i
KN³kmμkarniBnæ nig eroberog
lwm plÁún nig Esn Bisidæ
KN³kmμkarRtYtBinitübec©keTs
elak lwm qun elak Gwug sMNag elak nn; suxNa elakRsI Tuy rINa elak RBwm sunitü elak pl b‘unqay elak Titü em:g
KN³kmμkarRtYtBinitüGkçraviruTæ elak lwm miKÁsir
karIkMuBüÚTr½ kBaØa lI KuNÑaka elak Gwug sMNag
ii
Garmáfa esoePAKNitviTüafñak;TI 8 EdlGñksikSakMBugkan;enAkñúgédenH rYmman 11 emeron . enAkñúgemeronnImYy² eyIgxJúM)aneRCIserIslMhat; mk eFVIdMeNaHRsayKMrUy:agek,aHk,aybMput . eKalbMNgénkareroberogcgRkgKWedIm,ITukCaÉksarCMnYysRmab;Gñk sikSakñúgRKb;mCÄdæan nig müa:geTotedIm,IcUlrYmelIksÞÜyvisy½KNitviTüakñúg RbeTskm<úCaeyIg[kan;EtrIkceRmInqab;rhs½Rsbtamsm½yviTüasaRsþTMenIb. esovePAenHminl¥hYseKhYsÉgenaHeT . kMhusqÁgedayGectnaR)akd CamanTaMgbec©keTs nig GkçraviruTæ . ehtuenHeyIgxJMúCaGñkniBnæ rgcaMCanic©nUv mtiriHKn;EbbsßabnaBIGñksikSaRKb;mCÄdæanedaykþIrIkrayedIm,IEklMGesovenH [kan;EtmansuRkitüPaBRbesIreLIgEfmeTot . CaTIbBa©b; xJMú)aTGñkniBnæsUmeKarBCUnBrGñksikSaTaMgGs;mansuxPaBl¥ manR)aCJaQøasév nig TTYl)aneCaKC½yCanic©kñúgkarsikSa .
)at;dMbg éf¶TI 24 ExFñÚ qñaM2010 GñkniBnæ nig RsayRCav lwm plÁún Tel : 017 768 246 Email: [email protected] Website: www.mathtoday.wordpress.com
iii
matikarerOg eQμaHemeron TMB½r emeronTI1 cMnYnsniTan 001 emeronTI2 sV½yKuN 011 emeronTI3 TMhMsmamaRt nig PaKry 017 emeronTI4 kenSamBICKNit 024 emeronTI5 kenSamsniTan 040 emeronTI6 smIkardWeRkTImYymanmYyGBaØat 064 emeronTI7 vismIkardWeRkTImYymanmYyGBaØat 077 emeonTI8 bøg;kUGredaen nig Rkab 087 emeronTI9 RbU)ab 096 emeronTI10 kareRbobeFobRtIekaN 102 emeronTI11 ctuekaN 111
emeronTI1 cMnYnsniTan
lMhat; !-kñúgcMeNamcMnYnxageRkam etIcMnYnNaxøHEdles μI 5 ?
1
5,
1
5,
1
5,
1
5,
1
5,
1
5
.
@-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> )01.08()1.02(4)102( x> )0001.08()01.02(4)1004( K> )001,08()102()10008( X> )01,07()1,02(4)106()1007( g> )
1000
1(3)
100
1(9)
10
1(68)10(4)100(5
#-sresrcMnYnxageRkamCaRbPaK ³ k> x> 45.28 837.1 K>
50
191 X> 13.0
g> 734.0 $-sresrcMnYnxageRkamCacMnYnTsPaK ³ k>
100
7 x> 000,10
13 K> 42
3 X> 5.2
73
g> 65217
- 1 -
emeronTI1 cMnYnsniTan
- 2 -
%-bMeBjkñúg eday b¤ [)anRtwmRtUv ³ k>
7
4 7
3 x> 21 3
54. 5398. K> 0 0 X> 12
7 13
7
g> 12
101
13
72 c>
12
101
13
91
^-teRmobcMnYnsniTan 9
8,
12
11,
6
5,
4
3 tamlMdab;ekIn .
&-teRmobcMnYnsniTan 3
1,
8
3,
4
1,
5
2 tamlMdab;cuH.
*-k> etIcMnYnsniTan 9
4,
7
3,
2
1,
5
2 mYyNaEdlFMCageK ?
x> etIcMnYnsniTan 9
2,
10
3,
5
3,
6
5 mYyNaEdltUcCageK ? (-KNna rYc sRmYl ³ k> )
9
52(
8
1
x> )
9
52()
8
13(
K> )7
52(
25
12
X>
8
5
3
1
2
1
g>
4
1
8
5
3
1
2
1 c> 9
45
12
78
28
5
23
emeronTI1 cMnYnsniTan
q> 2
9
7
5
12
8
32
8
253
.
!0-KNna k>
16
10.
17
11.
5
4 x> 51
26.
16
17.
13
11
K> 22
26.
16
17
13
11
X>
22
21.
16
17
22
21.
8
11
g> 16
17
4
21
8
11 c>
21
11.
7
3
7
3.
21
11
!!-bgðajfa 9
13
4
13
9
13
4
13
!@-eKman f
e
b
a
d
c
b
a
f
e
d
c
b
a...
bgðajfa f
e
b
a
d
c
b
a
f
e
d
c
b
a...
!#> epÞógpÞat;fa ebI d
c
b
a enaH
f
e
d
c
f
e
b
a .
- 3 -
emeronTI1 cMnYnsniTan
- 4 -
dMeNaHRsay !-kñúgcMeNamcMnYnxageRkam etIcMnYnNaxøHEdles μI 5 ?
1
5,
1
5,
1
5,
1
5,
1
5,
1
5
.
eKman 51
5,5
1
5,5
1
5,5
1
5,5
1
5
nig 51
5
. dUcenHcMnYnEdlesμI 5 KW ³
1
5,
1
5,
1
5
. @-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> )01.08()1.02(4)102(
28.24
08.02.0420
x> )0001.08()01.02(4)1004(
0208.404
0008.002.04400
K> )001,08()102()10008(
008.8020
008.0208000
emeronTI1 cMnYnsniTan
X> )01,07()1,02(4)106()1007(
27.764
07.02.0460700
g> )1000
1(3)
100
1(9)
10
1(68)10(4)100(5
693.548
003.009.06.0840500
#-sresrcMnYnxageRkamCaRbPaK ³ k>
20
569
100
284545.28
x> 900
1241837.1
K> 50
69
50
191
50
191
X> 99
1313.0
g> 900
313734.0
$-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> 07.0
100
7
x> 0013.0000,10
13
- 5 -
emeronTI1 cMnYnsniTan
- 6 -
K> 1875.016
3
2
34
X> 175.040
7
5.2
73
g> 02607.0652
17
%-bMeBjkñúg eday b¤ [)anRtwmRtUv ³ k>
7
4 7
3 x> 21 3
K> 54.0 5398.0
X> 12
7 13
7
g> 12
101
13
72
c> 12
101
13
91
^-teRmobcMnYnsniTan 9
8,
12
11,
6
5,
4
3 tamlMdab;ekIn .
eday 9
8
12
11
6
5
4
3
dUcenH 9
8,
12
11,
6
5,
4
3 .
emeronTI1 cMnYnsniTan
&-teRmobcMnYnsniTan
3
1,
8
3,
4
1,
5
2 tamlMdab;cuH
eday 5
2
3
1
8
3
4
1
dUcenH 4
1,
8
3,
3
1,
5
2 .
