Teoria Isometria y Proyecciones

8/19/2019 Teoria Isometria y Proyecciones

1/34

1 , / / C Q A ? J ≠ K C R P M Q G Q M K ~ R P G A M Q 61

1,6 MOLVB@@FßK FPLJ¢QOF@>Cl sl_ npmwcaagâl gqmkÑrpga_* rmbmq jmq Ålesjmq clrpc jmq chcq _vmlmkÉrpgamq qml ges_jcq, N_p_ npmbsagp sl_ npmwcaagâl gqm+kÑrpga_* mpgclrc cj m`hcrm bc kmbm osc qsq

`mpbcq npglagn_jcq &m chcq' dmpkcl Åles+jmq ges_jcq aml cj nj_lm bc npmwcaagâl w*

nmp jm r_lrm* qc qcqescl cl j_ kgqk_ k_e+lgrsb, Mpgclr_bm bc cqr_ dmpk_* jmq `mpbcq bc sl as`m qc npmwcar_l bc k_lcp_ osc rmbmq kgbcl jm kgqkm w dmpk_l Ålesjmq ges_jcq clrpc qÖ &bc /0.è'* amkm qc kscq+rp_ cl j_ dgesp_ 1,14,

1,14 Npmwcaagål gqmkÜrpga_,

1,7 BGBP FPLJ{QOF@LPJ_q npmwcaagmlcq bc jmq `mpbcq bc sl as`m f_acl Ålesjmq bc /0.è clrpc qÖ, Cqrmq

`mpbcq nscbcl sq_pqc amkm bgbp fpljÉof+`lp n_p_ pc_jgx_p kcbgagmlcq, As_josgcp jÖlc_ n_p_jcj_ _ slm bc cqrmq `mpbcq qc bc+

lmkgl_ iÖkb^

fpljÑqof`^, Jmq

Ålesjmq

cl

j_ npmwcaagâl gqmkÑrpga_ bcj as`m qml bc

/0.è m 4.è* w rmbmq qml npmwcaagmlcq bc Ålesjmq bc 7.è, Cl sl_ npmwcaagâl gqmkÑ+rpga_ bc sl as`m* j_q a_p_q bc Éqrc w as_j+osgcp nj_lm n_p_jcjm _ j_q a_p_q* qc jj_k_

mi^ kl

fpljÑqof`l, Tc_ j_ dgesp_ 1,15,

Jálc_gqmkÜrpga_

1,15 Chcq gqmkÖrpgamq,

1,/. I£KB>P KL FPLJ{QOF@>PJ_q jÖlc_q bc sl bg`shm gqmkÑrpgam osc lm qml n_p_jcj_q _ jmq chcq gqmkÉrpgamq qc bclmkgl_l iÖkb^p kl fpljÉqof`lp &dgesp_ 1,16', Qâjm j_q jÖlc_q bc sl m`hcrm osc qc

bg`sh_l n_p_jcj_q _ jmq chcq gqmkÉrpgamq qc qcqe_l ges_jkclrc, J_q jÖlc_q lm gqm+

kÉrpga_q qc bg`sh_l cl Ålesjmq bgqrglrmq w lm qc qcqe_l bc j_ kgqk_ k_lcp_, Nmp jm r_lrm* j_q jmlegrsbcq bc jmq cjckclrmq s`ga_bmq _ jm j_pem bc j_q jÖlc_q lm gqm+

kÉpga_q lm nscbcl kcbgpqc bgpcar_kcl+rc aml j_ cqa_j_ bcq_ppmjj_b_,

1,16 @mpbcq lm gqmkÖrpgamq,

1,// BP@>IFJBQOLP FPLJ{QOF@LPQc nscbc cknjc_p sl cqa_jÖkcrpm gqmkÑ+rpgam n_p_ bg`sh_p bc dmpk_ amppcar_ npm+wcaagmlcq gqmkÉrpga_q, J_q bgqr_lag_q cl

cqr_ cqa_j_ qml bc T0-1 V cj r_k_àm tcp+b_bcpm* m bc _npmvgk_b_kclrc 6.# bcj r_k_àm pc_j, Cl j_ dgesp_ 1,17_ qc kscq+rp_ sl cqa_jÖkcrpm gqmkÑrpgam, J_ k_wm+pÖ_ bc j_q tcacq* sl `mqoschm m sl bg`shm gqmkÑrpgam qc apc_l cknjc_lbm sl_ pcej_ cqrÅlb_p* amkm cl j_ dgesp_ 1,17`* qgl rm +k_p cl asclr_ cj qcqem osc qc npmbsac cl j_q qsncpdgagcq glajgl_b_q _j pc_jgx_p sl

npmwcaagâl tcpb_bcp_,

&_' Npmwcaagål gqmkÜrpga_

1,17 Cqa_j_q gqmkÜrpga_ w mpbgl_pg_,

&`' Bg̀ shm gqmkÜrpgam


2/34

62 A ? N ≠ R S J M 1 @ M Q OS C H? B M R ~ A L G A M

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Sqrcb nscbc f_acp sl_ cqa_j_ gqmkÜrpga_ aml sl_ rgp_ bc n_ncj m bc a_prål amkm qc kscqrp_ _osá* amjma_lbm sl_ pcej_ amkél _ 23í bc sl_ álc_ fmpgxmlr_j w j_ pcej_ bc n_ncj _ 1.í bc j_ kgqk_ jálc_ fmpgxmlr_j, N_p_ k_pa_p jmq glapckclrmq cl j_ cqa_j_ gqmkÜrpga_* bg`shc jálc_q pcar_q &ncpnclbgasj_pcq _ j_ jálc_ fmpgxmlr_j' bcqbc j_q jálc_q bc bgtgqgål cl j_

pcej_ amkél,

Bc k_lcp_ _jrcpl_rgt_* nscbc _npmvgk_pqc _ sl_ cqa_j_ gqmkÜrpga_, J_q kcbgagmlcq _ cqa_j_ bc 7 ; / % + . * m j_ cqa_j_ _ rpcq as_prmq bcj r_k_ãm &m qs cosgt_jclrc kÖrpgam' nscbcl srgjgx_pqc amkm sl_ _npmvgk_agål,

1,/0 AF?RGLPFPLJ{QOF@LP

As_lbm sqrcb f_ac sl bg`shm sq_lbm kc+bgb_q qcqe_b_q* m as_lbm cj m`hcrm cl pc_+jgb_b qc npmwcar_ qm`pc sl nj_lm* cqrm qc bclmkgl_ molvb``fàk fpljÑqof`^ &dgesp_ 1,2._', As_lbm sqrcb f_ac sl bg`shm aml j_q kcbgb_q _ jmlegrsb amknjcr_ bcj m`hc+rm pc_j* cq sl _lpnrbgl fpljÑqof`l m af_r+

g l

fpljÑqof`l &dgesp_ 1,2.`' n_p_ glbga_p osc lm f_w qcqem,

Cj bg`shm gqmkÑrpgam cq a_qg 03# kÅq ep_lbc osc j_ npmwcaagâl gqmkÑrpga_* ncpm cj t_jmp ngarâpgam cq* m`tg_kclrc* cj kgq+km cl _k`mq, Amkm jmq `mqoschmq gqmkÉ+ rpgamq qc f_acl aml k_wmp p_ngbcx* nscqrm

osc nscbcl sq_pqc j_q kcbgb_q pc_jcq* Éq+rmq qc pc_jgx_l aml kÅq dpcasclag_,

Mlpf`flkbp ab ilp bgbp

fplj}qof`lpCj npgkc p n_q m n_p_ f_acp sl bg`shm gqm+kÑrpgam cq bcagbgp _ jm j_pem bc asÅjcq bgpcaagmlcq bcj chc qc t_l _ kmqrp_p j_ _jrsp_* j_ _lafsp_ w j_ npmdslbgb_b* pcq+

ncargt_kclrc, Cl j_ dgesp_ 1,2. qc kscq+rp_l as_rpm mpgclr_agmlcq bgdcpclrcq aml

!E" !F"

1,2. Nmqgagmlcq bc jmq chcq gqmkÖrpgamq,

j_q as_jcq sqrcb nscbc amkclx_p _ apc_p

sl bg`shm

gqmkÑrpgam

bcj

`jm osc

kmqrp_+bm, A_b_ dgesp_ cq sl bg`shm gqmkÑrpgam

bcj kgqkm `jmosc* ncpm aml sl_ cqosgl_ bgdcpclrc dpclrc _ qs nslrm bc tgqr_, Cqr_q qml qâjm _jesl_q bc j_q ksaf_q mpgclr_+agmlcq nmqg`jcq,

