jfl;ª\u6gsf sfJo ;';]nL
Proof ;Dkfbs
8f) s'df/k|;fb sf]O/fnf
k|sfzs
l8;L sf]7] slj uf]i7L jfl;ª\u6gsf sfJo ;';]nL M 1
Proof jfl;ª\u6gsf sfJo ;';]nL -sljtf ;ª\u|x_ k|sfzs M l8;L sf]7] slj uf]i7L ;jf{lwsf/ M k|sfzsdf ;+:s/0f M klxnf] @)^( -;g\ 2012_ cfj/0f M k|sfz g]kfn d'b|0f M ldl8ofh'd, bcrprint@gmail.com, 703-672-6719 Washington Ka Kabya Suseli ISBN : 978-9937-2-4661-3 email : kothekavita@googlegroups.com
jfl;ª\u6gsf sfJo ;';]nL M 2
ljifoqmd k|sfzsLo ;DkfbsLo 8f) s'df/k|;fb sf]O/fnf e"ldsf 8f) nId0fk|;fb uf}td cfgGbk|;fb zdf{ af]nL kxf8 dfnf slj / sljtf slkn l;6f}nf d]/f] b]z /ª p8\b} uPsf tl:a/x¿ ltdL slt lgb{oL p7 s'Des0f{ p7 uf]kfn /]UdL e]n]G6}g lbj;sf] pknIodf gj k|]dLx¿nfO{ d]/f] h"g s] gfd xf]nf ej ;'Gb/Lsf] dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/ uf]ljGb lu/L k]|/0ff cfkm“}n] /f]h]sf] kmls{xfN5' b]z Ps gh/d} dg k/fP“ d]/f] ;kgf gf/fo0f clwsf/L lk|o km"n :jfFu]x¿ ¿ksnf :vlnt ljrf/ k|sfz g]kfn k/fO{ ;x/ xfOs' km/s xfdLx¿ t'?Gt ;lxb 3f]if0ff u/ k|]dk|;fb ;+u|f}nf lbof] snz / hd/f o;kfnL ;[hgf / hLjg zLtsfnLg a'9f] ¿v
Proof
jfl;ª\u6gsf sfJo ;';]nL M 3
5 9 11 @% 26 28 29 31 ## 34 37 39 40 $# 44 45 47 49 %! 52 54 56 58 ^! 62 63 64 66 ^( 70 71 72 75 && 78 79 81 83
a;Gt >]i7 *% P k/b]l;Psf ldq 86 csnaxfb'/ cd]l/sfdf M Ps zAblrq 89 ;8s 93 df]/fn]; ufl;{of 96 af;' >]i7 !)! ljZjf;sf] cefj 102 cfpm sljtf 105 d]/L cfdf la/fdL l5g\ 107 Oltxf;df afFRg rfxg]x¿ 111 8f) df]xgk|;fb hf]zL !!% v} s] u/]5 < 116 dnfO{ t xf“;} p7\5 117 leGgtf x]g]{ ls ;dfgtf < 118 sljtf n]Vg ufx|f] 5 119 z/b lg/f]nf !@! lsg cfof} cd]l/sf < 122 pd/ v®ofd, vnLn lha|fg / d 124 clnslt cf“;' k}“rf] rflxPsf] 5 126 csd{0otf jf cl:tTjxLgtf 128 ;'bLkeb| vgfn !@( emª\sf/ 130 la5§ ef]/df w/f k|5Gg ¿k e]l6of];\ 132 cfkm}FnfO{ lrlGbgF 133 d s;/L k"0f{ ;+;f/ u5'{ < 135 xl/ l3ld/] !#& ctL{ 138 :jfutd\ 139 cfpg] k':tfnfO{ 140 kl/0flt 141 x]dGt >]i7 !$# 3f]8f / dfG5] 144 sf“8f / km"n 148 lgjf{;gsf] s73/fdf 150 xf]dgfy ;'j]bL !%% zLtnx/ 156 sljtfs';'d 159 ;]t' 161 ¿v 165
Proof
jfl;ª\u6gsf sfJo ;';]nL M 4
k|sfzsLo
of] Pp6f j;Gtsf] ;ª\s]t xf] ljz]if u/L sljtf ;flxTodf ?lr /fVg] o; jfl;ª\u6g l8;L jl/kl/sf s]xL ;fyLx¿n] a]nf avt cfgf] 3/df ;flxlTos sf]7] uf]i7L ub}}{ cfPsf lyP . t/ tLdWo] s'g}n] klg lg/Gt/tf kfPsf lyPgg\ . /x/d} uf]i7L x'GYof], /x/d} x/fpFYof], t/ o:tf] k|sf/sf] uf]i7LnfO{ cf}krfl/s ¿kdf ;+ul7t / lg/Gt/tf tyf lglZrt cfsf/ lbg] x]t'n] ToxL sf]7] sljtf uf]i7Ls} gfdaf6 v;v; 86sdsf ;+:yfks–;~rfns af;' >]i7n] !* l8;]Da/ @)!) b]lv p8la|haf6 ;'? ug{'eof] / qmdzM tnsf 7fpFdf c¿ uf]i7Lx¿ ;kmntfk"j{s cfof]hgf ul/P M bf];|f] xl/ l3ld/]n] % km]a|'c/L @)!! cn]Sh]lG8«ofdf t];|f] uf]kfn /]UdLn] @ clk|n @)!! dgf;;df rf}yf] cfgGb zdf{n] @ h'g @)!! cfln{ª\u6gdf kfFrf} ;'bLkeb| vgfnn] ^ cu:t @)!! xg{8gdf 5}7f}F xf]dgfy ;'j]bLn] % gf]e]Da/ @)!! p8la|hdf ;ftf}F k|]d ;+u|f}nfn] !& l8;]Da/ @)!! dSn]gdf tyf cf7f}F k|sfz g]kfnn] !! km]a|'c/L @)!@ kmN; rr{df .
Proof
cfufdL gjf}F uf]i7L slkn l;6f}nfn] d]l/NofG8df clk|n @*, @)!@ sf lbg cfof]hgf ug{] lgwf] ug{'ePsf] 5 eg] To;kl5 xfdL nut} b;f}F uf]i7Lsf] tof/Ldf x'g]5f}F . xfdLnfO{ k"0f{ cfzf 5 of] qmd lg/Gt/ cl3 al9 /xg] 5 . clxn];Dd ;f}xfb{|tf tyf tTk/tfsf ;fy uf]i7L cfof]hgf ug{] ;a} ;b:ox¿ wGojfbsf kfq t 5g\ g} . cfufdL cfof]hsx¿nfO{ klg clu|d wGojfb eGg' ;fd"lxs st{Jo xf] eGg] 7fg]sf 5f}F . clxn];Dd sf]s uf]i7Ldf ;xofqL eO{ lxF8]sf sljx¿ x'g\— cfgGb zdf{, a;Gt >]i7, af;' >]i7, uf]kfn /]UdL, uf]ljGb lu/L k|]/0ff, xl/ l3ld/], x]dGt >]i7, xf]dgfy ;'j]bL, slkn l;6f}nf, 8f) df]xg hf]zL, gf/fo0f clwsf/L, k|sfz g]kfn, k|]d ;+u|f}nf, z/b lg/f]nf tyf ;'bLkeb| vgfn . sf]7] uf]i7Lk|lt b]lvPsf] pT;fx x]bf{ cd]l/sfdf o;n] ;zQm e"ldsf v]n]/ Pp6f gofF Oltxf; /Rg ;S5 . log} sljx¿sf] jif{ lbgel/ jfrg ul/Psf sljtfx¿dWo]af6 clwsf+z sljsf rf/–rf/j6f sljtf ;ª\u|xsf] klxnf] pkxf/ xf]— jfl;ª\u6gsf sfJo ;';]nL . jfl;ª\u6gsf sfJo ;';]nL M 5
b'O{ dlxgfleq n]lvPsf sljtfdfq k9\g] eGg] lgwf] ul/Pcg';f/ g} sljtf ;ª\Vofdf j[l4 ePsf] 5 . clg o;/L !% hgf ;fyLx¿n] b'O{ b'O{ sljtf /Rbf jif{sf] !*) j6f sljtf g]kfnL ;flxTon] kfpg' eg]sf] rfgr'g] pknlAw xf]Og . uf]i7Lsf] csf{] dxÎjk"0f{ pknlAw ;g\ @)!! df g} o;sf b'O{ ;b:osf sfJos[lt k|sfzg x'g' xf] . k|]d ;+u|f}nfsf] æ;'sLw'kLÆ v08sfJo tyf 8f) df]xg hf]zLsf] æsxfF 5 7fpFÆ gfds sljtf ;ª\u|xdf ;ª\u[xLt sltko sljtfx¿ o;} sf]7] uf]i7Ldf jfrg ul/Psf 5g\ . pxfFx¿nfO{ awfO{ 5 . o;sf ;fy} uf]i7Lsf cGo s]xL ;fyLx¿ klg cfgf sljtf ;ª\u|x k|sfzg ug{ pBt x'g'x'G5 . pxfFx¿nfO{ xfd|f] clu|d z'esfdgf 5 . of] ;a} sf]7] uf]i7Lsf] of]ubfg xf] eGg xfdL sbflk xRsFb}gf}F .
Proof
af}l4s ;dfhsf] pTs[i6 cleJolQm ;flxTo xf] . ;r]t dfG5]sf ;'if'Kt efjgfsf] phfu/ ug{] dfWod klg ;flxTo xf] . To;leq ;a} /; d'6'sf s];|f s];|f /;fP/ kf]lvg ;S5g\ . ;a} efjgf e]l6g ;S5g\ . ToxfF k|]d– la5f]8 x'G5 . Joª\Uo–ljb|f]x x'G5 . ljs[lt–lj;ª\ultsf] kbf{kmf; x'G5 . xf:o–ljgf]bsf] v]n x'G5 . wd{–bz{g–;+:s[lt cflb ;asf] k|s6Ls/0f x'G5 . cd]l/sfsf] Jo:t hLjgdf s]xL ;do lgsfnL p:t}–p:t} ;fyLx¿ ldn]/ cfgf dgsf efjgf ;f6f;f6 ug{] dfWoddfq xf]Og gofF gofF l;h{gf ug{] ynf] klg ag]sf] 5— xfd|f] of] sf]s uf]i7L . k|To]s b'O{–b'O{ dlxgfdf ;~rfng x'g] o; uf]i7Ln] ;'t]sf ;fyLx¿sf] efjgfnfO{ Ao'FemfPsf] 5 . Ao'Fem]sfnfO{ p7fPsf] 5 . p7]sfnfO{ bf}8fPsf] 5 . ;fyLx¿sf gofF gofF efjx¿ k|s6 ePsf 5g\ . kl/is[t z}nLsf] ljsf; ePsf] 5 . 5Gbsf af/]df rfv a9]sf] 5 . cg'ej ;f6f;f6n] l;h{gfnfO{ yk pmhf{ k|fKt ePsf] 5 . of] Pp6f sfJo kf7zfnf klg xf] . nueu rf/ 306f sljtfs} af/]df 5nkmn x'G5, ljrf/ ljdz{ x'G5 / To;}df 8'a'NsL nufOG5 . cfgf sdL sdhf]/LnfO{ x6fpg c;n ;Nnfx–;'emfj cfbfg–k|bfg ul/G5 . jfrg ul/Psf sljtfk|lt 6Lsf l6Kk0fL ul/G5 . lrGtg–dgg / dGygaf6 /rgfdf k|f}9tf cfpF5 . lgTo–gjLg cfljisf/n] g]kfnL ;flxTosf] e08f/ eg{ dxÎjk"0f{ of]ubfg lbPsf] 5 . oL ;a} sljx¿ cd]l/sfdf a;]/ n]lv/x]sf 5g\ . ;a}sf sljtfdf b]z af]n]sf] 5, df6f] dUdufPsf] 5, ;+:s[lt Ao'Fem]sf] 5 . aflx/ a:g' k/]sf] kL8f 5, hLjgsf] c;fdfGo ef]ufO 5 / ;ª\3if{zLn b}glGbgLsf] syf 5 . jfl;ª\u6gsf sfJo ;';]nL M 6
efiff–lzNk / ;+j]bgfnfO{ ;a}n] ;dft]sf 5g\ . lj;ª\ult / lj/f]wfef;k"0f{ ;dfhdf afFr] klg k|]d, eft[Tj, pT;j, cfgGb, pNnf; / eljiosf] ;'gf}nf] ;kgf ;a} sljsf sndn] af]s]sf] 5 . hLjgsf] g};lu{stf, lgd{ntf / lgisn'lifttfnfO{ sn'lift / s[lqd k|ljlw¿kL a'N8f]h/n] a9f/]/ nfg vf]h]klg sljx¿sf sndn] ;'/lIft /fVg oyfzSo k|of; u/]sf 5g\ . o; s[ltn] cd]l/sfdf a;]sf g]kfnLx¿sf] k'/} k|ltlglwTj gu/] klg k|j[lQut lx;fan] of] s[lt sf];]9'ª\uf ;flat x'g]5 eGg] ljZjf; lnPsf 5f}F . of] cd]l/sfdf klg g]kfnL efiff–;flxTosf] ;'Gb/ eljiosf] cfzf nfUbf] s[lt eO lbP xfdL s[t–s[To x'g] lyof}F . Pp6f km"n km'Nb}df j;Gt cfof] eGg g;s] klg To; km"nn] j;Gt cfpFb} 5 eGg] ;ª\s]t rflxF cjZo lbg]5 . cGTodf, o; sljtf ;ª\u|xsf] ;Dkfbg ul/lbg] 8f) s'df/k|;fb sf]O/fnf, uxg e"ldsf n]lvlbg] 8f) nId0fk|;fb uf}td, 5kfOsf] uxg cleef/f af]lslbg] zfZjt k/fh'nL tyf k':tssf] cfj/0f agfOlbg] xfd|} ;d"xsf ;b:o k|sfz g]kfnnfO{ xflb{s s[t1tf k|s6 ub{5f}F . cfufdL lbgdf klg x/]s jif{ o:t} s[lt k|sfzg ug{] xfd|f] k|lta4tfdf ;a}af6 cflzjf{b kfcf}F .
Proof
wGojfb Û
l8;L sf]7] sljtf–uf]i7L
jfl;ª\u6gsf sfJo ;';]nL M 7
Proof
jfl;ª\u6gsf sfJo ;';]nL M 8
;DkfbsLo
g]kfnL 8fo:kf]l/s ;flxTo]ltxf;sf] sf];]9'Ëf] 8f) s'df/k|;fb sf]O/fnf sljtfsf af/]df s'/f ug'{ dfq klg /f]df~rsf] s'/f xf] . ;+;f/sf cGo s'g} s'/f ubf{ klg dfG5] Tolt /f]dfl~rt x'bF g} xf]nf hlt pm sljtf ;'Gbf jf /Rbf x'G5 . dnfO{ nfU5 dfG5]sf] ;aeGbf dL7f] af]nL sljtf xf] / dfG5]n] clxn];Dd sljtfeGbf dL7f] af]nL hfg]sf] klg 5}g . sljtfn] dfG5]nfO{ e|d / oyfy{df em'nfP/ cnf}lss cfgGbnf]sdf k'¥ofpF5 . oxL zlQmn] dfG5]x¿ sljtf;Fu cTolws 8/fpF5g\ klg / /dfpF5g\ klg . 8/fpF5g\ lsgeg] of] /x:odo 5, a'lemg;Sg' / kf/ kfOg;Sg' 5 . xhf/f}F jif{bl] v dfG5] sljtf n]lv/x]sf] 5, t/ sljtfsf] /x:o a'lem;s]sf] 5}g . slj /x:o vf]n/] /x:o afFsL g} /fV5 . dfof lsg u5{g\ eg] of] ;jf{lws ;'Gb/ / cfgGbbfoL 5 . dfG5] oxL ;'Gb/tf / cfgGbdf 8'a/] b'Mvk"0f{ hLjgsf] cFWof/f]df clnslt ;'vsf] pHofnf] xfN5 / /dfpF5 . sljtf /Rg' / ;'gfpg', sljx¿ e]nf eP/ sljtf ;'gfpg' / ;'Gg' o:tf sd{ x'g,\ h;n] sljtfnfO{ kl/jt{gzLn, ultzLn / lgTo gjLg agfO/xG5g\ . dnfO{ nfU5 o:tf sd{af6 sljtfsf] ch;|tf / cd/tf Jol~ht x'G5 . ;DejtM g]kfnL ;flxTodf of] k/Dk/f k"jk{ f| rLg sfnb]lv g} lyof] xf]nf, t/ To;sf] k|fdfl0fs Oltxf; eg] dfWolds sfnsf] df]tL d08nL -lj=;=+ !(#*_ agf/;af6 ;'? ePsf] b]lvG5 . ;DejtM of] sf]7] sljtf uf]i7L g} lyof] . o:tf slj uf]i7L xhf/f}F eP xf]nfg\, nfvf}F eO/x]sf xf]nfg\ / ltgn] g]kfnL sljtfnfO{ lg/Gt/tf lbO/x]sf xf]nfg\ . d of] …jfl;ª\u6gsf sfJo ;';n ] LÚ nfO{ o:t} uf]i7Lsf] Ps clt dxÎjk"0f{, P]ltxfl;s / d"t{ kl/0ffd dfGb5' . d]/f lk|o ldq xl/ l3ld/]n] /d]z vs'/n ] , sdndl0f bLlIft, sf]if/fh Gof}kfg], k|Xnfb kf]v/]n cflb ldn]/ rnfPsf] sf]7] slj uf]i7Ldf ;xefuL x'g] cj;/ h'/fOlbg'eof] . To;kl5 d c¿ b'O{ rf/ uf]i7Ldf ;lDdlnt ePF . To; lardf xl/ l3ld/]hL cd]l/sflt/ nfUg'eof] / uf]i7Ldf ;xeflutf klg sd eof] . xl/hL cd]l/sfaf6 kms{bF f ToxfF ePsf ;flxlTos ultljlwsf af/]df hfgsf/L lbg'xG' Yof] . cg];f;n] lgsfn]sf] klqsf k9\g] cj;/ klg ldNof] . pxfFaf6} …;]tÚ' sljtf;ª\ux| k9\g] cj;/ kfPF . dnfO{ cd]l/sfs} v;v; 86sdk|lt cfslif{t pxfFn] g} u/fpg' eof] . pxfF sf7df8f}F cfpg] lalQs} cd]l/sfdf klg sf]7] slj uf]i7L eO/xG5, xfdLx¿ ljb]zdf a;]/ klg g]kfnL
Proof
jfl;ª\u6gsf sfJo ;';]nL M 9
;flxTodf nflu/x]sf 5f}F eGg'xG' Yof] . o;/L d cd]l/sfdf sf]7] slj uf]i7L ug]{ / sljtf /Rg] sljx¿;Fu ck|ToIf ¿kdf hf]l8Fb} uPF . pxfFx¿sf /rgfn] dnfO{ k|efljt kfb}{ nu] . d ;f]Rb} lyPF olb pxfFx¿sf sljtf ;ª\ux[ Lt u/]/ k|sflzt ug{ kfP slt /fd|f] x'GYof] . o:t}df xl/hLn] eGg'eof]— æs'df/hL, tkfO{n + ] ;f]rs ] f] 7Ls xf], ca ;Dkfbgsf] lhDdf tkfO{+ g} lng'xf];\ .Æ o;/L pxfFn] of] u'?t/ bfloTj dnfO{ lbg' eof] . o;sf nflu d pxfF / o; ;°ngdf ;dflji6 ;a} sljx¿k|lt xflb{s cfef/ k|s6 ug{ rfxG5'' . ;~rf/ / k|ljlwn] b'lgof ;fgf] ePsf] 5 . g]kfnLx¿ ljZjel/ km}lnPsf 5g\ / pgLx¿ g]kfnL ;+:s[lt lgdf{0f / k|;f/df nflu/x]sf 5g\ . ljZj ;dIf g]kfnL ;+:s[ltnfO{ kl/lrt u/fpg] / Jofks agfpg] sfo{df o'/f]k, cd]l/sf, /l;of, c:6]l« nof, xªsª, c/a d'ns ' cflb ljleGg 7fpFdf a:g] g]kfnLx¿n] cfcfg} 8fo:kf]/f lgdf{0f u/]sf 5g\ / g]kfnL ;flxTonfO{ ljZjJofkL agfO/x]sf 5g\ . pgLx¿ ;flxlTos l;h{gfnfO{ j]e ;fO6df /fv]/ g]kfnL ;flxTonfO{ ax'sG] b|Ls/0f ul//x]sf 5g\ . :yfg / ;dosf ;Ldf eTsfP/ cfh g]kfnL ;flxTon] gofF–gofF laof8df cg]s ;flxTo aLh 5l//x]sf] 5 / ToxfFaf6 cg]s ;flxlTos aLhfª\s/' 6';fO/x]sf 5g\ / of] s[lt To:t} aLhfª\s/' sf] ;°ng xf] h:tf] nfU5 . o;n] ef]ln j[If¿k wf/0f ug]5 { , o;sf xfFuflaFuf km}ng] 5g\ / ltgdf /l;nf / ;':jfb' kmn nfUg]5g\, sljtfsf ;x[boL kf7s ltgaf6 lg:sg] /; ;]jg u/]/ /f]dfl~rt x'g5 ] g\ .
Proof
8fo:kf]l/s g]kfnLnfO{ k"0f{sfnLg ;flxTosf/ x'g cK7Øf/f] 5 . Jofj;flos cK7Øf/f / Jo:ttfn] pxfFx¿ ;lhnf] u/L cf]sg{ –kms{g klg kfpg' x'Gg xf]nf . o; ;°ngdf ;dflji6 sljx¿ k];fn] sf]xL 8fS6/, sf]xL OlGhlgo/, sf]xL cy{zf:qL / sf]xL cGo Joj;fodf ;ª\nUg b]lvg' x'G5 . pxfFx¿ s;/L ;flxTonfO{ ;do lbg'xG' 5, s;/L sf]7] slj uf]i7Ldf efu lng] ;do lgsfNg' x'G5 eGg] s'/f ;f]Rbf cfZro{ nfU5 . pxfFx¿sf] Tofu, ;dk{0f / ;flxTok|ltsf] nufj ;fFRr} k|/] 0ffbfoL / k|z; + gLo klg 5 . pxfFx¿sf] b]zk|ltsf], g]kfnL efiff / ;flxTok|ltsf] cufw cf:yf / cg'/fun] of] ;Dej ePsf] xf] . pxfFx¿sf] o:tf] sfo{ :t'To 5 . g]kfnL ;flxTodf pxfFx¿sf] sfo{nfO{ d df]tL d08nLs} lg/Gt/tf lbg] Ps P]ltxfl;s sfo{ dfGb5' . o;sf] ;flxlTos d"No s] xf]nf, g]kfnL ;flxTosf] Oltxf;df o;sf] d"Nof°g s;/L xf]nf Tof] kf7s / eljion] unf{, t/ dnfO{ nfU5 g]kfnL 8fo:kf]l/s ;flxTo]ltxf;df of] Ps sf];9] Ë ' f] ;flat x'g5 ] . kumar_koirala2008@yahoo.com
jfl;ª\u6gsf sfJo ;';]nL M 10
8fo:kf]l/s sfJo;';n] Ldf cg'el" tsf laDax¿ 8f) nId0fk|;fb uf}td
!= ljifo kl/ro g]kfnL efiff / ;flxTo ca g]kfnsf] dfq /x]g / of] g]kfndf dfq geP/ ljZjsf w]/} d'n'sx¿df lj:tf/ ePsf] 5 . g]kfnL efiff;flxTosf] of] lj:tf/ / JofksLs/0f cfhsf] e"d08nLs/0fn] dfq NofPsf] xf]OgÙ o;sf k5fl8 ljb]zdf /x]/ 8fo:kf]l/s hLjg latfO/x]sf zAbsdL{x¿sf] efiff;flxTok|ltsf] cufw :g]x / cf:yf klg sf/s tÎjsf ¿kdf /x]sf] 5 . ljZjsf ljleGg d'n'sdf 5l/P/ /x]sf tdfd g]kfnLx¿n] cfgf] efiff;flxTosf] ;d'Ggogsf nflu JolQmut / ;+:yfut ¿kdf pNn]vgLo of]ubfg lbPsf 5g\ . …l8;L sf]7] slj uf]i7LÚnufot w]/} ;+:yfx¿n] g]kfnL ;flxTosf ljleGg ljwfdf k'¥ofPsf] dxÎjk"0f{ of]ubfgsf] kl/0flt :j¿k k|sflzt ePsf k|z:t s[ltx¿n] ;d]t g]kfnL 8fo:kf]l/s ;flxTosf] ;d'Ggogdf cxd\ e"ldsf v]n]sf 5g\ . ljz]iftM cd]l/sfdf /x]sf g]kfnL ;flxlTos ;+:yfx¿ a9L ;lqmo b]lvG5g\ . o;} ;Gbe{df cd]l/sfsf] jfl;ª\ u6g 8L;Ldf /x]sf …l8;L sf]7] slj uf]i7LÚ gfds ;+:yfn] u/]sf sflJos ljdz{ / sljtfjfrg tyf s[lt k|sfzgsf ;Gbe{x¿ klg pNn]vgLo 5g\ . k|:t't sljtfs[lt …jfl;ª\u6gsf sfJo;';]nLÚ -@)^(_ gfds ;fd"lxs sljtf;ª\u|x g]kfnL 8fo:kf]l/s sljtfsf If]qdf Pp6f k[ys\ klxrfg af]s]/ cfPsf] b]lvG5 . @= s[ltut ;+/rgf / kl/df0ffTds d"No …jfl;ª\u6gsf sfJo;';]nLÚ cd]l/sfsf] jfl;ª\u6g 8L;Ldf /x]sf kGw| hgf g]kfnL 8fo:kf]l/s sljx¿sf pgfG;f7Lcf]6f sljtfx¿sf] ;fd"lxs sljtf;ª\u|x xf] / o; ;ª\u|xsf sljtfx¿ cGtj{:t', z}nL / no;+/rgfsf b[li6n] ;d]t k[ys\ k[ys\ lsl;dsf b]lvG5g\ . kGw| ;f]/ kª\lQmsf n3' cfsf/–k|sf/sf sljtfb]lv lnP/ kfFr k[i7;Ddsf nfdf sljtfx¿ /x]sf] o; ;ª\u|xsf sljtfdf d'Qm5Gb jf uBsljtfsf] ;+/rgfTds 9fFrfsf sljtf, zf:qLo jfl0f{s 5Gbsf sljtf / uLltno ;+/rgfsf sljtfsf ;fy} xfOs' sljtf;Ddsf /rgfx¿ /x]sf 5g\ . o;/L u'0ffTds d"Nosf b[li6n] dfq geO{ kl/df0ffTds d"Nosf b[li6n] klg Pp6} ;fd"lxs sljtfs[ltdf kGw| hgf sljx¿sf pgfG;f7Lcf]6f rolgt sljtfx¿ ;ª\u[xLt x'g'
Proof
jfl;ª\u6gsf sfJo ;';]nL M 11
k|flKtk"0f{ b]lvG5 . o; ;ª\u|xsf k|foM ;a} sljtfx¿ k|uLtfTds ;+/rgfdf n]lvPsf 5g\ / tL n3'¿ksf sljtfsf ¿kdf g} b]lvG5g\ . s]xL sljtf cfofd jf cfsf/–k|sf/sf b[li6n] nfdf b]lvP klg ltgdf Pp6} s]Gb|Lo efj jf ljrf/sf] cfj[lQ ePsfn] / kl/wLo ljrf/x¿n] s]Gb|Lo ljrf/nfO{ kl/k'i6tf k|bfg u/]sfn] tL sljtf km'6s/ sljtfs} ¿kdf /x]sf 5g\ .