*-k> etIcMnYnsniTan 9
4,
7
3,
2
1,
5
2 mYyNaEdlFMCageK ?
eKman 9
4
7
3
5
2
2
1 dUcenH
9
4 CacMnYnsniTanFMCageK .
x> etIcMnYnsniTan 9
2,
10
3,
5
3,
6
5 mYyNaEdltUcCageK ?
eKman 6
5
5
3
10
3
9
2 dUcenH
9
2 CacMnYnsniTanEdltUcCageK. (-KNna rYc sRmYl ³ k>
72
155
72
1649
9
23
8
1)
9
52(
8
1
x> 56
25
56
152175
7
19
8
25)
9
52()
8
13(
K> 175
391
175
47584
7
19
25
12)
7
52(
25
12
X> 15
4
5
8
6
23
8
5
3
1
2
1
- 7 -
emeronTI1 cMnYnsniTan
g>
4
1
8
5
3
1
2
1
9
20
3
8
6
5
8
25
6
23
c> 275
6
330
72
10
1
72
3724210
3534
9
49
12
72
7
5
17
9
45
12
78
28
5
23
q> 2546
2205
134
45
19
49
45
359919
49
9
7
5
118
19
8
49
2
9
7
5
12
8
32
8
253
!0-KNna k>
34
11
4.17
2.11
16.17.5
10.11.4
16
10.
17
11.
5
4
x> 24
11
17.3.8.2.13
13.2.17.11
51
26.
16
17.
13
11
K> 22
26.
16
17
22
26.
13
11
22
26.
16
17
13
11
176
45
176
221176
22.8
13.171
- 8 -
emeronTI1 cMnYnsniTan
X> 22
21.
16
17
22
21.
8
11
352
105
22.16
5.21
22.16
)1722(2122.16
21.1721.22
g> 16
17
4
21
8
11
16
45
16
178422
c>
21
11.
7
3
7
3.
21
11
049
0
49
1111
49
11
49
11
!!-bgðajfa 9
13
4
13
9
13
4
13
eKman 9.4
13.13
9.4
)49(13
9.4
4.139.13
9
13
4
13
ehIy 9.4
13.13
9
13
4
13
dUcenH 9
13
4
13
9
13
4
13 .
- 9 -
emeronTI1 cMnYnsniTan
!@-bgðajfa f
e
b
a
d
c
b
a
f
e
d
c
b
a...
eKman f
e
b
a
d
c
b
a
f
e
d
c
b
a...
EfmGgÁTaMgBIrnwg f
e
b
a..2 eK)an ³
f
e
b
a
d
c
b
a
f
e
d
c
b
a
f
e
f
e
b
a
d
c
b
a
f
e
f
e
d
c
b
a
f
e
b
a
f
e
b
a
d
c
b
a
f
e
b
a
f
e
d
c
b
a
...
)2
(.2
.
..2....2.
!#> epÞógpÞat;fa ebI d
c
b
a enaH
f
e
d
c
f
e
b
a .
eKman d
c
b
a
eK)an d
c
f
e
f
e
b
a )(
eKTaj f
e
d
c
f
e
b
a .
dUcenH ebI d
c
b
a enaH
f
e
d
c
f
e
b
a .
- 10 -
emeronTI10 kareRbobeFobRtIekaN
lMhat; !> DEFABC
cmxEF
cmxBC
)905(
)302(
FE
D KNna BC @> kñúgrUbxageRkam enHeK[
C B
A
nig PRPQ PTSPST eRbobeFob PQS nig PRT P
R Q S T
- 102 -
emeronTI10 kareRbobeFobRtIekaN
- 103 -
#> eK[ MBMT nig MOMA bgðajfa MBAMTO $> eK[ nig BCAB CDAD eRbobeFob nig AED CED
M
A O
B
T
A
B
C
DE
emeronTI10 kareRbobeFobRtIekaN
- 104 -
%> eK[ nig CDAB // TSTR bgðajfa DCTABT ^> eK[ nig CADBAD BCAD bgðajfa nig ACDABD ACAB
A
B
C
D
T
S
R
A
B D C
emeronTI10 kareRbobeFobRtIekaN
dMeNaHRsay !> DEFABC
cmxEF
cmxBC
)905(
)302(
KNna BC D
E F
A
eday DEFABC enaHeK)an EFBC
CB
naM[ 2 90530 xx
60
1202
309052
x
x
xx
cMeBaH 60x eK)an cmBC 15030)60(2 dUcenH . cmBC 150
- 105 -
emeronTI10 kareRbobeFobRtIekaN
@> kñúgrUbxageRkam enHeK[ nig PRPQ PTSPST eRbobeFob PQS nig PRT P
eKman PQ naM[ PR PQR sm)at vi)ak . PRQPQR
mü:ageTot enaH PTSPST PST sm)at vi)ak . PTPS
eKman PTRPTSPSTPSQ oo 180180
eday enaHeKTaj PRQPQR RPTQPS dUcenH PQS PRT ¬ tamkrNI C>m>C ¦
Q RS T
- 106 -
emeronTI10 kareRbobeFobRtIekaN
- 107 -
#> eK[ MBMT nig MOMA bgðajfa MBAMTO
eKman MBMT nig MOMA ¬ smμtikmμ ¦ ehIy ¬ mMurYm ¦ AMBOMT
dUcenH MBAMTO ¬ tamkrNI C>m>C ¦
M
A O
B
T
emeronTI10 kareRbobeFobRtIekaN
- 108 -
$> eK[ nig BCAB CDAD eRbobeFob nig AED CED eKman BCAB nig CDAD enaH ABC nig ADC CaRtIekaNsm)at man ][AC Ca)atrYm . eKTaj)an CabnÞat;BuHénmMu )(BD ABC nig ADC . eday ][BDE enaHeKTaj ECEA . RtIekaN nig AED CED manRCugbIb:unerogKñaCaRtIekaN b:unKña .
