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Algebra and Trigonometry Review .pdf

1. Algebra and Trigonometry review material from the Department of Mathematics at Vanderbilt University is summarized. Sets of numbers including natural numbers, integers, rational numbers, and real numbers are defined. 2. Operations on sets of numbers like addition, subtraction, multiplication, and division are explained. Properties of these operations such as commutativity, associativity, and distributivity are also covered. 3. Concepts involving inequalities, intervals, and absolute value are introduced. Examples are provided to illustrate key ideas.

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Algebra and Trigonometry Review Material Department of Mathematics Vanderbilt University June 2, 2004 http://atlas.math.vanderbilt.edu/~pscrooke/calculus/calculus.html
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Algebra and Trigonometry Review .pdf

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    Algebra and Trigonometry ReviewMaterial Department of Mathematics Vanderbilt University June 2, 2004 http://atlas.math.vanderbilt.edu/~pscrooke/calculus/calculus.html
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  • 14.
    1QSKDVGI LKK OWPRG LFONG QDEFGHIT POUGPRGH g1PR LKK PRG 1HHLP1OQLK QDEFGHI K1|G }_` ~ }`€T LQV Y ‚NGHM HGLK QDEFGH e SLQ FG PRODURP OW LI PRG ƒOH1GQPGV„ V1IPLQSG OW L JO1QP OQ L K1QG WHOE PRG OH1U1QY …O PRG IGP OW HGLK QDEFGHI 1I 1Q V1HGSP SOHHGIJOQVGQSG g1PR L K1QG OQ L JKLQGY † † † † ‡ ‡ ‡ ‡ ˆˆ‰‰ x -3 -1 4 -2 1 2 3 0 -4 Š 1UDHG hYhk jRG HGLK QDEFGH K1QG ‹GSLDIG SGHPL1Q IDFIGPI OW PRG HGLK K1QG LHG DIGV tD1PG OWPGQT gG LVOJP L IJGS1LK QOPLP1OQ WOH PRGE PRLP 1I SLKKGV
  • 15.
    Œ Y jRGIGP ^efh  e  _d OW LKK HGLK QDEFGHI FGPgGGQ h LQV _T 1QSKDV1QU h LQV _T 1I VGQOPGV FM Žh`_Y W gG gLQP LKK PROIG h
  • 16.
    QDEFGHI G‘SGJP WOH_`gG gH1PG Žh`_„ ] ^efh  e ’ _dY Q UGQGHLK gG RLNG PRG WOKKOg1QU QOPLP1OQ WOH SGHPL1Q IGPI OW QDEFGHI SLKKGV
  • 17.
  • 18.
    Œ Ž“`”„ ] ^ef“ e ’ ”d +•0
  • 19.
    Œ ƒ“`” ] ^ef“’ e  ”d +•0
  • 20.
  • 21.
    Œ – – – – —— — — ˜˜™™ b -3 -1 4 -2 1 2 3 0 -4 a Š 1UDHG hY_k jRG 1QPGHNLK ƒ“`” jRG ROKKOg S1HSKG LP e ] “ OQ PRG QDEFGH K1QG LFONG IROgI PRLP PRG 1QPGHNLK š›œ ž›Ÿ SOQPL1Q “T gR1KG PRG  KKGV¡1Q S1HSKG LP e ] ” IROgI PRLP 1P š›œ SOQPL1Q ”Y ¢G SLQ SOQI1VGH £
  • 22.
    Œ LI gGKKk Ž“`¤¥„] ^ef“  ed ƒ“`¤¥„ ] ^ef“ ’ ed ƒq¥`” ] ^efe  ”d ƒq¥`”„ ] ^efe ’ ”d ƒq¥`¤¥„ ] { COPGPRLP q¥ LQV ¤¥ LHGQGNGH 1QSKDVGV 1QPRG1QPGHNLKITI1QSGPRGM LHGQOPQDEFGHIY W LQV ¦ LHG IGPIT gG VGQOPG PRG IGP OW LKK GKGEGQPI OW POUGPRGH g1PR LKK GKGEGQPI OW ¦ FM § ¦` gR1SR gG HGLV LI ¨ DQ1OQ ¦Y© ª ƒL„ ^h`_`m`ad§ ^b`d ] ^h`_`m`a`b`d ƒF„ ^h`_`m`ad§ ^h`m`«`d ] ^h`_`m`a`«`d COPG PRLP gG VO QOP K1IP PRG ILEG GKGEGQP Pg1SG 1Q IGP QOPLP1OQY _
  • 23.
    ª ƒq_n«`qh §ƒrn«`mna ¬ ¬ ¬ ¬ ­ ­ ­ ­ ®®¯¯ 0.5 -3 -1 4 -2 0 -4 1 2 3 3.4 -2.5 Š 1UDHG hYmk ƒq_n«`h§ ƒrn«`mna ª ƒqhnb`hna§ ƒrn«`mna ] ƒqhnb`mna ° ° ° ° ± ± ± ± ²²³³ 0.5 -3 -1 4 -2 0 -4 1 2 3 -1.6 1.4 3.4 Š 1UDHG hYak ƒqhnb`mna =@A´µ¶· ¸¹ºA@BB´»¼B jRGHG LHG SGHPL1Q PR1QUI PO |GGJ 1Q E1QV gRGQ gOH|1QU g1PR QDEGH1SLK G‘JHGII1OQIY ¢RGQ LVV1QU OH EDKP1JKM1QU PgO QDEFGHI PRG OHVGH 1I QOP 1EJOHPLQPY Š OH G‘LEJKGT « ¤ m ] c ] m ¤ «Y Q UGQGHLKT WOH LKK HGLK QDEFGHIT “ ¤ ” ] ” ¤ “ LQV “” ] ”“ ƒ Œ „ jRG ILEG 1I QOP PHDG WOH IDFPHLSP1OQ OH V1N1I1OQT I1QSG « q m y] m q « LQV «½m y] m½«Y ¾OHGONGHT gRGQ gG LVV OH EDKP1JKM QDEFGHI gG VO QOP QGGV JLHGQPRGIGI PO IJGS1WM PRG OHVGH 1Q gR1SR PRG OJGHLP1OQ IRODKV FG JGHWOHEGVT I1QSG ƒ“ ¤ ”„¤ ¿ ] “ ¤ ƒ”¤ ¿„ LQV “ƒ”¿„ ] ƒ“”„¿ ƒ Œ „ ‹DPT LUL1QTPR1I 1I QOP PHDG WOH IDFPHLSP1OQ OH V1N1I1OQTI1QSG « q ƒm q _„ ] « q h ] aT gR1KG ƒ« q m„ q _ ] _ q _ ] rY jRDI gG QGGV JLHGQPRGIGI gRGQ gG JGHWOHE IDFPHLSP1OQ OH gRGQ gG VGLK g1PR EOHG PRLQ OQG OJGHLP1OQT I1QSG ƒ« Àm„ ¤ _ ] h« ¤ _ ] hT gR1KG « À ƒm ¤ _„ ] « À « ] _«Y jR1I SHGLPGI LQ ONGHLFDQVLQSG OW JLHGQPRGIGIT IO gG LUHGG PO JGHWOHE EDKP1JK1SLP1OQI m
  • 24.