#= sljtfsf] cGtj{:t' / sYo M cGtj{:t'sf b[li6n] o; ;ª\u|x leqsf sljtfdf ljljwtf b]lvP klg d"ntM 8fo:kf]l/s k|j[lQ leqsf w]/} pkk|j[lQx¿ g} a9L kfOG5g\ . k|0fok/stf, /fi6«k|]d, ef]ufO / cg'e"ltsf] cleJolQm, 8fo:kf]l/s hLjgsf kL8f, lg/fzf, cg'e"lt, ef]ufO, la/fgf]kg, ckl/roLs/0f, :jcl:tTjsf] vf]hL, cfTdklxrfgsf] vf]hL, ;+:s[lt r]tgf, o'uaf]wL ;dsfnLg r]tgf, :jb]zsf ljs[lt / lj;Ëltk|ltsf] lrGtf, cfzfjfbL hLjgb[li6 / cfbz{jfbL r]tgf o; s[lt leqsf sljtfdf a9L kfOg] cGtj{:t' x'g\ . o; ;ª\u|xsf sljtfdWo] cfgGbk|;fb zdf{sf] …af]nLÚ zLif{ssf sljtfdf dw'/ af]nL af]Ng cfu|x ul/Psf] efj k|:t't ul/Psf] 5 eg] …kxf8Ú zLif{ssf] sljtfdf u|fEotfsf] j}ej, …dfnfÚ sljtfdf cfbz{jfbL r]tgf / …slj / sljtfÚ sljtfdf clwsflJos r]tgfnfO{ cGtj{:t' agfOPsf] 5 . slkn l;6f}nfsf] …d]/f] b]zÚ df /fi6«jfbL r]tgf, …ltdL slt lgb{oLÚ df /fufTdstf, …p7 s'Des0f{ p7Ú df hfu/0fsf] cfXjfg / …/Ë p8\b} uPsf tl:a/x¿Ú df cf:yfsf] eUgtfnfO{ d"n cGtj{:t' agfOPsf] 5 . To:t} uf]kfn /]UdLsf …e]n]G6}g lbj;sf] pknIodf gjk|]dLx¿nfO{Ú df k|]dsf] pbfQtfsf] lrq0f, …d]/f] h"gÚ df k|0fok/stf, …s] gfd xf]nf ej ;'Gb/Lsf]Ú df ;f}Gbo{ r]tgf / …dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/Ú df /fli6«o lrGtf Pjd\ nf]stflGqs r]tgfnfO{ d"n cGtj{:t' agfOPsf] 5 . uf]ljGb lu/L k|]/0ffsf …cfkm}Fn] /f]h]sf]Ú / …kmls{xfN5' b]zÚ df 8fo:kf]l/s r]tgf / …Ps gh/d} dg k/fPFÚ df /fi6«af]wL efj tyf …d]/f] ;kgfÚ df :jKg laDasf cg'e"lt k|:t't ul/Psf] 5 . gf/fo0f clwsf/Lsf sljtf s]xL laDak/s ;d]t 5g\ . pgsf …lk|o km"nÚ df k|s[lt r]tgf, …:jfFu]x¿Ú df Oltxf;af]w / ;dsfnLg r]tgf, …¿ksnfÚ df k|s[ltsf] dfgjLs/0f / …:vlnt ljrf/Ú df j}rfl/s :vngk|ltsf] Joª\Uo efj 5 . k|sfz g]kfnsf …k/fO{ ;x/Ú / …8n/, sDKo'6/ / uf8LÚ df 8fo:kf]l/s r]tgf Pjd\ …km/s xfdLx¿Ú / …t'?Gt ;lxb 3f]if0ff u/Ú
Proof
jfl;ª\u6gsf sfJo ;';]nL M 12
df g]kfnsf] ;fdflhs, /fhgLlts b'b{zfnfO{ d"n cGtj{:t' agfOPsf] 5 . To;/L g} k|]d ;+u|f}nfsf …lbof], snd / hd/fÚ df Joª\Uo r]tgf, …o;kflnÚ df k|ljlw ;+:s[lt / ;f+:s[lts r]tgf, …;[hgf / hLjgÚ df cfbz{ r]tgf / …zLtsfnLg a'9f] ¿vÚ df k|s[lt r]tgf cleJol~ht 5 . 8f) df]xgk|;fb hf]zLsf] …v} s] u/]5 <Ú df hLjgsf] cl:tTjaf]w, …dnfO{ t xfF;} p7\5Ú df k|ljlw ;+:s[ltsf] ;Gbe{, …leGgtf x]g]{ ls ;dfgtfÚ df k|s[lt r]tgf / …sljtf n]Vg uf/f] 5Ú df sljtfdf ;+j]bgf JoQm x'g g;s]sf] efjnfO{ s]Gb|Lo ljifoj:t' agfOPsf] 5 . j;Gt >]i7sf …P k/b]l;Psf ldqÚ / …csnaxfb'/ cd]l/sfdfÚ sljtfdf 8fo:kf]l/s r]tgf, Oltxf;af]w / PsfsLkgÙ …;8sÚ df o'uaf]wL r]tgf / …df]/fn]; ufl;{ofÚ df 8fo:kf]l/s hLjgsf] ckl/roLs/0fnfO{ d"n cGtj{:t' agfOPsf] 5 . To:t} af;' >]i7sf] …ljZjf;sf] cefjÚ jt{dfgsf dfG5]df ljZjf;sf] ;°6 ePsf] efj, …cfpm sljtfÚ df sljTj r]tgfsf] cfdGq0f, …d]/L cfdf la/fdL l5g\Ú df k|tLsfTds ¿kdf g]kfnsf] b'/j:yfsf] lrq0f / …Oltxf;df afFRg]x¿Ú df oflGqs hLjgsf hl6ntfnfO{ cleJoQm ul/Psf] 5 . ;'bLkeb| vgfn zf:qLo jfl0f{s 5Gbdf cToGt ;zQm / snfTds lsl;dsf sljtf n]Vg] slj x''g\ . pgsf] …em°f/Ú df k|]dsf] pRrtf, pbfQtf / O{Zj/Tjsf] efj, …la5§ ef]/df w/f k|R5Gg ¿k e]l6of];\Ú df /fi6«jfbL r]tgfsf ;fy :d[lt laDa / …la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{Ú df hGe"ldk|ltsf] cz]if cf:yf / ;f+:s[lts r]tgf k|:t't ul/Psf] 5 .
Proof
z/b lg/f]nfsf …lsg cfof} cd]l/sf <Ú df 8fo:kf]l/s r]tgf, …pd/ v®ofd, vlnn lha|fg / dÚ df slj÷;flxTosf/ pd/ v®ofd / vlnn lha|fg;Fu …dÚ sf] ;dLs/0f, …clnslt cfF;' k}Frf] rflxPsf] 5Ú df dfgjLo ;+j]bgf / …csd{0otf jf cl:tTjxLgtfÚ df cfhsf] dfG5]df b]lvPsf] csd{0otfnfO{ d"n cGtj{:t' agfOPsf] 5 . xl/ l3ld/]sf] …ctL{Ú df hLjgsf] z"Gotf, …:jfutd\Ú df lj;Ët r]tgf, …cfpg] k':tfnfO{Ú df cfzfjfbL hLjgb[li6 / …kl/0fltÚ df lj;Ëltaf]w / ;f+:s[lts r]tgf d'Vo cGtj{:t' ag]/ cfPsf 5g\ . ;dsfnLg g]kfnL sljtfsf If]qdf x]dGt >]i7 klg ;zQm / k|efjk"0f{ sljtf n]Vg] sljsf ¿kdf lrlgG5g\ . o; ;ª\ u|xdf ;ª\u[xLt pgsf sljtfdWo] cfVofgfTds ;+/rgfdf n]lvPsf] …3f]8f / dfG5]Ú df g]kfnsf] /fhgLlts ;ËltxLgtf / ljs[lt, …sfF8f / km"nÚ df jt{dfgsf] qf;bL, …lgjf{;gsf] s73/fdfÚ df oflGqstf, ;+j]bgxLgtf / jfl;ª\u6gsf sfJo ;';]nL M 13
cfTd Joª\Uo tyf lj;[hgsf] kL8fnfO{ k|d'v cGtj{:t' agfOPsf] 5 . slj xf]dgfy ;'j]bLsf …zLtnx/Ú sljtfdf 8fo:kf]l/s r]tgf, ToxfFsf] kl/j]z lrq0f / ljb|f]xL r]tgf, cg'i6'k\ 5Gbdf n]lvPsf] …;]t'Ú df 8fo:kf]l/s hLjgsf kL8f, ef]ufO / cg'e"lt, …¿vÚ df e"d08nLs/0fn] NofPsf kl/jt{g / 8fo:kf]l/stf tyf …sljtf s';'dÚ sljtfdf Pp6L ;fgL aflnsfnfO{ sljtfsf] laDa k|bfg ul/Psf] efjnfO{ s]Gb|Lo cGtj{:t' agfOPsf] 5 . o;/L oL ;a} sljx¿sf sljtfsf] d"n cGtj{:t' 8fo:kf]l/s eP klg kl/wLo ¿kdf cGo ljljw cGtj{:t' cfPsfn] oL ;a} sljtfx¿ ljljwtfdo ag]sf b]lvG5g\ .
$= s[ltleqsf sljtfsf] k|j[lQut ljZn]if0f M s[ltleqsf k|foM ;a} sljtf k|j[lQut b[li6n] ljljwtfdo eP klg clwsf+z sljtfdf 8fo:kf]l/s r]tgf a9L d'vl/t ePsf] kfOG5 . ;dsfnLg o'uaf]wL r]tgf, hLjg / ;dfhsf] cfbzL{s/0fsf] rfxgf, :jb]zsf] lrGtf / rf;f], k|]dsf] pRrtf / pbfQtf, ;f}Gbo{ r]tgf, o'usf kl/jlt{t ;fdflhs, /fhgLlts / j}lZjs ;Gbe{, 8fo:kf]l/s ef]ufO / kL8fg'e"ltsf] k|s6Ls/0f, 8fo:kf]l/s hLjgsf] PsfsLkg, la/fgf]kg, cfTdklxrfgsf] vf]hL, cl:tTjaf]wL r]tgf / ckl/roLs/0fsf] cleJolQm Pjd\ ljb]z / :jb]zsf /fhgLlts ;fdflhs kl/j]zsf] t'ngf, ;f+:s[lts r]tgf, lj1fg– k|ljlwsf ;Gbe{sf] k|:t'lt, Oltxf;af]w / jt{dfgaf]wsf] ;dL/s0f, oflGqs hLjgz}nLsf] lrq0f, dfG5]df b]lvPsf] ljZjf;sf] ;°6, k|s[lt r]tgf / cfzfjfbL r]tgf, jt{dfgsf qf;bL / s'¿k oyfy{sf] lrq0f, cfhsf dfG5]sf] ;+j]bgxLgtfsf] cleJolQm, /fufTdstf cflb ljljw ljifoj:t' / k|j[lQaf6 oL sljtfx¿ lgld{t ePsf 5g\ . o; s[ltleqsf sljtfdf kfOg] k|d'v k|j[lQx¿sf] ljZn]if0f o;k|sf/ ul/G5 M $=! 8fo:kf]l/s hLjgsf kL8faf]w / cg'e"ltsf] k|s6Ls/0f M …jfl;ª\u6gsf sfJo;';]nLÚ g]kfnL 8fo:kf]l/s sljx¿sf sljtfx¿sf] ;ª\u|x ePsfn] o; ;ª\u|xsf sljtfx¿df 8fo:kf]l/s hLjgsf kL8faf]w / cg'e"ltsf] k|s6Ls/0f klg k|efjL ¿kdf cfPsf] b]lvG5 . o; qmddf 8fo:kf]l/s hLjgsf ljljw ef]ufO / tL ef]ufOx¿af6 lgM;[t kL8faf]wsf] cleJolQmsf sf/0f sltko sljtfx¿ ;+j]lbt lsl;dsf klg b]lvG5g\ . o:t} kL8faf]w / cg'e"ltsf] k|s6Ls/0f ul/Psf s]xL sljtf+zx¿nfO{ o;k|sf/ b]vfOG5 M
Proof
jfl;ª\u6gsf sfJo ;';]nL M 14
!= clwsf/ ddf 5}g Dofb yKg] s;f] u¿F b;jif{ kl5 kmfN5 t}F xf];\ bf]ifL egL a¿ -xf]dgfy ;'j]bL, ;]t'_ @ slt a:g' of] k/b]zdf of] Dn]R5sf] b]zdf hLjg latfpg] s'/} 5}g . -uf]ljGb lu/L k|]/0ff, kmls{xfN5' b]z_ #_ v} s'lGg s:tf] k/fO{ ;x/ xf] < dg vf]nL Ho"g lg /x/ ef] si6n] vfPF lg hflu/ P xh'/ Û dnfO{ t hflu/ lg hx/ ef] . -k|sfz g]kfn, k/fO{ ;x/_
Proof
pko'{Qm sljtf+zdWo] -!_ df cfk|jf;L hLjg ef]lu/x]sf g]kfnLx¿n] cfgf] Dofb yKg] clwsf/ gePsf] / pgLx¿n] bf]ifL 7x¥ofP/ hf eg]df hfg'kg]{ l:ylt /x]sf s'/f b]vfOPsf] 5 eg] -@_ df hLjg latfpg] s'/f gePsf] of] k/b]z jf Dn]R5sf b]zdf kL8f ef]u]/ a:g] rfxgf gePsf] s'/f k|:t't ul/Psf] 5 . -#_ df dg vf]n]/ afFRg klg /x/ ePsf], k/fO{ ;x/df si6n] hflu/ vfg' k/]sf] / clxn] ToxL hflu/ hx/ ePsf] s'/f k|:t't u/L 8fo:kf]l/s hLjgsf kL8faf]w / cg'e"ltnfO{ k|s6 ul/Psf] 5 . o;}k|sf/ o; ;ª\u|xsf cGo sljtfdf klg of] efj kfOG5 . $=@ PSnf]kg÷la/fgf]kg / ckl/roLs/0fsf] cleJolQm g]kfnL 8fo:kf]l/s sljtfsf] d"n k|j[lQ eg]sf] PSnf]kg÷la/fgf]kg / ckl/roLs/0fsf] cleJolQm xf] / of] k|j[lQ 8fo:kf]l/s g]kfnL sljtfdf ;a}eGbf a9L kfOG5 . o; s[ltleqsf w]/} sljtfdf klg of] k|j[lQ k|efjk"0f{ ¿kdf cleJol~ht ePsf] kfOG5 . o:tf k|j[lQsf sljtfdf cleJoQm of] k|j[lQ cfw'lgs hLjgz}nL afFr]sf] cfhsf dfG5]sf] ljz]iftf klg xf] . o; ;ª\u|xsf sljtfdf cleJol~ht PSnf]kg÷la/fgf]kg of ckl/roLs/0fsf] efjnfO{ k|:t't ug]{ s]xL sljtf+zx¿ o;k|sf/ 5g\ M !_ lbge/ h]nh:tf] sf]7fdf y'lgg' 5 lbge/ ;fgf] gflt x'G5, t/ g]kfnL k6Ss} a'‰b}g jfl;ª\u6gsf sfJo ;';]nL M 15
;fFemdf a'xf/L cfpF5] pm klg g]kfnL xf]Og 5f]/fsf] d'v x]g{ / af]Ng klg Ps xKtf s'g'{kg]{ 7fpF = = =. -j;Gt >]i7, csnaxfb'/ cd]l/sfdf_ @_ d]/f lk|o z'e]R5's hgx¿ Ifdf Û d}n] d]/f efjgfx¿nfO{ laqmL u/]F d}n] d]/f n]Vg] cf}Fnfx¿nfO{ lgjf{;g u/fPF Ifdf, d}n] lgik|of]hg :ki6Ls/0f lbP/ lhpg'nfO{ km]l/ Psk6s dL7f] lgx'F agfPF . -x]dGt >]i7, lgjf{;gsf] s73/fdf_ #_ tl:a/x¿af6 /ª p8\b} uPh:tf] 5 sfuhnfO{ dfpls/fn] vfnfg\ afFsL /xnfg\ s]jn l;;f / k|m]dx¿ dfq s'g} lbg hf]8n] xfjf cfpg] 5 k|m]dx¿ e'OFdf v:g] 5g\ l;;fx¿ em¥ofdem'?d x'g]5g\ . -slkn l;6f}nf, /ª p8\b} uPsf tl:a/x¿_ $_ ckl/lrtsf] eL8df pm ckl/lrt aGof] ldqd08nLsf] ;efdf pm u}/sfg'gL cfk|jf;L aGof] . -j;Gt >]i7, df]/fn]; ufl;{of_
Proof
pko'{Qm tYof°x¿dWo] sljtf+z -!_ df 5f]/f;Fu cd]l/sf uPsf] csn– axfb'/ ;dfVoftfsf dfWodaf6 8fo:kf]l/s hLjgsf] PsfsLkg÷la/fgf]kgsf] hLjg afFlr/x]sf tdfd g]kfnLx¿sf] ef]ufOnfO{ ;fwf/0fLs/0f ul/Psf] 5 . -@_ df ckl/roLs[t :jTj / la/fgf]kgnfO{ ToxfFsf] oflGqs hLjgz}nL;Fu ;dLs/0f u/]/ Jo~hgfTds / k|tLsfTds ¿kdf k|:t't ul/Psf] 5 . cfgf z'e]R5's;dIf cfgf efjgfx¿ laqmL u/]sf] / n]Vg] cf}Fnfx¿nfO{ laqmL u/fPsfdf Ifdf dfUg'n] oxL s'/f k'li6 u/]sf] 5 . -#_ df klg /Ë p8\b} uPsf] tl:a/ / l;;f Pjd\ k|m]ddfq afFsL /xg] s'/f k|:t't u/L cToGt snfTds / k|tLsfTds ¿kdf ckl/roLs/0fnfO{ cleJoQm ul/Psf] 5 . /Ë p8\b} uPsf] tl:a/ oxL la/fgf]kg / ckl/roLs[t g]kfnL dfgjLo cl:dtf xf] . -$_ df kl/lrtsf] eL8df …pmÚ ckl/lrt ag]sf] s'/f b]vfP/ 8fo:kf]l/s hLjgsf] ckl/roLs/0fsf] ef]ufOnfO{ k|:t't ul/Psf] 5 . jfl;ª\u6gsf sfJo ;';]nL M 16
$=# cfTdklxrfg, cl:tTjsf] vf]hL / ljZjf;sf] ;ª\s6sf] cleJolQm M ;dsfnLg g]kfnL 8fo:kf]l/s sljtfdf cfTdklxrfg / cl:tTjsf] vf]hL tyf ljZjf;sf] ;°6 ePsf] efj klg cleJol~ht ePsf] kfOG5 . o; sljtfs[ltleqsf sljtfdf klg of] k|j[lQ ;zQm ag]/ cfPsf] 5 . o:tf] cfTdklxrfgsf], cl:tTjsf] vf]hL / ljZjf;sf] ;°6sf] cleJolQm sxLF :ki6 ¿kdf / sxLF ;f°]lts Pjd\ k|tLsfTds ¿kdf klg cleJoQm ePsf] kfOG5 . cfTdklxrfg, cl:tTjsf] vf]hL / ljZjf;sf] ;°6sf] efjnfO{ cleJol~ht ug]{ s]xL tYof°x¿ o;k|sf/ 5g\M !_ cfFvfnfO{ cfsfzlt/ p7fP/ cfsfzsf] prfO gfKg vf]Hg]x¿ cfgf] prfOsf] ul0ft e'Nb} 5g\ . -gf/fo0f clwsf/L, :vlnt ljrf/_ @_ pgLx¿sf] cl:tTjsf e'Nsfx¿ ;jf{Ë gfËf] lbgsf sf]nfxnx¿df slxn] cb[Zo eP/ slxn] e"ldut eP/== ;a}nfO{ glhs}af6 lgofln/x] . -k|]dk|;fb ;+u|f}nf, o;kfln_ #_ To;}n], eGg'xf];\ tkfO{+ g} ljZjf;sf] vf8n k'l/g'÷ljZjf;sf] r§fg kUng'= = s] ;'vb ;dfrf/ xf] < -af;' >]i7, ljZjf;sf] cefj_
Proof
pko'{Qm sljtf+zx¿dWo] -!_ df cfgf] prfOsf] ul0ft e'n]sf] ;Gbe{ k|:t't u/]/ cfTdklxrfgsf] ;Gbe{nfO{ b]vfOPsf] 5 eg] -@_ df cl:tTjsf e'Nsf lbgsf] sf]nfxndf e"ldut ePsf] s'/f k|:t't ul/Psf] 5 / o;sf dfWodaf6 cl:tTjsf] vf]hL ul/Psf] efj b]vfOPsf] 5 . To:t} -#_ df ljZjf;sf] vf8n k'l/g' / ljZjf;sf] r§fg kUng' h:tf ;Gbe{sf dfWodaf6 cfhsf] dfG5]df ljZjf;sf] ;°6 k}bf ePsf] / dfG5] dfG5]sf aLr cljZjf; ePsf] s'/f k|:t't ul/Psf] 5 . $=$ b]zk|ltsf] lrGtf / /fi6«af]wsf] cleJolQm M :jb]zsf lj;Ëut kl/l:ylt b]v]/ / :jb]zsf] ljv08g b]v]/ /fi6«k|ltsf] lrGtfsf] efj JoQm ul/Psf sljtf / /fi6«af]wL efjgf ePsf jfl;ª\u6gsf sfJo ;';]nL M 17
sljtf klg g]kfnL 8fo:kf]/f sljx¿n] k|z:t n]v]sf 5g\ . o; leqsf sljtf klg o; b[li6n] k|efjk"0f{ b]lvG5g\ . :jb]zdf b]lvPsf] /fhgLlts, ;fdflhs, cfly{s cflb ;ËltxLgtfaf6 g]kfnL 8fo:kf]/f sljx¿df b]lvPsf] lrGtfn] pgLx¿df b]zk|ltsf] cufw :g]x /x]sf] s'/f cleJol~ht x'G5 . o; lsl;dsf] /fi6«af]wL r]tgf b]lvg' g]kfnL 8fo:kf]l/s sljtfsf] ljz]iftf klg xf] . jfl;ª\u6g 8L;Lsf g]kfnL 8fo:kf]/f sljx¿sf sljtfdf kfOg] :jb]zk|ltsf] lrGtf / /fi6«af]wsf] efjnfO{ cleJol~ht ug]{ s]xL tYof°x¿ o;k|sf/ 5g\ M !_ elTsof] b]z of] ;Kk} ‰ofn 9f]sf 9ln ;s] km'6\of] of] w}o{sf] afFw gj gf8L uln ;s] d]/f] /fi6« d'6' d]/f] Pl;ofsf] w/f]x/ dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/ . -uf]kfn /]UdL, dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/_ @_ == = g]kfnLn] /ftf/ft ub\bf/nfO{ klg ub\bLdf k'¥ofpF5 / xf]; cfPkl5 lxglxgfP/ cfg} ta]nLdf v'§f ahf/]/ plk|m/xG5 . -x]dGt >]i7, 3f]8f / dfG5]_ #_ lnnfd r9]sf] 5 d]/f] b]z Unf]an 6]G8/df /flvPsf] 5 d]/f] b]z x]/f}F s;n] t/ dfg]{ xf] d]/f] b]zsf] kfgLdf s;n] xft 8'afpg] xf] d]/f] b]zsf] vfgLdf s;n] kmf]S;f] km'nfpg] xf] d]/f] b]zsf] lr;f] xfjfdf . -slkn l;6f}nf, d]/f] b]z_
Proof
pko'{Qm sljtf+zdWo] -!_ df g]tfx¿n] b]znfO{ ljv08glt/ nu]/ 6'qmØfpg vf]hs ] fdf ulx/f] lrGtf JoQm ul/Psf] efj cleJol~ht 5 eg] -@_ df g]kfnsf] /fhgLlts ;ËltxLgtfaf6 pTkGg lj8Dagf k|:t't ub}{ ;f°]lts ¿kdf /fi6«af]wL r]tgf k|:t't ePsf] b]lvG5 . To:t} -#_ df :jb]zsf] jt{dfg l:ylt x]bf{ g]tfx¿n] b]znfO{ Unf]an 6]G8/df /fv]/ laqmL ug{ yfn]sf] h:tf] b]lvPsf] / ;Qfwf/L ;a}n] b]znfO{ zf]if0f u/]/ cfgf] :jfy{kl" t{ u/]sf x'gfn] jfl;ª\u6gsf sfJo ;';]nL M 18
To;k|lt lrGtf ul/Psf] efj cleJoQm ul/Psf] 5 . of] Psflt/ b]zk|ltsf] lrGtf / rf;f] xf] eg] csf{lt/ /fi6«af]wL r]tgf klg xf] . $=% /fufTds / ;f}Gbo{ r]tgfsf] cleJolQm g]kfnL 8fo:kf]l/s sljtfdf kfOg] csf]{ ;zQm d"n k|j[lQ /fufTds r]tgf / ;f}Gbo{ r]tgf klg xf] . of] k|j[lQ clwsf+z sljtfdf kfOG5 . ;dsfnLg r]tgf eGbf k[ys\ tyf xflb{s kIf;Fu ;Da4 /fufTds sljtfdf k|0fok/stf / cflTdstf kfOG5 . dfgjLo ;f}Gbo{, k|fs[lts ;f}Gbo{ / hLjg–hut\ut ;f}Gbo{sf ljljw cfofdx¿sf] k|:t'ltsf ;fy} xflb{s tyf efjgfTds kIfsf] k|antf x'g' o:tf sljtfsf] d"n ljz]iftf xf] . ;f}Gbo{k|ltsf] cg'/fu / To;sf] ulx/fOsf] laDa ptfl/Psf o; lsl;dsf sljtfdf ;+j]bgfTds kIfsf] k|antf kfOG5 . o; ;ª\u|xsf sljtfdf cleJol~ht /fufTds / ;f}Gbo{ r]tgfnfO{ o;k|sf/ b]vfOG5 M !_ km'Nbf] 56f ;'Gb/ Tof] 5/]/ d':sfg ofFSg] db hf] e/]/ xf] ¿k of] OGb|k'/L k/Lsf] s] gfd xf]nf ej;'Gb/Lsf] . -uf]kfn /]UdL, s] gfd xf]nf ej;'Gb/Lsf]_ @_ cfef Tof] r]tgf a'G5, a'G5 ;+;f/ r]tgf k|]ds} laDadf v'N5 k"0f{ ;+;f/ l;h{gf== l;h{gf O{zsf] ¿k k|]dsf] k|ltdf :jod\ k|]d em°f/df g[To a|Xdf08 /rgf :jod\ . -;'bLkeb| vgfn, emª\sf/_ #_ dfnf ;fOtsf] ;'ulGwt enf] ;f}uft ;jf]{Qd dfnf :jfut /Tg>L z'e ;'wf cfltYo cfe"if0f dfnf xf] pkxf/ k|]d lhtsf] ;Ddfg ;b\efjgf dfnf xf]Og dfq xf/ k"mnsf] cEof; w]/} 5g . -cfgGbk|;fb zdf{, dfnf_ $_ ;f}Gbo{sf] kl/efiffsf] rqmJo"xdf cledGo'em}F km;]/ lha|fgn] s'¿ktfdf klg ;f}Gbo{ cg'e"lt u/] v®ofdn] klg dlb/fsf pu| 5fnx¿df ¿k / hjfgLsf /Ëx¿ e/] . -z/b lg/f]nf, pd/ vøofd, vlnn lha|fg / d_
Proof
jfl;ª\u6gsf sfJo ;';]nL M 19
%_
d glhs 5', t/ 5'g g;s]sf] h:tf] of] /d/d dhf klg x'g ;S5 d a]r}g lyPF bz{gsf nflu== ltg} lyOg\ sljtf s';'d -xf]dgfy ;'j]bL, sljtf s';'d_
pko'Q{ m sljtf+zdWo] -!_ df ej;'Gb/Lsf ¿kdf b]lvPsL slNkt k]|o;Lsf dfWodaf6 ;f}Gbo{k|ltsf] tLj| cg'/fu cleJoQm ul/Psf] 5 eg] -@_ df k|d] nfO{ ;+;f/ a'Gg] r]tgfsf] cfdf, ;+;f/ssf] k"0f{tf, O{Zj/sf] ¿k, em°f/do g[To / a|Xdf08sf] /rgfsf ¿kdf k|:t't u/]/ /fufTds r]tgfsf] tLj|td cleJolQm k|:t't ul/Psf] 5 . -#_ df dfnfnfO{ ax'ljw laDa k|bfg u/L aflx/L ¿kdf xf/ jf cfe"if0fsf ¿kdf /x] klg o;sf] leqL cy{ ;f}Gbo{ /x]sf] s'/f b]vfOPsf] 5 . -$_ df slj vlnn lha|fg / pd/ v®ofdn] klg sljtfsf dfWodaf6 ;f}Gbo{s} pkf;gf u/]sf] s'/f k|:t't ul/Psf] 5 eg] -%_ df Pp6L ;fgL aflnsfnfO{ sljtfsf] laDa k|bfg u/L sljtfnfO{ dfgjLs/0f u/]/ /fufTds ;f}Gbo{ r]tgf cleJoQm ul/Psf] 5 . o;/L /fufTds ;f}Gbo{ r]tgfsf] k|s6Ls/0fsf b[li6n] o; ;ª\u|xsf sljtfx¿ k|efjk"0f{ b]lvG5g\ . $=^ :jb]zsf] o'uLg oyfy{ / /fhgLlts lj;Ëltsf] lrq0fM
Proof
cfk|jf;L g]kfnL sljx¿nfO{ :jb]zsf /fhgLlts, cfly{s, ;fdflhs cflb ljs[lt / lj;Ëltn] klg cfqmfGt kf/]sf 5g\ tL ofjt\ ;ËltxLgtfaf6 ;Ëltsf] rfxgf klg tL sljtfdf cleJoQm ePsf] kfOG5 . :jb]zsf] o'uLg oyfy{ / /fhgLlts ljs[lt tyf lj;Ëltsf] lrq0f ePsf / jt{dfgaf]w cleJoQm ePsf sljtfx¿ klg o;df /x]sf 5g\ . o:tf s]xL k|d'v sljtf+zx¿nfO{ o;k|sf/ b]vfOG5 M !_ b]zsf] /fhgLlt clnslt /fd|f] xf];\ nf]8;]l8ª 36f];\ wf/fdf kfgL em/f];\ ;+ljwfg agf];\, kmls{xfN5' b]z . -uf]ljGb lu/L k|]/0ff, kmls{xfN5' b]z_ @_ xfdL aGb's af]sfpF5f}F s0f{wf/x¿nfO{ clg e§L / uNnLx¿df efF8f demfpF5f}F, afnlbj; dgfpF5f}F / vft] agfpF5f} . -k|sfz g]kfn, km/s xfdLx¿_ jfl;ª\u6gsf sfJo ;';]nL M 20
#_ elgG5 nf]stGq of] pTs[i6 kl/kf6 xf], >Lv08 ;lk|Fb} hfFbf, lau|Fbf Tof] s'sf7 xf] . -uf]kfn /]UdL, dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/_ pko'Q{ m sljtf+zdWo] -!_ df b]zsf] /fhgLlt /fd|f] ePkl5, nf]8;]l8ª 36]kl5, wf/fdf kfgL cfPkl5 / ;+ljwfg ag]kl5 …dÚ ;dfVoftf :jb]z kms{g] s'/f b]vfP/ o'uLg oyfy{nfO{ k|:t't ul/Psf] 5 eg] -@_ df ef]lnsf s0f{wf/nfO{ aGb's af]sfpg] dfcf]jfbL /0fgLltk|lt / afnaflnsfx¿sf] zf]if0fk|lt Joª\Uo ul/Psf] 5 . -#_ df nf]stGq pTs[i6 kl/kf6L eP klg g]kfnsf g]tfx¿n] To;nfO{ lauf/]sf] efj k|:t't ul/Psf] 5 . oL ;a} sljtf+zx¿n] g]kfnsf] b'bz { f / lau|bF f] l:ylt b]vfP/ o'uLg oyfy{ k|:t't u/]sf 5g\ . $=& k|s[lt r]tgf, ;+:s[lt r]tgf / cfbz{ r]tgfsf] k|:t'lt M
Proof
o; leqsf sljtfdf k|s[lt r]tgf, ;+:s[lt r]tgf / cfbz{ r]tgf klg d"n k|j[lQ ag]/ cfPsf] b]lvG5 . o:tf sljtfdf Psflt/ :jb]zsf] k|s[lt / ;+:s[ltsf] dlxdfufg k|:t't ul/Psf] 5 eg] csf]{lt/ cfbz{k/s r]tgf klg cleJoQm ePsf] kfOG5 . o:tf sltko sljtfdf ;"lQmdotf klg kfOG5 . sltko sljtfdf k|s[lt r]tgf / ;+:s[lt r]tgf;Fu hf]l8P/ ;dsfnLg o'ur]tgf klg k|s6 ePsf] kfOG5 . k|s[lt, ;+:s[lt / cfbz{ r]tgf Jol~ht ug]{ s]xL sljtf+zx¿ o;k|sf/ 5g\ M !_ hgan eO af]nL 9fN5 ;fd|fHo ;Qf holjho p;}sf] af]N5 hf] ;To lgTo clxts/ ljiffn' jfSo tLtf tdfd k|sl6t ha x'G5g\ x'Gg cfgf] cwLg . -cfgGbk|;fb zdf{, af]nL_ @_ /ËLg km"n jf;gf dL7f] hudf 5/]/ hLjg aGYof] pbfpFbf] 3fd cfgGb e/]/ -k|]d ;+u|f}nf, zLtsfnLg a'9f] ¿v_ #_ sn° bDe, 8'ª\8'ªL s/fn Tof] gkm}lnof];\ ljzfn efn j}ejL ;'sLlt{ Tof] gj}lnof];\ k|zfGt efjgf v'nf];\ / k|]d/fu km}lnof];\ / :jTjsf] lrgf] Wjhf s;}u/L gd}lnof];\ -;'bLkeb| vgfn, la5§ ef]/df w/f k|R5Gg ¿k e]l6of];\_ jfl;ª\u6gsf sfJo ;';]nL M 21
$_
e}nf], Bf};L cem 3/3/} ofbdf lgTo v]N5' 3fF6" /Gsf] cem 5 dgdf uLt vf]h]/ ;'G5' sf}/f ;DemL h'?h'? u/L gfr"Fgfr"F d x'G5' la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ . -;'bLkeb| vgfn, d s;/L k"0f{ ;+;f/ u5'{_ %_ k'/fgf ;+:s[ltnfO{ cFufNg ;s]gf}F k|lta4 geP/ xf]nf xfdL kl5 k/]sf 5f}F lklNkn] /fli6«otfsf] Hof]tLdf afFlr/x]sf 5f}F -xl/ l3ld/], kl/0flt_
pko'{Qm sljtf+zx¿dWo] -!_ df /fd|f] af]n, dL7f] af]n eGg] cfbz{ r]tgf k|:t't u/L Psk6s tLtf] jfSo d'vaf6 lgl:s;s]kl5 Tof] cfgf] cwLgdf g/xg] s'/f k|:t't ul/Psf] 5 eg] -@_ df j;Gt Ct'sf] jf;GtL ;f}Gbo{sf] dlxdfsf dfWodaf6 k|s[lt r]tgf JoQm ul/Psf] 5 . To:t} -#_ df dfG5]leqsf sn° / bDe x6]/ j}ej, ;'sLlt{, zflGt, ;'efjgf, k|]d / :jTjsf] Wjhf km}lnof];\ eGg] cfzfjfbL cfbz{ b[li6 k|:t't ul/Psf] 5 eg] -$_ df k|jf;df /x]/ klg ;f+:s[lts kj{ / uLt g[To;Fu slj v]n]sf] / tbfsf/ ePsf] efj k|:t't u/L ;f+:s[lts r]tgf cleJoQm ul/Psf] 5 eg] -%_ df k'/fgf ;f+:s[lts k/Dk/fnfO{ cFufNg g;Sbf g]kfnLx¿ kl5 k/]sf] / ;+:s[lt ;+/If0fsf cefjdf /fli6«otf klg sdhf]/ x'g] s'/f k|:t't ul/Psf] 5 . o;k|sf/ pko'{Qm sljtf+zx¿n] k|s[lt r]tgf, ;+:s[lt r]tgf / cfbz{ r]tgf k|:t't u/L cfzfjfbL hLjgb[li6 ;d]t cleJoQm u/]sf 5g\ . $=* k|ljlw ;+:s[ltsf] k|of]u / oflGqs hLjgz}nLsf] lrq0f
Proof
o; leqsf sljtfx¿ cGtj{:t'sf b[li6n] ljljwtfdo 5g\ . pQ/cfw'lgstfjfbL k|j[lQaf6 klg tL ;Dk[Qm b]lvG5g\ . o;} qmddf o; ;ª\u|xsf sljtfdf Psflt/ k|ljlw ;+:s[ltsf] k|efj / k|of]u b]lvG5 eg] csf{lt/ ;xl/of hLjgsf / 8fo:kf]l/s hLjgz}nL afFr]sf dfG5]sf] hLjg oGqjt\ ePsf] ;Gbe{ klg k|:t't ul/Psf] 5 . k|ljlw ;+:s[lt / oflGqs hLjgz}nLsf] lrq0f ul/Psf s]xL sljtf+z o;k|sf/ 5g\M !_ km];a'sdf cfgf kmf]6fx¿nfO{ cknf]8 ub{5' To;}sf dfkm{t ;of}F;Fu uDeL/ Rof6 ub{5' jfl;ª\u6gsf sfJo ;';]nL M 22
sd;]sd lbgsf] b'O{ 306f df]afOdf af]Nb5' To;sf ;fy} Ps b'O{ 306f 6]S:6 d];]h k7fpF5' . -8f) df]xgk|;fb hf]zL, dnfO{ t xfF;} p7\5_ @_ ;do st} km'lTsPnf ls eg]/ xftdf, 3fF6Ldf, oGq em'G8ØfP/ 6fF;]/ hLjg rnfO/x]sf x'G5g\ . -af;' >]i7, Oltxf;df afFRg rfxg]x¿_ #_ d]/f] cfpg] k':tfnfO{ atfpg] s'g} Oltxf; 5}g t/ d pgLx¿nfO{ cjZo atfpg] 5' d]/f] h:tf] z"Go hLjg ltdLx¿n] afFRg' kg]{5}g . -xl/ l3ld/], ctL{_
Proof
pko'{Qm sljtf+zdWo] -!_ df cfhsf] dfG5] km];a's, Od]n OG6/g]6 Rof6 / cGo k|ljlw ;+:s[lt;Fu hLjg ;fl6/x]sf] s'/f b]vfOPsf] 5 eg] -@_ df xft, 3fF6L / oGqdf ;do 6fF;]/ lxF8\g] cfhsf dfG5]sf] oflGqs hLjgz}nLnfO{ k|:t't ul/Psf] 5 . To:t} -#_ df cfhsf] dfG5] / cem To;df klg 8fo:kf]l/s dfG5]n] cfgf] h:tf] z"Go / oflGqs hLjg cfpFbf] k':tfnfO{ x:tfGt/0f gug]{ clek|fo k|s6 ul/Psf] efj cleJoQm ul/Psf] 5 . o;/L cfhsf dfG5]sf] k|ljlw ;+:s[lt;Fusf] ;fdLKo / oflGqs hLjgz}nLnfO{ oL sljtf+zx¿n] Jol~ht u/]sf 5g\ .