A
B
C
DE
emeronTI10 kareRbobeFobRtIekaN
- 109 -
%> eK[ nig CDAB // TSTR bgðajfa DCTABT eKman enaH CDAB // TDSRAT ¬ mMuqøas;kñúg ¦ ¬smμtikmμ ¦ TSTR
ehIy DTSATR ¬mMuTl;kMBUl ¦ dUcenH TDSTAR
vi)ak SDAR nig TDTA eKman enaH CDAB // TCSTBR ¬ mMuqøas;kñúg ¦ ¬smμtikmμ ¦ TSTR
ehIy ¬mMuTl;kMBUl ¦ CTSBTR
A
B
C
D
T
S
R
emeronTI10 kareRbobeFobRtIekaN
dUcenH TCSTBR
vi)ak SCBR nig TCTB eday SDAR nig SCBR enaH CDAB . dUcenH DCTABT ¬tamkrNI C>C>C ¦ ^> eK[ nig CADBAD BCAD bgðajfa nig ACDABD ACAB
- 110 -
A
B CD
eKman naM[ BCAD ADB nig ADC CaRtIekaNEkg eday ¬tamsmμtikmμ ¦ CADBAD
eKTaj ACBCADBADABC oo 9090 naM[ ABC sm)at . vi)ak ACAB dUcenH . ACDABD
emeronTI11 ctuekaN
- 111 -
lMhat; !-RtIekaN mYyman ABC E nig D CacMnuckNþalén ][AB
nig ][AC erogKñanig 46,49 xBCxDE . KNnatémøén x . @-eKmanctuekaNEkg nigRbelLÚRkam . ABCE BCDE
bgðajfaRtIekaN ACD CaRtIekaNsm)at .
A
B
C
E
D
A
B
C D
EF
emeronTI11 ctuekaN
#-eKmanctuekaNBñay Edl nig ABCD ]//[][ CDAB X nig Y CacMnuckNþalénRCugeRTt . k> KNna AB ebI 6.12XY nig 3DC x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC . $-eKmanctuekaNBñaysm)at Edl ABCD ]//[][ ADBC nig . KNnargVas;mMuepSgeTot ? oA 67
A B
CD
YX
A
CB
o67
D
- 112 -
emeronTI11 ctuekaN
%-eKman CaRbelLÚRkamEdl ABCD CEAD nig CEDCDE bgðajfa CactuekaNesμI . ABCD
^-eKman CactuekaNesμI . ABCD
eKman ][][],[][ BCDFADEB . bgðajfa DFBE
CB
DA E
A B
C
E
F
D
- 113 -
emeronTI11 ctuekaN
&-eKman CactuekaNesμI . ABCD
bgðajfa nig ODC OCD CamMubMeBjKña ?
A
B
D
O
C
- 114 -
emeronTI11 ctuekaN
- 115 -
dMeNaHRsay !-RtIekaN mYyman ABC E nig D CacMnuckNþalén ][AB
nig ][AC erogKñanig 46,49 xBCxDE . KNnatémøén x .
eKman E nig D CacMnuckNþalén nig [][AB ]AC enaH ED Ca)atmFüménRtIekaN . ABC
eK)an 2
BCED eday 46,49 xBCxDE
eK)an 2
4649x
x
2349 xx naM[ 1x . dUcenH 1x .
A
B
C
E
D
emeronTI11 ctuekaN
- 116 -
@-eKmanctuekaNEkg nigRbelLÚRkam . ABCE BCDE
bgðajfaRtIekaN ACD CaRtIekaNsm)at .
eKman EDAEBC RCug ctuekaNEkg ABCE
nigRbelLÚRkam BCDE naM[ E CacMNuckNþalén AD ehIy eRBaHoCEA 90 ABCE CactuekaNEkg eKTaj)an CaemdüaT½rén CE AD . dUcenH CAD CaRtIekaNsm)at . smÁal; ³ eKman BEAC Ggát;RTUgctuekaNEkg . ABCE
ehIy CDBE RCugRbelLÚRkam BCDE
eKTaj)an CDAC dUcenH CAD CaRtIekaNsm)at .
A
B
C
D
EF
emeronTI11 ctuekaN
- 117 -
#-eKmanctuekaNBñay Edl nig ABCD ]//[][ CDAB X nig Y CacMnuckNþalénRCugeRTt . k> KNna AB ebI 6.12XY nig 3DC x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC . k> KNna AB ebI 6.12XY nig 3DC eKman X nig Y CacMnuckNþalénRCugeRTt AD nig BC enaH XY Ca)atmFüménctuekaNBañy . eK)an
2
CDABXY
naM[ CDXYAB .2
2.2232.253)6.12(2 AB . x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC
A B
C D
X Y
emeronTI11 ctuekaN
eK)ansmIkar 2
7412112
xxx
14
11332
33112
x
xx
xx
dUcenH 14x . $-eKmanctuekaNBñaysm)at Edl ABCD ]//[][ ADBC nig . KNnargVas;mMuepSgeTot ? oA 67
eday ABCD CactuekaNBañysm)atenaH oAD 67
ehIy oooo
CB 1132
6767360
dUcenH oAD 67 nig oCB 113
A
C B
o67
D
- 118 -
emeronTI11 ctuekaN
%-eKman CaRbelLÚRkamEdl ABCD CEAD nig CEDCDE bgðajfa CactuekaNesμI . ABCD
eKman A CaRbelLÚRkam enaH BCD BCAD nig CDAB eday enaH CEDCDE CDE CaRtIekaNsm)at vi)ak CECD . tamsmμtikmμ enaHeKTaj CEAD CDAD dUcenH ABCD CactuekaNesμI .
A D E
B C
- 119 -
emeronTI11 ctuekaN
^-eKman CactuekaNesμI . ABCD
eKman ][][],[][ BCDFADBE . bgðajfa DFBE eKman ][][],[][ BCDFADBE enaH ABE nig CDF CaRtIekaNEkg . eKman FCDEAB nig DCAB enaH . CDFABE
vi)ak DFBE .
A B
C
E
F
D
- 120 -
emeronTI11 ctuekaN
&-eKman CactuekaNesμI . ABCD
bgðajfa nig ODC OCD CamMubMeBjKña
A
- 121 -
eKman
2
ADCODC
nig
2
BCDOCD
eK)an ooBCDADC
OCDODC 902
180
2
dUcenH nig CamMubMeBjKña . ODC OCD
B
D
O
C
emeronTI2 sV½yKuN
- 11 -
lMhat; !-cUrsresrplKuNxageRkamCasV½yKuNrYcR)ab;eKal nig niTsSnþ k> 6666666 x> 888888 K>
n
aaaaa ....
X>
n
c
ab
c
ab
c
ab
....