    LQV V1N1I1OQI  HIPLQV PRGQ LVV1P1OQI LQV IDFPHLSP1OQIÁ EOHGONGHT gG JGHWOHE K1|G OJ¡ GHLP1OQI WHOE KGWP PO H1URPY …OT«Àm¤_ EGLQI h«¤_ ] hTgR1KG «qmq_ EGLQI _q_ ] rY P 1I GLIM PO OFIGHNG PRLP « À ƒm ¤ _„ ] « À m ¤ « À _T LQV PR1I L UGQGHLK JHOJGHPM OW QDEFGHIT gR1SR LKIO ROKVI 1W gG RLNG IDFPHLSP1OQ 1QIPGLV OW LVV1P1OQk “ƒ” ¤ ¿„ ] “” ¤ “¿ LQV ƒ”¤ ¿„“ ] ”“ ¤ ¿“ ƒ
  • 25.
    Œ „ “ƒ” q¿„ ] “” q “¿ LQV ƒ” q ¿„“ ] ”“ q ¿“ ƒ
  • 26.
    Œ „ W gGPL|G “ ] qhT gG UGP qƒ”¤ ¿„ ] q” q¿ LQV qƒ” q ¿„ ] q”¤ ¿T U1N1QU DI L gLM OW UGPP1QU H1V OW JLHGQPRGIGI gRGQ gG RLNG L E1QDI I1UQ 1Q WHOQPY $ª _ q ƒ« q h„ q mƒq ¤ _„¤ aƒhr q m„ ] _ q a q mƒq«„¤ a À ] _ q a ¤ h« ¤ _c ] ah ÂZ _ q ƒ« q h„ q mƒq ¤ _„¤ aƒhr q m„ ] _ q « ¤ h¤ _h q b ¤ ar q h_ ] ah Ã?B»·=Ä@ Ŷ·=@B …1QSG L HGLK QDEFGH e 1I L JO1QP OQ PRG HGLK K1QGT gG SLQ SOQI1VGH 1PI V1IPLQSG WHOE PRG OH1U1QTgR1SR gG SLKK PRG Œ OW e LQV VGQOPG FM fefY Æ Æ Æ Æ Ç Ç Ç Ç ÈÈÉÉ |x| -3 -1 4 -2 1 2 3 0 -4 x y |y| Š 1UDHG hY«k jRG LFIOKDPG NLKDG 1I PRG V1IPLQSG WHOE PRG OH1U1Q W PRG QDEFGH e 1I JOI1P1NGTPRGQ fef1I GtDLKPO PRG QDEFGH 1PIGKW ƒf_f] _„Y W PRG QDE¡ FGH 1I QGULP1NGTILM e ] q_T1PI V1IPLQSG fefWHOE PRG OH1U1Q 1I _Y COPG PRLP 1Q PR1I SLIG PRG LFIOKDPG NLKDG fef] _ 1I PRG QGULP1NG OW e ] q_TQLEGKM fef] fq_f] _ ] qƒq_„ ] qeÁ IO 1W e 1I QGULP1NGT fef] qeY jRG KLIP GtDLK1PM 1I L F1P Lg|gLHV I1QSG fef 1I QGNGH QGU¡ LP1NGT FDP gG QGGV PRG E1QDI I1UQ 1Q WHOQP OW eT I1QSG e RLI LQOPRGH QGULP1NG I1UQ ¨1Q© a
  • 27.
    1PÁ PR1I gLMPRG PgO QGULP1NG I1UQI SLQSGK ODP LQV gG UGP L JOI1P1NG ODPSOEGY …O gG SLQ VG QG PRG LFIOKDPG NLKDG OW L QDEFGH e LIk fef] u e 1W e Ê r qe 1W e ’ r ËGHG LHG IOEG JHOJGHP1GI OW PRG LFIOKDPG NLKDG PRLP ROKV WOH LKK HGLK QDEFGHIk ZDKG ‚‘LEJKG fq “f] f“f fq _f] f_fT FGSLDIG PRGM FOPR GtDLK _Y f“”f] f“fÀ f”f fƒq_„mf] fq _fÀ fmfT FGSLDIG FOPR GtDLK bY xxx “ ” xxx ] f“f f”f xxxx _ qmxxxx ] f_f fq mfT I1QSG PRGM FOPR GtDLK _ mY f“ ¤ ”f f“f¤ f”f fa ¤ ƒqm„f faf¤ fq mfT I1QSG h  Y #ª ƒL„ fh q }_f] qƒh q }_„T I1QSG h q }_ 1I QGULP1NGY ƒF„ xxxxx _ q }_ }_ q _xxxxx ] f_ q }_f f}_ q _f ] f_ q }_f fq ƒ}_ q _„f ] f_ q }_f f_ q }_f ] hY (ª W “ Ê _T  QV f“ q hfY …1QSG “ Ê _T gG UGP “ Ê hY …O “ q h Ê rT QLEGKM “ q h 1I QOQ¡QGULP1NGY jRDIT f“ q hf] “ q hY %ª feÌ ¤ hf] eÌ ¤ hT I1QSG eÌ ¤ h 1I JOI1P1NG WOH LKK NLKDGI OW eY ª W e ’ qmT SLKSDKLPG xxx «fef¤ _ xxx Y …1QSG «fef¤ _ 1I JOI1P1NGT xxx «fef¤ _ xxx ] «fef¤ _Y COgT I1QSG e 1I QGULP1NGT fef] qeÁ IOT «fef¤ _ ] «ƒqe„¤ _ ] q«e ¤ _Y «
  • 28.
    ͪ Š 1QV LKK NLKDGIOW e IDSR PRLP fef] mY ZGSLKK PRLP fef ] m 1I PRG V1IPLQSG WHOE e PO PRG OH1U1QT IO e SLQ FG OQKM qm OH mT QLEGKM e ] ÎmY Ϫ Š 1QV LKK NLKDGI OW e IDSR PRLP f_e q «f] Y ZGSLKK PRLP f_e q «f]  1I PRG V1IPLQSG WHOE _e q « PO PRG OH1U1QÁ IO _e q « SLQ FG OQKM q OH T QLEGKM _e q « ] ÎY …OT _e q « ] q OH _e q « ] T QLEGKM _e ] q_ OH _e ] h_Y …O e ] qh OH e ] bY ª jRG IGP Ðe xxx fef’ _Ñ SOQPL1QI LKK QDEFGHI OQ PRG HGLK K1QG PRLP LHG KGII PRLQ _ DQ1PI LgLM WHOE PRG OH1U1QY Ò Ò Ò Ò Ó Ó Ó Ó ÔÔÕÕ 3 -3 -1 4 -2 0 -4 1 2 Š 1UDHG hYbk jRG IGP Ðe xxx fef’ _ÑY ª jRG IGP Ðe xxx fefÖ _Ñ SOQPL1QI LKK QDEFGHI OQ PRG HGLK K1QG PRLP LHG EOHG PRLQ _ DQ1PI LgLM WHOE PRG OH1U1QY × × × × × × Ø Ø Ø Ø Ø Ø ÙÙÚÚ 3 -3 -1 4 -2 0 -4 1 2 Š 1UDHG hYk jRG IGP Ðe xxx fefÖ _ÑY ¸¹@Aµ´B@B hY ZGgH1PG Žqh`m„ WHOE 1QPGHNLK QOPLP1OQ PO IGP QOPLP1OQ LQV VHLg MODH LQIgGH OQ PRG HGLK QDEFGH K1QGY _Y ¢H1PG PRG IGP ^ef q m ’ e  rd 1Q 1QPGHNLK QOPLP1OQ LQV VHLg MODH LQIgGH OQ PRG HGLK QDEFGH K1QGY b
  • 29.
    mY ¢H1PG VOgQPRG WOKKOg1QU IGP OW QDEFGHI 1Q FOPR 1QPGHNLK LQV IGP QOPLP1OQY Û Û Û Û Ü Ü Ü Ü ÝÝÞÞ 3 -3 -1 4 -2 0 -4 1 2 aY ¢H1PG PRG 1QPGHNLK Žq_`_ 1Q IGP QOPLP1OQ DI1QU LFIOKDPG NLKDGIY ƒ…GG ‚‘LEJKGI hh LQV h_Y„ «Y Š 1QV LKK NLKDGI OW e IDSR PRLP fm q ef] _Y bY …OKNG fe q haf] r WOH eY Y …OKNG f_e ¤ mf] h WOH eY cY ßHLg OQ PRG HGLK QDEFGH K1QG PRG IGP OW e¡NLKDGI WOH gR1SR GLSR OW PRG WOKKOg1QU 1I PHDGY àIG MODH VHLg1QU PO gH1PG PRG IGP 1Q 1QPGHNLK QOPLP1OQY ƒL„ fef’ « ƒF„ fefÊ c ƒS„ fe q _f’ b ƒV„ fe ¤ hfÊ a 
  • 30.