Sqrcb nscbc mpgclr_p jmq chcq cl as_josgcp nmqgagâl* ncpm cj Ålesjm clrpc cjjmq bc`c qcesgp qgclbm /0.è, Aml cj dgl bc qcjcaagml_p sl_ mpgclr_agâl n_p_ jmq chcq* cjgh_ j_ nmqgagâl bcqbc j_ as_j qc qscjc tcp cj m`hcrm* m bcrcpkglc j_ nmqg+

agâl osc kchmp bcqapg`_ j_ dmpk_ bcj m`+

hcrm 9 m* kchmp

_ål*

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amq_q,Qg cj m`hcrm cq sl_ n_prc j_ge_* qc

tcpÅ kchmp aml cj chc k_wmp mpgclr_bm fmpgxmlr_jkclrc,

++++ P R D B O B K @ F> ++++++?jeslmq npmep_k_q bc qmdru_pc bc A?B jc lmrgdga_pÇl _acpa_ bc j_ d_jr_ bc qcqem cl jmq bg`shmq gqmkÖrpgamq _j gknpgkgpjmq m es_pb_pjmq* m n_p_ ncpkgrgpjc j_ qcjcaagål bc cqr_ mnagål,

1,/1 BI>?LO>@FßK AB RK AF?RGL FPLJ{QOF@L

Jmq m`hcrmq pcar_lesj_pcq qml dÅagjcq bc bg`sh_p kcbg_lrc j_ `lkpqor``fàk

ab

`^g^* j_ as_j amlqgqrc cl gk_egl_p cj m`hcrm clacpp_bm cl sl_ a_h_ pcar_lesj_p aswmq j_bmq amglagbcl aml j_q a_p_q npglagn_jcq bcj m`hcrm, Nmp chcknjm* gk_eglc cj m`hcrm

osc qc kscqrp_ cl j_q bmq tgqr_q bc j_ dgesp_ 1,2/ clacpp_bm cl sl_ a_h_ bc amlqrpsaagâl9 _ amlrgls_agâl* `sqosc j_q a_p_arc+pÖqrga_q gppcesj_pcq _ jm j_pem bc jmq `mpbcq bc j_ a_h_ amkm qc kscqrp_ cl j_ dgesp_,


3/34

1 , / 1 C J ? @ M P ? A G ± L BC SL B G @ S H M G Q M K ̈ R P G A M 63

c +

1,2/ Amlqrpsaagål bc sl_ a_h_,

0 Bg`shc j_q a_p_arcpáqrga_q gppcesj_pcq cl pcj_agål aml jmq j_bmq bc j_ a_h_

Cl j_ dgesp_ 1,20 qc kscqrp_ j_ dmpk_ bc amlqrpsgp sl bg`shm gqmkÑrpgam bc sl m`hcrm amknscqrm qâjm bc qsncpdgagcq °lmpk_+jcq¢, K lk k^ i cl cj Åk`grm rÉalgam qgelgdga_ °cl Ålesjm pcarm¢, Sl_ qsncpdgagc lmpk_j cq as_josgcp qsncpdgagc n_p_ jcj_ _ jmq j_+bmq bc j_ a_h_, Rcle_ cl asclr_ osc rmb_q j_q kcbgagmlcq qc f_+acl n_p_jcj_q _ jmq `mpbcq npgl agn_jcq bc j_ a_h_ cltmjtclrc9 cq

bcagp* n_p_jcj_q _ jmq chcq gqmkÉrpgamq, Lglesl_ kcbgb_ _ jm j_p+em bc sl_ jÖlc_ lm gqmkÑrpga_ nscbc f_acpqc bgpcar_kclrc amlj_ cqa_j_* nscqrm osc cqr_q jÖlc_q lm qc qcqe_l bc ges_j dmpk__ j_q jÖlc_q lmpk_jcq, Amkgclac cl as_josgcp_ bc j_q cqosgl_qbc j_ a_h_ cltmjtclrc w bg`shc _ jm j_gem bc j_q bgpcaagmlcq bcjmq chcq gqmkÉrpgamq,

/, Qcjcaagmlc jmq chcq _ jm j_pem bc jmq as_jcq cq`mx_pÇ j_q bgkclqgmlcq bc _jrsp_* ncqm w npmdslbgb_b

0 Jma_jgac j_q Çpc_q npglagn_jcq osc qc pcrgp_pÇl bcj `jmosc ejm`_j9 `mqoschc jgecp_kclrc _ jm j_pem bc jmq chcq gqmkÖrpgamq n_p_ bcdglgp j_ nmpagål osc qc osgr_pÇ

3, Mqaspcxa_ j_q jálc_q dgl_jcq2, Cq`mac jgecp_kclrc jmq cjckclrmq _ qcp pckmtgbmq bc j_ dmpk_ pcqr_lrc _ jm j_pem bc jmq chcq gqmkÖrpgamq

Qc b_l j_q tgqr_q mprmeml_jcq

1, Cq`mac jgecp_kclrc as_josgcp n_prc gknmpr_lrc osc _él lm f_w_ qgbm cvrp_áb_ cl rmbm cj `jmosc

Rmb_q j_q kcbgb_q bc`cl qcp n_p_jcj_q _ jmq `mpbcq npglagn_jcq bc j_

/, Bg`shc jgecp_kclrc j_q bkclqgmlcq bc j_ a_h_

1, Mqaspcxa_ j_q jálc_q dgl_jcq

1,20 N_qmq n_p_ f_acp sl bg`shm gqmkÜrpgam bc qsncpdgagcq lmpk_jcq,


4/34


1,/2 JBAFA>P AB R?F@>@FLK AB @LJMBKP>@FLKSrgjgac cj kÉrmbm osc qc kscqrp_ cl j_q dgesp_q 1,21_ w ` n_p_ jma_jgx_p jmq nslrmq amppcqnmlbgclrcq clrpc qÖ, Cl npgk cp js+e_p* bg`shc cj `jmosc cltmjtclrc npglagn_j* bcqnsÉq bg`shc j_q jÖlc_q bc amknclq_agâl &@> w ?>' _ r_k_àm amknjcrm cl cj bg`shm gqmkÑrpgam n_p_ jma_jgx_p j_ cqosgl_ > bcj ncoscàm

&_'

1,21 Kcbgb_q bc s`ga_agål bc amknclq_agål,

`jmosc m fscam pcar_lesj_p, Cqr_q kcbgb_q qc bclmkgl_l j b+afa^p

ab

`ljmbkp^`fàk, Amkm qml n_p_jcj_q _ jmq `mpbcq bcj `jmosc npglagn_j cl jmq bg`shmq bc ksjrgtgqr_* qcpÅl n_p_jcj_q _ jmq kgqkmq `mpbcq cl jmq bg`shmq gqmkÉrpgamq &qgesgclbm j_ pcej_ bc n_p_jcjgqkm',

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Kgb_ bgpcar_kclrc

j_q bgkclqgmlcq osc cqrÅl _ jm j_g\m bc j_q jÖlc_q gqmkÉrpga_q &cl cqrc a_qm*

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Sqc j_ rpgemlmkcrpÖ_ m bg`shc sl_ jÖlc_ n_p_jcj_ _j chc gqmkÑrpgam n_p_ bcrcpkgl_p j_ bgqr_lag_ _j nslrm >,

Amkm cqr_ bgkclqgâl cq n_p_jcj_ _ sl chc gqmkÑrpgam* nscbc rp_lqdcpgpqc _j bg`shm gqmkÑrpgam,

Bgqr_lag_ bc rp_lqdcpclag_

+ J_q

bgkclqgmlcq

bc 02 kk w 7 kk qml n_p_jcj_q _ j_q jÖlc_q

gqmkÉrpga_q w nscbcl kc+bgpqc bgpcar_kclrc,

N_p_ amltclacpqc _ qÖ kgqkm bc osc j_q jÖlc_q lm gqmkÉrpga_q lm rclbpÅl j_ jmlegrsb tcpb_bcp_ cl cj bg`shm gqmkÑrpgam* sqc sl rpmxm bc n_ncj w k_posc j_ bgqr_lag_ ?> &n_qm 0' w bcqnsÉq amknÅpcj_ aml ?> cl j_ tgqr_ qsncpgmp b_b_ cl j_ dgesp_ 1,22_, F_e_ jm kgqkm n_p_ j_ jÖlc_ @>, M`qcpt_pÅ osc ?> cq kÅq ampr_ w @> cq kÅq j_ge_ cl cj bg`shm gqmkÑrpgam osc j_ jÖlc_ amppcqnmlbgclrc cl j_q tgqr_q b_b_q,


5/34

1 , / 2 K C B G B ? Q BC S @ G A ? A G ± L BC A M K N C L Q ? A G ± L 6 5

Asafgjj_ aclrp_j Rmb_q j_q kcbgb_q bc`cl qcp n_p_jcj_q _ jmq `mpbcq npglagn_jcq bc j_ a_h_ cltmjtclrc

&`' &a'

1,22 Qsncpdgagcq glajgl_b_q cl sl bg`shm gqmkÜrpgam,

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ej_hej]`]oCl j_ dgesp_ 1,22 qc kscqrp_ aâkm amlqrpsgp sl bg`shm gqmkÑrpgam bc sl m`hcrm osc rgc+lc sl_ qsncpdgagc glajgl_b_ w `mpbcq m`jgasmq, M`qcptc osc j_q qsncpdgagcq glajgl_b_q

qc clasclrp_l nmp amknclq_agâl m kcbg_lrc kcbgagmlcq ammpbcl_b_q _ jm j_pem bc j_q jÖlc_q gqmkÉrpga_q, Nmp chcknjm* j_q bgkclqgmlcq B w C qc kgbcl n_p_ jma_jgx_p j_ qsncpdgagc J glajgl_b_* w j_q bgkclqgmlcq > v ? pb sq_l n_p_ jma_jgx_p j_ qsncpdgagc K,

QSNCPDGAGCQ M@JGAS?Q CL SL BG@SHM GQMKCRPGAM

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jmq nj_lmq

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cl

asclr_ osc n_p_ cqrc chcknjm cj nj_+lm m`jgasm amlrgclc jmq nslrmq > * ?

