LI/OU [1E)KEI= GA\R O)/NTOS AU)TOU= GE/GONEN €H( SPORA/]1, E)PI\ DE\ TW=N E(PTAMH/NWN E)N TW=| DIAME/TRW|. KAI\ TA\ €ME\N E)NNEA/MHNA TELEIOU=TAI E)PI\ ME\N TH=S MEGI/STHS A)POKUH/SEWS €H(MERW=N <*S3*P*H> KAI\ W(RW=N <*H>, E)PI\ DE\ TH=S ME/SHS H(MERW=N <*S3*O*G> €W(RW=N <*H>, E)PI\ DE\ TH=S E)LAXI/STHS H(MERW=N <*S3*N*H> W(RW=N <*H>: €TA\ DE\ E(PTA/MHNA TELEIOU=TAI E)PI\ ME\N TH=S MEGI/STHS H(MERW=N €<*S3*I#2> W(RW=N <*H>, E)PI\ DE\ TH=S ME/SHS [2H(MERW=N]2 <*R*S3*A> W(RW=N <*H>, €E)PI\ DE\ TH=S E)LAXI/STHS H(MERW=N <*R*O#2> W(RW=N <*H>. 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EI) DE\ LA/BOIS E)LA/T-€TOUS MOI/RAS, OI(=ON DEKAPE/NTE KAI\ TO\ TRI/TON, KAI\ E)KBA/LOIS €W(S H(ME/RAS A)PO\ TH=S H(ME/RAS TH=S PROGENOME/NHS SUNO/DOU, E)N-€TO\S PESEI=TAI O( A)RIQMO\S TH=S META\ TH\N SPORI/MHN W(/RAN E)SO-€ME/NHS SUNO/DOU: DEI=N OU)=N OI)/ESQAI E)NNEA/MHNON TEXQH/SESQAI TO\ €SPEIRO/MENON KATA\ TH\N W(/RAN TAU/THN. OI(\ DE\ LABO/NTES TA\S €W(/RAS, TH\N SPORI/MHN KAI\ TH\N GENE/QLION, LAMBA/NOUSI TH\N €PRO\ TH=S SPORI/MHS W(/RAS SU/NODON KAI\ TH\N W(/RAN, KAQ' H(\N €GE/GONEN, KAI\ E)NARMO/ZOUSI TOU=TO TO\ O)RQOGW/NION TRI/GWNON, TH\N €O)RQH\N E)PI\ TH=S MOI/RAS TIQE/NTES KAI\ E)F' E(KA/TERA TH\N ME\N €TW=N <*S3> MOIRW=N E(STW=SAN, TH\N DE\ TW=N <*R*K> MET' AU)TH/N, ... €... TH\N TW=N <*R*N>. META\ DE\ TAU=TA TH\N [PRO\] TH=S W(ROSKO-€POU/SHS MOI/RAS TH=S GENE/SEWS [4H(ME/RAN]4 SU/NODON EU(RO/NTES €SKOPOU=SIN EI)S POI/AN E)MPI/PTEI TOU= SPORI/MOU TRIGW/NOU PLEU-€RA/N: KAI\ E)A\N ME\N EI)S TH\N U(POTEI/NOUSAN, E)NNEAMHNIAI=ON LE/-€GOUSIN: E)A\N DE\ EI)S TH\N U(PTI/AN, E(PTAMHNIAI=ON: E)A\N DE\ EI)S €TH\N O)RQH/N, A)/LOGON EI)=NAI ZW=|ON H)\ TERATW=DES. SKOPOU=SI DE\ €KAI\ TA\S MOI/RAS TW=N DU/O SUNO/DWN, TH=S TE PRO\ TH=S SPORA=S @1 KAI\ TH=S PRO\ TH=S E)SOME/NHS GENE/SEWS: KAI\ E)A\N ME\N EU(/RWSI €TH\N MI/AN E)PI\ TH=S U(POTEINOU/SHS, TH\N DE\ MI/AN E)PI\ TH=S U(PTI/AS, €E)NNEA/MHNON TH\N KU/HSI/N FASIN: E)A\N DE\ TH\N ME\N E)PI\ TH=S €U(PTI/AS, TH\N DE\ E)PI\ TH=S O)RQH=S, E(PTA/MHNON: E)A\N DE\ TH\N ME\N €E)PI\ TH=S U(POTEINOU/SHS, TH\N DE\ E)PI\ TH=S O)RQH=S, A)LO/GOU TINO\S €H)\ A)LLOKO/TOU GE/NESIN EI)=NAI. KAI\ SU/MFWNA TAU=TA TOI=S PERI\ €TO\ TRI/GWNON A)RIQMOI=S: H( ME\N GA\R U(POTEI/NOUSA KAI\ H( U(PTI/A €<*E> KAI\ <*D>, H( DE\ U(PTI/A KAI\ O)RQH\ <*D> KAI\ <*G>, H( DE\ O)RQH\ KAI\ €U(POTEI/NOUSA <*G> KAI\ <*E>: DIO\ E)KEI=NAI ME\N KATA\ FU/SIN AI( KUH/-€SEIS, E)C A)RTI/WN OU)=SAI KAI\ PERITTW=N, H( DE\ TRI/TH PARA\ FU/-€SIN, E)K DU/O OU)=SA PERITTW=N. €@*META\ DE\ TO\N OU)RANO\N KAI\ TH\N A)PO\ TW=N OU)RANI/WN E)PI/-€SKEYIN TH=S KATA\ TH\N SPORA\N EU)KAIRI/AS OI( FU/LAKES KAI\ EI)S €TH\N U(PO\ SELH/NHN TA/CIN O(RA/TWSAN TH/N TE O(/LHN KAI\ TH\N €MERIKH/N: TH\N ME\N O(/LHN EI)S TA\S PERITROPA\S TW=N W(RW=N A)PO-€BLE/PONTES, KAI\ TI/NES EI)S TH\N GONH\N E)PITHDEIO/TERAI, KAI\ KATA\ €TA\S TW=N KAQEIRGNUME/NWN KRA/SEIS. KAI\ GA\R TW=N ZW/|WN KAI\ €TW=N FUTW=N TA\ ME\N QERINH=S DEI=TAI KATASTA/SEWS EI)S TO\ GO/NI-€MON TH=S OI)KEI/AS FU/SEWS, TA\ DE\ TH=S E)NANTI/AS. OI( DE\ LO/GOI €TH=S FU/SEWS OI( PLEI=STOI PROE/RXONTAI TOU= E)/AROS, TA\ DE\ €SPE/RMATA TH=S METOPWRINH=S OU)/SHS W(/RAS KATABA/LLETAI EI)S GH=N. €DIO\ KAI/ FASI TW=N W(RW=N TH\N ME\N XEIMERINH\N EI)=NAI *KRONI/AN, €KRU/PTOUSAN U(PO\ GH=S TA\ SPE/RMATA KAQA/PER E)KEI=NOS TA\ E(AU-€TOU= GENNH/MATA, EI) BOU/LEI QEOLOGIKW=S LE/GEIN, KAI\ DIA\ TH\N €YU/CIN H(\N E)NDI/DWSI TOI=S GIGNOME/NOIS FUSIKW=S: TH\N DE\ E)NAN-€TI/AN TAU/TH|, TH\N QERINH/N, *)AREI+KH\N DIA\ TH\N QE/RMHN, H(\N @1 PARE/XEI TOI=S FUSIKOI=S, KAI\ DIA\ TH\N E(TERO/THTA TH\N DIAKRITI-€KH\N PA/NTWN, H(\N H( TH=S QERMO/THTOS E)NEIKONI/ZETAI DIA/KRISIS: €TH\N DE\ E)ARINH\N *DI/I+ON W(S GENNHTIKH\N KAI\ E)KFANTIKH\N TW=N €KEKRUMME/NWN LO/GWN, O(\ KAI\ O( *ZEU\S EI)S TO\N PATE/RA DRA=| TA\ €GENNH/MATA AU)TOU= TA\ KEKRUMME/NA AU)TO\S EI)S TO\ E)MFANE\S €PROA/GWN: TH\N DE\ METOPWRINH\N *)AFRODI/THS: E)N TAU/TH| GA\R H( €KATABOLH\ GI/NETAI TW=N SPERMA/TWN EI)S GH=N, TOU=TO DE\ *)AFRO-€DI/THS E)/RGON TA\ GO/NIMA MIGNU/NAI KAI\ EI)S KOINWNI/AN A)/GEIN €TH\N TH=S GENE/SEWS AI)TI/AN [1KAI\ DIA\ TAU=TA A)/RA KAI\ O( MU=QOS €TH\N *KO/RHN A(RPASQH=NAI/ FHSIN E)N TH=| W(/RA| TAU/TH|, TH=S €ZW|OGONI/AS TW=N MERIKW=N PA/NTWN PROI+STAME/NHN, PROSQEI\S O(/TI €KAI\ E)N TH=| I(STOPOII/A| TO\N SKORPI/ON U(FAI/NOUSA, TO\N TA\ ME/SA €TH=S W(/RAS EI)LHXO/TA TAU/THS, U(POMEI/NEIEN TH\N A(RPAGH/N: KAI\ €GA\R DIA\ TH\N MESO/THTA KAI\ DIA\ TO\ GO/NIMON OI)KEI/WS E)/XEI PRO\S €TH\N ZW|OGONI/AN O( SKORPI/OS, KAI/ TINES AU)TO\N KAI\ W(S TO/TE €TW=N SPERMA/TWN SKORPIZOME/NWN O)NOMASQH=NAI/ FASIN]1. 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A)LL' H(\ ME\N KAI\ PEI/QETAI TW=| €E)N AU)TH=| PROFH/TH| KAI\ GI/NETAI E)PISTATIKWTE/RA PERI\ TH\N E)KLO-€GH/N, H(\ DE\ A)PEIQH/SASA MIKRO\N U(/STERON METAMELEI/AS A)NA-€PI/MPLATAI KAI\ KAKW=N, E)PIDRAMOU=SA DIA\ PA/QOS TOU/TOIS, W(=N €O( E)N AU)TH=| PROFH/THS A)NE/STELLEN. €@<20*EI)PO/NTOS DE\ TAU=TA TO\N PRW=TON LAXO/NTA E)/FH €EU)QU\S E)PIO/NTA TH\N MEGI/STHN TURANNI/DA E(LE/SQAI>20 €ME/XRI TOU= <20E)/QEI A)/NEU FILOSOFI/AS A)RETH=S METEILHFO/TA>20 €[&p. 619bc$]. *TOU\S ME\N LO/GOUS TOU= PROFH/TOU DI' AU)TW=N €E)PIDEI/KNUSIN TW=N E)/RGWN E)NARGESTA/TOUS O)/NTAS E)/K TE TW=N €A)PERISKE/PTWS E)PITREXO/NTWN TAI=S AI(RE/SESIN DIA\ TA\S PROFAINO- @1ME/NAS DUNA/MEIS KAI\ E)K TW=N DIA\ KRI/SIN KAI\ LOGISMO\N €A)KRIBH= MENO/NTWN A)METABLH/TWN E)F' OI(=S EI(/LONTO BI/OIS: POLLH\N €DE\ PROSE/QHKEN H( TOU= MU/QOU SKHNH\ TOI=S LO/GOIS E)/M[F]A[SI]N, €EI)PO/NTOS TO\N E)K TOU= PRW/TOU KLH/ROU PROSELQO/NTA TH=| AI(RE/SEI €TOIOU/TOIS SFA/LMASI PERIPESEI=N KAI\ E)PEISAGAGO/NTOS TRAGIKA\ €PA/QH TH=| E)PISTA/SEI KAI\ QRH/NOUS KAI\ KOPETOU/S, OI)MWZOU/SHS €TA\ AI(REQE/NTA TH=S YUXH=S KAI\ PRO\ TW=N E)KBA/SEWN A)NAKLAO-€ME/NHS KAI\ OU)K E)XOU/SHS A)NADU=NAI TA\ AI(REQE/NTA: PROEI/RHTAI €GA\R TH\N E(LOME/NHN E)C A)NA/GKHS TW=| BI/W| SUNE/SESQAI, KAI\ TOU= €PANTO\S A)PAITOU=NTOS KAI\ TOU= DAI/MONOS A)POPLHROU=NTOS TH\N €AI(/RESIN. 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EI) DE\ A)POBLE/YEIAS KAI\ EI)S AU)TO\N TO\N O(/LON €DHMIOURGO\N KAI\ TO\ A)/TREPTON TW=N QEW=N KAI\ A)MEI/LIKTON, OU(\S €KAI\ H( <20E)/NQEOS POI/HSIS>20 FU/LAKAS W)NO/MASE TOU= *DIO/S, E)/XOIS A)\N €KAI\ TH\N E)N TW=| PATRI\ TW=N DITTW=N TOU/TWN GENW=N PROUPA/R-€XOUSAN AI)TI/AN: DIA\ ME\N GA\R TO\ O)\N TO\ DHMIOURGIKO\N PA/NTA €KEKO/SMHTAI, DIA\ DE\ TH\N A)/TREPTON E)N AU)TW=| FROURA\N ME/NEI €PA=SA H( DIAKO/SMHSIS AI)W/NIOS, PA/SHS A)TACI/AS A)/RDHN A)FANI-€ZOME/NHS. I)/DOIS D' A)\N E)KEI= KAI\ TH\N *DI/KHN TH\N META\ TOU= €*DIO\S TA\ PA/NTA KATEUQU/NOUSAN_E(/PETAI GA\R AU)TW=| PRO\ <20TOU= €QEI/OU NO/MOU TIMWRO/S>20_KAI\ TH\N E)NO/PLION TA/CIN, MEQ' €H(=S DIATA/TTEI TO\ PA=N, W(/SPER LE/GOUSIN OI( TA\S TITANOMAXI/AS TE €KAI\ GIGANTOMAXI/AS A)NAGRA/YANTES. A)LLA\ TAU=TA ME\N KAI\ <20EI)SAU=-€QIS>20. TO\ D' E)/CWQEN>20 KAI\ <20E)/NDOQEN>20 DU/NAITO A)/N TIS KAI\ @1 OU(TWSI\ NOEI=N: H( PLHMMELH\S KAI\ A)/TAKTOS TW=N SWMA/TWN R(OH\ €POTE\ ME\N GI/NETAI PARA\ TH\N A)DUNAMI/AN TW=N LO/GWN, POTE\ DE\ €PARA\ TH\N PLEONECI/AN TH=S U(/LHS: EI)SI\ DE\ OI( ME\N LO/GOI TOI=S €POIHTIKOI=S AI)TI/OIS OI)KEI=OI, H( DE\ U(/LH DIA\ TH\N E(AUTH=S A)ORI-€STI/AN KAI\ TO\ PO/RRW TH=S U(FE/SEWS CE/NH TW=N KOSMOU/NTWN AU)TH/N. €OU)KOU=N H( A)NANTAGW/NISTOS R(W/MH TW=N QEW=N KAI\ H( A)/TREPTOS €TA/CIS KAI\ H( TH=S DHMIOURGI/AS FROURA\ PANTOI/WS A)NAIROU=SA €TH\N PLHMME/LEIAN A)NANEOI= ME\N TOU\S LO/GOUS KAI\ PARAMUQEI=TAI €TH\N A)SQE/NEIAN AU)TW=N, KATAGWNI/ZETAI DE\ TH\N PLEONECI/AN TH=S €U(/LHS, OU)X O(/TI A)NQI/STATAI TOI=S QEOI=S TOI=S PARA/GOUSIN AU)TH/N, €A)LL' O(/TI DIA\ TH\N A)ORISTI/AN FEU/GOUSA TO\N KO/SMON KRATEI=TAI TOI=S €EI)/DESI DIA\ TH\N DHMIOURGIKH\N FROURA/N, PRO\S H(\N OU)DE\N A)NQI/-€STASQAI DUNATO/N, PA/NTA DE\ EI)=NAI KATH/KOA DEI= PRO\S AU)TH/N, €O(/PWS A)\N A)EI\ DIAME/NH| TA\ E)N TW=| KO/SMW| PA/NTA KAI\ H)=| PRAGMA/-€TWN O( DHMIOURGO\S A)IDI/WN PATH/R, A(/TE A)KI/NHTOS W)\N KAI\ E)N €AI)W=NI XWRISTW=S I(DRUME/NOS. €@<20*FU/SIN GA\R OI)=MAI/ TINA TW=N FULA/KWN TH=S YUXH=S €E)LE/GOMEN A(/MA ME\N QUMOEIDH=, A(/MA DE\ FILO/SOFON DEI=N €EI)=NAI DIAFERO/NTWS, I(/NA PRO\S E(KATE/ROUS DU/NAINTO €PRA=OI KAI\ XALEPOI\ GI/GNESQAI>20 [&`18 A. cf. rep. II 375 C €&`376 C$]. €@*TO\ FILO/SOFON KAI\ TO\ QUMOEIDE\S A)MFO/TERA PERIE/XEI TA\ €GE/NH, TO/ TE E)PIKOURIKO\N KAI\ TO\ LEGO/MENON I)DI/WS FULAKIKO/N, €W(/SPER KAI\ TO\ E)PIQUMHTIKO\N E)FARMO/SEI TW=| TRI/TW| TW=| KALOU-€ME/NW| QHTIKW=|: DIO/TI GA\R TH\N A)/NW PO/LIN A)NTIDIEI=LE PRO\S €TH\N KA/TW, TOI=S DITTOI=S O)NO/MASI TOU/TOIS TA\S DIAFORA\S TW=N €E)N AU)TH=| TA/CEWN E)DH/LWSEN, W(S EI)/ TIS EI)S OU)RANO\N KAI\ GE/NESIN €TO\N KO/SMON DIELO/MENOS E)/LEGEN E)N TW=| OU)RANW=| DAIMONI/AS TE €EI)=NAI TA/CEIS KAI\ QEI/AS, A)MFOTE/RAS DE\ FULAKTIKA\S TH=S GENE/-€SEWS KAI\ TOU= PANTO\S E)KA/LEI: TO\ GA\R PA=N FROUREI=TAI ME\N €KAI\ U(PO\ QEW=N, FROUREI=TAI DE\ KAI\ U(PO\ DAIMO/NWN, U(P' E)KEI/-€NWN ME\N O(LIKW=S KAI\ E(NIAI/WS KAI\ E)CH|RHME/NWS, U(PO\ TOU/TWN @1 DE\ MERIKW=S KAI\ PEPLHQUSME/NWS KAI\ PROSEXE/STERON TOI=S U(P' €AU)TW=N FROUROUME/NOIS: PERI\ GA\R E(/KASTON QEO\N PLH=QOS TE/TA-€KTAI DAIMO/NWN MERIZO/MENON AU)TOU= TH\N MI/AN KAI\ O(/LHN PRO/-€NOIAN. PROSH/KEI DH\ OU)=N TO\ ME\N FILO/SOFON [2TOI=S]2 QEOI=S KAQ-€O/SON H(/NWNTAI PRO\S TO\ NOHTO\N KAI\ KAQO/SON PEPLH/RWNTAI TOU= €O)/NTOS, TO\ DE\ QUMOEIDE\S TOI=S DAI/MOSI KAQO/SON A)NASTE/LLOUSI €PA=SAN PLHMME/LEIAN E)K TOU= PANTO\S KAI\ KAQO/SON DORUFOROU=SI €TOU\S QEOU\S W(/SPER O( QUMO\S TO\N LO/GON, KAI\ KAQO/SON SWTH=RE/S €EI)SI TW=N QEI/WN NO/MWN KAI\ TW=N TH=S *)ADRASTEI/AS QESMW=N. €DIA\ DE\ TAU/TAS TA\S AI)TI/AS PRA=OI ME/N EI)SI TOI=S OI)KEI/OIS, E)M-€MELW=S AU)TW=N PARAMUQOU/MENOI TH\N A)SQE/NEIAN W(S FU/SEI SUG-€GENW=N, XALEPOI\ DE\ TOI=S E)/CWQEN, W(S E)CH|RHME/NWS KAI\ KAT' €A)/KRAN U(PERBOLH\N A)FANI/ZONTES AU)TW=N TH\N A)ORISTI/AN. €@<20*TI/ DE\ TROFH=S; A)=R' OU) GUMNASTIKH=| KAI\ MOUSIKH=| €MAQH/MASI/ TE O(/SA PROSH/KEI TOU/TOIS E)N A(/PASI TEQRA/-€FQAI;>20 [&`18 A. cf. rep. III 401 ss$] €@*OI( ME\N EI)RHME/NOI LO/GOI TU/POI TINE\S H)=SAN E)PI\ PA/NTAS €KOINH=| DIATEI/NONTES KATA\ TH\N DHMIOURGIKH\N DIAKLH/RWSIN KAI\ €TH\N E(TERO/THTA TH\N QEI/AN, DIORI/ZONTES TA\ PROSH/KONTA E)PITH-€DEU/MATA E(KA/STOIS KAI\ DIANE/MONTES TA\S DUNA/MEIS OI)KEI/WS TOI=S €U(PODEXOME/NOIS: E)NTEU=QEN DE\ LOIPO\N U(FAI/NETAI TW=N POLITW=N €O( BI/OS DIA\ TROFH=S KAI\ E)PITHDEUMA/TWN KAI\ KOINWNI/AS KAI\ €PAIDOPOII/AS PROI+W\N EI)S TE/LOS A)P' A)RXH=S DEO/NTWS. 