    áâã 78 ä78åæ7: ¸¹º»¼@¼ÄB W“ LQV w LHG QDEFGHIT gRLP VO gG EGLQ gRGQ gG gH1PG PRG G‘JHGII1OQ “çè éGPêI LQIgGH PR1I tDGIP1OQ FM FGU1QQ1QU g1PR PRG I1EJKGIP SLIGI gRGHG ODH 1QPD1P1OQ IGHNGI LI L QLPDHLK UD1VGY Š 1HIPT 1W w 1I L JOI1P1NG 1QPGUGH ƒPRLP 1IT w SODKV FG hT_TmTGPSY„T “ç XDIP EGLQI PRLP gG EDKP1JKM “ FM 1PIGKW w P1EGIY ª ƒL„ më ] m Àm Àm Àm ] ch ƒF„ ìh eíî ] h e À h e À h e ] h e î ƒS„ ƒq_„ï ] ƒq_„ƒq_„ƒq_„ƒq_„ƒq_„ ] qm_ ð=·@B ñ»A ¸¹º»¼@¼ÄB WPR1I1IgRLP gG EGLQ FM “ç gRGQ w 1I L JOI1P1NG1QPGUGHTgRLP HDKGIIRODKV G‘JOQGQPI OFGMè éGP DI SOQI1VGH gRLP “ò À“ç IRODKV FGT gRGQ FOPR v LQV w LHG JOI1P1NG 1QPGUGHIY jR1I 1IXDIP “ EDKP1JK1GV FM 1PIGKW v P1EGIT EDKP1JK1GV FM “T w EOHG P1EGIY jRDI gG RLNG “ P1EGI 1PIGKW v ¤ w P1EGIY jR1I 1I XDIP “òóçT LQV gG RLNG PRG WOKKOg1QU HDKGk “ò À“ç ] “òóç ƒh„ ª ¢G RLNG « î À«Ì ] ƒ« À« À«„ƒ« À«„ ] « À« À« À« À« ] «ï ] « î óÌ jR1I LKIO PGKKI DI ROg gG IRODKV VG QG PRG G‘JHGII1OQ “ôk 1W HDKG ƒh„ 1I PO ROKV WOH LKK QDEFGHIT gG IRODKV RLNG PRLP “ç ] “çóô ] “ç À“ôT IO PRLP “ô RLI PO FG h gRGQGNGH “ y] rY …O KGP DI EL|G PR1I VG Q1P1OQ WOH LKK QDEFGHI “ gR1SR LHG QOP rk c
  • 31.
    “ô ] hgRGQ “ y] r ƒ_„ ¢RLP OPRGH HDKGI IRODKV G‘JOQGQPI OFGMè õOQI1VGH gRLP RLJJGQI gRGQ gG HL1IG L JOgGH PO L JOgGHT gRGHG FOPR JOgGHI LHG 1QPGUGHIk ƒ“ò„ç ] ƒ“ À“ ÀnnnÀ“„ ÀnnnÀƒ“ À“ ÀnnnÀ“„ jRGHG LHG w UHODJI OW “êI LQV GLSR UHODJ SOQPL1QI v “êIY jRGHGWOHG gG RLNG vw “êI POPLKT LQV gG QOg RLNG PRG HDKG ƒ“ò„ç ] “òç ƒm„ ª ¢G RLNG ƒaÌ„ î ] ƒa Àa„ î ] ƒa Àa„ƒa Àa„ƒa Àa„ ] a Àa Àa Àa Àa Àa ] aö ] aÌ÷ î éGPêI IDJJOIG PRLP gG gLQP PRGIG Q1SG HDKGI PO FG OFGMGV QO ELPPGH gRLP QDEFGHI gG SROOIG LI ODH G‘JOQGQPIT LQV IGG ROg PR1QUI RLNG PO gOH| ODPY W w 1I L JOI1P1NG 1QPGUGH LQV “ y] rT gG EDIP RLNG PRLP h ] “ô ] “çøç ] “ç À“øçT IO PRLP gRGQ gG V1N1VG FOPR I1VGI FM “çT gG UGP PRLP h “ç ] “øçY éGP DI PL|G PR1I LI ODH VG Q1P1OQ OW “øçT IO PRLP gG SLQ VG QG JOgGHI g1PR QGULP1NG 1QPGUGHI LI G‘JOQGQPIk “øç ] h “ç ƒa„ $ª ƒL„ eø î ] h e î ] h e Àe Àe ƒF„ hmøÌ ] h hmÌ ] h ƒhm„ Àƒhm„ ] h hbi i
  • 32.
    ð¶ù´µ¶·B …DJJOIG LUL1Q PRLPw 1I L JOI1P1NG 1QPGUGHY …1QSG “ú ] “T gG RLNG PRLP “ ] “ú ] “ç÷úûç ] ƒ“úûç„ç FGSLDIG gG gLQP HDKG ƒm„ LFONG PO FG PHDG WOH LKK G‘JOQGQPIY ‹DP PR1I XDIP ILMI “úûç 1I PRG QDEFGH PRLP EDIP FG HL1IGV PO PRG JOgGH w PO UGP PRG QDEFGH “Y üOD ELM HGSLKK PRLP gG RLNG L IJGS1LK QLEG WOH PR1I QDEFGHk gG SLKK 1P PRG wPR HOOP OW “T LQV gG SLQ gH1PG 1P DI1QU
  • 33.
