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gfgc.kar.nic.in · 2 PÀ£ÀßqÀ ªÁåPÀgÀt zÀ¥Àðt ªÀÄÄ£ÀÄßr 0iÀiÁªÀ...

Date post: 30-Nov-2018
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ªÉÄʸÀÆgÀÄ ¸ÀPÁðgÀ ¥ÀoÀå ¥ÀŸÀÛPÀUÀ¼À E¯ÁSÉ («zÁå ¸ÀA±ÉÆÃzsÀ£À ±ÁSÉ) PÀ£ÀßqÀ ªÁåPÀgÀt zÀ¥Àðt (8, 9 ªÀÄvÀÄÛ 10£É0iÀÄ vÀgÀUÀwUÀ½UÉ) 1971 ¨É¯É gÀÆ: 2-00
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  • g Pg

    o PU ES (z Azs S)

    Pq Pgt zt (8, 9 v 100i vgUwUU)

    1971

    g: 2-00

  • Pq Pgt zt 2

    r 0ii s0izg zV 0iU iqPzg D s0i Pgt jZ0i CvP. Pgt ez s0i Czs0i t Uz. s0i Czs0iz DgAsz 0iUU P Pgtz CjAlirzg Az PV Pgt z jZ0i ir CPvz. F zAz PAqj U oPz Pgt z R 0iU CrVz. PAqj Avz JAl, MAv v v0i vgUwU oPz PU PPAz irgAv Pgt, CAPg v bAzU CAU MUAq Pq Pgt ga F PPAq w0i gav: 1. q|| . Z. Ao, JA.J., .Zr., Av sg, PlP z0i zsgq. ... ... ... CzsPg

    2. . JA. Jg, Pq Arvg, U|| Al 0ig PAqj , AUg. ... ... ... zg

    3. r. gt, Pq Arvg, nZg mAU Elm avzU. ... ... ... zg F w0ig G0iP CsUAU F Pq Pgt z Ugvg. Aq w0ijU F C P0iPV ES It0iiVz. n. . wUq, qgPg Ds mP P

  • Pq Pgt zt 3

    z iv

    g gdz zS0i Ul qsU 8, 9, 10 0i UU zyU G0iUPV v CsPPj MAz Pgt oP gaPAz, Czg D0ii vgUwUU 0ivz CAPg, bAzU sU EgPAz zS0ig wi MAz w0i 0izg.

    zS0ig tz oPPj P l UzlPAq sAz PptP JA zsvvPUtV 0i gu iqv, 0iv C0i0i F P gaVz. Ezg oPz 0i Q C P 0iU UAxz jtvUV, fe0i PqssU CPvUV zg Pq Gzs0ig CAxU PqU Z PPqz P oPz UUtV zs0iU DjPAq o PAz av.

    vU zP z P gu0i PqVz. sz zAvU vjVz. D gu0i Dzsgz v gZ0i PAz ir zs0i PPg Cj, Pgt sz 0iA P rz zsZvggz Gzs0ig PvAz sv. zyU G0iUzAz ZV zAvU CrVz.

    CAPgU sV P lPA GzAz Uz0i ivU v gr0iV ivU s zAvU gAsz w, vzAvg zU ; guir vU Vz. Cg oPU Ag GzguUv iV Z P Vz. P Pq oPz gV GzguU PqVz.

    (qs0i) g vgUwU0i P Uq Uzz sU jZ0i irPPVgzjAz C Uq GzguU PqVz. sQ v0iU gu iqU Ez zAz Uq v Uqz Jgq gU Vz. i Pgtz CP Uq, Uqz GzguU n0i PqVz. Q0iiz PguAvz Wz zsvU

  • Pq Pgt zt 4

    n0iAz Pl Czg Uq Uq zsvgU v CU Cx, Q0iizz MAzAz g E PqVz. Cz UqAz UqP gAvgAz CP U MAz n0i g0i Czs0iz PqVz. Ez Avgz zyU se 0i G0iP CAAz sz. F UAxz zU G0igzAz zsz JZjP z. Dzg s0iAz gzzjAz, 0iUU CUtvzzjAz, UtU Cv Gzg z0i gzg wzg ztz jrUz.

    P C s zAz w Czs0iz P0i Cs U P zstV PqVz. D CsU CV Gzs0ig irPUz. DU Pgto tUz. UAxAvz R aU UU jVz.

    F Pz gZ0i Pg U PlzPV oP sUz CPjUU PvdgVz.

    AUg . Z. Ao

    14-4-70 (w0i gV)

  • Pq Pgt zt 5

    0iiPtP

    l pP- (i) Pgtz Gz .. XV (ii) Pq PgtPgg v Cg .. XVII UAxU Czs0i 1. AePgt .. 1 AeU .. 1 I Pq ti .. 1 (1) gU .. 2 (2) AdU .. 3 (3) 0iUU .. 3 II gU Zg .. 3 III AdPgU .. 5 IV UtvPgU .. 6 V A0iPPgU (MvPgU) .. 7 VI CPg l .. 8 VII gA .. 9 2 Czs0i. APgt .. 12 I A .. 12 II Pq AU .. 13 1. A .. 13 2. DU A .. 15 (1) 0iPgU A .. 16 (2) PgU A .. 17 3. Dz A .. 19 III Pw s .. 22 IV gA .. 25 V Av AU .. 28 1. Av g AU .. 28

  • Pq Pgt zt 6

    l (1) t W A .. 28 (2) UtA .. 30 (3) A .. 31 (4) 0iu A .. 33 2. Av Ad AU .. 35 (1) dA .. 35 (2) v A .. 37 (3) CP A .. 38 VI gA .. 40 Czs0i 3. z-Cz-vv-vz Pgt .. 43 I z CZUq U .. 44 II Cz U .. 44 (1) Av sAz Az U .. 44 (2) Az sAz Az .. 45 U (3) EAVAz PqP Az .. 45 P0iiUwg U (4) ZV sAz Az .. 46 U (5) AvAz v g .. 46 virPAq PqP Az U III vv vz gU .. 47 Czs0i 4. z Pgt .. 62 (z-Pw-sQ v0i) I z .. 62 II PwU .. 64 (1) ZPU .. 65 (2) UtZPU .. 66

  • Pq Pgt zt 7

    l (3) ASZPU .. 67 (4) AS0iZPU .. 67 (5) sU .. 68 (6) jitZPU .. 68 (7) PgZPU .. 69 (8) UZPU .. 69 (9) U .. 69 1. gxP U .. 70 2. xP U .. 70 3. DvxP U .. 70 III AUU .. 71 (1) AU, AU, APAU .. 71 (2) APAU, APAU .. 72 vAPAUU (3) AU, AU, APAU gg 0iUU U .. 73 [ZAU (AUU)] IV ZU .. 77 V sQv0iU .. 82 VI PwUU sQv0iU .. 105 g CxU v 0iUU VII sQl .. 113 VIII gA .. 114 Czs0i 5. Q0iiz Pgt .. 118 I Q0iiPw (zsv) .. 118 1. zsv (dzsv) .. 119 2. v0iiAvzsv (vzsv) .. 119 II PPzsv, CPPzsv .. 122 III Q0iiz .. 123 IV Q0iiz gU GAmUP .. 125 (1) viPz Q0iizU .. 125

  • Pq Pgt zt 8

    l (2) svPz Q0iizU .. 126 (3) svPz Q0iizU .. 127 (1) zsx (+Cx) gU .. 129 (2) zsxP gU .. 130 (3) AsxP gU .. 132 V Q0iiz gU P .. 134 gU (1) viPz P .. 134 0iUU (2) svPz P .. 135 gU (3) svPz P .. 137 gU Q0iizU PlUP .. 137 (4) zsxz g P .. 138 gU (5) zsxz g P .. 140 gU (6) Asxz g P .. 143 gU VI Pt0iUU .. 147 VII Pt0iUz Q0iizz .. 149 AU VIII gA .. 152 Rz P zsvU-Cx- .. 156 Q0iizU n Czs0i 6. i Pgt .. 173 I Cji .. 175 II iz zsU .. 177 (1) vvgi .. 177 (2) Pzsg0ii .. 179

  • Pq Pgt zt 9

    l (3) Ui .. 182 (4) CAi .. 184 (5) zAzi .. 186 (6) i .. 187 (7) Q0iii .. 189 (8) UPi .. 191 Uq, qUq PU .. 193 0iUVg Rz P iU n III gA .. 199 IV gQ .. 201 Dzs0i 7. PzAv, vvAv Pgt .. 205 I PzAvPgt (PPgt) .. 205 (1) PzAv U .. 206 (2) PzAv sU (sPzAv) .. 210 (3) PzAv0iU (C0iPzAv) .. 213 II gA .. 217 III vvAvU .. 220 (1) vvAv U .. 221 (2) vvAv sU .. 223 (3) vvAv0iU .. 224 IV gA .. 226 Dzs0i 8. C0i Pgt .. 229 (1) i0iU .. 229 (2) CPgu0iU .. 230 (3) sZP0iU .. 230 (v0iU) (4) Q0iixP0iU .. 230 (5) AAzsxP0iU .. 230 (6) PzAv0iU .. 231

  • Pq Pgt zt 10

    l (7) vvAv0i .. 231 (8) CzsguxP0i .. 232 gA .. 232

    Czs0i 9. PU .. 235 I C0iiP .. 236 II Dzsg .. 237 III PU PgU .. 239 (1) iP .. 239 (2) A0ifvP .. 240 (3) P .. 240 IV Psd .. 241 V gw .. 242 VI gA .. 244 Czs0i 10. bAz .. 247 I bAzA UAx Pv Zg .. 248 II Pq PU .. 248 III z .. 249 (1) .. 249 (2) 0iw .. 251 (3) UtU .. 252 IV iv, Ug, WU .. 252 V ivUtz bAz zU .. 254 (1) PAz zz Pt .. 255 (2) lU PtU .. 256 (1) gl .. 256 (2) Pl .. 257 (3) sUl .. 258 (4) sl .. 259 (5) jl .. 260 (6) zsPl .. 261

  • Pq Pgt zt 11

    l (3) gU ew0i z PtU .. 262 (1) GvgU0i Pt .. 263 (2) AzgU0i Pt .. 264 (3) vgU0i Pt .. 266 VI CPgUtU .. 267 (4) vew0i bAz PtU .. 270 (1) Gvivz Pt .. 270 (2) ZAPivz Pt .. 271 (3) zQrvvz Pt .. 272 (4) vsQrvvz Pt .. 273 (5) Ugvz Pt .. 274 (6) Ugvz Pt .. 275 VII CAUtU .. 276 VIII gA .. 277 Czs0i 11. CAPgU .. 280 I CxAPg .. 283 (1) GiAPg .. 283 (2) gPAPg .. 285 (3) GvPAPg .. 287 (4) zAvAPg .. 289 (5) CxAvgAPg .. 290 (6) APg .. 292 II APgU .. 295 (C) C .. 295 (1) v .. 295 (2) bP .. 296 (D) 0iPAPg .. 297 III gA .. 298

  • Pq Pgt zt 12

    l

    Czs0i 12. R aU .. 301 (1) tg a .. 301 (2) Czsg a .. 301 (3) Cg a .. 302 (4) xP a .. 303 (5) sZP a .. 303 (6) Gzgt a Cx P .. 304 a (7) Dgt a .. 305 (8) guvP a .. 306 (9) CP a .. 306 (10) ixP a .. 306

    * * * * *

  • Pq Pgt zt 13

    v ASU

    (1) g (28) vzU (2) Ad (29) Pw (3) 0iU (30) z (4) Mlti0i CPgU (31) z (5) g (32) sQv0iU (6) Wg (33) PwszU (7) vg (34) ZPU (8) Ct (35) UtZPU (9) t (36) ASZPU

    (10) CP (37) AS0iZPU (11) CV0i Ad (38) sU (12) UtvPg (39) jitZPU (13) ew0i A0iPPg (40) PgZPU (14) ew0i A0iPPg (41) UZPU (15) A (42) U (16) A (43) AU (17) DUA (44) AU (18) DzA (45) APAU (19) Pws (46) APAU (20) tWA (47) APAU (21) UtA (48) vAPAU (22) A (49) ZAUU (23) 0iuA (50) KPZ, ZU (24) dA (51) Zz DUU (25) vA (52) sQ (26) CPA (53) sQl (27) vvU (54) zsv

    F UAxz Pgt vUU DAU AS0i PV Pnz. EzjAz zyUU Pz 0iz v qQPz sUzAz s U iqVz.

  • Pq Pgt zt 14

    (55) vzsv (v0iiAvzsv) (84) UP i (56) Av PwU Pqz (85) gQ

    zsvUP (86) PzAv (57) guxz E v0i (87) P gU (58) PP zsvU (88) PzAv s (59) CPP zsvU (89) PzAv0iU (60) Q0iizU (90) vvAvU (61) viPz Q0iizU (91) AUz vv v0iU (62) svPz Q0iizU (92) vv sU (63) sv Pz Q0iizU (93) vvAv0iU (64) zsxP Q0iizU (94) C0iU: (65) zsxP Q0iizU (i) i0iU (66) AsxP Q0iizU (ii) CPgu0iU (67) Pl (iii) sZP0iU (68) Q0iixP0iU (iv) Q0iixP0iU (69) Pt0iUU (v) AAzsxP0iU (70) Pvj Pt 0iUz (vi) PzAv0i

    AU (vii) vvAv0i (71) CP PvUgU AU (viii) CzsguxP0iU (72) U PvVgU

    AU (95) P

    (73) (96) Dzsg (74) i (97) iP (75) Cji (98) A0ifvP (76) i zsU (99) P (77) vvg i (100) gw (78) Pzsg0i i (101) (79) U i (102) UtU (80) CA i (103) iv, Ug v WU (81) zAz i (104) MAz ivPz CPgU (82) i (105) UgU (83) Q0ii i (106) UgUU CPgU

  • Pq Pgt zt 15

    (107) PAzzz Pt (121) zQrvv Pt (108) gl Pt (122) v sQrvv Pt (109) Pl Pt (123) Ugv Pt (110) sUl Pt (124) Ugv Pt (111) sl Pt (125) GiAPg (112) jl Pt (126) CszgPAPg (113) zsPl Pt (127) GvPAPg (114) GvgU Pt (128) zAvAPg (115) AzgU Pt (129) CxAvgAPg (116) AzgU Pt (130) APg (117) vgU Pt (131) APg (118) CPgUtU (132) v (119) Gviv Pt (133) bP (120) ZAPiv Pt (134) 0iPAPg

    * * * * *

  • Pq Pgt zt 16

    pP

    UU -| A0iz 0iA vz-| z wV-| AzU RzvA ||

    - Pgd (Q..1260)

    Pz q0i J gU gg ivqzjAz, g0izjAz q0iv. v v ZgU Jg iw P EjU w0irvg. Drz ivU, DqPz ivU Uvz 0i P g0iz gtU0iz. g0iz, ivqz RV U P DVz. MAzAz P MAzAz Cxz. U GZgU gtU0iiU CxtVgP. zV ivqz, g0iz Gv zAv PtVz. zAvPPz v g0i gtU0i t Zj, zV g0iPUz; Cz C ivqz CxtVgP. v U AAzs U U0i EgPAz Pgt Uvrz. DzzjAz zV, CxtV ivq v g0i Q0i q0iPzg CV Pgt Cs iq PUz. dUw J sU D0ii0i sU g CU Pgt Cs iqP. Pq s0i P0ig Pq Pgt CV N, Czg U z gU, CU AAzs V w0iPUz.

    gUU zz xU t0i DVz0iAz F Az0i wz. PgtAz z, zAz Cx, CxAz e GAmUvz. s0i PPzg,

    PgtAz zi| Pgtz zxxz vv PA vvP| PAQ QAiPz zsU sA ||10|| w: (.w.)