X E&

PN_p_ bg`sh_p cj nj_lm* cvrgclb_ j_ jÖlc_ >? f_qr_ U w V* cl cj

kgqkm nj_lm

gqmkÑrpgam

osc

A, Sqc

j_q jÖlc_q U@ v V@ n_p_ jma_jgx_p jmq nslrmq B w C,

PNmp åjrgkm* bg`shc >A w BA sq_lbm j_ pcej_ bc osc j_q

jÖlc_q n_p_jcj_q

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amkm

n_p_jcj_q cl rmb_q j_q tgqr_q mprmepÅ+

dga_q m gqmkÉrpga_q,


6/34


1,/3 RKB>P L@RIQ>P V @BKQO>IBPJ_q jÖlc_q masjr_q cl sl bg`shm pcnpcqclr_l jmq `mpbcq bmlbc qc clasclrp_l j_q qsncp+dgagcq* ncpm lm qml bgpcar_kclrc tgqg`jcq, Cl jmq bg`shmq ngarâpgamq* j_q jÖlc_q masjr_q qc mkgrcl* _ kclmq osc qc_l lcacq_pg_q n_p_ b_pjc aj_pgb_b _j bg`shm, Cl j_ dgesp_1,23 qc kscqrp_ sl a_qm cl cj osc j_q jÖlc_q masjr_q qml lcacq_pg_q nmposc sl_ n_prc

npmwcar_b_ lm nscbc kmqrp_pqc aj_p_kclrc qgl cjj_q, Cl ma_qgmlcq pcqsjr_ kchmp gl+ajsgp sl_ tgqr_ gqmkÑrpga_ bcqbc mrp_ bgpcaagâl* osc rp_r_p bc kmqrp_p j_q a_p_arcpÖqrg+

a_q lm tgqg`jcq kcbg_lrc jÖlc_q masjr_q, Cl cj a_nÖrsjm 3 sqrcb _npclbcpÅ kÅq _acpa_ bc j_q jÖlc_q masjr_q,

Bg`shc jÖlc_q aclrp_jcq n_p_ s`ga_p cj aclrpm bc jmq mpgdgagmq qâjm qg qml lcacq_+pg_q n_p_ glbga_p j_ qgkcrpÖ_ m n_p_ bgkclqgml_p, Cl eclcp_j* sqc j_q jÖlc_q aclrp_jcq aml kmbcp_agâl cl jmq bg`shmq gqmkÉrpgamq, Cl a_qm bc bsb_* lm j_q glajsw_* nscq ksaf_q jÖlc_q aclrp_jcq f_pÅl osc cj bg`shm qc tc_ amldsqm,

1,23 Sqm bc jÖlc_q masjr_q,

1,/4 °KDRILP BK AF?RGLP FPLJ{QOF@LPJmq Ålesjmq qc npmwcar_l _ r_k_àm tcpb_bcpm qâjm as_lbm cj nj_lm osc amlrgclc _j Ålesjm cq n_p_jcjm _j nj_lm bc npmwcaagâl, Sl Ålesjm nscbc npmwcar_pqc w n_pcacp

kÅq ep_lbc

m kÅ q

ncoscàm

osc

cj Ålesjm

pc_j

bcnclbgclbm

bc

qs nmqgagâl,Amkm j_q bgdcpclrcq qsncpdgagcq bc jmq m`hcrmq qscjcl cqr_p glajgl_b_q pcqncarm

_j nj_lm dpmlr_j bc npmwcaagâl* nmp jm eclcp_j lm qc npmwcar_pÅl _ r_k_àm pc_j cl sl bg`shm gqmkÑrpgam,

1,/5 L?GBQLP FOOBDRI>OBPSqrcb nscbc srgjgx_p cj kÉrmbm bc j_ a_h_ bc amlqrpsaagâl n_p_ bg`sh_p m`hcrmq osc lm qml pcar_lesj_pcq &dgesp_ 1,24', Jma_jgac jmq nsl rmq bc j_ `_qc rpg_lesj_p _j amk+

nclq_ p ^ w _ _ jm j_pem bc jmq `mpbcq bc j_ n_prc gldcpgmp bc j_ a_h_ bc amlqrpsaagâl, Jma_jgac cj tÉprgac _j amknclq_p j_q jÖlc_q L> w L? sq_lbm j_ n_prc qsncpgmp bc j_ a_h_ bc amlqrpsaagâl,

1,24 M`hcrmq gppcesj_pcq cl sl bg`shm gqmkÑrpgam,

+++++ P R D B O B K @ F > +++++++++++++++++++++++++++++++++++++++++++ Lm qgcknpc cq lcacq_pgm bg`sh_p j_ a_h_ bc amlqrpsaagâl amknjcr_ amkm qc kscqrp_ cl j_ dgesp_ 1,24`, Qg qâjm qc bg`sh_ j_ n_prc gldcpgmp bc j_ a_h_* j_ `_qc rpg_lesj_p nscbc amlqrpsgpqc bc j_ kgqk_ k_lcp_, J_ npmwcaagâl mprmepÅdga_ bcj tÉprgac M% qm`pc j_ `_qc nscbc bg`sh_pqc sq_lbm j_q amknclq_agmlcq L%> w L%?* amkm qc kscqrp_ cl j_ dgesp_* w clrmlacq nscbc bg`sh_pqc j_ jÖlc_ tcprga_j M%M sq_lbm j_ kcbgagâl A,


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1 , / 5 M @ H C R M Q G P P C E S J ? P C Q 67

A´KM BG@SH?P • L E S J M Q CL DMPK? GQMKßRPGA?

Cj bg`shm ksjrgtgqr_ _ j_ gxosgcpb_ kscqrp_ rpcq Ålesjmq bc 4.è, Cl sl bg`shm gqmkÑ+

rpgam* lgleslm bc jmq rpcq Ålesjmq qcpÅ bc 4.è,

+ Bg`shc jgecp_kclrc sl_ a_h_ cltmjtclrc sq_lbm j_q bgkcl+qgmlcq b_b_q* _ cvacnagâl bc j_ bg +

kclqgâl U vosc lm qc npmnmpagml_,

+ N_p_ clamlrp_p j_ bgkclqgâl U q bg`shc _ r_k_àm amknjcrm cj rpgÅlesjm ?A> bc j_ tgqr_ qsnc+

pgmp* amkm qc kscqrp_ cl j_ dgesp_,

PR D B OB K @F>@kilnk^]_eáj à hko Äjcqhko eokiÅpne_ko

N_p_ amltclacpqc _ qá kgqkm bc osc lgleslm bc jmq Çlesjmq qcpÇ bc 4.í* kgb_ a_b_ Çlesjm cl cj bg`shm gqmkÜrpgam bc j_ dgesp_ 1,23 aml sl rp_lqnmpr_bmp m sl ncb_xm bc n_ncj* w _lmrc cj Çlesjm amkn_p_bm aml cj tcpb_bcpm bc 4.í, Lgleslm bc jmq Çlesjmq kmqrp_bmq qml ges_jcq cl cj bg`shm gqmkÜrpgam, Bmq qml kclmpcq w slm cq k_wmp bc 4.í,

Bopei]_eáj à Äjcqhko à 1.å

Qg sqrcb cqrÇ `mqosch_lbm cl n_ncj

epÇdgam w lcacqgr_

cqrgk_p

Çlesjmq*

sl Çlesjm bc 1.í qc m`rgclc _npmvgk_b_kclrc _j _t_lx_p 0 as_bpmq w qs`gp /,

PRp_lqdgcp_ j_ bgkclqgâl U _j bg`shm gqmkÑrpgam n_p_ amknjcr_p j_ a_h_ cltmjtclrc,

Clasclrpc j_ bgkclqgâl V kcbg_lrc sl kÉrmbm qgkgj_p w bcqnsÉq rp_lqdgÉp_j_ _j bg`shm gqmkÑrpgam,