%= lgisif{ ;dsfnLg g]kfnL d"n k|jfxsf sljtfsf] ;dli6 / ;ª\s'n j[Qaf6 8fo:kf]l/s g]kfnL sljtf;d]t cufl8 a9]sf] 5 . sltko cGtj{:t' / k|j[lQsf b[li6n] ;dsfnLg d"n k|jfxsf g]kfnL sljtf / g]kfnL 8fo:kf]l/s d"nk|jfxdf ;dfgtf kfOG5 eg] 8fo:kf]l/s ef]ufO / cg'e"ltsf] k|s6Ls/0fdf eg] 8fo:kf]l/s g]kfnL sljtfdf k[ys\tf;d]t b]lvG5 . 8fo:kf]l/s r]tgf pQ/cfw'lgstfjfbL ax'njfbL k|j[lQ ePsfn] / ;dsfnLg g]kfnL sljtfsf] d"n k|j[lQleq 8fo:kf]l/s k|j[lQ klg kg]{ ePsfn] 8fo:kf]l/s g]kfnL sljtfnfO{ ;dsfnLg g]kfnL sljtfsf] d"nk|jfxaf6 k[ys\ ug{ ldNb}g . o;} ;Gbe{df k|sflzt o; …jfl;ª\u6gsf sfJo;';]nLÚ gfds sljtf– ;ª\u|xleqsf ;a} sljtfx¿ 8fo:kf]l/s r]tgfsf /fd|f sljtf dflgG5g\ . s]xL sljtf snfTds b[li6n] b'a{n 5g\ . s]xL zf:qLo 5Gbsf sljtfdf jfl;ª\u6gsf sfJo ;';]nL M 23
5Gbf]eË;d]t 5 tfklg cGtj{:t'sf b[li6n] tL sljtf /fd|} b]lvG5g\ . jfl;ª\u6g 8L;Ldf /x]sf g]kfnL sljx¿sf] o; ;ª\u|xleqsf w]/} sljtfn] ;dsfnLg g]kfnL 8fo:kf]l/s sljtfdf k|ltlglwTj ug]{ Ifdtf /fV5g\ . of] o; s[ltsf] k|flKt xf] . ljZj sljtf lbj; @! dfr{, @)!@
lqe'jg ljZjljBfno g]kfnL s]Gb|Lo ljefu sLlt{k'/, sf7df8f}F gautamlaxman@yahoo.com
Proof
jfl;ª\u6gsf sfJo ;';]nL M 24
cfgGbk|;fb zdf{ •• af]nL •• kxf8 •• dfnf •• slj / sljtf
Proof
hGd M @)@! df3 !, /fd]5fk xfn M g]kfnL b"tfjf; jfl;ª\u6gdf ;]jf/t Od]n M ananda@nepalembassyusa.org zdf{ k];fn] g]kfn ;/sf/sf] s"6g}lts ;]jfdf ;+nUg x'g'x'G5 . pxfFdf xfO:s'n k9\bfb]lv g} sljtfk|lt ulx/f] ?lr hfu]sf] yfxf kfOG5, t/ vf; sljtf n]vgsf] ;'?jft eg] cd]l/sf k'u]kl5 g} ePsf] b]lvG5 . pxfF sljtfsf pkf;s t x'g'x'G5, t/ To;sf] pkf;gf ;w}F ul//xg kfpg' x'Gg . pxfFsf sljtf nf]snofTds / 5Gbf]a4 x'G5g\. pxfF cfgf efj / ljrf/nfO{ nofTds 9Ëdf JoQm ug{ ;Sg'x'G5 . oxL ;fdYo{n] pxfFsf sljtf kf7ssf] dg 5'g] ePsf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 25
af]nL duh x[bo kmf]S;f] cf]7 lha|f] unfsf] rn s;/taf6} aG5 af]nL snf xf] k|d'v 5 lrh af]nL efjgf JoQm x'G5 dg'h u'0f o;}n] hLj pTs[i6 aG5 . cjt/0f xjfdf WjgLsf] ¿kaf6 d'v eO{ ha af]nL k'U5 >f]tf ;dLk tj kl/ro cfkm} lbG5 :ki6 kf/L tg dg an cfo' a'l4 ;f/f v'nfO{ .
Proof
syg jrgleq} ¿k :j¿k v'N5 . lgot zs'g ;f/f af]nLdf k|:6 x'G5 . k|an u0fs af]nL of]Uotf Ifdtfsf] k|yd ;"rs of] xf] ;+:s[lt ;Eotfsf] . lxF8 8'n 5 xjfdf sf]xL ;Qm}g b]Vg g t sxLF ;lsPnf lk6\g kqm]/ /fVg t/ klg alnof] of] lr5{ 5ftL sn]hf] n8 le8 sn s':tL o;af6} x'g] xf] .
sxLF t dnd k§L cf}ifwL /fdaf0f sxLF eO{ ;/L uf]nL af]nLn] lnG5 Hofg gj /; ;a vf]nL cfF;' xfF;f] sxLF t sxLF cj;/ /fd|f af]nLn] lbG5 Kof/ . jfl;ª\u6gsf sfJo ;';]nL M 26
jrg /; ePsf :jflbnf zAbleq ub u/n ljifflb 5g\ ls cd[t dGq jbg ;tx dfly efjgf cGt/Ë ;xh k|s6 x'G5g\ laDaWjlg t/Ë . hgan eO{ af]nL 9fN5 ;fd|fHo ;Qf ho ljho p;}sf] af]N5 hf] ;To lgTo clxts/ ljiffn' jfSo tLtf tdfd k|sl6t ha x'G5g\ x'Gg cfgf] cwLg .
Proof
d[b' jrg pHofnf] k"l0f{dfsf] k|sfz zLtn zdg af8L wtL{df u5{ /fh qm"/ jrg cFWof/f] cf}F;Lsf] /ft qf; k|b"if0f ljif 5b}{ u5{ cfg} ljgfz .
lxts/ lk|o af]nL zlQm xf] Oi6ldq hut jz u/fO{ nf]sdf zflGt 55{ snx lh/x gf;L ljZj aGw'Tj a9\5 sn'lift ljif>fk aG5 cd[t dGq .
jfl;ª\u6gsf sfJo ;';]nL M 27
kxf8 8fF8f eGHofª a]F;L au/ gbgbL gfua]nL 3'd]sf . cUnf xf]rf l7s}sf km/s z/L/sf z[Ìnf z}ndfnf .. b[Zo o:tf xhf/f}F dg dw'/;df /D5 r'n'{Dd 8'A5 . wtL{df :ju{ eGg] :yn olb 5 eg] of] 5 xfd|f] kxf8 .. df6f] lblG5g\ oxLFsf] kmn ando cf}ifwL cGgkfgL . o} xfjfn] agfO{ hLjg /;do k'mN5 ;fFRrf] hafgL .. k[YjLsf] afuafgL ljljw ¿k 56f hLjhGt' xhf/ . wtL{df :ju{ eGg] :yn olb 5 eg] of] 5 xfd|f] kxf8 ..
Proof
a:y] oxLF tk:of Clifd'lg plxn] 1fg pBfgdfg . s0ff{nL zKtsf];L c6'6 gbgbL o;leq} d'xfg .. k[YjLsf] lz/ o} xf] gu/ 5 lzjsf] ;Eotfsf] l;/fg . wtL{df :ju{ eGg] :yn olb 5 eg] z}n xf] oxL hfg .. dfG5]sf rfn r]i6f ;/nkg enf 5}g st'{t kfk . d}q]o efj dL7f] jrg ;'dw'/f] efjgf lgisn° .. x]bf{ :j¿kaf6} 5n/lxt 56f :jtM 5n{ª\ª x'G5 . wtL{df :ju{ eGg] :yn olb 5 eg] of] 5 xfd|f] kxf8 .. ;ª\nf] tfhf lxdfgL hn / kjgdf b"/ 5g\ /f]u Jofw . ToxLsf] 3fd5fof rng hLjg oL ;Demgfo'Qm lk|o .. ofqf ;+;f/af6} k|ltlbg 5 log} x]g{ b[Zo xd];f . wtL{df :ju{ x]g]{ /x/ olb eP x]g{ hfpm kxf8 .. jfl;ª\u6gsf sfJo ;';]nL M 28
dfnf dfnf aGb5 k'ik kq nltsf wfuf] l;of]df pgL zf]ef a9\5 unf k'/} z/L/sf] h:n] nufP klg dfnf z'4 ljlzi6 ck{0f ;a} ;Tsd{df wd{df w]/} 5g\ o;leq cy{ dlxdf n]Vb} 5' ;ª\If]kdf . dfnf dfnf dfnf dfnf
;fOtsf] ;'ulGwt enf] ;f}uft ;jf]{Qd :jfut/Tg>L z'e ;'wf cfltYo cfe"if0f xf] pkxf/ k|]d lhtsf] ;Ddfg ;b\efjgf xf]Og dfq xf/ km"nsf] cEof; w]/} 5g .
Proof
k"/} hLjgsf] jw" / j/sf]] ;DaGwsf] aGwg ;fIfL nf]s, ;dfh ;+:s[lt ;a} x'G5g\ oxLF c°g kf/:kl/s ;fj{ef}d xssf] ;lGw ;lx5fk xf] dfnf xf]Og dfq xf/ km"nsf] ljZjf;sf] ef/ xf] . g]tfhLk|lt pRr dfgkbsf]] ;Ddfgsf] Bf]ts lhDd]jf/L ;lxt k"0f{ dtsf] ljZjf;sf] lnvt b:tfj]h v'nf c7f]6 kbsf] st{Jo :jLsf/ xf] dfnf xf]Og dfq xf/ km"nsf] bfloTjsf] ef/ xf] . d[To'df z'ehGd sd{x¿df k'ikf~hnL ck{0f ug]{ ;+:s[lt ljBdfg 5 ;a} ;+;f/sf wd{df of] rf]vf] pkxf/ :jfut labfO{df / ;Ddfgdf dfnf Ps 5 cy{ sfd dlxdf w]/} y/L x'G5g\ . jfl;ª\u6gsf sfJo ;';]nL M 29
a]jf:tf pkof]udf x'guP ljZjf;df 3ft xf] dfnf dfq g;Dem wf/0f u/L of] k"mnsf] xf/ xf] dfnf xf]Og dfq ¿k /l;nf zf]efk|ef k:sg] dfnfsf] dlxdf / cy{ ga'emL lg:;f/ xf] k}/g] . /fvL OHht km"nsf] / s'nsf] cfbz{ cfltYosf] /fvL cfb/ Kof/ dfg dgsf] ;b\efj ljZjf;sf] oL oyfy{ s'/f / sfd dlxdf a'em\b} ;xL sf/0f Dffnfsf] pkof]u OHht u/f}F hf] ub{5f}F wf/0f .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 30
slj / sljtf slj afbn xf] sljtf kfgL ;\'vsL b'MvsL ;FlugL /fgL dgdlGb/df sljtf gfgL gedf ejdf axg] kfgL . sljtf dgdf gedf kfgL algg] axg] logsf] afgL z'e ;fOtdf logsf] hGd hlxn] tlxn] clxn] x'Gg .
Proof
slj afbn xf] sljtf kfgL sljtf /; -vlgh_ xf] slj xf] vfgL /; Tof] lemsbf ylkFb} hfg] slj xf] o;/L a9\g] vfgL . sljtf /zgf -ls/0f_ slj xf] bLk rlDsnf] /zdL alnof] tfk wldnf] cldnf] td of] tf]8L slj hLjg afNb5 aQLem}{F . slj slj slj slj slj
nf]rg x'g\ sljtf b[li6 x'g\ hggL sljtf ;[li6 dfgj xf] sljtf wd{ hLjg xf] sljtf dd{ . of}jg xf] sljtf k|]d jfl;ª\u6gsf sfJo ;';]nL M 31
slj b]x eP sljtf cfTdf slj zAbno sljtf efj hlt k|d] u¥of] ulx/f] /fu slj ;fu/ xf] sljtf kfgL 5 Ogf/;/L /l;nf] vfgL hlt vr{ u¥of] j;'bf -pbf/_ bfgL sljtf hnlw el/nL 1fgL . slj xf] ;do sljtf P]gf hghLjgsf] l:ylt Tof] x]g{ cl3sf] ;do o;n] af]N5 casf] kl5sf] ljifo vf]N5 .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 32
slkn l;6f}nf •• d]/f] b]z •• /ª p8\b} uPsf tl:a/x¿ •• ltdL slt lgb{oL •• p7 s'Des0f{ p7
Proof
hGd M ebf} !^, @))@, cf7/fO{ r'xfg8fF8f, t]x|y'd xfn M d]l/NofG8, cd]l/sf Od]n M kapil2002bs@yahoo.com dfgljsLdf :gfts u/]sf l;6f}nfn] lj=;+= @)#) b]lv g} sljtf n]Vg yfn]sf] b]lvG5 . g]kfnsf] jt{dfg /fhgLlts ljs[lt / lj;Ëltk|lt tLj| Joª\Uo k|xf/ ug{ ;Sg] l;6f}nfsf sljtfsf] s]Gb| b]zk|]d /x]sf] b]lvG5 . pgsf sljtfsf] cleJolQm kIf ;zQm / cfsif{s 5 . pgsf sljtfn] h:tf;'s} kf7snfO{ klg tfGg ;S5g\ . Åbo ;+j]Btf g} pxfFsf sljtfsf] zlQm xf] . jfl;ª\u6gsf sfJo ;';]nL M 33
d]/f] b]z d]/f] d]/f] d]/f] b]z
b]z 5 b]zsf] gfd 5 b]zsf] l;dfgf klg 5 x'g gfd / l;dfgf rflxG5 ..!..
d]/f] b]z;Fu ;"o{ rGb| clg tf/fd08n 5 cfg} hldg 5 cfg} cfsfz 5 5 j6} Ct'x¿ 5g\ clt ;'Gb/ 5 d]/f] b]z ..@..
Proof
xhf/f}F jif{sf] cf/f]x cj/f]xsf] ufyfdo ljut 5 dfs'/fsf] hfnf]df h]lnPsf] lemFufsf] h:tf] jt{dfg 5 eljio s:n] kf] b]V5 / Û s'/} gu/f}F ..#..
afx'ann] hf]ufPsf] /ut kl;gfn] l;l~rt df6f]df km'n]sf u'/fF; nfn'kft] / ;okqL km"nx¿ lxdfnsf km]bLdf pld|Psf of;f{u'Daf, h6fd;L, kfFrf}Fn], vfgSkf, a'9Lcf]Qmf], x6\r'/ ;~hLjgL h:tf hl8a'6Lx¿ 3fdnfO{ :jfut / labfO{ ug]{ lxdr'r'/fx¿ jfl;ª\u6gsf sfJo ;';]nL M 34
dgdf]xs em/gf, vf]nf, gbgbL, tfntn}ofx¿ 8fFkm], d'gfn, sf]OnL, do"/ zflGtb"t k/]jfx¿ Psl;Ë] u}F8f, afx|l;Ë] h/fof] 3f]/n, emf/n, af3, efn', xfQL, ag]n gfRg] n]sa]F;Lsf hËnx¿ dlGb/ dl:hb luhf{, u'Daf, u'?åf/fx¿ ;a} ;a} s;}n] b[li6aGwsLdf t s;}n] ef]uaGwsLdf lnPsf 5g\ ..$..
Proof
lnnfddf r9]sf] 5 d]/f] b]z Unf]an 6]G8/df /flvPsf] 5 d]/f] b]z x]/f}F s;n] t/ dfg]{ xf] d]/f] b]zsf] kfgLdf s;n] xft 8'afpg] xf] d]/f] b]zsf] vfgLdf s;n] kmf]S;f] km'nfpg] xf] d]/f] b]zsf] lr;f] xfjfdf s;n] ljhosf] ´G8f kmx/fpg] xf] d]/f] b]zsf] ;u/dfyfdf s;sf] ;flns pleg] xf] d]rL / dxfsfnLsf] au/df ..%.. e'OFrfnf] cfPkl5 k'/fgf ;flns 9Nbf /x]5g\ e'\OFrfnf]kl5 gofF ;flns aGbf /x]5g\ csf]{ e'OFrfnf] cfpF5 km]l/ 9N5g\ ;flns km]l/ aG5g\ km]l/ 9N5g\, km]l/ aG5g\ km]l/ 9N5g\ of] d]/f] b]zn] ef]Ub} cfPsf] lgolt xf] ..^.. d t vfln d"ltsf{/ dfq g x'F gofF gofF ;flns s'Fb]/ cfgf] u'hf/f ul//x]5' cr]n gofF g]kfnsf] gf/f v'a} u'lGhPsf] 5 jfl;ª\u6gsf sfJo ;';]nL M 35
ToxL gf/f ;'Gb} cfkmg} 6\jfs6\jfs] / l5gf]n] 7"nf] 5k8 9'Ëfdf gofF g]kfnsf] ;flns s'Flb/x]sf] 5' kl5 d]/f ;Gtfg b/;Gtfgn] oxL 9'Ëfdf s'FlbPsf] eP klg cfgf k'vf{sf] b]z o:tf] /x]5 eg]/ b]Vnfg\ / zf]wkq n]v]/ g]kfn /fi6«sf] Oltxf;df ljBfjfl/lw u/]/ kZrftfk ldl>t ;Gtf]ifsf] nfdf] ;f; km]nf{g\ ..&..
Proof
jfl;ª\u6gsf sfJo ;';]nL M 36
/ª p8\b} uPsf tl:a/x¿ leQfdf ;hfOPsf ltd|f cf:yfsf dxfg\ g]tfsf 7"nf 7"nf tl:a/sf d'xf/x¿ ;w}F Ps}gf;sf b]lvGgg\\ slxn] xfF;]h:tf, slxn] l/;fPh:tf slxn] uDeL/ d'b|fdf slxn] pbf; pbf; t slxn] Psbd} lg/fz lg/fzh:tf lau't emfg]{ dx r'xfpg] b}jLzlQm 5}g tL tl:a/x¿df s]jn cf:yf, ljZjf;, cfbz{, lgi7f, g}ltstf / OdfGbfl/tfsf k|tLs x'g\ tL tl:a/sf cg'xf/x¿
Proof
t/ nfU5 tL tl:a/x¿nfO{ x]g]{ ltd|f cfFvfdf km'nf] kb}{ uPh:tf] 5 ltd|f] cf:yf r/d/fpg yfn]h:tf] 5 . ljZjf; 8udufpg nfu]h:tf] 5 cfbz{ s] xf] < lal;{ g} ;Sof} g}ltstf t stf stf uf]Ko sGt'/df ef]6]tfNrf nufP/ aGb u/]5f} OdfGbfl/tf klg RofltP/ w'hf w'hf eP5 To;}n] xf]nf M tl:a/x¿af6 /ª p8\b} uPh:tf] 5 jfl;ª\u6gsf sfJo ;';]nL M 37
sfuhnfO{ dfpls/fn] vfnfg\ afFsL /xnfg\ s]jn l;;f / k|m]dx¿ dfq s'g} lbg hf]8n] xfjf cfpg]5 k|m]dx¿ e'OFdf v:g]5g\ l;;fx¿ em¥ofdem'?d x'g]5g\ afFsL /xG5g\ k|m]dsf efFlrPsf 6'qmfx¿ cj;fg x'g]5 cf:yfsf dxfg\ tl:a/x¿sf]
Proof
jfl;ª\u6gsf sfJo ;';]nL M 38
ltdL slt lgb{oL ltdL slt lgb{oL xF Û lr;f] kfgL, tftf] 3fd / zLtn xfjf hgd b]lvsf d]/f ;fyL lyP a;f}{F jif{b]lv pgLx¿sf] ;fy kfP/ d x'ls{Psf] lyPF t/ d ltd|f nflu sfl6PF 6'qmf 6'qmf kfl/PF ltd|f] qm"/tf a9\b} uof] cfuf] nufP/ bgbgL afNof} d an]F ltd|f nflu dnfO{ cfuf]n] 89fof] t/ kf]n]g ddf k/f]ksf/sf] efjgf lyof] .