@-cUrsresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna k> 23 24 x> 32 78 K> 34 63 ` X> 33 127 #-cUrsresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna
k> 23 34 x> )2(3
242
23
K> 223 532 X> 343 325 $-ctuekaNEkgmYymanbeNþayRbEvg 13 b nigTTwgRbEvg 12 b KNnabrimaRtctuekaNEkgenaHebI 3b .
emeronTI2 sV½yKuN
- 12 -
%-KNnatémøénkenSamxageRkam ³ k> cMeBaH 22 23 xyyx 5x nig 4y x> cMeBaH ))(65( 3322 nmnm 1m nig 2n
K> cMeBaH 2432 cba 3,2 ba nig 1c ^-sRmYlkenSamxageRkam ³ k> x> )4)(4)(4( 425 743 2222
K> 364
3
4
3
4
3
4
X> 612
23222
743
&-sRmYlkenSamxageRkam ³
k> ))(3( 5734 yxyx x>
42
4332
6
22
3
ba
baba
K> )4)(2)(5(
)5)(32(322
3482
xaxaax
xaxa
X> 33222
382
)4()2)(5(
)32(
xaxaax
xa
g> 42
530
32
6
)2(2
3
ba
baba
emeronTI2 sV½yKuN
- 13 -
dMeNaHRsay !-sresrplKuNxageRkamCasV½yKuNrYcR)ab;eKal nig niTsSnþ k> 766666666 maneKal 6 nig niTnSnþ 7
x> 66 8)8(888888 maneKal 8 nig niTnSnþ . 6
K> n
n
aaaaaa ....
maneKal a nig niTnSnþ n
X> n
n
c
ab
c
ab
c
ab
c
ab
....
maneKal c
ab nig niTnSnþ . n
@-sresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna k> 2562.2.4.4.424 23 x> 219527.7.7.8.878 32 K> 174966.6.6.3.3.3.36.363 3434 ` X> 59270412.12.12.7.7.7127 33
emeronTI2 sV½yKuN
- 14 -
#-cUrsresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna k> 5763.3.4.4.434 23
x> 512
60
12
464
2.2.3
2.24.4.4
)2(3
242
23
K> 18005.5.3.3.2.2.2532 223 X> 27161253.3.32.2.2.25.5.5325 343 82
$-ctuekaNEkgmYymanbeNþayRbEvg 13 b nigTTwgRbEvg 12 b KNnabrimaRtctuekaNEkgenaHebI 3b . tag P CabrimaRtctuekaNEkg] eK)an )(2)11(2 2323 bbbbP
ebI eK)an . 3b 72)927(2)33(2 23 P
%-KNnatémøénkenSamxageRkam ³ k> cMeBaH 22 23 xyyx 5x nig 4y eK)an 460)4)(5(2)4()5(323 2222 xyyx
x> cMeBaH ))(65( 3322 nmnm 1m nig 2n
eK)an 126)81)(620())(65( 3322 nmnm
emeronTI2 sV½yKuN
K> cMeBaH 2432 cba 3,2 ba nig 1c eK)an 1296)1()3()2(22 243243 cba
^-sRmYlkenSamxageRkam ³ k> 11425425 44)4)(4)(4( x> 157431743 222222
K> 3
4
3
4
3
4
3
4
3
4 364364
X> 3.23.2
3.2
3.2.2.3
3.2
612
2322 635
411
42
4731
2
743
192 . &-sRmYlkenSamxageRkam ³ k>
2
1121153745734 3
3.3))(3(y
xyxyxyxyx
x>
342
4332
42
4332
2
1
6
.3
6
22
3
abba
ba
ba
baba
K> 746
116
322
3482
4.8.5
5.32
)4)(2)(5(
)5)(32(x
xa
xa
xaxaax
xaxa
- 15 -
emeronTI2 sV½yKuN
X> 16278148
24615
33222
382
2.2.5
2
)4()2)(5(
)32(xa
xa
xa
xaxaax
xa
g> a
b
ba
ba
ba
baba
36
2
6
)2(2
3
42
53
42
530
32
.
- 16 -
emeronTI3 TMhMsmamaRt nig PaKry
- 17 -
lMhat; !-cUrrktémø x kñúgkrNInImYy²xageRkam ³ k> 5:7:4 x x> 5:998: x @-k>eK[ nig 18:5: ba 138 ba . cUrrktémøén x . #-ebI nig d CacMnYnviC¢man . bgðajlkçNHsmamaRt cba ,,
d
c
b
a dUcxageRkam ³
k> ad x> bcd
b
c
a
K> a
c
b
d X>
a
b
c
d
g> d
dc
b
ba
c> d
dc
b
ba
q> ebI c enaH dc
a
dc
ba
C> ebI a nig c enaH b ddc
dc
ba
ba
$-eK[ 9:7:6:: cba
k> rktémø a nig c ebI cmb 21 x> rktémø a nig b ebI gc 720
emeronTI3 TMhMsmamaRt nig PaKry
%-k>eK[ nig 20:13:7:: cba 520 cba cUrrktémøén ? cba ,,
x>eK[ 15:8:6:: zyx nig gyz 98 . cUrrktémøén zyx ,, ? K>eK[ . 9:6:4:: cba
cUrrktémøén ebI cba mab 34 .
- 18 -
emeronTI3 TMhMsmamaRt nig PaKry
- 19 -
dMeNaHRsay !-rktémø x kñúgkrNInImYy²xageRkam ³ k> 5:7:4 x eK)an
7
20
7
54
x
x> 5:998: x eK)an
5
792
5
899
x
@-eK[ nig 18:5: ba 138 ba . cUrrktémøén b . eKman a enaH 18:5: b 6
23
138
185185
baba
eKTaj)an 108618 b . #-ebI nig d CacMnYnviC¢man . bgðajlkçNHsmamaRt cba ,,
d
c
b
a dUcxageRkam ³
k> bcad
eKman d
c
b
a
KuNGgÁTaMgBIrnwg bd eK)an d
cbd
b
abd b¤ . bcad
emeronTI3 TMhMsmamaRt nig PaKry
- 20 -
x> d
b
c
a
eKman d
c
b
a naM[ ad bc
EckGgÁTaMgBIrnwg cd eK)an cd
bc
cd
ad
dUcenH d
b
c
a .
K> a
c
b
d
eKman d
c
b
a naM[ ad bc
EckGgÁTaMgBInwg ab eK)an ab
bc
ab
ad
dUcenH a
c
b
d .
X> a
b
c
d
eKman d
c
b
a naM[ ad bc
EckGgÁTaMgBInwg ac eK)an ac
bc
ac
ad
dUcenH a
b
c
d .
emeronTI3 TMhMsmamaRt nig PaKry
- 21 -
g> d
dc
b
ba
eKman d
c
b
a
Efm 1 elIGgÁTaMgBIrénsmIkareK)an 11 d
c
b
a
eday b
ba
b
a 1 nig
d
dc
d
c 1
dUcenH d
dc
b
ba
c> d
dc
b
ba
eKman d
c
b
a
Efm elIGgÁTaMgBIrénsmIkareK)an 1 11 d
c
b
a
eday b
ba
b
a 1 nig
d
dc
d
c 1
dUcenH d
dc
b
ba
q> ebI c enaH dc
a
dc
ba
eKman d
c
b
a naM[
dc
ba
d
b
c
a
.
emeronTI3 TMhMsmamaRt nig PaKry
- 22 -
C> ebI a nig c enaH b ddc
dc
ba
ba
eKman d
c
b
a naM[
dc
ba
dc
ba
d
b
c
a
dUcenH dc
dc
ba
ba
.