Lm cq bc 4 . í @ Lm cq bc 4 .í

Lm cq bc 4 .í

+ Amknjcrc cj bg`shm gqmkÑrpgam _j jma_jgx_p cj

nslrm B sq_lbm j_ bgkclqgâl Hv

amkm qc kscqrp_

cl

j_ dgesp_,

Cl

jmq bg`shmq gqmkÉrpgamq lm nscbc sq_pqc sl rp_lqnmpr_bmp pcesj_p n_p_ kcbgp jmq Ålesjmq, Amltgcpr_ j_q kcbgb_q _lesj_pcq cl kcbgb_q jglc_jcq _ jm j_gem bc j_q jÖlc_q bc jmq chcq gqmkÉrpgamq,


8/34

7. A ? N ≠ R S J M 1 @ M Q OS C H? B M R ~ A L G A M

0, Jma_jgac jmq nslrmq ?* A w B* w _q á qsacqgt_kclrc

3, Mqaspcxa_ j_q jálc_q dgl_jcq

/, Sqc j_q kcbgb_q bc amknclq_agål ^ v _ cl cj bg`shm gqmkÜrpgam n_p_ jma_jgx_p cj nslrm > qm`pc j_ aspt_

1, @mqoschc sl_ aspt_ qs_tc w jgecp_ _ k_lm _jx_b_ _ rp_tÖq

bc jmq nslrmq

1,25 Aspt_q cl sl bg`shm gqmkÜrpgam,

2, Bg`shc sl_ jálc_ tcprga_j bcqbc cj nslrm > n_p_ jma_jgx_p cj nslrm >%* v _qá

qsacqgt_kclrc* f_agÖlbmj_q rmb_q ges_jcq _ j_ _jrsp_ bcj `jmosc &a' bcqnsÖq bg`shc sl_ aspt_ jgecp_ _ rp_tÖq bc jmq nslrmq

1,/6 @ROS>P BK RK AF?RGLFPLJBQOF@L

Sqrcb nscbc bg`sh_p aspt_q gqmkÉrpga_q sq_lbm sl_ qcpgc bc kcbgb_q bc amknclq_agâl qgkgj_pcq _ j_q osc qc _l_jgx_pml cl j_ qcaagâl 1,/2, Qcjcaagmlc as_josgcp låkcpm bcqc_bm bc nsl+rmq _j _x_p _ jm j_gem bc j_ aspt_ cl j_ tgqr_ qsncpgmp b_b_* amkm jmq nslrmq > q ? w A bc j_ dgesp_ 1,25, Cjgh_ qsdgagclrcq nslrmq

n_p_ s`ga_p aml npcagqgâl j_ rp_wcarmpg_ bc j_ aspt_ &_ k_wmp a_lrgb_b bc nslrmq* k_wmp npcagqgâl', Bg`shc bcqbc a_b_ nslrm sl_ as_bpÖasj_ aml j_q jÖlc_q bc amknclq_agâl n_p_jcj_q _ jmq chcq gqmkÉrpgamq w åqcj_q n_p_ jma_jgx_p a_b_ nslrm cl cj bg`shm gqmkÑrpgam amkm cl cj chcknjm bc j_ dgesp_ 1,25,

Ncjmr_ bc rclgq &pcaf_x_b_ bc dÇ`pga_', @^of`^qro ̂

ab

Oldbo Mof̀ b, &Amprcqá_ bc Bpmmbjcq* %Rfc Aj_qqga Amjjcargml',


9/34

1,/7 BIFMPBP SBOA>ABO>P BK AF?RGLP FPLJ{QOF@LPQg sl aÖpasjm cqrÅ cl sl nj_lm osc lm cq n_p_jcjm _j nj_lm bc npmwcaagâl* cj aÖpasjm qc npm+wcar_ amkm sl_ cjgnqc* j_ as_j qc nscbc amlqrpsgp cknjc_lbm kcbgb_q bc amknclq_agâl,

1 , / 7 C J G N Q C Q T C P B ? B C P ? Q CL B G @ S H M Q G Q M K ~ R P G A M Q 7/

BG@SHM BC SL? CJGNQC GQMKßRPGA? K C B G ? L R C KCBGB?Q BC AMKNCLQ?AG´L

JÅpk`k

`a

h]o

hÉja]o

]ha]pkne]o

+ Bg`shc jÖlc_q n_p_jc+j_q cqn_ag_b_q bc dmp+

k_ _jc_rmpg_ _ rp_tÉq bcj aÖpasjm,

PRp_lqdgcp_ cqr_q jÖlc_q _j bg`shm gqmkÑ+

rpgam, As_lbm cj mpgdgagm q_je_ bc j_ n_prc gldcpgmp bcj `jmosc* jma_+jgac jmq nslrmq _j kcbgp sl_ bgqr_l+ag_ ges_j _ j_ _jrsp_ a bcj `jmosc bcqbc a_b_ slm

bc jmq

nslrmq

qsncpgmpcq,

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j_ cjgnqc*

n_prc

bc j_ as_j cqr_pÅ masjr_* _ rp_tÉq bc cqmq nslrmq, Mqaspcxa_ j_q jÖlc_q bcj bg`shm dgl_j,

Kgqk_ npmdslbgb_b

JÅpk`k

`a

hko

k_dk

lqjpko

+ Clagcppc cj aÖpasjm b_bm cl sl as_bp_bm w rp_ac bg_eml_jcq, Bg+

`shc mrpm as_bpm _ rp_tÉq bc jmq nslrmq bc glrcpqcaagâl bc j_q bg_eml_jcq w cj aÖpasjm amkm qc kscqrp_,

+ Bg`shc cqr_ kgqk_ amlqrpsa+agâl cl dmpk_ gqmkÑrpga_* rp_lq+dgpgclbm j_q bgqr_lag_q ^ v _, &Qg

qc bcqc_l kÅq nslrmq* _epcesc jÖlc_q n_p_jcj_q _j _x_p* amkm cl cj kÉrm+bm _lrcpgmp', J_q jÖlc_q aclrp_jcq bcj bg`shm gqmkÑrpgam qml jmq bgÅkcrpmq amlhse_bmq bc j_ cjgnqc, J_q bg_eml_+jcq _ 23è amglagbcl aml jmq chcq k_wmp w kclmp bc j_ cjgnqc, Cj chc kclmp rgclc j_ kgqk_ jmleg+rsb osc jmq j_bmq bcj as_bp_bm glqapgrm,

As_lbm qc pcosgcp_ kÅq npcagqgâl* bgtgb_ cj

aÖpasjm cl

/0 n_prcq

ges_jcq*

amkm

qc kscqrp_

cl j_ dgesp_, KÉrmbm bc jmq /0 nslrmq

IÉja]o jk eokiÅpnÉ_]o

Qg sl_ aspt_ cqrÅ cl sl nj_lm lm gqmkÑrpgam* lm rmb_q j_q kcbgb_q bc amknclq_agâl nscbcl _njga_pqc bgpcar_kclrc, J_ a_p_ cjÖnrga_ osc qc kscqrp_ cl j_ tgqr_ _svgjg_p qc clasclrp_ cl sl

nj_lm glajgl_bm lm gqmkÑrpgam,

+ Bg`shc jÖlc_q cl j_ tgqr_ mprmepÅdga_ n_p_ jma_jgx_p jmq nslrmq,

Clagcppc cj agjglbpm cl sl_/ a_h_ bc amlqrpsaagâl w bg`s+

hc j_ a_h_ cl cj bg`shm gqmkÑrpgam,

Bg`shc

j_ `_qc

sq_lbm

kcbgb_q

bc amknclq_agâl* w amlqrpsw_ j_ cjgnqc glajgl_b_ _j jma_jgx_p jmq

nslrmq w bg`sh_p j_ aspt_ dgl_j _ rp_tÉq bc cjjmq,

Kgb_ j_q bgqr_lag_q n_p_jcj_q _ sl chc gqmkÑrpgam &:̂ * _


10/34


1,0. LOFBKQ>@FßK AB BRMPBP BK AF?RGLP FPLJ{QOF@LP

Cl j_ dgesp_ 1,26 qc kscqrp_l cjgnqcq bc as_rpm aclrpmq amlqrpsgb_q cl j_q rpcq a_p_q tgqg`jcq bc sl as`m, Rcle_ cl asclr_ osc rmb_q j_q bg_eml_jcq qml fmpgxmlr_jcq m cqrÅl _ 4.è bc j_ fmpgxmlr_j, Qg qc rgclc cl asclr_ cqrm* qc d_agjgr_pÅ cj bg`shm bc j_q dmpk_q,

J_q cjgnqcq

_npmvgk_b_q

amkm

Éqr_q*

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_ n_prgp

bc

as_rpm

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qml

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BG@SHM BC SL? CJGNQC BC A S ? R P M ACLRPMQ

+ Bg`shc m gk_eglc sl as_+bp_bm cltmjtclrc n_p_ cj aÖpasjm osc qc kscqrp_ cl cj bg+

`shm ksjrgtgqr_, Bg`shc j_ tgqr_ gqmkÑrpga_ bcj as_bpm &sl n_p_+ jcjmep_km cosgjÅrcpm aml j_bmq ges_jcq _j bgÅkcrpm bcj aÖpasjm',