  • Pq Pgt zt 17

    PAPV Pgt Nz P. s0i 0iU w0i P. U Az U s0i P0i iqv zg PAvgz zz s0i g V Uz. zz s0i , GPAq g vAz0i Pq r P CjP. P zV g0iz, ivqz Cs ir, Av dAUAzPP. qsU Nz P F Pgtzg J AzsU ZV Cj0iPA SzAz F P gaVz.

    * * * * *

    w: PgtA zAiPA: zAzxePA: CxeA vvZgPA: vveA Q zgPA zsUz PgtA PgtzAiA. -tztA -Pgd

  • Pq Pgt zt 18

    Pq PgtPgg v Cg UAxU

    Pq s azz. Ez zQtsgvz zVg zq sU UP jzz. v, vU, 0ii, vU D UP jzU. F Lz sU M vAz dwz CPvAV0ijz U. ig 2 g UAz Pq JA ivq s P0iz. aPz F Pqs0i Uq JAz Pg0iv. Uqz F s0i g w0irU CP Pgt UAxU z zAgPg gzg. Cg AP jZ0i F PU PqVz.

    (1) 20i U

    Q... 1145 gz UA PlP s st, PPUAgq UAxU gz. PPzg 10i sUz w JA jAz gz Zg PgtP AA zzVz. F w0i A, , i, vv, DSv-JA 5 sUUz, APV Uq Pgt 0iU Czg jVz. PlPs st JA UAx Pq PgtUAx zg Av s0i g0inz. F PAz Av g Pq Pgt w0i Z CPVz. Cz Pq Avz vz s0iAz vjPq zsVz.

    (2) Pgd

    Q... 1260 gz Pgd JA tzt JA j Pq PgtUAx gaz. Ez U Uq s0i g w0iPjU Gv PUr0iAwz. E vAz0iiz Pd JA, zgiz d JA zq PU. vvz (v0i vAz) Pt JA zA. EAx zAg gAg0i nz Pgd zA DVzAz C gz tztA Pgt UAxAz UvUz. F Pgt UAxz A, , i, vv, DSv, zsv, CsA, C0i JA JAl Czs0iU. UAxz P0ig

  • Pq Pgt zt 19

    0iUgA Czs0i xt0i w0i G0iPVz. Pgtz vU PAzzz. Ml 322 vU.

    (3) smPAPz

    Q.. 1604g ijz smPAPzA JA j qsz Pq PgtUAx gz. Dzg Ez Avzz. FV zQt Pq f0ig q (AVvg) JA Hjg eg oz UgVz CPAPz JAg smPAP UgU. smPAP Av, Pq F Jgq sU zA Vz. Pqs0i AvzAv 0iU gg q0ivP s0iA z DV AvszAjU vjPq GzAz F UAx Avz gazz Pq sUAz zq 0i 0i. Az t v vAd U Avs0i V Czs v s JA PgtUAxU PV gazg. CU U0i MAz z Pz smPAPz Pqz F Pgtz vU, CUU s gaz.

    F z l U w, PlPs st U, Pgd tzt, smPAPz Pq s0i g wvP Pgt UAxU. EA Pz P0ig Pq s0i A Pz Pq sVAv nU ilUArz. F Pz s0i Uq JAz Pg0iv. P RV Uq s0i PV Cs iqzg evU Uq s0i z jZ0i irPPUvz. DzzjAz RV Uq Pgt Nzzg evU Uq jZ0i irP PU P Pgtz CAU PqU U PqPUz. Dzg Uq Pgt zsV w0iPV. Uq PU V Nzwg P D UU C wzg P.

    * * * * *

  • Pq Pgt zt 20

    CzsAi 1

    Ae Pgt

    AeU

    I - Pq ti

    ivq ivU PPUVgv. PU zUAz Prgv. zU CPgUAz Prgv.

    oU V Az. F Pz , oU, V, Az - U zU. MAzAz zz CP CPgU. JA D G JA g g CPgU. Pq s0i ivqU EAx 50 CPgU v. Pqz F 50 CPgU iU ti Cx CPgi Jv.

    o JA zz J CPgU JAz FU qt. D, oC, D, J_ U JAl CPgU F zz Ez Uv. , o, , _ U F CPgU CU Az Eg D, C, D, J JA F CPgU GZg irzAv sV GZg iqU. EU GZg iq Az D E K_ Ev gU P P. Cx Azzg ggP. UAzg Ezg Az D gzg D Jz. Az Ezg Jz, Cz o U gzg DU, GZg iq DU. D, E, J, M - EAx CPgUzg vAvV GZg iqz. DzjAz_

    (1) vAvV GZgiqU CPgU gUAz PgAiv.

    (2) gU AiAz iv GZgiqU CPgU AdUAz PgAiv.

    F g AdUz EAz UAi CPgU. CU rj-

  • Pq Pgt zt 21

    gAU JA g C A U C - E CPgU. E CPgz Az AiAz. Dzg Cz Utvoz g Ai. CzP sAi Cg Jv, Ezg UAi zBR JA z z G B S C JA CPgUAi. GPgz Az MAzg Az U B U gg CPg U JA jz. A U gg Cg B U gg U AiUUAz PgAiv.

    AiU (A, B) U vPV (vB) GZg iqU. EAz CPgz AAzs E AzU GZg iq gv. AiU JAzg AAzs, JAzg Az, JAz Cx. DzjAz MAz CPgz AAzs Az Ai GZg iq g EP AiU UA g Az.

    RV E gz AAzs qz JAzg gPgU Az AzU GZgUv. CA, EA, JA, MA, NA, CB, EB, GB,__ U E gz AAzsAz GZjzz, CzAi A B U Aii CPg AAzsz gzg, GZgiq gz E.1 DzjAz

    (3) gU Az gz GZjU Cg (A), U (B) UU AiUU JAz g.

    jzAv CPgU (1) gU, (2) AdU, (3) AiUU _JAz g sU iqz. Uzg C Aii? JAz PV wAit.

    (1) gU

    C D E F G H I I2 J K L M N O JAz Ml gU (14)

    1 Cg, UU AdPgU AzAi UA, gA UAi gz GZjz. EAx GZg grAi. z, GvU iv GAl. 2 I JA gAz Prz U Pqz ivU gz EzjAz Ez Plg . DU Ml CPgU AS 50 P wAiiV 49 DU. Dzg 50 CPgUAz IPg tiAi j z rP.

  • Pq Pgt zt 22

    (2) AdU

    Aii g -{9

    (3) AiUU

    Cg (A) U (B) - 2 (4) 14 gU, 34 AdU, 2 AiUU; Ml 50 CPgU Pq sAi. EP Pq ti Jg.

    II - gU Zg

    z 14 gU C, E, G, I, J, M F Dg gU MAz ivAi Pz3 GZjv.

    (5) MAz ivAi Pz GZj gUU gUg.

    (6) Jgq ivU Pz GZjq D, F, H, I, K, L, N, O F JAl gU WgUg.

    AiU JAz Aie CAzg Pq JAz, Ez JA zsvAz n PrU JA Cx Pqv. DzjAz AiUAzg, AiizzgAz CPg AAzsz GZjUz CPgAz wAiP. 3 MAz iv PAzg C JA CPg GZj J P rAiz C P. CAzg Jz zAv, lPVAi zAv GZjP. Cz JU C Pg J Pz GZj C PP MAz iv Pz. U lPV 1 iv Pz GZj g gz. Ez CPg Z Jzg D JAz Jgq ivU P vUzPz. g ivU PzgU Jz z.

    P S U W Y - PU - 5 Z b e ghi k - ZU - 5 m o q qs u - lU - 5

    v x z zs - vU - 5

    s s i - U - 5

  • Pq Pgt zt 23

    z gU Jgq ivU PQAv ZP Jz z GAl.

    Cu3 Nr . zg3 Pq

    F ivU u Pgz Ag D Pg, zg JA g Pgz Ag K Pg Jgq ivU PQAv Z P CAzg g ivU PzgU Jz GZjv. AzsAi4 (PgAiU) PAi g U g ivU P vUzPAq GZjv. Ez vgz.

    (7) g ivU Pz GZjq gU v gU5

    GzguU:- CP3 E q. Ci3 U . zg3 gQ. UgU3 vU g. Pg3 j. gU3 sU Pr. (E (3) JAz Ugvirg gU vU)

    U jzAv gU , W, vUAz g jw.

    4 AzsAiAzg PgAiP (CTPgt). Cu JAz PgAiU t Pgz Ag D Pg AzsAi g, Ct Az Cu JA, zAi Ct JAAi t Pgz Ag CPg MAz ivAi Pz GZjz zg, Cu JAAi tPgz Ag DPg givAi g. D gU PUq (3) JAz ggz vgA UgwUV iv. 5 W vUU MAz Uz Gzgu Pqz. P1 P2 P3...... JAz P PVzz U PVvv. 1Ai PPgz Ag G Pg zg, JgqAi PPgz Ag GPg W, gAi PPgz Ag G Pg v. E PV MAz iv, Jgq iv, g ivU Pz GZj gU.

  • Pq Pgt zt 24

    III - AdPgU

    z 34 AdU z 25 AdU JAzg: PPgAz PgzgV AdU Lzzg UUV gAiv. DzjAz E VAi AdU JAz PgAiv. F VAi AdU Ct6, t v CP JA g jwAi CPgU. CU PU rj:-

    U

    C

    t

    t

    C

    t

    t

    CP Ml

    CPgU

    PU P S U W Y 5

    ZU Z b e ghi k 5

    lU m o q qs u 5

    vU v x z zs 5

    U s s i 5

    5 5 5 5 5 25 (8) Ct:- wAiAz Uz 1Ai, 3Ai AdU CtU

    (9) t:- wAiAz Uz 2Ai, 4Ai AdU tU

    (10) CP:- wAiAz Uz 5Ai Ad CP z. EU GZguU V Ai PUzjAz E CPg.

    6 Ct JAzg Pr GjAz GZj AdPg; t Azg Z GjAz GZj AdPg; CP Azg V AiAz GZj AdPg. (P=U) (t=Gg) (C=) (=Z). P Cj GZj CPg CP.

  • Pq Pgt zt 25

    F 25 CPgU PU, ZU, lU, vUUAz sV UPgUAz jlg, Aii g F MAv CPgU Aii U Ez v. Uz EP Ezz jAz E CVAi AdU.

    (11) AiPgAz PgzgVg 9 AdU CVAiAdU .

    IV - UtvPgU

    AdPgU zg U gz Cxvz U iqUz E. CUU gU g P. z+K=z, +C=, g+G=g - U gU jz Ai zg JAz GZg iq gv. Cx Az gzg Cz, Cg Jz. F Ai Az wz. zg JAzU Czgg z K C g G Ad gU rrAiiV gAi. Adz g j MAz DPgz CPg ir gAiv. PU Png nAi rj:-

    Ad g UtvPg Ad g UtvPg P + C = P m + K = m P + D = P + L = Z + E = a + M = Z + F = a + N = v + G = v + O = v + H = v P + I = P m + J = m + I =

    EzgAv J gU (14 gU) 34 AdUAi j DPgz CPgU irPv. E UtvPgUAz PgPv.

    (12) AdUU gU j UtvPgU7.

    7 grAi PUtv JzAl. PUtv JAzg P+C=P, P+D=P, P+E=Q, U PPgz gU jz DU P P Q Q JA UtvPgU PUtvU. EP JAz PgAig.

  • Pq Pgt zt 26

    V - AAiPPgU (MvPgU)

    (1) CP JA z Aii Aii CPgU JAz rj. C + P + P + C - U CPgU Pr CP VzAi? Ezg UAi Ct JA, C + u + u + C JA PgU j Ct Vz. P JAzg = P + P + C; t JAzg = u + u + C. E Jgqgq Ad jPAq MAzPgVz. F Jgq AdU MAz ewAi JAzg ewAi AdU.

    (13) MAz ewAi (ewAi) Jgq AdU j DU CPg ewAi AAiPPgz8. EzP vAz g9.

    GzguU:- CP (P + P) Ct (u + u) Cd (e + e) Pl (m + m) v (v + v)

    (2) sP JA z s+C+P+v+C JA Lz CPgU. C JA z C++m+G JA CPgU. JA z +v+g+F JA CPgU. F GzguU Jgqgq gg AdU j MAzAz CPgUV. Dzg U E jg AdU gg ewAi, JAzg ewAi AdU.

    JAz +m JA AdUAz, P JAz P+v JA AdUAz, JAz +v+g JA AdUAz j DVg AAiPPg (MvPg)Vz.

    (14) gg ewAi Jgq Cx Z AdU j DU CPgP ewAi AAiPPg Jvg.

    8 AAiP JAzg ZV jz JAz Cx. Jgq AdU zsz Aii P A Ez gz AAiPPgz. (A=ZV), (AiP=jz) 9 v JAz MAz ewAi Jgq AdU gzP iv PgAiUz. gg ewAi Ad jzg v JP.

  • Pq Pgt zt 27

    GzguU:- ( + v + g) CPg (P + ) e (e + k) x ( + ; g + x) Q (P + v)

    VI - Aii Aii CPgU J (Aii Aii z) lv?

    EzgU 50 CPgU UU gV wj. F CPgU Pz sUAz gl AzjAz lv. U gl UAl, zq, zs (UAi Uz sU), vn, - Ev CAiU AiAz g g CPgUUv. Uzg Aii Aii CPgU J lv? JA UU F PV guAi rj:-

    (1) C, D, P, R, U, W, Y, v U (B) - E PAoz lvzjAz E PAo tUvg.

    (2) E, F, Z, b, d, gh, k, Ai, - EU v (zqAi) AiAz lvzjAz E vPg Ug.

    (3) I, I, l, o, q, qs, t, g, - CPgU UAi Uz zsAzg AiAz lv. DzzjAz E zsU .

    (4) v, x, z, zs, , , - CPgU U AiAz lvzjAz E zAv tU. (zAv=)

    (5) G, H, , s, , s, - CPgU vnAi (Nz) AiAz lvzjAz E N tUg.

    (6) Y, k, t, , - tU Pz AiAz lvzjAz E PU (CPU) J.

  • Pq Pgt zt 28

    (7) J, K, L - CPgU l PAo v v (zq) Ugqg Ai PUzjAz E PAov CPgU.

    (8) M, N, O - CPgU PAo v vn (N) Ugqg AiAz lvzjAz E PAo tU.

    (9) - JAPg (zAv) v vn (N) Ugqg AiAz lvzjAz Ez zAv tz.