Proof
ltdLnfO{ Gofgf] ePsf] cg'ej dnfO{ x'GYof] / ;Gtf]if nfUYof] ltdLnfO{ cl3 a9L kf]Nof] ls eG7fg]/ clns sd aNg nfu]sf] lyPF kmnfdsf] nf}/f]n] aln/x]sf] dnfO{ 3f]r]/ km]l/ cfgf] qm"/tf b]vfof} af]/fdf aGb u/]/ cf/gdf k'¥ofof} km]l/ cfuf] nufof} / kmnfd ttfof} clg d]/f] csf]{ efOnfO{ sf6\g] aGr/f] / lrg]{ cf/f agfof} .
jfl;ª\u6gsf sfJo ;';]nL M 39
p7 s'Des0f{ p7 p7 s'Des0f{ p7 ;'Tg';Dd ;'Tof} ca Ao"Fem afFb/n] ltd|f] ;'Gb/ czf]sjfl6sf tx;gx; kf¥of] ;f/f n°f hnfof] ;Ltfsf] va/ /fdsxfF k'¥ofof] ltd|f] ;'gsf] n°fdf /fdn] wfjf af]Nof] ;a} axfb'/x¿n] /fj0fsf] g'gsf] ;f]emf] ul/;s] OGb|lhtn] 7"n} k/fqmd b]vfP/ lktfhLsf] l/g r'Qmf u/]/ labf eof] s'nËf/ /x]5 ljeLif0f zq'nfO{ c°dfn u¥of]
Proof
p7 p7 l56f] p7 ltd|} cf; afFsL 5 ca /fj0fnfO{ ltdLnfO{ yfxf 5}g t/ ltd|f bfh'nfO{ yfxf 5 ltdL klg dfl/G5f} / p klg dfl/g]5 t/ klg ltdLn] n8fOF t n8\g} k5{ Ao"Fem l56f] Ao"Fem ;'t]/ afFRg' t dg'{ xf] n8]/ dg'{ g} afFRg' xf] jfl;ª\u6gsf sfJo ;';]nL M 40
/fdsf] dfq Oltxf; n]lvGg /fj0fsf] klg Oltxf; n]lvG5 Oltxf; /fd elQmsf] dfq n]lvGg /fj0f elQmsf] klg n]lvG5 Ao"Fem s'Des0f{ ca Ao"Fem ;'Tg' ;'Tof} ca p7 hfu hfu ca hfu ..
Proof
jfl;ª\u6gsf sfJo ;';]nL M 41
Proof
jfl;ª\u6gsf sfJo ;';]nL M 42
uf]kfn /]UdL •• e]n]G6}g lbj;sf] pknIodf gj k|]dLx¿nfO{ •• d]/f] h"g •• s] gfd xf]nf ej ;'Gb/Lsf] •• dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/
Proof hGd:yn M k'nfrf}/, DofUbL xfn M elh{lgof, cd]l/sf Od]n M saroj.gopal@gmail.com /]UdL ljåfg\ ;flxTosf/ x'g'x'G5 . pxfFn] hg;ª\Vofzf:q, cfof]hgf Joj:yfkg / cy{zf:q u/L tLg ljifodf :gftsf]Q/ ug'{ ePsf] 5 . pxfFsf ljleGg cGt/f{li6«o hg{ndf cg';GwfgfTds n]v / sfo{kq k|sflzt 5g\ . pxfF Ps cToGt sf]dn Åbosf slj klg x'g'x'G5 . pxfF ljz]if u/L sljtfnfO{ g} a9L k|]d ug'{x'G5 . oxL k|]dn] pxfFnfO{ cg];f;sf] s]Gb|Lo sfo{;ldltsf] pkfWoIf / ;lrj agfof] . cfhLjg ;b:o agfof] . sljtf k|]ddf cfs07 8'a]sf /]UdLsf sljtf /f]dfgL efjn] el/Psf 5g\ . pxfFsf sljtfn] kf7snfO{ k|]dsf] lgtfGt gjLg b'lgofFdf k'¥ofpF5g\ . oxL zlQm / ;fdYo{n] ubf{ pxfFsf sljtf ;'Gb/ ePsf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 43
e]n]G6}g lbj;sf] pknIodf gj k|]dLx¿nfO{ b'O{ d'6'nfO{ Pp6f kf/L hf]8\g] tGt' dfof hf]8]kl5 yfxf gxf];\ ;Ldf bfofF afofF .. …d]/f]Ú …ltd|f]Ú eGg] x'Gg xfd|f] ;'? x'G5 k|]o;Lsf] cfFvf b'Vbf lk|otd ?G5 .. ljZjf;sf] dxnleq dfof hudufpF5 ljZjf; 9n] dfofn'sf] ;+;f/ 8udufpF5 dfofleq :jfy{ k;] ljif emg\ knfpF5 d'emf{pF5 rf]vf] dfof d'6' vNanfpF5
Proof
sdn\ h:tf nfUg] cfFvf tL/ h:t} bfU5g\ ;ª\uLt h:tf nfUg] efvf emL/ h:t} nfU5g\ a}/L xf]Og ghftL Tof] j}/Tj xf] w/fk a]OdfgL dfof xf]Og dfofn' xf] v/fa ;fFrf] dfof cd"No 5 gagfP ;:tf] e]n]G6}Gsf] lbg} e]6L ckgfP h:tf] dfof hfg] sb/ u/] ;ª\nf] kfgL h:tf] aUbf :jfyL{ gfnLleq uGbf kfgL h:tf] jf;gfsf] sfdgfnfO{ k/ kG5fP/ zLtn\ dGn] ljrf/ u/L /fd|f] 7DofP/ nfpFbf dfof lr/ x'G5 h'gL h'gL;Dd cfsfzdf ;"o{ rGb| /lx/x];Dd .. jfl;ª\u6gsf sfJo ;';]nL M 44
d]/f] h"g s[i0f kIfsf] cf]/fnf];Fu} 36\b} lg/fzfsf] cfFwL;Fu n8\b} ps';d's';, d]/f] h"g ;'if'Kt ljZjf;sf] lbof]— …rfFbLsf] 3]/fÚ a]/]/ a;]sf] 5, pHofnf lbgsf]] af6f] x]/]/ a;]sf] 5 .
Proof
;Dk"0f{ kftn] Tofu]kl5 jf;GtL laxfgLsf] k|tLIffdf cfgf u'efx¿df k|f0f–kv]?sf] /Iff ub}{, cw{–r]t, z[Ëf/ ljd'v lzlz/sf ¿vh:t}, z'Sn kIfsf] k|tLIffdf d]/f] h"g dfgf}F, Pp6f tkf]Wofgdf a;]sf] .
bzdLsf] psfnf] kf/ u/]kl5 ha d]/f] h"gsf] k|ef 5fpg]5, km]l/ dfG5], :ofn, lu4x¿ /dfpFb} d]/f] h"gs} uLt ufpg cfpg]5g\ dWo j;Gtdf km"n} km"ndf em'n]sf, r]/Lsf af]6 jl/kl/ /f]dfG;]nLx¿sf] le8 nfu];/L, jfl;ª\u6gsf sfJo ;';]nL M 45
hf8fdf aNbf] cfufsf] jl/kl/ tdf;], tfKg]x¿sf] tfFtL;/L km]l/ dfG5], :ofn, lu4x¿ d]/f] h"g;Fu} k|Lt nfpg cfpg]5g\ s[i0f kIfdf kmut PSnf], d]/f] h"g z'Sn kIfsf] :d[ltdf afFR5, ha cfpF5 z'Sn kIf, d]/f] h"g;Fu} ;f/f ;+;f/ xfF:5 .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 46
s] gfd xf]nf ej ;'Gb/Lsf] km"Nbf] 56f ;'Gb/ Tof] 5/]/ d':sfg ofFSg] db hf] e/]/ xf] ¿k of] OGb|k'/L k/Lsf] < s] gfd xf]nf ej ;'Gb/Lsf] ..
Proof
cfXjfg dL7f] k|0foL 5 efj z[Ëf/sf] /fu 5/L k|efj tf]8\5Øf} tkf]Wofg Clif w/Lsf] s] gfd xf]nf ej ;'Gb/Lsf] .. xf] of] s6fIfL cg'/fu s:tf] ;Ddf]xgL km"n k/fu h:tf] gfgf cn°f/ dl0f w/Lsf] s] gfd xf]nf ej ;'Gb/Lsf] .. nfnL cwsf]{ /ut} ;/Lsf] of xf] ls Kofnf /;–dfw'/Lsf] Kof/L s'df/L hnsL k/Lsf] s] gfd xf]nf ej ;'Gb/Lsf] ..
jfl;ª\u6gsf sfJo ;';]nL M 47
cfFvf abfdL 3g s]z /flz d':sfg dL7f] cw/} 5 Kof;L cfsfz kf] xf} ls kl5 em/Lsf] s] gfd xf]nf ej ;'Gb/Lsf] .. lxF8\bf 5 rfn xl/0f} ;/Lsf] dL7f] 5 ;'uGw jl/kl/ hf] jf0fL 5 dfw'o{ 3'n] ;/Lsf] s] gfd xf]nf ej ;'Gb/Lsf] ..
Proof
jfl;ª\u6gsf sfJo ;';]nL M 48
dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/ elTsof] b]z of] ;Kk} ‰ofn 9f]sf 9ln ;s] km'6Øf] of] w}o{sf] afFw gj gf8L uln ;s] d]/f] /fi6« d'6' d]/f] Pl;ofsf] w/f]x/ dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/ .. of}6f /dfOnf] ;fgf] zfGt b]z lr/Lsg du|fGtL, lnDa'jfg\, g]jf, dw];\ s]–s] egLsg RofTg] /fi6« egL ;'Gbf cfTdf ?G5 w/ w/ dfl;G5 ls st} /fi6« nfU5 lrGtf a/f]a/ ..
Proof
ef]Uof xf] /fi6« of] d}n] ;s]sf] ef]Ug' kb{5 ldNb}g km]l/ df}sf of] ;s]sf] hf]8\g' kb{5 eGg]sf xftdf b]Vbf 8f9' kGof}F 3/L3/L dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}Fel/ .. s8f efif0f Sof dL7f] /fi6«jfb lknfpg] ljb]zL :jfy{sf ;fd' xft km]l/ ldnfpg] of] bf]wf/] rl/q 5 ;w}F ;Qf jl/kl/ dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}Fel/ ..
elgG5 nf]stGq of] pTs[i6 kl/kf6 xf] >Lv08 ;lk|Fb} hfFbf, lau|Fbf Tof] s'sf7 xf] nf]stflGqs b]Vbfdf leqL OR5f y/Ly/L dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}Fel/ .. jfl;ª\u6gsf sfJo ;';]nL M 49
/fi6« ;jf]{kl/ /fvL /fHgLlt rNg' kb{5 OdfgL bLk–aftLdf /fHgLlt aNg' kb{5 v} ljrf/ lnO{ o:tf] cfpGg Sj} cl3 ;/L dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}}Fel/ .. kmls{Gg nf]ssf] cfzf hf] s';L{df uP klg lr/]sf sfgjfnf x'g\ h'g} hf]uL eP klg ltg} nDk6\ a"9f x7L ;w}F ;Qf jl/kl/ dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}Fel/ ..
Proof
o'jf x] b]zsf tf/f b]znfO{ p7fpg] ef/L 5 sfFwdf ltd|f] cfzf k'gM hufpg] arfpm b]z of] Kof/f] nf]stGq cl3 ;/L dfl;G5 ls st} /fi6« nfU5 lrGtf ;w}Fel/ ..
jfl;ª\u6gsf sfJo ;';]nL M 50
uf]ljGb lu/L k]|/0ff •• cfkm}Fn] /f]h]sf] •• kmls{xfN5' b]z •• Ps gh/d} dg k/fPF •• d]/f] ;kgf
Proof
hGd M @)!% j}zfv %, 6]Ss/ eG;f/L xfn M dgf;;, elh{lgof Od]n M
gggprerana@gmail.com
;flxTosf/ uf]ljGbn] @)#$ ;fndf syf k|sflzt u/fP/ ;flxToofqf ;'? u/]sf] b]lvG5 . pxfFn] rf/j6f pkGof;, tLgj6f syf;ª\u|x, kfFrj6f sljtf;ª\u|x, rf/j6f lgaGw;ª\u|x, Pp6f ;dfnf]rgf;ª\u|x, b'O6f cg"lbt / 5 j6f ;Dkflbt s[lt k|sflzt u/fO;Sg' ePsf] 5 . pxfF slj, lgaGwsf/, cfVofgsf/, ;dfnf]rs, gf6ØsdL{ / ;Dkfbs klg x'g'x'G5 . pxfFsf] ;flxTo n]vgn] g]kfnL ;flxTodf ljz]if / leGg :yfg agfPsf] 5 . g]kfnL efiff;flxTo ;]jfdf ;dlk{t pxfFsf] ax'd'vL ;flxlTos JolQmTj pbfx/0fLo ePsf] 5 . vf; u/L pxfFsf] sfJodf hLjgsf ax'/Ë kfOG5g\ . pxfFsf] sfJo OGb|]0fLdf kf7sx¿ cfg} ?lrcg';f/sf efj / ljrf/sf /Ëx¿ b]Vb5g\ . oxL sfJo zlQmn] pxfFsf] sfJosnf k'likt / kNnljt ePsf] b]lvG5 . jfl;ª\u6gsf sfJo ;';]nL M 51
cfkmF}n] /f]h]sf] of}6f b'Vvsf] ef/L la;fpg] ynf]sf] vf]hLdf lyPF cGg afnL t lyP g} la;fO/fVg vnf] vf]Hb} lyPF vf]hLsf] of] lg/Gt/ qmd k|flKtsf] cft'/tf, of}6f cf}8fxf, of}6f 56k6L clg of}6f clenfiffn] 8f]¥ofP/ cj;/sf] :ju{ dflgg] ;+of]usf] s]Gb|laGb' 7flgg], b'lgofFsf] uGtJosf] k|yd /f]hfO dflgg] of] kftfn e"lddf kfOnf 6]Sg cfOk'u]F .
Proof
;'Vvsf] csf]{ kf6f] b'Vv xf] eGg] la;]{sf] /x]5', x/]s cu|ufdL kfOnf ;kmntfsf] ;"rs xf] eGg] x]Ssf g} ePg5 dnfO{, 6f9f k'u]kl5 jfl;ª\u6gsf sfJo ;';]nL M 52
;'vkl5 nfUg] sNkgfdf cfgf] ;fysf] ;'v st} 5'6]sf] kQ} ePg5 dnfO{ . b'Vv t ;fFRr} ;fFRr} k/b]zdf kf] k|s6 x'Fbf]/x]5, b'VvnfO{ t k/b]zdf gSsnL ;'vsf] hnkn] 9flsPsf] kf] x'g] /x]5, kL8fnfO{ t k/b]zdf v'/fs dfg]/ a:g] cfbt kf] agfOFbf] /x]5 .
Proof
cfg} lagfsf] vf]hLdf ef}Ftfl//x]sf] d[u eP5' ;'gsf] d[usf] kl5 nfUbf nfUbf ysfOn] ulnt eP5' cfg} /f]hfOsf] b'MvnfO{ ;'v dfg]/ a:g] cfbtsf] gzfn] nÝ eP5' .
jfl;ª\u6gsf sfJo ;';]nL M 53
kmls{xfN5' b]z sxfF a:5' / d of] k/b]zdf kmls{xfN5' b]z . b]zsf] /fhgLlt clnslt /fd|f] xf];\ nf]8;]l8ª 36f];\ wf/fdf kfgL cfcf];\ kmls{xfN5' b]z .
Proof
;+ljwfg agf];\ bf]xf]/f] gful/stf kfOof];\ zflGt ;'/Iff ;'lw|of];\ af6f] lrNnf] agf];\ w"nf] d}n]f gxf];\ kmls{xfN5' b]z .
slt a:g' of] k/b]zdf hxfF ckgTj 5}g bf}Ft/L;Fu aft dfb}{ lrof lkpg] rf}tf/f] 5}g of] csf{sf] b]zdf hLjg latfpg] s'/} 5}g kmls{xfN5' b]z jfl;ª\u6gsf sfJo ;';]nL M 54
5f8]/ cfPsf] hflu/ k'ga{xfnLdf xf];\ C0f ;fk6L h] lyof] ;a} dfkm xf];\ laxfg p7\g] lalQs} :6f/ aS; skmL r':sL nfpg kfOof];\ kmls{xfN5' b]z . 5f]/f5f]/Lsf] eljio x]g{' k¥of] o;f] k9fO ;s"g\ logn] laxfaf/L e}hfcf];\ /fd|f] 3/jf/ b]lvof];\ gfltgfltgfsf] d'v x]g{ kfOof];\ To;kl5 t oxfF a:g] s'/} 5}g kmls{xfN5' b]z .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 55
Ps gh/d} dg k/fPF ltd|} ;b\efjn] tflgP/ cfPF of] s:tf] ;+of]u Ps gh/d} k|Llt a:of] sf]nf]/f8f] ;'6'Ss eG5' d}n] ltdLnfO{ Psbd} dg k/fPF . of}6f ;fgf] g]kfn sfvdf /fv]/ a;]sL /lx5Øf} stfstf vf]sgf h:tf] stfstf e}F;]kf6L a'ªdtLsf] 5]pd} k'u]F ls em}F af]N8/nfO{ gh/ nufpFbf kxf8sf] Tof] ;'Gb/ sfvaf6 :joDe"af6 sf7df8f}F x]/]em}F ltd|f] :j¿kn] d Psbd} tflgPF sf]nf]/f8f] ;'6'Ss eG5' ltdLnfO{ d}n] Ps gh/d} dg k/fPF .
Proof
ltd|f] ;'Gb/tf stfstf kl/lrtemF} nfUof] ltdL5]p k'Ubf d]/f] ;f/f ;°f]r efUof] x]l//x]F ltdLnfO{ ckns g d}n] cfFvf lemDsfPF jfl;ª\u6gsf sfJo ;';]nL M 56
g ltdLn] cfFvf lemDSofof} gh/n] gh/df gh/ l6sfPkl5 b'lgofFdf s] x'G5 ToxL kl/0flt ;sf/]F sf]nf]/f8f] d}n] ltdLnfO{ em'Ns] 3fd ;fIfL /fvL dg k/fPF . ltd|f lk|ox¿ slt xf]nfg\ hflGbgF d ltd|f] ;f}Gbo{sf] Onfsfaf6 6f9f hfg} ;lSbgF d dg k/fPkl5 5]Sg] kxf8 klg kmf]8\g' k5{ afwf aGwgsf kxf8x¿ d kmf]g{ tof/ 5' Psbd lbuGtdf d}n] cfkm"nfO{ ltd|f] Gofgf] lk|o sfvdf kfPF sf]nf]/f8f] ltdLnfO{ d}n] Ps gh/d} dg k/fPF .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 57
d]/f] ;kgf of}6f ;kgf b]v]sf] lyPF ToxL ;kgf g} e}lbof] hLjgsf] unkf;f] ;kgf hlt;'s} ;fgf] eP klg cfsf/ t To;sf] ;Un} x'G5 ;Unf] ;kgfn] dfG5]sf] lhGbuL af]s]sf] x'G5 lhGbuL af]Sg] ;kgf b]v]kl5 t;{g' :jfefljs dflgFbf] /x]5
Proof
ha yfxf kfPF d}n] ;kgf b]Vg s'g} cg'dlt rflxFb}g ;kgf b]Vg s;}n] /f]Sg ;Sb}g s;}n] 5]Sg ;Sb}g s'g} d"No ltg'{ klg kb}{g d}n] 7"n} ;kgf b]v]F .
d]/f] ;kgfsf] cfsf/ b]v]/ dfG5]x¿ tl;{g yfn] efufefu ug{ yfn] laTof;} kg{ nfu]sf] em}F ug{ nfu] jfl;ª\u6gsf sfJo ;';]nL M 58
dfG5]x¿sf] t;f{On] d kf] tl;{g yfn]F d]/f] ;kgf dfG5]x¿sf nflu b':dg eof] / d]/f ;kgfnfO{ ltgn] ljiffQm agfOlbP . d}n] tL ljiffQm ;kgfnfO{ lyryfr kf/]/ /; lgsfn]F / 3636L lkOlbPF
Proof
Tof] /; d}n] lgn]F eg] d ;lsg] kSsf lyof] d]/f] ;dflKt;Fu} d]/f] ;kgfsf] cGTo x'g]lyof] d]/f] ;kgf hf]ufpg d}n] Tof] ljifnfO{ s07df /fv]F / gLns07 ag]F . lgrf]l/P/ ;fgf] ePsf] d]/f] ;kgf s07df a;]sf] 5 gLns07df a;]sf] 5 .
jfl;ª\u6gsf sfJo ;';]nL M 59
Proof
jfl;ª\u6gsf sfJo ;';]nL M 60
gf/fo0f clwsf/L •• lk|o km"n •• :jfFu]x¿ •• ¿ksnf •• :vlnt ljrf/
Proof
hGdM @)@( ebf} !#, v]afª &, tfKn]h'ª xfn M p8la|h, elh{lgof Od]n M narayanadhikari2004@hotmail.com @)$^ ;fnb]lv ;flxTo sd{df k|j[Q x'g'x'g] clwsf/Lsf] klxnf] k|sflzt /rgf …gf/LÚ xf] . pxfFsf sljtfdf /fi6«elQmsf] ;';]nL, k|0fosf] ulx/f] /fu, dfgjLotfk|ltsf] cufw cf:yf Jol~ht ePsf] b]lvG5 . efjgf, ljrf/ / lzNksf] ;dGjo / ;Gt'ng zlQmn] pxfFsf sljtfaf6 ljz]if sfJo ;f}Gbo{ k|s6 x'G5 . oxL ;f}Gbo{n] pxfFsf sljtf clws k7gLo ag]sf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 61
lk|o km"n km"n /ËLg 5 ;'Gb/ 5 . km"n ;'ulGwt 5 / t dg k/fpg]x¿sf] eL8 5 . laxfg ;a]/} km"nsf] /ªdf nfnL 5g{ pHofnf] v:bf gv:b} uugdf ;"o{ d':sf/fpF5g\ /ljsL/0f;Fu /ËLg ;'ulGwt km"nsf] cw/df df}/L x'g\ jf ed/f k|]dk"0f{ dw'/;df lnKt x'G5g\ . lsgls km"n /ËLg 5 ;'Gb/ 5 . km"n ;'ulGwt 5 / t dgk/fpg]x¿sf] eL8 5 .
Proof
cb[Zo kjg x'g\ jf lglzdf h"g sf] nf]lePsf 5}gg\ km"n;Fu laxfg cfpF5 df]tL´}F zLtsf uxgf lnP/ km"nnfO{ lbg cfpF5 dfnf´}F OGb|]0fL lnP/ km"nnfO{ ;fF´ cfpF5 l;Gb"/´}F ;u/ lnP/ km"nnfO{ sf] nf]leFb}gg\ k"mn;Fu cGwsf/ lbg] /ft klg rlDsnf] rGb|df lbP/ lIflthkfl/ l8nd'lg ´l/lbG5 lsgls km"n /ËLg 5 ;'Gb/ 5 km"n ;'ulGwt 5 / t dg k/fpg]x¿sf] eL8 5 .
jfl;ª\u6gsf sfJo ;';]nL M 62
:jfFu]x¿ e'OFdf c;/Nn /ª 3f]K6ØfP/ cfsfz /Fufpg] :jfª gu/ cfg} P]gf cufl8 pleFbf t s;nfO{ ;'Gb/ nfUb}g / < h:t} s'¿k cg'xf/ klg . cfkm\gf k'vf{sf] jL/tfsf] Oltxf; k9\g g;Sg]n] v} Û s] cfw'lgs Oltxf; /Rnfg\ eljiosf nflu / <
Proof
gofF Oltxf;sf nflu gofF k[i7 / gofF cWofosf ;6\6fdf clg km]l/ lsg rflxof] afO;] / rf}aL;] /fHosf h]/S; skLx¿ < gfnfkfgLsf] o'4df a}/Ln] ;d]t xfg]sf ;nfdLsf :jfledfgx¿ d]rLb]lv dxfsfnLsf] axfa;Fu} lgu'/d'G6L nlqP/ lsg aUb}5g\ ljb]zlt/ <
To;}n] oxfF eGg ;lsGg sfnfkfgLx¿df gfnfkfgLs} Oltxf; gbf]xf]l/Pnf :jfFu]x¿ uugd'lgsf] gbL gLn} b]lvG5, /ª g5/ km"n cfkm}F ;'ulGwt 5, cQ/ g5s{ . jfl;ª\u6gsf sfJo ;';]nL M 63
¿ksnf ´kSs 3fF;df laxfgLkv, zLth:t} k/]nLdf 5kSs yf]kfyf]kf ag]/ ´g{ tof/, a/km´}F cfF;'sf l9sfx¿
ltd|} x'g\ ;a ;a} ¿ksnf
u'kmfleq u'kmfsf] 5taf6 tktk emg]{ tks]gLem}F cgGt sfnb]lv embf{emb}{, /lrt ;'Gb/ lqm:6nh:t}
Proof
ltd|} x'g\ ;a} ¿ksnf
lg:k§ cFWof/f]df Ps em'Nsf], h"gsf] ls/0fn] 5g]{ Hof]lt eGbf s] sd 5 ltd|f] d':sfg < cgGt v'N5 d]/f] dgleq
ltd|} x'g\ ;a ;a} ¿ksnf
snsn ub}{ d'xfgaf6, ;nn aUg] cg'kd gbL 5ª5ª 5ª5ª 5x/f, 5x/faf6 ´g]{ ´/gf´}F
ltd|} x'g\ ;a ;a} ¿ksnf jfl;ª\u6gsf sfJo ;';]nL M 64
;fu/sf aLrdf ;fF´kv, lIflthaf6 5l/g] k|sfz hndfly / hnd'lg laDa, aGb5 h:tf] cb\e't /rgf
ltd|} x'g ;a ;a} ¿ksnf
OGb|]0fL;Fu /dfpg] r/L, do"/sf] /ËLg KjfFveGbf s]df sdL 5 ltd|f] ¿ksnf, dg} layf]N5 kjg;Fu p8\bf
Proof
ltd|} x'g\ ;a ;a} ¿ksnf
jfl;ª\u6gsf sfJo ;';]nL M 65
:vlnt ljrf/ :vlnt ljrf/ lnP/ lrNnf ;8sdf lxF8\g] < ljj]sleq ltvf sfF9f x'g]x¿ cfZro{ Û km"nsf] sljtf n]V5g\ / eG5g\, sfF9}n] t km"nsf] /Iff u/]sf] 5 km"nnfO{ sfF9fdf ´f/]/ dfq x]/ s] bzf x'G5 km"nsf] < km"n /QmfDo x'G5 km"nsf] ;'ef; /QmfDo x'G5 km"n t p8\g' kYof]{ dg dgleq t/ sfF9f sfF9} xf] :vlnt ljrf/´}F o;}sf] eon]— g km"n p8\5 r/L´}F dg dg g x'G5 dg /ª /ª . sfF9f t l;km{ cfgf] efnf pFef] t]:of{P/ km"nsf] k|tLIff ul//x]sf] 5 / :vlnt ljrf/ klg Pp6f sfF9f g} xf]
Proof
cfFvfnfO{ cfsfzlt/ p7fP/ cfsfzsf] prfO gfKg vf]Hg]x¿ cfg} prfOsf] ul0ft e'Nb} 5g\ ;d'b| t6df 3'd]/ sxfF ;fu/leqsf] df]tL l6Kg ;lsG5 < cd[taf]6 lrGg g;s] ;+;f/ cfg} k]jf eP/ dfq s] x'G5 < jfl;ª\u6gsf sfJo ;';]nL M 66
:vlnt ljrf/df dfg / dof{bfsf] aLh /xGg h:tf] e":vngkl5 xl/ofnL /xGg xl/ofnL /fVg :vngkl5 ljrf/sf] gofF a]gf{ pdfg'{k5{ h:tf] Ct'n] gofF kfn'jf xfN5 j;Gtdf ;'Gb/ ljrf/sf nflu ljb|'k lzlz/nfO{ cljlR5Gg a9fb}{
Proof
lxF8]/ ofqf ;lsGg hLjgsf nflu rl/q / ljrf/df :vng zf]let x'Gg sfFr'nL km]l/G5 :jfefljs g} k'/fgfsf] k|lt:yfkg h:t} ljrf/sf] sfFr'nL km]l/g'k{5 t/ ljrf/sf] :vng /f]lsof];\
jfl;ª\u6gsf sfJo ;';]nL M 67
Proof
jfl;ª\u6gsf sfJo ;';]nL M 68
k|sfz g]kfn •• k/fO{ ;x/ •• xfOs' •• km/s xfdLx¿ •• t'?Gt ;lxb 3f]if0ff u/
Proof hGd M dfr{ )#, tD3f;, u'NdL xfn M kmN; rr{, elh{lgof ;Dks{ M
prakashnepal7@yahoo.com
g]kfn k];fn] sDKo'6/ OlGhlog/ eP klg g]kfnL ;flxTo l;h{gfdf ;dlk{t JolQmTj x'g'x'G5 . cg];f; d]6«f] jfl;ª\u6gsf] cWoIf, cGt/f{li6«o snfsf/ d~r cd]l/sfsf] ;lrj, k|jQmf / cd]l/sf g]kfn ;f];fO6Lsf] k"j{ ;~rf/ lgb]{zs klg x'g'x'G5 . pxfFsf y'k|} km'6s/ ;flxlTos /rgf k|sflzt ePsf 5g\ . nf]sno / uBnodf sljtf l;h{gf ug]{ g]kfnsf sfJodf ef}ltstflt/ nxl;P/ lbUe|fGt ePsf] dfgj hLgjk|lt ulx/f] Joª\Uo ul/Psf] kfOG5 . To:t} pxfFsf sfJodf b]zk|]dsf] pRr / pbfQ efj klg cGtM k|jflxt b]lvG5 . ;Dk|]if0fLo sfJo lzNkn] pxfFsf sljtf ;+j]B ePsf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 69
k/fO{ ;x/ v} s'lGg of] s:tf] k/fO{ ;x/ xf] < dgvf]nL Ho"g lg /x/ ef] si6n] vfPF lg hflu/ P xh'/ dnfO{ t hflu/ lg hx/ ef] s;/L 7l8G5g\ ;'gsf dxn oL < cfkm"nfO{ t Ho"g lg /x/ ef] dfG5]n] dfG5]sf] Jofkf/ u/] ls < Odfg–hdfg a;fOF ;/] ls < …cfkm"ÚnfO{ n'sfpg] gSsnL ;x/ ef] dg vf]nL Ho"g lg /x/ ef]
Proof
Ao"Fl´G5 /flt cGw]/ gu/L v]n x'G5 /ftd} a'em"F d s;/L bfOefO glrGg] a]Odfg ;x/ ef] dg vf]nL Ho"g lg /x/ ef]
cflQPsf r]x/f ¿k/Ë 5}g dgdf Ps/QL 5}g lg r}g cf;}df bf}8g] of] s:tf] ;x/ ef] dg vf]nL Ho"g lg /x/ ef] /x/}/x/df skfn km'n]Úl; l9nf] eP/ cfFvf v'n]Úl; Pp6f hLjg lg a]lylt ;x/ ef] dg vf]nL Ho"g lg /x/}/x/ ef] v} s'lGg of] s:tf] k/fO{ ;x/ xf] dg vf]nL Ho"g lg /x/ ef] jfl;ª\u6gsf sfJo ;';]nL M 70
xfOs' 8n/, sDKo'6/, uf8L b];L;fx', 6]an, …u'8df]lg{ª ;/Ú …Xofe c gfO; 8]ÚÒ cd]l/sf . af; a;]sf] r/L, lu4sf cfFvf qflxqflx, eTs]sf] u'F8Ò g]kfn . 8n/, sDKo'6/, uf8L b]Vbfdf d:tL, ;fFRr}df ;f:tLÒ cd]l/sf .