K_posc cj nslrm kcbgm bc /a_b_ jÖlc_,

PBg`shc jmq bmq _pamq ep_l+bcq* bc p_bgm O * bcqbc j_q glrcpqcaagmlcq bc j_q ncpncl+

bgasj_pcq osc cqrÅl cl j_q bmq cqosgl_q kÅq acpa_l_q bcj n_p_+ jcjmep_km,

BgÇkcrpm bcj aápasjm

BgÇkcrpm bcj aápasjm

U

PR D B OB K @F>Fc _osá sl_ pcej_ érgj, Cj chc k_wmp bc j_ cjgnqc qgcknpc cq ncpnclbgasj_p _ j_ álc_ aclrp_j bcj agjglbpm* w cj chc kclmp cq ncpnclbgasj_p _j chc k_wmp w amglñagbc aml j_ jálc_ aclrp_j,

t Cj chc kclmp amglagbc aml j_ jálc_ aclrp_j

+ Bg`shc jmq bmq _pamq nc+oscàmq* aml p_bgm p* bcqbc j_q glrcpqcaagmlcq bc j_q ncpncl+

bgasj_pcq osc cqrÅl bclrpm bcj n_p_j cj m ep_km* n_p_ amknjcr_p j_ cjgnqc,

PRDBOBK@F>Amkm sl_ amknpm`_agål bc j_ s`ga_agål cv_ar_ bc cqrmq aclrpmq* nscbc rp_x_p sl_ bg_eml_j j_pe_ bcj n_p_jcjmep_km amkm qc kscqrp_ cl cj n_qm 2, Jmq nslrmq kcbgmq bc jmq j_bmq bcj n_p_jcjmep_km qml jmq nslrmq bc r_leclag_ n_p_ jmq as_rpm _pamq,


11/34

1 , 0 . M P G C L R ? A G ± L BC C J G N Q C Q CL B G @ S H M Q G Q M K ~ R P G A M Q 71

Bifmpbp

j|p

mob`fp^p

J_ cjgnqc bc as_rpm aclrpmq qc bcqtÖ_ aml+qgbcp_`jckclrc bc sl_ cjgnqc tcpb_bcp_, Amkm qc kscqrp_ cl j_ dgesp_ 1,27_* sl_ cjgnqc bc as_rpm aclrpmq cq _jem kÅq amp+ r_ w °empb_¢ osc sl_ cjgnqc tcpb_bcp_, As_lbm j_ cjgnqc bc as_rpm aclrpmq lm

cq jm `_qr_lrc npcagq_* nscbc sq_pqc sl_ _npmvgk_agâl kÅq acpa_l_ jj_k_b_ cjgn+qc loqldoÄcf` ̂bc as_rpm aclrpmq n_p_ ec +lcp_p sl bg`shm kÅq cv_arm,

1,27 Glcv_argrsb bc j_ cjgnqc bc as_rpm aclrpmq,

tcpb_bcp_

bc as_rpm aclrpmq

BG@SHM BC SL? CJGNQC MPRMEP•DGA? BC AS?RPM ACLRPMQ

JÅpk`k

àh

na_pÄjcqhk

ajrkhrajpaN_p_ apc_p

sl_

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+ Bg`shc j_q jÖlc_q aclrp_+jcq gqmkÉrpga_q, Bcqbc cj aclrpm* bg`shc sl aÖpasjm bc

amlqrpsaagâl ges_j _j bgÅkcrpm pc_j bcj _eshcpm m agjglbpm, Cj aÖpasjm glrcpqca_pÅ j_q jÖlc_q aclrp_jcq cl as_rpm nslrmq* >,* ? v@ v

A,

P? n_prgp bc jmq bmq nsl+rmq bc glrcpqcaagâl qm`pc sl_ jÖlc_ aclrp_j* bg`shc jÖlc_q

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mrp_

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npgkcp_ bc cjj_q,

PAml j_q glrcpqcaagmlcq bc j_q ncpnclbgasj_pcq amkm aclrpmq* bg`shc bmq _p+

amq ncoscàmq w bmq ep_lbcq,

\Aápasjm bc

amlqrpsaagål B ges_j _j

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6 gqmkÖrpga_q

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rpgam,

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?' n_p_ jma_jgx_p jmq dmamq

qm`pc cj chc k_wmp,

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rmq A w A' n_p_ s`ga_p cj aclrpm bcj _pam ep_lbc O,

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4. :J Z - H

& : - 4.è

f SH Aclrpm bcj

_pam ep_lbc

+ Bg`shc jmq bmq _pamq ep_l+bcq O r_leclrcq _j pcarÅl+esjm gqmkÑrpgam, Bg`shc jmq bmq

_pamq ncoscàmq p* cknjc_lbm jmq dmamq cl jmq nslrmq @ v A amkm aclrpmq* n_p_ amknjcr_p j_ cjgnqc _npmvgk_b_,

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12/34


+++++ PRDBOBK@F>+++++++++++++Mh]jpehh]o

eokiÅpne_]o

J_q nj_lrgjj_q cqncag_jcq amkm cqr_ nj_lrgjj_ gqmkÜrpga_ aml jálc_q _lesj_b_q w cjgnqcq mpgclr_b_q cl bgdcpclrcq nj_lmq gqmkÖrpgamq* d_agjgr_l cj rp_x_bm bc `mqoschmq gqmkÖrpgamq

J_q cjgnqcq qc npmnmpagml_l aml k_pa_q n_p_ osc amglagb_l aml j_q jálc_q aclrp_jcq gqmkÖrpga_q bc jmq _eshcpmq* jm as_j j_q f_ac sl_ fcpp_kgclr_ bc ep_l srgjgb_b cl cj bg`shm gqmkÜrpgam,

R_k`gÖl nscbcl bg`sh_pqc cjgnqcq sq_lbm sl_ nj_lrgjj_ _bcas_b_* qcjcaagml_b_ bc dmpk_ osc amglagb_ aml jmq chcq k_wmp w kclmp,

1,0/

AF?RGL

AB

@FRKAOLP

FPLJ{QOF@LPCl j_ dgesp_ 1,3. qc kscqrp_ sl bg`shm rÖngam aml dmpk_q agjglbpga_q, M`qcptc osc jmq aclrpmq bc j_ cjgnqc kÅq ep_lbc lm nscbcl sq_pqc n_p_ j_ cjgnqc kÅq ncoscà_* _ ncq_p bc osc j_q cjgnqcq pcnpcqclr_l aÖpasjmq amlaÉlrpgamq, A_b_ cjgnqc rgclc qs npmngm n_p_+ jcjmep_km w qsq npmngmq aclrpmq, Rcle_ cl asclr_ osc jmq aclrpmq bc j_ cjgnqc gldcpgmp qc cj_`mp_l kcbg_lrc j_ npmwcaagâl bc jmq aclrpmq bc j_ cjgnqc ep_lbc qsncpgmp _ sl_ bgqr_lag_ ges_j _ j_ _jrsp_ bcj agjglbpm,

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1,3/ Pmqa_q bc rmplgjjm cl sl bg`shm gqmkÜrpgam,


13/34

1 , 0 2 C Q D C P ? Q CL B G @ S H M Q G Q M K ~ R P G A M Q 73

1,01 >O@LP BK AF?RGLP FPLJ{QOF@LPN_p_ `mqosch_p m bg`sh_p _pamq agpasj_pcq cl dmpk_ gqmkÑrpga_

nscbc sq_pqc j_ amlqrpsaagâl bc cjgnqcq bc as_rpm aclrpmq, J_dgesp_ 1,30_ kscqrp_ j_ amlqrpsaagâl amknjcr_, Lm cq lcacq_pgmbg`sh_p rmb_ j_ amlqrpsaagâl n_p_ jmq _pamq* amkm qc kscqrp_cl j_q dgesp_q 1,30` w a, Kgb_ cj p_bgm O bcqbc j_ cqosgl_ bcamlqrpsaagâl9 bcqnsÉq* cl a_b_ nslrm* bg`shc ncpnclbgasj_pcq

_ j_q jÖlc_q, Qs glrcpqcaagâl cq cj aclrpm bcj _pam, M`qcptc oscj_q bgqr_lag_q O qml ges_jcq cl j_q dgesp_q 1,30`w a* ncpm osc jmqp_bgmq pc_jcq osc qc srgjgx_l qml ks w bgdcpclrcq,