    (10) Cg (A) - PAo v Pz AiAz lvzjAz Ez PAoP tz.

    F jwAi CPgU l jwAi Uzg.

    VII - gA

    EzgU Pgt Nzg wAiPz P AeU jv. Ezg g, Ad, AiU - JA Lv CPgU UU, gU , W, vU UU, AdU VAi, CVAi AdUAzg? VAi AdU Ct, t, CPUAzg? UtvPg, ewAi - ewAi AAiPPgUAzg? Aii Aii CPgU J lv? Ev CAU UU gV v. F J CAU A lz ag UgU AiAz APV wAi z.

  • Pq Pgt zt 29

    Pq ti 50 CPg

    gU-14 AdU-34 AiU-2

    g Wg v g Cg (A) U (B) (1 ivAi (2 iv (3 iv

    P) P) P) VAi Ad-25 CVAi Ad-9 (P PgAz PgzgU) (Ai PgAz PgzgU)

    Ct t CP

    (Ml-g, Ad, AiUU j 50 CPgU)

    * * * * *

  • Pq Pgt zt 30

    Cs U

    (1) C JA zg g, AdU r gj. (2) zg JA zg WgU? (3) CP, E q F Pz Ag vgU Ugwj. (4) Cu, Ev U F Pz Ag , W, vU Ugwj. (5) P C C q C D q G - F Ad gU Pr ir gj. (6) CAvBPgtAz F zz Ag Cg UU Aii Aii gU Az A? (7) Av U Az F Pz Ag CP tU? (8) , - F AAiPPgU jg AdU? r gj. E JAx AAiPtUg? (9) Pd JA Ag ewAi v ewAi AAiPPgU wj. (10) UtvPg, CP, Ct, t, v gUAzg? GzguUAU jj. (11) F PU ng U tUj:- (C) wAiAz Uz 1Ai, 3Ai AdU _____________ (D) g ivU Pz GZj gP _________ Jvg. (E) Cg UUU ___________ JAz g. (F) AdUU gU j ___________ J. (G) Jgq Cx CP AdU j DU CPgP ________ Jg.

    * * * * *

  • Pq Pgt zt 31

    Czs0i 2

    APgt10

    I - A

    ivqU P U rr0iiV . Hg Hg JAgq U Hgg JAz Pr0i ivqv. C + C JAgq gU C JAz Pr v. g Hg + Hg JA U, C + C JA Pw v0iU Pr0i v. CAzg, C A0i v. M U rr zg, Pw v0iU iv A0i v. C rr0iiV Uz E. F PU r:-

    Pw + v0i = Prz g Dq + E = Dr g + C = g P + EAz = PAz zg + EU = zjU

    zU Pr0iizg z Cx rr0iiV0i z.

    z + z = Prz g - Prz g C + CAUr = CAUr - C CAUr CU + E = CV - CU E t + CAUr = tAUr - t CAUr

    10 A JAzg Jgq CPgU gg 0ii P A Ez gz JAz Cx. Adz Az ggz MAz jwAz A0i DVz. CPgU Jqqz CzsivP zsz gP0i Cx AP0i A0iz. Av 0iAz EzP g. Pw v0iUAv U A0i P. zzU rr0iizg z, A ir0iizg z. Cz g EZ. Pw v0iU JAzg - GzguU:- g Pw, C JAz v0i - Egq Pr Dz g g z Pz.

  • Pq Pgt zt 32

    g CP GzguU Pw v0iU j C Pr0i vz rr gAv0i E. Dq E JAz 0iig . P C v Jgz. Dr P U Pr0i P. Dr JA (Dq+E) G+E gU A v. P+C JA C+C gU gg Av. Cgq AU z gU Jgq Pq Uv. F AP0i PAz U DUvz. E Pw v0iU AP0i w GzguU.

    C CAUr JA zU Pzg A0iiUAv CAUr JAzzg z; Cx P A ir C CAUr JAzzg z. Cz EZ0i CAgvz. CAUr JU (C+CAUr) E A gU C+C JA. EU z CPg vUzPv. DzjAz Jgq CPgU AP0i A0izAzUv. Ezg v U z:-

    (15) Jgq tU (CPgU) PAzAv gz A0iz.

    (i) gz Az g Az U A0iizg gA0iv. (ii) gz Az Ad Az Cx Adz Az Ad Az A0iizg AdA0iv. (iii) U A0iiUU P vU D Az CPgU GAmU. C APgU Jv. CU Az w0it.

    II - Pq AU

    1. A

    Hg + C JA G JA gz Az C JA g Az. Pr gzg Hg C = Hg JAzv. CAzg gPgzg G Pg lv. Ezg U PV E P GzguU rj:-

  • Pq Pgt zt 33

    iv + E = iw (GPg Ezv) (G + E)

    Dq + E = Dr (GPg Ezv) (G + E)

    g + M = g (JPg Ezv) (J + M)

    U + Cz = Uz (JPg Ezv) (J + C)

    + J = (GPg lv) (G + J)

    GzguU, Jgq gU AU z0i g EzAvUz (Uz) PAq gvz. Dzg P PqU gz Az g AzU irzg Cx Pqz. F PV GzguU rj:-

    + EAz - E irzg Az JAzUz (J + E)

    Ug + C - E irzg Ug DUz (G + C)

    Uzg Cx U iqgz. C g zs (iU) CjPUz. Uzg Mn AU v U z:-

    (16) gz Az g Az A0iiUU zg g Cx Pqz Pz iv Uz. EzP A0iAz g.

    GzguU:-

    Hg + C = Hg (GPg ) (G + C)

  • Pq Pgt zt 34

    zg + EAz = zjAz (GPg ) (G + E)

    + JAz = Az (GPg ) (G + J)

    K + Dzz = Kzz (GPg ) (G + D)

    EU + D = EU (JPg ) (J + D)

    C + Hg = Cg (CPg ) (C + H)

    2. DU A

    z A0i Cx PqzAwzg iv iqP, Ezg iqgz JAz wj.

    + C JA irzg DUz, Ug + C JA irzg Ug DUz

    JAz Az wj. Uzg + C, Ug + C E PqU zz zsz gz Az g Az0iizjAz C r r C Pq 0iUU. DU D Jgq gU zsz Pr CPUAv 0iiPg, Pg zV jzU GZgiq CPUz. U zV g CPg DUiPg. U CPg j A0i DUA. F PV GzguU rj:-

    0iPgU gzP

    v + C = v + 0ii + C = v0i P + C = P + 0ii + C = P0i Z + C = Z + 0ii + C = Z0i + EAz = + 0ii + EAz = Az

  • Pq Pgt zt 35

    U + C = U + 0ii + C = U0i Pg + C = Pg + 0ii + C = Pg0i g + EAz = g + 0ii + EAz = gAz

    PgU gzP

    Ug + C = Ug + + C = Ug v + C = v + + C = v U + EU = U + + EU = UU D + GAUg = D + + GAUg = DAUg D + Hg = D + + Hg = Dg D + M = D + + M = D + C = + + C =

    vjg 0iPgU, PgU A Ag U A0i ir gz, g0i gz. U irzg Cx UzAz PArj. DzzjAz F DUAU v F PVAv z:-

    (17) gz Az g AzU A irzg Cx PqAwz D Jgq gU zsz 0iPg Cx Pg zV j v. EzP DU A Jg.

    0iPgU PgU J gvAz w0it:-

    (1) 0iPgU A:- D, E, F, J, K, L U Az g Azg D Jgq gU zsz 0ii Pg DUUz.

    GzguU:- 11P+Cz =P+0ii+Cz=P0iz (D+C) Vj+C=Vj+0ii+C=Vj0i (E+C)

    11P JAz gPu iq JAxz KPPgzsv. Uqz P zsv P0ii DUzAz Pg Mvg.

  • Pq Pgt zt 36

    12+C=+0ii+C=0i (F+C) Pg+C=Pg+0ii+C=Pg0i (J+C) 13+E=+0ii+E= (K+E) +C=+0ii+C=0i (L+C)

    (2) PgU A:-

    (i) G, H, I, N gU Az g Azg q Pg DUV gz.

    GzguU:- q+C=q++C=q (G+C) +EAz=++EAz=Az (H+E) iv+C=iv++C=iv (I+C) U+C=U++C=U (N+C)

    (ii) CPgz Az CPg Azg PgUUz. (Pw v0i gU iv F A0iiUz)

    GzguU:- +C=++C= +C= ++C= P+C=P++C=P w+C=w++C=w +C=++C=

    12 JAz Pq iq JAxz Pq KPPg zsv. 13 JAz Pq U Dg sPu0i Cxz KPPg zsvVz.

  • Pq Pgt zt 37

    (iii) D14 JA z Az G, H, M, N U Azg q Pg DUV gzAl. (A0i iqz0i z)

    GzguU:- D + GAUg = D + + GAUg = DAUg D + Hl = D + + Hl = Dl D + MAm = D + + MAm = DAm D + Nl = D + + Nl = Dl

    A iqgzP-D GAUg, D Hl, D MAm, D Nl (U z)

    (iv) F z Az G, H, M, N U Azg, 0iPgU zg iqz; Cx PgUzg iqz

    GzguU:- F + GzP = F + 0ii + GzP = F0izP FzP F + Hg = F + 0ii + Hg = F0ig Fg F + Hl = F + 0ii + Hl = F0il Fl F + M = F + 0ii + M = F0i F F + MAm = F + 0ii + MAm = F0iAm FAm F + NP = F + 0ii + NP = F0iP FP F + N = F + 0ii + N = F0i F

    14 D Azg, P Pq C, C, Cz JA UU D JAz DzV gz. U DzV Az DPg D z. Gz.:-C+UAq= D UAq; C+AU=D AU; Cz+P= D P EzgAv P Pq - E+UAq=F UAq; E+AU=F AU; Ez+P=F P Ev PqU E, E, Ez JAzP F DzV Azg Ez F g

  • Pq Pgt zt 38

    F z PqU AU iqz0i F GzP, F Hg, F MAm, F N U0i g0iz

    (v) N Pgz Az g Azg PgU gzAz Az z0i. Dzg P Pq 0iPgU gzAl.

    GzguU:- U + C = U (PgU Az) (N + C) + C = 0i (0iPgU Az) (N + C) 3. Dz A

    EzgU gz Az g Azg A0i, DUA0i DU Zg rz. FU gz Az Ad AzU Cx Adz Az Ad AzU K APg q0izAz w0it.

    + P = U ( + UD) Z + P = ZU (Z +UD) l + vg = lzg (l + zDg) Pu + Pl = PAUl (PA + UJl) Pu + = PA (PA + C)

    GzguUg, + P JAgq U 2 0i z [Gvgz]15 z z0i P PgP U Pg Az. ZU JA0i EzgAv0i PPgP UPg Az. l + vg JAgq zU 2 0i zz zPgz v PgP z Pg Az. [CAzg v JA AdP z JA Ad Az] Pu + JA PgP Pg Az. U A 0iiUU MAz CPgz z gAz CPg gz Dzz. Pq AU F DzUP0i Gvg zz D0ig AdP iv JAz RV UzngP.

    15 Jgq zU z0i z z; Jgq0i z Gvgz. iz U z rP. 0i + P-JAgq zU 0i JAz z; P JAz Gvg z U w0iP

  • Pq Pgt zt 39

    (18) A0iiUU MAz CPgz z (z) gAz CPg gz DzA0iz.

    Uzg J F DzA0iiUz? 0ii CPgP 0ii CPg DzV gz? JAz gV w0it.

    (i) iz16 Gvgzz D0ig P v AdUU PV U z AdU DzV g.

    GzguU:- + P = + U D = U (PPgP UPgz) + Pq = + U Cq = Uq (PPgP UPgz) P + Pr = P + U Hr = PUr (PPgP UPgz) J + Pg = J + U Cg = JUg (PPgP UPgz) + P = = U J = U (PPgP UPgz) + v = + z M = z (vPgP zPgz) g + v = g + z C = gz (vPgP zPgz) Pu + = Pu + C = PA (PgP Pgz) + v = + Cv = (Av) (PgP Pgz)

    16 i JAzg? JAz Az i Pgt JA j sUz jz. DU V wzgz. FU APgU Uzg P. E + P-JA + P + D = UD = U JAz P AdP U Ad Az JAz w0iP. EzgAv GzU w0iP.

  • Pq Pgt zt 40

    P Pq F DzU gz Egz GAl

    + Pl = Pl v + Pl = vPl

    (ii) iz Gvgzz D0ig AdUU Pg DzV gz17

    GzguU:- g + = g + M = g (PgP Pgz) J + g = J + Jg = Jg (PgP Pgz) g + = g + C = (PgP Pgz) g + g = g + Jg = gg (PgP Pgz) Pq + = Pq + J = Pq (PgP Pgz) J + = J + C = J (PgP Pgz) + iv = + Dv = v (PgP Pgz) + = + C = (PgP Pgz)

    Ezg U.......Qu, Jg0i, ZP, P, Pr, g, gq EvU Pgz Agz Uj.

    F Dz P Pq g. CzP Gzgu:-

    Pu + l = Pul (Pul DU) Q + q = Qq (Qq DU) + = ( DU)

    17 AdUU JAzg , , iUU JAz, PgAzg JA AdAz w0iP. GZgu0i s zAz -Ev gz. Dz gz P AdPgP JAz J PqU w0iP.

  • Pq Pgt zt 41

    (iii) iz Gvgzz D0ig PgP iV P Pq ZPg, P Pq dPg, P Pq bPg DzV gzAl. Dzg zz P0i 0ii, U Eggz.

    GzguU:- (1) PgP ZPg gzP__ E + g = E + Z Cg = EAZg u + g = u + Z Cg = tg (2) PgP dPg gzP__ + gAU = + e JgAU = AegAU + qg = + e Mqg = Aeqg vu + qg = vu + e Mqg = vuqg (3) PgP bPg gzP__ Eg + g = Eg + b Dg = EZg u + g = u + b Dg = ug g + g = g + b Dg = bg

    P Pq F PgP 0ii DzU ggzAl.

    0ii + = 0i, j, Pu, Pu, g, 0i, .

    III - Pw s

    EzgU Pqz AUz , DU, Dz AU ZgV wj. gz Az g Azg Cx DUU 0iizz gAz A0iiUP JAz Az v. Dzg F PV P Gzgu rj:- C + J ZVz? C0i + Ez? N + Ez? N + C Az? CP + Ev

    PU rj. C + J ZVz, D PgP ( Adz A DPgP) J Pg gVz (JzjU Az). Az z

  • Pq Pgt zt 42

    0iz Pg E 0iPgUUPVv? CzgAv, C0i + Ez JA N Pgz Az E Pg Az. N + Ez JA N Pgz Az E Pg Az, CP + Ev JA0i D Pgz Az E Pg Az. F Pq0i gz Az g Azg U, DUU iqgz. C V0i U qP. U Ez jw0i EgzP Pws JAz Pgtz vg. DzjAz Pw sP v PVAv z:-

    (19) gz Az g Azg, P PqU , DU zz APgUUz Ez U0i EgzP Pw sg.

    Uzg JAx Pq F Pws gzAz (APgUg P0i) Uj:-

    (i) vgU18 Az ggzg APg iqgz (Pws gz).