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TA/X' €OU)=N EI) LE/GOIMEN TROFH\N ME\N TH\N TELEIO/THTA TH\N A)POPLHROU=SAN €E(/KASTON TW=N AU)TW=| PROSHKO/NTWN A)GAQW=N KAI\ AU)TA/RKH POIOU=-€SAN KATA/ TE TA\S NOH/SEIS KAI\ TA\S PRONOI/AS, MOUSIKH\N DE\ KAI\ €GUMNASTIKH\N TH\N ME\N E)NARMONI/OUS A)POTELOU=SAN TA\S ZWA/S, €TH\N DE\ E)/NRUQMON KAI\ E)MMELH= TH\N QEI/AN KI/NHSIN E)RGAZOME/NHN, €A)EI\ TO\ AU)TO\ THROU=SAN EI)=DOS KAI\ TH\N AU)TH\N E(/CIN A)/TREPTON €TW=N QEI/WN O)XHMA/TWN_DIA\ TAU=TA GA\R DH\ KAI\ *SEIRH=NAS €<20A)LLAXOU=>20 PROSEI=PE TA\S QEI/AS YUXA\S KAI\ E)/NRUQMON TH\N OU)-€RANI/AN A)PEFH/NATO KI/NHSIN: GUMNASTIKH\ ME\N GA\R E)N E)KEI/NOIS, €I)ATRIKH\ DE\ E)N TOI=S U(PO\ SELH/NHN, TOI=S KAI\ TO\ PARA\ FU/SIN €E)PIDEXOME/NOIS_TA/X' OU)=N EI) TAU=TA LE/GOIMEN, O)RQW=S A)\N LE/-€GOIMEN: A)/NWQEN GA\R A)PO\ TW=N NOHTW=N E)FH/KOUSI DUNA/MEIS €E)F' O(/LON TO\N OU)RANO\N A(RMONI/AN TE E)PILA/MPOUSAI TAI=S ZWAI=S €TH\N A)RI/STHN KAI\ A)/TREPTON R(W/MHN TOI=S O)XH/MASIN AU)TW=N, E)PEI\ þï€´°³¶ÿï°±°ÿï‚éî Ôéÿ¡˜©ˆ–KAI\ TA\ MAQH/MATA NOH/SEIS EI)SI\ TW=N YUXW=N TW=N OU)RANI/WN, €KAQ' A(\S A)NATRE/XOUSIN E)PI\ TO\ NOHTO/N, E(PO/MENAI TW=| MEGA/LW| €*DII\ KAI\ QEW/MENAI TO/N TE E(NIAI=ON A)RIQMO\N KAI\ TO\N W(S A)LH-€QW=S OU)RANO\N KAI\ TO\ NOERO\N SXH=MA. DIO\ DH\ KAI\ A)RIQMHTI-€KH\N A)\N EI)/POIS E)N AU)TAI=S TH\N A)LHQESTA/THN KAI\ A)STRONOMI/AN €KAI\ GEWMETRI/AN: KAI\ GA\R TO\ AU)TOTA/XOS O(RW=SI KAI\ TH\N AU)TO-€BRADUTH=TA, TA\ PARADEI/GMATA TW=N KAT' OU)RANO\N PERIO/DWN, @1 KAI\ O(/LWS TH\N PRWTOURGO\N KAI\ NOERA\N PERIFORA\N KAI\ TO\N €QEI=ON A)RIQMO\N KAI\ TA\ SXH/MATA TA\ NOERA\ KAI\ PRO/ GE TOU/TWN €TH\N DIALEKTIKH/N, KAQ' H(\N TO\ NOHTO\N A(/PAN NOOU=SI KAI\ E(NI/-€ZONTAI PRO\S TH\N MI/AN TW=N E(NA/DWN A(PASW=N AI)TI/AN: KAI\ EI) €DEI= DIELO/NTA LE/GEIN, DIA\ ME\N TW=N TOIOU/TWN MAQHMA/TWN E)NER-€GOU=SI PERI\ TA\ PRW=TA, DIA\ DE\ TH=S GUMNASTIKH=S A)XRA/NTWS €PROI/+STANTAI TW=N DEUTE/RWN, DIA\ DE\ TH=S MOUSIKH=S E)NARMONI/WS €TO\N SU/NDESMON SUNE/XOUSI TW=N O(/LWN. €@<20*TOU\S DE/ GE OU(/TW TRAFE/NTAS E)LE/XQH POU MH/TE €XRUSO\N MH/TE A)/RGURON MH/TE A)/LLO POTE\ MHDE\N KTH=MA €AU)TW=N I)/DION NOMI/ZEIN>20 [&`18 B. cf. rep. III 416 D ss$]. €*(\A ME\N E)PI\ TH=S EU)NOMWTA/THS PO/LEWS PROSTE/TAKTAI, DH/LHN €E)/XEI TH\N AI)TI/AN KAI\ EI)/RHTAI PRO\S TOU= *SWKRA/TOUS E)N E)KEI/NOIS: €PW=S DE\ KAI\ EI)S TO\N OU)RANO\N TAU=TA METOI/SOMEN; H)= KATIDO/N-€TES, DI' H(\N AI)TI/AN A)/NQRWPOI XRUSO\N KAI\ A)/RGURON DIW/KOUSI €KAI\ TI/ POTE E)NNOOU=NTES E)/RWTA TOU=TON E)RW=SIN A)PE/RANTON: €DH=LON DH\ O(/TI TA\S E(AUTW=N XREI/AS E)K PANTO\S QERAPEU/EIN E)QE/-€LONTES KAI\ TA\ PRO\S H(DONH\N E(AUTOI=S E)KPORI/ZEIN E)PIQUMOU=N-€TES: DIA\ GA\R TAU=TA KAI\ TO\N POLUA/RATON PLOU=TON E)KPLH/TTON-€TAI. <20TOI=S GOU=N PLOUSI/OIS POLLA/ FASI TA\ PARAMU/QIA €EI)=NAI>20 KATA\ TO\N <20*KE/FALON>20 [&rep. I 329 E$]. EI) DH\ TAU=TA OU(/TWS €E)/XONTA/ E)STIN, H( TW=N OU)RANI/WN QEW=N TELEIO/THS AU)TA/RKHS OU)=SA €KAI\ PRO\S TO\ KALO\N E)STRAMME/NH KAI\ TO\ A)GAQO\N OU)DE\N DEI=TAI €TH=S E)PEISA/KTOU TAU/THS KAI\ FAINOME/NHS AU)TARKEI/AS OU)DE\ EI)S €XREI/AN BLE/PEI KAI\ TH=S XREI/AS STOXA/ZETAI, PO/RRW DE\ A(PA/SHS €E)NDEI/AS I(DRUME/NH KAI\ TH=S U(LIKH=S A)NA/GKHS KAI\ PLH/RHS OU)=SA TW=N €A)GAQW=N TH\N H(GEMONIKH\N E)/XEI TA/CIN E)N TW=| PANTI/. KAI\ MH\N €KAI\ TO\ MERISTO\N KAI\ DIH|RHME/NON A)GAQO\N OU) PROSI/ETAI, TO\ €DE\ KOINO\N KAI\ E)PI\ TA\ O(/LA DIATEI=NON KAI\ A)ME/RISTON PROBE/-€BLHTAI KAI\ KATA\ TOU=TO XARAKTHRI/ZETAI DIAFERO/NTWS. E)FAR-€MO/SEI A)/RA KAI\ TOU/TOIS TO\ <20MH/TE XRUSO\N MH/TE A)/RGURON @1 MH/TE A)/LLO MHDE\N KTH=MA NOMI/ZEIN I)/DION AU)TW=N>20. EI) €DE\ BOU/LEI, KAI\ TOU=TON LEGE/SQW TO\N TRO/PON FUSIKW=S: KAI\ €XRUSO\S KAI\ A)/RGUROS KAI\ E(/KASTA TW=N META/LLWN, W(/SPER KAI\ €TW=N A)/LLWN, A)PO\ TW=N OU)RANI/WN E)N GH=| FU/ETAI QEW=N KAI\ TH=S €E)KEI=QEN A)PORROI/AS. LE/GETAI GOU=N *(HLI/OU ME\N O( XRUSO/S, *SELH/-€NHS DE\ O( A)/RGUROS, *KRO/NOU DE\ MO/LUBDOS KAI\ *)/AREWS O( SI/DH-€ROS. TAU=TA DH\ OU)=N GENNA=TAI ME\N E)KEI=QEN, U(FI/STATAI DE\ E)N €GH=| KAI\ OU)K E)N E)KEI/NOIS TOI=S TA\S A)PORROI/AS A)FIEI=SIN: OU)DE\N €GA\R A)PO\ TW=N E)NU/LWN E)KEI=NA EI)SDE/XETAI: KAI\ E)/STI PA/NTA ME\N €E)K PA/NTWN, E)PIKRATEI= DE\ O(/MWS A)/LLH E)N A)/LLOIS I)DIO/THS, OI(=S €ME\N *KRO/NIOS, OI(=S DE\ *(HLIAKH/, PRO\S H(\N KAI\ A)PIDO/NTES OI( €TOU/TWN FILOQEA/MONES TO\ ME\N EI)S TH/NDE, TO\ DE\ EI)S A)/LLHN €DU/NAMIN A)NAPE/MPOUSIN. OU)/T' OU)=N I)/DIA TAU=TA TW=N QEW=N E)STIN, €A)LLA\ KOINA/_PA/NTWN GA/R E)STIN E)/KGONA_OU)/TE E)N E)KEI/NOIS €E)STI/N_OU) GA\R DEI=TAI AU)TW=N TA\ POIOU=NTA_A)LLA\ KATA\ €TA\S E)C AU)TW=N A)PORROI/AS E)NTAU=QA SUMPH/GNUTAI. DIA\ TI/ €OU)=N PARA\ A)NQRW/POIS MERISTW=S TAU=TA SPOUDA/ZETAI; DIO/TI €ZWH\N E)/XOUSIN E)/NULON KAI\ PRO\S TO\ MERIKO\N A)POTEI/NONTAI TOU= €O(/LOU A)POSTA/NTES: DIA\ GA\R TOU=TO TO\ E)MO\N KAI\ OU)K E)MO\N POLU\ €PAR' AU)TOI=S, E(/NWSIS DE\ KAI\ KOINWNI/A ZWH=S E)KLE/LOIPEN. €@<20*)ALL' W(S E)PIKOU/ROUS MISQO\N LAMBA/NONTAS TH=S €FULAKH=S PARA\ TW=N SW|ZOME/NWN U(P' AU)TW=N, O(/SOS €SW/FROSI ME/TRIOS, A)NALI/SKEIN TE DH\ KOINH=| KAI\ SUN-€DIAITWME/NOUS MET' A)LLH/LWN ZH=N, E)PIME/LEIAN E)/XON-€TAS A)RETH=S DIA\ PANTO/S, TW=N A)/LLWN E)PITHDEUMA/TWN €SXOLH\N A)/GONTAS>20 [&`18 B. cf. rep. 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SUNTELEI= DE\ AU)TOI=S €H( TOU/TWN I(STORI/A PRO/S TE TH\N GNW=SIN TW=N O(MOI/WN, A)F' W(=N €H( TW=N O(/LWN A)NA/MNHSIS, KAI\ PRO\S TH\N TOU= ME/LLONTOS GNW=SIN: @1 DIA\ GA\R TW=N TOIOU/TWN THRH/SEWN EU(RI/SKOUSI TA\S POIHTIKA\S €TW=N SXHMA/TWN TW=N OU)RANI/WN DUNA/MEIS: TI/NWN GA\R O)/NTWN €TI/NA SUNE/BH LABO/NTES E)/XOUSI TA\S TW=N E)SOME/NWN AI)TI/AS A)PO\ €TW=N AU)TW=N SULLOGI/ZESQAI SHMEI/WN. DOKEI= D' E)/MOIGE KAI\ O( €TW=N <20*PUQAGOREI/WN>20 LO/GOS MIMEI=SQAI TH\N TW=N *AI)GUPTI/WN €TOIAU/THN I(STORI/AN, O( PARASKEUA/ZWN TA\S YUXA\S KAI\ TW=N PRO-€TE/RWN A)NAMIMNH/SKESQAI BI/WN: W(S GA\R E)F' E(NO\S A)NDRO/S, MA=L-€LON DE\ YUXH=S MIA=S, DIAFO/ROUS BI/OUS, OU(/TWS E)F' E(NO\S E)/QNOUS €TA\S DIAFO/ROUS PERIO/DOUS PROSH/KEI LAMBA/NEIN. W(S OU)=N E)N €E)KEI/NOIS AI( TW=N PROBEBIWME/NWN A)NAMNH/SEIS TELEIWTIKAI\ TW=N €YUXW=N EI)SIN, OU(/TW DH\ KAI\ E)N TOU/TOIS AI( TW=N PRO/SQEN PE-€RIO/DWN I(STORI/AI MEGI/STHN EI)S FRO/NHSIN PARE/XONTAI SUNTE/-€LEIAN. E)/TI TOI/NUN KAI\ PRO\S TH\N TOU= PANTO\S O(MOIOU=NTAI €DIAKO/SMHSIN AI( TOIAU=TAI THRH/SEIS: TOU\S ME\N GA\R E(STW=TAS €LO/GOUS MIMOU=NTAI TH=S FU/SEWS, DI' W(=N A)KINH/TWN MENO/NTWN €KAI\ TOI=S METABALLOME/NOIS H( TA/CIS E)PIGI/GNETAI. EI) TOI/NUN €I(ERW=N TO\ A(GIW/TATO/N E)STIN O( KO/SMOS, E)N W(=| ME/NOUSIN OI( LO/GOI €DIAIWNI/WS OI( SUNE/XONTES TO\ PA=N, E)/XOI A)\N EI)KO/NA TH=S TOU/TWN €SUSTA/SEWS H( E)N TOI=S I(EROI=S A)POGRAFH\ TW=N PALAIW=N E)/RGWN, €KAI\ LE/GOI A)\N O( LO/GOS O( TW=N *AI)GUPTI/WN, O(/TI KAI\ O(/SON E)STI\ €MO/NIMON E)N TOI=S AI)SQHTOI=S KAI\ A)RARO\S KAI\ A)EI\ W(SAU/TWS €E)/XON, TOU=TO A)PO\ TW=N NOHTW=N PARAGI/GNETAI QEW=N, O(/SON DE\ €KINOU/MENON A)/LLOTE A)/LLWS, GIGNO/MENO/N TE KAI\ A)POLLU/MENON, €TOU=TO E)K TH=S NE/AS E)FH/KEI DHMIOURGI/AS, E)PEI\ KAI\ TO\ I(ERATI-€KO\N GE/NOS TO\ MEMNHME/NON TW=N PALAIW=N EI)KO/NA FE/REI TA/CEWS €QEI/AS SUNEKTIKH=S TW=N O(/LWN KAI\ MONI/MOU KAI\ TH=| QEI/A| MNH/MH| €TA\ PA/NTA FROUROU/SHS, A)F' H(=S KAI\ H( NE/A DHMIOURGI/A PLH-€ROUME/NH TAUTO/THTA KAI\ SUNOXH\N KAI\ STA/SIN E)PILA/MPEI TOI=S €POLUMETABO/LOIS PRA/GMASI. €@<20*TA\ DE\ PAR' U(MI=N KAI\ TOI=S A)/LLOIS A)/RTI KATESKEU-€ASME/NA E(KA/STOTE TUGXA/NEI GRA/MMASI KAI\ A(/PASIN O(PO/-€SWN PO/LEIS DE/ONTAI>20 [&`23 A$]. @1 @*(H KATASKEUH\ SU/MBOLO/N E)STI TH=S A)EI\ NE/A DHMIOURGOU/SHS €AI)TI/AS KAI\ TA\ MH/PW O)/NTA PARAGOU/SHS KAI\ PA/NTA PRO\S TH\N €MI/AN SUNTE/LEIAN TOU= KO/SMOU SUNARMOZOU/SHS: KAI\ GA\R E)N TAI=S €OI)KI/AIS KATASKEUH\N KALOU=MEN TH\N PA/NTWN TW=N A)NAGKAI/WN €PARASKEUH/N. TOIAU=TA DE/ E)STIN E)N ME\N TAI=S PO/LESI GRA/MMATA €KAI\ TE/XNAI KAI\ A)GORAI\ KAI\ LOUTRA\ KAI\ PA/NTA TA\ O(/MOIA, E)N €DE\ TW=| PANTI\ TA\ E)/GXRONON KAI\ MERIKH\N E)PIDEXO/MENA SU/STASIN. €W(S OU)=N TA\ I(ERA\ TA\S U(PODOXA\S E)SH/MAINE TW=N A)IDI/WN LO/GWN €KAI\ TA\S SUNEKTIKA\S DUNA/MEIS KAI\ FROURHTIKA/S, OU(/TWS AI(/DE €AI( PO/LEIS DHLOU=SI TA\S TW=N A)EIMETABO/LWN U(POSTA/SEIS E)K POL-€LW=N KAI\ A)NOMOI/WN KAI\ QNHTW=N SUNESTW/SAS. 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KAI\ €MH\N KAI\ TOU\S TRO/POUS TW=N EU)XW=N A)FORIZO/MEQA POLUEIDEI=S €O)/NTAS, TOU\S ME\N KATA\ GE/NH KAI\ EI)/DH TW=N QEW=N: DHMIOURGIKH\ €GA/R E)STIN EU)XH\ KAI\ KAQARTIKH\ KAI\ ZW|OPOIO/S: DHMIOURGIKH\ €ME/N, OI(=ON U(PE\R O)/MBRWN KAI\ A)NE/MWN: OI( GA\R DHMIOURGOI\ TH=S €TOU/TWN AI)/TIOI GENE/SEWS: KAI\ AI( TW=N *EU)DANE/MWN EU)XAI\ PARA\ €*)AQHNAI/OIS PRO\S TOU/TOUS E)GI/NONTO TOU\S QEOU/S. KAQARTIKAI\ €DE/, AI( E)PI\ A)POTROPAI=S LOIMIKW=N NOSHMA/TWN H)\ PANTOI/WN MO-€LUSMW=N, OI(/AS DH\ KAI\ E)N TOI=S I(EROI=S E)/XOMEN A)NAGEGRAMME/NAS. €ZW|OPOIOI\ DE/, W(S AI( U(PE\R TH=S TW=N KARPW=N GENE/SEWS QERA-€PEU/OUSAI TOU\S KREI/TTONAS H(MW=N TH=S ZW|OGONI/AS AI)TI/OUS: KAI\ €TELESIOURGOI/, DIO/TI PRO\S TA\S TA/CEIS TAU/TAS H(MA=S A)NATEI/NOUSI @1 TW=N QEW=N: KAI\ O( E)NALLA/TTWN TH\N TOU/TWN KRI/SIN A)POPI/PTEI €TH=S O)RQO/THTOS TW=N EU)XW=N. 