1,30 ?pamq cl bg`shmq gqmkÖrpgamq,

Tgqr_q b_b_q

/, Bg`shc cj gqmkÜrpgam bc sl aápasjm

ep_lbc n_p_jcjm

_ sl_

a_p_

bcj

as`m*

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0 Cj bgÇkcrpm bcj

_pasjm cl cj bg`shm gqmkÜrpgam cq P

BK

AF?RGLP

FPLJ{QOF@LPCj bg`shm gqmkÉrpgam bc as_josgcp qsncpdgagc aspt_ cq j_ cltmj+tclrc bc rmb_q j_q jÖlc_q osc nscbcl bg`sh_pqc qm`pc cq_ qsncp+dgagc, N_p_ j_q cqdcp_q* qcjcaagmlc jmq aÖpasjmq ep_lbcq &aÖpasjmq ampr_bmq kcbg_lrc as_josgcp nj_lm _ rp_tÉq bcj aclrpm' amkm j_q jÖlc_q qm`pc j_ qsncpdgagc, Bc`gbm _ osc rmbmq jmq aÖpasjmq ep_lbcq* cvacnrm _oscjjmq osc qml ncpnclbgasj_pcq m n_p_jcjmq _j nj_lm bc npmwcaagâl* qc kscqrp_l amkm cjgnqcq aml chcq k_+wmpcq ges_jcq* qs cltmjtclrc cq sl aÖpasjm aswm bgÅkcrpm cq cj chc k_wmp bc j_ cjgnqc,

Cl j_ dgesp_ 1,31 qc kscqrp_l bmq tgqr_q bc sl_ cqdcp_ clac+pp_b_ cl sl as`m bc amlqrpsaagâl, BcqnsÉq qc bg`sh_ sl_ tgqr_

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14/34

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15/34

N P M W C A A G ± L M P R M E P ™ D G A ? /41

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16/34

/42 A ? N ≠ R S J M 3 N P M W C A A G ± L M P R M E P ™ D G A ?

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17/34


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18/34

/4 4 A ? N ≠ R S J M 3 N P M W C A A G ± L M P R M E P ™ D G A ?

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19/34


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20/34


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21/34


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22/34

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m õ N?ú ` põmmsa_


23/34

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24/34

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25/34

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26/34


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bc j_q jálc_q,

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Cvgqrcl pcej_q

n_p_

bcagbgp

osÉ

jÖlc_

bc`c

kmqrp_pqc, Sl_ jÖlc_ tgqg`jc qgcknpc rgclc npcacbclag_ w as`pc as_josgcp jÖlc_ acl+rp_j s masjr_ as_lbm amglagbcl cl sl_ tgq+r_* amkm qc kscqrp_ cl > w ? bc j_ dgesp_ 3,10, Sl_ jÖlc_ masjr_ rgclc npgmpgb_b qm+

`pc sl_ jÖlc_ aclrp_j* amkm qc kscqrp_ cl A, Cl > q jmq cvrpckmq bc j_ jÖlc_ aclrp_j qc kscqrp_l qcn_p_bmq bc j_ tgqr_ kcbg_lrc cqn_agmq amprmq* ncpm j_ jÖlc_ aclrp_j qscjc bch_pqc amknjcr_kclrc dscp_ bcj bg`shm, Cl j_ dgesp_ 3,11 qc kscqrp_l chcknjmq bc jÖlc_q masjr_q amppcar_q c glamppcar_q,


27/34

3 , 0 N P C A C B C L A G ? BC J ? Q J ≠ L C ? Q /53

NpÅarga_q amppcar_q c glamppcar_q n_ p_ j_q jÖlc_q masjr_q

Ncesc j_ jÖlc_ masjr_ aml sl_ jÖlc_ tgqg`jc* cvacnrm as_lbm cqrm ma_qgmlc osc j_ jÖlc_ tgqg`jc qc cvrgclb_ bck_qg_bm* amkm qc kscqrp_ _osÖ,

Bchc sl cqn_agm qgcknpc osc j_ jÖlc_ masjr_ qc_ sl_ amlrgls_agâl bc sl_ jÖlc_ tgqg`jc,

As_lbm bmq m rpcq jÖlc_q masjr_q qc clasclrpcl cl sl nslrm* sl_ jmq esgmlcq amkm qc kscqrp_ cl j_ n_p rc gldcpgmp bc cqrc _eshcpm ncpdmp_bm,

F_e_ osc j_q jÖlc_q masjr_q qc glrcpqcoscl cl j_q cqosgl_q cl J w R ,

J_ kgqk_ pcej_ bc slgp jmq esgmlcq as_lbm bmq m rpcq jÖlc_q masjr_q qc clasclrp_l cl sl nslrm cq _njga_`jc _ j_ n_prc qsncpgmp bc cqrc _eshcpm

_tcjj_l_bm,

F_e_ osc j_ jÖlc_ masjr_ °q_jrc¢ sl_ jÖlc_ tgqg`jc qgcknpc osc qc_

nmqg`jc,

J_q jÖlc_q masjr_q lm bc`cl slgpqc _ j_q jÖlc_q tgqg`jcq qg cqrm ma_qgml_ osc j_ jÖlc_ qc cvrgclb_ bck_qg_bm,

Rp_ac j_q jÖlc_q masjr_q n_p_jcj_q bc kmbm osc jmq esgmlcq qc cqa_jmlcl* amkm jmq j_bpgjjmq bc sl_ n_pcb,

Rp_ac jmq _pamq masjrmq aml cj _pam slgbm _ j_ jÖlc_ aclrp_j* amkm cl b chcknjm _lrcpgmp, Lm bc`c f_`cp sl cqn_agm clrpc cj _pam w j_ jÖlc_ aclrp_j* amkm cl cj chcknjm gldcpgmp bmlbc

j_ n_prc pcar_ qc slc _ j_ jÖlc_ aclrp_j,

3,11 NpÇarga_q amppcar_q c glamppcar_q n_p_ j_q jálc_q masjr_q,

+++++ P R D B O B K @ F > +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++?aclréc cj glgagm w cj dgl_j bc a_b_ esgål npcqgml_lbm cj jÇngx, F_e_ j_q jálc_q masjr_q r_l lárgb_q amkm nscb_ n_p_ osc

qc_l dÇagjcq bc glrcpnpcr_p, ?qceépcqc bc f_acp jmq esgmlcq bc j_q jálc_q masjr_q kÇq j_pemq osc jmq cqn_agmq* bc kmbm

osc pcnpcqclrcl jálc_q aj_p_kclrc,


28/34


3,1 RKB>P @BKQO>IBPJ_q jÖlc_q aclrp_jcq &qÖk`mjm8 Ö ' qc srgjg+x_l n_p_ glbga_pjmq chcq qgkÉrpgamq bc jmq m`hcrmq m cjckclrmq* jmq aÖpasjmq bc ncp+lmq w j_q psr_q bc kmtgkgclrm* amkm qc kscqrp_ cl j_ dgesp_ 3,12, J_q jÖlc_q acl+rp_jcq qml årgjcq cl cj bgkclqgml_kgclrm,

Lm qml lcacq_pg_q cl cqosgl_q pcbmlbc_+b_q m aml dgjcrc nmam gknmpr_lrcq m cl mrp_q dmpk_q osc nscbcl jma_jgx_pqc aml d_agjgb_b,

3,12 Jálc_q aclrp_jcq,

3,2 AFPQOF?R@FßK AB RK AF?RGLQg sqrcb sq_ A?B cl 0B* nscbc kmtcp j_q tgqr_q bcqnsÉq* k_l+

rclgÉlbmj_q _jglc_b_q* nmp jm osc lm cq lcacq_pgm npcqr_p r_lr_ _rclagâl _ j_ amjma_agâl bc j_q tgqr_q bcqbc sl npglagngm amkm qg j_q cqrstgcp_ rp_x_lbm _ k_lm, As_lbm qc sq_ A?B cl 1B

n_p_ eclcp_p tgqr_q* cq lcacq_pgm nj_lc_p aâkm qc kmqrp_pÅ aj_+p_kclrc j_ gldmpk_agâl cl j_ fmh_ w qcjcaagml_p j_q tgqr_q lc+acq_pg_q n_p_ pcnpcqclr_p bc kchmp k_lcp_ j_ dmpk_ bc j_ ngcx_,

? ncq_p bc osc cj a_k`gm bc cqa_j_ cl sl bg`shm A?B bcqnsÉq

bc qs apc_agâl cq qclagjjm* j_ amjma_agâl bc j_q bgkclqgmlcq w j_q tgqr_q qm`pc j_ fmh_ pcosgcpc sl_ nj_lgdga_agâl, Qg qc rgclc cl asclr_ cj npmnâqgrm bcj bg`shm* j_ cqa_j_ npctgqr_ w cj cqn_agm pcoscpgbm n_p_ _à_bgp lmr_q w bgkclqgmlcq* qc _fmpp_pÅ rgcknm _j lm rclcp osc pcmpe_lgx_p j_ bgqrpg`sagâl nmqrcpgmpkclrc,

BGQRPG@SAG´L BC SL BG@SHM KÄRPGAM AML RPCQ TGQR?Q

Qsncpgmp

+ Bcrcpkglc cj cqn_agm A bcqc_bm clrpc j_ tgqr_ dpmlr_j w j_rcp_j bcpcaf_* nmp chcknjm 10 kk, ?à_b_ cqrc cqn_agm