    Cu(3) + Ev = Cu, Ev zg(3) + E Uw = zg, E Uw Ci(3) + Cz P = Ci, Cz P gi(3) + C q = gi, C q Ug(3) + Gzj = Ug, Gzj

    (ii) sZP0iUz19 C! C! C0i! CPm! N! b! __ Ev U Az g gzU A PgUU.

    (B F sZP0iU gAvUVgv. EU Az g Azg Pws gz)

    GzguU:- C0i + CUv? = C0i! CUv? C + Cz ? = C! Cz ? CPm + EAzU 0i? = CPm! EAzU 0i? N + C? = N! C? 18 vgAzg Azs0i g g. F GzguU(3) F UgwAz ag gU vUAz w0iP. Az gU z Pq CAzg AePgtz F 0i wz. 19 F sZP0iU v0iUAz Pg0ig.

  • Pq Pgt zt 43

    J + Czs? = J! Czs b + Cz = b! Cz.

    (iii) D JA z Az C D L O gU Azg APg iqgz (Pws gz).

    D + CAUr = D CAUr D + DP = D DP D + Cg = D Cg D + Ov = D Ov D + Lg = D Lg D + Ozg = D Ozg D + Dq = D Dq

  • Pq Pgt zt 44

    IV - gA

    EzgU Pq s0i g , DU, Dz AU UU wj. gz Az g Azg Cx DU AUUv. gz Az Ad Cx Adz Az Ad Azg DU Dz AU jZ0i irPArj. CAvg gz Az g Azg A0iiUz Eg Pws Cjwj. Ez PU ag gS avU P V ElPj.

    (1) Pq AU

    DU Dz g+g-z gP g+g-zsz g+Ad,

    Cx0iiUzU 0iPg Cx Ad+Ad PgU 1. Gvgzz D0i

    P v U U z UUv. 2. UU Pg DzUvz. 3. PgP Z d b U DzUv.

    (2) gz Az g Azg A0iiUgz Pws

    * * * * *

  • Pq Pgt zt 45

    Cs U

    1. A0iAzg? 2. zg + C, Hg + Hg, ev + Dv, Ug + C, + C Ez Pr gz 0ii A JAz wj. 3. 0iPgU PgU AU J gv, wj. 4. v + C, iv + C, + C, Vj + C, j + C E Pr gz 0ii A JAz wj. E irzg U gUUwz? 5. C, Hg, zg, 0i, Ug, iv, v, F zUg AU r gz 0ii 0ii AUAz jj. 6. F PU ng U j0iiz Az vAj:- (i) iz Gvgzz D0ig Pv UU ____________ (ii) + ______ = U, Ez + _______ = EAZg g + ______ = g, g + _______ = gg (iii) D JA z Az C D L O gU Azg ____________ (iv) gz Az g Azg P Pq , DU, DzU DU. EzP ______________ (v) gP g gzU CxP gzg __________ g Uz. (vi) _______ gU Az g Azg q 0iPgUUz. (vii) iz Gvgzz D0ig UU _______ DzV gz. (viii) sZP0iU Az g Azg __________ (ix) vP g gzg ______________ 7. F PV PU zU. C w j:- (i) vgAzg, MAz iv0i Pz GZj g. (ii) DU A0iAzg MAz CPgz z gAz CPg gz. (iii) AdU C PgAz O PgzgU . (iv) MAz Adz Az EAz Ad AzU A0iiUz.

  • Pq Pgt zt 46

    8. FPU ng U Az Dgtz Png j0iiz MAz Gvg Dj gj.

    (i) Hgg= (A, DU A, DzA) (ii) +C=(DU A, DzA, A) (iii) C z Az CPg gzg

    (A, DUA, A0iiU) (iv) v0iz Az g Azg Jz.

    (Pws, DU, Dz) (v) EPgP g gzg

    (0iPgU, PgU, Uz) (vi) gP g gzg g Uz.

    (z, zsz, Gvgz) (vii) vgP g gzg gz.

    (0iPgU, PgU, Pws) (viii) vgAzg

    (MAz ivPz GZj g, Jgq ivPz GZj g, g ivPz GZj g)

    (ix) DzAzg (MAz CPgz z g gAz CPg, zV g CPg, EzAvU CPg)

    * * * * *

  • Pq Pgt zt 47

    V - Av AU

    1. Av g AU

    (1) gi0it v UAx. (2) gz0i 0i CvAv gzz.

    F Jgq PU Pq PU C? Dzg Ezg AvAz Az U ZV. gi0it v UAx gz0i 0i CvAv g -U F K U Av U DV. U s0i gg UAz Avz CP U Az j. PU v PU Pz Av U j P gzg. DzjAz AvAz PqP Az qwg U APgUAz Pq sez zAz w0iz G0iPzz.

    Jgq Av U j A0iizg Av A0i DUvz. MAz Av Pq zq j A0iizg Pq A0i DUvz.

    Avz gP g gV gAU, AdP Ad gV Ad AU DU. z gAU Zg w0it.

    (1) t W A

    (C) zs irz. (D) gi0it Nz. (E) jg Pq P. (F) Ugz q.

    F PU zs gi0it jg Ugz F U DVg APgU Uj.

    z + Cs = z0ii + D + s = zs (D + C)

  • Pq Pgt zt 48

    E D JA gz Az C JA g Az. F Jgq gU tgU20, CAzg i z nzU. MAz , MAz W C.

    E U MAzg Az MAz AzU Cgq V CU z Czgz MAz Wg gz. U gz DzAz Az wj. Ezg U0i jg _

    j + Fg = g + F + g = jg-JA (E + F)

    E Pgz Az F Pg Az. Egq V CU z F JA Wg DzV gz. Ezg v F PVAv z:-

    (20) tgU MAzg AzAz AzU Cgqg z MAz Wg DzV gz. EzP tWA0iAz g.

    GzguU:- z + Cg = zg (CPgP CPg gV DPgz) (C + C) g + Cg = gg (CPgP CPg gV DPgz) (C + C) + Dv = v (DPgP DPg gV MAz Wg Dz) (D + D) P + EAz = PAz (EPgP EPg gV FPgz) (E + E) Vj + F = Vj (EPgP FPg gV FPgz) (E + F) Q + F = Q (FPgP FPggV FPgz) (F + F)

    20 CD, EF, GH, II F gU t gU. CC, CD, DD, DC-U Azg t gU. FF, EE, FE, EF-U Azg t gU. Ezg U0i GH, II U t gU Zg Pq.

  • Pq Pgt zt 49

    Ug + Gz = Ugz (GPgP GPg gV HPgz) (G + G) zs + Gv = zsv (HPgP GPggV HPgz) (H + G)

    (2) UtA

    (C) g Az. (D) zAz s. (E) q. (F) gz0iv. (G) Q U Azg

    F PUg g, zAz, , gz0i, F U r gzg UU rj.

    g + F = g (C + F = K) (C + F) z + EAz = zAz (C + E = K) (C + E) + F = (D + F = K) (D + F) g + Gz0i = gz0i (C + G = N) (C + G) + I = g (D + I = Dg) (D + I)

    J GzguU z g C Cx D DV. gz (Jzj) E, F, G, I Ev gU. E Cx F gz K Pg Az. G gz N Pg Az. I gz Cg Pg Az. CAzg z v gz Jgq gU V CU z K N Cg U DzUV A JAz Uv. EzP i v U z.

  • Pq Pgt zt 50

    (21) C D PgUU E F PgU gzg Cgqg z K Pg, G H PgU gzg Cgqg z N Pg, I Pg gzg Cgqg z Cg Pg DzUV gv. EzP UtA JAz g.

    GzguU:- g + EAz = gAz (CPgP EPg gV KPgz) (C + E) zsg + EAz = zsgAz (DPgP EPg gV KPgz) (D + E) + Fg = g (DPgP FPg gV KPgz) (D + F) ZAz + Gz0i = ZAzz0i (CPgP GPg gV NPgz) (C + G) KP + H = KP (CPgP HPg gV NPgz) (C + H) z + I = z (CPgP IPg gV Cg Dz) (C + I) + I = (DPgP IPg gV Cg Dz) (D + I)

    (3) A

    (1) C KPP g. (2) Pzg0i CgAz Prz. (3) i0iz UAl. (4) gt vAz Prz P.

    F PU Ag KPP, Cg, , v zU r gzg C F PVAv DU:-

    KP + KP = KP + LP (C + K + L) (C + K) C + Lg = C + Lg = Cg (C + L = L) (C + L)

  • Pq Pgt zt 51

    + N = + O = (C + N = O) (C + N) + Ov = + Ov = v (D + O = O) (D + O)

    z J PqU C Cx D gU. JzjU K, L, N, O gV. K Cx L gzU MAz L Pg, N Cx O gzU MAz O Pg DzUV CAzg D Jgq gU z A. Uzg Ezg v U z:-

    (22) 21C D PgUU K L PgU gzg Cgqg z L Pg, N O PgU gzg Cgqg z O Pg DzUV gv. EzP A 0ig.

    GzguU:- P + KPg = PPg (CPgP KPg gV LPgz) (C + K) d + LP = dP (CPgP LPg gV LPgz) (C + L) z + Lg = zg (DPgP LPg gV LPgz) (D + L) d + NW = dW (CPgP NPg gV OPgz) (C + N) W + Ozg = Wzg (CPgP OPg gV OPgz) (C + O) + Ozg = zg (DPgP OPg gV OPgz) (D + O)

    21 C D PgUU JAzg, C Cx D PgU 0iizzgAz gP JAzx. K L PgU gzg JAzg, K Cx L PgU 0iizzg MAz gzg JAz Cx.

  • Pq Pgt zt 52

    (4) 0iu A

    Av Pgtz P AeU irPArzg. Czg Pg 0iu JAzg 0i g F AdU. 0iu A0iAzg F CPgU DzV gz DVz. F CPgU 0ii CPgP DzV gvAz rj:-

    (1) C CvAv gP. (2) F Avgz qv. (3) z vfvz D.

    F g PU Ag CvAv Avg vfv F U r gzg:-

    (1) Cw + CAv = Cv + 0ii + CAv = CvAv (E + C = 0iiC) E EPgz z 0ii PgzVz. (2) + CAvg = + CAvg = Avg (G + C =C) E GPgz z PgzVz. (3) v + Dfv = vg + Dfv = vfv (I + D = gD) E IPgz z g PgzVz.

    Uzg zg E, G, I PgUU, PV 0ii, , g U DzV A0iAz Uv. JzjU JAx gU EgPAzP MAz z. Cw + EZ U EPgz Az EPg Azg CwZ JAz tW A0iiUwv. DzjAz tg JzjU ggzAz Uv. Ezg v F PVAv z.

    (23) 22E, F, G, H, I PgUU tz g gzg E F PgUU 0ii Pg, G H PgUU Pg, I PgP g (gs) DzUV gv. EzP 0iu A0iAz g.

    22 0iu JAzg 0i g F CPgUAz Az wz0i. Pg DzV g GzguU Pq s0i EzjAz vz Cz Pnz.

  • Pq Pgt zt 53

    GzguU:-

    Cw + Cg = Cvg (EPgP 0ii Pgz) (E + C) ew + Cwv = evwv (EPgP 0ii Pgz) (E + C) Pn + C = Pl (EPgP 0ii Pgz) (E + C) Uw + CAvg = UvAvg ( " ) (E + C) w + Gvg = vvg ( " ) (E + G) w + Cx = vx ( " ) (E + C) Cw + D = Cv ( " ) (E + D) C + Dv = Czsv ( " ) (E + D) Ug + De = Uge (GPgP Pgz) (G + D) + D = (GPgP Pgz) (G + D) zs + Dsgt = zssgt (HPgP Pgz) (H + D) zs + Ct = zst (HPgP Pgz) (H + C) v + Cx = vx (IPgP g Pgz) (I + C) iv + CA = ivA ( " ) (I + C) Pv + Cx = Pvx ( " ) (I + C)

  • Pq Pgt zt 54

    2. Av Ad AU

    (1) dA

    d JAzg Av Pgtz dUqz F Lz AdU w MAz Ae. d JAzg F Lz tUz dUqz AdU DzV gz JAz Cx. 0ii CPgP E DzV gv? JA UU w0it.

    (1) UAvz jv. (2) CdAv JAzg gAv JAz Ae. (3) tRU q JA g GAl. (4) D qU g zAz JAz. (5) C JAzg UgP g.

    F PU Ag UAv, CdAv, q, zAz, C F U r gzg__ P + CAv = U + CAv = UAv (z PPgP UPgz) (P + C = UC) CZ + CAv = Ce + CAv = CdAv (ZPgP dPgz) (Z + C = eC) m + D = q + D = q (lPgP qPgz) (m + C = qC) v + DAz = z + DAz = zAz (vPgP zPgz) (v + D = zD) C + = C + = C (PgP Pgz) ( + = )

    F Lz GzguU Pl rzU, z CAvzg P, Z, m, v, UU PV U, e, q, z, U DzUV A. F zg UxtUU Cz Uz g0i tU DzUV g A0i Av U Jgq DVzU iv gz. Pqz Pv UU Uz U DzV gzAl. Dzg Pv U Gvgzz D0igP. Ez P Pqz DzA0iAz w0iP. U z P0i

  • Pq Pgt zt 55

    PZlv UU Udqz U DzV gz dA0iz. Ezg v F PVAv z.

    (24) z P0ig PZlv AdUU 0ii t gzg (JzjU Azg) 0iB Cz Uz g0i AdPgU DzUV gv. EzP dA0ig. 0iB JAz gzjAz PR, Zb, lo, vx, s, , , Y, k, t, , CPgU gzg (JzjU Azg) g0i CPgU DzV P Pq g. CAzg dA0iiU.

    GzguU:-

    P + z = Uz = U (PPgP UPgz) P + z = Uz = U ( ) P + C = UC = U ( ) P + z = Uz = U ( ) P + UAv = UUAv = VUAv ( ) P + zv = Uzv = Uv ( ) 23CZ + CAv = CeCAv = CdAv (ZPgP dPgz) CZ + D = CeD = Ce ( ) m + D = qD = q (lPgP qPgz) m + CAU = qCAU = qAU ( ) m + CAU = qCAU = qAU ( ) gm + g = gqg = gq ( ) v + Gz = zGz = zz (vPgP zPgz) v + Gvg = zGvg = zvg ( ) av + DAz = azDAz = azAz ( ) v + s = zs = z ( ) v + GzU = zGzU = zzU ( ) 24C + D = Cd = C (PgP Pgz) 25C + Z = Cz = C (PgP Pgz)

    23 CZ JAzg Av Pgtz g JAz Cx. CdAv JAzg gAvAz w0iP. 24 C=P 25 C=q

  • Pq Pgt zt 56

    26C + CA = CCA = CA (PgP Pgz) 27C + = C = C (PgP Pgz)

    dA0iiUgzP GzguU

    P+ZP=PP P+vl=Pl v+P=v E J0i g0i tz Dz P+a=Pa P+w=Pw

    (2) v A

    JAzg Pg ZUPgU. (=Pg, Z=Z b d gh k) F Dg CPgU JA AeAz Av Pgtz PgPv. EU DzV gz vA Jz. Uzg E 0ii CPgUU 0iiU CzV gvAz 0iat.