Proof
;f]´f] dg, s~rg lxdfn l/Qf] yfnÒ g]kfn .
8n/, sDKo'6/, uf8L lg/fz dg, sRrf] wgÒ cd]l/sf . k'vf{sf] ynf], ;a}sf] enf] wgn] g} s] g} gfKbf]/}5 / cflv/df Kof/f] Ò cfg} g]kfn .
jfl;ª\u6gsf sfJo ;';]nL M 71
km/s xfdLx¿ km/s 5 xfdLx¿df / cd]l/sLx¿df ljrf/ / ;f]rdf xfdL 6fo/ afN5f}F ;8sx¿df cd]l/sf km"n km'nfpF5— uNnL uNnLdf …:ofn'6Ú u5{g\ cf]afdf— aRrfx¿nfO{ xfdL aGb's af]sfp5f}F …s0f{wf/Úx¿nfO{ clg e§L / uNnLx¿df efF8f d´fpF5f}F, afnlbj; dgfpF5f} / ævft]Æ agfp5f}F
Proof
v} s;/L a'´] cd]l/sLx¿n] b]znfO{ xfdLx¿n]eGbf cln km/s pgLx¿ lj/f]w u5{g\— …Kn] sf8{Ú x¿df / aQL km'6fpFb}gg\ /]lnª klg efFRb}gg\ pgLx¿ cln a]Un} a'‰5g\— dfG5]nfO{ pgLx¿ cln km/s a'‰5g\— dfgjtfnfO{ / eGb}gg\ hftkft ;/fKb}gg\ af]S;Lx¿nfO{ sfnf] df];f] klg bNb}gg\— lj/f]wsf] gfddf h'n'; lgsfNb}gg\— kf6L{sf] gfddf / rSsf hfd ub}{gg\— :jf:gL kf]On uPsf] lgx'Fdf
jfl;ª\u6gsf sfJo ;';]nL M 72
s;/L eof}F km/s xfdLx¿— laNs'n o;/L < s;/L cfP lj;Ëlt— dfq eTsfpg] < s;/L ;f]Rof}F eTsfpg— af6fsf /]lnª / k'nx¿ km'6fNg aQLx¿ eTsfpg 3/sf afb{nLx¿ < s;/L ;S5 g]kfnL dg elTsg o;/L < s;/L ;S5 g]kfnLkg vl:sg o;/L < / uf]8\g ;S5f}F km"nx¿ /f]Kg adsf l5sf{x¿ < cxF— d t dflGbgF— of] g]kfnL dg xf] dt dflGbgF— of] g]kfnL kg xf] dflGbgF— eTsfpg] ;+:sf/ xfd|f] xf]
Proof
xfdLx¿ dgx¿eGbf 6f9f uof}F kgx¿eGbf 6f9f eof}F lsg :jtGq ljrf/ af]Sg ;Sb}gg\ xfd|f dgx¿ lsg :jtGq ljrf/ y]Ug ;Sb}gg\ xfd|f tgx¿ cd]l/sLx¿ h:t} o;}n] km/s 5 xfdLx¿df / cd]l/sLx¿df ljrf/ / ;f]rdf xfdLx¿, kf6L{ af]s]/ hGdG5f}F— hGdhft / kf6L{–kf6L{sf] /ut aUb5 xfd|f] z/L/df jfl;ª\u6gsf sfJo ;';]nL M 73
kf6L{n] lg0f{o u5{ xfd|f afFRg] lbgx¿ / xfd|f ljrf/x¿ kf6L{n] lr5{ xfd|f 5ftLx¿ b]z agfpg] lgx'Fdf / /f]Kg abgfd lj;Ëltx¿ o;}n] t eGg ;Sb}gf}F xfdL untnfO{— …untÚ / b]Vg ;Sb}gf}F ;xLnfO{— …;xLÚ To;}n] xfdL k/b]zdf klg eTsG5f}F / 6'qmf 6'qmf eP/ em5f}{+ e'OFdf cfk;–cfk;df cfxl/; / 8fxfn] cf]OnfpF5f}F, ax'nfpF5f}F / 89]/ v/fgL x'G5f}F dfgf}F eTsg'— xfd|f] lgoltdf 5 eTsfpg'— xfd|f] /utdf 5 lsgls xfdL cfkm" laNs'n xf]Ogf}F xfdL t kf6L{sf uf]6L xf}F xfdL g]kfnL xf}F .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 74
t'?Gt ;lxb 3f]if0ff u/ pxfF x'g'x'GYof]— dxfg\ Ps xf]gxf/ x'g'x'GYof]— gef …lg ljj]s ;fgf] ´u8fdf kg'{ef] xfgfxfg ubf{ dg'{ef] dfGg' x'Gy]g s;}sf] 8/ ;/sf/ – ;lxb 3f]if0ff u/
Proof
xf] t lg s:tf] lj8Dagf 7]Ssfk§fsf] s'/f] lyof] efuaG8fsf] r'/f] lyof] cln emd]nfdf kg'{ef] b'O{rf/ uf]nL …lg eg'{ef] h]nlt/ a;fOF ;g'{ef] ToxfF …lg xfgfxfgdf kg'{ef] xfgfxfgd} dg'{ef] ;/sf/— ;lxb 3f]if0ff u/ .
pxfFsf] of]ubfgsf] s'/} gu/f}F kf6L{ wfGg'df 7"nf] xft g]tfx¿sf] ;w}F ;fy 7]Ss} 7]Ssfn] knfÚsf] kft u'G8f eGg] rf]yfn]x¿nfO{ lbg'x'GYof] pxfF nftsf nft h] u/] lg pxfFnfO{ gnfUg] aft jfl;ª\u6gsf sfJo ;';]nL M 75
;xL x'g'x'GYof] xfd|f ;/ ;/sf/— ;lxb 3f]if0ff u/ . pxfFsf] d[To' df]tL;/L 5 pxfFsf] of]ubfg Hof]lt;/L 5 pxfF gx'Fbf— uf/f] efÚ5 kf6L{sf] Ps— xf]gfxf/ ufÚ5 kf6L{sf] ;|f]t— ;'s]em}F efÚ5 xfd|f] ;|f]t Úlg— c¿n] vfÚ5 o:tf] dfG5] Úlg d/]/ hfFbf b]zn] lg a]:;/L 3f6f vfÚ5 ;lxb agfpg ca]/ gu/ ;/sf/— ;lxb 3f]if0ff u/ .
Proof
kf6L{sf] u'G8fsf] n8fOF geGg" pxfFsf] d[To'nfO{ ;fdfGo g7fGg" gq t …6fo/Ú aln g} /xG5g\ g]kfn aGb rln g} /xG5g\ hgtfsf 3/ hln g} /xG5g\ /utsf vf]nf alu g} /xG5g\ To;}n] x]/ x} eGof 5' klxn} gdfgLsg s;}sf] 8/ ;/sf/— ;lxb 3f]if0ff u/ .
jfl;ª\u6gsf sfJo ;';]nL M 76
k|]dk|;fb ;+u|f}nf •• lbof] snz / hd/f •• o;kfln •• ;[hgf / hLjg •• zLtsfnLg a'9f] ¿v
Proof
HfGd M ;g\ !(%*, t]x|y'd, cf7/fO{, Ojf, ebf}/] xfn M dSn]g, elh{lgof Od]n M psangraula@gmail.com ;+u|f}nfn] sf]nlDaof ljZjljBfnoaf6 cy{zf:qdf Pd\=P= u/]sf] b]lvG5 . @)$! ;fnb]lv ;flxTo l;h{gfdf Psf]xf]l/g' ePsf ;+u|f}nfsf] …;'sLw'kLÚ gfds v08sfJo k|sflzt b]lvG5 . pxfFsf sljtf k|tLs, laDa / Jo~hgf zlQmn] ;DkGg 5g\ . sfJofTds ;f}Gbo{ zlQmn] cf]hk"0f{ ePsf 5g\ . nofTdstfn] k7gLo / >j0fLo ag]sf 5g\ . efj ufDeLo{ pxfFsf sljtfsf] d'Vo zlQm xf] . jfl;ª\u6gsf sfJo ;';]nL M 77
lbof] snz / hd/f yfnLleqsf] dlnnf] afn'jfdf h'jf8]sf] sf}8fh:t} 5/k:6 eP/ tF5f8 d5f8 ub}{ pld|Psf snzsf] prfO e]6\g k|lt:kwf{ ub}{ p7]sf lwklwk] lbof]sf] k|sfzdf cfgf] sflGt / ;'Gb/tf b]vfpg tNnLg hd/fx¿, cfg} 5fofFsf] cf];n] 8'ª\ 8'ª\tL uGxfPsf km]b / h/fx¿ Tot}lt/ cfg} ;fd|fHo 7fgL v]ln /xg], sL/f, km6\ofª\u|f, sldnf / laR5Lx¿ ;a}nfO{ kfn]/ d]d] k]d] x'dsf] d'b|fdf bzdLsf] lgolt kv]{/ a;]sf WofgdUg hd/fx¿ d]/f] sf7df8f}F ;x/sf 3/x¿
Proof
jfl;ª\u6gsf sfJo ;';]nL M 78
o;kfln o;kfln klg pgLx¿ Od]naf6 cfP, cgnfOgdf e]l6P km];a'ssf leTtfdf 7]nd7]n b]lvP . o;kfln klg gfgLx¿ xfd|f 3/sf lk|o kfx'gf ag]/ cfP sDKo'6/leq, 3/leq / dgleq ce]B lsNnf ag]/ a;] .
Proof
o;kfln klg pgLx¿ cd]l/sL ;dfhdf v08j[li6sf] ememNsf] lbg] pgLx¿sf cl:tTjsf e'Nsfx¿ ;jf{Ë gfª\uf] lbgsf sf]nfxnx¿df slxn] cb[Zo eP/ slxn] cw{ e"ldut ag]/ Hf]flvdk"0f{ sfo{sf] u[xsfo{ u/]em}F of}6f clGtd o'4sf] tof/Ldf h'6] h;/L o'uo'unfO{ k|efj kfg]{ o'ufGtsf/L qmflGtdf nfu]em}F lbgel/ otfptf 6xln /x] ;a}nfO{ glhsaf6 lgofln /x] . o;kfln klg pgLx¿ cfgf cfgf sfdaf6 ;a} kms]{kl5
jfl;ª\u6gsf sfJo ;';]nL M 79
cfgf e"ldut hLjgsf j:qx¿ k'msfP/ lbgel/sf] sf]nfxnaf6 d'Qm eP/ o'4 n8\g hfg'eGbf cl3sf] l;kfxL h;/L ljhoL d'b|fdf pgLx¿n] d'lQmsf] uLt ufP dGqd'Uw agfP/ xfdLnfO{ xif{ / v';Lsf] gfr grfP . o;kfln klg pgLx¿n] n3'tfef;sf] efjgfaf6 d'Qm aGg dgf]j}1flgs :jtGq tfk k|fKt ug{ cyf{t\ cfg} cl:tTj klxrfg ug{ yk pmhf{ a6'n] 3/leq / ;a}sf dgleq o'uo'u;Dd emfFlu /xg] ;f+:s[lts sNkj[Ifsf] chDd/L la?jf /f]k] / Kfm]l/ csf]{ jif{ e]6\g] afrf ub}{ o;kfln klg b;F} ltxf/ xfdLaf6 labf eP .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 80
;[hgf / hLjg ;|i6fsf] nflu pj{/ ynf] hut\ / hLjg xf] ;[hgf km'6\g] kljq d'xfg clj/n hLjg xf] ;kgf b]Vg] Efljio n]Vg]] hLjg b[li6 xf] Af|Xdf08 leq cfgf] af; a:g] ;|i6f / ;[li6 xf] .. km"naf/L /fd|f] uf]8d]n u/] j;Gt TofF x'G5 dfnLsf ;fy au}+Frfdfem t'nkm"n TofF x'G5 1fg / >d nug ;wF} kof{o hLjgsf] Jft{dfg;Fu lhpg' g} kg]{ oyfy{ hLjgsf] ..
Proof
5f]lkg' k5{ df6f]n] lap pdfg{ la?jf pv]Ng' k5{ 7fpF ;fg'{ k5{ a9fpg la?jf k|;j kL8f ;xg' k5{ pd|g la?jf lr/kmf/sf] kL8f ;xg' k5{ 7fpF ;fg{ la?jf .. sljn] n]v] sljtf aG5 dfnLn] /f]k] km"n hLjg xfF:5 ;[hgf xfF;] ;[li6sf] of}6} d"n dfnLsf] sfd au}Frfdfem ;'Gb/ km"n km'Nb5g\ ;[hgf¿kL k|s[ltleq hLjg em'Nb5g\ .. ks]6 cfgf] bl/nf] kf/] rf]/Lsf] 8/ x'Gg ldn]/ d'7L b/f] gkf/] cf}+Fnfsf] e/ x'Gg g7f];L cfuf] aNb}g ;fyL g hLjg rNb5 k/df0f'x¿sf] 3if{0f ge} /s]6 sfF hNb5 < sfd ug{ yfn] nIonfO{ ;wF} ;fydf /fv]/ jfl;ª\u6gsf sfJo ;';]nL M 81
;[hgf cfkm}F cﾂｪ\s'g{ yfN5g\ hldg kmf6]/ Kflx/f] n8f];\ cl;gf k/f];\ ;[hgf /f]lsGg ch/ cd/ c7f]6 ;fd' afwfn] 5]lsGg .. ;[hgf km"N5 /ﾃ記g eO{ hLjg ag]/ hLjg v'N5 axf/ NofO{ ;[hgf eg]/ ;[hgf s] xf] hLjg s] xf] r/fr/ cfFvfdf ;a}n] cfdf ;Dem]/ a:5g\ k|s[lt sfvdf ..
Proof
jfl;ﾂｪ\u6gsf sfJo ;';]nL M 82
zLtsfnLg a'9f] ¿v tL ;a} uP cfcfgf] af6f] d PSnf] eP5' /f]P/ sf6]F Tof] lr;f] /ft d gfËf] eP5' . lxhf] g} h:tf] nfUb5 cem} d;Fu cfPsf ldn]/ a:of}F gªdf;' agL h] hlt ePsf lhªl/Ë d]/f] z/L/dfly sk8f ag] tL phf8 d]/f] hLjgdfly j;Gt ag] tL ..
Proof
pg]? cfP ;'jf; NofP jf;gf dudu ;'Gb/ nfUg] Tof] x/fe/f k|s[lt hudu snfsf/ ldnL agfPh:tf] k|s[lt Tof] ¿k ;Dem]/ a:5' Tof] v';L If0f clxn] s'¿k ..
xfjfsf] emf]Fsf a]:;/L rNbf cfgGb x'GYof] dg ;Fu;Fu} x'Fbf xfjfdf e'mNbf rËfem}F x'GYof] tg If0fIf0fdf xfjf rln g} /xf];\ sNkGYof] dgn] pg]?;Fu 8f]nfO{ /fVg] dg uYof]{ tgn] .. l;/]6f] rN5 la5§} lr;f] xNnG5' a];/L la5f]8df ltgsf] dgnfO{ afFwL tª\u|G5' o;/L pg]/sf ;fydf h] em]Ng' k/f];\ /dfOnf] nfUbYof] pdË dgdf rf}aL;} 306f hLjg hfUbYof] .. ;';]nL ltgsf] of] dg} xg]{ dw'/ sf]dn t/lËt x'g] dgnfO{ 5'g] ;ËLt sf]dn jfl;ª\u6gsf sfJo ;';]nL M 83
Tof] dGb dGb xfjfsf] nx/ ;ËLt ag]/ 3/ u/L a:of] of] 5ftLleq cld6 ag]/ .. /dfOnf nfUg] tL If0fx¿ ;kgf ePsL of km]l/ slxNo} gcfpg] u/L daf6 uPsL sfxfNfL nfUbf] of] l7xL lr;f] slxn] hfg] xf] t';f/f] lxpF Tof] lr;f] ldnL ls dnfO{ nfg] xf] .. x/]s k6s lxpFb cfO{ k/LIff ln/G5 ;fysf ;fyL x/]/ nfG5 emg\ b'Mv lb/G5 o;kfln d}n] w]/} g} r]tF] csf]{ ;fn la;{GgF a]n}df ;DemL Joj:yf u5'{ lsdfy{ la;{GgF ..
Proof
pg]/sf ;fydf OGb|]gL agL emNsGy]F jgdf ;do;Fu} ¿k/Ë km]/L vs{Gy]+ jgdf sn]hL uf9f a}hgL /ftf ;'gf}nf ;a} ¿k ldnfO{ kfnf] k'¥ofpg] uy]{+ hLjgsf ;a} ¿k .. kfn'jf agL j;Gtdfem knfO{ e// ;+;f/ v';L agfO{ ;w}F gfr]/ km// /ËLg k"mn jf;gf dL7f] hudf 5/]/ hLjg aGYof] pbfpFbf] 3fd cfgGb e/]/ ..
ljutsf /fd|f If0fnfO{ ;DemL lbg sf6\5' clxn] 3'd]/ cfpg] j;Gt ;DemL dg afFW5' clxn] cfzfsf] Hof]lt dgdf /fvL cfFvf d vf]Nb5' ToxL Hof]ltleq hLjgrqm k|s[lt af]Nb5' t';f/f], l7xL, lxpFnfO{ y]Ug] Gofgf] d e]6\b5' .. jfl;ª\u6gsf sfJo ;';]nL M 84
a;Gt >]i7 •• P k/b]l;Psf ldq •• csnaxfb'/ cd]l/sfdf M Ps zAblrq •• ;8s •• df]/fn]; ufl;{of
Proof hGd M kmfNu'g $, @)!@ -j;Gt–k~rdL_, t]x«y'd DofUn'ª ahf/ xfn M l:k|ªlkmN8, elh{lgof Od]n M bmshrestha1@gmail.com cd]l/sfaf6 cfly{s ljsf;df Pd=P;= u/]sf j;Gt >]i7n] @)@# ;fnd} x:tlnlvt klqsfsf] ;Dkfbg u/]sf], @)@( ;fndf sf7df8f}Fdf cfOP:;L k9\bf …k'an {] L w'gÚ k|sflzt u/]sf] b]lvG5 . pxfFsf] ;flxlTos n]vgsf] cf/De eg] @)@^ ;fnb]lv ePsf] yfxf kfOG5 . pxfFsf tLg j6f sljtf– ;ª\u|x k|sflzt b]lvG5g\ . pxfF cd]l/sf g]kfnL ;flxTo ;dfhsf] k"j{ s]Gb|Lo cWoIf, g]kfnL cd]l/sg kl/ifb\sf] k"j{ dxf;lrj tyf g]kfnL ;flxTo k|lti7fg, pQ/ cd]l/sfsf jt{dfg cWoIf x'gx' G' 5 . pxfFn] ljleGg kqklqsf / :dfl/sfx¿sf] ;Dkfbg;d]t ug'{ ePsf] 5 . pxfFsf sljtfsf] d"n efj b]zk|d] / dfgjtf /x]sf] kfOG5 . pxfFsf sljtf dfld{s 5g\ . nofTds / ;Gt'lnt cleJolQm sf}znn] ;'Gb/ ePsf 5g\ . g]kfnL Åbosf] dd{ JoQm ug{;Sg] zlQmn] g} pxfFsf sljtf a9L ;+jB ] ePsf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 85
P k/b]l;Psf ldq P k/b]l;Psf ldq /fv]/ k/]nLleq b]zsf] lrq 5f]k]/ 5ftLel/ dfofn'sf dfofx¿ dl:tisel/ yf]k/]/ b]zsf kmfF6x¿ ltdL cljrn / clj/n Jo:t 5f} lbg /ft k/b]zsf] sfd} sfddf cfF;' v;fNb} cfg} xftdf
Proof
k|To]s cª\u|]hLsf w'gleq cfgf] efiffsf] ;ËLt eb{5f} k|To]s kf˘rfTo gfrleq ‰ofp/] / ;f]/7Lsf] tfn vf]Hb5f} k|To]s kxf8sf y'DsLx¿df nfnL u'/fF;sf af]6 vf]Hb5f} clg k|To]s gbLx¿df sf];L / s0ff{nLsf] 5fofF e]6\b5f} ltdL k/]b]zL eP klg k/b]zsf] x/ sf]0fleq b]zsf] cfef; vf]Hb5f} k/b]zsf k|To]s 5fofFx¿df cfg} b]zsf] dfof vf]Hb5f} t/ yfÚ5
jfl;ª\u6gsf sfJo ;';]nL M 86
ltdL gx'g';Fu} b]zdf ltd|f] 7"nf] cefj 5 ltd|f] kf}/vsf] b]zdf 7"nf] vfFrf] 5 b]zn] ;xL lbzf ge]6\g'df ;xL cy{df ltd|f] cefj v6\s]sf] 5 To;}n] t P k/b]l;Psf ldq xftdf xft ldnfpm zflGt / ljsf;sf] uLt ufpm cfcfgf] kf}/vsf] ufyf af]s]/ cfpm s]xL geP b]zsf] lxt ;f]r/ cfpm t/ k6s–k6s gbf]xf]¥ofpm ;tLn] ;/fk]sf] b]z eg]/ af/Daf/ lwsfg]{ gu/ hgtf p:t}÷ b]z p:t} eg]/
Proof
d t eG5' b]zsf] clxtdf af]Ng] ltdLnfO{ s]xL xs 5}g b]znfO{ ;w}F ;/fKg] ltdL;Fu s]xL clwsf/ 5}g lsgeg] b]zn] ltdLnfO{ xf]Og ltdLn] b]z 5f]8]/ cfPsf xf} jfl;ª\u6gsf sfJo ;';]nL M 87
b]zsf] df6f] / dfofn] xf]Og ltdLn] g} df6f] / dfof Tofu]/ cfPsf xf} To;}n] P k/b]l;Psf ldqx¿ b]znfO{ cledfgn] xf]Og :jfledfgn] prfn vf]qmf] cfZjf;gn] xf]Og ;Sbf] ;xof]un] k"/f u/ b]znfO{ 3[0ffn] xf]Og dfofn] x]/ ;tLn] ;/fk]sf] geg]/ zflGt / ;'Gb/tfsf] Bf]ts agfpm Oltxf;sf] dfu{ x]/]/ eljiosf] /]vf sf]/ e"uf]n]sf] lbzfn] xf]Og b[96f / sd{7tfn] eljio sf]/ P k/b]l;Psf ldqx¿ b]zsf] ;'Gb/ eljio ltdL hxfF /x] klg ltd|f] dgsf] ;'Gb/ efjgfn] lgwf{/0f ub{5 .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 88
csn axfb'/ cd]l/sfdf M Ps zAb lrq krxQ/ jif{sf] rfp/L k/]sf] cg'xf/ af]s]/ 3/fo;L af]emb]lv lgj[Q ag]/ ctLtsf] y'k}| ;DemgfnfO{ slt la;]{/ slt cWdf}/f] :d[ltdf afFr]/ df]6f] kfj/jfnf r:df k'5\b} nfdf] ;f; km]b}{ csn axfb'/ /fO{ Ps emns aflx/L lxpFsf] y'k|f] lgofN5 a"9f cfFvfn] EofP;Dd lgofN5 ;u/dfyfsf] b]zdf hGd]/ klg gb]v]sf] lxpF dHhfn] Ps 6s x]l//xG5 . a'9Øf}nLn] lhp Tolt rNb}g t/ dgdf w]/} s'/f rN5 .