    LI ý }“Y ƒ…1QSGPRG ItDLHG HOOP OSSDHI IO WHGtDGQPKMT gG gH1PG 1P EOHG I1EJKMk “úûÌ ] }“Y„ jRG gOH| gG XDIP V1V IROgI PRG WOKKOg1QU WOHEDKLk “úûç ] ý }“ ¢G RLNG XDIP IL1V PRLP ý }“ 1I PRG QDEFGH PRLPTgRGQ HL1IGV PO PRG JOgGH wT U1NGI PRG QDEFGH “Y ¢RGQ w 1I LQ GNGQ 1QPGUGHT PRGHG LHG UGQGHLKKM Ÿþ› QDEFGHI PRLP tDLK1WM WOH PR1I VG Q1P1OQY Š OH G‘LEJKGT _ LQV q_T gRGQ ItDLHGVT FOPR U1NG PRG QDEFGH ak ƒ_„Ì ] a ] ƒq_„Ì Q IDSR SLIGITgG ILM PRLP ý }“ 1IPRG ž›žžœÿ Ÿœ››ŸY …O }a ] _TQOP q_TGNGQ PRODUR _ LQV q_ LHG FOPR ItDLHG HOOPI OW aY jO HGJHGIGQP FOPR HOOPIT gG DIG PRG JKDI¡OH¡E1QDI I1UQk Î}a ] ^q_`_d #ª ƒL„ }hbi ] hbiúûÌ ] hm ƒF„ _ }c ] _ Àcúû î ] _ À_ ] a »A@ ð=·@B ñ»A ¸¹º»¼@¼ÄB üOD IRODKV UGP DIGV PO SOQNGHP1QU HLV1SLKI PO G‘JOQGQPI LQV N1SG NGHILTI1QSG MOD g1KK RLNG PO VO PR1I 1Q ELQM V1GHGQP |1QVI OW JHOFKGEIY QOg1QU ROg PO VG QG “úûç PGKKI DI ROg PO VG QG JOgGHI gRGHG ODH G‘JOQGQP 1I L JOI1P1NG HLP1OQLK QDEFGHT PRLP 1IT 1W ODH G‘JOQGQP 1I v w WOH PgO JOI1P1NG 1QPGUGHI v LQV wY ¢G RLNG PRG WOHEDKL “òûç ] “ò÷úûç ] ƒ“ò„úûç ] ƒ“úûç„ò ƒ«„ LUL1Q FGSLDIG HDKG ƒm„ EDIP IP1KK FG OFGMGVY hr
  • 34.
    (ª m_ î ûï ] ƒm_úûï„ î ]_ î ] c Š 1QLKKMT 1W gG RLNG L QGULP1NG HLP1OQLK G‘JOQGQP qv w WOH JOI1P1NG 1QPGUGHI v LQV wT gG RLNG “ø ý ] h “ ý LI gLI PRG SLIG g1PR QGULP1NG 1QPGUGHIY jRGHG LHG PgO EOHG VGPL1KI OW gR1SR gG EDIP PL|G QOPGY éGP w FG L JOI1P1NG 1QPGUGHY W “ LQV ” LHG PgO QDEFGHIT 1P VOGIQêP ELPPGH 1Q gRLP OHVGH gG EDKP1JKM “ LQV ”T IO gG RLNG PRLP ƒ“”„ç ] ƒ“”„ Àƒ“”„ ÀnnnÀƒ“”„ ] “ À“ ÀnnnÀ“ À” À” ÀnnnÀ” ] “ç À”ç U1N1QU DI PRLP ƒ“”„ç ] “ç À”ç ƒb“„ Q WLSPT KGP DI VG QG PR1I PO FG PRG SLIG WOH QDEFGHI wT IO PRLP PR1I 1I L UGQGHLK HDKG WOH G‘JOQGQPIY Š 1QLKKMT gG SOQI1VGH PRG G‘JHGII1OQ “ ” çY …1QSG h ” ] ”øúT gG RLNG PRLP “ ” ] “ À h ” ] “ À”øúY …O gG |QOg PRLP “ ” ç ] ƒ“”øú„ç ] “ç Àƒ”øú„ç ] “ç À”øç ] “ç ”ç WOH LQM QDEFGH w PRLP gG ELM SROOIGY jR1I U1NGI DI PRG WOKKOg1QU WOHEDKLk “ ” ç ] “ç ”ç ƒb”„ %ª ƒL„ ƒ«e„ î ] « î Àe î ] h_«e î ƒF„ ƒm¿
  • 35.
    „ë ] mëÀ¿ë À
  • 36.
    ë ] chÀ¿ë À
  • 37.
  • 38.
    ë ƒS„ ì_e m íî] ƒ_e„ î m î ] _ î Àe î _ ] ce î _ hh
  • 39.
    éGPêI IDEELH1pG PRGHDKGI PRLP gGêNG WODQV WOH G‘JOQGQPIY Š OH LQM QDEFGHI “`eT LQV T LQV LQM JOI1P1NG 1QPGUGH wT PRG WOKKOg1QU WOHEDKLI LHG PHDGk “ô ] h gRGQ “ y] r “ó ] “ À“ “ø ] h “ “úûç ] ý }“ ƒ“ „ ] “ “û ] ƒ“ „úû ] ƒ“úû „ ƒ“”„ ] “ À” “ ” ] “ ” ý }“” ] ý }“ ý }” ý “ ” ] ý }“ ý }” @ÄÄ´¼ ð´ù »ñ ð¶ù´µ¶·B éGPêI IDJJOIG PRLP gG LHG U1NGQ PRG G‘JHGII1OQ a ¤ }me LQV gG gLQP PO UGP H1V OW PRG HLV1SLKY P 1I 1Q PR1I I1PDLP1OQ PRLP gG gLQP PO EL|G DIG OW PRG OW PRG U1NGQ G‘JHGII1OQk a q }me h_
  • 40.
    ¢RGQ gG EDKP1JKMPRGIG PgO G‘JHGII1OQI POUGPRGHT gG OFPL1Q PRG WOKKOg1QU WOHEDKLk ƒa ¤ }me„ƒa q }me„ ] hb ¤ a}me q a}me q ƒ}me„Ì ] hb q me Q UGQGHLKT PRG SOQXDULPG OW LQ G‘JHGII1OQ “ ¤ ”}¿ 1I U1NGQ FM PRG WOHEDKL “ q ”}¿T LQV XDIP LI 1Q PRG G‘LEJKG LFONGT EDKP1JKM1QU PRG  HIP G‘JHGII1OQ FM 1PI SOQXDULPG UGPI H1V OW PRG HLV1SLKk ƒ“ ¤ ”}¿„ƒ“ q ”}¿„ ] “Ì ¤ “”}¿ q “”}¿ q ƒ”}¿„Ì ] “Ì q ”Ì¿ COPG PRLP gRGQ gG EDKP1JKM LQ G‘JHGII1OQ FM 1PI SOQXDULPGT PRG HGIDKP 1I L QGg G‘JHGII1OQ ƒg1PRODP L HLV1SLK„ gROIG NLKDG 1I š œœžŸ WHOE PRLP OW PRG G‘JHGII1OQ g1PR gR1SR gG IPLHPGVY ¸¹@Aµ´B@B Q JHOFKGEI h¡hcT I1EJK1WM GLSR OW PRG WOKKOg1QU G‘JHGII1OQI LI EDSR LI JOII1FKGT FM gH1P1QU PRGE g1PR LI WGg LQV LI I1EJKG G‘JOQGQPI LI MOD SLQY hY eû î eøÌ _Y }h« Àh«øúû î mY _ î ûÌ_ûÌ aY }eøÌ}aeï «Y ƒ_e„ë bY hbïû hbúûÌ hbû Y cÌû î cY }e î ó î iY hrrrô ¤ húôôô hrY ƒö„ç ~ } úôç hhY ƒúûÌ„ë h_Y qc _ hmY bÌ Àbø b haY ƒe „ î e Ì î h«Y _ô À_ú À_Ì À_ î À_ë hbY ƒƒ_Ì„Ì„Ì hY ƒe „ ƒ_ „ø hcY ƒbô„úôôô hiY ì_e î ae Ìíî _rY ƒ_e øÌ„ø î ƒeøú øÌ„ _hY ƒeÌ „ î ƒeô „Ìë hm
  • 41.
    __Y ìme Ì _ íîìaeÌ ë í Ì _mY q_ÌeÌû î øúûÌ øÌû î! eúûÌ î ûÌ øú ! _aY ƒ“”Ì¿„ø î ƒ“øÌ”¿Ì„øÌ _«Y ƒ¿øÌ“”øë„Ì ƒ_“ø̔̄ î # øÌ Q JHOFKGEI _b¡_iT  QV PRG SOQXDULPG OW PRG U1NGQ G‘JHGII1OQT LQV gH1PG ODP PRG G‘JHGII1OQ gR1SR HGIDKPI WHOE EDKP1JKM1QU PRG U1NGQ G‘JHGII1OQ FM 1PI SOQXDULPGY _bY m€ ¤ }he _Y e q «}b _cY q_ ¤ e}m ¤ _iY h a q _ « ha
  • 42.