    + = + = (PgP Pg gV PgP Pgz) 0i + ZAP = 0i + ZAP = 0iAP (PgP ZPg gV PgP Pgz) v + av = Z + av = av (vPgP ZPg gV vPgP ZPgz) v + av = Z + av = av (vPgP ZPg gV vPgP ZPgz) v + bv = Z + bv = Zv (vPgP bPg gV, vPgP ZPgz)

    J GzguU Ul rj. z CAvz Pg E vUz Lz CPgU 0izzgAz CPggvz. gz (Jzj) Pg E ZUz 0iizzgAz CPgz. U E

    26 CA=j CA 27 C=z (C CAzg g)

  • Pq Pgt zt 57

    MAzPAz AzU Pgz Pg, vUz CPgUz ZUz CPgU DzUV A. CAzg_ v x z zs UU__ Z b d gh k CPgU DzV gv JAz Uv. Ezg v F PVAv z:-

    (25) PgvUPgUU Pg ZUPgU gzU (JzjU AzU) PgP Pg, vUP ZU DzUV gv.

    0i + 0i = 0i + 0i = 0i0i (PgP Pg gV PgP Pgz) + ZAZ = + ZAZ = AZ (PgP ZPg gV PgP Pgz) + Z = + Z = (PgP ZPg gV PgP Pgz) gv + ZAz = gZ + ZAz = gZAz (vPgP ZPg gV vPgP ZPgz) dUv + ew = dUZ + ew = dUew (vPgP dPg gV vPgP ZPgz, CAvg dPgz) 0i + jj = 0i + jj = 0ijj

    Ezg U-Zav, ZZg, dew, ew, Aw, EvU.

    (3) CP A

    Y, k, t, , -F Lz CPgU CPPgUAz A AePgtz wz. F CPPgU DzV g A0i CP A0iz. Uzg E 0ii CPgP 0iiU DzV gv? 0ii CPg gVgP? JA UU w0it.

    (1) P + 0i = Y + 0i = Y0i (E PPgP Pg gV PPgP YPgzVz) (2) m + R = u + R = tR (E lPgP Pg gV lPgP tPgzVz)

  • Pq Pgt zt 58

    (3) v + i = + i = (E vPgP Pg gV vPgP PgzVz) (4) C + 0i = Ci + 0i = C0i28 (E PgP Pg gV PgP PgzVz)

    F GzguU CQzU z P0i Uz z0i CPgUz P, m, v, Ev CPgU. JzjU CPPg Az. Dz PgtAz F Uz z0i CPgUz P l v Ev AdUU Cz Uz CPPg (Lz0i t) DzV Az0iAz w0iP. CAzg Uz z0i AdP Czgz Dz CPPg gP0i CP A0iz. Ezg v F PVAv z:-

    (26) U x tUU 0ii CPPg gzg, CUU CAzg P Z l v AdUU PV Y k t AdU DzUV gv.29

    GzguU:- P + U = Y + U = YU30 (PPgP Pg gV YPgz) m + i = u + i = u (lPgP Pg gV tPgz) P + izsg = Y + izsg = Yzsg31 (PPgP Pg gV YPgz) av + 0i = a + 0i = a0i (vPgP Pg gV Pgz) av + = a + = a (vPgP PggV Pgz) v + t = + t = t (vPgP Pg gV Pgz)

    28 C0i=j 0i, CAzg d0i JAz Cx. 29 ZPgP k Pg DzV g GzguU zzjAz D Gzgu Pn. 30 YU=PUg D (CUdU) 31 Yzsg=iw izsg.

  • Pq Pgt zt 59

    EzgAv, Y32, Y, Gz, v0i Ev

    VI - gA

    EzgU Av gA AdAU UU g 0iU wgj. Czg gA F PV UgUAz ag jw0i r rj.

    Av AU

    gAU AdAU (i) tWA (i) dA

    (Wgz) (dUqz Dz) (ii) UtA (ii) vA

    (K, N, Cg Dz) (Pg ZUz) (iii) A (iii) CPA

    (L, O Dz) (Y,k,t,, U Dz) (iv) 0iuA

    (0i, , g Dz)

    * * * * *

    32 Y=iw ; Y=iv, ; Gz= zAz Prz; v0i=g0iP.

  • Pq Pgt zt 60

    Cs U

    (1) gi0it, zg, Cgj, gAvP, sP, zsv, jg, 0iwg, g-F tWAU r gj. (2) zAz, g, , P, z, gz0i, ZAzz0i,

    sUz0i, zz, sUz, z, , Avv, gd-F UtAU r gj.

    (3) PPg, CvAv, UvAvg, Avg, KPP, UAv, zAz, -F U , 0iu, d, CP AUz GzguU. CU Ugw. (4) ng U tUj:- (i) tgU MAzg Az MAz AzU Cgqg z ___________ g DzV gz. (ii) UtA0i C D PgUU E F PgU gzg _________ Pg, ______ PgU gzg N Pg, I Pg gzg ______ Pg DzV g. (iii) C D PgUU K L PgU gzg _____ Pg DzV gz. EzP __________________ A0ig. (iv) C D PgUU N O PgU gV Pg DzV gzP A0ig. (5) PU P AU r gz. Cz Pr gz Az Dgtz Png MAz j0ivg j:- Cw + D ______________ (tW, d, 0iu) v + Cx _____________ (0iu, tW, Ut) av + DAz ____________ (d, CP, tW) (6) F PV PU vU. D vU jrj:- (i) Avzg EPgP tz g gzg Pg DzV gz. (ii) Ux tUU 0ii CPPg gzg Cz Uz g0i t DzV gz. (iii) C D PgUU K L PgU gV L Pg DzV gzP UtA0ig. (iv) Avzg U x tUU Cz Uz g0i t DzV g AU vA0ig.

  • Pq Pgt zt 61

    (v) Avzg E G I PgUU tz g gzg PV 0i, , g AdU DzV g AU tWA0ig.

    * * * * *

  • Pq Pgt zt 62

    Czs0i 3

    z-Cz-vv-vz Pgt

    0iiz zz s0iiU, Cz v vvt g g sU AAzs q0iv, D0ii s0i U v jPAq 0ivz. q Pq s0i F vvPUtV CP U j. Pq U Pq g g sU j. sU U PqP gAz 0iv. g sUAz U U jPAqg v U iv Pqgz. C EgP; gs U EgP. DU s0i Av Zz. F PV MAz Gzgu0i Uj:-

    mgU dzAz Nqqz fz R Uj0iAz w0iP.

    F P Pq s0i Pzg, Pq U evU g g sU U Ezg ZV.

    (i) mg - Ez EAV sAz Az . (ii) dz - Ez A sAz Az . (iii) f R - F U Av sAz Az U. (iv) Nqq, Uj, , w0iP - E Pq s0i U.

    Cz-C, EAz, E, EU, G-Ev Pq v0iU EAV, A, Av U Az Az, C Pq UV ir.

    GzguAz Pq s0i g s0i U jPAr JAz UvUz. Pq s zq UP jz s0iAz wj. Av s D0ig s. DgjU zqjU a PAz AAzs z, Cgqwz Av-Pv sU U V CAAz gv Az. CAvg g g z0ig APAz, s U, EAV, ZV sU jz. U g g sUAz Az U? CZUq sU? JAz V w0iz.

  • Pq Pgt zt 63

    CZUq U z Uv. GzU Cz Uv. Cz Av-Pv UP Pqs0i UtPUtV C zuUAz v a vUAz irPAq, CP vzU JA jnz. P Av U 0ii v iqz Cz Cxz G0iVv. C vvU Jv. FU F J z, Cz, vv, vzU ZgV V wzPt.

    I - z CZUq U

    , , Uz, w, Pz, g, Vq, , D, vAPt, qt, qt, qUt, vg, vU, E, g, wAU, P, , , U, U, g, w, MAz, Jgq, g, Z, Pr, U, ZV, wP, qP, g, , , , Cg, qP, CV, Cg, Cg, j, Gq, vq, P, P, , Pt, v, Q, U, Pg, g, ZU, vtU, PU, t, zq, z, Pjz, jz, e, v, , g, fU, C, Pg, DP, vg, g, g, Pg, g, g, g, , g, , gV, e, , J, Ju, u -EvU.

    II - Cz U

    (1) Av sAz Az U33

    s, y, , Dg, Cg, gw, , Azs, A, g, Pt, sgv, vW, sgv, Pig, v, iv, zg, zj, CAU, CAUP, AU, AU, iU, zv, 0iiv, z0i, I, , 33 Av sAz PqP Az U w0i V PUt 0iU qP:- (i) I, , , P, d, v U, , CPgUg U; (ii) sgv, gi0itU zz gt UAxU g Q, , gv, , IU zzg gU v Iv, i, , Pv, 0iU, PgtU; (iii) , C, C, , , , g, B, zB, z, zg Ev GU P U, Gz:-Zv, CZv, zgZg, CUv, ... ... ... Ev; (iv) Ez E CP U. E gz P iv.

  • Pq Pgt zt 64

    It, Iv, z, gt, , , DU, Gv, Cgt, t, Pw0i, , z, AZ, v0i, z, KP, C, , Dvg, g, AUg, zsg, Pv, U, U, Ut, U, Zj, zy, C, P, wx, Czs, CP, CP, CQ, Q, , e, z, zd, , z0i, WnP, WnPv, , U, Uv, v, v, Pv, DU, Dz, , CUg, g, j, Ug, U, CPg, Aw, gd, gt, ZPw, Av, Aqg, id, ZPv, , CPg, z, Pw, P, UAx, Al, v, zs, P, U, gP, 0i, Czs0i, Pgt, jZz, DdP, ddP, i, DP, s, sg, UAzs, ZAz, , PAP, g, , z, v, R, zAv, AY, P, R, R, v, v, Gvg, zQt, , , Iv, DU0i, F, 0i, DP, UU, 0i, 0iAq, dUv, , Gv, Rg, g, Ad, , v, s, s, sd, sAd, , GgU, Ozs, z, D0i, , 0iU, v, vi, vP, vi, AU, 0iz, Uz, zAq, t, t0iU, zs, zjz, , zv, iU, zs, zs, zg, U, , q, KPz, zz, P, z, AP, gP, P, wy, AZAU, AZ, z, zsvg, Pj, P, Uzj, z, v, UAU, 0i, gw, , , , , Fg, g -Ev.

    (2) Az sAz Az U

    Cf, PZj, v0iig, z, PS, Sig, gg, gv, , P, d, zu, Zu, Adg, PA, zg, C, P, g, Pa, dzg, U, Sf, zg, zzg, g, zR, zP, Cg, g, zS, PUz, AzP, dg, SAz, d, , Q-AvzU.

    (3) EAVAz PqP Az P0iiUwg U

    gq, g, Pm, AP, ZP, Z, 0ig, n, g0iA, AZ, U, , , , Pq, Pg, nPm, m, Zg, gA, , Pe, 0in, jPq, DQd,

  • Pq Pgt zt 65

    qd, Dq, , jfg, sZg, e, q, m, mv, P, lg, en, , rV, qPg, , q, P, n, q, m, m, JQP, rmAm, UAm, CAmAm, Dqg, j, q, j, , CVPg, , Aq, P, m, e, J.J.J.., .J., JA.J., JJ.., D, ig, Pgg, sg, jqg, j, , qg, Ag, iP, , s, , Cq, i, i, , nPm, , JdP, PAU, n, QPm, m, , Q, mAU, PPnAU, rP, P, n, , , , EAP, l, q, Z, m, -EvU.

    (4) ZV sAz Az U

    Cig, , , d-EvU.

    (5) AvAz v g virPAq PqP Az U

    :-34Ezg C zu Az, Z zu Az JAz Jgq sU iqz.

    (i) C zu A AzU:

    GzguU:- v, Q, i, zv, gd, , 0i, v, v, v, 0iv, jv-EvU.

    (ii) Z zu A AzU:

    GzguU:- Pg, g, , Av, lP, g, vt, U, w, , Z, Pd, CAZ, PAv, Cd, P-EvU.

    34 CP U vz g A gV AvAz A. Pv JA sAz A.

  • Pq Pgt zt 66

    AvAz CASv zU PqP vz gV AgzjAz, CU PqP Az P gV0i w0iPzz Czz. D UU FU Zg iqt.

    III - vv vz gU35

    Av v PvUAz D s0i U PqP vUzPU P v ir PrUg PqP jPArzgAz F Az0i jVz.

    (27) vvU-AvAz Pg Azz Pqz q U vvU. vv JAzg CzP, JAzg izz-E CzP JAzg AvP i (JAz Cx) E Pg Av UAz Pg0ig (PqP AvP E igUAz vv0i). Cz vz U Av gU vv UAz Pg0iz grU Az.

    GzguU:- g, , P, Av, , ZAz, g, U, Pv, v, , , , zs, P, s, s, 0i, w, w, , , P, P, g, Vj, , , , j, s, 0iw, w, w, Uw-Ev.

    35(i) vv vzU ZgV FU gr0ig ZgP Pge PgtPgg 0iP vz. vv JAzg PqP, AvP z JAz Cx. F U Pq zq0i, Av zq0i j i iqz JAz F PqP, AvP JAxz vvg. FU gr0ig vzz Av g vv JAx DU Eg. vv U Pgd t, AZ, vgt ........ Ev 21 U n ir E vv JAz jnz. (ii) C vAz PqP Az U Pgd Av JAz Pgz. GzguU:- i-i, v-v. FU gr0i Av JAz P. (iii) vAz CAzg Avz v g PzPAq PqP AzU vzU. GzguU:- Pg-Pg, s-__ Ev. Ez 0iz C0i. FU gr0i F C0i zu Az. Av Pg Azg vzAz, vzz Av g vvAz, 0ii Pg Azgz Pq vvAz Pg0iqwz.

  • Pq Pgt zt 67

    (28) AvAz PqP gU C PgU, t PgU, A Ag U vzUAz Pg0ig (vv JAzg CzjAz JAzg AvAz s JAzg nz Cx z JAz Cx). (C Pg Az U Av JAz Pg0iz rP)

    GzguU:- i, v, G, u, Cd, Ae, j, , z, dP, z, UAm, eV, g0i, Qg, lP, Av, P, Q, avg, l, D, Pvj-Ev.

    (i) C v A PqP Ag Av U n:-

    Av g v g Av g v g z0ii z0i, z0i V V, V Pgu Pgu, Pgt i j j zs zs C C zs zs g0i g0i Gzgu Gzgu 0iAs 0iAs gw gw i i Q Q v v Uj Uj s s P P UAU UAU Pij Pij Az Az Uzj Uzj Pj Pj gi g Gi G P P, P zi z 0iiv 0iiv Pi P e e D D gS gS A A z z

  • Pq Pgt zt 68

    Av g v g Av g v g z z zP zP 0iP 0iP iv iv z z S S P P s s UAzsj UAzsj

    -EvU

    J GzguU RV Avz D PgAv U J PgAvUV (i-i Ev); P C PgAvU J PgAvUV (zs-zs); P WAvU AvUV (Q-Q); P DPgAvU CPgAvUV0i DV (z0ii-z0i); U V w0iz. U C vUAq E Pqz PwUU. EU Pqz v0iU Zz. (EAx AvUAz Pg Pg0igAz Az wz).