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PA/LIN D' AU)= METABALW\N TO\N €PRW=TON *DI/A PROSAGOREU/EI KAI\ BASILE/A TOU= NOHTOU=, TO\N DE\ @1 DEU/TERON A)/RXONTA, KAI\ O( AU)TO\S AU)TW=| GI/GNETAI *ZEU\S KAI\ *KRO/NOS €KAI\ *OU)RANO/S. PA/NTA GOU=N TAU=TA/ E)STI TO\ PRW=TON, OU(= PA/NTA €O( <20*PARMENI/DHS>20 [&`141 E s$] A)FEI=LE, PA=N O)/NOMA KAI\ PA=SAN SXE/-€SIN KAI\ PA/NTA LO/GON. KAI\ H(MEI=S ME\N OU)DE\ PATE/RA TO\N PRW=TON €H)NESXO/MEQA KALEI=N, O(\ DE\ TO\ AU)TO\ KAI\ PATE/RA KAI\ E)/GGONON €KAI\ A)PO/GONON A)PE/FHNEN. <20*)ATTIKO\S>20 DE/, O( TOU/TOU DIDA/-€SKALOS, AU)TO/QEN TO\N DHMIOURGO\N EI)S TAU)TO\N A)/GEI TA)GAQW=|, €KAI/TOI A)GAQO\S ME\N KALEI=TAI PARA\ TW=| *PLA/TWNI, TA)GAQO\N DE\ €OU)/, KAI\ NOU=S PROSAGOREU/ETAI, TA)GAQO\N DE\ AI)/TION A(PA/SHS €OU)SI/AS KAI\ E)PE/KEINA TOU= O)/NTOS E)STI/N, W(S E)N <20*POLITEI/A|>20 €[&VI 509 B$] MEMAQH/KAMEN. 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DIAFE/ROUSI DE\ OU(=TOI, DIO/TI O( ME\N PRW=-€TOS NOU=S O)/NTWS E)STI\N O(/ E)STIN, O( DE\ DEU/TEROS E)/STI ME\N TO\ €E)N AU)TW=| NOHTO/N, E)/XEI DE\ TO\ PRO\ AU)TOU= KAI\ METE/XEI PA/NTWS €E)KEI/NOU KAI\ DIA\ TOU=TO DEU/TEROS, O( DE\ TRI/TOS E)/STI ME\N TO\ E)N €AU)TW=| KAI\ OU(=TOS: PA=S GA\R NOU=S TW=| SUZUGOU=NTI NOHTW=| O( €AU)TO/S E)STIN: E)/XEI DE\ TO\ E)N TW=| DEUTE/RW| KAI\ O(RA=| TO\ PRW=TON: €O(/SW| GA\R PLEI/WN H( A)PO/STASIS, TOSOU/TW| TO\ E)/XEIN A)MUDRO/-€TERON. TOU/TOUS OU)=N TOU\S TREI=S NO/AS KAI\ DHMIOURGOU\S U(POTI/-€QETAI KAI\ TOU\S PARA\ TW=| <20*PLA/TWNI>20 [&Tim. 40E s$] TREI=S €BASILE/AS KAI\ TOU\S PAR' <20*)ORFEI=>20 [&frg. 74. 85 p. 186$] TREI=S, €*FA/NHTA KAI\ *OU)RANO\N KAI\ *KRO/NON, KAI\ O( MA/LISTA PAR' AU)-€TW=| DHMIOURGO\S O( *FA/NHS E)STI/N. A)/CION OU)=N E)KEI=NA KAI\ PRO\S €TOU=TON LE/GEIN, O(/TI PANTAXOU= O( *PLA/TWN A)PO\ TOU= PLH/QOUS €E)PI\ TA\S E(NA/DAS A)NATRE/XEIN EI)/WQEN, A)F' W(=N KAI\ H( E)N TOI=S €POLLOI=S PROELH/LUQE TA/CIS. 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DIA\ ME\N OU)=N TH=S TETA/RTHS KAI\ TH=S PE/MPTHS €TOU\S LO/GOUS PERIE/XEI PA/NTWN TW=N PRW/TWS AU)TH=S METEXO/N-€TWN, TH\N ME\N PRO/ODON AU)TW=N DIA\ TH=S TETA/RTHS A)NEGEI/ROUSA, €TH\N DE\ E)PISTROFH\N DIA\ TH=S PE/MPTHS PAREXOME/NH: DIO\ KAI\ €TH\N ME\N PRO\S TH\N DEUTE/RAN A)NH/GAGE, TH\N DE\ PRO\S TH\N TRI/-€THN, E)PEIDH\ TA\ ME/RH MIMEI=TAI TA\ O(/LA KAI\ A)NA\ LO/GON E)STI\N €AU)TOI=S. DIA\ DE\ TH=S E(/KTHS KAI\ TH=S E(BDO/MHS AU)TOU\S W(S <20PRO-€EI/RHTAI>20 [&p. 219, 15 ss$] TOU\S STEREOU\S O)/GKOUS U(FI/STHSI, GEN-€NW=SA ME\N AU)TOU\S KATA\ TH\N E(/KTHN, E)PISTRE/FOUSA DE\ KATA\ €TH\N E(BDO/MHN: KATALH/GEI GA\R A)/XRI TH=S TOU/TWN PROO/DOU TO\ €O(LIKO\N AU)TH=S EI)=DOS. 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METE/XEI ME\N OU)=N KAI\ H( KI/NHSIS TH=S O(/LHS YUXH=S €GNW/SEWS, KAQO/SON E(AUTH\N GIGNW/SKEI KAI\ EI)S E(AUTH\N BLE/-€POUSA KINEI=, METE/XEI DE\ KAI\ H( GNW=SIS KINH/SEWS, KAQO/SON €METABATIKH/ E)STIN. 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E)F' OI(=S <20*(IPPO-€KRA/THS>20 O( *XI=OS O( TO\N TOU= MHNI/SKOU TETRAGWNISMO\N €EU(RW/N, KAI\ <20*QEO/DWROS>20 O( *KURHNAI=OS E)GE/NONTO PERI\ €GEWMETRI/AN E)PIFANEI=S. PRW=TOS GA\R O( *(IPPOKRA/THS TW=N €MNHMONEUOME/NWN KAI\ STOIXEI=A SUNE/GRAYEN. <20*PLA/TWN>20 €D' E)PI\ TOU/TOIS GENO/MENOS MEGI/STHN E)POI/HSEN E)PI/DOSIN €TA/ TE A)/LLA MAQH/MATA KAI\ TH\N GEWMETRI/AN LABEI=N DIA\ €TH\N PERI\ AU)TA\ SPOUDH/N, O(/S POU DH=LO/S E)STI KAI\ TA\ €SUGGRA/MMATA TOI=S MAQHMATIKOI=S LO/GOIS KATAPUKNW/SAS €KAI\ PANTAXOU= TO\ PERI\ AU)TA\ QAU=MA TW=N FILOSOFI/AS €A)NTEXOME/NWN E)PEGEI/RWN. 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KAI\ ME/NTOI KAI\ O( *KUZIKHNO\S <20*)AQH/NAIOS>20 KATA\ €TOU\S AU)TOU\S GEGONW\S XRO/NOUS KAI\ E)N TOI=S A)/LLOIS ME\N €MAQH/MASI, MA/LISTA DE\ KATA\ GEWMETRI/AN E)PIFANH\S E)GE/-€NETO. DIH=GON OU)=N OU(=TOI MET' A)LLH/LWN E)N *)AKADHMI/A| €KOINA\S POIOU/MENOI TA\S ZHTH/SEIS. <20*(ERMO/TIMOS>20 DE\ O( €*KOLOFW/NIOS TA\ U(P' *EU)DO/COU PROHUPORHME/NA KAI\ €*QEAITH/TOU PROH/GAGEN E)PI\ PLE/ON KAI\ TW=N STOIXEI/WN €POLLA\ A)NEU=RE KAI\ TW=N TO/PWN TINA\ SUNE/GRAYEN. <20*FI/-€LIPPOS>20 DE\ O( *MENDAI=OS, *PLA/TWNOS W)\N MAQHTH\S KAI\ @1 U(P' E)KEI/NOU PROTRAPEI\S EI)S TA\ MAQH/MATA, KAI\ TA\S ZH-€TH/SEIS E)POIEI=TO KATA\ TA\S *PLA/TWNOS U(FHGH/SEIS KAI\ €TAU=TA PROU/BALLEN E(AUTW=|, O(/SA W)/|ETO TH=| *PLA/TWNOS FI-€LOSOFI/A| SUNTELEI=N. OI( ME\N OU)=N TA\S I(STORI/AS A)NAGRA/-€YANTES ME/XRI TOU/TOU PROA/GOUSI TH\N TH=S E)PISTH/MHS €TAU/THS TELEI/WSIN. 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KAI\ TH=| PROAIRE/SEI DE\ *PLATWNIKO/S E)STI KAI\ TH=| €FILOSOFI/A| TAU/TH| OI)KEI=OS, O(/QEN DH\ KAI\ TH=S SUMPA/SHS €STOIXEIW/SEWS TE/LOS PROESTH/SATO TH\N TW=N KALOUME/NWN €*PLATWNIKW=N SXHMA/TWN SU/STASIN. POLLA\ ME\N OU)=N KAI\ €A)/LLA TOU= A)NDRO\S TOU/TOU MAQHMATIKA\ SUGGRA/MMATA @1 QAUMASTH=S A)KRIBEI/AS KAI\ E)PISTHMONIKH=S QEWRI/AS €MESTA/. TOIAU=TA GA\R KAI\ TA\ O)PTIKA\ KAI\ TA\ KATOPTRIKA/, €TOIAU=TAI DE\ KAI\ AI( KATA\ MOUSIKH\N STOIXEIW/SEIS, E)/TI DE\ €TO\ PERI\ DIAIRE/SEWN BIBLI/ON. 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DE/DEIKTAI €A)/RA TO\ PROKEI/MENON DIA\ TOU= AU)TOU= QEWRH/MATOS MH\ €PROSEKBLHQEI/SHS TINO\S TW=N TOU= TRIGW/NOU PLEURW=N. @1 @*DIA\ TOU/TOU TOI/NUN DUNATO\N KA)KEI=NO DEIKNU/NAI, €O(/TI A)PO\ TOU= AU)TOU= SHMEI/OU E)PI\ MI/AN EU)QEI=AN DU/O €KA/QETOI OU)K A)XQH/SONTAI. E)/STWSAN GA\R A)PO\ TOU= SH-€MEI/OU E)PI\ TH\N DU/O KA/QETOI AI( @3 €. O)RQAI\ A)/RA EI)SI\N AI( U(PO\ € GWNI/AI. A)LL' E)PEI\ TRI/GW-€NO/N E)STI TO\ , DU/O O(POIAIOU=N €GWNI/AI DU/O O)RQW=N E)LA/SSOUS EI)SI/N. €AI( A)/RA U(PO\ GWNI/AI DU/O O)RQW=N E)LA/SSOUS €EI)SI/N. A)LLA\ KAI\ I)/SAI DUSI\N O)RQAI=S DIA\ TA\S KAQE/TOUS: €O(/PER A)DU/NATON. OU)K A)/RA A)PO\ TOU= AU)TOU= SHMEI/OU DU/O €KA/QETOI E)PI\ TH\N AU)TH\N EU)QEI=AN A)XQH/SONTAI. €{1&Prop. XVIII, theor. 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AI)/TION DE\ O(/TI TA\ ME\N TW=N TRIGW/NWN I)SO/THTO/S €E)STI MO/NHS E)/KGONA, TA\ DE\ A)NISO/THTOS MO/NHS, TA\ DE\ A)M-€FOTE/RWN, W(DI\ ME\N DIA\ TH=S I)SO/THTOS, W(DI\ DE\ DIA\ TH=S þï€´°³¶ÿï°±±ÿï‚éî Åõãÿ›‚ºˆ“A)NISO/THTOS U(FISTA/MENA: KAI\ TA\ ME\N O)/NTA TW=| PE/RATI €SUGGENH=, TA\ DE\ TH=| A)PEIRI/A|, TA\ DE\ KATA\ TH\N MI=CIN A)M-€FOTE/RWN A)POGENNW/MENA, W(/STE DIA\ PA/NTWN H( TRIA\S €AU(/TH PEFOI/THKEN, OI(=ON GRAMMW=N, GWNIW=N, SXHMA/TWN, €KAI\ E)N TOI=S SXH/MASI TRIPLEU/RWN, TETRAPLEU/RWN, E(CH=S €A(PA/NTWN. A)LLA\ KAI\ TO\ PE/RAS OU(= ME\N DIA\ TH=S O(MOIO/TH-€TOS, OU(= DE\ DIA\ TH=S I)SO/THTOS E)MFANTA/ZETAI TOI=S GEW-€METRIKOI=S EI)/DESI, KAI\ TO\ A)/PEIRON OU(= ME\N DIA\ TH=S @1 A)NOMOIO/THTOS, OU(= DE\ DIA\ TH=S A)NISO/THTOS, KAI\ TO\ MIKTO\N €O(/TE ME\N E)C O(MOIOTH/TWN, O(/TE DE\ E)C I)SOTH/TWN. AI)/TION DE\ KAI\ €TOU/TWN O(/TI TA\ EI)/DH TA\ GEWMETRIKA\ TW=| POSW=| PROSH/KEI €KAI\ TW=| POIW=|. DIO/TI TW=N DU/O TOU/TWN E)PISHMAINOME/NWN €DH=LON [1%1]1 KAI\ O(/TI <20PANTO\S TRIGW/NOU>20 LE/GWN O( STOI-€XEIWTH\S OU)XI\ KAI\ TOU= I)SOPLEU/ROU LE/GEI, A)LLA\ TOU= E)/XON-€TOS MEI/ZW KAI\ E)LA/TTW PLEURA/N. DEI= GA\R TO\ DEDOME/NON €H(GOU/MENON NOMI/ZEIN, E(PO/MENON DE\ [1%1]1 TO\ ZHTOU/MENON. €O(\ D' A)\N MEI/ZONA PLEURA\N E)/XH| KAI\ E)LA/SSONA, TOU=TO U(PO\ €TH\N MEI/ZONA PLEURA\N TH\N MEI/ZONA GWNI/AN [E(/CEI]. €@*)EPEIDH\ DE\ O( GEWME/TRHS E)N TH=| KATASKEUH=| LABW\N €TO\ TRI/GWNON KAI\ MEI/ZONA TH\N TH=S , I(/NA €DEI/CH| TH=S PRO\S TW=| GWNI/AS TH\N PRO\S TW=| MEI/ZONA, €A)FEI=LEN A)PO\ TH=S TH=| I)/SHN TH\N , FAI/H D' A)/N €TIS O(/TI PRO\S TW=| DEI= GENE/SQAI TH\N A)FAI/RESIN, FE/RE €KAI\ E)PI\ TAU/THS TH=S U(POQE/SEWS DEI/CWMEN TO\ PROKEI/ME- @1NON, W(S <20*PORFU/RIOS>20. E)/STW GA\R H( I)/SH TH=| KAI\ €E)KBEBLH/SQW H( E)PI\ TO\ KAI\ KEI/SQW H( TH=| €@@@@@3 I)/SH. O(/LH A)/RA H( I)/SH TH=| , €@@@@@KAI\ E)PEZEU/XQW H( . E)PEI\ OU)=N €@@@@@H( TH=| I)/SH, KAI\ H( U(PO\ €@@@@@ I)/SH TH=| U(PO\ DIA\ TO\ €@@@@@PE/MPTON. H( A)/RA U(PO\ MEI/-€@@@@@ZWN TH=S U(PO\ . E)STI\N DE\ KAI\ €@@@@@H( U(PO\ MEI/ZWN TH=S U(PO\ €@@@@@. TOU= GA\R MI/A PLEURA\ €E)KBE/BLHTAI H( , KAI\ H( U(PO\ E)KTO\S OU)=SA TH=S €A)PENANTI/ON KAI\ E)NTO\S MEI/ZWN E)STI/. POLLW=| A)/RA MEI/ZWN €H( U(PO\ TH=S U(PO\ , O(/PER E)/DEI DEI=CAI. €@*AI( ME\N OU)=N GEWMETRIKAI\ DEI/CEIS TOIAU=TAI. DH=LON €DE\ O(/TI TO\ AI)/TION TOU/TOU TOU= SUMPTW/MATO/S E)STIN H( TH=S €PLEURA=S AU)TH=S TH=S U(POTEINOU/SHS TH\N GWNI/AN U(PEROXH\ €KATA\ TO\ ME/GEQOS H)\ E)LA/TTWSIS: MEI/ZWN ME\N GA\R OU)=SA €DII/+STHSIN E)PI\ PLE/ON TH\N GWNI/AN, E)LATTOUME/NH DE\ SUN-€ELATTOI= KA)KEI/NHN KAI\ E)PI\ MEI=ON SUNA/GEI. TOU=TO DE\ €DIA\ TH\N E)P' A)/KRON TA/SIN TH=S EU)QEI/AS. E)P' A)/KRON GA\R €AU)TH\ TETAME/NH KAI\ TW=N GWNIW=N TA\ MEGE/QH KATA\ TH\N €E(AUTH=S AU)/CHSIN KAI\ MEI/WSIN SUMMETATI/QHSIN. KAI\ €TAU=TA LE/GOMEN E)F' E(NO\S TRIGW/NOU, E)PEI\ DUNATO\N KAI\ €TH\N AU)TH\N GWNI/AN U(PO\ MEI/ZONOS KAI\ E)LA/SSONOS EU)QEI/AS €U(POTEI/NESQAI KAI\ TH\N AU)TH\N EU)QEI=AN MEI/ZW KAI\ E)LA/TTW @1 GWNI/AN U(POTEI/NEIN. E)/STW GA\R EI) TU/XOI TRI/GWNON I)SO-€SKELE\S TO\ , KAI\ EI)LH/FQW E)PI\ TH=S TO\ SHMEI=ON, €KAI\ I)/SH H( TH=| [6E)PI\ TH=S @3 €]6 KAI\ E)PEZEU/XQW H( . TH\N €OU)=N PRO\S TW=| GWNI/AN U(PO-€TEI/NOUSIN AI( , W(=N H( ME\N €MEI/ZWN H( DE\ E)LA/SSWN, KAI\ MU-€RI/AS O(/SAS LABEI=N DUNATO\N €KATA\ TO\N AU)TO\N LO/GON TH\N €GWNI/AN U(POTEINOU/SAS MEI/ZOUS KAI\ E)LA/SSOUS EU)QEI/AS €PA/LIN E)/STW TO\ I)SOSKELE/S, KAI\ E)LA/SSWN H( TW=N € , KAI\ I)SO/PLEURON TRI/GWNON @3 €E)PI\ TH=S TO\ , KAI\ E)PEZEU/XQW €H( KAI\ E)KBEBLH/SQW E)PI\ TO\ . E)PEI\ €OU)=N TOU= TRIGW/NOU E)KTO/S E)STIN €H( U(PO\ GWNI/A, MEI/ZWN E)STI\ TH=S €U(PO\ , KATA\ TA\ AU)TA\ DH\ KAI\ €H( U(PO\ MEI/ZWN TH=S U(PO\ . O(/LH A)/RA H( U(PO\ € MEI/ZWN TH=S U(PO\ KAI\ U(POTEI/NEI A)MFOTE/RAS H( €AU)TH\ EU)QEI=A MEI/ZONA KAI\ E)LA/SSONA GWNI/AN. DE/DEIKTAI €DE\ O(/TI TH\N AU)TH\N GWNI/AN MEI/ZOUS EU)QEI=AI KAI\ E)LA/S-€SOUS U(POTEI/NOUSIN. A)LL' E)PI\ TOU= AU)TOU= TRIGW/NOU @1 MI/A EU)QEI=A MI/AN U(POTEI/NEI GWNI/AN KAI\ H( ME\N MEI/ZWN €TH\N MEI/ZONA E)K PANTO/S, H( DE\ E)LA/SSWN TH\N E)LA/SSONA: €KAI\ TO\ AI)/TION E)QEWRH/SAMEN. €{1&Prop. XIX, theor. XII$. <20*PANTO\S TRIGW/NOU U(PO\ TH\N €MEI/ZONA GWNI/AN H( MEI/ZWN PLEURA\ U(POTEI/NEI.