Proof
ufpFdf t /ft 5 o; ;do a:t' efp ;a uf]7df x'ln;s] xf]nfg\ g/fd|f] ;kgf b]lvof] v} s] g/fd|f] ;dfrf/ cfpg] kf] xf] ls < gofF3/]sf] afa' ladf/ lyof] s]xL kf] eof] ls < ;fFlxnL bldgL a}gL cf]5Øfg k/]sL lyO{ jfl;ª\u6gsf sfJo ;';]nL M 89
36gf kf] 36Øf] ls < g/dfOnf] nfu]/ cfpF5 clg /;fPsf cfFvfnfO{ xftn] k'R5 t/ cfh oqf] jif{sf] 9lNsFbf] pd]/df pm cfh cd]l/sfdf 5 ef]hk'/sf] lbª\nf ahf/df g} p;n] ;'g]sf] xf] cd]l/sf t/ 5f]/f;Fu 8LeL k/]/ cfPkl5 emg\ /fd|f];Fu a'‰g yfNof] cd]l/sf ;'?df t pm sd v';L ePg b]v]/ cd]l/sf pGglt÷ult / ljsf; b]v]/ 7x/fof] cd]l/sf :ju{ xf] clg pm /dfpFb} uof] cd]l/sfdf
Proof
pm w]/} v';L x'G5 clg /dfpF5 klg hlxn] hlxn] st} g]kfnLx¿sf] e]nf x'G5 cfg} efiff af]Ng]÷st} cfg} If]qsf slt 6f9fsf gft]bf/ e]6\5 o:tf] cj;/df clg ;f]W5 e]6]hltnfO{ gfgL s] y/L < 3/ stf k¥of] lg < s;sf gflt < s;sf 5f]/f < k|Zgsf] nfdf] km]xl/:t t];f{pF5 emfkf eg]sf] < s'g ufpF < @))& ;fnsf] qmflGtdf la/f6gu/df ePsf] qmflGtdf p;n] n8]sf] j[tfGt sxG5 p;nfO{ To;}n] dgk5{
jfl;ª\u6gsf sfJo ;';]nL M 90
o:tf] g]kfnLx¿sf] hd36df bdsf] /f]uL :ofF :ofF ub}{ a"9f] vf]S5 cF tfKh]h'ª eg]sf] < ;f]W5 csf]{;Fu b]zsf] y'k|} ufpF k'u]sf] 5 y'k|} hftLo efiff a'‰5 t/ yf]/} efiff af]N5 klg hflu/sf] l;nl;nfdf km'ª\lnª\ tfKn]h'ª a;]sf] syf xfN5 ;f]W5 gfgL s] ha]u'÷dfb]g÷k|;fO{+÷k|wfg s] k¥of} lg < cflb cflb
Proof
t/ csn axfb'/ /fO{ cd]l/sfsf] 5f]6f] a;fOkl5 g} cfgf] ufpF kms{g xtfl/Psf] 5 ca lsgls pm cfgf] lbgrof{ b]v]/ lbSs 5 lbge/ h]n h:tf] sf]7fdf y'lgg' 5 lbge/ ;fgf] gflt x'G5, t/ g]kfnL k6Ss a'‰b}g ;fFemdf a'xf/L cfpF5] pm g]kfnL xf]Og 5f]/fsf] d'v x]g{ / af]Ng klg Ps xKtf s'g'{kg]{ 7fpF cfgf] efiff af]Ng / wLt df/]/ ulkmg' klg s'g} rf8 kj{ kv{g'kg]{ 7fpF o:t} lx;fan] k"/f 5 dlxgf lalt;s] t/ 5f]/fsf] 5'§L g} ldNb}g cfgf] b]z hfg o:tf] :ju{h:tf] b]zdf klg csn axfb'/ v';L 5}g cfFvf /dfP klg p;sf] dg /dfPsf] 5}g cd]l/sfsf] ljsf;sf] v';Ldf eGbf cfgf] b]zsf] b'Mvdf a9L lrlGtt 5 jfl;ª\u6gsf sfJo ;';]nL M 91
cfg} kl/jf/ geP klg ufpFn]sf] Kof/ / lrGtf a];L 5 eG5— …csf{sf] /fd|f] ljsf;eGbf cfg} ufpF Kof/f] nfU5 csf{sf] v';L / ;Gtf]ifeGbf cfg} b'Mv, ufpF / ufpFn]df dg /dfpF5Ú clg pm cd]l/sfnfO{ 3/ aflx/ y'lk|Psf] lr;f] lxpF;Fu bfFHb5 cd]l/sf lxpFh:tf] lr;f] /x]5 x]bf{ ;]tf] /fd|f] ;kmf 5'g, v]Ng dg nfUg] t/ s]xL If0fdf g} xft s7Øflª\u|P/ 6s\6lsP/ kmfn]/ efUg'kg]{ w]/} a]/ 5f]O /fVg} g;lsg] To;}n] csn axfb'/ /fO{ xtfl/G5 cfg} Kof/f] ufpF lbª\Unf ef]hk'/ kms{g
Proof
jfl;ª\u6gsf sfJo ;';]nL M 92
;8s /ft ;'t]sf] 5 lg:tAwtfdf r'krfk r'krfk lyof] sf]nfxn klxn] ca dTy/ e}s]sf] 5 /ftsf kx/]bf/x¿ uh{G5g\ va/bf/L ub}{ clwsf/ vf]l;Gg eG5g\ t/ klg /ftsf] z"GotfnfO{ lrb}{ sf]nfxn ;'? x'G5 ah|G5g\ xfQL k}tfnfx¿ ;8s dfly dfly
Proof
;8s ;'Tb}g hf] slxNo} ;8s hf] e]befj hfGb}g slxNo} cfkm" lslNrP/÷lylrP/ klg ;a}sf] uGtJo lglZrt u5{ hlxn] klg b[Zox¿ ;NanfpF5g\ st} qmflGtsf st} ;dy{gsf st} lj/f]wsf 36gf kl/36gfx¿ km]l/G5g\ t/ ;8s cfkm" ndtGg k/]/ lylrPsf] 5 hlxn] klg lslrPs} 5 jfl;ª\u6gsf sfJo ;';]nL M 93
t/ klg ;8ssf] kIfdf kl/eflift aGb}gg\ cfjfhx多 5ftLel/ j]bgfn] k'l/P/ ;'T5 slxn] cfFvfel/ v';Lsf] pGdfb af]s]/ ljho pT;j u5{ slxn] t/ x/If0f x/kn k}tfnfd'lg lylrP/ klg b[9 ;xofqLem}F ag]/ o'uf}F o'u afFr]sf] 5 ;8s st} nfdf] cTof; nfUbf] u/L t]l;{Psf] 5 st} kmgkmgL 3'd]sf] 5 uf]nfsf/ aGb} t/ klg lglZrt 5 uGtJo ;a}sf] ;'g;fg /ftdf ha lg:tAwtf 5fpF5 kx/]bf/ va/bf/L u5{ ;'Tg b]pm ;8snfO{ zflGt b]pm ;8snfO{ kNofsk'n's x]/]sf gh/x多 v:ofsv';'s u/]sf cfjfhx多 If0f e/d} sf]nfx/ ag]/ t]l;{G5g\ ;8sdfly pkm\ e|flGtsf] kxf8n] lylrP/ cGof}n kl/j]zdf afFlwP/
Proof
jfl;捉\u6gsf sfJo ;';]nL M 94
x/kn x/If0f ljjz 5 cfkm" lslNrg÷cfkm" lylrg of] ;8s . ;8sx¿ prflnG5g\ cfjfhn] ;8sx¿ s'lNrG5g\ k}tfnfn] ljleGg juL{otfdf ljeflht ;8s slxn] lgn{Hh ag]/ ;fIfL a:5 c/fhstf lj?4sf] k|bz{gsf/Ldfly ePsf] g[z+; xTofsf] ;8s df}gtfdf afFlwP/ afWo aG5 d"sbz{s aGg clg lbgx'F anfTs[t aGg To;}n] P ldq sljx¿ hgclwsf/sf kIfkftL xf} eg] ;8ssf] clwsf/sf] af/]df sljtf sf]g]{ u/ .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 95
df]/fn]; ufl;{of uDeL/ zfGt d'b|fdf cfufsf] nKsf af]s]/ cfFvfdf alni7 kfv'/f / pGgt 5ftL ePsf] df]/fn]; ufl;{of ljzfn hgnx/sf] le8df bx|f] d'7L s:b} lrRofof] æxfd|f] eljio s;}n] y'Gg ;Sb}gÆ le8n] lrRofof] æy'Gg ;Sb}g÷y'Gg ;Sb}g÷y'Gg ;Sb}g pm km]l/ lrRofof] æ:jtGqtf xfd|f] s;}n] 5]Sg ;Sb}gÆ km]l/ le8n] bf]xf]¥ofof] æ5]Sg ;Sb}g÷5]Sg ;Sb}g÷5]Sg ;Sb}gÆ
Proof
gful/s :jtGqtfsf clwsf/L af]n] z/0ffyL{ ;DaGwL a'Fbf a'Fbf s]nfP k6s–k6s sfª\u|];df ax; eP cem;Dd df]/fn];sf] eljiodfly lg0f{o ePg cd]l/sfdf a;]sf] pGgfO; jif{kl5 cfh crfgs df]/fn]; cj}wflgs ePsf] 5 pm cj}wflgs x'gfdf g t p;sf] s'g} bf]if 5 g t p;sf] s'g} /x/ 5 jfl;ª\u6gsf sfJo ;';]nL M 96
bf]if lyof] t p;sf afa'cfdfsf] h;n] cfgf] pHHjn eljiosf] nflu / pRr lzIffsf] nflu o; b]zdf lelqg' b'O{ jif{sf] df]/fn]; cfgf] afa'cfdf;Fu pgLx¿sf] xft ;dfTb} sfg'gL ¿kdf o; b]zdf lelqPsf lyof] . s] b'O{ jif{sf] df]/fn];n] o; b]zdf lelqg' g} ck/fw eof] < of] cx+ k|Zg p;sf] hLjgsf]
Proof
;f/f hut\sf k|f0fLx¿ efjL ;Gtltsf] nflu ;'Gb/ eljiosf] nflu h;/L Ps b]zaf6 csf]{ b]z lelqG5g\ To;/L g} df]/fn]; lelqof] o; b]zdf pGgfO; jif{;Dd pm jl~rt ePg lzIffdf÷:jf:Yodf clg sfxLF st} klg oqf] jif{;Dd p;nfO{ yfxf ePg pm cj}wflgs xf] eg]/
jfl;ª\u6gsf sfJo ;';]nL M 97
t/ cfh PsfPs pm xtk|e eof] pm xtfz eof] p;n] cfkm};Fu k|Zg u¥of] / cfgf] b]z vf]Hg yfNof] kl/lrtsf] le8df pm ckl/lrt aGof] ldq d08nLsf] ;efdf pm u}/ sfg'gL cfk|jf;L aGof] sfg'gL ¿kdf /xFbf a:bf pm cfh u}/ sfg'gL 7xl/of] .
Proof
lsgls cfh h'g wtL{df pGgfO; jif{sf] k"/f hjfgL latfof] hxfF p;n] af]Ng l;Sof] lxF8\g l;Sof] clg snf / ;+:s[lt l;Sof] dfof kfpg l;Sof] clg dfof lbg l;Sof] ToxL b]zn] cfh p;nfO{ eGb} 5 ltdL cj}wflgs xf} ltdL u}/ sfg'gL xf} ltdL kms{ hfpm clg To;kl5 PsfPs p;sf] xfF;f] vf]l;of]
jfl;ª\u6gsf sfJo ;';]nL M 98
?g] cfF;' l/lQof] clg eljio /f]lSsof] . df]/fn]; ufl;{of ls+st{Joljd"9 ag]/ ;f]W5 cfgf] afa'cfdfnfO{ ca d sxfF hfpmF < ;f]W5 cfgf] eljiosf] af/]df t/ cxF pQ/ s;};Fu 5}g pm ;f]R5 clg ljb|f]x af]N5 o;/L g} o; ;Eo ;dfhdf cft°sf/L hGd ef] xf]nf
Proof
df]/fn]; dWo hjfgLdf hLjgsf] rf}/:tfdf l7Ë plePsf] 5 g t cl3 a9\g ;S5 g t s]xL ;f]Rg ;S5 g t ;f]r]sf] s'/f ug{ ;S5 g t kms{g g} ;S5 cfkm" hGd]sf] b]zdf hxfF pm ckl/lrt 5 ;a};Fu / l;Ë} b]z;Fu p;nfO{ 1fg 5 pm hGd]sf] b]zdf a]/f]huf/sf] kxf8 5
jfl;ª\u6gsf sfJo ;';]nL M 99
nfu' kbfy{sf] e08f/ 5 clg b]z 5f]8\g]sf] hdft lbgx'F a9\bf] 5 clg s;/L kms{g ;S5 pm o:tf] b]zdf To;}n] pm km]l/ klg uDeL/ d'b|fdf pQ]lht ag]/ bx|f] d'7L s:b} lrRofpF5 ltdL lsg ;'Gb}gf} kl/jt{g nfu' u/ xfd|f] eljio ltdL y'Gg ;Sb}gf} 5]Sg ;Sb}gf} /f]Sg ;Sb}gf} .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 100
af;' >]i7 •• ljZjf;sf] cefj •• cfpm sljtf •• d]/L cfdf la/fdL l5g\ •• Oltxf;df afFRg rfxg]x¿
Proof hGd M @)!^, sf7df8f}F xfn M p8la|h, elh{lgof Od]n M
basushrestha@gmail.com
af;' >]i7n] @)#@ ;fnb]lv ;flxTodf snd rnfpg yfn]sf] b]lvG5 . pxfF d"ntM sljtf, syf / lgaGw dg k/fpg'x'G5 . ;flxTosf] ljz]if cg'/fun] ubf{ g} pxfF cg];f; 8L;L d]6«f] RofK6/sf] b'O{ k6s pk;efklt / Ps k6s ;efklt x'g'eof] . pxfF cd]l/sfaf6 ;'? ul/Psf] k|l;4 ;flxlTos j]e–;fO6 …v;v; 86sdÚsf ;+:yfks x'g'x'G5 . pxfFsf sljtfdf jt{dfg g]kfnsf] /fhgLlts cl:y/tf, lj;Ëlt / ljs[lt, v:sFbf] /fhgLlts d"No, g]t[TjbfoL ju{df b]lvPsf] lglxt :jfy{ / To;n] /fi6«nfO{ kf/]sf] b'ik|efjk|lt lrGtf k|s6 ul/Psf] b]lvG5 . pxfFsf sljtf d"ntM ;d;fdlos /fli6«o ;d:ofdf s]lGb|t b]lvG5g\ . pxfFsf] sfJofTds cleJolQm snf klg ljifofg'¿k / k|efjsf/L b]lvG5 . jfl;ª\u6gsf sfJo ;';]nL M 101
ljZjf;sf] cefj o'uf}Fo'ub]lv kq] r6\6fgem}F txtx nfu]/ a;]sf lgZrn ljZjf;x¿ cfh PsfPs nfefn] kufNg yfn]sf 5g\ o'uf}Fo'u;Dd crn / c6n /x]sf ljZjf;sf cUnf lxdfnx¿ cfh crfgs tftf] df};dn] aUg yfn]sf 5g\
Proof
d]/f] dg cflQPsf] 5 cfFvfx¿ ;hn ePsf 5g\ Åbosf] ult tLj| 5 kfOnf cl:y/ / clglZrt 5g\ d cl:y/ x'Fb} 5' t/ sf/0f vf]Hb} 5' nfefsf] clg df};dsf] s] sf/0fn] km'6Øf] Hjfnfd'vL < s] sf/0fn] tfTof] df};d < sf/0f h] eP klg gx'g] eO/x]sf] 5 ljZjf;sf] hu g} xlNnPkl5
jfl;ª\u6gsf sfJo ;';]nL M 102
ljZjf;sf] cfwf/ g} x/fPkl5 ljZjf;sf] pbfx/0f g} klUnPkl5 slxNo} gd]l6g] u/L d, tkfO{+, ltdLx¿sf] cl:tTjdf cfFr cfpg]5 ;DaGwdf lr/f kg]{5 x]/fOdf wld/f nfUg]5 dfgjtfjfb / eft[Tjdf vf]6 nfUg]5 clg xfdL PSn} PSn} lgh{g hËndf kz'em}F cfgf] efiff cfkm}n] dfq a'‰g]u/L sf6\g' kg]{5 lbgx¿ gL/; gL/; clg ljs/fn /ftx¿
Proof
tl;{g' kg]{5 cfkmGtx¿;Fu clg cfg} :j/x¿df j/j/ a:g]x¿ k/k/ x'g]5g\ jt{dfgdf cufl8sfnfO{ e]6\g] of k5fl8sfnfO{ s'g]{ k|yf x/fP/ tL b'j}y/L eGbf a]Un} clg PSn} af6f] /f]Hg' kg]{ x'G5 ljZjf;sf] cefjdf jfl;ª\u6gsf sfJo ;';]nL M 103
t/ gx'g' eO/x]sf] 5 xfdL Tot} pGd'v eO/x]sf 5f}F cljZjf;sf] vf8n vGb} ljZjf;sf] vf8n k'b}{ 5f}F clg ToxL cljZjf;sf] vf8nsf] lkFwdf xfdL af; a:g vf]Hb} 5f}F . To;}n] eGg'xf];\ tkfO{+ g} ljZjf;sf] vf8n k'l/g' ljZjf;sf] r§fg kUng' ljZjf;sf] lxdfn kUng' s] ;'vb ;dfrf/ xf] <
Proof
jfl;ª\u6gsf sfJo ;';]nL M 104
cfpm sljtf af]nfpF5' ltdLnfO{ cfpFb} cfpFlbgf} sltv]/ cfpF5Øf} ltdL eGb} elGbgf} dfofu/L ;'D;'DofpF5' km'Q} eflu xfN5Øf} slxn] cfpg] kvf{Odf dnfO{ 5f]l8 hfG5Øf} e]6nfO{ ck"/f] g} agfO lxF8\5Øf}} ltdL ;'G5' km]l/ k'Uof} c/] ;fyLsxfF ltdL p;sxfF eg] ltd|f] lbg /ft af; d}n] rflxF ltdL kfpg slt u/fF} cf;
Proof
rfxgf 5 dgdf ltdL ;Fw} a;] x'GYof] ltdLnfO{ cl3 /fvL n]Vg kfP x'GYof] afFlw /fv"F ltdLnfO{ OR5f oxL hfUof] o;f] x]5{', km]l/ eG5' sljtf t efUof]
ltdL eP j]b af]Ny]F, bz{g klg lbGy]F ;'v b'Mv h] 5g\ ;f/f To;df kf]lvlbGy]F P]gf agfO{ ;+;f/nfO{ x]/ elg lbGy]F Dffgj dg, dfgj ;f]r To;df xfln lbGy]F hLjg d]/f] l;Fufg{nfO{ ltd|f] vfFrf] k¥of] slt k|of; u/]F t/ vf]O / uhf{] 6¥of] < ltdL eg] 6f9f–6f9f dg b'vfO{ efU5Øf}} wL/tfsf] d]/f] ;Ldf ltdL ;f/f gf£5Øf} jfl;ª\u6gsf sfJo ;';]nL M 105
cfpm d]/f] 5]pdf a; kf]v ltd|f ;|f]t afFlrlbG5' jfrLjfrL ltd}| lnO{ cf]t ;fbf sfkL a;]sf 5g\ ltdL To;df kf]t h;} ls;fg v]tdf u5{ d]xgtsf] hf]t af]n]F af]nF] d}n] af]n]F ltdL cfof} Sof/] Åbosf] em°f/df tf/ aHof] Sof/] zfGt tfn dfem 7"nf] nx/ rNof] Sof/] a'em] ;an] rfn x]/L sfJo cfof] Sof/]
Proof
Pp6f sYo /Rg b]pm clg ltdL hfg" d}n] rfx] cfudgsf] ;':t kfOnf rfNg" ltd|f] ;fy kfPF eg] aG5' x]/ slj gq ldq;fd' d]/f] x'Gg /fd|f] 5lj
jfl;ª\u6gsf sfJo ;';]nL M 106
d]/L cfdf la/fdL l5g\ clxn] d]/L cfdf la/fdL l5g\ cf]5Øfgdf ynf k/]sL l5g\ pu| Joyfn] 56k6fO /x]sL l5g\ cg]s /f]u 5g\ t/ lgbfg ePsf] 5}g To;}n] clxn] d]/L cfdf la/fdL l5g\
Proof
z®ofdf ynf k/]sf] lgs} eO;Sof] s}®ofF} 8fS6/ cfpF5g\ gf8L lgwf/ 5fD5g\, lgsf] x'g] vf]qmf] cfZjf;g lbG5g\ hfG5g\ slt 8fS6/ t km]l/ kms+{b}gg\ klg To;}n] lgs} k6s 8fS6/ km]l/of] g;{ klg km]l/of] cf}iflwd"nf] ul/of], km]l/of] t/ cxF s;}n] hftL ug{ ;s]gg\ s;}n] lgsf] ug{ ;s]gg\ d]/L cfdfnfO{
;fob 8fS6/sf] ;§f lrlsT;s ePsf] eP Û ;fob g;{sf] ;§f kl/rfl/sf ePsf] eP Û cfdfsf] /f]u lgsf] x'GYof] ls < cfdf plxNo} tªlu|O ;lSyg\ ls < dgdf Pp6f lemgf] z°f plAhO /xG5 t/ clxn] d]/L cfdf la/fdL l5g\ jfl;ª\u6gsf sfJo ;';]nL M 107
cfdf la/fdL ePsf] df}sf 5f]k]/ ;Flwof/n] s/];fsf] ;Ldf sf]kg{ yfn]sf] 5 cfFug aLrsf] t'n;L d7 p;}sf] xf] eGg yfn]sf] 5 3/sf] w'/Ldf /x]sf] k/fnsf] s'Ogf] klg cfg} eGg yfn]sf] 5 . l7s o;}a]nf bfh'efOsf dltof/n] cFl;of/sf] gfddf c+zsf] nfuL la/fdL cfdfnfO{ lryf]g{ l;sfO/x]sf 5g\ cfdfsf] z/L/df ePsf] Psw/f] sk8f klg a? cfdf gfË} eP klg Roft]/ aG8f ug{ tlD;/x]sf 5g\ xfdLnfO{ a:g af; ePg eGb} cfdfnfO{ lry|flry|f kf/]/ lryf]g{ gª\u|f ltvfb{} 5g\ cfdfsf] 5ftL r';]/ x'ls{Psf ;Gtfgn] cfdfsf] ToxL 5ftLdf ljb|'ktfn] el/Psf] tf08j gfr gflr/x]sf 5g\ ta t dltof/sf] cf8df plePsf c+l;of/x¿sf] rsf{] / a]cy{sf] o:tf] cfjfhn] cfdf emg} la/fdL x'g yfn]sL l5g\
Proof
d eg] cfdfsf] cf}iflwd"nf]df bf}l8pmF of l5d]sLsf] bfaLnfO{ lg:t]h u¿F of bfh'efOsf] cfk;L /8fsf]nfO{ ;fDo kf¿F jfl;ª\u6gsf sfJo ;';]nL M 108
c;d~h;df k/]/ uGtJo x/fP/ rf}tf/Ldf a;]sf] a6'jf em} /ge'Nndf k/]sf] 5' ;defjn] Pp6} kf]N6f]df x'ls{Psf tL ;Gtfgaf6 cfh crfgs cf/f]lkt aGb} l5g\ sf]xL nfvfkfvf eof] /] sf]xL 7"nf;fgf eP /] sf]xL wgLul/a eP /] t/ d b]V5' h] hlt 5g\ ltgnfO{ ;Gtfgsf] ¿kdf dfq b]Vg] cfdfsf] d'6' Pp6} dfq 5 / dfof Pp6} dfq 5 cfdfsf] Tof] Pp6} d'6' / dfof ;j{yf dfq b]Vb5'
Proof
a]nf a]nfdf clnstf xnrn ul5{g\ s]xL vflG5g\, clnslt xfFl:5g\ / slxn] t gflR5g\ klg t/ of] bL3{sfnLg aGg} ;Sb}g lsgeg] ;xg ;Sb}gg\ cfdfsf b':dgx¿n] b':dg dfq lsg eGg] cfg} ;Gtfgx¿n] lryf]g{ sf]kg{ yfN5g\ jfl;ª\u6gsf sfJo ;';]nL M 109
yfN5g\ cfg} cfdfsf] OHht n'6\g ;xg ;s];Dd leqleq} b'lV5g\ cfdf clg kL8fn] 56\k6fpFl5g\ lrRofpFl5g\ s/fpFl5g\ c;Xo ePkl5 a]xf]; eP/ n8\l5g clg c;Qm la/fdL x'lG5g\ d]/L cfdf / clxn] klg la/fdL g} l5g\ .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 110
Oltxf;df afFRg rfxg]x多 lxhf]sf] k|flKtnfO{ ;Dem]/ ;bf ;kmn ePsf] 7fg]/ To;}df /dfpg / e'Ng rfxg]x多nfO{ d s] egf}F v} < lxhf]sf] b'Gb'DeL / rdssf] pHofnf]nfO{ ;DemL cfhsf] cGwsf/df clg c;kmntfdf lrQ a'emfpg]x多nfO{ d s] egf}F v} <
Proof
lxhf]sf] k|ultnfO{ klg cfhs} pGglt 7fg]/ hxfFsf] ToxLF a;]/ l:y/ eP/ klg cufl8 a9]sf] 7fGg]nfO{ d s] egf}F v} <
cufl8 a9\g kfOnf / af6f] lbg] uf]/]6f] / k|sfz lbg] s'6f] / snd clg lgdf{0fsf Hofan lbg]nfO{ g} l:y/ u/fpg] dgl:yltnfO{ d s] egf}F v} < jfl;捉\u6gsf sfJo ;';]nL M 111
hLjg xf] a9\g'k5{ lg/Gt/ cufl8 gbLem}F, ;doemF} gbL pb\ud :yn ;Dem]/ /f]lsFb}g em/gf kxf8sf] vf]Fr ;Dem]/ c8\b}g ;do dWofXg of z"Go ;do kv{]/ a:b}g logLx¿ t cufl8 a9\g'sf] gfd hLjg xf] ;kmntf / cf}lrTonfO{ ;fsf/ kfg{ sxLF st} g/f]lsO{ lg/Gt/ cufl8 a9\g' / sxLF st}af6 xfDkmfn]sf] jL/tfnfO{ g;DemL lg/Gt/ aUg' xf] eGg] a'em]sf] 5
Proof
a'em]sf] 5 ;don] klg ;f/f dfgj hflt p;df afFlwPsf] 5 p;sf] knkndf s'lb/x]sf 5g\ dflg;x¿ :jfF :jfF / jfF jfF ub{} ;do st} km'lTsPnf ls eg]/ xftdf, 3fF6Ldf, oGq em'G8ØfP/, 6fF;]/ hLjg rnfO/x]sf x'G5g\ t/ ;do cfkm} udSs k/]/ slxn] klg l:y/ ePsf] 5}g jfl;ª\u6gsf sfJo ;';]nL M 112
p t rNg' / cufl8 a9\g'df g}} ;kmntf b]V5 / ;kmn 7fG5 lsgeg] p;n] klg a'em]sf] 5 hLjg eg]sf] cufl8 a9\g' xf] k/Gt' s]xL of sf]xLnfO{ ljuts} cfzlQmdf /d]/ rnfodfg hLjgnfO{ l:y/tfdf kl/0ft u/]/ hxfFsf] ToxLF crn / cGwsf/sf] n]kdf a:g rfxg]x多 b]v]/ ;do, gbL clg em/gf 5Ss k/]sf] 5 ltgLx多 dfq xf]Og ;fyL ltgnfO{ b]v]/ d klg 5Ss k/]sf] 5'
Proof
ltgLx多 dfq xf]Og ;fyL d klg 5Ss k/]sf] 5'
jfl;捉\u6gsf sfJo ;';]nL M 113
Proof
jfl;ª\u6gsf sfJo ;';]nL M 114
8f) df]xgk|;fb hf]zL •• v} s] u/]5 < •• dnfO{ t xfF;} p7\5 •• leGgtf x]g]{ ls ;dfgtf < •• sljtf n]Vg ufx|f] 5
Proof hGd M @)!$ ;fn, sf7df8f}F xfn M l:k|ËlkmN8, elh{lgof Od]n M
mohan_p_joshi@yahoo.com
k];fn] dl8sn 8fS6/ / k|fWofks ;d]t ePsf hf]zLsf cf}ifwL / :jf:Yo;DaGwL lstfax¿ k|sflzt b]lvG5g\ . pxfFsf] …sxfF 5 7fpFÚ gfds sljtf;ª\u|x k|sflzt ePsf] 5 . pxfFsf sljtfdf Psflt/ hLjgk|lt ulx/f] lrGtg ul/Psf] b]lvG5 eg] csf{tkm{ xn'sf xf:o / Joª\Uo klg ul/Psf] kfOG5 . sljsd{sf] bfloTjaf]w u/]/ klg sljtf n]lvPsf] b]lvG5 . h]xf];\ hf]zL sljtfnfO{ efj jf ljrf/n] dfq geP/ z}nL / lzNkn] klg ;+oldt / ;Gt'lnt kf/]/ k|:t't ug'{x'G5 . nofTdtf / ;/ntf pxfFsf sljtfsf k|d'v nIf0f ePsf 5g\ . oxL zlQmn] pxfFsf sljtf Åbo:kzL{ ePsf 5g\ . jfl;ª\u6gsf sfJo ;';]nL M 115
v} s] u/]5 < lhGbuLn] v} s] u/]5 < vfln ¿vx¿nfO{ x]/]5, hËnsf] efj} e'n]5, lrqx¿df gh/ c8\sfP5, …Sofgef;Úsf] xf];} u'dfP5, ljZj dfglrqsf cg]sg\ wsf{ x]g{d} Jo:t ag]5 ;fFlRrs}sf] w/tLdf tL wsf{ 5}gg\ eGg] la;]{5, 8fF8fsfF8f / cfsfznfO{ cnucnu b]v]5, Pp6} NofG8:sf]ksf ¿kdf bz{g ug{ ;s]g5, sflGtk'/ / eQmk'/nfO{ leGgleGg eg]5, km'nrf]sLaf6 cleGg b]lvg] pkTosf e'n]5 .
Proof
of] lhGbuLn] v} s] u/]5 < vfln c+zx¿d} cfFvf uf8]5, k"0f{nfO{ ;Demg} 5f8]5 .
jfl;ª\u6gsf sfJo ;';]nL M 116
dnfO{ t xfF;} p7\5 dnfO{ t xfF;} p7\5 tkfO{+ s:tf] p6\k6Øfª ug'{x'G5, clnslt lj>fd u/ eGg'x'G5 . tkfO{+nfO{ yfxf 5}g d slt Jo:t 5' < s] s] ub{5' < n ;'Ggf];\— km];a'sdf cfgf kmf]6f cknf]8 ub{5', ltg}dfkm{t ;of}F;Fu uDeL/ Rof6 ub{5', sd;]sd lbgsf] b'O{ 306f df]afOndf af]Nb5', To;sf ;fy} Ps–b'O{ 306f 6]S:6 d];]h k7fpF5', lel8of] u]d lhTgnfO{ Hofg lbP/ v]Nb5', cfOKof8sf s}of}F ufgf l:sk ub}{ ;'Gb5', x/]s ufgf cfwf ;'g]kl5 kmf:6–km/jf8{ ub{5', l/df]6 lyRb}lyRb} l6eLsf Rofgn km]b{5', ;+;f/el/ s]s] eO/fÚ5 lbgsf] b'O{ k6s x]b{5', Tof] ;a u/L aNntNn /fltsf] b'O{ ah] ;'Tb5' .