    (ii) z P0ig IPg C Cg JAz vU. P JPgAvU DU. CAvg Pq PwUU.

    Av g v g Av g v g Pv Pv, Pvg v vg zv zv, zvg v vg v v, vg sv svg iv iv v vg

    (iii) P PgAv U P0i Pg irPAq Pq PwUU.

    Av g v g Av g v g gd gd Pj Pj gg gg Dv Dv 0i 0i zs zs zs zs

  • Pq Pgt zt 69

    (iv) P AdAv U P0i Ad irPAqU Cx EAz Cz Ad v GPgzqU vUAq Pq PwUUv.

    Av g zu0iiz gU zs zs zs ( + G) g g g ( + G) 0i 0i 0i ( + G) ( + G) vd vd vd ( + G) 0i 0i 0i ( + G) 0i 0i 0i ( + G) 0i 0i 0i ( + G)

    (v) P Avz xisPAv KPZU v P0i Adzq EAz Cz Ad v GPg jPAq Pqz PwUUv.

    Avz xi

    KPZz g

    PgUAq g

    Avz xi

    KPZz g

    PgUAq g

    wv wv P P Pv Pv vP vP Av Av P P 0iv 0iv v v v v

    (vi) Avz xisQ0i ZAvVg P AU AdAv U v P0i U irPAq Pqz PwUUv.

  • Pq Pgt zt 70

    xi sQ Z

    g

    Pg g

    xi sQ Z

    g

    Pg g

    zAB - zA sUAvB - sUAv AvB - Av AvB - Av B -

    (vii) Avz P AdAv U D Adz Az, MAz C Pgzq CAzg CPgAvUV Pqz PwUUv.

    AdAv Av

    PgUAq g

    AdAv Av

    PgUAq g

    zz zz Zvg Zvg Az Az zs zs gv gv PPs PPs Ut se Ut sd

    F EzgU z AvAz PqP g U P0i C PgAz UU V wj. E C Pg P0i Az vz UAz P (E Pg Av JAz gAz Az wz).

    FU z z, zsz0i ZV Pg Az CP U jZ0i irPt.

    (viii) Avz , U Ag U Pqz PgVg, v 0iPgP dPg Ag vz U (Pq PwU) DUv.

    Av Pg Av Pg Av Pg g g g g g g Ozs Oz 0izs ez AP AP 0iz dz Aw Aw 0i d

  • Pq Pgt zt 71

    Av Pg Av Pg Av Pg g g g g g g DP (i) DU t t z e (ii) DP 0i d Azs Ae g g 0iP dP zs e P P 0i d 0iw dw Pg Pd 0iAv dAv a a 0ii d 0iU dU CAP CAP 0iiv ev 0iU dU Ap An 0iV eV zzsg ezg g g GzU GdU g t u Azs Ae g g g zv dd s z z z

    (ix) Uz xiPgUAz Prz CP Av U Cz Uz g0i tUUv. C EAx z0i EgPA 0i.

    Av Pg Av Pg Av Pg g g g g g g qgP qgU a f ew e DP DU Z e w P U PlP PqU Zvg Zzg P U Cl Cq sw vP wU vl vq zw z

  • Pq Pgt zt 72

    (x) Avz uPgUAz Prz CP CPgU CtUV Pq PwUUv.

    Av Pg Av Pg Av Pg g g g g g g bAz ZAz WlP UqU zs z bAz ZAz Wu Uu zs z b Z U Un zs z PApP PAnP WP UU zsg zg Ap An CW CU zs z s ghlw drw st t qsP qP PAs P WAm UAm gr gr

    (xi) Avz P RPg U UPgUV bPgz MwAz Prz CPg Ctz MwAz Pr oPg qPgV, bPg PgV0i, xPg zPgV0i v lPgV0i, PgV0i gAvg A Pq PwUUv.

    GzguU: RPg

    UPgUzP bPg

    PgVgzP oPg

    qPgzzP R U bjP jU Pog Pq R U bwP wU o q

    xPg zPgzzP

    xPg lPgzzP

    xPg PgzzP

    y UAy UAl Ux U

    bPgz MvPg Ctz MwAz

    PrzzP

    EZ EZ

  • Pq Pgt zt 73

    E CP Pg gU F PU Uj:- Av g

    - Pg g

    Av g

    - Pg g

    P - P PgAl - Ugm w - w i - i - t jZ - t - C0i - C0i zP - U - g - g U - U P - P PPl - P P - U - m - Cv - Cz AZ - AZ CAU - GAUl Av - Av - l u - u EP - EnU g - g PAq - PA - zr - zA t - t vw0ii - vU g - g Zvy - Zw wv - z zsi - zt v - v (Oq) wP - wU 0iP - P s - gt - g W - U gP - gU gP - gP - P - P RAq - jPAq P - P g - gj CPg - CPg CAzP - CAzt P - P 0i - Pt - t wUt - wUt Pg - Pg w - w 0i - d -

  • Pq Pgt zt 74

    Av g

    - Pg g

    Av g

    - Pg g

    Z - w - ZPg - Pg P - P U - aU w - w - ZP Pvj - Pvj A - CAZ Pg - Pg v - va PP - PP PA - PAZ gP - gP v - Z CP - JP g - vg zt - zt 0i - 0i sg - g 0ii - e s - dm - dq tv - tv vP - vU P - vU E - J PAg - PvAj - g - nP - U gv - g - t d - d vA - vA v - v Dg - Cg PP - PP AzsP - AzU v - Uzs - Uz P - P sg - zA - zq 0iit - 0it P - P w0ii - U I - j CP - CU U - U GzU - GdU sAUg - AUg Ae - U - U 0ie - d Dg - CZj PAZ - PAZ U - U

  • Pq Pgt zt 75

    Av g

    - Pg g

    Av g

    - Pg g

    zs - z ew - e sdAU - dAU Ci - Ci P - Pt zs - z 0ig - g dg - dg Udg - Udg gw - gw Dg - Cd zsQ - qV g - g P - Pr 0i - ZvzAv - ZzAv v - lt z - l Cv - CU - z vjv - vj KPg - JPg De - Du Zv - ZP t - u Zv - Z fjP - fjU z - z e - t - Pi - P vP - ivP PA - PA AdgQ - AdgQ CU - CU - z Pz - Uz gvt - gt zv - dd CAvBg - CAvg UAy - UAl CZP - CZU PQ - PP CPgi - CPgi ZnP - ZnU QgUg - Qg zP - zU UqsUg - Uqg P - U

    U CP Av-Pv sU PqP gU gAvg A gz EzgU V Vz.

    EzgU Avz CP U gAvg A PqP Az UU wgj. Pqz CP U PPP gAvg A.

  • Pq Pgt zt 76

    Uqz CP U FV Pqz (Uqz) gAvg A 0iUUw. CU UU FU V Rz P CAU C w0iP.

    (1) Pg0iiz CP U Pg0iiUv.

    Uq - Uq Uq - Uq - A - A - u - u - gq - gq j - j gz - gz - - g - g - z - 0ii - z g - g - - - - Q - Q Aq - Aq U - U v - v gq ggq - Z - Z u - t U - U Az - Az U - U Azg - Azg AU - AU U - U Av - Az A - A - Az - Az - - - U - U - Z - AZ - g - g g - g g - g q - q zU - zU - j0i - j0i -

  • Pq Pgt zt 77

    Uq - Uq Uq - Uq z - z - z - z jz - jz U - P

    GzguU P Pq CAvzg JA AdAv U GPgAvUVgz Uj. (Gz:- -, -__Ev)

    FU P0i AdU 0ii 0ii v AzvAz wj.

    (2) , t, , g, AdU CAvz G P U GPgAvUUv. P Ez EAz AdAz Pr v (MvPg) Uv. 0iPgAvU EPgAvUUv v v UUv.

    GzguU:- (i) PgAv GPgAvUzP v vzq GPgAv UzP:-

    - - K-K C-C D-D w-w - - () v-v J-J

    (ii) tPgAvU GPgAvUzP v vAz Prz GPgAvUUzP:-

    Pu-Pt u-t u-t Gu-Gt u-t Pu-Pt u-t iu-it

  • Pq Pgt zt 78

    (iii) PgAv U vAz Pr GPgAvUzP v vz GPgAvUUzP

    - Cg - Cg - - - P - P P - P Mg - Mg - - e - e r - r P - P - Cj - Cj r - r - g - g - Z - Z

    (iv) PgAvUz U GPgAvUUzP v EAz Pgzq GPgAvUUzP

    g - g GU - GU Gg - Gg g - g v - v g - g - - - v - v e - e P - P - g - g P - P Mg - Mg D - D - Cg - Cg U - U P - P - (U) P - P

    (v) gPgAvUz U GPgAvUUzP

    g-g g-g Pg-Pg vg-vg g-g g-g g-g g-g (g) vg-vg Gg-Gg

  • Pq Pgt zt 79

    (vi) 0iPgAv U EPgAv v vAz Prz EPgAv UUzP

    v0ii-v P0ii-P 0ii- 0ii- P0ii-P 0ii- 0ii- 0ii- 0ii-

    (vii) CgAz Prz J U Cz Uqz gAvgV.

    vAl-vl gAd-gd qA-q PA-P vAP-vP Az-z Aw-w tAfU-tfU PgAqU-PgqU tA-t vgA-vg fAU-fU PqAw-Pqw Az-z AP-U PAP-PAP A- gAU-gU MgAv-Mgv Al-l qAU-qU vAnU-vnU

    (viii) E P gAvgU rj.

    P36-Pv-Pv J0ii-Ju U-Uz-Uz 0ii-u -v-v Pu-PtP Cz-Cz-z u-tP (tP) vv-vv-v -P v-v- Mg-M Jv-Jv, Jl-J U-U Cv-Cv, Cl-C vU-vU ZZ-ZZ Uz-Uz PZ-PZ z-z z-z v-vg

    36 E0i Pg gPgzg U g. g v PU 0iU, Plgs 0iU J0i . zyU zAz CAz PV Zg iqz V z Sz.

  • Pq Pgt zt 80

    Gz-Gz Pz-Pjz E-Eg CA-C zA-jz vt-vA zA-jz v-w P-P -g P-Pg P-Pv -

    * * * * *

  • Pq Pgt zt 81

    Czs0i 4

    z Pgt (z-Pw-sQv0i)

    I - z

    ivq ivU CP U0i Ugv. D UU g g g Pngv. CAzg MAzAz ew0i U MAzAz UA ir Pgtz v. GzguU F PV ivU0i U rj.

    1. Dv 0i ZV Pnz. 2. MPUg PAz 0i 0ig.

    F PU:- 1. Dv, 0i, MPUg, PAz, 0i-E zU. 2. Pnz, 0ig-E Q0iizU. 3. ZV-JAz C0i.

    U Dq ivU RV g UAUV iqv. (1) z (2) Q0iiz (3) C0i-E D g UAU.

    0i 0izAz Az 0i U 0i

    E zU. F zU JAz g. F gz JA zz g Cx Pw Jv.

    Pnz, Pl, Plv, Pnzg, Pl, Pl, Pl-E Q0iizU. EUU g, Pl JAz. F Pl JA g Q0iizz g. EzP zsv JA EAz gAl.

    Azg U gU. Q0i0i z Q0iizz.

  • Pq Pgt zt 82

    ZV, lU, U v Dzg-EAx P U s0i gv. EU MAz gVgv. z Q0iizUAv g g g Az. E g gAz n. E gU. EU C0iAz Pg0iz.

    U q ivU, zz g UAUz zU, Q0iizU E C0iUVgv; EU FU zU ZgV w0it. z JAzg g PwAzP v0i wz g. F PU rj:-

    Pw + sQv0i = z + G = 0i P + C = P + EAz = Az + P = P + C = 0i

    E , P, , , -zz PwU. G, C, EAz, P, C-E sQv0iU. 0i, P, Az, P 0i-E zU

    (29) Pw:-zz gV0i, Q0i0i Cx Pqz0i Eg Pw0iz. EP wPU JA g GAl. GzguU:-g, , t, G, , , P, Cq, Ug, lt, d, t, UAq, qU, , P, AZ, P, , t, t, PnU, z,-Ev.

    (30) z:-PwUU v0iU j z U.

    (31) z:-PwUU sQ v0iU j z U.

    (32) sQv0i:- vAvV Cxz, PwU Az j, g g CxAliq G, C, EAz, U, P, zAz, C, C, K, Eg, F, D, EvUU sQv0iUg.

  • Pq Pgt zt 83

    GzguU:- Pw + sQv0i = z qU + G = qU AZ + C = AZ m + EAz = mAz z + P = zP zP + zAz = zP zAz CP + C = CP v + C = v0i vAz + K = vAz0i g + D = gi

    F PwU g jw0i U. g, tU, U-Ev CP U0i Ugz Uj. E CP U0i U. CU g F PU rj:-

    II - PwU 1. dz PwU 2. v () Uz (i) g g PwU Ax (i) Jgq g zU j (ii) tU g Ax MAzzU iU (iii) U Ut, sU (ii) Q0iiPw (zsv)Az Ax nz PzAv PwU (iv) P, , Cv, P, (iii) vvv0i j GAmz ASU a U vvAv PwU

    F azAv PwU RV Jgq U0i:

    (1) d PwU (2) vUz i, PzAv, vvAvU.

  • Pq Pgt zt 84

    (1) d PwU_ GzguU:-, , d, , g, P, , qt, Jgq, Pjz, zq, t-EvU.

    (2) v () PwU_ (i) iU37-U, zqg, V, Pt, EP, e, zg-Avz. (ii) PzAvU38-irz, iqP, il, Nl, Nz, Nz, w, EvU. (iii) vvAvU39-MPU, UtU, rU, Ug, MPVw, eu, zqv, iUg-EvU.

    jg i, PzAv, vvAvU A g g Czs0iU gV w0ij. FU d Pw, sQv0i, zU Zg w0it.

    (33) ZPPwU RV: (1) ZPU, (2) UtZPU, (3) ASZPU, (4) AS0iZPU, (5) sU, (6) jitZPU, (7) PgZPU, (8) UZPU, (9) U -JAz CP UA iqz.

    (1) ZPU

    (34) U g U ZPU.

    GzguU:- Zv U-, AU, , P, zP, Jv, J, j, -Avz.

    37iAzg Jgq Cx CP zU CxPUtV j MAz zUP. Vqg, gU, Cg-E (i) zU. EU Vq+g=Vqg JAz, gz+P=gU JAz, Cg+=Cg JAz Jgqgq zU jgz Uj. 38 zsvUU (Q0iiPwUU) Pv v0iU j PzAvU. iq+C=iq, EzgAv-U, g, l, il, Nl Ev. 39 zU g CxU Ug, Pg, DrU Ev v0i j Dz-Ug, iUg, rU, rU, UtU EvU vvAvU.

  • Pq Pgt zt 85

    Zvz U-P, g, , d, J, , t, P, l, Cq, o, , ,-Avz.