$-eK[ 9:7:6:: cba
k> rktémø a nig c ebI cmb 21 eKman 9:7:6:: cba
eKTaj 7
6ba nig
7
9bc eday b cm21
dUcenH cmccma 27,18 . x> rktémø a nig b ebI gc 720 eKman 9:7:6:: cba
eKTaj 9
7,
9
6 cb
ca eday gc 720
dUcenH gbga 560,480 %-k>eK[ nig 20:13:7:: cba 520 cba cUrrktémøén ? cba ,,
eKman 20:13:7:: cba
emeronTI3 TMhMsmamaRt nig PaKry
b¤ 1340
520
2013720137
cbacba
eKTaj 260,169,91 cba . x>eK[ 15:8:6:: zyx nig gyz 98 . rktémøén zyx ,, eKman 15:8:6:: zyx b¤ g
yzzyx14
7
98
8151586
eKTaj gzgygx 210,112,84 K>eK[ . 9:6:4:: cba
cUrrktémøén ebI cba mab 34 . eKman 9:6:4:: cba
b¤ mabcbacba
172
34
46964964
eKTaj mmcba 3231719 .
- 23 -
emeronTI4 kenSamBICKNit
- 24 -
lMhat; !-KNna k> 222 573 xxx x> tyxtyxtyx 244444 2
2
3
K> X> )1)(2( 2 xyx )4)(( 2 yyx
@-eKmanBhuFa 132 42 xxxA nig 323 432 xxxxB k> KNnapldk rYcbRgYm nig erobrytamlMdab;sV½yKuNcuH BA
én x . x> sresrpldk AB
#-KNnaplbUkxageRkam ³ k> x> 2222 23 yxyx )2()35( 2323 abbaabba
K> )423()34( 2334 zyxzyx
X> )543()424()35( 23233 ttttbtt
$-eK[kenSam )()()( baxxabbxa . KNnarYcbRgYmnigerobryBhuFaenHtamlMdab;cuHéndWeRkGefr .
emeronTI4 kenSamBICKNit
%-sMNYrdEdldUclMhat;TI$ cMeBaHkenSamxageRkam ³ k> )()()( 22 yaaayxayaxy
x> )3)(2(2)3)(1()2)(1( tttttt K>
4
39)3)(5()
2
3)(
2
5( bbbb
^-RsaybBa¢ak;smPaBxageRkam ³ k> 42 1)1)(1)(1( xxxx
x> 32)1)(1(35 22 bbbb
&-muFaKNnaedayeRbIsmPaBsMxan;²
2222
2222
4654,101102
,15,25,39,15,2119,6654,4139
*-BnøatkenSamxageRkam nig erobryBhuFaenHtamlMdab;éndWeRkGefr k> )169(16)12(9 222 xxxx
x> 2222 )1(25)243(4 aaaa
K> 5)3(9)3( 22 baba
X> g> xyxyxx 12)34( 2 33 )2()1( xx
c> )5)((6 baba
- 25 -
emeronTI4 kenSamBICKNit
(-dak;kenSamxageRkamCaplKuNktþa ³ k> 2)12(16)12(9 xx
x> )4(5)123( 2 aaa
K> 22 )3(9)3( baba
X> )2()84( yxyyxx g> 32 )2(27)1(8 xx
c> )5)(()1022( bababa !0> dak;kenSamxageRkamCaplKuNktþa k> )1)(32()15)(32( xxxx x> )23)(17()17( 2 aaa
K> )75)(32()32( 2 xxx
X> )45)(13()13)(2()32)(13( xxxxxx g> yyyy 8)14)(8( 2
c> byaybxax 88
q> bybxayax 22
- 26 -
emeronTI4 kenSamBICKNit
!!> dak;kenSamxageRkamCaplKuNktþa k> x> 14252 a 2 b K> 49 2 x X> 22 4 yx
g> c> 22 1625 yx xx 805 3 q> 2234 xax C> 2549 2 b Q> 2222 425 ztbx j> 2222 cbxa d> z> 4)1( 2 x 22 )2(9 aa
!@> dak;kenSamxageRkamCaplKuNktþa k> 32 32248 xxx x> 523 35515 xxx K> xaaxabx 22 3612 X> xyyxyx 2416 222
g> 22 2 cxacxca c> 44224 4168 babaab !#> dak;kenSamxageRkamCaplKuNktþa ³ k> 232 xx x> 8143 2 xx K> 242 xx X> 7152 2 xx g> c> 201814 2 aa 239 2 aa q> 357124 2 xx C> 156 2 xx
- 27 -
emeronTI4 kenSamBICKNit
!$> eK[BhuFa 1582 bbA k> etIeKRtUvykcMnYnNamkbEnßmelI bb 82 edIm,I[)anCakaer éneTVFa ? x> edayeRbIlTæplmundak; A CakaeréneTVFadWeRkTI ! . K> sMNYrdEdlcMeBaHBhuFa 342 xxB nig 384 2 xxC .
- 28 -
emeronTI4 kenSamBICKNit
dMeNaHRsay !-KNna k> 222222 5510573 xxxxxx x> tyxtyxtyxtyxtyx 2444244444
2
72
2
3
K> yxyxxxyx 22)1)(2( 232
X> yyxyxyyx 44)4)(( 2222
@-eKmanBhuFa 132 42 xxxA nig 323 432 xxxxB k> KNnapldk rYcbRgYm nig erobrytamlMdab;sV½yKuNcuH BA
én x eK)an ³ )323()132( 43242 xxxxxxxBA
2233
323132234
43242
xxxx
xxxxxxx
x> sresrpldk AB
eK)an 2233)( 234 xxxxBAAB
- 29 -
emeronTI4 kenSamBICKNit
- 30 -
#-KNnaplbUkxageRkam ³ k> 222222 523 yxyxyx
x> abbaabbaabba 47)2()35( 232323 K> )423()34( 2334 zyxzyx zyyxx 32334 2334 X> t )543()424()35( 23233 tttbtt 12 3 132 2 btt t
$-eK[kenSam )()()( baxxabbxa . KNn ;cuHarYcbRgYmnigerobryBhuFaenHtamlMdab éndWeRkGefr . tag )()()( baxxabbxaA
abxba 2)(2 abbxax
bxaxbxababax
222
%-sMNYrdEdldUclMhat;TI$ cMeBaHkenSamxageRkam ³ k> )()()( 22 yaaayxayaxy
xyaxayyaa
ayaaayaxyayxy
2223
2322
emeronTI4 kenSamBICKNit
- 31 -
x> 3( ))(2(2)3)(1()2)(1 tttttt
1732
122232232
222
tt
tttttt
K> 4
39)3)(5()
2
3)(
2
5( bbbb
4
3 b
4
39152
4
15 22 bbbb
ybBa¢ak;smPaBxageRkam ³
nH .