>20}1 €@*TOU=TO/ E)STI TO\ A)NTI/STROFON TW=| EI)RHME/NW| QEWRH/-€MATI. KAI/ E)STIN A(PLOU=N E)N E(KATE/RW| TO/ TE DIDO/MENON €KAI\ TO\ ZHTOU/MENON. KAI\ TO\ E)KEI= SUMPE/RASMA U(PO/QESI/S €E)STIN E)NTAU=QA, H( DE\ E)KEI= U(PO/QESIS TOU/TOU SUMPE/-€RASMA. PROTE/TAKTAI D' E)KEI=NO, DIO/TI DEDOME/NHN E)/XEI €TH\N A)NISO/THTA TW=N PLEURW=N, E(/PETAI DE\ TOU=TO TA\S GW-€NI/AS A)NI/SOUS U(POQE/MENON. 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I)/SH A)/RA KAI\ H( BA/SIS H( TH=| , €KAI\ PA/NTA PA=SIN, W(/STE KAI\ H( U(PO\ GWNI/A I)/SH TH=| @1 PRO\S TW=| . E)LA/SSWN DE\ [H( PRO\S TW=| ] TH=S U(PO\ . €H( A)/RA U(PO\ E)LA/SSWN TH=S U(PO\ . TETMH/SQW €OU)=N DI/XA H( U(PO\ TH=| EU)QEI/A|: MEI/ZWN A)/RA H( €TH=S . E)PEI\ OU)=N TRIGW/NOU TOU= H( PRO\S TW=| GW-€NI/A DI/XA E)TMH/QH TH=| KAI\ MEI/ZWN H( TH=S , DIA\ €TO\ PRODEIXQE\N MEI/ZWN H( TH=S . H( DE\ TH=| €DE/DEIKTAI I)/SH. MEI/ZWN A)/RA H( TH=S . DE/DEIKTAI €A)/RA TO\ ZHTOU/MENON. þï€´°³¶ÿï°±±ÿï‚éî Åõãÿ›‚Áˆ‰@*KAI\ FANERO\N O(/TI TH\N POIKILI/AN TH=S A)PODEI/CEWS €PARAITOU/MENOS O( STOIXEIWTH\S TO\N TRO/PON TOU=TON E)FU-€LA/CATO KAI\ TH=| E)K DIAIRE/SEWS EI)S TO\ A)DU/NATON A)GOU/SH| €DEI/CEI PROEXRH/SATO BOULO/MENOS TO\ A)NTI/STROFON POI-€H=SAI TW=| PROHGOUME/NW| MHDENO\S METACU\ PAREMPI/PTON-€TOS, E)PEI\ KAI\ TO\ O)/GDOON A)NTISTRE/FON PRO\S TO\ TE/TARTON €POLLH\N E)NEPOI/HSE TARAXH\N DUSEPI/GNWSTON POIH=SAN €TH\N A)NTISTROFH/N. AI(RETW/TERON GA\R TO\ DI' A)DUNA/TOU €DEIKNU/NAI TA\ A)NTISTRE/FONTA META\ TOU= TH\N SUNE/XEIAN €FULA/TTEIN H)\ TO\ DIAKO/PTEIN TH\N SUNE/XEIAN META\ TH=S €PROHGOUME/NHS A)PODEI/CEWS. DIO\ DH\ TA\ A)NTI/STROFA €PA/NTA SXEDO\N DI' A)DUNA/TOU DEI/KNUSI. @1 {1&Prop. XX, theor. XIII$. <20*PANTO\S TRIGW/NOU AI( DU/O €PLEURAI\ TH=S LOIPH=S MEI/ZONE/S EI)SI PA/NTH META-€@@@@LAMBANO/MENAI.>20}1 €@*TOU=TO TO\ QEW/RHMA DIASU/REIN ME\N EI)W/QASIN OI( €*)EPIKOU/REIOI KAI\ O)/NW| LE/GONTES AU)TO\ DH=LON EI)=NAI KAI\ €MHDEMIA=S DEI=SQAI KATASKEUH=S: O(MOI/WS D' A)NEPISTH/MO-€NOS E)/RGON EI)=NAI TA/ TE E)MFANH= PARAMUQI/AS A)CIOU=N KAI\ €TOI=S A)DH/LOIS AU)TO/QEN PISTEU/EIN. O( GA\R TAU=TA SUGXE/WN €FANERO/S E)STI TO/ TE A)NAPO/DEIKTON KAI\ TO\ A)PODEIKTO\N €A)GNOW=N. O(/TI DE\ KAI\ O)/NW| TO\ PROKEI/MENON QEW/RHMA €GNW/RIMON KATASKEUA/ZOUSIN E)K TOU= TEQE/NTOS XO/RTOU €KATA\ TO\ E(/TERON PE/RAS TW=N PLEURW=N TO\N O)/NON TH\N €MI/AN O(DEU/EIN PLEURA\N A)LLA\ MH\ TA\S DU/O TROFH=S O)RE-€GO/MENON. €@*PRO\S DE\ TAU=TA LEKTE/ON O(/TI SAFE\S ME\N KATA\ TH\N €AI)/SQHSIN E)/STW TO\ QEW/RHMA, OU)/PW DE\ SAFE\S KATA\ TO\N €E)PISTHMONIKO\N LO/GON. POLLA\ GA\R TOU=TO PE/PONQE TW=N €PRAGMA/TWN, OI(=ON QERMAI/NEI TO\ PU=R: KAI\ TOU=TO TH=| €AI)SQH/SEI SAFE/S, A)LLA\ PW=S QERMAI/NEI TH=S E)PISTH/MHS €E)/RGON E(LEI=N, PO/TERON A)SWMA/TW| DUNA/MEI H)\ SWMATIKAI=S €TOMAI=S, SFAIRIKOI=S MORI/OIS H)\ PURAMOEIDE/SI. PA/LIN O(/TI €KINOU/MEQA TH=| AI)SQH/SEI DH=LON, PW=S DE\ KINOU/MEQA, €PARASTH=SAI TW=| LO/GW| XALEPO/N, PO/TERON KATA\ A)MERE/S, €H)\ KATA\ DIA/STHMA: PW=S DE\ A)/PEIRA DI/I+MEN. EI)S A)/PEIRON €GA\R DIAIRETO\N PA=N ME/GEQOS. E)/STW TOI/NUN KAI\ TOU= @1 TRIGW/NOU TO\ MEI/ZOUS EI)=NAI TA\S DU/O TH=S MIA=S TH=| AI)SQH/-€SEI KATAFANE/S, A)LLA\ PW=S TOU=TO GI/NETAI TH=S E)PISTH/MHS €E)/RGON EI)PEI=N. €@*)ALLA\ PRO\S ME\N TOU\S *)EPIKOUREI/OUS KAI\ TAU=TA A)R-€KOU/NTWS A)NTEIRH/SQW: DEI= DE\ KAI\ TA\S A)/LLAS A)PODEI/CEIS €TOU= PROKEIME/NOU QEWRH/MATOS SUNTO/MWS I(STORH=SAI, €O(/SAS OI( PERI\ <20*(/HRWNA>20 KAI\ <20*PORFU/RION>20 A)NE/GRAYAN €TH=S EU)QEI/AS MH\ PROSEKBALLOME/NHS, O(\ PEPOI/HKEN O( STOI-€XEIWTH/S. E)/STW TRI/GWNON TO\ @3 €. DEI= DH\ DEI=CAI TA\S €TH=S MEI/ZOUS. TETMH/SQW DI/XA €H( PRO\S TW=| GWNI/A. E)PEI\ OU)=N €TRIGW/NOU TOU= GWNI/A E)KTO\S €H( U(PO\ , MEI/ZWN E)STI\ TH=S U(PO\ : A)LL' H( U(PO\ € TH=| U(PO\ I)/SH: H( A)/RA U(PO\ MEI/ZWN TH=S U(PO\ €, W(/STE KAI\ H( PLEURA\ TH=S MEI/ZWN. DIA\ TA\ €AU)TA\ DH\ KAI\ H( TH=S MEI/ZWN. TRIGW/NOU GA\R TOU= € E)KTO\S H( U(PO\ KAI\ MEI/ZWN TH=S U(PO\ , TOUT-€E/STIN TH=S U(PO\ , W(/STE KAI\ H( TH=S MEI/ZWN. AI( €A)/RA TH=S O(/LHS MEI/ZOUS. O(MOI/WS DEI/COMEN KAI\ €E)PI\ TW=N A)/LLWN. €@*PA/LIN E)/STW TRI/GWNON TO\ : EI) ME\N OU)=N I)SO/-€PLEURO/N E)STI TO\ , PA/NTWS AI( DU/O MEI/ZOUS TH=S LOI-€PH=S_TRIW=N GA\R I)/SWN DU/O O(POIAOU=N DIPLA/SIA TOU= E(NO/S @1 _EI) DE\ I)SOSKELE/S, H)/TOI E)LA/SSONA E)/XEI TW=N I)/SWN €E(KATE/RAS TH\N BA/SIN H)\ MEI/ZONA. EI) ME\N OU)=N E)LA/SSWN H( €BA/SIS, PA/LIN AI( DU/O MEI/ZOUS TH=S LOIPH=S: EI) DE\ MEI/ZWN €@@@@@3 H( BA/SIS, E)/STW H( MEI/ZWN, €@@@@@KAI\ A)FH|RH/SQW I)/SH E(KATE/RA| €@@@@@E)KEI/NWN H( , KAI\ E)PEZEU/XQW €@@@@@H( . E)PEI\ OU)=N TRIGW/NOU TOU= €@@@@@ E)KTO\S H( U(PO\ GWNI/A, €@@@@@MEI/ZWN E)STI\ TH=S U(PO\ . DIA\ €TA\ AU)TA\ DH\ KAI\ H( U(PO\ TH=S U(PO\ MEI/ZWN. AI( €A)/RA PERI\ TH\N GWNI/AI MEI/ZOUS O(/LHS TH=S PRO\S TW=| , €W(=N H( U(PO\ I)/SH TH=| U(PO\ , E)PEI\ KAI\ H( TH=| € I)/SH. LOIPH\ A)/RA H( U(PO\ TH=S U(PO\ MEI/ZWN, €W(/STE KAI\ H( TH=S MEI/ZWN. H)=N DE\ H( TH=| I)/SH. €AI( A)/RA MEI/ZOUS TH=S . EI) DE\ SKALHNO\N TO\ €, E)/STW MEGI/STH H( , ME/SH H( , E)LAXI/STH H( €. H( ME\N OU)=N MEGI/STH MEQ' E(KATE/RAS LHFQEI=SA PA/N-€TWS MEI/ZWN TH=S LOIPH=S: KAI\ GA\R KAQ' AU(TH\N E(KATE/RAS €MEI/ZWN. EI) DE\ TH\N KAI\ DEI=CAI ZHTOI=MEN TH=S €MEGI/STHS OU)/SHS MEI/ZONAS, W(S E)PI\ TOU= I)SOSKELOU=S POI-€H/SOMEN A)PO\ TH=S MEGI/STHS A)FELO/NTES TH=| E(TE/RA| I)/SHN, €KAI\ E)PIZEU/CANTES A)PO\ TOU= , KAI\ A)POXRHSA/MENOI TAI=S €E)KTO\S TW=N TRIGW/NWN GWNI/AIS. @1 @*PA/LIN E)/STW TRI/GWNON TUXO\N TO\ . LE/GW O(/TI €AI( MEI/ZOUS EI)SI\ TH=S . EI) GA\R MH/, H)/TOI I)/SAI €EI)SI/N, H)\ E)LA/SSOUS, E)/STW-@3€SAN I)/SAI, KAI\ A)FH|RH/SQW €TH=| I)/SH H( . LOIPH\ €A)/RA H( TH=| I)/SH. €E)PEI\ OU)=N H( TH=| €I)/SH, GWNI/AS I)/SAS U(PO-€TEI/NOUSIN. O(MOI/WS DH\ KAI/, E)PEI\ H( TH=| I)/SH, GW-€NI/AS I)/SAS U(POTEI/NOUSIN. AI( A)/RA PRO\S TW=| GWNI/AI €I)/SAI KAI\ AI( PRO\S TW=| , O(/PER A)DU/NATON. PA/LIN DH\ €E)/STWSAN E)LA/SSOUS AI( @3 € TH=S , KAI\ A)FH|RH/SQW €TH=| ME\N I)/SH H( , TH=| DE\ € H( . E)PEI\ OU)=N I)/SH H( € TH=| , I)/SH H( U(PO\ €TH=| U(PO\ , KAI\ E)PEI\ I)/SH H( TH=| , I)/SH H( U(PO\ €TH=| U(PO\ : DU/O A)/RA AI( U(PO\ I)/SAI DUSI\N €TAI=S U(PO\ KAI\ . PA/LIN E)PEI\ TRIGW/NOU TOU= € E)KTO\S H( U(PO\ , MEI/ZWN TH=S U(PO\ , KAI\ GA\R €TH=S U(PO\ . KATA\ TA\ AU)TA\ DH\ KAI/, E)PEI\ TRIGW/NOU €TOU= E)KTO\S H( U(PO\ , MEI/ZWN TH=S U(PO\ , KAI\ @1 GA\R TH=S U(PO\ MEI/ZWN. AI( U(PO\ MEI/ZOUS €E)KEI= DU/O TW=N U(PO\ . H)=SAN DE\ KAI\ I)/SAI AU)TAI=S: €O(/PER A)DU/NATON. AI( A)/RA OU)/TE I)/SAI EI)SI\N TH=| , €OU)/TE E)LA/SSOUS, A)LLA\ MEI/ZOUS. O(MOI/WS DE\ KAI\ E)PI\ TW=N €A)/LLWN. €{1&Prop. XXI, theor. 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KAI\ PARA\ TAU/TAS A)/LLH LH=YIS €OU)K E)/STIN. €@*(ECAXW=S OU)=N LAMBANOME/NWN TW=N GWNIW=N O( GEW-€ME/TRHS TREI=S MO/NAS E)KLE/CATO KAI\ TAU=TA EI)S TA\ E(PO/MENA €SUMPTW/MATA TW=N PARALLH/LWN A)PE/FHNEN O)/NTA XARA-€KTHRISTIKA/. TOU/TWN DE\ TW=N TRIW=N MI/A ME/N E)STIN E)K €TW=N MH\ E)PI\ TA\ AU)TA/, E)K ME\N TW=N E)NTO\S LHFQEISW=N €MO/NON, A(\S KAI\ E)KA/LESEN E)NALLA/C, W(S PARALELEI=FQAI €TA\S E)KTO\S OU)/SAS A)MFOTE/RAS KAI\ TH\N ME\N E)KTO/S, TH\N DE\ €E)NTO/S, E)K DE\ TW=N E)PI\ TA\ AU)TA/, TW=N DE\ E)NTO\S A)MFOTE/-€RWN, A(\S DUSI\N O)RQAI=S EI)=NAI/ FHSIN I)/SAS, KAI\ W(=N H( ME/N €E)STIN E)NTO/S, H( DE\ E)KTO/S, A(\S EI)=PEN I)/SAS EI)=NAI, U(POLEIPO-€ME/NHS DE\ MIA=S LH/YEWS TH=S E)KTO\S A)MFOTE/RAS U(PO-€TIQEME/NHS. €@*(HMEI=S OU)=N FAMEN O(/TI KAI\ TAI=S PARALHFQEI/SAIS €TRISI\N U(POQE/SESIN TA\ AU)TA\ E(/PETAI. E)/STWSAN GA\R E)PI\ €TA\ AU)TA\ ME/RH A)/MFW E)KTO\S AI( @3 € . LE/GW O(/TI AU(=TAI DU/O €O)RQAI=S EI)SIN I)/SAI. 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E)/OIKEN DE\ O( GEW-€ME/TRHS TAU/TAS E)KLE/CASQAI TW=N U(POQE/SEWN, O(/SAI H)\ €KATAFATIKO\N PLEONA/ZON E)/XOUSIN, H)\ A(PLOU/STERAI/ EI)SIN, €KAI\ DIA\ TOU=TO LABEI=N E)K ME\N TW=N MH\ E)PI\ TA\ AU)TA\ MO/-€NAS TA\S E)NTO/S, A(\S DH\ KE/KLHKEN E)NALLA/C, E)K DE\ TW=N €E)PI\ TA\ AU)TA\ [TA\S E)NTO\S KAI\ TH\N ME\N E)NTO/S, TH\N DE\] @1 E)KTO/S, TA\S DE\ A)/LLAS DI' A)POFA/SEWS MA=LLON DHLOUME/-€NAS H)\ W(S POIKILWTE/RAS FULA/CASQAI. A)LL' OU)=N EI)/TE €TAU/THN, EI)/TE A)/LLHN AI)TI/AN R(HTE/ON, DH=LON E)K TOU/TWN, €PO/SA E)STI\ TA\ E(PO/MENA AU)TOI=S. €{1&Prop. XXVIII, theor. 