    $:% 4å7: 787æ6å' (»·) ¼»´¶·B [ 1Q PRG NLH1LFKG e 1I LQ LKUGFHL1S G‘JHGII1OQ OW PRG WOHE “çeç ¤ “çøúeçøú ¤ nnn¤ “úe ¤ “ô` gRGHG “çT“çøúT nnnT“úTLQV “ô LHG HGLKQDEFGHI SLKKGV PRG * OWPRG JOKMQOE1LKT “ç y] rT LQV w 1I L QOQQGULP1NG 1QPGUGH SLKKGV PRG
  • 43.
    OW PRG JOKMQOE1LKY [JOKMQOE1LK g1PR VGUHGG h 1I SLKKGV
  • 44.
  • 45.
    Y [ JOKMQOE1LKg1PR VGUHGG _ 1I SLKKGV '
  • 46.
  • 47.
    Y [ JOKMQOE1LKg1PR VGUHGG m 1I SLKKGV OH +
  • 48.
    Y [ JOKMQOE1LKg1PR OQKM OQG PGHE 1I SLKKGV L TLQV L JOKMQOE1LK g1PR G‘LSPKM PgO PGHEI 1I SLKKGV L Y ª ƒL„ aeÌ ¤ e q h 1I L tDLVHLP1S JOKMQOE1LKY ƒF„ që î e ¤ _h 1I L K1QGLH JOKMQOE1LKY ƒS„  1I L EOQOE1LK OW VGUHGG rY ƒV„ eúôú q h 1I L F1QOE1LK OW VGUHGG hrhY =·Ä´º·) ´¼ (»·) ¼»´¶·B jRG
  • 49.
    Œ . OWEDKP1JK1SLP1OQ ONGH LVV1P1OQ LQV IDFPHLSP1OQ ILMI PRLP WOH LQM HGLK QDEFGHI “T ”T LQV ¿T “ƒ” ¤ ¿„ ] “” ¤ “¿` LQV “ƒ” q ¿„ ] “” q “¿n ¢RGQ EDKP1JKM1QU PgO JOKMQOE1LKIT PRG V1IPH1FDP1NG KLg EGLQI PRLP GNGHM PGHE 1Q PRG  HIP JOKMQOE1LK EDIP FG EDKP1JK1GV FM GNGHM PGHE 1Q PRG IGSOQVk ƒe ¤ _„ƒ_eÌ q ae ¤ h„ ] ƒe„ƒ_eÌ„ q ƒe„ƒae„ ¤ ƒe„ƒh„¤ ƒ_„ƒ_eÌ„ q ƒ_„ƒae„¤ ƒ_„ƒh„n h«
  • 50.
    ¢G SLQ I1EJK1WMPR1I G‘JHGII1OQ FM EDKP1JKM1QU LQV SOKKGSP1QU K1|G JOgGHI OW ek ƒe ¤ _„ƒ_eÌ qae ¤ h„ ] _e î q aeÌ ¤ e ¤ aeÌ q ce ¤ _ ] ƒ_e î „¤ ƒqaeÌ ¤ aeÌ„¤ ƒe q ce„¤ ƒ_„ ] _e î ¤ ƒqa ¤ a„eÌ ¤ ƒh q c„e ¤ _ ] _e î q e ¤ _n ¢RGQ EDKP1JKM1QU PgO F1QOE1LKITIPDVGQPI IOEGP1EGI  QV 1P RGKJWDK PO HGEGEFGH PRG LSHOQME Š éT gR1SR IPLQVI WOH ¨ Š 1HIP ÂDPGH QQGH éLIPY© ª ƒaeë ¤ h„ƒeÌ ¤ me„ ] JHOVDSP OW Š 1HIP PGHEI ¤ JHOVDSP OW ÂDPGH PGHEI ¤ JHOVDSP OW QQGH PGHEI ¤ JHOVDSP OW éLIP PGHEI ] ƒae넃eÌ„¤ ƒae넃me„¤ ƒh„ƒeÌ„¤ ƒh„ƒme„ ] aeö ¤ h_eï ¤ eÌ ¤ me +¶µÄ»A´¼ (»·) ¼»´¶·B !
  • 51.
    L U1NGQ JOKMQOE1LKEGLQI  QV1QU PgO OH EOHG JOKMQOE1LKI OW IELKKGH VGUHGG gROIG JHOVDSP 1I PRG U1NGQ JOKMQOE1LKY P 1I K1|G ¨DQVO1QU© EDKP1JK1SLP1OQY Š OH G‘LEJKGT aeÌ q ae q m WLSPOHI LI ƒ_e ¤ h„ƒ_e q m„ FGSLDIG ƒ_e ¤ h„ƒ_e q m„ ] aeÌ q be ¤ _e q m ] aeÌ q ae q mn , /- . / - !*-/ /)/ /0 )1 hY jHM  QV1QU L •
  • 52.
    T L PGHEPRLP V1N1VGI GNGQKM 1QPO GLSR PGHE OW PRG JOKMQOE1LKY ª Š 1QV L SOEEOQ WLSPOH OW _e î ¤ aeÌ q haeY …1QSG _e V1N1VGI GNGHM PGHE GNGQKMT gG SLQ WLSPOH ODP _e PO UGP _e î ¤ aeÌ q hae ] _eƒeÌ ¤ _e q „n hb
  • 53.
    _Y jHM DI1QUOQG OW PRG WOKKOg1QU •
  • 54.
  • 55.
    k ƒh„ “Ì q”Ì ] ƒ“ q ”„ƒ“ ¤ ”„ ƒ_„ “Ì ¤ _“”¤ ”Ì ] ƒ“ ¤ ”„Ì ƒm„ “Ì q _“” ¤ ”Ì ] ƒ“ q ”„Ì ƒa„ “ î q ” î ] ƒ“ q ”„ƒ“Ì ¤ “” ¤ ”Ì„ ƒ«„ “ î ¤ ” î ] ƒ“ ¤ ”„ƒ“Ì q “” ¤ ”Ì„ $ª aeë q ieÌ ] ẽaeÌ q i„ õOEEOQ Š LSPOH ] ẽƒ_e„Ì q mÌ„ ] ẽ_e q m„ƒ_e ¤ m„ Š OHEDKL ƒh„ #ª ieÌ ¤ ace ¤ ba ] ƒme„Ì ¤ _ƒme„ƒc„¤ cÌ ] ƒme ¤ c„Ì Š OHEDKL ƒ_„ mY W PRG JOKMQOE1LK 1Q tDGIP1OQ 1I tDLVHLP1ST PRGQ PRG WOKKOg1QU WOHEDKL ELM FG DIGWDKk eÌ ¤ ƒ“ ¤ ”„e ¤ “” ] ƒe ¤ “„ƒe ¤ ”„n 21NGQ L JOKMQOE1LK OW PRG WOHE e̤¿e¤
  • 56.
    TPO DIG PR1IWOHEDKLTPHM PO  QV PgO QDEFGHI “ LQV ” gROIG IDE 1I ¿ LQV gROIG JHOVDSP 1I
  • 57.