dUcenH
^-Rsa k> 1( 42 1)1)(1)( xxxx
eKman ( 21)1)(1 xxx nig 1 42222 )(1)1)(1( xxxx dUce x 42 1)1)(1)(1( xxx
x> 5 2b 32)1)(1(3 2 bbb
eKman 32)1(35)1)(1(35 2222 bbbbbb 32)1)(1(35 22 bbbb
emeronTI4 kenSamBICKNit
- 32 -
&-muFaKNnaedayeRbIsmPaBsMxan;²
eK)an ³
2 10102 222
2222
4654,1
,15,25,39,15,2119,6654,4139
159911600140)140)(140(4139 2 3564363600)660)(660(6654 3991400)120)(120(2119 22525100100)510(15 22
15211801600)140(39 22 62525200400)520(25 22 203)101102)(101102(101102 22 8008100)4654)(4654(4654 22 *-Bnøa tatkenSamxageRkam nig erobryBhuFaenH mlMdab;éndWeRkGefr
k> 9 )169(16)12( 222 xxxx
man 22 )12( xx 22 ]1)2[( xx
1464
1)2(2)2(234
222
xxxx
xxxx
emeronTI4 kenSamBICKNit
- 33 -
tag
A )169(16)12(9 222 xxxx
713290369
169614493654369
)169(16)1464(9
234
2234
2234
xxxx
xxxxxx
xxxxxx
x> 2222 )1(25)243(4 aaaa )1232(25)41628249(4 234234 aaaaaaaa 41141874661 234 aaaa K> ( 5)3(9)3 22 baba
5276910
52799622
222
babba
bababa
X> xyxyxx 12)34( 2
xyx
xyxxyx
93
12342
22
g> ( 33 )2()1 xx
999
81261332
2323
xx
xxxxxx
c> 6 )5)(( baba 655222 baabba
emeronTI4 kenSamBICKNit
- 34 -
(-dak;kenSamxageRkamCaplKuNktþa ³ k>
2)12(16)12(9 xx
)732)(12(
)732)(12(
)16329)(12(
)]12(169)[12(
xx
xx
xx
xx
x> )4(5)123( 2 aaa
)53)(4(
)4(5)4(3
aa
aaa
K> ) 22 3(9)3( baba
)3)(3(8
)3(8 2
baba
ba
X> )2()84( yxyyxx
)4)(2(
)2()2(4
yxyx
yxyyxx
c> ) 5)(()1022( bababa
)2)(5(
)5)(()5(2
baba
bababa
emeronTI4 kenSamBICKNit
- 35 -
!0> dak;kenSamxageRkamCaplKuNktþa k> )1)(32()15)(32( xxxx
)12)(32(2
)24)(32(
)115)(32(
)]1()15)[(32(
xx
xx
xxx
xxx
x> )23)(17()17( 2 aaa
)34)(17(
)2317)(17(
)]23()17)[(17(
aa
aaa
aaa
K>
)75)(32()32( 2 xxx
)103)(32(
)103)(32(
)7532)(32(
)]75()32)[(32(
xx
xx
xxx
xxx
X> )45)(13()13)(2()32)(13( xxxxxx
)52)(13(
)52)(13(
)45232)(13(
)]45()2()32)[(13(
xx
xx
xxxx
xxxx
emeronTI4 kenSamBICKNit
- 36 -
g> yyyy 8)14)(8( 2
)15)(8(
)14)(8(
)8()14)(8(
yy
yyy
yyyy
c> 8 byaybxax 8
))(8(
)8()8(
yxba
baybax
q> bybxayax 22
)2)(( bayx
)(2)( yxbyxa
!!> dak;kenSamxageRkamCaplKuNktþa
k> )5)(5(525 222 aaaa
x> b )12)(12(1)2(14 222 bbb K> 9 )23)(23(2)3(4 222 xxxx
X> )(x )22()2()(4 2222 yyxyxyx
g> )45)(45(1625 22 yxyxyx
c> )4)(4(5805 3 xxxxx q> )4(4 22223 axxxax
emeronTI4 kenSamBICKNit
- 37 -
C> 49 )57)(57(252 bbb Q> )25)(25(425 2222 tzxbtzxbztbx
k enSamxageRkamCa lKuNktþa k>
j> ))((2222 bcaxbcaxcbxa d> ( )1)(3()21)(21(4)1 2 xxxxx z> 3)(23()2(9 22 aaaa )1)(12(4)2 aaaa !@> da ;k p 3 2 32248 xxx
8 )324(
)432(82
2
xxx
xxx
> x 523 35515 xxx
5 )137(
)713(532
32
xxx
xxx
K> xaaxabx 2 2 3612
3 )24( axbax X> xyyxyx 2416 222
2 )128( xxyxy g> 22222 )()2(2 xacxaxaccxacxca
emeronTI4 kenSamBICKNit
- 38 -
c> (44168 44224 abbabaab )42 333 babab !#> dak;kenSamxageRkamCaplKuNktþa ³ k> )2)(1(2223 22 xxxxxxx x> )3 4)(23(81223814 22 xxxxxxx K> )62)(62(6)2(24 22 xxxxx g>
minGacdak;CaplKuNktþa)an . q>
201814 2 aa
)5a7)(2(2
)105147(2
)1097(22
2
a
aaa
aa
c> 239 2 aa
357124 2 xx
)73)(58(
)58(7)58(3
35561524 2
xx
xxx
xxx
C> 156 2 xx
)16)(1(
166 2
xx
xxx
emeronTI4 kenSamBICKNit
!$> eK[BhuFa 1582 bbA k> etIeKRtUvykcMnYnNamkbEnßmelI bb 82 edIm,I[)anCakaer
éneTVFa ? eKBinitüeXIjfa )( 22 bb )4)((28 bb
dUcenHeKRtUvEfmtY 642
- 39 -
1 KWfa 2 168 bb 2)4( b x> eday AeRbIlTæplmundak; CakaeréneTVFadWeRkTI ! eK)an
1582 bbA
)14)(14(
1)4(
1516)168(2
2
bb
b
bb
)3)(5( bb
K> sMNYrdEdlcMeBaHBhuFa 342 B xx
nig 384 2 xxC .