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DE/ON GA\R H)=N H)\ €TA\S TREI=S U(POQE/SEIS DIALABEI=N KAI\ POIH=SAI TRI/A QEW-€RH/MATA, H)\ EI)S E(\N SUNA/GEIN PA/SAS QEW/RHMA, W(/SPER €E)POI/HSEN O( *(IERAPOLI/THS <20*AI)GEI/AS>20 O( TH\N E)PITOMH\N GRA/-€YAS TW=N STOIXEI/WN, H)\ DIELEI=N EI)S DU/O BOULO/MENON €EU)/TAKTON POIH/SASQAI TH\N DIAI/RESIN KAI\ XWRI\S ME\N €LABEI=N TA\S U(POQE/SEIS, E)F' W(=N I)/SAI EI)SI\N AI( GWNI/AI, €XWRI\S DE\ E)KEI/NHN, E)F' H(=S DU/O O)RQAI=S EI)SIN I)/SAI. NU=N @1 DE\ E)N E(NI\ ME\N QEWRH/MATI TA\S E)NALLA\C I)/SAS U(PE/QETO, €E)N E(NI\ DE\ TH\N E)KTO\S [I)/SHN TH=| E)NTO\S] KAI\ TA\S E)NTO\S KAI\ €E)PI\ TA\ AU)TA\ ME/RH DU/O O)RQAI=S I)/SAS. TI/ OU)=N TO\ AI)/TION €TH=S TOIAU/THS DIAIRE/SEWS; EI) OU)=N PRO\S TH\N I)SO/THTA €TW=N GWNIW=N A)PE/BLEYEN TH\N PRO\S A)LLH/LAS H)\ TH\N PRO\S €TA\S DU/O O)RQA/S, OU)DE\ TAU/TH| DIE/STHSE TA\ PROKEI/MENA €QEWRH/MATA A)P' A)LLH/LWN, A)LLA\ PRO\S E)KEI=NO TO\ TA\S €GWNI/AS H)\ E)PI\ TA\ AU)TA\ ME/RH LAMBA/NESQAI H)\ MH\ E)PI\ TA\ €AU)TA/. 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H( GA\R H)\ €TE/MNEI TH\N , W(S O( STOIXEIWTH\S E)/LABEN, H)\ E)PI\ TW=| €PI/PTEI, W(S E)N TH=| PRO\ TAU/THS KATAGRAFH=|, H)\ TE/MNEI TH\N €, W(S NU=N U(PEQE/MEQA. KAI\ DE/DEIKTAI KATA\ PA/SAS TA\S €PTW/SEIS TO\ QEW/RHMA A)LHQE/S. PLH\N O(/TI DITTH=S OU)/SHS €TW=N TRAPEZI/WN DIAFORA=S KAI\ TW=N ME\N OU)DETE/RAN TW=N €A)PENANTI/ON E)XO/NTWN PARA/LLHLON, TW=N DE\ MIA=| MI/AN, €E)PI\ TW=N PARA\ TW=| GEWME/TRH| TRAPEZI/WN TO\ E(/TERO/N E)STIN €EI)=DOS KAI\ E)PI\ TH=S KATAGRAFH=S TAU/THS. H( GA\R TH=| € PARA/LLHLOS. €{1&Prop. XXXVI, theor. XXVI$. <20*TA\ PARALLHLO/-€GRAMMA TA\ E)PI\ I)/SWN BA/SEWN O)/NTA KAI\ E)N TAI=S €@AU)TAI=S PARALLH/LOIS I)/SA A)LLH/LOIS E)STI/.>20}1 €@*TO\ ME\N PRO\ TOU/TOU TA\S BA/SEIS TA\S AU)TA\S E)LA/M-€BANEN, TOU=TO DE\ I)/SAS ME/N, DIAFEROU/SAS DE\ A)LLH/LWN. €KOINO\N DE\ A)MFOTE/ROIS TO\ E)N TAI=S AU)TAI=S U(POTI/QESQAI €PARALLH/LOIS TA\ PARALLHLO/GRAMMA. 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EI) DE/ TIS €MH/TE KOINO\N ME/ROS E)XOU/SAS U(POQOI=TO TA\S TW=N PARAL-€LHLOGRA/MMWN BA/SEIS, MH/TE KEXWRISME/NAS A)LLH/LWN, €A)LL', O(/PER U(POLEI/PETAI MO/NON, SUNAPTOU/SAS A)LLH/LAIS €KAQ' E(\N SHMEI=ON, W(S E)PI\ TW=N , E)ROU=MEN O(/TI I)/SH €H( TH=| KAI\ TH=| , W(/STE KAI\ H( TH=| . AI( GA\R @1 TA\S I)/SAS KAI\ PARALLH/LOUS E)PIZEUGNU/OUSAI KAI\ AU)TAI\ €I)/SAI KAI\ PARA/LLHLOI/ EI)SI. PARALLHLO/GRAMMON A)/RA €@@@@@@3 E)STI\ TO\ E)PI\ TW=N €@@@@@@AU)TW=N BA/SEWN KAI\ E)N €@@@@@@TAI=S PARALLH/LOIS TAI=S €@@@@@@ . I)/SA A)/RA TA\ €@@@@@@ PARALLHLO/GRAM-€@@@@@@MA/ E)STIN. €@*(HMEI=S ME\N OU)=N KATA\ TH\N PRW/THN E)PIBOLH\N TA\S TOU= €QEWRH/MATOS KATASKEUA\S DIEI/LOMEN, EI)PO/NTES TA\S BA/-€SEIS H)\ KOINO\N E)/XEIN ME/ROS, H)\ A(/PTESQAI MO/NON A)LLH/-€LWN, H)\ DIESTA/NAI A)P' A)LLH/LWN. DUNATO\N DE\ KA)\N €A(/PTWNTAI, W(S AI( , E)KTO\S O(/LON TO\ TH=S €U(POTI/QESQAI, H)\ TH\N PLEURA\N E)FARMO/ZOUSAN TH=| , €H)\ TH\N TE/MNOUSAN TH\N , H)\ TH\N PI/PTOUSAN W(S €DIA/METRON TH=| _O(/TE KAI\ H( H( AU)TH\ E)/STAI TH=| €_H)\ TH=S E)KBEBLHME/NHS E)PI\ TO\ TH\N PI/PTOU-€SAN E)KTO\S TOU= , KAI\ TH\N H)\ TE/MNOUSAN TH\N , H)\ €E)FARMO/ZOUSAN %2%2%2 @1 {1[&Prop. XXXVII, theor. XXVII$. <20*TA\ TRI/GWNA TA\ €E)PI\ TH=S AU)TH=S BA/SEWS O)/NTA KAI\ E)N TAI=S AU)TAI=S €@PARALLH/LOIS I)/SA A)LLH/LOIS E)STI/N>20.]}1 €@%2%2%2 A)POFAI/NONTAI. KAI\ GA\R I)/SWN E)KEI/NWN €A)/NISA TA\ XWRI/A, KAI\ A)NI/SWN I)/SA DEI/KNUNTAI. TOIOU=TON €DE/ TI PEPO/NQASIN OI( XWROGRA/FOI TA\ MEGE/QH TW=N PO/-€LEWN E)K TW=N PERIME/TRWN SULLOGIZO/MENOI. H)/DH DE/ TINES €KOINWNOI\ KTHMA/TWN E)N TH=| DIAIRE/SEI PARELOGI/SANTO €TOU\S SUNDIANEMOME/NOUS TH=| U(PEROXH=| TH=S PERIME/TROU €PARAXRHSA/MENOI, KAI\ PLEI/ONA LABO/NTES TW=N A)PELQO/N-€TWN_EI)LHFO/TES TO\ [1%1]1 U(PO\ TH=S MEI/ZONOS PERIME/-€TROU PERIEXO/MENON E)MBADO\N EI)=TA [1%1]1 A)MEI/YANTES XWRI/A €PERIOXH=| E)LA/SSONI [1%1]1 XRW/MENA_BELTI/STWN A)PHNE/G-€KANTO DO/CAN. DUEI=N GOU=N PROKEIME/NWN I)SOSKELW=N €TRIGW/NWN, W(=N TO\ ME\N E(KATE/RAN TW=N I)/SWN E)/XEI PE/NTE, €TH\N DE\ BA/SIN E(\C TW=N AU)TW=N, TO\ DE\ E(KATE/RAN ME\N TW=N €I)/SWN PE/NTE, TH\N DE\ BA/SIN O)KTW\ TW=N AU)TW=N, OI(=ON PH/-€XEWN, DAKTU/LWN, KOMIDH=| A)PATA=| TO\N A)/PEIRON TOU/TWN €EI)S AI(/RESIN. TOU=TO ME\N GA\R TH\N PERI/METRON E)/XEI DE/KA €KAI\ O)KTW/, QA/TERON DE\ E(\C KAI\ DE/KA TW=N AU)TW=N ME/TRWN. @1 A)LL' O( GEWMETRIKO\S OU)K A)GNOH/SEI O(/TI I)/SA E)STI\ TA\ €XWRI/A, KA)\N AI( PERI/METROI A)/NISOI W)=SIN. DW/DEKA GA\R €E(KA/TERO/N E)STIN. E)A\N GA\R A)GA/GH|S A)PO\ TH=S KORUFH=S €KA/QETON DI/XA ME\N DIAIRH/SEIS TA\S BA/SEIS KAI\ POIH/SEIS €E)N QATE/RW| ME\N TRIW=N, E)N DE\ LOIPW=| TETTA/RWN TO\ H(/MISU €TH=S BA/SEWS, AU)TH\N DE\ TH\N KA/QETON A)NA/PALIN OU(= ME\N €TETTA/RWN, OU(= DE\ TRIW=N. DEI= GA\R TO\ A)PO\ TH=S PENTA/DOS €I)/SON [EI)=NAI] TW=| TE A)PO\ TH=S KAQE/TOU KAI\ TW=| A)PO\ TH=S €H(MISEI/AS TH=S BA/SEWS. A)LL' EI) ME\N AU(/TH TRIW=N, H( €KA/QETOS TETTA/RWN, [EI) D'] AU(/TH TETTA/RWN, E)KEI/NH DH-€LADH\ TRIW=N. POIH/SAS OU)=N TH\N KA/QETON E)PI\ TO\ H(/MISU €TH=S BA/SEWS E(/CEIS TO\ I)/SON TW=| TRIGW/NW| XWRI/ON. TOU=TO €DE\ TAU)TO/N E)STIN KAQ' E(KA/TERON, EI)/TE TO\N TRI/A E)PI\ TO\N €TE/SSARA, EI)/TE TO\N TE/SSARA E)PI\ TO\N TRI/A POIH/SEIAS. €@*TAU=TA ME\N OU)=N EI)/RHTAI PRO\S E)/NDEICIN TOU= TH\N €I)SO/THTA TW=N XWRI/WN MH\ PA/NTWS E)K TW=N PERIME/TRWN €LAMBA/NEIN, I(/NA MH\ QAUMA/ZWMEN, EI) TW=N E)PI\ TH=S AU)TH=S €BA/SEWS TRIGW/NWN E)P' A)/PEIRON AU)/CESQAI KATA\ TA\S LOI-€PA\S PLEURA\S DUNAME/NWN E)NTO\S TW=N AU)TW=N PARALLH/-€LWN O(/MWS H( TW=N XWRI/WN I)SO/THS A)NECA/LLAKTOS DIAME/NEI. €DEI= DE\ E)KEI=NA TW=N TRIGW/NWN E)N TAI=S AU)TAI=S PARALLH/-€LOIS LE/GEIN, O(/SA TA\S BA/SEIS E)PI\ TH=S E(TE/RAS E)/XONTA €TW=N PARALLH/LWN E)REI/DEI TA\S KORUFA\S E)PI\ TH=S LOIPH=S, €KAI\ W(=N H( E)PI\ TA\S KORUFA\S E)PIZEUGNUME/NH MI/A TE/ E)STIN €EU)QEI=A KAI\ PARA/LLHLOS TAI=S BA/SESIN E)PI\ MIA=S EU)QEI/AS €KEIME/NAIS. @1 {1&Prop. XXXVIII, theor. XXVIII$. <20*TA\ TRI/GWNA TA\ €E)PI\ I)/SWN BA/SEWN O)/NTA KAI\ E)N TAI=S AU)TAI=S PAR-€@@ALLH/LOIS I)/SA A)LLH/LOIS E)STI/N.>20}1 €@*)ESTI\ ME\N KAI\ TOU=TO TO\ QEW/RHMA TOPIKO\N A)NA/LO-€GON TOI=S PARALLHLOGRA/MMOIS KAI\ TH\N TW=N TRIGW/NWN €QE/SIN E)PI\ TW=N I)/SWN BA/SEWN U(POTIQE/MENON. 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E)N E(NI\ €D' OU)=N E)KEI/NW| TA\ TE/TTARA TAU=TA QEWRH/MATA PERIE/XETAI, €OU) MO/NON O(/TI DIA\ MIA=S A)PODEI/CEWS DEI/KNUSIN, O(/SA E)N €TOI=S TE/TRASIN PERIE/XETAI TOU/TOIS, A)LL' O(/TI KAI\ PLE/ON €TI PROSTI/QHSIN TH\N TAUTO/THTA TW=N LO/GWN, KA)\N A)/NISOI €AI( BA/SEIS W)=SI. €@*TAU=TA PERI\ TOU/TWN: O(/TI DE\ KAI\ TOU=TO POLU/PTW-€TO/N E)STI TO\ QEW/RHMA KAI\ DUNATO\N TA\S BA/SEIS TA\S TW=N €TRIGW/NWN H)\ TAU)TO\N ME/ROS E)XOU/SAS LAMBA/NEIN, W(S E)PI\ €TW=N PARALLHLOGRA/MMWN, H)\ MHDENI\ ME\N KOINW=| ME/REI €XRWME/NAS, KAQ' E(\N DE\ SHMEI=ON A)LLH/LAIS SUNAPTOU/SAS, €H)\ KAI\ PA/NTH KEXWRISME/NAS, W(/STE EI)=NAI METACU\ GRAM-€MH/N, DH=LO/N E)STI TOI=S KAI\ MIKRA\ SUNEI=NAI DUNAME/NOIS, €KAI\ O(/TI KATA\ PA/SAS TA\S PTW/SEIS, O(/PWS A)\N E)/XH| TA\S €BA/SEIS KEIME/NAS H)\ TA\S KORUFA/S, H( AU)TH\ ME/QODOS, A)/GEIN €PARALLH/LOUS TAI=S PLEURAI=S KAI\ POIEI=N E(KA/TERON TW=N €TRIGW/NWN [PARALLHLO/GRAMMON KAI\ DIA\ TOU/TWN TH\N €TW=N TRIGW/NWN] I)SO/THTA KATASKEUA/ZEIN. @1 {1&Prop. XXXVIIII, theor. XXVIIII$. <20*TA\ I)/SA TRI/-€GWNA TA\ E)PI\ TH=S AU)TH=S BA/SEWS O)/NTA KAI\ E)PI\ TA\ €AU)TA\ ME/RH E)N TAI=S AU)TAI=S PARALLH/LOIS E)STI/N.>20}1 €@*(/OTE ME\N TH\N I)SO/THTA DEIKNU/NAI PROU)/KEITO, TO/TE €TE/TTARA QEWRH/MATA TO\N A)RIQMO\N E)POIOU=MEN, DU/O ME\N €E)PI\ TW=N PARALLHLOGRA/MMWN, DU/O DE\ E)PI\ TW=N TRIGW/-€NWN LAMBA/NONTES, H)\ E)PI\ TW=N AU)TW=N H)\ E)PI\ I)/SWN KEI/-€MENA BA/SEWN. NUNI\ DE\ A)NTISTRE/FONTES TA\ ME\N E)PI\ TW=N €PARALLHLOGRA/MMWN A)NTISTRE/FONTA PARH/KAMEN, TA\ DE\ €E)PI\ TW=N TRIGW/NWN MNH/MHS H)CIW/SAMEN. AI)/TION DE\ O(/TI €TRO/POS ME\N TH=S A)PODEI/CEWS O( AU)TO\S KAI\ E)P' E)KEI/NWN €A)PARALLA/KTWS DIA\ TH=S EI)S A)DU/NATON A)PAGWGH=S KAI\ €TH=S O(MOI/AS KATASKEUH=S, A)RKOU/MEQA DE\ E)PI\ TW=N A(PLOU-€STE/RWN, LE/GW DH\ TW=N TRIGW/NWN, U(PODEI/CANTES TH\N €ME/QODON KATALIPEI=N TOI=S A)GXINOUSTE/ROIS KAI\ E)PI\ TW=N €U(POLOI/PWN TA\ AU)TA\ SULLOGI/ZESQAI, E)PEI/, O(/TI GE H( €AU)TH\ KAI\ E)PI\ TOU/TWN ME/QODOS, R(A/|DION SUNIDEI=N. LA-€BO/NTES GA\R PARALLHLO/GRAMMA I)/SA E)PI\ TH=S AU)TH=S BA/-€SEWS, H)\ KAI\ E)PI\ TW=N I)/SWN, E)ROU=MEN O(/TI KAI\ E)N TAI=S €AU)TAI=S PARALLH/LOIS E)STI/N. EI) GA\R MH/, H)\ E)NTO\S PESEI=-€TAI QA/TERON TW=N E)N TW=| E(TE/RW| PARALLH/LWN E)KBALLOME/-€NWN, H)\ E)KTO/S. 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EI) GA\R PARALLHLO/GRAMMON I)/SON EU(RI/SKETAI @1 PANTI\ EU)QUGRA/MMW|, ZHTH/SEWS A)/CION, MH\ KAI\ TA\ EU)QU/-€GRAMMA TOI=S PERIFEROGRA/MMOIS I)/SA DEIKNU/NAI DUNATO/N. €KAI\ O( <20*)ARXIMH/DHS>20 E)/DEICEN, O(/TI PA=S KU/KLOS I)/SOS E)STI\ €TRIGW/NW| O)RQOGWNI/W|, OU(= H( ME\N E)K KE/NTROU I)/SH E)STI\N €MIA=| TW=N PERI\ TH\N O)RQH/N, H( DE\ PERI/METROS TH=| BA/SEI. €A)LLA\ TAU=TA E)N A)/LLOIS: E)PI\ DE\ TA\ E(CH=S I)/WMEN. €{1&Prop. XLVI, probl. XIIII$. <20*)APO\ TH=S DOQEI/SHS EU)-€@@QEI/AS TETRA/GWNON A)NAGRA/YAI.>20}1 €@*DEI=TAI ME\N TOU= PROBLH/MATOS TOU/TOU DIAFERO/NTWS €EI)S TH\N TOU= E)FECH=S QEWRH/MATOS KATASKEUH/N, E)/OIKEN €DE\ TW=N DU/O GENE/SEIS E)QELH=SAI PARADOU=NAI TW=N E)N þï€´°³¶ÿï°±±ÿï‚éî Åõãÿ›ƒ§ˆŒEU)QUGRA/MMW| A)RI/STWN, I)SOPLEU/ROU TRIGW/NOU KAI\ TETRA-€GW/NOU: DIO/TI DH\ KAI\ PRO\S TH\N SU/STASIN TW=N KOSMI-€KW=N SXHMA/TWN KAI\ MA/LISTA TW=N TETTA/RWN, W(=N KAI\ €GE/NESI/S E)STI KAI\ A)NA/LUSIS, TOU/TWN XREI/A TW=N EU)QU-€GRA/MMWN. 