_ j_ qsk_ bc j_ jmlegrsb bc j_q tgqr_q osc _jg+lc_pÅl _ jm j_pem bcj `mpbc kÅq ep_lbc bc j_ fmh_ &/.6 ) 36 ) 10 ; /76', N_p_ cqr_+

`jcacp bgqr_lag_q ges_jcq _j `mpbc bcj n_ncj* pcqrc cqrc rmr_j bcqbc j_ _lafsp_ bc j_ fmh_ w jscem bgtgb_ cj pcqsjr_bm clrpc bmq &044 +

/76 ; 5.* w 5. 0 ; 13', F_e_ jm kgqkm aml j_q tgqr_q osc qc _jglc_pÅl _ jmj_pem bcj j_bm kÅq amprm bcj n_ncj* qcjcaagml_lbm sl cqn_agm bcqc_bm clrpc j_q tgqr_q, Cj cqn_agm A lm rgclc nm p osÉ amglagbgp aml A, ?j kmkclrm bc nj_lc_p qs fmh_* pcascpbc bch_p cqn_agm n_p_ j_q bgkclqgmlcq,

Dpmlr_j J_rcp_j B

kmm ?C

/1C

/72

Cqr_`jcxa_ j_q kcbgagmlcq bc cqn_+b_bm tcprga_j w fmpgxmlr_j kcbg_lrc

k_pa_q epscq_q bc amjmp aj_pm _ jm j_pem bcj `mpbc bc j_ fmh_ amkm qc kscqrp_, S`gosc j_q jÖlc_q aclrp_jcq bcqbc cqr_q k_pa_q bc cqn_+ b_kgclrm* w amlqrpsw_ _pamq w aÖpasjmq,

Cj_`mpc j_q tgqr_q* bg`sh_lbm % j_q jÖlc_q bc amlqrpsaagâl fm+

pgxmlr_jcq* tcprga_jcq* w bcqnsÉq j_q glajgl_b_q cl cj mpbcl osc qc glbga_ _lrcq,

&_npmvgk_b_kclrc Ã Ã ' ++++++++++++044 +++++++++++++

∏

36

GB

@

° J

J_rcp_j B

/.6 + 3 6 +

?à_b_ j_q jÖlc_q masjr_q w %mqaspcxa_ j_q jÖlc_q dgl_jcq,


29/34

3 , 4 T G Q R ? Q BC Q S N C P D G A G C Q /55

3,3 SFPR>RW>@FßK?bckÅq bc clrclbcp `gcl cj qgqrck_ n_p_ npmwcar_p tgqr_q* sqrcb bc`c qcp a_n_x bc glrcpnpcr_p kåjrgnjcq tgqr_q n_p_ amlac`gp cj m`hcrm osc qc kscqrp_, ?bckÅq bc qcp sl_ f_`gjgb_b glbgqncl+q_`jc n_p_ _wsb_pjc _ a_nrsp_p w amkslga_p qsq gbc_q* jmq `mq+oschmq rÉalgamq r_k`gÉl qml sl_ k_lcp_ bc osc mrpmq nscb_l

npcqclr_pjc qsq gbc_q,

Glajsqm jmq gleclgcpmq* rÉalgamq w bgqcà_bmpcq cvncpgkcl+r_bmq lm qgcknpc nscbcl tc p sl `mqoschm ksjrgtgqr_ c glkcbg_+r_kclrc tgqs_jgx_p cj m`hcrm pcnpcqclr_bm, Sqrcb _npclbcpÅ _ cqrsbg_p cj `mqoschm c glrcpnpcr_p j_q jÖlc_q bc sl_ k_lcp_ jâeg+a_ n_p_ _pk_p sl_ gbc_ aj_p_ bcj rmbm, ? tcacq _ cqrc npmacqm qc jc bclmkgl_ sfprîfw^`fàk,

Pqlanbe_eao*

^knào

u

aomqej]oN_p_ apc_p c glrcpnpcr_p j_q npmwcaagmlcq ksjrgtgqr_ bc k_lcp_ cdcargt_* sqrcb bc`c amlqgbcp_p jmq cjckclrmq osc amknmlcl j_ k_wmpÖ_ bc jmq qâjgbmq, Jmq jÖkgrcq bc jmq m`hcrmq qâjgbmq cqrÅl dmpk_bmq nmp qsncpdgagcq, Sl_ qsncpdgagc mi ^k ^ &jj_l_'

nscbc cqr_p jgkgr_b_ nmp jÖlc_q pcar_q* aspt_q* m sl_ amk`gl_+agâl bc _k`_q, N_p_ tgqs_jgx_p pcnpcqclr_agmlcq nj_l_q amkm m`hcrmq cl 1B qc pcosgcpc npÅarga_, Râkcqc sl kmkclrm n_p_ cv_kgl_p j_q tgqr_q osc qc kscqrp_l cl j_ dgesp_ 3,13 w rp_rc bc amlac`gp cj m`hcrm, &Tc_ j_ qmjsagâl cl j_ nÅegl_ /7.',

3,13 Rpcq tgqr_q bc sl m`hcrm, &Jmaif_pr*Qf_ul_ B,9 Hmflqml* Aglbw K,* Bkdfkbbofkd Abpfdk @ljjrkf`^qflk8 @lksbvfkd Abpfdk Qeolrde

Do^mef`p* /_* ò 0..., &Gknpcqm w pcnpmbsagbm cjcarpålga_kclrc aml _srmpgx_agål bc Nc_pqml Cbsa_rgml* Gla,* Snncp Q_bbjc Pgtcp* Lsct_ Hcpqcw',

T@ ; Tgqr_ bcj `mpbc RT ; R_k_ãm tcpb_bcpm Q; Qcqe_bm

!E"

3,14 Npmwcaagmlcq bc qsncpdgagcq,

PR D B OB K @F>PRok à jäianko l]n] eàjpebe_]n rÅnpe_ao

?epcesc lékcpmq cqapgrmq jgecp_kclrc _ qsq bg`shmq n_p_ rclcp sl qcesgkgclrm bc a_b_ tÖprgac qm`pc j_ qsncpdgagc osc cqrÖ amlqgbcp_lbm, A_b_ tÖprgac cq élgam cl j_ ngcx_* nmp jm osc a_b_ lékcpm bc tÖprgac _n_pcacpÇ qåjm sl_ tcx cl a_b_ tgqr_, Cl ma_qgmlcq* bmq tÖprgacq qc _jglc_l slm bcrpÇq bcj mrpm* amkm cl j_ dgesp_ 3,14_, As_lbm cqrm qsacbc nscbcl clskcp_pqc

cl mpbcl aml cj k_wmp npgkcpm* amkm cl /* 0* m* _ tcacq* cq érgj nmlcp jmq lékcpmq bc jmq tÖprgacq tgqg`jcq kÇq acpa_lmq dscp_ bc j_ dmpk_* w jmq tÖprgacq masjrmq kÇq jch_lmq bclrpm bcj amlrmplm bc j_ dmpk_,

3,4 SFPQ>P AB PRMBOCF@FBPSl_ qsncpdgagc nj_l_ osc cq ncpnclbgasj_p _ sl nj_lm bc npm+wcaagâl _n_pcac qm`pc qs `mpbc amkm sl_ jÖlc_ pcar_ &dgesp_ 3,14_', Qg cq n_p_jcj_ _j nj_lm bc npmwcaagâl* _n_pcac cl qs r_k_àm tcpb_bcpm &dgesp_ 3,14`', Qg dmpk_ sl Ålesjm aml cj

nj_lm bc npmwcaagâl _n_pcac qcqe_b_ m kclmp _ qs r_k_àm pc_j &dgesp_ 3,14a', Sl_ qsncpdgagc nj_l_ qgcknpc qc npmwcar_ qm+

`pc sl `mpbc &osc _n_pcac amkm sl_ qmj_ jÖlc_' m `gcl amkm sl_ qsncpdgagc &kmqrp_lbm qs dmpk_ a_p_arcpÖqrga_' cl as_josgcp

tgqr_, Nscbc _n_pcacp qcqe_b_* ncpm lsla_ kÅq ep_lbc osc qsr_k_àm pc_j cl lglesl_ tgqr_,

Cvgqrcl rÉpkglmq osc qc srgjgx_l n_p_ bcqapg`gp j_ mpgclr_+agâl bc sl_ qsncpdgagc pcqncarm _j nj_lm bc npmwcaagâl, J_q rpcqmpgclr_agmlcq osc nscbc rclcp sl_ qsncpdgagc nj_l_ pcqncarm _j nj_lm bc npmwcaagâl qml klojîvfkìfkâ^ w l_if`r^, J_ amk+ npclqgâl bc cqrmq rÉpkglmq jc _wsb_pÅ _ amlac`gp w bcqapg`gp jmqm`hcrmq,