Proof
ca t a'‰g'ef] tkfO{+n], d slt Jo:t 5' < d;Fu 6fOd xf]nf t lj>fd u/]/ v]/ kmfNg] < cfhsf] dfG5]nfO{ gx'g] k'/fgf] afgL cFufNg] <
jfl;ª\u6gsf sfJo ;';]nL M 117
leGgtf x]g]{ ls ;dfgtf < eG5g\ sf];LnfO{ k"j{sf] s0ff{nLnfO{ klZrdsf] pQ/lt/ vf]Hb} hfFbf kfgL t b'j}sf] lxdfnsf] kft /ËLg nfn'kft]sf] km"n nfnLu'/fF;sf] lgofn]/ x]bf{ b'j}n] nfnL t nfn} lnPsf]
Proof
:jfbdf cldnf] l;GsL xf] /; dL7f] rfgfsf] oL b'O6} vfGsLsf] d"n t cflv/ d"n} xf] nfx'/]sf] km"n w]/} /ªsf] ;]tf] / kx]Fnf] ;'gufefsf] df6f]d'lg t b'j}sf] ufgf]d} lhGbuL ag]sf] cfF}nfsf] zf]ef cf}F7Ln] 3fF6L ;'xfPsf] l;qmLn] cflv/ b'j} uxgfn] ;f}Gbo{ kfPsf] ;'g}n] dgdf]xs d"lt{ ag]sf] 3/sf] hu eO{ a;]sf] h'g 9'Ëfdf 9n] lg 9'Ëf cflv/ rf]O6f r§fgsf]
jfl;ª\u6gsf sfJo ;';]nL M 118
sljtf n]Vg ufx|f] 5 sljtf n]Vg ufx«f] 5 To;} sxfF cfpF5 / Û skLdfly rNof] eGb}df sndn] sfJo NofpF5 / Û efj/; rflxG5 kB To;} cfpF5 / Û uGb} dfqf ldnfof] eGb}df zAbn] uhn NofpF5 / Û
Proof
kfgLdf t}l/g ufx|f] 5 hLp kmfNb}df x'G5 / Û zjf;gn] t}¥ofpF5 d'9] ann] x'G5 / Û hLjg a'‰g ufx«f] 5 /x:o To;} v'N5 / Û /fd|/L cfkm}FnfO{ x]/f}F c¿nfO{ x]/]/ x'G5 / Û
jfl;ª\u6gsf sfJo ;';]nL M 119
Proof
jfl;ª\u6gsf sfJo ;';]nL M 120
z/b lg/f]nf •• lsg cfof} cd]l/sf < •• pd/ vøofd, vnLn lha|fg / d •• clnslt cfF;' k}Frf] rflxPsf] 5 •• csd{0otf jf cl:tTjxLgtf
Proof hGd M h"g @@, !(%!, zflGtgu/, ´fkf xfn M d]l/NofG8, cd]l/sf Od]n M sniraula7@gmail.com lg/f]nfn] cª\u|]hL / ;dfhzf:qdf Pd=P= ug'{ePsf] 5 . pxfF cg];f; jfl;ª\u6g 8L;L d]6«f] RofK6/sf] k"j{ cWoIf x'g'x'G5 . pxfF d"ntM cfVofgsf/sf ¿kdf ;'kl/lrt x'g'x'G5 . pxfFsf P3f/j6f pkGof; k|sflzt 5g\ . pxfFn] g]kfnL / cª\u|]hLdf Joª\UofTds :tDe n]vg klg ug'{ePsf] b]lvG5 . To:t} ljB'tLo ;fO6df klg pxfFsf y'k}| sljtfx¿ k|sflzt b]lvG5g\ . pxfFsf sljtfsf] s]Gb|Lo k|j[lQ xf:o Joª\Uo g} xf] . pxfFsf sfJodf ;fdflhs, ;f+:s[lts / /fhgLlts lj;Ëlt, ljs[lt / lj8Dagfk|lt ulx/f] Joª\Uo ul/Psf] kfOG5 . pxfFsf sfJodf b]zk|]dsf] ;'jf; klg dudufPsf] 5 . pxfF ;/n / ;Dk|]if0fLo cleJolQm sf}znn] cfgf sfJonfO{ snfTds kfg{ l;kfn' b]lvg' x'G5 . jfl;ª\u6gsf sfJo ;';]nL M 121
lsg cfof} cd]l/sf < s] s] g kfpFnf egL cd]l/sf cfof} afa'–a/fh]n] gvfPsf] d;fn]bf/ uf]tf vfof} cfpg t cfof} ;a} s'/f 5f8]/ cfgf] :jfledfg cfgf] jr{:j ;a} u'dfof} To;} egLsg lg/fzfjfbLx¿ s'ln{G5g\ cfkm" s]xL ug{ ;Qm}gg\ csf{nfO{ bf]if lbG5g\ lg/y{s efj'stfsf Ifl0fs nx/df /dfpg] tL cd]l/sfsf] s]jn v]bf] dfq u5{g\
Proof
cd]l/sfnfO{ klg cfg} d'n'sh:tf] 7fG5g\ e}k/L cfpg] labf oxfF klg c;Lldt xf];\ eG5g\ laxfg xflh/ u/]/ lg:s]sf] dfG5] a]n'sL kfFr aHg nfUbf dfq kmls{G5g\ xfd|f] b]z sfd} gu/L vfg] b]z xf] To;sf] cfg} kl/kf6L 5 cd]l/sf sfd} dfq u/]/ vfg] b]z xf], o;sf] klg cfg} rng 5 xfd|f] b]zdf sfdrf]/nfO{ ;w}F xfO–xfO 5 o; b]zdf sfdrf]/nfO{ ;w}F afO–afO 5 d t eG5' oxfF cfpg'eGbf cl3 cfgf] cfTdf;Fu s'/f ug'{k5{ of] cj;/n] el/Psf] b]z xf] cj;/sf] vf]hLdf nfUg'k5{ cfgf] kf}/vn] /ftf/ft s/f]8klt aGg] 7fpFdf ;xL af6f]sf] ls6fg ug{ ;Sg'k5{ jfl;ª\u6gsf sfJo ;';]nL M 122
of] sd{7 dfG5]x¿n] agfPsf] b]z sd{7tfd} c8]sf] 5 of] Odfgbf/L / ;RrfOsf] jh|–s7f]/ hudf plePsf] 5 o;df cfgf] Odfgbf/L xfNg;s] nf]s–k/nf]s ;k|G5 a]OdfgLsf] af6f] lnP Oxnf]s;d]t lalu|G5 To;}n] P d]/f ;fyLefO lbbLalxgLx¿ :jb]zdf cfkmGtnfO{ lrÝL k7fpFbf cSsf;–ktfnsf] ;kgf gb]vfpm cd]l/sfdf t ¿vdf 8n/ kmN5 egL cfkmGtsf] laNnaf7 gnufpm
Proof
n]lvb]pm oxfF sfd gu/] hLjg clt sl7g 5 oxfF ;w}Fel/ sfd 5 km';{bsf] sdL 5 aNntNn kfPsf] Ps lbg] km';{bd} cfTd;Gt'li6sf] ;':s]/f 5
u5'{ eGg]nfO{ oxfF cj;/sf] vfFrf] 5}g p2]Zo lnP/ lxF8\g]sf nflu af6f]df sfF8f 5}g lg?2]Zo lxF8\g]sf nflu of] d?e"ld ;dfg 5 ;kmn ToxL aGg] 5 h;sf] xftdf tL/–sdfg 5 .
jfl;ª\u6gsf sfJo ;';]nL M 123
pd/ vøofd, vnLn lha|fg / d ;f}Gbo{ sxfF x'G5, s;df x'G5, slt x'G5 lar/f vnLn lha|fgn] t hfg]gg\ pd/ v®ofdn] ;d]t ;'/fdf ;'Gb/L b]v] c;nL ;f}Gbo{sf] dd{ a'em]gg\ æ/f]6Lsf] Pp6f 6'qmf, ;'/fsf] Pp6f lunf;, ;fydf ltdLÆ -clg d]/f] pkxf;_ pd/ v®ofdn] t b]v] dlb/fd} d:tL lal;{lbP cfgf] Oltxf; t/ d g t v®ofd g} x'F, g t vnLn lha|fg Pp6f aa'/f] g]kfnL ;w}F nvt/fg
Proof
tfklg Psflt/ lha|fgsf] af]nL n6k6fPs} x'G5 csf]{lt/ v®ofdsf] vx/] TolQs} aU5 ;f}Gbo{sf] kl/efiffsf] rqmJo"xdf cledGo'em}F kmF;]/ lha|fgn] s'¿ktfdf klg ;f}Gbo{ cg'e"lt u/] v®ofdn] klg dlb/fsf pu| 5fnx¿df ¿k / hjfgLsf /Ëx¿ e/] . v®ofdn] eg]em}F æuf]Ko s'/f cgGt 5 g t ltdLnfO{ yfxf 5 g t dnfO{ a'sf{ k5fl8 s]jn xfdL b'O{s} dfq rrf{ 5 jfl;ª\u6gsf sfJo ;';]nL M 124
a'sf{ vf]Ngf;fy g ltdL 5Øf} g d]/f] g} cl:tTj 5Æ d]/f] klg ToxL xfnt 5— ltd|f] ¿ksf] cufl8 g d]/f] cl:tTj 5 g t ;Ksf] k5fl8 d]/f] s'g} tfl/km 5 s]jn Ps emns b]v]sf] e/df ;Dk"0f{ hLjg clezKt 5 ca t o:tf] nfU5 lsg d v®ofdsf] Kofnfleq ;'6'Ss kl;gF lsg lha|fgsf] s'¿ktf cFufNg] kl/efiffleq lg;°f]r cfTdbfx ul/gF cflv/ ;f}Gbo{n] clt lbUe|ldt ePsf] dfG5] d s'¿ktfleq klg ;f}Gbo{ x'G5 v'§Øfpg} ;lsgF .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 125
clnslt cfF;' k}Frf] rflxPsf] 5 lhGbuLe/ cfzf / lg/fzfsf] aaG8/leq kfª\u|f 3'd]em}F 3'Dbf 3'Dbf slxn] xif{sf] t slxn] la:dftsf] x'G8/Ldf 5fnx¿n] lsgf/nfO{ emD6]sf] b]Vbf clg lsgf/sf afn'jf 5fn;Fu} nxl;P/ ;d'b|d} ljnLg ePsf] b]Vbf r;Ss d'6' rs{G5 cfFvfdf kfgL eg{ dg nfU5 t/ b'j} cfFvf l/Qf 5g\ To;}n] dnfO{ clnslt cfF;' k}Frf] rflxPsf] 5
Proof
;'Sv / zflGtsf] nflu ;a} 5f]8]/ d'Unfg k:g'\ efjLsf] s/fdt xf]nf j}ej / dfgsf] vflt/ ;ft ;d'b| gf£g' sd{sf] n]vf x'Fbf] xf]nf sd{sf] cyfx dd{ ga'emL cfkmGt 5f8\g' ljlwsf] s7f]/ ljwfg xf]nf ;kg} ;kgfx¿ af]s]/ cfPsf oL cfFvfx¿df k6Ss} kfgL 5}g To;}n] t eG5' dnfO{ clnslt cfF;' k}Frf] rflxPsf] 5
t/ s;n] kf] b]nf / cfF;' k}Frf] oxfF oxfF cfF;'sf PsPs yf]kf 8n/sf gf]6;Fu ufFl;Psf 5g\ jfl;ª\u6gsf sfJo ;';]nL M 126
/ftel/ em/]sf cfF;'sf yf]kf laxfg hd]/ a/km aG5g\ ToxL a/km lbpF;f] kl;gf;Fu ldl;P/ klUnFb} cfF;'sf yf]kf aG5g\ sd{n] g} n]v]sf] xf] jf b}jn] g} lrtfPsf] xf] tL cfF;'sf yf]kf lkpFbf /utsf 3'6\sf aG5g\ cfFvfaf6 /ut x}g cfF;' aufpg'5 To;}n] t dnfO{ clnslt cfF;' k}Frf] rflxPsf] 5
Proof
jfl;ª\u6gsf sfJo ;';]nL M 127
csd{0otf jf cl:tTjxLgtf slt g} sf]l;; ubf{ klg o; Åboleq /x]sf] lg/fzfsf] sxfnLnfUbf] cFWof/f] r'seGbf klg sfnf] eOlbP/ d]/f] cl:tTj sfnfDo x'g k'u]sf] 5 d]/f] rf/}lt/ d]/f csd{0otfsf d]/f clt/l~ht lgliqmotfsf d]/f d"NoxLg dfGotfsf dfkb08 agfOPsf 5g\ d]/f] c;dy{tfsf PsPs /];f ;Fufn]/ Oltxf;sf kfgf agfOPsf 5g\
Proof
d t Ps ;'vb p2]Zo k|flKtsf] k5fl8 bu'/]sf] dfG5] cfgf] uR5]n] EofP;Dd sd{ ug]{ dfG5] d]/f zlQm tGt'x¿ lgliqmotd l:yltdf k'lu;Sbf klg cfzfsf] lau'n km'Sg] dfG5] cfh d]/f] rf/}lt/ nId0f/]vf sf]l/Psf] 5 elgG5 efUodfly e/ kgf{n] dflg;sf] sd{0otf cf]/fnf] nfUb5 t/ of] sxfjt d]/f xsdf nfu' gxf]nf lsg ls d]/f] t efUo g} ;bf vf]6f] /lxcfPsf] 5 sd{0otfsf] t s'/} gu/f}F csd{0otfn] g} ;w}F ?jfO/x]sf] 5 . jfl;ª\u6gsf sfJo ;';]nL M 128
;'bLkeb| vgfn •• emª\sf/ •• la5§ ef]/df w/f k|5Gg ¿k e]l6of];\ •• cfkm}FnfO{ d lrlGbgF •• d s;/L k"0f{ ;+;f/ u5'{ <
Proof
hGd M lj= ;+= @)@^, kNofª\vf]nf, j;Gtk'/, tgx"F xfn M xG8{g, elh{lgof Od]n M reachtosudip@yahoo.com
vgfnn] @)$$ ;fnb]lv ;flxTo n]vg ofqf ;'? u/]sf] b]lvG5 . pxfFsf] …dw'snzÚ gfds sljtf;ª\u|x k|sflzt 5 . pxfF cGt/f{li6«o g]kfnL ;flxTo ;dfh, l8;L RofK6/sf] k"j{ pkfWoIf x'g'x'G5 / cGo ljleGg ;+:yfx¿;Fu klg cfj4 x'g'x'G5 . pxfFn] g]kfn /fi6« a}+ssf] ;flxlTos k|sfzg …ldld{/]Úsf] ;Dkfbg ;d]t ug'{ePsf] 5 . pxfF d"ntM slj g} x'g'x'G5 . k|foM zf:qLo 5Gbdf sfJofTds efj JoQm ug{ ?rfpg] vgfnsf sljtfdf sf]dn ljrf/ / efj ;f}Gbo{ 5rlNsPsf] 5 . pxfFsf sljtf zf/bLo rGb|dfsf] zLtntf;Fu t'ngLo b]lvG5g\ . pxfFsf] sfJo– lzNk ;fFRr} dgd'Uwsf/L b]lvG5 . jfl;ª\u6gsf sfJo ;';]nL M 129
emª\sf/ Hof]lt ;+;f/sf] b[li6 ;[li6sf] b[li6 r]tgf 1fg lj1fgsf] Hof]lt k|]d ;+;f/sf] 3gf cfef Tof] r]tgf a'G5 a'G5 ;+;f/ r]tgf k|]ds} laDadf v'N5 k"0f{ ;+;f/ l;h{gf
Proof
;kgf lhGbuL a'G5 lhGbuL ;kgf :jod\ leq l/ª\6f 5'6L ?G5 kmGkmgL k|]ddf :jod\ wtL{df ;kgf km'N5 :jKgdf w/tL :jod\ cd"t{ r]tgf k|]d d"t{ ;+;f/ of] :jod\ k|]d cfwf/df ;[li6 ;[li6 cfwf/ k|]dsf] wtL{df hnem}F k|f0f ;[li6df k|]dsf] :jod\
jfl;ª\u6gsf sfJo ;';]nL M 130
k|]d xf] r]tgfaLh ;[li6sf] kfn'jf km"n k|]d pNnf;sf] /Ë ;[li6sf] e'Ne'n] d"n l;h{gf O{zsf] ¿k k|]dsf] k|ltdf :jod\ k|]d emGsf/df g[To a|Xdf08 /rgf :jod\
Proof
jfl;ª\u6gsf sfJo ;';]nL M 131
la5§ ef]/df w/f k|5Gg ¿k e]l6of];\ ;d'b|leqsf] snf eP/ df]tL emlNsof];\ a;/] :j0f{e"M ;ef ;'zflGt uLt ufOof];\ / ;f}dg:on] d[b" ;'ef; ljZj 9flsof];\ v'n]/ 1fgsf] k|ef lgzf k|dQ gfl;of];\ la5§ ef]/df w/f k|5Gg ¿k e]l6of];\ pvfnL å]ifsf] h/f dg'iotf lkmFhfl/of];\ d[bËgfbdf :jod\ eljio gt{gf u/f];\ e'nL cg]stf / cft{gf k|;Ggtf lkmFhfl/of];\
Proof
lgMzAb zAbdf v'nf];\ ;du| efjgf km"nf];\ bl/b| bfgjL bzf d/L ;d[l4 Tof] v'nf];\ / gL/Jof]dem}F agL / 5ftL of] km/flsof];\ ;nLn z}ndf gofF k|eft Hof]lt km}lnof];\ sn° bDe 8'ª\8'ªL s/fn Tof] gkm}lnof];\ ljzfn efn j}ejL ;'sLlt{ Tof] gj}lnof];\ k|zfGt efjgf v'nf];\ / k|]d/fu km}lnof];\ / :jTjsf] lrgf] Wjhf s;}u/L gd}lnof];\ d ljZjdfgjL ag"F / eft[efj km}lnof];\ ;'sd{ ;Eotf lglw st} s;} gd}lnof];\ hlt 5 afFRg' lhGbuL v'n]/ xfF:g kfOof];\ / d[To' e]6 Tof] x'Fbf d/]/ afFRg kfOof];\
jfl;ª\u6gsf sfJo ;';]nL M 132
cfkm}FnfO{ d lrlGbgF ;Demgfleq d]/f] 5 5fofF ltd|f] cem} klg d'6'leq st} rN5 dfof ltd|f] cem} klg ;kgfdf ;w}F 3'D5' d]/f] g]kfn lblGbg ljgf g]kfnsf] ;fyL cfkm}FnfO{ d lrlGbgF lj/Qm ;kgfleq /Qm /l~ht /ft 5 ;du| ;kgf laDa eTs]sf] Oltxf; 5 t}klg ;kgf a'G5', l;h{gf a'G5' lblGbg ljgf g]kfnsf] ;fyL cfkm}FnfO{ d lrlGbgF
Proof
cfFvfdf nflndf af]S5', nfnLu'/fF;sf] ;w}F 5ftLdf efjgf af]S5', ;f/ a'4Tjsf] ;w}F t}klg v'Ng ;Qm}g :jKg, lgdf{0fdf lsg < ljgf g]kfnsf] ;fyL cfkm}FnfO{ d lrlGbgF xftn] ;'D;'DofP/ gS;f g]kfnsf] 5'Fb} emNofF:; slxn] x'G5' n]sa]F;L kxf8 u} u08sL slxn] t5'{, t/fO{ em5'{ l5lG5g ljgf g]kfnsf] ;fyL cfkm}FnfO{ d lrlGbgF d hxfF hfpmF g]kfn kfOnf kfOnf e/L xftdf rN5 g]kfn sd{sf c~h'nL e/L b[li6 g]kfnsf] af]sL ub{5' ljZjbz{g ljgf g]kfnsf] ;fyL cfkm}FnfO{ d lrlGbgF
jfl;ª\u6gsf sfJo ;';]nL M 133
d s;/L k"0f{ ;+;f/ u5'{ < d]/f] cfg} lk|o 5 tgx"F 5ftLdf rNdnfO{ r"FbL d]/} ;a g;g;f aU5 Tof] ;NanfO{ yfgLdfO{sg hutsf km"nsf 8f]nL x]5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5{' < d]/f] hGd:yn 5 /l;nf] eL/df sf]lknf 5g\ af/L6f/L jg rx'/sf ofb tL rf]l6nf 5g\ l;DkfgLsf] ;/; hnsf] :jfb Tof] ofb u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ <
Proof
af6f] v'Nb} klg cem lyof] k"0f{ Tof] ef] ls P]n] d]/} 7fpF kl5 lbg s'g} kfpFnf x]g{ d}n] kmsL{ k'vf{lt/ ljutsf] yfTynf] ofb u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ <
d}n] la;]{+ lsg ;dosf] uLtdf g} dnfO{ cfkm}FnfO{ klg e'lnlbP em}F 5 e]p gkfO{ s:tf] xf] of] ;'v ls b'Mv v} lhGbuL k|Zg u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ < d}n] d]/f]kg lg s;/L lal;{PF nf}g cfdf /D3f d]/f] cem 5 pm ?Fb} 3fF;Lsf] ;Demgfdf /fvL tGxf};'/ Åbodf :jKgdf u} bu'5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ <
jfl;ª\u6gsf sfJo ;';]nL M 134
df/L 8'AsL don dgsf u08sLdf d w'G5' d:of{ª\bLsf nx/ dgd} km"n tf/]/ ?G5' bf]af6f]sf a/lkknsf] 5fxf/L ofb u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ < e}nf] Bf};L cem 3/3/} ofbdf lgTo v]N5' 3f6' /Gsf] cem 5 dgdf uLt vf]h]/ ;'G5' sf}/f ;DemL h'?h'? u/L gfr"FgfrF" d x'G5' la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ <
Proof
dL7f] cfg} hg hutsf] nf]sefsf ;';]nL Kof/f] cfg} /g / jgsf] ;Demgfsf t/]nL ;DemL cfg} ljut dgsf uLt u'Gu'g\ d u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ < kfOnfdf cem lg d ;w}F 6]S5' Bf}/fnL 8fF8f pSnLpSnL cem lg d ;w}F k'Ub5' sf]6 8fF8f g]6f] sf6] klg lbglbg} ;lDemO{ ofb u5'{ la;L{ cfg} :yn d s;/L k"0f{ ;+;f/ u5'{ <
jfl;ª\u6gsf sfJo ;';]nL M 135
Proof
jfl;ª\u6gsf sfJo ;';]nL M 136
xl/ l3ld/] •• ctL{ •• :jfutd\ •• cfpg] k':tfnfO{ •• kl/0flt
Proof
hGd M @)!# dª\l;/ &, vf]6fª, BflDn6f/, aflaofvs{ xfn M cn]Sh]lG8«of, elh{lgof Od]n M gomahari@hotmail.com
lqe'jg ljZjljBfnodf efiff;flxTo k|fWofkg u/]/ tLgbzs latfO;Sg' ePsf l3ld/]n] @)#) ;fnb]lv ;flxlTos /rgf k|sflzt ug{ k|f/De ug'e{ Psf] xf] . sl/a rf/ bzs nfdf] l;h{g ofqfdf pxfFn] y'k|} km'6s/ ;flxlTos /rgf k|sflzt u/fO;Sg' ePsf] 5 . pxfF ;flxTosf wd{1 / dd{1 x'gx' G' 5 . pxfF yf]/} n]v/] w]/} eGg vf]Hg'xG' 5 . ;ª\VofTdstfdf eGbf u'0ffTdstfdf, k|rf/–k|;f/df eGbf PsfGtsf] l;h{gtkdf ljZjf; u/]/ /dfpg'xG' 5 . g]kfnL efiff;flxTosf] ;]jfdf ;dlk{t l3ld/]sf sljtfn] ljk/Lt b[Zo laDa l;h{gf u/]/ sfJoefj uDeL/ agfPsf 5g\ / jt{dfgdf b]lvPsf ljifd kl/l:yltnfO{ Jol~ht u/]sf 5g\ . efjL lkF9LnfO{ cGof}nk"0f{ jt{dfg;Fu kl/lrt u/fP/ efjL hLjgdf lg/fz gx'g k|l] /t ug]{ efj JoQm u/]sf 5g\ . lg/fzfk"0f{ jt{dfgnfO{ Jol~ht u/L pHofnf] eljiosf] ;°]t u/]sf 5g\ . l3ld/]sf sljtfdf zAbfn°f/ / cyf{n°f/sf] dfq geP/ laDa / k|tLssf] klg ;"Id / ;r]t k|of]u kfOG5 . oxL zlQmn] pxfFsf sljtfsf] efj snfTds / uDeL/ ag]sf] 5 . jfl;ª\u6gsf sfJo ;';]nL M 137
ctL{ hL0f{–zL0f{ z/L/ lnP/ ;dosf] lzv/ k'Ug] a]nf ef] kfPsf] cd"No j/bfgnfO{ clezfkdf abNg] a]nf ef] g bfg lbPF, g dfg lbPF g t s'g} pknlAwsf] ;Ddfg lnPF g d'7L lbPF g df6f] lbPF g s'g} ;zQm of]ubfg} lbPF
Proof
d}n] hLjg kfPsf] lyPF t/ d ;fFRr} eG5'— aflrgF d}n] cd[t kfPsf] lyPF t/ d}n] ;fFRr} To;nfO{ lkOgF ca t ljZjf;sf] efiff 5}g j/bfgsf] klg cfzf 5}g To;}n] d}n] d]/f] cfpg] k':tfnfO{ atfpg] s'g} Oltxf; 5}g t/ d pgLx¿nfO{ cjZo atfpg]5'— æd]/f] h:tf] z"Go hLjg ltdLx¿n] afFRg' kg]{5}g .Æ
jfl;ª\u6gsf sfJo ;';]nL M 138
:jfutd\ d}n] oxfF w]/} y/Lsf dfG5] km]nf kf/]F— of}6f rf}tf/L h:tf]df /]nsf] Kn]6kmd{ h:tf]df cem eg"F— s'g} ljzfn tLy{d]nf h:tf]df dfG5]— leGg–leGg pd]/sf leGg–leGg cfsf/–k|sf/sf leGg–leGg /Ë–la/Ësf nf]Ug]dfG5]–:jf:gLdfG5] hdftsf–hdft, x'nsf–x'n cfpg] cfO/x]sf] 5, hfg] uO/x]sf] 5 jftfj/0f st} ;'Gb/ 5÷dgdf]xs 5 5xf/L 5÷xl/ofnL 5 st} ljiffQm 5÷b'u{lGwt 5 phf8 5÷d?e"ld 5 st} a'4sf] efp 5 st} o'4sf] 3fp 5 sf]xL lxF8\g] tof/Ldf 5g\ sf]xL le8\g] tof/Ldf 5g\ km';{b s;}nfO{ 5}g t/ klg== = :jfut rflxF oxfF ;a}nfO{ 5 k|tLIff s;}nfO{ 5}g
Proof
jfl;ª\u6gsf sfJo ;';]nL M 139
cfpg] k':tfnfO{ d lxF8\bflxF8\b} yfls;s]F nfdf] ofqfsf ;xefuL ltdL kv{g' k5{ tnaf6 cfPsfnfO{ af6f] b]vfpg'k5{ kfnf] ltd|f] xf] lhDd]jf/L ltd|f] xf] gq e6\ls b]nfg\ sf]xL lx6n/ aGnfg\ sf]xL lagnfb]g xf]nfg\ uXgfPsf] Oltxf;nfO{ gfs y'g]/ eP klg Psl5g kv{ ;f]emf] af6f] b]vfpm hxfF lr;f] atf; rnf];\ h?jf kfgL e]l6of];\ ;"of]{bo;Fu} wtL{ d';'Ss xfF;f];\
Proof
rf/}lt/ lIflth b]lvg] 7fpFdf v'nf ljBfnodf Pp6f la;f}gL agfpFnf clg wtL{sf] syf ;'gfpFnf ltd|f] h?/t 5— …;'Gg]nfO{ ;'gsf] dfnfÚ xf]nf eGg]nfO{ t …km"nsf] dfnfÚ 5Fb} 5 cjsfz k|fKt hLjgn] ;'gsf] dfnf nufOlbFb} Pp6f ;Qf x:tfGt/0f ug'{5 . jfl;ª\u6gsf sfJo ;';]nL M 140
kl/0flt kljq kfjge"lddf klxn]–klxn]sf kxndfg -lje"lt_x¿sf] k/fqmd / kl/>dn] k|z:t kl;gfåf/f k|aGw ePsf] kf}/vdf k':tf}–k':tf kflnof}F xfdL kNnljt eof}F xfdL / k'i6 eof}F xfdL ku]{lnP ljrf/x¿ klGkP– ;fg, dfg, OHht / uf}/j ÛÛ
Proof
kl5;DDDDd== = = = = = = = k/–k/af6 k|zl:t ufOPsf lyP k6s–k6s kbsx¿ kfOPsf lyP k/fO{n] klg k|z+;f u/]sf lyP kfgL gkfP/ xfdL t[Kt ePsf lyof}F k/rqmL 5Ss k/]sf lyP k/b]zL rlst ePsf lyP k/d]Zj/n] jf:tjdf xfdLnfO{ cfzLjf{b lbPsf lyP kl/jt{g x'Fb}–x\'Fb} cfof] kfkL o'usf] k|f/De eof]— k/Dk/fdfly e'OFrfnf] uof] kltt ljrf/n] k|>o kfP jfl;ª\u6gsf sfJo ;';]nL M 141
k|To]s JolQmsf] k]6 kfNg] kl/of]hgf aGof] kq dfgl;stf ljsl;t eof] kuflnP–ljhosf s[ltx¿ kvflnP– jL/tfsf :d[ltx¿ kfun x'Fb} 5f}F— Psflt/ kª\u' aGb} 5f}F— csf{lt/ k'vf{sf] k|an kblrXgnfO{ k5Øfpg ;s]gf}F k'/fgf ;+:s[ltnfO{ cFufNg ;s]gf}F k|lta4 geP/ xf]nf xfdL kl5 k/]sf 5f}F lklNkn] /fli6«otfsf] Hof]ltdf afFlr/x]sf 5f}F .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 142