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EI) OU)=N KAI\ O( XRO/NOS TH=S A)NQRWPI/NHS ZWH=S €PRO\S TO\N TH=S PRONOI/AS O)FQALMO\N KAI\ O( TO/POS OU(=TOS EI)S KO/LASIN TO\ MHDE/N €E)STI, KAI\ DIA\ TAU=TA KATAFRONEI=SQAI EI)KO\S E(KA/TERON, KAI\ BLE/PEIN TH\N €A)NABOLH\N TOU= XRO/NOU EI)S TH\N META/STASIN TH\N A)PO\ TW=N E)LATTO/NWN €E)PI\ TA\ MEI/ZONA DIKAIWTH/RIA TW=N DEOME/NWN MEGA/LWN POINW=N, KAI\ TH\N €A)PO\ TOU= TO/POU TOU= META\ TW=N TIMWRIW=N KAI\ EU)PAQEI/AS TINA\S E)/XONTOS €EI)S TO\N XW=RON TW=N TIMWRIW=N MO/NWN: I(/NA KA)N TOU/TW| TW=| BRAXEI= XRO/NW| €TH\N DI/KHN E)PIKREMAME/NHN E)/XONTES NU/TTOUSAN A)FANW=S, A)NEGEI/ROUSAN €TA\S E)N AU)TOI=S FANTASI/AS TW=N A(MARTHMA/TWN E)/N TE U(/PNOIS KAI\ E)GRHGO/RSESI, €KAI\ E)LE/GXOUSAN AU)TOU\S PAR' E(AUTW=N DUSFORW=SI: KAI\ E)N E(AUTOI=S TO\ @1 €DIKASTH/RION W(=N E)/PRACAN E)/XONTES DEIMAI/NWSI: KAI\ META\ TOU=TO ... AI)/-€SQWNTAI KAI\ E)N TO/POIS, E)N OI(=S E)/RHMOI TW=N O(PWSOU=N EU)FRAI/NEIN DUNAME/NWN €EI)SI/. PA=S <20GA\R O( A)DIKH/SAS EU)QU\S>20 U(POBE/BLHTAI <20TH=| DI/KH|, KAI\ TO\ €GLUKU\ TH=S A)DIKI/AS W(/SPER DE/LEAR>20 KATAPIW/N [&Plut. vind. 554F$], €A)GXO/MENOS TO\N LOIPO\N DIATELEI= XRO/NON TOI=S TH=S KOLA/SEWS E)N TW=| ZH=N €PROOIMI/OIS TH\N KO/LASIN MELETW=N: DIA\ GA\R TO\ ME/GEQOS TH=S TIMWRI/AS €OU)K A)QRO/A GI/NETAI PROSBOLH/, TA\ DE\ KATECANISTA/MENA DEI/MATA TH=S €YUXH=S PRO/DROMA TW=N MEGI/STWN AU)TOI=S MEMHXA/NHTAI $10[2PAQHMA/TWN]2$. €<20FASI\ GA\R>20 KAI\ <20*)APOLLO/DWRON ... O(RA=N E)KDERO/MENON E(AUTO\N KAI\ €KAQEYO/MENON ..., TH\N DE\ KARDI/AN E)K TOU= LE/BHTOS U(POFQEGGO-€ME/NHN "3E)GW/ SOI TOU/TWN AI)TI/A>20"3 [&Plut. vind. 555 B$]: <20OI( DE\ *PTOLE-€MAI/OU TOU= *KERAUNOU= FI/LOI>20 $10KALOU/MENON AU)TO\N E(W/RWN$ <20E)PI\ DI/KHN €U(PO\ *SELEU/KOU>20, $10GUPW=N KAI\ LU/KWN DIKAZO/NTWN$ [&ib. 555 B$]. €$10[2TOIAU=TA]2$ ... TW=N E)PHRTHME/NWN KOLA/SEWN, E)PIFEROME/NWN KATA\ PRO/-€QESIN TOI=S E(AUTW=N A(MARTH/MASI. €@*TOU=TO ME\N OU)=N MO/GIS W(/SPER KU=MA DIENHCA/MEQA. @*META\ DE\ TOU=TO SKOPW=MEN E)/NNATON___, PW=S TW=N A(MARTO/N-€TWN A)/LLWN O)/NTWN, OI(=ON PATE/RWN H)\ KAI\ TW=N A)NWTE/RW TOU/TWN, EI)S TOU\S €A)POGO/NOUS LE/GETAI XWREI=N H( DI/KH ...: EI) ME\N E)/DOSAN E)KEI=NOI TH\N TW=N €A(MARTHMA/TWN DI/KHN, PERITTO\N KAI\ GELOI=ON TH\N PRO/NOIAN A)/LLHN E)/TI €TOI=S MET' E)KEI/NOUS DIAMHXANA=SQAI TIMWRI/AN, W(/SPER OU)DE\N A)/LLO BOULO-€ME/NHN H)\ TW=N EI)S A)NQRW/POUS TIMWRIW=N E)MFOREI=SQAI: EI) D' E)PI\ TW=N A(MAR-€TO/NTWN A)FEI=SA TH\N POINH/N, E)P' A)/LLOUS AU)TH\N METATI/QHSI TOU\S MH\ A(MAR-€TO/NTAS, OU) DIAFEU/GEI TO\ A)DIKEI=N, TO\N ME\N A)DIKOU=NTA PERIORW=SA, TW=| DE\ €MH\ A)DIKH/SANTI TH\N TOU= A)DIKH/SANTOS E)PA/GOUSA DI/KHN. ˆ‹@*TO\ DE\ PROGONIKW=N A(MARTHMA/TWN DI/KAS TI/NEIN TINA/S___ @1 ˆ”___$10 [2*EI) OU)=N, W(S DE/DEIKTAI, ZW=ON E(/N E)STI KAI\ PO/LIS E(KA/STH KAI\ GE/NOS €E(/KASTON]2$, TI/ QAUMA/ZOMEN, EI) TA\ TW=N PROGO/NWN KAI\ ME/XRI TW=N €A)POGO/NWN E)KDI/DOTAI, KAI\ ... TW=N E)N A)/LLOIS XRO/NOIS PRAXQE/NTWN, H)\ €A)MEINO/NWN H)\ XEIRO/NWN, E)N A)/LLOIS E)/XEI TH\N A)MOIBH/N; OU) GA\R MO/NON E(/KASTON €H(MW=N A)F' W(=N E)/PRACEN E)N A)/LLW| XRO/NW| TO\N KARPO\N E)/XONTA KAI\ DEXO/MENON €TH\N DI/KHN H( PRO/NOIA DEI/KNUSIN, A)LLA\ KAI\ ... TO\ GE/NOS W(S E(/N ..., OU)K €A)MELHQE/NTWN ME\N OU)DE\ TW=N PRW/TWN PRACA/NTWN_OU)DE\ GA\R QE/MIS TI\ €PARORA=SQAI, PRONOI/AS OU)/SHS: KAI\ TW=N $10[2U(STE/RWN]2$ DE\ DIA/ TE TH\N PRO\S €E)KEI/NOUS W(S A)RXHGE/TAS SUMPA/QEIAN KAI\ TH\N MET' AU)TW=N W(S EI)S E(\N ZW=ON @1 €TE/LESIN PARADEXOME/NWN TH\N A)P' E)KEI/NWN KAQH/KOUSAN MOI=RAN: GEGO/NASI €GA\R E)C E)KEI/NWN ..., W(/ST' EI)KO/TWS KAI\ TIMW=NTAI H)\ KOLA/ZONTAI DI' E)KEI/NOUS. €EI) DE\ PA/NTWN E(NO\S O)/NTWN MERW=N KAI\ A)/LLWN A)/LLOIS SUNHRTHME/NWN MH\ €OI( E)GGU/S, A)LL' OI( PORRW/TERON TW=N O(MOI/WN TOI=S E)/MPROSQEN TUGXA/NOUSIN, €OU)DE\N OI)=MAI QAUMASTO/N: OU)DE\ GA\R TW=N MERW=N PA/NTWN H( AU)TH\ PRO\S €PA/NTA O(MOIO/THS, A)LLA\ TW=N ME\N MEI/ZWN, TW=N DE\ E)LA/TTWN, OU)DE\ LO/GOS €O( AU)TO/S, A)LL' O( ME\N MA=LLON SUNDE/WN, O( DE\ H(=TTON: KAI\ TAU=TA OU)XI\ TOI=S €E)GGU\S E)/XEI TO\ MEI=ZON H)\ TO\ MA=LLON: OU)DE\N GOU=N KWLU/EI TA\ PORRW/TERON €MA=LLON TW=N E)GGU/TERON O(MOIOU=SQAI. KAI\ TAU=TA KAI\ A)PO\ TW=N I)ATRIKW=N €E)/RGWN DH=LA: <20TW=N GOU=N I)SXI/WN>20 NOSOU/NTWN OU) TA\ E)GGU\S, A)LLA\ <20TO\N €A)NTI/XEIRA KAI/OUSI KAI\ TOU= H(/PATOS U(POU/LOU GEGONO/TOS TO\ €E)PIGA/STRION A)MU/SSOUSI KAI\ TW=N BO/WN>20 TW=N XHLW=N MALAKIW/N-€TWN <20PROSALEI/FOUSIN>20 ... TA\ KE/RATA [&3cf.& Plut. vind. 559 E%3F$]. €ME/LLEI GA\R AU)TOI=S OU) DIA\ TW=N E)GGU/S, A)LLA\ DIA\ TW=N SUMPAQW=N DRA=N €EI)S TA\ DEO/MENA TH=S I)A/SEWS. OI(/ TE OU)=N PRW=TOI PLHMMELH/SANTES PA/NTWS €E)/DOSAN TH\N E)PI\ TOI=S A(MARTH/MASI DI/KHN___: KAI\ OU)DE\ OU(=TOI PA/-€SXOUSIN A)DI/KWS, A)LL' O)/NTES TW=N E)GGU/TERON MA=LLON KA)KEI/NOIS E)OIKO/TES, €A)PO\ TH=S O(MOI/AS ZWH=S KAI\ SUMPAQOU=S TW=N O(MOI/WN TUGXA/NOUSIN E)K TH=S €PRONOI/AS. @1 ˆ’___*KAI\ GA\R E)N TOI=S BI/OIS H(MW=N DRA/MATI ME\N A)NA/LOGON H( €SU/MPASA TOU= GE/NOUS PERI/ODOS, TW=| DE\ POIHTH=| TOU= TOIOU/TOU DRA/MATOS €H( EI(MARME/NH, TOI=S DE\ EI)S TO\ DRA=MA TELOU=SIN ... AI( A)/LLAI KAI\ A)/LLAI YUXAI/, €PLHROU=SAI TH\N EI(MARTH\N TAU/THN SKHNH/N. ___ ˆ—A)QLOQETEI= DE\ H( PRO/NOIA TAI=S YUXAI=S KAI\ TIMA=| DI' A)/LLAS A)/LLAS, KAI\ A)TIMA/ZEI €DIA\ TH\N O(MOIO/THTA TH=S ZWH=S. ___ @*TO\ DE\ KAI\ DI' A)/LLAS A)/LLAS KOLA/ZESQAI DOKEI= ME\N EI)=NAI QAUMASTO/N, €E)/STI DE\ KAI\ TOU=TO LO/GON E)/XON DIA\ TH/N, W(S EI)/RHTAI, TH=S ZWH=S U(POFUO-€ME/NHN O(MOIO/THTA, TH=S PRONOI/AS OI(=ON FUTOU= TINA\ R(I/ZAN PONHRA\N E)K-€KOPTOU/SHS, H(\N E)KEI/NH| PROI+DEI=N R(A/|DION. KAI\ GA\R TOI=S SKORPI/OIS SUNAPO-€GENNA=TAI TO\ KE/NTRON KAI\ TAI=S E)XI/DNAIS O( I)O/S: KAI\ H(MEI=S ME\N PLHGE/NTES €U(P' AU)TW=N GINW/SKOMEN TI/S O( I)O\S KAI\ TI/ TO\ KE/NTRON: E)/STI DE\ E)N TW=| PANTI\ €TO\ GINW=SKON TAU=TA KAI\ PRO\ TH=S PLHGH=S. TO\N AU)TO\N OU)=N KAI\ H( PRO/NOIA €TRO/PON TA\S E)NOU/SAS KH=RAS TAI=S YUXAI=S SUGGENEI=S O(RW=SA TW=N A(MAR-€TO/NTWN PRW/TWN, FE/REI E)P' AU)TA\S TH\N TIMWRI/AN, KA)\N MH\ PRA/CWSIN A(/PER €E)KEI=NOI, TH\N FU/SIN O(MOI/AN E)XOU/SAS, PROANAIROU=SA TH\N KAKI/AN W(/SPER @1 €E)PI/LHYIN U(POFUOME/NHN. <20W(S GA\R A)KROXORDO/NES KAI\ MELA/SMATA €KAI\ FAKOI\ PATE/RWN E)N PAISI\N ... A)FANISQE/NTES A)NE/KUYAN>20 E)N €TOI=S TOU/TWN E)KGO/NOIS [&Plut. vind. 563 A$], OU(/TW KAI\ H)QW=N I)DIO/THTES €A)NABLASTA/NOUSIN E)N TOI=S POLLOSTOI=S, A(\S A)/LLOIS ME\N A)GNW/STOUS EI)=NAI, €TW=| E(NI\ DE\ TW=| PA/NTA GINW/SKONTI KAI\ GINW/SKEIN $10[2DOTE/ON]2$ KAI\ PROAFANI/ZEIN: €DHLOU=N DE\ TH\N O(MOIO/THTA DIA\ TOU= DOKEI=N E)KEI/NOIS TI/NEIN DI/KAS TOI=S U(P' €E)KEI/NWN H(MARTHME/NOIS A)KOLOUQOU/SAS. KAI\ TOU=TO ME\N OU)=N DIA\ TOU/TWN €E)/STW DH=LON. ___ @*TE/LOS DE\ H)/DH TW=N A)PORHMA/TWN PROSQH/SW DE/KATON KAI\ AU)TO/N, þï€´°³¶ÿï°±²ÿ˜¾‚W(/S FASI <20TO\N KOLOFW=NA>20 [&3cf. &Plut. vind. 549 D%3E$]. *TH=S GA\R PRO-€NOI/AS, $10[2W(S EI)/RHTAI]2$, TW=| POLUUMNH/TW| E(NI\ PA/NTA GINWSKOU/SHS KAI\ €EI)S TO\ A)GAQO\N A)NAGOU/SHS, PW=S KAI\ A)/GGELOI PRONOEI=N LE/GONTAI KAI\ ... €YUXAI/; ___ @1 ˜ÀˆŠ___*KAI\ GA\R E)N H(MI=N E)/GKEITAI/ TI KRU/FION TOU= E(NO\S I)/XNOS, €$10[2O(\ KAI\ TOU= E)N H(MI=N NOU= E)STI QEIO/TERON]2$, EI)S O(\ KAI\ TELE/SASA YUXH\ KAI\ I(DRU/SASA €E(AUTH/N, E)/NQEO/S E)STI KAI\ ZH=| TH\N QEI/AN ZWH\N KAQ' O(/SON QE/MIS AU)TH=|. @*OI( ME\N $10[2DH\]2$ QEOI\ PRONOOU=SI PA/NTWN___. A)/GGELOI DE\ KAI\ €DAI/MONES KAI\ H(/RWES KAQ' O(/SON E)/XOUSI/ TI SPE/RMA TOU= E(NO\S KAI\ AU)TOI\ €PRONOOU=SIN, OU) KAQ' O(/SON ZW=NTES H)\ NOOU=NTES EI)SI/___. †YUXH=S GA\R TO\ KINEI=N, NOU= DE\ TO\ GINW/SKEIN I)/DION___ ˆˆTO\ DE\ PRONOEI=N TOU= E)N AU)TOI=S E)STIN E(NO/S, KAQ' O(\ GA\R $10[2MIMOU=NTAI]2$ TOU\S €QEOU/S, KATA\ TOU=TO DH\ SUMPRONOOU=SIN AU)TOI=S: TO\ GA\R PRW/TWS PRONOOU=N €QEO/S, DIO/TI KAI\ TO\ PRW/TWS A)GAQO/N. YUXAI\ DE\ META\ TOU/TOUS, O(/TAN TW=| €A)GAQW=| E)NIDRUNQW=SIN, E)NQE/WS TE E)NERGOU=SI KAI\ META\ TW=N QEW=N PRONOOU=SI €$10[2KAI\ META\ TW=N KREITTO/NWN H(MW=N GENW=N]2$ A)SXE/TWS, $10[2W(=N KAI\ E)KEI=NOI]2$: KAI\ €AU)TW=N H( PRO/NOIA OU)K E)N LOGISMOI=S STOXASTIKOI=S TW=N E)SOME/NWN €W(/SPER TW=N E)NTAU=QA POLITIKW=N, A)LL' E)N TW=| E(NI\ $10[2TW=| YUXIKW=|]2$ STA/SIN €LABOU=SAI KAI\ DIA\ TOU=TO PERILAMFQEI=SAI TW=| E(NIAI/W| FWTI\ TW=N QEW=N €O(RW=SIN A)XRO/NWS TA\ E)N XRO/NW|, KAI\ A)DIAIRE/TWS TA\ DIAIRETA/, KAI\ TA\ E)N €TO/PW| PA/NTA A)/NEU TO/POU, KAI\ EI)SI\N OU)X E(AUTW=N, A)LLA\ TW=N E)LLAMPO/NTWN. €KAI\ YUXAI=S ME\N TOU=TO POTE\ SUMBAI/NEI TO\ PA/QOS: TOI=S DE\ A)GGE/LOIS PRO\ €AU)TW=N $10[2KAI\ TOI=S A)/LLOIS GE/NESIN]2$ A)EI\ PA/RESTI: DIO\ KAI\ A)EI\ PRONOOU=SI KREIT-€TO/NWS H)\ KATA\ LOGISMO\N E)NERGOU=NTES, OU)K E)FEPO/MENOI TOI=S GINOME/NOIS, €A)LLA\ PA/NTA O(RW=NTES KATA\ TO\ E)N TOI=S QEOI=S KAT' AI)TI/AN E(/N, ..., TH=S €TOIAU/THS E)NERGEI/AS U(/FESIN OU)K E)/XONTES. TW=N ME\N OU)=N YUXW=N TW=| A)EI\ €PRONOEI=N DIAFE/ROUSIN, W(S EI)/POMEN: AU)TW=N DE\ W(=N EI)SIN O)PADOI\ QEW=N TW=| @1 €$10[2OU) KAQ' O(/LOUS E(AUTOU\S PRONOEI=N, A)LLA\ KATA\ TO\ QEIO/TATON E(AUTW=N]2$ KAI\ KAQ' O(\ €SUNH/NWNTAI TOI=S QEOI=S. E)KEI/NWN ME\N GA\R E(/KASTOS E(/N: TOU/TWN DE\ E(/KASTOS €E(NOEIDH/S: E)/XWN OU)=N TI KAI\ A)/LLO PARA\ TO\ E(/N, TW=| ME\N E(NI\ MIMEI=TAI TO\N €$10[2PRO\ AU(TOU=]2$ QEO/N, OU(= KAI\ E)CH/RTHTAI: TW=| DE\ A)/LLW| KAT' A)/LLHN E)NE/RGEIAN €ZH=|: KAI\ E)/STI KATA\ ME\N TO\ E(\N H( U(/PARCIS H( E(KA/STOU, KATA\ DE\ TO\ OU)X E(\N TO\ €O)\N TO\ E)N AU)TOI=S, OU(= H( U(/PARCIS. ___$10 [2*)EN PA=SI DE\ TO\ PRW/TISTON]2$ W(S DUNA/MEWS PA/SHS, OU(/TW KAI\ €PRONOI/AS KREI/TTWN___, W(S PA=SIN E)FETO\N KAI\ OU(= E(/NEKA PA/NTA KAI\ €W(S AI)/TION PRONOI/AS. ___ @1 ï°±³ÿ˜Š@*SKO/PEI ... 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[1&Proclus, lib. 