    F ZPU (1) gqs, (2) CAQv, (3) CxP-JAz g sU iqz.

    (1) gqs-grAz Az iZPU gqsU.

    GzguU:-, v, , AU, qU, lt, z-EvU. E Ag Ev U J UU C iZPU.

    (2) CAQv-gz G0iUP ElPAq gU CAQv U.

    GzguU:-UAU, v, Pj, i0i, Az, g, P, APg, gAU, w, AUg, sgv, PlP, D, -EvU (E gqsUU El gU DV).

    (3) CxP-CxP CUtV El gU CxP U.

    GzguU:-PAl, , Qq, j, zA, gV, 0iV-EvU.

    (2) UtZPU

    F PV PU Uj_ (1) PAm0i vAz. (4) 0i CQ P (2) zq P Ez. (5) Pj0i Ez (3) aPP Egvg.

    PU PA JAz m0i tz Ut, zq JAz P jw0i, aP JAz P jw0i, 0i JAz CQ0i Ut, Pj0i JAz 0i tz jw0i w U. EUU tUAz g.

  • Pq Pgt zt 86

    (35) U Ut, jw, sU w tU UtZPU.

    GzguU:-zq, aP, Qjz, M0i, Plz, z, Pjz, z, 0i, jz, jz, Qjz, Jz-zz.

    F tU 0iizP z0i CAx U U.

    t Pj0i zq P aP U

    E Pj0i, zq, aP F U tU. , P, U Ev U U.

    (3) ASZPU

    (36) AS0i U ASZPU

    GzguU:-MAz, Jgq, v, g, P-EvU. (MAz , Jgq Pzg, g D-U ASZPU UtZPU Av zUU tU DVgv).

    (4) AS0iZPU

    g P, g U, Lg zyU-JA F PU g, g, Lg zz U F Pz ASAz Prz U wvz? EAx UAz AS0i, U wPU gv.

    (37) ASAz Prz U U AS0iZPU.

    GzguU:- AS AS0i g g, g0i Jgq Eg, Jgq0i Lz Lg, Lz0i

  • Pq Pgt zt 87

    (5) sU

    (38) U v Q0i0i s w U sU40.

    zg s - (vvAv s) Pjzg s - P (vvAv s) jzg s - j (vvAv s) jzg s - g=() (vvAv s) qzg s - l (PzAv s) iqzg s - il (PzAv s) Pqzg s - Pl (PzAv s)

    Ezg U- (Uq), P (Uq), PA=PZ0izg s, A (Uq) E w0iz.

    (6) jit ZPU

    (1) C zq P (2) E dg UA (3) J PU? - Ev PU C, E, J-Ev U MAz Uvz Cv, AS0i , CAzg rz Cv, AS E E. EAx U P jitU iv wv. EAx U jit ZPU Jvg.

    (39) U i Cv, jit, Uv-EvU U jitZPU. GzguU:-C, E, , P, Cv, Ev, Jv, -EvU. jitP:- U, P HgU-Ev. UvP:- Uqz, D0i, zv-Ev. CvU:- C zg, E PU-Ev.

    40sU zsvUAz lvP PzAvsUAz, Pw UAzAmU sU vvAv sUAz g. F 0i D0iiPgtU gV w0iwj. D 0i V wz, C.

  • Pq Pgt zt 88

    (7) PgZPU

    (1) CAx Am? (2) CAv Zg q. (3) JAx t. (4) EAxg GAm? - Ev U w, jwU wv.

    (40) U w Cx jwU w U PgZPU. E MAz U0i UtZPU Cz.

    GzguU:- CAx, CAxz, EAx, EAxz, EAxz, JAv, JAx, CAx, CAx, CAxz, CAv, EAv, CAvz-Ev.

    (8) UZPU

    (41) PU (lU) g a U UZPU . GzguU:- Gvg, zQt, , , F, 0i, DU0i, Iv, q, vAP, qU, q, DZ, FZ-EvU.

    (9) U

    g PrU z. C AUq vPtg glg. Cg C t0i wzg.

    F PU C AUq JAzg g AUq JAz Cx. Cg C JAzg gPtv0ig D Pr JAz Cx. C, Cg, C Ev U zU z gAz U0i U. U ZPU z CP zV P g U0i U 0iVv. EAx U U.

    (42) ZPUz zU z Av C (a) U U.

    GzguU:- Cz, Ez, 0iiz, J (J), K, C, E, 0ii, C, E, 0ii, v, v, , , Dz, Dg,

  • Pq Pgt zt 89

    Dg, K, K*, DA (D)*, A ()*, A ()* -EvU.

    GzguU Ag U g sU iqz.

    (1) gxP U. (2) xP U. (3) DvxP U.

    1. gxP U GzguU:-(i) - E Gv g U. (ii) - E zs g U. (iii) C-Cg C-Cg E x g U Cz-C

    2. xP U GzguU:- 0iiz, K, Kvgz, Dz, K, K EvU xP U. (E U AAz UzjAz U g).

    3. DvxP U GzguU:- v-v EU DvxP UAz z rP.

    EzgU z (1) ZP, (2) UtZP, (3) ASZP, (4) AS0iZP, (5) s, (6) jitZP, (7) PgZP, (8) UZP, (9) -PwU AU, AU, APAU UAz, KPZ, Z szUAz, G, C, EAz, U, P, zAz, C, C, K, Eg, F, D, Ev sQ v0iUAz CP g szU s0i q0i. CU g FU w0it.

    F U Uqz P0i. Uq PU Nz zyUz EU UU wgP. K, Eg, F, D, sQv0iU UU v.

  • Pq Pgt zt 90

    III - AUU (1) AU, AU, APAU

    (i) UU z. (ii) v Gz 0ijU z. (iii) Pv 0ivz.

    PU , UU, v, 0ijU, -JA zU , U - JAgq U GZjzU U UAq JAx 0iz. v, - JA CAzU U AU JA Cx 0iz. Pv, -U 0iU irzU AUz, UAqz g zxAx zsUz (0iz). Ez APAUg. Uzg AU, AU, APAUUU vU F PVAv z.

    (43) AU:- 0ii 0iU irzU UAq JAx U 0iz Cz AUz.

    GzguU:- zq, zP, P, , APg, , qU, Pl, Cg, zs, Aw, dn, QAv, vAz, i, zg, Ct, v, aP, a, g, P, APgZg, zU, z, P, P,-Ev.

    0ii zg sU UAq JAx 0iz. DzjAz E AUU.

    (44) AU:- 0ii 0iU irzU sU AU JA Cx 0iz Cz AUz.

    GzguU:- zq, zQ, Cv, aP, zq, Aqw, vAV, zj, w, CP, Cg, gt, v, Cf, z, Z, MPVw, qVw, Pl, M0i, tw, Gzs0i, CzsP, a, U, P, , AU-EvU.

    (45) 0ii 0iU irzU AU UAq Jgq Cz Cx U 0iz Cz APAUz.

  • Pq Pgt zt 91

    GzguU:- , , AQ, Uz, vl, Pv, Pzg, Pt, Jv, j, , PnU, P, EnU, , V, z, , q, d, , , AZ, P, J, , , t, P, PA, g, Uq, U, , , AUg, DP-EvU.

    (2) APAU, APAU, vAPAU

    zAv AUU g U0iizg M P U (1) AUAPAUU, (2) P APAUU, (3) P vV APAUU, (4) v P AU, AU, APAU gg 0iU iqv. CU UU w0it.

    (46) APAUU:- g, ZAz, , AU-Ev UZP U AUzAv0i, APAUzAv0i, 0iV v. DzjAz E APUAz Pg0iv.

    GzguU:- g rv (APAU) g rz (AU) 0i Pqvz (APAU) 0i Pqv (AU) ZAzz0iv (APAU) ZAz Gz0iz (AU)

    (E g, ZAz, -U AU APAUUgqg 0iUVgz Ptz)

    (47) APAUU:- zvZPUz U AU APAUUgqg 0iVqv. EAx APAU UAz Pg0ig.

    GzguU:- zv Mv (APAU) zv Mz (AU) Q M/Mv (APAU) Q Mz (AU) gw P irv (APAU) gw P irz (AU)

  • Pq Pgt zt 92

    qV Nzvz (APAU) qV Nz (AU)

    g zv, Q, gw, qV-Ev U AU APAUUgqg 0iVngzjAz E APAU UAz PgPqv.

    (48) vAPAUU:- , U, zAq, d41, P -zz U 0iiU APAUz0i 0iVq zjAz E vAPAUUAz Pg0ig.

    GzguU:- dv. U Cvz. d jz. zAq Av. P Vz.

    , P, U-E UAq Uzg DVgz, uzg DVgz. Dzg 0iU iv APAUz JAz w0iP. d JA t, UAq Jgq DVgz. Dzg 0iU iv AP AUz JAz w0iP. zAq JAzg , t, AU Kzg Egz. 0iU iv APAUz. DzzjAz d, zAq, U, -EAx U vAPAUUAz w0iP.

    (3) AU, AU, APAU gg 0iUU U

    [ZAU (AUU)]

    (1) vAz. (E AU) (2) v. (E AU) (3) . (E APAU)

    41d APAUzg, zd, d, Pd, d JA U iv AUU. (d zg, v, P, -Ev GUPzg AUAz w0iP. GU=v0i)

  • Pq Pgt zt 93

    GzguU JA 0iizP qz (tV qz) Cz AU Azvz. Dzg D z AU AzvzzjAz EzP AUAz, ZAUAz g.

    vAz-JA vAz JA AUP CzjAz C AUz. v-JA v JA AUP CzjAz C AUz. -JA JA APAUP CzjAz C APAUz.

    DzjAz JAzP vAvV 0ii AU zP DU. DzjAz EAx UU AU Cx ZAU UAz Pg0ig.

    (49) ZAU (AUU):- , , v JA U, M0i, Pl, 0i, Pj0i zz UtZP U, , P, J-Ev U g AUU MAzjw 0iVqzjAz E AUU Cx ZAUU JAz g.

    GzguU:- (i) -JAzP- zq (AU) zq (AU) zqzAv (APAU)

    (ii) -JAzP- UAq (AU) AU (AU) P (APAU)

    (iii) v-JAzP- v aPAz wz (AU) v aPAz wz (AU) v tzAz sv (APAU)

  • Pq Pgt zt 94

    (iv) M0i-JAzP- M0i qU (AU) M0i qV (AU) M0i (APAU)

    (v) Pl-JAzP- Pl (AU) Pl AU (AU) Pl (APAU)

    (vi) J-JAzP- J UAqg Azg (AU) J AUg Azg (AU) J zU z (APAU)

    EzgU (1) AU (2) AU (3) APAU (4) APAU (5) APAU (6) vAPAU (7) AU (ZAU)-JA K U0i AU PwU U AzvA UU wj.

    FU AUAz U g U vUzAz qt.

    (i) UtZP U g AUU U vUv?

    APAU AU AU Mv (M0iz) M0i M0i

    (AU, AUU Mv JAzg Az C-C JA U gv. Mv+C-M0i JA vPg, Pgz Ag E PgP J PgzVgz Uj).

    Ez (E0iz) E0i E0i zqz zq zq aPz aP aP Jz (J0iz) J0i J0i z (0iz) 0i 0i v (z)

  • Pq Pgt zt 95

    GzguUAz AU AUU, C, C JA C, C-JA, v JA iv JA gz Uj.

    (ii) U g AUU U g zsjvAz Uj.

    APAU AU AU Cz C C Ez E (Fv) E (FP) Dz D D 0iiz 0ii 0ii (ZAU) (ZAU) v v v (ZAU) (iii) ASZPU g AUU U g AzvA z Uj. APAU AU AU MAz M M Jgq Eg Eg g g g

    Jgq zAq A ASZPU AU, AUU MAzg zsj.

    (iv) P CPgAv AU UU AUz E, J, v0iU j AUUv.

    GzguU:- CPgAv AU AU gU Cg Cg (E v0i) CtU CtV (E v0i) qU qV (E v0i)

    iz UUv.

  • Pq Pgt zt 96

    et eu (J v0i) zq zq (J v0i) qU qV (E v0i) zP zQ (E v0i) -EvU

    IV - ZU

    Z JAzg AS. U MAz Cx E ZV P zAl. CAx 0iz Cx Q MAzVzg CAxz KPZ Jv. Jgq Cx CzQAv ZVzg Z Jv.

    (50) MAz JAz U KPZU. MAzQAv Zz UAz w P Zv.

    Pq s0i KPZ ZUAz Jgq ZU. Av s0i KPZ, Z, ZUAz g UUAl. (PtU, PU, PU-E ZUzg EP Pqz Zz g v0i. DzjAz MAzQAv ZVgz ZAz Pg0iqv). GzguU:- KPZ Z Cg Cgg (Cg+Cg) Cg Cg0ig (Cg+Cg) (+) (+) g gU (g+U) Q QU (Q+U) U (+U) Ct CtAg (Ct+CAg) vAz vAzU (vAz+U) v v0ig (v+Cg)

    E vvv0iUAz g. D Pgtz Ezg UU z.

  • Pq Pgt zt 97

    Z GzguU UzU RV UvU 0iAzg -PwU Zz zU CU Az Cg, , U, CAg-Ev ZZP DUU Ag. F ZZP DUU 0ii z gv JAz Uj:-

    Pw + DU + v0i = z Cg + U + G = CgU Cg + U + C = CgU Cg + U + EAz = CgUAz Cg + CgU + EAz = CggUAz Ct + CAg + EU = CtAjU Ct + CAgU + EU = CtAgUU vAz + CgU + C = vAz0igU v + CgU + EU = v0igUU

    F GzguU Az wzgzAzg z Z ZP DUU PwU v0iP (sQv0iP) zsz gAA. Uzg RV g F DUU Zg PV w0it.

    (51) Zz PwU v0iP zsz Cg, U, CgU, CAg, CAgU, Eg, g, , C, P, g-Ev DUU gv.

    GzguU:- (i) Cg gzP:- AU AUUgqg, Cg DU gz. Cg + Cg + G = Cgg Cg + Cg + C = Cgg qU + Cg + EAz = qUjAz

    Uqz F v0iU Cg, U, Cg, CP, CAg, CAgU, Eg, g, g-Ev g zsjv. Uqz E GPgAvUUv. U P Pq P DUvz.

  • Pq Pgt zt 98

    EzgAv-qUg, qV0ig, zPg, zQ0ig, z0ijAz, z0ijU, zg, zjU, Qj0ig, Qj0ijAz, Qj0ijU, j0ig, j0ig, j0ig-EvU.

    (ii) U gzP:- F DU AU, AU, APAU gg P Pq gzAl. (C) AUP: vAz + U + G = vAzU42 vAz + U + C = vAzU Ug + U + EAz = UgUAz (D) AUP: t + U + G = tU t + U + C = tU t + U + EAz = tUAz EzgAv-zsU, CU, CPU-Ev.

    (iii) CgU:- AU AUUgqg F CgU JA DU Zz gz. (C) AUP:- + CgU + G = 0igU AUg + CgU + C = AUgU v + CgU + EAz = v0igUAz (D) AUP:- g + CgU + C = ggU g + CgU + EU = ggUU EzgAv-zqgU, aPgU, vAz0igU, zAgU, PgU, RgU-Ev.