    Y (ª Š LSPOH e̤ hme ¤ __Y …1QSG hh¤ _ ] hm LQV hh À_ ] __T gG SLQ  QV PRG WLSPOHIk eÌ ¤ hme ¤ __ ] ƒe ¤ hh„ƒe ¤ _„n h
  • 58.
    ƒa„ W PRGJOKMQOE1LK RLI WODH PGHEIT 1P ELM FG JOII1FKG PO •
  • 59.
    Y %ª Š LSPOH _e î qceÌ ¤ me q h_Y COPG PRLP PRG  HIP PgO PGHEI RLNG L SOEEOQ WLSPOHT LI VO PRG KLIP PgO PGHEIY 2HODJ PGHEI g1PR SOEEOQ WLSPOHI LQV JDKK ODP PROIG WLSPOHIk _e î q ceÌ ¤ me q h_ ] ƒ_e î q ceÌ„¤ ƒme q h_„ ] _ẽe q a„¤ mƒe qa„ COg gG RLNG PgO PGHEIT GLSR OW gR1SR RLI L WLSPOH OW ƒe q a„Y 3DKK ODP PRLP SOEEOQ WLSPOHk _e î q ceÌ ¤ me ¤ h_ ] _ẽe q a„¤ mƒe q a„ ] ƒe q a„ƒ_eÌ ¤ m„ ð»»ÄB »ñ (»·) ¼»´¶·B jRG
  • 60.
    OW L JOKMQOE1LK“çeç ¤ “çøúeçøú¤ nnn¤ “úe ¤ “ô LHG PROIG QDEFGHI WOH gR1SR “çç ¤ “çøúçøú ¤ nnn¤ “ú ¤ “ô ] rn ª e ] _ 1I L HOOP OW PRG JOKMQOE1LK eÌ ¤ e q b FGSLDIG _Ì ¤ _ q b ] rY [ JOKMQOE1LK SLQ RLNG OQKM LI ELQM V1IP1QSP HOOPI LI 1PI VGUHGGY ƒP ELM RLNG WGgGHT FDP 1P SLQQOP RLNG EOHGY„ W e ] 1I L HOOP OW L U1NGQ JOKMQOE1LKTPRGQ e q 1I L WLSPOH OW PRLP JOKMQOE1LKY , /- . / - !. -, //-, /! /)/ /0 )1 ƒh„ jHM WLSPOH1QU PRG JOKMQOE1LKY …1QSG L JHOVDSP GtDLKI pGHO 1W LQV OQKM 1W LQM OW 1PI WLSPOHI GtDLKI pGHOT PRG HOOPI OW L JOKMQOE1LK LHG PRG HOOPI OW 1PI WLSPOHIY ͪ ¢RLP LHG PRG HOOPI OW eÌ q be q arè Q OPRGH gOHVIT gRLP e¡NLKDGI EL|G eÌ q be q ar ] rè eÌ q be q ar ] r ƒe q hr„ƒe ¤ a„ ] r e q hr ] r OH e ¤ a ] r e ] hr OH e ] qa hc
  • 61.
    jRDI eÌ qbe q ar RLI HOOPI e ] qaT hrY Ϫ ¢RLP LHG PRG HOOPI OW aeë q ieÌè aeë q ieÌ ] r ẽ_e q m„ƒ_e ¤ m„ ] r eÌ ] r OH _e q m ] r OH _e ¤ m ] r e ] r OH e ] m _ OH e ] qm _ jRDI aeë q ieÌ RLI HOOPI e ] rT îÌT q îÌY ƒ_„ W PRG JOKMQOE1LK 1I tDLVHLP1S LQV OW PRG WOHE “eÌ ¤ ”e ¤ ¿ PRGQ 1PI HOOPI LHG U1NGQ FM PRG '
  • 62.
  • 63.
    k e ] q”Î }”Ì q a“¿ _“ 45 œ 67 š Ÿ8 9 ›: 7 þ þ ; žš Ÿ5 œ ››Ÿ ›9 67 š Ÿ8 = › ;ž›: ËOgGNGHT WLSPOH1QU 1I IOEGP1EGI WLIPGHY ª ¢RLP LHG PRG HOOPI OW _eÌ q ae ¤ hè ËGHG “ ] _T ” ] qaT LQV ¿ ] hT IO PRG tDLVHLP1S WOHEDKL U1NGI HOOPI e ] qƒqa„Î ? ƒqa„Ì q aƒ_„ƒh„ _ƒ_„ ] _ Î }_ _ n jRDI _eÌ q ae ¤ h RLI HOOPI e ] Ìó@Ì Ì LQV e ] Ìø@Ì Ì Y ª ¢RLP LHG PRG HOOPI OW eÌ q ae ¤ iè Q PR1I SLIGT PRG tDLVHLP1S WOHEDKL U1NGI e ] qƒqa„ Î ? ƒqa„Ì q aƒh„ƒi„ _ƒh„ ] a Î }q_r _ n hi
  • 64.
    ¢RGQGNGH L HOOP1QNOKNGI PRG ItDLHG HOOP OW L QGULP1NG QDEFGHT gG SLKK PR1I HOOP 0
  • 65.
    Y ELU1QLHM HOOPILHG QOP HGLK QDEFGHI LQV VO QOP SODQP LI HGLK HOOPIY P 1I LIIDEGV PRHODURODP EOIP SLKSDKDI SODHIGI PRLP HOOPI EDIP FG HGLK QDEFGHIY ¢RGQ PR1I LIIDEJP1OQ 1I ELVGT1ELU1QLHM HOOPI VO QOP SODQP LI HOOPIY jRDI PO LQIgGH PRG tDGIP1OQT ¨¢RLP LHG PRG HOOPI OW eÌ q ae ¤ iè©T gG gODKV ILM PRLP eÌ q ae ¤ i RLI QO HGLK HOOPI I1QSG 1PI OQKM HOOPI LHG 1ELU1QLHMY …1QSG PR1I JOKMQOE1LK 1I tDLVHLP1S LQV RLI QO HGLK HOOPIT gG SLKK 1P LQ
  • 67.
  • 68.
    Y ÃùA¶¼µ@ù ð»»ÄB+ ´¼ù´¼C@µD¼´E=@B jRG PRHGG PGSRQ1tDGI VGISH1FGV LFONG g1KKFG GQODUR PO  QV PRG  QV PRG HOOPIOWELQM OW PRG JOKMQOE1LKI MOD g1KK GQSODQPGHY ËOgGNGHT PO  QV PRG HOOPI OW IOEG JOKMQOE1LKIT GIJGS1LKKM JOKMQOE1LKI OW VGUHGG m OH R1URGHT MOD g1KK QGGV EOHG LVNLQSGV PGSRQ1tDGIT IDSR LI PRG WOKKOg1QUk hY jRG -+
  • 69.