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OU)X OI(=O/N TE>20 [&p. 142 B$]. @1 *TELEUTA=| DE\ PERI\ AU)TH=S DIALEGO/MENOS W(DI/: <20*)=AR' €OU)=N A)/LLO H)\ O(/TI OU)SI/AS METE/XEI TO\ E(\N, €TOU=T' A)\N EI)/H TO\ LEGO/MENON, E)PEIDA/N TIS €SULLH/BDHN EI)/PH| O(/TI E(\N E)/STI; *PA/NU GE>20 €[&p. 142 C$]. *TRIA\S OU)=N AU)TH\ PRW/TH NOHTH\, TO\ €E(\N, TO\ O)\N, KAI\ SXE/SIS A)MFOI=N, DI' H(\N KAI\ TO\ E(\N €TOU= O)/NTOS E)STI\ KAI\ TO\ O)\N TOU= E(NO\S, PA/NU GE €QAUMASTW=S KAI\ DIA\ TOU/TWN E)KDEIKNUME/NOU TOU= €*PLA/TWNOS O(/TI KAI\ O( PATH\R TOU= NOU= PATH/R E)STI, €KAI\ O( NOU=S TOU= PATRO\S, KAI\ W(S H( DU/NAMIS KE/-€KRUPTAI METACU\ TW=N A)/KRWN .... €@*META\ DE\ TAU/THN E)FECH=S H( <20DEUTE/RA>20 TH\N €PRO/ODON E)/LAXEN, H(\N KATA\ TH\N O(LO/THTA TH\N €NOHTH\N, W(/SPER E)N *SOFISTH=| DIEI/LOMEN, [O( *PAR-€MENI/DHS] XARAKTHRI/ZEI ... *)EN TAU/TH| DE\ TA\ ME/RH €KAI\ TO\ O(/LON, TH=S DUNA/MEWS E(AUTH\N E)KFAINOU/SHS: €DIAKRI/SEWS GA\R OU)/SHS, KAI\ ME/RH E)STI\ KAI\ TO\ E)K €TOU/TWN O)/LON. *KALEI=TAI TOI/NUN H( DEUTE/RA TRIA\S €O(LO/THS NOHTH/. *ME/RH DE\ AU)TH=S TO\ E(\N KAI\ TO\ þï€´°³¶ÿï°²°ÿ›‰ßˆ”O)\N, A)/KRA LE/GW: ME/SH DE\ H( <20DU/NAMIS>20 OU)=SA KA)N-€TAU=QA SUNA/PTEI, KAI\ OU)X E(NOI= [1KAQA/PER E)N TH=| €PRO\ AU)TH=S]1 TO\ E(\N KAI\ TO\ O)\N, KAI\ E)PEI\ ME/SH €E)STI\N A)MFOI=N, DIA\ ME\N TH\N PRO\S TO\ O)\N KOINW-€NI/AN, E(\N O)\N A)POFAI/NEI TO\ E(\N, DIA\ DE\ TH\N PRO\S €TO\ E(\N, E(\N A)POTELEI= TO\ O)/N. *KAI\ OU(/TWS TO\ E(\N O)\N €E)K MERW=N E)STI DUOI=N, TOU= TE E(NO\S O)/NTOS KAI\ TOU= €O)/NTOS E(NO\S, W(/SPER AU)TO\S O( *PARMENI/DHS FHSI/N. €*)/ARXETAI ME\N OU)=N TW=N PERI\ TH=S TRIA/DOS TAU/THS €LO/GWN E)NQE/NDE: <20*PA/LIN DE\ LE/GWMEN, E(\N EI) €E)/STI, TI/ SUMBH/SETAI: SKO/PEI OU)=N EI) €OU)K A)NA/GKH TAU/THN TH\N U(PO/QESIN TOI-€OU=TON O)\N TO\ E(\N SHMAI/NEIN, OI(=ON ME/RH €E)/XEIN>20 [&p. 142 C$]. *TELEUTA=| DE\ OU(TWSI\ LE/GWN: €<20*KAI\ O(/LON A)/RA E)STI\N O(\ A)\N E(\N H)=|, KAI\ MO/-€RION E)/XEI>20 [&p. 142 D$]. *DIA\ DE\ TOU/TWN O( *PAR-€MENI/DHS O(LO/THTA TH\N DEUTE/RAN A)FORI/ZETAI TA/-€CIN TW=N NOHTW=N. *(WS GA\R TO\ EI)=NAI PA=SIN A)PO\ €TH=S PRW/THS, OU(/TWS TO\ O(/LON A)PO\ TH=S DEUTE/RAS €KAI\ H( PANTELH\S DIAI/RESIS A)PO\ TH=S TRI/THS ....@2 @*META\ GA\R TH\N KRU/FION E(/NWSIN TH=S PRW/THS €KAI\ TH\N TH=S DEUTE/RAS DUADIKH\N DIA/KRISIN H( TH=S €<20TRI/THS>20 A)POGENNA=TAI PRO/ODOS, E)K MERW=N ME\N €E)/XOUSA TH\N U(PO/STASIN, PLEIO/NWN DE\ MERW=N, W(=N €TO\ PLH=QOS W)DINEI= H( PRO\ AU)TH=S. *(ENA\S ME\N GA/R €E)STIN E)N TAU/TH| KAI\ <20DU/NAMIS>20 KAI\ O)\N, A)LLA\ €TO\ E(\N PLHQU/NETAI, KAI\ TO\ O)\N KAI\ H( DU/NAMIS .... €*AI)TI/A DE\ TH=S PROO/DOU TAU/THS H( DU/NAMIS: DUO-€POIO\S GA\R H( DU/NAMIS KAI\ PLH/QOUS E)RGA/TIS, TO\ €ME\N GA\R E(\N EI)S PLH=QOS PROKALOUME/NH, TO\ DE\ O)\N €EI)S METOUSI/AN TW=N QEI/WN E(NA/DWN E)PISTRE/FOUSA. €*PO/QEN A)/RXETAI PERI\ TAU/THS H(MA=S TH=S TRIA/DOS €A)NADIDA/SKWN O( *PARMENI/DHS, KAI\ POU= TO\N PERI\ €AU)TH=S SUMPERAI/NETAI LO/GON; *)ARXH\ ME\N OU)=N AU(/TH €TW=N LO/GWN H(/DE: <20*TI/ OU)=N; TW=N MORI/WN E(KA/-€TERON TOU/TWN TOU= E(NO\S O)/NTOS, TO/ TE E(\N €KAI\ TO\ O)\N, A)=RA A)POLEI/PESQON H)\ TO\ E(\N €TOU= O)/NTOS EI)=NAI MO/RION, H)\ TO\ O)\N TOU= €E(NO\S MO/RION; *OU)K A)\N EI)/H>20 [&p. 142 D$]. €*TELEUTH\ DE\ H(/DE: <20*OU)KOU=N A)/PEIRON A)\N TO\ €PLH=QOS OU(/TW TO\ E(\N O)\N EI)/H; *)/EOIKE/ GE>20 €[&p. 143 A$] .... *(/OTAN ME\N GA\R LE/GHTAI TOU= €E(NO\S O)/NTOS MO/RIA PA/NTA TA\ DEU/TERA KAI\ O(/SA DIA\ €TH\N TH=S DUNA/MEWS DIAKRITIKH\N AI)TI/AN A)NAFAI/-€NETAI, TH\N A)PO\ TH=S MONA/DOS E)FH/KOUSAN E(/NWSIN €EI)S TH\N TRI/THN TRIA/DA PARADI/DWSIN O( LO/GOS. €*(/OTAN DE\ H( DU/NAMIS DIAKRI/NOUSA KAI\ SUNA/PTOUSA €TA\S E(NA/DAS KAI\ TA\ O)/NTA TO\ PLH=QOS A)POTELH=|, €TO/TE DH\ PA/NTWS H( METOUSI/A TH=S DUA/DOS A)NA-€FAI/NETAI, KAQA/PER, OI)=MAI, KAI\ O( *PARMENI/DHS €E)NDEI/KNUSI LE/GWN: <20*(/WSTE A)NA/GKH DU/O A)EI\ €GIGNO/MENON MHDE/POTE E(\N EI)=NAI>20. *KAT' €A)MFOTE/RAS A)/RA TA\S PROU+PARXOU/SAS TRIA/DAS AU(/TH €PROELH/LUQE, <20R(E/OUSA>20, KATA\ TO\ *LO/GION, KAI\ €E)PI\ PA=N PROI+OU=SA TO\ NOHTO\N PLH=QOS. *TH=S GA\R €R(OH=S TAU/THS KAI\ TOU= A)PERILH/PTOU TH=S DUNA/MEWS €TO\ A)/PEIRON PLH=QOS E)NDEIKTIKO/N. *PRW=TON ME\N TOI/-€NUN E)/FHN TH\N TRIA/DOS TAU/THS U(PO/STASIN TW=N €PRO\ AU)TH=S H)RTHME/NHN DIA\ TOU/TWN A)PODEIKTE/ON: @1 E)PEIQ' O(/TI KAI\ PRWTOGENH\S H( TRIA\S AU(/TH KATA\ €TO\N *PARMENI/DHN: PRW/TH| GA\R AU)TH=| TOU= GI/GNE-€SQAI METADI/DWSI, KAI\ TO\ PLH=QOS TO\ E)N AU)TH=| €GIGNO/MENON A)POKALEI=. *LE/GEI GA\R OU)=N OU(/TWS: €<20*KAI\ GI/GNETAI TO\ E)LA/XISTON E)K DUOI=N €AU)= MORI/OIN TO\ MO/RION>20. *KAI\ PA/LIN: <20*(/O TI/ €PER A)\N MO/RION GE/NHTAI, TOU/TW| TW=| MO-€RI/W| A)EI\ I)/SXEI,>20 KAI\ E)N TOI=S E(CH=S. [1&Proclus, €&lib. III, p. 163_167.$]1 €@[<20*TRIA/DES NOHTAI\ A(/MA KAI\ NOERAI/>20.] *(O €ME\N DH\ PERI\ TW=N NOHTW=N LO/GOS H(MI=N E)NTAU=QA €PERIGEGRA/FQW TH\N TOU= *PLA/TWNOS PERI\ AU)TW=N €A)NAPLW/SAS MUSTAGWGI/AN. *)EXO/MENON DE/ E)STI €PA/NTWS TH\N PERI\ TW=N NOERW=N QEW=N A)NASKE/YASQAI €KATA\ TO\N AU)TO\N TRO/PON U(FH/GHSIN. *)ALL' E)PEIDH\ €TW=N NOERW=N, TA\ ME/N E)STI <20NOHTA\ KAI\ NOERA\>20, €O(/SA <20NOOU=NTA NOEI=TAI>20, KATA\ TO\ *LO/GION, TA\ €DE\ NOERA\ MO/NON, A)PO\ TW=N NOERW=N A(/MA KAI\ NOHTW=N €A)RCA/MENOI LE/GWMEN TA\ KOI=NA PRW=TON PERI\ AU)-€TW=N DIORIZO/MENOI, A)F' W(=N KAI\ TH\N PERI\ TH=S €E(KA/STHS TA/CEWS DIDASKALI/AN SAFESTE/RAN POIH-€SO/MEQA. *PA/LIN TOI/NUN A)NAMNH/SWMEN H(MA=S AU)TOU\S €W(S A)/RA TREI=S EI)SIN AU(=TAI MONA/DES O(LIKAI\ PA/N-€TWS E)PE/KEINA TW=N KATA\ ME/RH DIH|RHME/NWN QEW=N, €<20OU)SI/A, ZWH\, NOU=S>20. *KAI\ TAU=TA PRO\ TW=N MERI-€KW=N METE/XEI TW=N U(PEROUSI/WN E(NA/DWN: E)CH/|RHTAI €DE\ H( OU)SI/A TW=N LOIPW=N, ME/SHN DE\ E)/LAXEN H( €ZWH\ TA/CIN, TO\ DE\ PE/RAS TH=S TRIA/DOS TAU/THS €E)PISTRE/FEI PRO\S TH\N A)RXH\N O( NOU=S: KAI\ PA/NTA €TAU=TA NOHTW=S ME\N E)/STIN E)N OU)SI/A|, NOHTW=S DE\ €KAI\ NOERW=S E)N TH=| ZWH=|, NOERW=S DE\ E)N TW=| NW=|. €[1&Proclus, lib. IV. p. 179.$]1 €@*LEI/PETAI DH\ KAI\ PERI\ TH=S TRIADIKH\S AU)TOU= €[TOU= A)RIQMOU=] DIAIRE/SEWS EI)PEI=N E(POME/NWS TW=| €*PARMENI/DH|. *TRI/A TOI/NUN E)C A)RXH=S TAU=TA PE/FH-€NEN H(MI=N KATA\ TH\N TOU= E(NO\S DIA/KRISIN A)PO\ TOU= €O)/NTOS <20TO\ E(\N, H( E(TERO/THS, TO\ O)/N>20. *KAI\ €TREI=S AU(=TAI MONA/DES TH=S E(TERO/THTOS OU)/TE TW=| €E(NI\ AU)TH=S OU)/SHS OU)/TE TW=| O)/NTI: TAU=TA GA\R KA)\N €E)N TOI=S NOHTOI=S H)=N, H( DE\ E(TERO/THS E)NTAU=QA PRW=-@2TON. *)ALL' E)PEIDH/PER A)/NW ME\N H( DU/NAMIS SUN-€AGWGO\S H)=N, E)NTAU=QA DE\ DIAKRITIKH\ TW=N A)/KRWN, €OU) MO/NON MONA/DES EI)SI\ TREI=S, A)LLA\ KAI\ DUA/DES €TREI=S, TO\ E(\N META\ TH=S E(TERO/THTOS, KAI\ H( E(TERO/-€THS META\ TOU= O)/NTOS KAI\ TO\ E(\N META\ TOU= O)/NTOS: €AI)TI/A GA\R KAI\ TH=S TOIAU/THS DIAKRI/SEWS H( E(TE-€RO/THS TH\N E(/NWSIN A)KRAIFNH= TOU= E(NO\S O)/NTOS OU) €FULA/TTOUSA. *MONA/DES OU)=N TREI=S KAI\ DUA/DES €TREI=S, A)LLA\ KAI\ TRIA/DES TREI=S AI( AU)TAI\ GE/NOINTO €A)\N, O(TE\ ME\N H(MW=N A)PO\ TOU= E(NO\S A)RXOME/NWN, O(TE\ €DE\ A)PO\ TOU= O)/NTOS, O(TE\ DE\ A)PO\ TH=S E(TERO/THTOS: €MONADIKW=S A)/RA KAI\ TRIADIKW=S U(FE/STHKEN H( TRIA\S €AU(/TH .... *KAI\ MEXRI\ TOU/TWN H( PRWTI/STH QEO/THS €E)KPE/FANTAI GO/NIMOS OU)=SA TW=N PRWTI/STWN A)RI-€QMW=N, KATA\ ME\N TO\ E(\N TW=N E(NIAI/WN, KATA\ DE\ €TH\N E(TERO/THTA TW=N GENNHTIKW=N, KATA\ DE\ TO\ O)\N €TW=N OU)SIWDW=N. *)EPEIDH\ DE\ A)PO\ TAU/THS NOHTH=S €OU)/SHS H( MET' AU)TH\N, A)NA/GKH DH/POU KAI\ TH\N €MONA/DA DU/NAMIN E)/XEIN GO/NIMON, KAI\ TH\N DUA/DA €KAI\ TH\N TRIA/DA. *TAU/TAS ME\N OU)=N TA\S DUNA/MEIS €O( *PARMENI/DHS A)POKALEI= TO\ <20A(/PAC, TO\ DI\S, TO\ €TRI/S>20 [&p. 143 E$] .... *)ARXO/MENOS DE\ O( *PARMENI/-€DHS TW=N PERI\ AU)TOU= [TOU= A)RIQMOU=] LO/GWN E)NTEU=-€QEN: <20*)/IQI DH\ KAI\ TH=|DE E)/TI. *PH=|; *OU)SI/AS €FAME\N METE/XEIN TO\ E(\N, DIO\ E)/STI; *NAI/. €*KAI\ DIA\ TAU=TA DH\ TO\ E(\N O)\N POLLA\ E)FA/NH>20 €[&p. 143 A$]: SUMPLHROI= ME\N TO\N PERI\ TH=S PRW/-€THS MONA/DOS LO/GON W(DI/: <20*TRI/A DE\ OU) PERITTA\ €KAI\ DU/O A)/RTIA; *PW=S D' OU)/>20 [&p. 143 D$]; €*TO\N DE\ PERI\ TH=S DEUTE/RAS: <20*)/ARTIA/ TE A)/RA €A)RTIA/KIS A)\N EI)/H KAI\ PERITTA\ PERIT-€TA/KIS KAI\ A)/RTIA PERITTA/KIS KAI\ PE-€RITTA\ A)RTIA/KIS>20 [&p. 144 A$]. *TO\N DE\ PERI\ €TH=S TRI/THS KAI\ E)FECH=S TRIA/DOS E)N TOU/TOIS: <20*OU) €MO/NON A)/RA TO\ O)\N E(\N POLLA/ E)STIN, A)LLA\ €AU)TO\ KAI\ TO\ E(\N U(PO\ TOU= O)/NTOS DIANENE-€MHME/NON POLLA\ A)NA/GKH EI)=NAI. *PANTA/-€PASI ME\N OU)=N>20 [&p. 144 E$]. *(H TOI/NUN <20PRW-€TI/STH TRIA\S TW=N NOHTW=N KAI\ NOERW=N €QEW=N>20 DIA\ TOU/TWN H(MI=N U(PO\ TOU= *PLA/TWNOS E)K- @1PE/FANTAI, KATA\ ME\N TH\N PRWTI/STHN MONA/DA €PRW/TAS E)/XOUSA TW=N A)RIQMW=N DUNA/MEIS, TO\ <20PE-€RITTO\N>20 LE/GW KAI\ TO\ <20A)/RTION,>20 KAI\ DIA\ TOU/TWN €SUMPLHROUME/NH TW=N A)RXW=N, AI( KAI\ E)N TOI=S NOH-€TOI=S H)=SAN KRUFI/WS, MONA\S, DUA\S, TRIA/S: KATA\ €DE\ TH\N DEUTE/RAN, TA\S DEUTE/RAS A)PO\ TOU/TWN U(F-€ISTAME/NAS: H( GA\R TW=N EI)DW=N TOU= A)RTI/OU TOMH\ €DEUTE/RAN E)/LAXE TA/CIN, KAI\ TO\ <20PERITTA/KIS €PERITTO\N>20 U(FEIME/NON E)STI\ TW=N PRW/TWN PERIT-€TW=N: KATA\ DE\ TH\N TRI/THN, TA\S MERIKWTE/RAS €AI)TI/AS TW=N QEI/WN A)RIQMW=N: DIO\ KAI\ O( KATAKER-€MATISMO\S E)NTAU=QA KAI\ H( A)PEIRI/A KAI\ H( PANTELH\S €DIAI/RESIS KAI\ O( E(NIAI=OS A)RIQMO\S KAI\ OU)SIW/-€DHS .... þï€´°³¶ÿï°²°ÿ›‰ãˆ@*(H ME\N OU)=N PRWTI/STH TA/CIS TW=N NOHTW=N KAI\ €NOERW=N OU(/TWS U(PO\ TOU= *PARMENI/DOU TEQEW/RHTAI. €*META\ DE\ TAU/THN H( TO\N ME/SON KATE/XOUSA TO/PON €TW=N NOHTW=N KAI\ NOERW=N, H(\N MIKRW=| PRO/TERON €SUNEKTIKH\N A)PEKALOU=MEN, E)KFAI/NETAI. *KALEI=TAI €DE\ AU)TH\ TRIXW=S, <20E(\N POLLA\, O(/LON ME/RH, €PEPERASME/NON A)/PEIRON>20 .... *(ECH=S GA/R E)STIN €A)LLH/LOIS TO\ E(\N, TO\ O(/LON, TO\ PEPERASME/NON, KAI\ €TA\ TOU/TOIS OI(=ON A)NTI/STOIXA, TA\ POLLA\, TA\ ME/RH, €TA\ A)/PEIRA. *KAI\ E)/STI TO\ ME\N E(\N AU)TO\ H( A)RXH\ €TW=N LOIPW=N: TO\ DE\ O(/LON H)/DH SXE/SIN E)/XEI PRO\S €TA\ ME/RH KAI\ DUA/DOS E)/MFASIN, KAI\ PRO/EISIN EI)S €TH\N PRO\S TA\ ME/RH SU/NTACIN: TO\ DE\ PEPERASME/-€NON H)/DH PLH=QO/S E)STI