nig
eK)an )1)(3(1)2(34 22 xxxxxB )32)(12(1)22(384 22 xxxxxC
emeronTI5 kenSamsniTan
- 40 -
lMhat; !-KNnatémøelxénkenSamsniTanxageRkam ³ k>
3
)1(3
x
xx cMeBaH 2
1,1 xx nig
3
2x
x> 12
42
2
aa
a cMeBaH 2
1,2 aa nig 1a
K> 45
32
yy
y cMeBaH 1,0 yy nig 2
1y
X> xyx
yx
2
43 cMeBaH 1x nig 4
1y
g> 22
3
)()1( baab
bb
cMeBaH 56a nig b 125
@-rktémøénGefr x edIm,I[kenSamsniTanxageRkammann½y ³ k>
76
7
x
x x> 2)3(
3
x
x
K> )3)(4(
1
xx
x X> 16
32122
2
x
xx
#-rktémøénGefr edIm,I[kenSamsniTanxageRkamKμann½y a
k> 1a
a x> 13 a
ab
emeronTI5 kenSamsniTan
- 41 -
K> 1)1(
42
2
a
aa X> aa
a
3
2 9)3(
$-rktémøénGefr x edIm,I[kenSamsniTanxageRkames μInwgsUnü ³
k> x
x
2
32 x> 1
3 2
x
x
K> 4
5)12)(5(2
x
xxx X> 12
4)3(2
22
x
xx
%-sRmYlkenSamsniTanxageRkam ³
k> yx
x2
3
7
14 x> 3
42
)2(
8
abx
xba
K> 3
2
)(
)(
ba
bax
X> )9(18
)3(922
xba
xab
g> 2
32
xy
xyyx c> 15
251 2
x
x
q> 9
)1)(5()3)(1(2
x
xxxx
C> )32)(1(7)1(8
)3)(1(2)33(23
2
xxx
xxx
Q> )1()2)(1()17)(1(
)3)(22()32)(1(2
xxxxx
xxxx
emeronTI5 kenSamsniTan
j> mnanama
mnanama
2
2
d> bcacaba
bcacaba
2
2
z> yx
yxayax
33 D>
22
2
aa
aa
Z> 82
1242
2
aa
aa N> 22
22
32 baba
ab
t> 5105
4842
2
xx
xx f> 22
22
274
53
yxyx
yxyx
T> 76
211722
2
yy
yy .
^-rkplKuN nig plEckénkenSamsnITanxageRkam ³
k> 4
22
4
3
10
6
3
4
x
yx
xy
yx x>
322
2
15
4
54
72
yx
xy
xy
yx
K> 2
54
2
2
3
2
4 ab
dc
dc
ba X>
b
ba
ba
ba
90
40
28
64 22
2
33
g> 4
)3)(3(
3
)4(
b
bb
b
bb
c> )12)(52(
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)53)(53(
)32)(43(
xx
xx
xx
xx
q> yy
y
y
yy
3
9
)3(
32
2
2
2
C> 2222 2 yxyx
yx
yx
yx
- 42 -
emeronTI5 kenSamsniTan
Q> 2
22
)7(
49
)7(
49
a
a
a
a
j> yvxvyuxu
yvxvyuxu
yvxvyuxu
yvxvyuxu
d> 34
82
23
12
2
2
2
bb
bb
bb
b
z> 824
65
86
623 2
2
xyxy
yy
xx
yxxy
D> 2
2
2
2
1
532
32
152
m
mm
mm
mm
Z> nm
nm
nmnm
nmnm
2
2
232
23222
22
&> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k>
7
2
7
12 aa x>
14
3
14
yy
K> 1
1
1
xx
x X> 6
2
6
b
y
b
y
g> yx
y
yx
x
66 c>
x
ba
x
ba
33
q> ba
b
ba
a
22
C> ba
b
ba
a
2222
- 43 -
emeronTI5 kenSamsniTan
*> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k>
4
2
2
3 yxyx
x> 6
5
3
2 yxyx
K> yzxy
65 X>
bc
a
ab
c
42
3
g> 3
3
62
4
aa
a c> 22 )()( ba
ba
ba
ba
q> ab
ba
ca
ac
bc
cb
C> dc
b
bc
c
36
2
510
4
Q> a
a
a
a
312
2
82
1
j> ))(())(())(( bcac
c
abcb
b
cbba
a
d> 222 1
1
5
5
4
4
a
a
aa
a
aa
a
z> )(
))((
)(
))((
abb
bybx
baa
byax
ab
xy
D> 2
2
44
22
a
a
aa
a
Z> 12
56
127
342
2
2
2
pp
pp
pp
pp
N> 65
107
168
432
2
2
2
nn
nn
nn
nn
- 44 -
emeronTI5 kenSamsniTan
t> 168
4
4
2
6
3222
xx
x
x
x
xx
x
f> 31530
2542
351730
723202
2
2
2
xx
xx
xx
xx
T> 3512
25
16
2092
2
2
2
aa
a
a
aa
F> 213712
15224
81449
65562
2
2
2
yy
yy
yy
yy
(> sRmYlkenSamsniTanxageRkam ³
k> 5
1
5
13
1
6
1
x>
4
7
2
53
8
3
2
56
K> 7
5
6
57
5
6
5
X>
xx
x
3
11
3
g> x
x
x
15
3
5
23
2
c>
1
21
3
kk
k
kk
q>
)1(2
x
y
x
y
y
x
x
y
y
x
- 45 -
emeronTI5 kenSamsniTan
- 46 -
C>
22
24
ba
ab
ab
b
ba
ab
ba
aba
Q>
abbaba
ba
baba
bba 1112)(2233
22
j>
ba
a
a
ba
ba
b
ba
babaa
baba
aba2
)2(33
22
22
2
d> ab
baaab
baa
1
)(1
1 z> b
b
b
b
2
11
21
2
11
21
!0-k> zyx ,, CacMnYnsniTanxusBIsUnü . ebI
x
y
y
xC
z
x
x
zB
y
z
z
yA ,, cUrbgðajfa ³
CBACBA ..222 minGaRs½ynwg zyx ,, . x> CacMnYnsniTanxusBIsUnü . cba ,,
bgðaj[eXIjfaebI 1abc enaHeK)an ³ )
1)(
1)(
1(4)
1()
1()
1( 222
cc
bb
aa
cc
bb
aa
!!-rktémø x edIm,I[kenSamsniTan )25)(3(2
)62)(15.03(
xx
xx
es μInwgsUnü .
emeronTI5 kenSamsniTan
- 47 -
dMeNaHRsay !-KNnatémøelxénkenSamsniTanxageRkam ³ k>
3
)1(3
x
xx cMeBaH 2
1,1 xx nig
3
2x
-cMeBaH 1x enaH 4
1
31
)11(31
3
)1(3
x
xx
-cMeBaH 2
x1 enaH
5
8
32
1
)12
1(3
2
1
3
)1(3
x
xx
-cMeBaH 3
x2 enaH
11
5
33
2
)13
2(3
3
2
3
)1(3
x
xx
x> 12
42
2
aa
a cMeBaH 2
1,2 aa nig 1a
K> 45
32
yy
y cMeBaH 1,0 yy nig 2
1y
-cMeBaH 0y enaH 4
3
4)0(50
30
45
322
yy
y
-cMeBaH 1y enaH 5
1
4)1(51
31
45
322
yy
y
emeronTI5 kenSamsniTan
- 48 -
-cMeBaH 2
y1 enaH 2
42
5
4
1
32
1
45
32
yy
y
X> xyx
yx
2
43 cMeBaH 1x nig 4
1y
eK)an 13
8
4
19
13432
xyx
yx
@-rktémøénGefr x edIm,I[kenSamsniTanxageRkammann½y ³ k>
76
7
x
x mann½yluHRtaEt 6 07 x b¤ 6
7x
x> 2)3(
3
x
x mann½yluHRtaEt 03 x b¤ 3x
K> )3)(4(
1
xx
x
mann½yluHRtaEt 0)3)(4( xx b¤ 3,4 xx
X> 16
32122
2
x
xx
mann½yluHRtaEt 0)4)(4(162 xxx
b¤ 4,4 xx .