    ILMI PRLP 1WPRG SOGF S1GQPI OW L JOKMQOE1LK “çeç ¤ “çøúeçøú ¤ nnn¤ “úe ¤ “ô LHG 1QPGUGHIT PRGQ LQM HLP1OQLK HOOP ƒPRLP 1IT LQM HOOP PRLP SLQ FG G‘JHGIIGV LI L WHLSP1OQ OW 1QPGUGHI„ RLI PRG WOHE ÎG H gRGHG I LQV J LHG JOI1P1NG 1QPGUGHITI 1I L V1N1IOH OW “ôT LQV J 1I L V1N1IOH OW “çY ª Š 1QV LKK HLP1OQLK HOOPI OW me î ¤ eÌ q h_e q aY ËGHG w ] mT “ç ] mT LQV “ô ] qaY …1QSG I 1I L V1N1IOH OW “ô ] qaT I SODKV FG hT _T OH aY …1QSG J 1I L V1N1IOH OW “ç ] mT J SODKV FG h OH mY ËGQSG LQM HLP1OQLK HOOP OW PRG JOKMQOE1LK EDIP FG OQG OW PRG WOKKOg1QUk Îh`Î_`Îa`Îh m`Î_ m`Îa m jO VGPGHE1QG gR1SR OW PRGIG LSPDLKKM LHG HOOPIT IDFIP1PDPG GLSR OQG 1QPO PRG JOKMQOE1LKk _r
  • 70.
    e me î ¤ eÌq h_e q a h qh_ qh b _ r q_ r a h«b qa qhm_ ú î qô K qú î r …1QSG PRG JOKMQOE1LK 1I SDF1ST 1P RLI LP EOIP PRHGG HOOPIY ¢G RLNG WODQV PRHGG HOOPI ƒe ] _T q_T LQV qú î „T IO gG RLNG WODQV PRG HOOPI OW PRG JOKMQOE1LKY _Y W MOD SLQ  QV OQG HOOP OW L JOKMQOE1LK ƒJGHRLJI FM LJJKM1QU PRG ZLP1OQLK ZOOP jRGOHGE LI gG V1V 1Q PRG KLIP G‘LEJKG„T PRGHG LHG PgO EGPROVI OW LPPGEJP1QU PO  QV PRG HGEL1Q1QU HOOPIY ÂQG OW PRGIG EGPROVI 1I SLKKGV Œ Y $ª Š 1QV LKK HOOPI OW eë q e î q eÌ q hae q _aY jRG ZLP1OQLK ZOOP jRGOHGE PGKKI DI PRLP LKK HLP1OQLK HOOPI EDIP FG OW PRG WOHE ÎG H T gRGHG I LQV J LHG JOI1P1NG 1QPGUGHIT I 1I L V1N1IOH OW “ô ] q_aT LQV J 1I L V1N1IOH OW “ç ] hY ËGQSG PRG SLQV1VLPGI WOH HLP1OQLK HOOPI LHG Îh`Î_`Îm`Îa`Îb`Îc`Îh_`Î_an …1QSG ƒa„ë q ƒa„ î q ƒa„Ì q haƒa„ q _a ] rT e ] a 1I L HOOP LQV IO e q a 1I L WLSPOHY àIG JOKMQOE1LK KOQU V1N1I1OQ PO V1N1VG PRG JOKMQOE1LK FM e q ak _h
  • 71.
    e î ¤meÌ ¤«e ¤b eq a eë qe î qeÌ qhae q_a qƒeë qae î „ me î qeÌ qhae q_a qƒme î qh_eÌ„ «eÌ qhae q_a qƒ«eÌ q_re„ be q_a qƒbe q_a„ r ƒ…1QSG gG |QGg e q a gLI L WLSPOH OW ODH JOKMQOE1LKTgG G‘JGSPGV PO UGP r LI ODH  QLK HGEL1QVGHY„ jRDI eëqe î qeÌqhaeq_a ] ƒeqa„ƒe î ¤me̤«e¤b„Y jO WLSPOH e î ¤me̤«e¤bT gG LJJKM PRG ZLP1OQLK ZOOP jRGOHGE LQV UGP SLQV1VLPG HLP1OQLK HOOPI Îh`Î_`Îm`ÎbY …1QSG ƒq_„ î ¤ mƒq_„Ì ¤ «ƒq_„ ¤ b ] rT e ] q_ 1I L HOOP LQV IO e q ƒq_„ ] e ¤ _ 1I L WLSPOHY àIG JOKMQOE1LK KOQU V1N1I1OQ LUL1Qk eÌ ¤e ¤m e ¤ _ e î ¤meÌ ¤«e ¤b qƒe î ¤_eÌ„ eÌ ¤«e ¤b qƒeÌ ¤_e„ me ¤b qƒme„ ¤b„ r ƒ[I FGWOHGT gG G‘JGSPGV PO UGP r LI ODH  QLK HGEL1QVGH I1QSG gG |QGg PRLP e ¤ _ gLI L WLSPOH OW e î ¤ meÌ ¤ «e ¤ bY„ __
  • 72.
    ËGQSG eë qe î q eÌ q hae q _a ] ƒe q a„ƒe ¤ _„ƒeÌ ¤ e ¤ m„Y jO  QV PRG HOOPI OW eÌ ¤ e ¤ mT DIG PRG tDLVHLP1S WOHEDKLk e ] qhÎ ? hÌ q aƒh„ƒm„ _ƒh„ ] qhÎ }qhh _ jRGIG LHG 1ELU1QLHM HOOPIT LQV IO PRG HGLK HOOPI OW PRG OH1U1QLK JOKMQOE1LK LHG e ] a LQV e ] q_Y mY 21NGQ OQG HOOP OW L JOKMQOE1LKTPRG OPRGH EGPROV WOH  QV1QU PRG HGEL1Q1QU HOOPI 1I L JHOSGII SLKKGV + Œ Y ¢R1KG JOKMQOE1LK KOQU V1N1I1OQ KGPI MOD V1N1VG LQM JOKMQOE1LK1QPO LQM OPRGH JOKMQOE1LKTIMQPRGP1S V1N1I1OQ 1I OQKM JOII1FKG 1WPRG V1N1IOH1I L JOKMQOE1LKOW PRG WOHE eq Y ƒGGJ 1Q E1QV PRLP SODKV FG QGULP1NGTIO e¤_ ] eqƒq_„ 1I IDSR L JOKMQOE1LKY„ jO DIG IMQPRGP1S V1N1I1OQ PO V1N1VG e q 1QPO “çeç ¤“çøúeçøú¤ nnn¤“úe¤“ôT FGU1Q g1PR PRG WOKKOg1QU V1LUHLEk “ç “çøú ÀÀÀ “ú “ô W L JOgGH OW e 1I E1II1QU WHOE PRG JOKMQOE1LKTEL|G IDHG PO JKLSG L r 1Q POJ HOg OW PRG SOHHGIJOQV1QU SOKDEQ 1Q PRG V1LUHLEY Š OH G‘LEJKGT PO V1N1VG e ¤ _ 1QPO eë q eÌ ¤ hT FGU1Q g1PR q_ h r qh r h CG‘PT gH1PG “ç 1Q PRG FOPPOE HOg OW PRG SOKDEQ g1PR “ç 1Q PRG POJ HOgY jRGQT WOH GLSR SOKDEQ WHOE KGWP PO H1URPT ƒL„ EDKP1JKM PRG NLKDG 1Q PRG FOPPOE HOg OW PRG JHGN1ODI SOKDEQ FM T ƒF„ gH1PG PR1I NLKDG 1Q PRG E1VVKG HOgT _m
  • 73.