PE/RATOS KAI\ E(NO\S METE/XON, €KAI\ OI(=ON TRIA/S E)STI: OU)/TE GA\R PE/RAS MO/NON W(S H( €MONA\S, OU)/TE A)/PEIRON MO/NON W(S H( DUA\S, A)LLA\ €PE/RATOS METE/XON O(\ PRW=TO/N E)STI TRIA/S. *PA=N ME\N@2 OU)=N PEPERASME/NON O(/LON E)STI\N, OU) PA=N DE\ O(/LON €PEPE/RASTAI: KAI\ GA\R TO\ A)/PEIRON O(/LON, EI)/TE €PLH=QO/S E)STIN, EI)/TE ME/GEQOS: KAI\ PA=N ME\N TO\ €O(/LON E(/N E)STI, OU) PA=N DE\ E(\N O(/LON: TO\ GA\R A)/SXE-€TON PRO\S TO\ PLH=QOS OU)X O(/LON. *)EPE/KEINA A)/RA TO\ €ME\N E(\N TOU= O(/LOU, TO\ DE\ O(/LON TOU= PEPERASME/NOU. €*TO\N AU)TO\N DH\ TRO/PON KAI\ TA\ A)/PEIRA ME/RH TOU= €PEPERASME/NOU LE/GETAI: KAQ' E(AUTO\ GA\R OU)K E)/STI €TO\ A)/PEIRON: W(=| KAI\ DH=LON W(S OU)K E)/STIN E)N TW=| €POSW=| TO\ A)/PEIRON, A)LL' E)N TH=| DUNA/MEI. *OU) PA/NTA €DE\ TA\ ME/RH A)/PEIRA: KAI\ GA\R KATA\ TO\ PE/RAS €E(NI\ XARAKTHRI/ZETAI TW=N MERW=N: KAI\ AU)= TA\ ME\N €ME/RH POLLA/ E)STI, TA\ DE\ POLLA\ OU) PA/NTWS ME/RH. €*TA\ TOI/NUN POLLA\ PRO\ TW=N MERW=N, TAU=TA DE\ PRO\ €TW=N A)PEI/RWN: A)NA/LOGON A)/RA TW=| ME\N E(NI\ TA\ €POLLA\, TW=| DE\ O(/LW| TA\ ME/RH, TW=| DE\ PEPERA-€SME/NW| TA\ A)/PEIRA, KAI\ TREI=S AU(=TAI SUNOXIKAI\ €MONA/DES TH\N ME/SHN SUMPLHROU=SI TA/CIN TW=N NOH-€TW=N KAI\ NOERW=N .... *TOIAU/TH TI/S E)STI KAI\ H( €SUNEKTIKH\ TRIA\S, H(\N O( *PARMENI/DHS DIA\ TOU/TWN €A)PE/FHNE: <20*TO\ E(\N A)/RA O)\N E(/N TE/ E)STI KAI\ POL-€LA\, KAI\ O(/LON KAI\ MO/RIA, KAI\ PEPERA-€SME/NON KAI\ A)/PEIRON PLH/QEI>20 [&p. 145 A$]. €@*TO\ DE\ TRI/TON FASI\ TW=| SWTH=RI, KAI\ H(MEI=S €<20TH\N TELESIOURGO\N DIAKO/SMHSIN TW=N €QEW=N>20 A)NUMNH/SWMEN, E(PO/MENOI TW=| *PARMENI/DH| €KATA\ TO\ E(CH=S. *OU)KOU=N, DIO/TI ME\N TE/LOS H)=N TH=S €SUNEKTIKH=S TO\ PEPERASME/NON, H( TELESIOURGO\S TA\ €E)/SXATA E)/XEI: TO\ GA\R PE/RAS E)/SXATON. *)ALL' E)KEI= €ME\N TO\ PEPERASME/NON E)LE/GETO TO\ E(\N, E)NTAU=QA €DE\ E)/SXATON E)/XON, W(S KATA\ ME/QECIN TO\ PERA- @1TWTIKO\N TW=N POLLW=N KATADECA/MENON: KA)KEI= ME\N €TO\ PE/RAS H)=N O(\ DH\ KAI\ SUNEI=XE TO\ A)/PEIRON, E)N-€TAU=QA DE\ E)/SXATON E)/XON KAI\ <20ME/SON>20 A)\N E)/XOI KAI\ €<20A)RXH\N>20, KAI\ TE/LEION A)\N EI)/H: TO\ GA\R E)K PA/NTWN €TOU/TWN SUMPLHROU/MENON TE/LEIO/N E)STI. *)ENTAU=QA €TOI/NUN KAI\ H( E)K TW=N MERW=N A)NEFA/NH TELEIO/THS: €H( GA\R SUMPLH/RWSIS TW=N MORI/WN A)PERGA/ZETAI €TO\ TE/LEION. *KAI\ MH\N, KAI\ DIO/TI ME/SON E)/XEI KAI\ €A)/KRA TOIOU=TON E(\N, SXH=MA A)\N E)/XOI <20PERIFERE\S €H)\ MIKTO\N H)\ EU)QU/>20: PA/NTA GA\R TAU=TA ME/SOU €DEI=TAI KAI\ A)/KRWN, TA\ ME\N META\ A(PLO/THTOS, TA\ €DE\ META\ SUMPLOKH=S. *TREI=S OU)=N H(MI=N PEFH/NASIN €I)DIO/THTES: PRW/TH ME\N H(\N E)LE/GOMEN E)/SXATA €E)/XEIN, DEUTE/RA DE\ H( KATA\ TO\ TE/LEION, TRI/TH DE\ €H( KATA\ TO\ SXH=MA .... €@*PRO\S DE\ AU)= TOI=S EI)RHME/NOIS KAI\ TH\N TA/CIN €TW=N TRIA/DWN A)PO\ TW=N E)N AU)TAI=S TELW=N QEWRH/-€SWMEN. *TH=S ME\N GA\R PRW/THS TO\ PE/RAS A)RIQMO\S, €TH=S DE\ DEUTE/RAS TO\ PEPERASME/NON KAI\ A)/PEIRON, €TH=S DE\ TRI/THS PERIFERE\S, MIKTO\N, EU)QU/ .... *SUN-€ELO/NTES OU)=N EI)/PWMEN O(/TI PA=SA NOHTH\ KAI\ NOERA\ €TRIA\S KATA\ ME\N TH\N A)KRO/THTA TH\N E(AUTH=S SUN-€H=PTAI PRO\S TO\ NOHTO\N, KATA\ DE\ TH\N MESO/THTA €TH\N OI)KEI/AN E)KFAI/NEI DUNA/MIN, KATA\ DE\ TH\N A)PO-€PERA/TWSIN PERILAMBA/NEI TH\N A)PEIRI/AN TW=N DEU-€TE/RWN. [1&Proclus, lib. IV, p. 229_241$.]1 €@[<20*QEOI\ NOEROI/>20. *KRO/NOS, *(RE/A, *ZEU/S.] *PRW=TON €PERI\ TOU= PATRO\S TW=N NOERW=N KAI\ AU)= TH=S SUNTE-€TAGME/NHS AU)TW=| DUNA/MEWS TH=S A)XRA/NTOU QEW-€RH/SWMEN O(POI=A/ FHSIN [O( *PARMENI/DHS]: META\ €GA\R TO\ SXH=MA TO\ TRIPLEKE\S KAI\ TH\N PA/NTA TE-€LESIOURGOU=SAN TW=N QEW=N TA/CIN E)MFAI/NETAI ME\N €TO\ E)N <20E(AUTW=| KAI\ E)N A)/LLW|>20: SUNQH/MATA DE\ €TAU=TA TH=S NOERA=S A)KRO/THTOS E)PIDEI/KNUTAI TW=N €NOERW=N MONA/DWN .... *TAU=TA TOI/NUN KAI\ O( *PAR-€MENI/DHS E)NDEIKNU/MENOS TOI=S DITTOI=S TOU/TOIS €SUNQH/MASI TH\N TA/CIN TAU/THN A)POSEMNU/NEI, KAI\@2 TO\N PRW/TISTON BASILE/A KAI\ PATE/RA TW=N NOERW=N €DIA\ TOU/TWN XARAKTHRI/ZEI TW=N I)DIOTH/TWN: KAI\ €GA\R E)N E(AUTW=| E)STI KAI\ E)N A)/LLW|: KAQO/SON ME\N €GA/R E)STIN O( O(/LOS NOU=S [*KRO/NOS], PRO\S E(AUTO\N €E)NERGEI=, KAQO/SON DE\ E)N TOI=S PRO\ AU)TOU= NOHTOI=S €E)STIN, E)N A)/LLW| TH\N E(AUTOU= PANTELH= NO/HSIN €I(/DRUSE. *TOU=TO GA\R TO\ <20E)N A)/LLW|>20 TOU= <20E)N E(AUTW=|>20 €KREI=TTO/N E)STIN, EI)/PER, W(S AU)TO\S O( *PARMENI/DHS €DIATA/TTETAI, <20KATA\ ME\N TO\ O(/LON>20 AU)TW=| TO\ €<20E)N A)/LLW|>20 PROSH/KEI, <20KATA\ DE\ TA\ ME/RH>20 TO\ €<20E)N E(AUTW=|>20. *POU= DH\ OU)=N PROU+PA/RXEI TO\ <20A)/LLO>20 €KAI\ POI/A| TA/CEI PROSH/KEI TW=N PRO\ AU)TOU= QEW=N; €*)\H KAI\ TOU=TO DAIMONI/WS TW=| H(METE/RW| KAQH-€GEMO/NI GE/GRAPTAI: KAI\ TO\ <20A)/LLO>20 TH=| TA/CEI €DIAFE/REI TAU/TH| KAQ' H(\N H( TH=S E(TERO/THTOS DU/-€NAMIS PRW=TON E)CE/LAMYEN, E)/KGONOS OU)=SA TH=S €NOHTH=S KAI\ PATRIKH=S DUNA/MEWS. *DIO\ KAI\ E)N TH=| €PRW/TH| TRIA/DI KRUFI/WS H)=N TO\ <20A)/LLO>20, KAQO/SON €KAI\ H( DU/NAMIS KAI\ DIAFERO/NTWS E)KFAI/NETAI €KATA\ TH\N PRWTI/STHN TA/CIN TW=N NOHTW=N O(MOU= €KAI\ NOERW=N: E)KEI= GA\R H( PRW/TH E(TERO/THS KAI\ €TO\ QH=LU TW=N QEW=N, KAI\ H( PATRIKH\ DU/NAMIS KAI\ €A)/FQEGKTOS .... €@*DEUTE/RA DE\ META\ TAU/THN [TH\N PRW/THN NOE-€RA\N TA/CIN] H( TA\ ME/SA GE/NH PERIE/XOUSA TW=N €O(/LWN KAI\ TH=S PROO/DOU TOI=S PA=SIN AI)TI/A [*(RE/A] €KAI\ TH=S GONI/MOU DUNA/MEWS, SUNEXH\S OU)=SA PRO\S €TAU/THN A)NAFAI/NETAI. *TI/ DH\ OU)=N E)STI TW=| NOHTW=| €PANTAXOU= KAI\ TW=| O)/NTWS O)/NTI SUNEXE\S A)/LLO €PLH\N TH=S ZWH=S; ME/SH GA\R AU(/TH TOU= TE NOU= €KAI\ TOU= NOHTOU=, SUNA/PTOUSA TW=| NOHTW=| TO\N €NOU=N KAI\ TH\N NOHTH\N A)POTUPOUME/NH| DU/NAMIN €TH\N SUNAGWGO\N TOU= TE E(NO\S KAI\ TOU= O)/NTOS .... €*KAI\ OU(/TW DH\ <20TO\ E(\N KINEI=SQAI KAI\ E(STA/-€NAI>20 LE/GWN [O( *PARMENI/DHS], KATA\ ME\N TH\N €<20KI/NHSIN>20 TH\N ZWOGO/NON U(/PARCIN PARADI/DWSI €TW=N QEW=N KAI\ TH\N GENNHTIKH\N TW=N O(/LWN PHGH\N @1 KAI\ TH\N PA/NTWN A)RXHGO\N AI)TI/AN: KATA\ DE\ TH\N €<20STA/SIN>20 TH\N TH=| KINH/SEI SUNTETAGME/NHN A)/XRAN-€TON MONA/DA, TH\N TA\ ME/SA SUNE/XOUSAN TH=S FROU-€RHTIKH=S TRIA/DOS .... €@*TO\ TRI/TON TOI/NUN TW=| SWTH=RI/ FASI KAI\ TH\N €<20DHMIOURGIKH\N MONA/DA>20 [*DI/A] NOH/SWMEN, €E)KFAINOME/NHN META\ TW=N E)N AU)TH=| SUSTOI/XWN €QEW=N .... *KAI/ MOI DOKEI= KAI\ O( *PARMENI/DHS DIA\ €TAU=TA TA\ TH=S DHMIOURGI/AS SUNQH/MATA DIELW\N €E)N ME/SOIS AU)TOI=S E)KFH=NAI TA\S I)DIO/THTAS TH=S TE €A)XRA/NTOU MONA/DOS KAI\ TH=S DIAIRETIKH=S, KAQ-€O/SON KAI\ AU(=TAI PERIE/XONTAI/ PWS E)N TH=| MIA=| €DHMIOURGI/A|. *PRW/TISTON ME\N GA\R A)PODEI/KNU-€SI TW=N SUMPERASMA/TWN O(/TI TO\ E(\N <20TAU)TO\N €E(AUTW=|>20, DEU/TERON DE\ O(/TI <20E(/TERON E(AUTOU=>20, €KAI\ TRI/TON O(/TI <20TW=N A)/LLWN E(/TERON>20, TE/TAR-€TON DE\ O(/TI <20TAU)TO\N TOI=S A)/LLOIS>20: TH=| ME\N €E(NW/SEI TH=| PATRIKH=| TH\N DIAIRETIKH\N DU/NAMIN €SUNTA/TTWN, TH=| DE\ XWRISTH=| TW=N DEUTE/RWN U(PER-€OXH=| TH\N PRONOHTIKH\N AU)TW=N AI)TI/AN SUMPLE/KWN. €[1&Proclus, lib. V, p. 326_335.$]1 €@[<20*QEOI\ A)FOMOIWTIKOI\ KAI\ H(GEMONI-€KOI/>20.] *EI) TOI/NUN KAI\ H(/DE TW=N QEW=N [<20A)FOMOIW-€TIKW=N>20] H( TA/CIS A)PEIKA/ZEI TA\ AI)SQHTA\ TOI=S €NOEROI=S KAI\ PA/NTA TA\ MEQ' E(AUTH\N KATA\ TH\N €PRO\S TA\ AI)/TIA PARA/GEI MI/MHSIN, O(MOIO/THTOS €DH/POU TOI=S MEQ' E(AUTH/N E)STIN AI)TI/A PRWTOUR-€GO/S. *EI) DE\ TAU/THS, KAI\ A)NOMOIO/THTOS TH=S TH=| €O(MOIO/THTI SUSTOI/XOU: PA/NTA GA\R TA\ MET-@2E/XONTA TOU= O(MOI/OU KAI\ TOU= A)NOMOI/OU META-€LAGXA/NEIN A)NA/GKH .... *(/OTI DE\ A)PO\ TH=S DH-þï€´°³¶ÿï°²°ÿ›‰èƒMIOURGIKH=S MONA/DOS KAI\ TW=N E)KEI= PROU+PARXO/NTWN €SUNQHMA/TWN KAI\ TAU=TA PRO/EISIN EI)S TH/NDE TA/-€CIN, I(KANW=S O( *PARMENI/DHS H(MI=N A)PODEI/KNUSI: €TO\ GA\R <20TAU)TO\N>20 TO\ DHMIOURGIKO\N KAI\ TO\ <20E(/TE-€RON>20 TH=S E)NTAU=QA PROE/STHKEN <20O(MOIO/THTOS>20 KAI\ €<20A)NOMOIO/THTOS>20 AI)/TION, W(S AU)TO/S FHSI. €[1&Proclus, lib. VI, p. 384_385.$]1 €@[<20*QEOI\ A)PO/LUTOI>20]. *LOIPO\N TOI/NUN H(MI=N €E)STI TO\N *PARMENI/DHN E)PIMARTU/RASQAI TH=S PERI\ €TW=N QEW=N TOU/TWN [<20A)POLU/TWN>20] DIDASKALI/AS. €*KAI\ GA\R O( *PLA/TWN E)N E)KEI/NW| TH\N MI/AN AU)TW=N €I)DIO/THTA SAFE/STATA PARE/DWKE. *META\ GA\R TH\N €TW=N A)FOMOIWTIKW=N DIAKO/SMWN PRO/ODON TO\ E(\N €<20A(PTO/MENON>20 DEI/KNUTAI <20KAI\ E(AUTOU= KAI\ TW=N €A)/LLWN>20. *(/APANTA GA\R TA\ QEI=A GE/NH META\ €TH\N MONA/DA TH\N DHMIOURGIKH\N DIPLASIA/ZEI €TA\S E(AUTW=N E)NERGEI/AS: KAI\ GA\R PRO\S E(AUTA\ KAI\ €PRO\S TA\ A)/LLA TA\ MEQ' E(AUTA\ PE/FUKEN E)NERGEI=N, €PROO/DOIS XAI/RONTA KAI\ TH=| PRONOI/A| TW=N DEUTE/-€RWN, U(PHRETOU=NTA TH=| BOULH/SEI TOU= PATRO\S, €KAI\ TH\N U(PERFUA= KAI\ A)ME/RISTON AU)TOU= KAI\ €PANTELH= POI/HSIN PROKALOU/MENA, KAI\ TOI=S DEU-€TE/ROIS E)POXETEU/ONTA. *TOU=TO DH\ OU)=N PRO\ TW=N €A)/LLWN A(PA/NTWN TO\ TH=S A(FH=S KAI\ DIAIRE/SEWS €TH=S PRO\S TA\ KATADEE/STERA PW=S OU)XI\ TH\N <20A)PO/-€LUTON>20 H(MI=N I)DIO/THTA PARI/STHSI; TO\ ME\N GA\R €<20A(/PTESQAI>20 TH=S PRO\S H(MA=S SUGGENEI/AS H)=N KAI\ @1 TH=S SUNTETAGME/NHS PRONOI/AS: TO\ DE\ AU)= MH\ €<20A(/PTESQAI>20, TH=S E)CH|RHME/NHS KAI\ XWRISTH=S A)P' €AU)TW=N U(PEROXH=S .... *TO\ TOI/NUN <20A(PTO/MENON TW=N €A)/LLWN E(\N KAI\ OU)X A(PTO/MENON>20 KAI\ SUNE/-€ZEUKTAI PRO\S TA\ A)/LLA KAI\ U(PERI/DRUTAI AU)TW=N: €DIO\ DH\ KAI\ A(/MA TH/N TE TW=N U(PERIDRUME/NWN KAI\ €TH\N TW=N E)GKOSMI/WN E)/LAXE DU/NAMIN: E)N ME/SW|@2 GA\R O)\N A)MFOTE/RWN E)N E(NI\ SUNEI/LHFE TA\S DIH|RH-€ME/NAS TW=N A)/KRWN I)DIO/THTAS. *KAI\ MH\N KAI\ €<20E(AUTOU=>20 PRO\ TW=N A)/LLWN <20A(/PTETAI/ TE KAI\ €OU)X A(/PTETAI>20: DIO/TI DH\ KAI\ E)N AU)TW=| PLH=QO/S €E)STI KAI\ DIA/KRISIS O(LO/THTOS KAI\ TW=N TAU/THS €MERW=N KAI\ E(/NWSIS PANTO\S TOU= PLH/QOUS SUNA-€GWGO/S. [1&Proclus, lib. 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