    (iv) CAg:- F DU AU AUUgqg gzAl. (C) AUP:- Ct + CAg + G = CtAg Ct + CAg + C = CtAg Ct + CAg + EAz = CtAjAz EzgAv-vAg, iAg, CdAg-Ev.

    42vAzU, UgU JA E Mg Pjv zg Ugxz ZZP DUU Az E ZzAv0i 0iVqv. DzjAz Ugz Z 0iUAz sP.

  • Pq Pgt zt 99

    (D) AUP:- CP + CAg + G = CPAg CP + CAg + C = CPAg EzgAv-v0iAg, CAg, 0iAg-Ev.

    (v) CAgU43:- CAg JA DU AgqU U JAz Az j CAgU JAz DUzAl. GzguU:- CtAgU, CPAgU, v0iAgUU, vAgU -Ev.

    (vi) Eg:- Aqw JA Pw0i Eg JA DU Zz gz. DU w JAzP gz. Aqw + Eg + G = Arg Aqw + Eg + C = Arg - Ev.

    (vii) g44:- AUz iv PavV F v0i DUV gz. GzguU:- Cvg (Cvg Uq g) vg (vg Uq g)

    (viii) :- P , UtZP, APAU, Z z iv F JAz DUV gz. DU Pw0i P0i CPg (Ad g vz UtvPg) Uz.

    GzguU:- Cz + + G = C (zPg) Cz + + C = C (zPg) 0iiz + + C = 0ii (zPg) aPz + + CP = aPP (zPg) aPz + + G = aP (zPg) zqz + + C = zq (z) J + + C = J ( E 0ii E)

    43CAg, CAgU-jz CtAg, CtAgU EU Cxz szzg U 0iUU Egv. 44 g DU Cx g DU Z gU Uqz iv PAqgv. Pgd tztz v 101 g z.

  • Pq Pgt zt 100

    g JA Z ZP DU Az Pgz Az U JAz iV gzAl. Dzg 0iiz? JA xP z Az g. GzguU:- Cz + + U + G = CU Cz + + U + C = CU Cz + + U + EAz = CUAz Cz + + U + EU = CUU EzgAv-zqU aPU JU-Ev.

    (ix) C :- APAUz P Pq C JAz DUV gzAl. GzguU:- Ez + C + G = E0i Ez + C + C = E0i Qjz + C + CP = Qj0iP jz + C + C = j0i-EvU.

    (x) P:- U, U, U-F g PwU Z z P JAz DUV gz. DU U, U, U, JAzP P JA CPg DzUz. GzguU:- U + P + G = P + P + G = P U + P + EAz = P + P + EAz = PAz U + P + C = P + P + C = P-Ev

    (xi) g:- AS0iZPU iv g JAz DUV gz. GzguU:- g + g + C = g g + g + G = g + g + EAz = jAz45

    EzgAv-Eg, Lg, gg, g, g, Lgg-Ev. (Eg JA Jgq JAz Eg JAz, g JA g

    45 +g+EAz-E JA P0i A0iPPg JAz PgV JAz G0iz.

  • Pq Pgt zt 101

    JAz JAz, gg JA g JAz g JAz G0iz. Lgg JA Lg JAz G0iz.)

    V - sQ v0iU

    EzgU Pw, AU v ZU UU Cjwgj. F PwUU 8 zsz sQv0iU46 CP PgPxU g. FU U g v0iU? CU 0id JAz w0it. F PV PU rj:-

    v UAz ZAq Mzz F P-, v, U, ZAq-U P PwU Mzz JAzg CxUwg.

    , v, U, ZAq F PwUU gg Pz MAz AAzsz. F AAzs v0iU GAliqv. UAz rj.

    JA Pw0i G v0i jzU JA PvzV Mz0i P irz JA Cx 0iz-A K Mzz? JAz. DU ZAq JA Pw0i Pixz C v0i j ZAq JA Pzv. Mz0izP Ez Pv. EzgAv Az 0iizjAz? JA lz. DU U JA Pw0i Az zsxP (PguxP) EAz v0i j UAz JA PguxP zz AAzsmv. v JA Pw0i C JA AAzsxP v0i j v AAzsz U Az JA AAzs avUz.

    E Ag PwU _ 1. JA0i G v0i Pvxz, 2. ZAq JA0i C v0i Pixz,

    46sQv0iU K iv. Azs0i jzg JAmU. Dzg Azs0i xi sQ0i0i j Azs xisQ0iz. E vUU 8 sQ0iAz z. EU , Azs0iz Gz Dg sQU PgPxU.

  • Pq Pgt zt 102

    3. v JA0i C v0i AAzsz, 4. UAz JA0i EAz v0i zsxz JAzg Pguxz j Pz gg AAzsAliq.

    P PwU 0iU iqz zs. 0iU iq gz JAz guAz CxUz. Cz G, C, EAz,-Ev v0iU 0iUP 0iU. P Pq PU sQv0i EzAv PAqAzg C Az V0iAz sP. GzguU:- ZAq Jz -JA P ZAq Jz-U 0iVlg JAzg sQv0i AAz Uz. Dzg C G JA sQv0i Az Vz JAz w0iP. Uzg sQv0iAzg? JA UU PVAv v z.

    (52) Pv, P, Pgt, Az, Cz, DPguPgPx U sVPq g sQ Jz.

    sQ0i PgPxU j. Czg U Azs sQ0i j. P xi, w0ii, vw0ii, Zvy, AZ, F Dg sQU PgPxU sV PqAxU. CU 0i FU w0it.

  • Pq Pgt zt 103

    47 xisQv0i Uq-Uq Jgqg EAz, PwU xisPAv gUVgvAz DzsP sdg C0iVz. 48 PPq sQv0iU g Ez MAz Pw0i C gvAz w0igz. MAzAz Pq0i MAzAz sQv0i gvzAz w0iP. Uqz vw0ii sQv0i J JAz PPq CPgAv APAU UU iv gz. GzguU:- Pz, 0iz-Ev.

    sQU-PgPxU-v0iU-zU

    AS sQU CxU (PgPxU)

    sQv0i Uq zU Uq zU Uq Uq KPZ Z KPZ Z

    1 xi47 Pvx G i g gg gi gg 2 w0ii Pix C CA g gg gA ggA

    3 vw0ii Pgux (zsx)

    EAz EA, gAz gjAz gA gjA EAz, gAzA gjAzA EAz gAz gjAz

    4 Zvy Az (PqP)

    U, EU, P, CP48

    U, P, P

    gU gjU gAU gU

  • Pq Pgt zt 104

    49 AZsQv0i Pqz EAz, Czg Pg vw0ii sQv0i iqzAz, Av Pgtzz U Pqz AZ sQ EgPAz wz Pq PgtPgg AAz D sQ0i v AggAz DzsP zAg v. 50 sQU AAzs0iz PgP0i. J PgPxU AAzsz sQ gvzzjAz Ez gV PgPxzAz w0iP. 51 Azs0iAz JAl0i sQ0i. Ez x0i0i jg. Ez PgPx. Eg v0i Zz iv gz.

    AS sQU CxU

    (PgPxU)

    sQv0i Uq zU Uq zU Uq Uq KPZ Z KPZ Z

    5 AZ49 Cz (CUP)

    zAz CvtA, g zAz

    gg zAz

    gvtA ggvtA

    CvtAzA gvtAzA ggvtAzA CvtAz gvtAz ggvtAz

    6 50 AAzs C C g gg g gg

    7 CPgt C, M g gg g gg C, g gg M, J g gg

    8 Azs51 Pg0iP (CTPgt)

    D, Eg, D, Eg, gi gjg gi gjg K, F K, F g ggU g gUg

  • Pq Pgt zt 105

    sQv0iU PwU gU g P DUiPg U FU qt.

    [DUiPg JAzg PwU v0iP zsz g (zV g) CPg Cx CPgU.]

    (1) C PgAv Pw Ct _

    KPZ Z xi - Ct

    + G = Ct

    +

    + G = Ct CtAg

    w0ii - Ct

    + C = Ct

    +

    + C = Ct CtAg

    vw0ii - Ct

    + EAz = Ct

    +

    + EAz = CtAz CtAjAz

    Zvy - Ct

    + EU = Ct

    +

    + EU = CtU CtAjU

    AZ - Ct

    + zAz

    = Ct

    +

    + zAz

    = Ct CtAg

    zAz

    zAz

    - Ct

    + C = Ct

    +

    + C = Ct CtAg

    - Ct

    + C = Ct

    +

    + C = Ct CtAg

    Azs

    - Ct

    + K = Ct

    +

    + K = Ct CtAg

    Ct

    + D = Ct

    + D = Cu CtAg

    Ct JA CPgAv AUz KPZz sQv0iU J PqU PwU v0iP zsz Pg DUV gvz. Azs0i D v0i gzU iv PgUU.

    (2) C PgAv AU CP _

    KPZ Z xi - CP

    + G = CP

    +

    + G = CP CPAg

    w0ii - CP

    + C = CP

    +

    + C = CP CPAg

    vw0ii - CP

    + EAz = CP

    +

    + EAz = CPAz CPAjAz

  • Pq Pgt zt 106

    Zvy - CP

    + EU = CP

    +

    + EU = CPU CPAjU

    AZ - CP

    + zAz

    = CP

    +

    + zAz

    = CP CPAg

    zAz

    zAz

    - CP

    + C = CP

    +

    + C = CP CPAg

    - CP

    + C = CP

    +

    + C = CP CPAg

    Azs

    - CP

    + K = CP

    +

    + K = CP CPAg

    CP

    + D = CP

    + D = CP CPAg

    AUzAv0i F AU CPgAv Pw0i KPZz sQv0iU gU B J PqU PgU Agz Ptz. Azs0i D sQv0i jzU iv Pg U52.

    wzAv iV CPgAv AU, AUU KPZz sQv0iU gU Pg DUUvzAz w0iP. Z z g. C g Z ZP DU gz Az0i wz.

    FU EAz U0i DU gz PV CPgAv APAUz Uj.

    (3) g JA C PgAv APAU Pw_

    sQ KPZ Z xi - g + G = g + + G = g gU w0ii - g + C = g + + C = g gU vw0ii - g + EAz = g + z + EAz = gAz gUAz Zvy - g + P = g + + P, EU = gP gUU

    52 Ct, CP JA U Uq KPZz gU PV PVAvUv. CtA, CtA, CtA, (CtAzA, CtAz), CtAU, CtvtA, (CtvtAzA, CtvtAz), Ct, Ct, Cu, Ct-Ev, CPA, CPA, CPA, (CPAzA, CPAz), CPAU, CPvtA, CPvtAzA, CPvtAz, CP, CP, CP, CP-Ev.

  • Pq Pgt zt 107

    AZ - g + zAz = g + z + zAz = gz gU zAz zAz - g + C = g + z + C = gz gU - g + C = g + z + C = gz gU Azs - g + = g + + K = g gUg

    g JA CPgAv APAU Pw0i 8 zsz sQv0iU azU xi, w0ii, AzsU Pg, Zvy0iz g PqU z Pg DUUV A JAz Uj.

    DzjAz CPgAv APAU PwU KPZz sQ v0iU gU 0iB xi, w0ii, AzsU Pg, vw0ii, AZ, , U z Pg DUV g. 0iB g JAz gzjAz tZPUz CPgAv APAUU P Pq zPg g.

    GzguU:- CPgAv APAU Pt:- Pt, Pt, PtAz, PtU, Pt zAz, Pt, Pt, Pt (Pt)

    CPgAv APAU Ugq :- Ugq, Ugq, UgqAz, UgqU, Ugq zAz, Ugq, Ugq, Ugq (Ugq).

    Pt Ugq F Jgq CPgAv APAU PwU w0ii, vw0ii, Zvy, AZ, , U AUzAv PgU, xi v AzsU Pg, Azs0i PAz53 Pg, vw0i0i PAz PtAz, UgqAz JAz DzU z Pg DUUUvAz w0iP.

    (4) E JA DU g Zg Ug, Hg, U, zs-zz GPgAv PwUU vw0ii, AZ, , sQU E JA DU PV gz.

    53 P JAzg 0iiz MAz z Pg P Pq gz, P Pq ggz, P Pq g Pg gz JAz Cx.

  • Pq Pgt zt 108

    (PV gzAz gzjAz gAz DU gzAz w0iP. Cx 0ii DU gz EgzAz w0iP).

    GzguU:-

    (i) UgAz (EU) UgAz (PgU) (ii) HjAz (EU) HjAz (0ii DU E) vw0ii (iii) zsAz (EU) zsAz (PgU) (iv) UAz (EU) UAz (PgU)

    (i) UgzAz (EU) -- (ii) HjzAz (EU) HgzAz (0ii DU E) AZ (iii) zszAz (EU) -- (iv) UzAz (EU) --

    (i) Ug (EU) -- (ii) Hj (EU) Hg (0ii DU E)

    (iii) zs (EU) -- (iv) U (EU) --

    (i) Ug (EU) -- (ii) Hj (EU) Hg(0ii DU E)

    (iii) zs (EU) -- (iv) U (EU) --

    (5) Cg JAU g Zg (i) GPgAvUz jz, Qjz Avz UtZP U, (ii) MAz JA ASZP z (iii) Cz, Ez Avz (iv) Pqz, Uz Ev Gz v0iiAv PzAvUU vw0ii, AZ, , sQU Cg JAU gz. GzguU:-

    (i) UtZPU - jz, Qjz-Ev sQ :- jz vw0ii jz + Cg + EAz = jzjAz (Cg DU) AZ jz + Cg + zAz = jzgzAz (Cg DU) jz + Cg + C = jzg (Cg DU)

  • Pq Pgt zt 109

    jz + Cg + C = jzg (Cg DU)

    :- Qjz vw0ii Qjz + Cg + EAz = QjzjAz (Cg DU) AZ Qjz + Cg + zAz = QjzgzAz (Cg DU) Qjz + Cg + C = Qjzg (Cg DU) Qjz + Cg + C = Qjzg (Cg DU)

    (ii) ASZP - MAz vw0ii MAz + Cg + EAz = MAzjAz (Cg DU) AZ MAz + Cg + zAz = MAzgzAz (Cg DU) MAz + Cg + C = MAzg (Cg DU) MAz + Cg + C = MAzg (Cg DU)

    (iii) - Cz, Ez-EvU :- Cz vw0ii Cz + Cg + EAz = CzjAz (Cg DU) AZ Cz + Cg + zAz = CzgzAz (Cg DU) Cz + Cg + C = Czg (Cg DU) Cz + Cg + C = Czg (Cg DU)

    :- Ez vw0ii Ez + Cg + EAz = EzjAz (Cg DU) AZ Ez + Cg + zAz = EzgzAz (Cg DU) Ez + Cg + C = Ezg (Cg DU) Ez + Cg + C = Ezg (Cg DU)

    (iv) Gz v0iiAv PzAvU - Pqz, Uz-Ev :- Pqz vw0ii Pqz + Cg + EAz = PqzjAz (Cg DU) AZ Pqz + Cg + zAz = PqzgzAz (Cg DU) Pqz + Cg + C = Pqzg (Cg DU)


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