    ƒS„ LVV PR1INLKDG PO PRG NLKDG 1Q PRG POJ HOgT LQV ƒV„ gH1PG PRG HGIDKP OW PR1I LVV1P1OQ 1Q PRG FOPPOE HOgY ‚NGQPDLKKM MOD g1KK UGP L QDEFGH 1Q PRG KOgGH H1URPRLQV SOHQGH OW PRG V1LUHLEY W PR1I QDEFGH 1I QOP rT PRGQ e q 1I QOP L WLSPOH OW PRG JOKMQOE1LK LQV IO 1I QOP L HOOPY W PR1I QDEFGH 1I rTPRGQ eq 1I L WLSPOH OW PRG JOKMQOE1LKT 1I L HOOP OW PRG JOKMQOE1LKT LQV PRG QDEFGHI 1Q PRG FOPPOE HOg PO PRG KGWP OW PRG NGHP1SLK K1QG PGKK MOD PRG SOGF S1GQPI OW PRG OPRGH WLSPOHT PRG JOKMQOE1LK “çeç ¤ nnn¤ “ô e q Y #ª Š 1QV LKK HOOPI OW e î q aeÌ q _e ¤ mY jRG ZLP1OQLK ZOOP jRGOHGE U1NGI DI SLQV1VLPG HLP1OQLK HOOPI Îh LQV ÎmY àIG IMQPRGP1S V1N1I1OQ PO IGG 1W h 1I L HOOPk h h qa q_ m h qm q« h qm q« q_ …1QSG q_ y] rT e ] h 1I QOP L HOOPY jHM e ] qhk qh h qa q_ m qh « qm h q« m r …1QSG r LJJGLHI 1Q PRG KOgGH H1URPRLQV SOHQGHT e ] qh 1I L HOOP LQV e î q aeÌ q _e ¤ m ] ƒe ¤ h„ƒeÌ q «e ¤ m„n COPG ROg PRG QDEFGHI 1Q PRG FOPPOE HOg OW PRG V1LUHLE ƒhT q«T LQV m„ U1NG DI PRG SOGF S1GQPI OW PRG OPRGH WLSPOHY jO  QV PRG HOOPI OW eÌ q «e ¤ mT DIG PRG tDLVHLP1S WOHEDKLk e ] qƒq«„Î ? ƒq«„Ì q aƒh„ƒm„ _ƒh„ ] «Î }hm _ ËGQSG PRG HOOPI OW PRG OH1U1QLK JOKMQOE1LK LHG e ] qhT « ¤ }hm _ T LQV « q }hm _ Y _a
  • 74.
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  • 75.
    …1EJK1WM PRG WOKKOg1QUG‘JHGII1OQI FM EDKP1JKM1QU LQV SOKKGSP1QU K1|G JOgGHI OW eY «Y _eƒe î q h„ bY ƒaeë ¤ _eÌ q „eÌ Y ƒ«e q h„ƒe ¤ b„ cY ƒeÌ q h„ƒeÌ ¤ h„ iY ƒe ¤ _„Ì hrY ƒe q h„Ì hhY ƒ_eÌ q h„ƒhq e q meÌ„ h_Y ƒqeÌ ¤ _e q m„ƒhae î ¤ h„ hmY ƒ“e ¤ ”„ƒ¿e ¤
  • 76.
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  • 77.
    Š 1QV LKK HGLKHOOPI OW PRG WOKKOg1QU JOKMQOE1LKIY mmY eÌ ¤ hre q hh maY eÌ q ae ¤ a m«Y eÌ q i mbY eÌ ¤ _«e ¤ hrr mY eÌ q e q h mcY e î ¤ _eÌ ¤ _e miY qeÌ ¤ ae ¤ h arY _eÌ q e ¤ _ ahY eÌ ¤ ae ¤ i a_Y meÌ ¤ e ¤ _ àIG PRG LVNLQSGV HOOP¡ QV1QU PGSRQ1tDGI V1ISDIIGV 1Q PR1I IGSP1OQ PO  QV LKK HGLK HOOPI OW PRG WOKKOg1QU JOKMQOE1LKIY amY e î q beÌ ¤ e q b aaY e î ¤ eÌ q _ae ¤ mb a«Y _eë q ie î q _eÌ ¤ mie q hc abY eë q ae î ¤ beÌ q ae ¤ h aY _eë ¤ h«e î ¤ _«eÌ q ce ¤ hb acY aeï q hbeë ¤ he î q hieÌ ¤ hme q m aiY eë q eÌ ¤ h_ «rY eë q e î q _e q a «hY eë q hmeÌ q h_e «_Y meë q me î q be q h_ _b
  • 78.
    9:' 567åæ 67æå jRGI1EJKGIP WOHE OW LQ LKUGFHL1S WHLSP1OQ 1I L
  • 79.
    L gR1SR 1IL tDOP1GQP OW PgO JOKMQOE1LKIY ‚‘LEJKGI OW HLP1OQLK G‘JHGII1OQI LHG _ «“” ` me ¤ a î e ` LQV e ¤ « c n M »N@BÄ C@AB [ WHLSP1OQ 1I IL1V PO FG 1Q .
  • 80.
    1W LKK SOEEOQWLSPOHI OW PRG QDEGHLPOH LQV VGQOE1QLPOH RLNG FGGQ SLQSGKGVY ª ZGVDSG PRG WOKKOg1QU WHLSP1OQI PO KOgGIP PGHEIk ƒL„ eë q _e î eÌ q _e ] e î ƒe q _„ eƒe q _„ ] eÌ ƒF„ _eÌ ¤ e q m a q «e ¤ eÌ ] ƒe q h„ƒ_e ¤ m„ ƒh qe„ƒa q e„ ] ƒe q h„ƒ_e ¤ m„ qƒe q h„ƒa q e„ ] _e ¤ m qƒa q e„ ] _e ¤ m e q a [ ¢[ZCC2 [‹Âàj õ[Cõ‚éC2 k me ¤  e y] m ¤  ¢G SLQQOP SLQSGK PRG eêI FGSLDIG e 1I QOP L WLSPOH OW œœ; PGHE 1Q PRG QDEGHLPOH LQV œœ; PGHE 1Q PRG VGQOE1QLPOHY jRG WHLSP1OQ me ¤  e 1I LKHGLVM 1Q KOgGIP PGHEIY =·Ä´º·) ´¼ ¶¼ù O ´A ´ù´¼ ¢RGQ EDKP1JKM1QU WHLSP1OQI gG DIG PRG WOKKOg1QU HDKGk P Q À R S ] P R Q S PRLP 1IT gG EDKP1JKM QDEGHLPOHI POUGPRGH LQV VGQOE1QLPOHI POUGPRGHY _
  • 81.
    ª ¾DKP1JKM LQVHGVDSG PO KOgGIP PGHEIk ƒL„ e ¤ _ e ¤ h À e e ¤ h ] eƒe ¤ _„ ƒe ¤ h„Ì ƒF„ e T À T Ì eÌ Ì ] e T Ì T eÌ Ì ] T e ƒS„ _e q c e ¤ _ À eÌ ¤ ae ¤ a eÌ q hb ] _ƒe q a„ e ¤ _ À ƒe ¤ _„Ì ƒe ¤ a„ƒe q a„ ] _ƒe q a„ƒe ¤ _„Ì ƒe ¤ _„ƒe ¤ a„ƒe q a„ ] _ƒe ¤ _„ e ¤ a ƒV„ “ 씿 “Ìí ] “ h À ”¿ “Ì ] “”¿ “Ì ] ”¿ “ Q OHVGH PO V1N1VG WHLSP1OQIT gG DIG PRG WOKKOg1QU HDKGk ìP Q í ìR S í ] P Q À S R PRLP 1ITgG EDKP1JKM PRG QDEGHLPOHFM PRG HGS1JHOSLKOWPRG G‘JHGII1OQ 1Q PRG VGQOE1QLPOHY ª ß1N1VG LQV HGVDSG PO KOgGIP PGHEIk ƒL„ e e ¤ eÌ ƒe ¤ „ î ] e e ¤ À ƒe ¤ „ î eÌ ] e ƒe ¤ „ î eÌ ƒe ¤ „ ] ƒe ¤ „Ì e ƒF„ e q e T e T À ] e q e T e T ] e q e T À T e ] eƒ q „ T À T e ] eT ƒ q „ eT ] q _c