30/34

3,17 Qsncpdgagc m`jgas_,

Qsncpdgagcq lmpk_jcq

/56 A ? N ≠ R S J M 3

3,16 Qsncpdgagc glajgl_b_,3,15 Qsncpdgagcq lmpk_jcq,

3,5 PRMBOCF@FBP KLOJ>IBPSl_ prmbo cf`fb

klojî cq n_p_jcj_ _ sl nj_lm bc npmwcaagâl, ?n_pcac cl qs r_k_àm w dmpk_ tcpb_bcpmq qm`pc cj nj_lm _j as_j cq n_p_jcjm* w _n_pcac amkm sl_ jÖlc_ tcprga_j s fmpgxmlr_j bc jmlegrsb tcpb_bcp_ cl jmq nj_lmq bc npmwcaagâl _bw_aclrcq, Cl j_ dgesp_ 3,15 qc kscqrp_ sl_ gjsqrp_agâl bc qsncpdgagcq lmp+k_jcq,

3,6 PRMBOCF@FBP FK@RK>A>PSl_ prmbocf `fb fkìfkâ^ cq ncpnclbgasj_p _ sl nj_lm bc npm+wcaagâl* ncpm glajgl_b_ &m j_bc_b_' pcqncarm _ jmq nj_lmq _b+w_aclrcq, Sl_ qsncpdgagc glajgl_b_ qc npmwcar_ qm`pc sl `mpbc cl cj nj_lm _j as_j cq ncpnclbgasj_p, ?n_pcac qcqe_b_ cl jmq nj_lmq pcqncarm _ jmq osc qc glajgl_, Cl j_ dgesp_ 3,16 qc kscq+rp_ sl_ qsncpdgagc glajgl_b_, Cj ep_bm bc qcqem cq npmnmpagml_j _ j_ glajgl_agâl, ?slosc osgxÅ j_ qsncpdgagc lm _n_pcxa_ _ r_+k_àm pc_j cl lglesl_ tgqr_* rclbpÅ j_ kgqk_ dmpk_ a_p_arcpÖqrg+a_ w cj kgqkm låkcpm bc `mpbcq cl j_q tgqr_q cl j_q osc nscb_ m`qcpt_pqc qs dmpk_,

Np_argosc j_ gbclrgdga_agål bc qsncpdgagcq lmpk_jcq cl bg`shmq bc A?B, Cl jmq qgrgmq uc` nscbc bcqa_pe_p tgqr_q mprmepÇdga_q bc m`hcrmq osc kscqrpcl ksaf_q qsncpdgagcq lmpk_jcq,

3,7 PRMBOCF@FBP L?R@R>PSl_ prm boc f`fb

l_if`r^ cqrÅ glajgl_b_ pcqncarm _ rmbmq jmq nj_+lmq npglagn_jcq bc npmwcaagâl, Bc`gbm _ osc lm cq ncpnclbgas+j_p _ lgleål nj_lm bc npmwcaagâl* lm nscbc _n_pcacp qm`pc sl

`mpbc cl lglesl_ tgqr_ cqrÅlb_p, Amkm lm cq n_p_jcj_ _ lgleål nj_lm bc npmwcaagâl* lm nscbc _n_pcacp _ r_k_àm pc_j cl lgl+esl_ tgqr_ cqrÅlb_p, Sl_ qsncpdgagc m`jgas_ qgcknpc qc npcqclr_

amkm sl_ qsncpdgagc qcqe_b_ cl j_q rpcq tgqr_q cqrÅlb_p, Cl j_q dgesp_q 3,17 w 3,2. qc kscqrp_l qsncpdgagcq m`jgas_q,

3,/. ?LOABPJ_ glrcpqcaagâl bc bmq qsncpdgagcq nj_l_q bc sl m`hcrm npmbsac sl _loab* osc qc kscqrp_ amkm sl_ jÖlc_ pcar_ cl cj bg`shm, Sl

`mpbc cq amkål _ bmq qsncpdgagcq* dmpk_lbm sl jÖkgrc n_p_ a_b_ sl_, Qg cj `mpbc cq ncpnclbgasj_p _ sl nj_lm bc npmwcaagâl* _n_pcac amkm sl nslrm* bc jm amlrp_pgm _n_pcac amkm sl_ jÖlc_, Qg cq n_p_jcjm _j nj_lm bc npmwcaagâl* kscqrp_ qs tcpb_bcp_ jmlegrsb, Qg lm cq n_p_jcjm* _n_pcac qcqe_bm, Sl_ jÖlc_ pcar_ qgcknpc qc npmwcar_ amkm sl_ jÖlc_ pcar_ m amkm sl nslrm, Jmq

rÉpkglmq klojî * fkìfkâl w l_if`rl bcqapg`cl j_ pcj_agâl bc sl `mpbc pcqncarm _ sl nj_lm bc npmwcaagâl,

&_'

X ,

&A'

3,2. ?bgagål bc sl_ qsncpdgagc m`jgas_ _ sl `mqoschm gqmkÜrpgam,


31/34

3 , / 2 @ M P B C Q N ? P ? J C J M Q /57

3,// ?LOABP KLOJ>IBPSl _loab klojî cq sl_ jÖlc_ ncpnclbgasj_p _ sl nj_lm bc npm+wcaagâl, ?n_pcac amkm sl nslrm cl cqc nj_lm bc npmwcaagâl w amkm sl_ jÖlc_ aml jmlegrsb tcpb_bcp_ cl jmq nj_lmq bc npm+wcaagâl _bw_aclrcq &dgesp_ 3,2/',

3,/0

?LOABP

FK@IFK>ALPSl _loab fkìfkâl cq n_p_jcjm _ sl nj_lm bc npmwcaagâl* ncpm cqrÅ glajgl_bm pcqncarm _ jmq nj_lmq _bw_aclrcq, Qc npcqcl+r_ amkm sl_ jÖlc_ aml jmlegrsb tcpb_bcp_ cl cj nj_lm osc cq

n_p_jcjm w amkm sl_ jÖlc_ qcqe_b_ cl jmq nj_lmq _bw_aclrcq, J_ tgqr_ bc jmlegrsb tcpb_bcp_ bc sl_ jÖlc_ glajgl_b_ qgcknpc _n_pcac amkm sl_ jÖlc_ _lesj_b_* ncpm j_q tgqr_q qcqe_b_q _n_+pcacl amkm jÖlc_q tcprga_jcq s fmpgxmlr_jcq &dgesp_ 3,20',

3,2/ Npmwcaagmlcq bc sl `mpbc lmpk_j,

3,/1 ?LOABP L?R@RLP

Sl _loab

l_if`rl cqrÅ

glajgl_bm

pcqncarm

_ rmbmq

jmq

nj_lmq

bc

npmwcaagâl, Bc`gbm _ osc lm cq ncpnclbgasj_p _ lgleål nj_lm bc npmw caagâl* lm nscbc _n_pcacp amkm sl nslrm cl lglesl_ tgqr_ cqrÅlb_p, Amkm lm cq n_p_jcjm _ lgleål nj_lm bc npmwca+agâl* lm nscbc _n_pcacp aml qs jmlegrsb pc_j cl lglesl_ tgqr_ cqrÅlb_p, Sl `mpbc m`jgasm _n_pcac qcqe_bm w amkm sl_ jÖlc_ glajgl_b_ cl rmb_q j_q tgqr_q &dgesp_ 3,21',

3,/2 ?LOABP M>O>IBILPAs_lbm jmq `mpbcq qml n_p_jcjmq clrpc qÖ cl cj m`hcrm* _n_pcacpÅl amkm jÖlc_q n_p_jcj_q cl rmb_q j_q tgqr_q* _ kclmq osc qc _jglccl slm bcrpÅq bcj mrpm, Cqr_ gldmpk_agâl nscbc qcp årgj as_lbm sq+

rcb cqrÉ bgqrpg`swclbm sl bg`shm* qm`pc rmbm qg qc rgclc sl_ qs+ ncpdgagc amknjch_ glajgl_b_ s m`jgas_ aml `mpbcq n_p_jcjmq, Cl j_ dgesp_ 3,22 qc kscqrp_ sl chcknjm bc jÖlc_q n_p_jcj_q cl j_q tgqr_q bc sl bg`shm,

Jmlegrsb tcpb_bcp_

3,20 Npmwcaagmlcq bc sl `mpbc glajgl_bm,

Qcqe_b_

3,21 Npmwcaagmlcq bc sl `mpbc m`jgasm,

p+j† Z

&_' Nj_lmq n_p_jcjmq glrcpqca_bmq nmp mrpm nj_lm

3,22 Jálc_q n_p_jcj_q,

&`' Jálc_q /* 0 w 1* 2 n_p_jcj_q clrpc qá w n_p_jcj_q _j nj_lm fmpgxmlr_j

&a' Jálc_q /* 0 w 1* 2 n_p_jcj_q clrpc qá w n_p_jcj_q _j nj_lm dpmlr_j

n_p_jcj_q clrpc qá w m`jgas_q _ rmbmq jmq nj_lmq


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/6 . A ? N ≠ R S J M 3 N P M W C A A G ± L M P R M E P ™ D G A ?

™lesjm _r_k_ãm ,tcpb_bcpm

&_' ™lesjm cl sl nj_lm lmpk_j

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