x]dGt >]i7 •• 3f]8f / dfG5] •• sfF8f / km"n •• lgjf{;gsf] s73/fdf
Proof
hGd M dª\l;/ $, @)!$, Dofun'ªahf/, t]x|\y'd xfn M l:k|ªlkmN8, elh{lgof Od]n M shresthahemanta@hotmail.com
lzIff zf:qdf :gfts >]i7 g]kfnL efiff;flxTosf ljlzi6 ;fws x'g'x'G5 . g]kfn k|1f k|lti7fgdf b'O{ bzseGbf a9L / ;flxTosf/ kqsf/ ;‹df klg sl/a b'O{ bzs hlt g} sfo{ u/]/ pxfFn] ;flxlTos, k|fl1s / ;flxlTos kqsfl/tfdf ljz]if of]ubfg k'¥ofpg'ePsf] 5 . pxfF lb Ps]8]dL ckm g]kfnL kf]o6\; PG8 /fO6;{ jfl;ª\u6g 8L;Lsf k"j{ pkfWoIf, g]kfnL ;flxTo k|lti7fg pQ/ cd]l/sfsf dxf;lrj x'g'x'G5 . cfwf bh{g hlt ;flxlTos ;f+:s[lts ;‹;+:Yffsf cfhLjg ;b:o x'g'x'G5 . pxfF Psflws ;flxlTos ;‹;+:yfaf6 k'/:s[t / ;Ddflgt klg x'g'x'G5 . pxfFsf b'O6f sljtf;ª\u|x / Pp6f Joª\Uosf] >Jo Sof;]6 k|sflzt 5g\ . pxfFn] ljleGg ;flxlTos s[lt / klqsfsf] ;Dkfbg klg ug'{ePsf] 5 . pxfFsf sljtfsf] d"n :j/ Joª\Uo / ljb|f]x xf] . ;dsfnLg g]kfnL sljx¿dWo] pxfF lgtfGt leGg / gjLg b]lvg' x'G5 . sljtfTds ;+/rgf, Joª\Uo / ljb|f]xsf b[li6n] pxfF :juL{o slj ljgo /fjn;Fu t'ngLo b]lvg' x'G5 . pxfFsf] lzNk cToGt k|efjsf/L b]lvG5 . jfl;ª\u6gsf sfJo ;';]nL M 143
3f]8f / dfG5] Psk6s ljZjsLlt{dfg /fVg] t/Ëdf Pp6f dGqL 3f]8fdf a;]/ ;u/dfyf r9\of] xif{ a9fOF eof] km"n, dfnf / cla/n] 9kSs} 5f]lkg' eof] dGqLhL
Proof
tyflk 3f]8f eg] afFlwO{ g} /Xof] ta]nfdf
ta]nfd} a;]/ x]l//x\of] xiff]{Nnf;, :jfut / lbu\ljhosf] kj{ x]bf{ x]b}{ e|d eof] p;nfO{ ;u/dyfdf k'Ug] pm lyof] ls dGqL < 3f]8f cflv/ 3f]8f g} xf] ljb|f]xnfO{ r'krfk 3'6'Ss lgNof] / dflnssf] ;'vnfO{ cfTd;ft\ ub}{ jfl;ª\u6gsf sfJo ;';]nL M 144
uj{ ug{] sf]l;; u¥of] …sDtLdf cfg} 9f8n] k'¥ofPsf] xf] ;DdfggLo dGqLnfO{ ;u/dfyfsf] 6'KkfdfÚ 3f]8fn] x]l//x\of] dfG5]sf] ck"j{ /ldtf dfG5]sf] cGwf]kgf / zlQmsf] cf/fwgf t/ cxF, s;}n] p;sf] rf;f] ;d]t /fv]gg\
Proof
la:tf/ la:tf/ dfG5]sf] le8 a9\b} uof] le8 ;Fu;Fu} ljrf/sf] klg le9 a9\g yfNof] ljrf/ eg]sf] dfG5]eGbf vt/gfs xltof/ xf] s]xL wfl/nf ljrf/x¿ 3f]8fnfO{ 3]g{ k'u] 3f]8fsf] Tof] cb[Zo zlQmnfO{ vf]tNg yfn] / ljb|f]xL ljrf/x¿ 5g{ yfn] Pp6fn] eGof]– …jL/ t of] 3f]8f xf] ;Ddfg o;sf] x'g'k5{Ú
jfl;ª\u6gsf sfJo ;';]nL M 145
csf]{n] eGof]– …of] t ;fwg dfq} xf] dGqLn] gnu]sf] eP s;/L k'UYof] of] ;u/dfyf <Ú t];|f]n] yKof]– …cflv/ dfG5] klg 3f]8} xf] ;Demf}F clxn] 3f]8fs} ;Ddfg eO/x]sf] 5Ú Pp6f bfz{lgs cfP / dfxf}]nnfO{ bz{gdo agfpFb} eg]]– …jf:tjdf dfG5] 3f]8}] xf] af]Sg' oL b'j}sf] ;a}eGbf 7"nf] u'0f xf] 3f]8fn] dfG5] af]S5 dfG5]n] dfG5]s} af]em af]S5 hLjge/ s'b\5, bu'5{ / ;a}nfO{ 7]ufg nufO ;s]kl5 cGTodf oxL 3f]8f h:t} cfkm\g} cfFugdf PSnf] / lgM;xfo eP/ a:g afWo x'G5Ú
Proof
;'g]/ of] bË k¥of] 3f]8f / 7fGof] …cxf Û d klg dfG5] h:t} /x]5'Ú jfl;ª\u6gsf sfJo ;';]nL M 146
To:t}df csf]{n] ;xL yfKof]– …ztk|ltzt ;xL dfG5] 3f]8} xf] To;dfly klg g]kfnL t afOkÌL 3f]8f xf] / g} t g]kfnLn] /ftf/ft ub\bf/nfO{ klg ub\bLdf k'¥ofpF5 / xf]; cfPkl5 lxglxgfP/ cfg} ta]nfdf v'§f ahf/]/ plk|m/xG5Ú
Proof
;'g]/ of] km'Q lgl:sof] 3f]8fsf] d'vaf6– …y'Ss, d t g]kfnL h:t} kf] /x]5'Ú
jfl;ª\u6gsf sfJo ;';]nL M 147
sfF8f / km"n r'krfk vlk /Xof] vlk g} /x\of] km"nn] sfF8fsf] HofbtL t/ vKgfsf] ;Ldf elTsPkl5 Ps lbg /utn] ntkltPsf] cg'xf/ lnP/ km"nn] sfF8fnfO{ egL– æa}u'gL /x]5f} u'gsf] abnfdf ltdLn] dnfO{ v'g lbof}Æ
Proof
nfhn] lz/ lgx'/fof] sfF8fn] / zfnLg x'g] r]i6f ub}{ eGof]– æhGdhft u'g clnslt kf]lv xfn]5 dfkm kfpF5' ls <Æ ljZjf;3ftn] 9'Ëf alg;s]sL km"nn] cfj]zdf egL– æ;k{ /x]5f} ltdL Joy{} d}n] b'w lknfPFÆ jfl;ª\u6gsf sfJo ;';]nL M 148
sfF8f cflv/ sfF8f g} lyof] km"nsf] jrg krfpg} ;s]g / PSsl; hfOnfUof] km"ndfly t/ aLr}df /f]s]/ km"nn] sfF9fnfO{ ;/fk lbO{– æ;f; /x];Dd ltd|f] xftn] d]/f] z/L/ 5'g g;sf];\ ltdLaf6} c;'/lIft /x]5' d To;}n] ca cfOGbf d]/f] ;'/Iffsf] cleef/f ltdLn] g} r'sfpg' k/f];\Æ
Proof
o;/L >flkt sfF9fx¿ ToxL lbgb]lv cfhGd km"nx¿sf kx/]bf/ eP/ ple/x]5g\, ple/x]5g\
jfl;ª\u6gsf sfJo ;';]nL M 149
lgjf{;gsf] s73/fdf xh'/ d g} x'F y'k|} z'elrGtsx¿n] cleof]u yf]k/]sf] cleo'Qm x]dGt >]i7 ddfly slj ljKnj k|tLssf] cleof]u 5 sljtf lsg n]Vg 5f]8] < snfsf/ nIdL >]i7sf] cleof]u 5 lsg gofF sljtf ;'gfpg 5f]8] < g]kfndf 3/hd ePsL ;fyL sNkgf lkofsf] cleof]u 5 8n/sf] xltof/n] cfgf] sndsf] lga lsg efFr] < otf v;v; 86sdsf] sf/f]af/ ug]{ ;Dkfbs af;' >]i7 5g\ pgsf] cleof]u 5 vfln d lsg k'/fg} sljtf ;'gfpF5' Pp6L k'/fgf k|]ldsf 5] p;sf] t emg}
Proof
jfl;ª\u6gsf sfJo ;';]nL M 150
dxfcleof]u 5 eG5]– æxTof/f xf} ltdL cfkm" leqsf] ;[hgzLntfnfO{ df/]/ cfkm"nfO{ ltdLn] xTof/f ;flat u/fPsf 5f}Æ yk uha t cem of] 5 ls oL ;f/f cleof]ux¿ oyfy{ x'g\ eg]/ ;f5L lsgf/fdf cfg} >LdtLn] NofKr] nufPsf] a'9L cf}Fnfsf] 9®ffa|] 5fk 5
Proof
d lg/Lx k|ltjfbL dg'jf cleof]udf bh{ ePsf cf/f]ksf Ps Ps tL/x¿n] 3fOt] eP/ a;f}{+b]lv ljlIfKt 5' k|ltjfbsf nflu ;flatL aofg lbg k6s k6s h'd'{/fPsf] 5' t/ vu|f; ePsf] h"g;Fu Hof]lt lbg] zlQm sxfF x'G5 / < ddfq ;flnsem}F lg/Gt/, lg?Q/ cfg} Åbosf] s73/fdf lz/ em'sfP/ ple/x]sf] 5' d]/f r]tgfx¿ km/f/ ePsf 5g\ ts{x¿ e"ldut ePsf 5g\
jfl;ª\u6gsf sfJo ;';]nL M 151
d[tjt\ ;+j]bgzLntfx¿ lhpg'sf] k|nodf ufl8Psf 5g\ ;g\ b'O{ xhf/sf] Pp6f p/f7 nfUbf] udL{df cd]l/sfsf] ljzfn cfsfzleq afkm h:t} x/fPsf] d]/f] ef}lts b]x kQ} ePg sxfFsxfF s;/L r'Oud x'Fb} uof] d 6fFl;Fb} uP tGsFb} uP / pKsfpg} g;Sg] u/L cfkm\g} hLjgaf6 lgjf{l;t ePF
Proof
lgjf{l;t 5 d]/f] dl:tis lgjf{l;t 5 d]/f] x[bo lgjf{l;t 5g\ d]/f cfFvf / sfgx¿
cxf] Û slt sl7g x'Fbf] /x]5 lgjf{;gsf] Zjf; k|Zjf; d ;+j]bgxLg lg:nf]6 afn'jf eP5' r]tgxLg 6'lqmPsf] k|:t/ eP5' dnfO{ s'g} cfnf]sn] tfGg ;Sb}g s'g} :kz{n] 5'g ;Sb}g jfl;ª\u6gsf sfJo ;';]nL M 152
h] b]V5', ;'G5' / ef]U5' ;a} ;kf6 nfU5g\ of] eofjx lg/fzfdf d /; s;/L lgsfnF" < z"Go, z"Go ;a} z"Godf d sljtf s;/L n]v"F < v} slxNo} ljB't\ dx;'n jfkt sljtf dfluPg kfgLsf] z'Ns e'QmfgL sljtfn] ug{ ;lsPg 3/ ef8fsf] ef/ yfDg} k¥of] cfpg hfg hLjgnfO{ uf8Ldf /fVg} k¥of] h'u'K;f 5 vr{sf] u'h'N6f] s|]l86 sf8{sf] df/ vKg} k¥of] sljtfnfO{ ufF; agfpg ;lsPg ;flxTonfO{ skf; agfpg ;lsPg ;fFrL g} cg'j{/ ePsf] 5 d]/f] cIf/sf] v]tL v} s;/L s] n]v"F < To;}n] ofb cfO/xG5 af/Daf/ slj ljZjljdf]xgsf] sljtf …d eft hf]8"F ls sljtf n]v"F <Ú
Proof
jfl;ª\u6gsf sfJo ;';]nL M 153
d]/f z'e]R5's lk|o hgx¿ Ifdf d}n] d]/f efjgfnfO{ laqmL u/]F d}n] d]/f n]Vg] cfF}nfnfO{ lgjf{l;t u/fPF Ifdf d}n] lgik|of]hg :ki6Ls/0f lbP/ lhpg'nfO{ km]l/ Ps k6s dL7f] lgx'F agfPF .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 154
xf]dgfy ;'j]bL •• zLtnx/ •• sljtfs';'d •• ;]t' •• ¿v
Proof
hGdM ;g\ !($&, tfsd, DofUbL xfnM p8la|h, elh{lgof Od]n M hsubedi@gmail.com
xf]d ;'j]bLn] :gftsf]Q/ txsf] z}lIfs of]Uotf k|fKt ug'{ePsf] 5 . pxfF k"jL{o bz{gsf cWo]tf x'g'x'G5 . jt{dfg g]kfnL ;flxTodf pxfFsf] kl/ro pxfFs} ;flxlTos s[lt / sd{n] lbPsf 5g\, c¿n] lbO/xg' kb}{g . lj=;+= @)@% df lbNnLsf] g]kfnL 5fq ;‹n] lgsfn]sf] …lxdfnLÚ klqsfdf k|sflzt …cljj]sÚ gfds syfaf6 pxfFsf] ;flxlTos ofqf k|f/De ePsf] b]lvG5 . rf/ bzs nfdf] ;flxlTos ofqfdf pxfFn] gf}j6f pkGof;, gf}j6f sfJofTds s[lt, b'O6f syf;ª\u|x, tLgj6f ;dfnf]rgf / cGo cfwf bh{g hlt ljljw s[ltx¿ k|sflzt u/fO;Sg' ePsf] 5 . slj, cfVofgsf/, ;dfnf]rs, lgaGwsf/, ;Dkfbs cflb ljljw JolQmTjsf wgL ;'j]bL ljz]if u/L slj / cfVofgsf/sf ¿kdf k|Voft x'g'x'G5 . pxfFsf sljtf, uBfTds, kBfTds / nf]snofTds 5g\ . pxfFsf sljtf efj / ljrf/ b'j}sf] ufDeLo{n] cf]hk"0f{ 5g\ . pxfFsf] z}nL lzNk k|jfxk"0f{ b]lvG5 . pxfFsf] sfJo zlQm / ;f}Gbo{ pbfx/0fLo kfOG5 . jfl;ª\u6gsf sfJo ;';]nL M 155
zLtnx/ of] gLnf] uugdf sxfF x':;' cfof] xfd|f] ;+/rgfdf sxLF g sxLF t r'xfj6 5 g]tfsf] aLrdf Ps b/f/ cfof], ;+:yfsf] aLrdf Ps km/f/ cfof] 3/ ufpF ;x/ Aff6f] sf/ / cfjt hfjt x':;'n] 9fs]/ cGwf] ePsf] 5 3/3/d} hf8f]n] 8lNnPsf] 5 geP af6f]df u'8\g]
Proof
sf/, 6«s / hxfhn] Ps csf{nfO{ xfg]/ S|of; kf/]sf] 5 hf8f]n] ;'gfdL h:t} dfG5]dfly cfs|d0f u/]sf] 5 cfafnj[4 slt slt zLtnx/n] d/] …Go'hÚ t ;'Gg} g x'g]5 zLt–o'4eGbf of] rsf]{ ;a}nfO{ a/km agfP/ cfPsf] 5
kmf]g 5}g Od]n :sfOk s]xL 5}g cfof] eg] …l/l;eÚ ug]{ 5}g jfl;ª\u6gsf sfJo ;';]nL M 156
ug]{ klg s;nfO{ < zLtnx/n] ;a} bfFt ls6]sf 5g\ d/]sf] d'bf{ h:t} yf]t] bfFt b]vfP/ a;]sf 5g\ S|of; xf]nf eGg] qf; xf] cfkmGts} kmf]g klg alxisf/ u/]sf 5g\ . ljs[ltsf] of] lj8Dagf zLtnx/sf] xf] ls s;}sf] :jfyL{kgf <
Proof
uug :jR5 lyof] ;dfh :jR5 x'g'k5{ snf uGtJo lyof] ;]jf nIo x'g'k5{ o;dfly zLtnx/ sxfFaf6 cfof] < of] k|s[ltdf z'4Ls/0f x}g xfd|f] Psk6s km]l/ csf]{ hg–o'4 x'g'k5{ .
uw{j zLtnx/n] x':;'nfO{ xTs]nfn] 5]s]/ cfafnj[4 hf8f]n] dfg]{ u/]sf] 5 zLtnx/sf] of] cfs|d0f /f]Sg 3g3f]/ jiff{ / 3fd rflxPsf] 5 r'gfp lht]/ ltg} hgtfnfO{ la;{g] g]tfnfO{ Psk6s hldgdf ptfg'{ k/]sf] 5 xfdL hf] hxfF a;]sf 5f}+ jfl;ª\u6gsf sfJo ;';]nL M 157
ToxL 8fo:kf]/faf6 of] k|fs[lts ;fdflhs k|sf]k lj?4 of] zLtnx/sf] lj?4 P6d ad 5f]8\g'k/]sf] 5 cd]l/sf a;]/ …lx6Ú eP klg g]kfnL zLtnx/l;t g]kfnLn] o'4 n8\g}k5{, d"nynf]sf] dfofsf sfFwdf of}6f aGb's /fVg}k5{,
Proof
ax'¿kL zLtnx/ of] bzfgg 5, xft nfdf] 5 df}};dsf] gfddf tfgfzfx ag]sf] 5 o;sf] 3'D6f] p3f/]/ kmfNgnfO{ hg–hfu[lt cfhsf] cfjZostf ag]sf] 5 k|lt/Iff u/ efO xf] Û gq of] dfG5] vfFb} lxF8]sf] 5, 8fo:kf]/fdf ;d]t of] cfPsf] 5 zLtnx/ 5fPsf] 5
jfl;ª\u6gsf sfJo ;';]nL M 158
sljtfs';'d cl:t k5f}6L kfn'jf b]v]/ cfPF v8]/Ldf a9\g g;s]/ 6qmSs plePsL Pp6L cljsl;t d'n'ssL dflnsfh:t} skfn sf6]sL lagf z[ﾂｪ\uf/ g} ;'8f]n pQ/L If]qsL aflnsf h:t} Gffd t ;f]w]sf] x'F la;]{F s;/L < gftf] klg ul/a b]zsf] nfPsf] x'F sf]dnfﾃ記 ﾂｿk}n] pgL d]/L ldt gfltgL eOg\
Proof
k|s[ltn] pgL d]/L 5f]/L eOg\ clg ddtfsL clwi7fqL b]jL lyOg\ tL sxfF uOg\ sf] lyOg\ ltgL s] ;fFRf} cK;/fn] em'SofPsL xf]Ogg\ geP d}n] 3/df cfpm eg]sf] klg xf] lsg cfOgg\ jf s] ef] < d ladf/ lyPF dnfO{ d]/f] qmflGtsf] ceLi6 st} n's] h:t} d glhs 5' t/ 5'g g;s]sf] h:tf] of] /d/d dhf klg x'g ;S5 stfstf dhf n'6]sf] klg x'g ;S5 jfl;ﾂｪ\u6gsf sfJo ;';]nL M 159
d a]r}g lyPF bz{gsf] nflu crfgs s;}n] 9f]sf 9S9Sofof] aflx/ x]/]F Pp6f Eofg kfls{ª n6df lyof] d}n] xtf/df d"nåf/ vf]n]F Ps aflnsf km"nh:t} plePsL lyOg\ tL pg} lyOg\ sljtfs';'d h;nfO{ d}n] tLg lbgb]lv klv{/x]sf] lyPF xif{ljef]/ eP/ sljtfl;t s';'dnfO{ ufF;]/ a}7s sf]7fdf x]/]F sf]7] uf]i7Lsf sljx¿ 6Gg a;]sf lyP d]/L sljtfn] ;f]d/; ljt/0f ub{} lyOg\ s';'dsf] xftaf6 v;]sf] ;'/fl;t sljtf u'gu'gfOg\ Pp6L ckl/lrt aflnsfnfO{ Pp6f df;df kfPF ldt gfltgLnfO{ g} d}n] cfh crfgs kfPF b]v]F nfUof] dLt alxgLnfO{ k|ToIf e]6]F d]/L sljtf s';'dnfO{ cfh sljsf] aLrdf kfPF
Proof
d]/f] a]r}gL la;fpg] cj;/ kfPF of] slj d08nLdf cd]l/sf PSn} a:bfsf] cljsl;t b]zsf] cfkmGtsf] ef]s d]6\g] d]/L ldt gfltgLnfO{ sljtfdf grfP/ of] cd]l/sfdf cfgGbsf] ;f; km]/]F s';'d g} sljtf ag]/ bz{g lbof] d]/L gfltgL ltdLnfO{ wGojfb lbPF sljx¿nfO{ sljtf lbPF .
jfl;ª\u6gsf sfJo ;';]nL M 160
;]t' ! ;]t'sf] pkdf lbG5' ar]sf] hlt of] lbg sfnsf] k"j{ ;GWofdf b;} jif{ /x] lsg < @ clwsf/ ddf 5}g Dofb yKg] s;f] u¿F Û bz jif{kl5 kmfN5 t}F xf];\ bf]ifL egL a? . # bz of] jif{df d}n] ;]t' of] kf/ ug'{ 5 ;]t'df kb /fv]/ d}n] …dÚ l;4 ug'{ 5 . $ kbfjln eP z'4 ck/fw x'Fb}g x} p2]Zo d'Vo dfg]/ ;]t' of] kf/ u5'{ x} . % a;]sf] ;]t'df P]n] lxF8]sf] klg b]V5' d} b; of]hg nfdf] ef] b; jif{ sl/ad} . ^ ;]t'sf] x]t' xf] cfTdf, cfTdf of] kl/j]zsf] lhhLljiff /x];Dd dfG5] xf] sNk sNksf] . & e|"0fdf d lyPF …dª\sLÚ cfh dfG5] d af]Nb5' b;} jif{kl5 x'G5' …c:t'Ú of] e]b vf]Nb5' . * cflbddf lyPF j:t' dfG5] 5' clu a9\b5' ;]t'df kfp /fv]/ cflb cGTo d x]b{5' .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 161
( ;f}Gbo{ ;fu/} aLr d t/]sf] /x]5' x] Û afofFdf d[To'sf] 5fn bfofFdf lhGbuL 5 /] Û !) ;kgfsf] lsgf/fdf nfu]sf] k'ndf d 5' k'n};fy au]sf] 5' hLjg\ d[To' d x]b{5' . !! cfgGbsf] ;Ldf 5}g ;]t'df bz jif{sf] oxL ;j{:j hfg]/ ef]U5' …dÚ b]x–d'lQm of] . !@ t/]kl5 5 of] …gfl:tÚ …gfl:tÚ Tof] kf/df klg ;]t'd} /xbf;Dd …cl:tÚsf] j]bgf klg . !# j]bgf efjgf kL8f d[To'–qf; ;a} ldnL c¿sf] aLrdf a:g' cfl:ts lbg 5g\ slt < !$ b;} jif{ /x] z]if clxn] ;]t'd} a; /ft lbg nufP/ /fd|f] sfd u/L ;s . !% ltdL a;] klg k'n /f]lsFb}g sbflk g} ldlt k'u]kl5 kmfN5 k'nn] ck/fwLem}F+ . !^ ;]t'df lhGbuL ltd|f] 8fof:kf]/f ;dfg 5 8fof:kf]/f eg] o:t} bf]efgsf] ;dfg 5 .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 162
!& 8fof:kf]/f agL x]5'{ b'O{ b]z a/fa/ ;]t'sf] hLjgL d]/f] b;} jif{ r/fr/ . !* ;]t'df d 5Fbf;Dd b]Vg]5' ;dbzL{ e} Gff3] of] ;]t'sf] ;Ldf d uPF ck/fwL e} . !( d]/f] dfq 5 of] ljZj eGg] Tof] ck/fwL xf] ck/fwL agfP/ sf6L kmfN5 dnfO{ Tof] . @) To;}n] d :jod\ P]n] r9]sf] ;]t'df d 5' b; jif{el/ d}n] h] ;S5' lbg ;Sb5' . @! b;} a;]{ eof] ;]t' z]if s] gfu x'G5 / < sfn}sf] k]6df k'Ubf j]bgf s] /xG5 / < @@ d x'F k|s[ltsf] kft k'u] ldlt d emb{5' ;]t'af6 em/] kZrft\ d hflGbgF s] ub{5' < @# 5f]8]sf] b'lgofF d}n] cd]l/sf k;]/ g} 8fof:kf]/f aGof] ;]t' of]eGbf k/ 5}g So} . @$ 5f]k]sf] 5 h/fn] g} Joflwsf] 5}g qf; So} Aff]6 x'F jif{n] ubf{ d[To' ckl/xfo{ g} .
Proof
jfl;ª\u6gsf sfJo ;';]nL M 163
@% d[To'sf] kl5 nfu]/ sxfF hfG5f} ltdL eg of] lgif]w g ugf{n] dfG5] ?G5 lbg}lbg . @^ d[To'sf] gfd xf] cGt cgGt;Dd rNb5 ;Totf ;]t' xf] d]/f] z]if jif{ b;} /Ú5 . @& cjz]if 5 of] hLjg\ b; jif{ /rfpg d[To'sf] ;fy hf]8]/ ;]t' of] 5 6'6fpg . @* hLjg\\af6 n7f] tfgL d[To'df nuL 6fFUb5 lhhLljiff eof] ;]t' b;} jif{ of] dfUb5 . @( bz a;]{ 5 of] ;]t' hLjg\ d[To' a/fa/ km"nsf] ;fydf sfF8f g ePsf] sxfF 5 / <
Proof
jfl;ª\u6gsf sfJo ;';]nL M 164
¿v ljZju|fdsf] /fhwfgL d:t lgb|fdf lyof] deg] ;'g;fg cFw]/L /ftdf PsfsL lxFl8/x]sf] lyPF crfgs of}6f ¿v b]v]F of}6f dfG5]n] p;sf] km]b sfl6/x]sf] lyof] lar/f ¿v ;:j/ l;/l;/ sx/fO/x]sf] lyof] .
Proof
xfFuf] d]/} sf6]/ laF8 p;n] agfof] uf]8d]n u5{' eGYof] nufpFnf kfgL eGYof] p;nfO{ wGojfb Û vfg] kfgL h/}af6 ;'sfPsf] 5 aGr/f] lnP/ km]b sf6\g cfPsf] 5 dnfO{ 9nfpg kl5 nfPsf] 5 . kz' x}g dfG5] xf], lrg]sf] klg 5' af]Ng ;Sg] eP xfFufn] em\ofKkf] v'jfpy]F To;} To;} rkfpFy]F t/ d k/]F ¿v oL xfFuflaFuf kftkltË/sf] d :jod\ cfwf/ x'F
jfl;ª\u6gsf sfJo ;';]nL M 165
j[l4 / ljsf;sf] kl/jf/ x'F p;}sf] klg d ;/sf/ x'F hLjgsf] cffwf/ x'F . To;}n] t df}g 5' 5ftL l5ofl5of kl/Gh]n klg of] b'of]{wgnfO{ w[t/fi6« ag]/ ljgfznfO{ klg kfln/fv]sf] 5' dtfGt/nfO{ arfO/fv]sf] 5' . d]/} km]b sf6]sf] b]Vbf dfG5] h:tf] xLg s]xL 5}g h:tf] nfU5
Proof
b'v]sf] 5 dft[e"ld x'F ;GtfgnfO{ s;/L 5f;"F Û of] ¿v b]Vbf d of}6f ljrf/ x'F h:tf] nfU5 sf6] sfl6GgF of}6f bz{g x'F h:tf] nfU5 of}6f v}/f] ¿v x'F h:tf] nfU5 . h/f ufl8O ;s]sf] cg]s 8fo:kf]/fsf] of}6f sNkj[If x'F h:tf] nfU5 . d]/L d]/f] d]/L d]/f
cfdfnfO{ wGojfb ¿knfO{ wGojfb >LdtLnfO{ wGojfb jg:klt c¿ n8fs'x¿nfO{ wGojfb Û jfl;ª\u6gsf sfJo ;';]nL M 166
h;n] hlt rf]6 vfP klg d]/f] ;fy 5f]8]gg\ tL z'4 cfTdfx¿nfO{ wGojfb Û wGojfb tL lj/f]wLx¿nfO{ h;n] d]/} 3fF; vfP/ d}nfO{ sf6\g cfP d d/]sf] 5}g, d b[Zo klg 5}g csf6Ø ¿v eP/ d sfl6P/ s'FlbPsf] 5' zflnu|fd h:t} of}6f ¿vsf] cf6{df ;flnsem}F bz{g ag]/ plePsf] 5' .
Proof
d]/f] v08g d08g rln/xf];\ d d}nfO{ x]/]/ xfFl;/x"F /ftdf klg d km'ln/x"F nf;df klg d ;kgf b]lv/x"F d c¿sf] 3/ agfpg alnof] lg/fn alg/x"F Hof]lt ag]/ Go'of]s{df uLtf alg/x"F . d Ps ¿v x'F s;}n] sf6] klg d ;ldwf alg/x"F cfuf] nufP klg emg\ d Hof]lt alg/x"F . s;}n] v08g u/] klg d Ps bz{g alg/x"F
jfl;ª\u6gsf sfJo ;';]nL M 167
cg]s g]kfnL 8fo:kf]/fdf of}6f ¿v alg/x"F . ;'g;fgdf ;'Gbf;'Gb} eGg yfn]sf] eGbfeGb} dgsf] efjn] wfdL h:t} sfd]sf] d]/f] ¿k agfof] ¿v x/fof] w]/} xfFuf kmf6]sf] afx«l;Ë] d PsfsL jfl;ª\\6gsf] h/f–of] Û ¿v s/fof] Û km]b sf6\g] dfG5] x/fof] Û
Proof
jfl;ª\u6gsf sfJo ;';]nL M 168