emeronTI5 kenSamsniTan
- 49 -
#-rktémøénGefr edIm,I[kenSamsniTanxageRkamKμann½y a
k> 1a
a Kμann½yluHRtaEt 01 a b¤ 1a . x>
13 a
ab
Kμann½yluHRtaEt 013 a b¤ 1a
K> 1)1(
42
2
a
aa
Kμann½yluHRtaEt 0)2(1)1( 2 aaa
b¤ 2,0 aa
X> aa
a
3
2 9)3(
Kμann½yluHRtaEt 0)1)(1(3 aaaaa
b¤ 1,1,0 aaa $-rktémøénGefr x edIm,I[kenSamsniTanxageRkames μInwgsUnü ³ k>
x
x
2
32
es μIsUnüluHRtaEt 032 x b¤ 2
3x .
emeronTI5 kenSamsniTan
- 50 -
x> 1
3 2
x
x es μIsUnüluHRtaEt 0)3)(3(3 2 xxx b¤ 3,3 xx . K>
4
5)12)(5(2
x
xxx
es μIsUnüluHRtaEt 0)22)(5(5)12)(5( xxxxx b¤ 1,5 xx .
X> 12
4)3(2
22
x
xx
es μIsUnüluHRtaEt 0)3)(33(4)3( 22 xxxx
b¤ 3,1 xx . %-sRmYlkenSamsniTanxageRkam ³
k> y
x
yx
x 2
7
142
3
Edl 0,0 yx
x> 2333
42
3
42
8
8
)2(
8
ax
b
xba
xba
abx
xba
Edl 0,, xba
emeronTI5 kenSamsniTan
- 51 -
K> ba
x
ba
bax
3
2
)(
)( Edl a b
X> )3(2
1
)3)(3(18
)3(9
)9(18
)3(9222
xaxxba
xab
xba
xab
Edl 3,0,0 xba .
g> y
yx
xy
yxxy
xy
xyyx 2
2
2
2
32 )(
Edl 0,0 yx
c> )51()51(
)51)(51(
15
251 2
xx
xx
x
x
Edl 5
1x
q> 9
)1)(5()3)(1(2
x
xxxx
)3)(3(
)1(8
)3)(3(
)53)(1(
xx
x
xx
xxx
C> )32)(1(7)1(8
)3)(1(2)33(23
2
xxx
xxx
1322
37
)1322)(1(
)37)(1(
)21714888)(1(
)6299)(1(
)32)(1)(1(7)1)(1(8
)3)(1(2)1(9
22
22
2
2
xx
x
xxx
xx
xxxxx
xxx
xxxxxx
xxx
emeronTI5 kenSamsniTan
Q> )1()2)(1()17)(1(
)3)(22()32)(1(2
xxxxx
xxxx
1,277
9
)12187)(1(
)2632)(1(
)1()2)(1()17)(1)(1(
)3)(1(2)32)(1(
2
2
xxx
xxxx
xxx
xxxxxx
xxxx
j> mnanama
mnanama
2
2
na
na
na
nama
nama
manmaa
manmaa
,
))((
))((
)()(
)()(
d> bcacaba
bcacaba
2
2
ba
ba
caba
caba
bacbaa
bacbaa
))((
))((
)()(
)()(
Edl . ca
- 52 -
emeronTI5 kenSamsniTan
- 53 -
z> yx
yxayax
33
yx
a
yx
ayx
yx
yxyxa
,3
1
)(3
)1)((
)(3
)()(
D> 22
2
aa
aa
2)2)(1(
)1(
a
a
aa
aa Edl 1a
Z> 82
1242
2
aa
aa
2,
4
6
)2)(4(
)2)(6(
)31)(31(
)42)(42(
9)1(
16)2(2
2
aa
a
aa
aa
aa
aa
a
a
N> 22
22
32 baba
ab
ba
ab
baba
abab
32)32)((
))((
Edl b¤ 0 ba ba .
emeronTI5 kenSamsniTan
- 54 -
t> 5105
4842
2
xx
xx
5
4
)1(5
)1(42
2
x
x Edl 1x
f> )4)(2(
53
274
53 22
22
22
yxyx
yxyx
yxyx
yxyx
T> 76
211722
2
yy
yy
1
32
)7)(1(
)7)(32(
y
y
yy
yy Edl 7y
^-rkplKuN nig plEckénkenSamsnITanxageRkam ³
k> yx
yx
xy
yx
5
4
10
6
3
44
22
4
3
x> yxyx
xy
xy
yx 2322
2
515
4
54
72
K> b
dac
ab
dc
dc
ba
63
2
4
42
2
54
2
2
X> a
b
b
ba
ba
ba
7
36
90
40
28
64 22
2
33
g> )3(4
)3)(3(
3
)4(
bbb
bb
b
bb
emeronTI5 kenSamsniTan
- 55 -
c> )12)(52(
)32)(32(
)53)(53(
)32)(43(
xx
xx
xx
xx
)12)(52)(53)(53(
)32()32)(43( 2
xxxx
xxx
q> yy
y
y
yy
3
9
)3(
32
2
2
2
1)3()3(
)3)(3)(3(2
yyy
yyyy Edl 3,0 yy
C> 2222 2 yxyx
yx
yx
yx
1)(
))((
)( 2
yx
yx
yxyx
yx Edl yx
Q> 2
22
)7(
49
)7(
49
a
a
a
a
7,)7(
)7)(7(
)7)(7)(7)(7(2
aa
aa
aaaa
j> yvxvyuxu
yvxvyuxu
yvxvyuxu
yvxvyuxu
2
2
)(
)(
))()()((
))()()((
yx
yx
vuyxvuyx
vuyxvuyx
emeronTI5 kenSamsniTan
d> 34
82
23
12
2
2
2
bb
bb
bb
b
3
4
)3)(1)(2)(1(
)4)(2)(1)(1(
b
b
bbbb
bbbb
Edl . 2,1 bb
z> 824
65
86
623 2
2
xyxy
yy
xx
yxxy
1)3)(2(
)2)(4(
)4)(x2(x
)3)(y2(x
yy
yx
Edl 3,2,4,2 yyxx .
D> 2
2
2
2
1
532
32
152
m
mm
mm
mm
3,1;
)1(
)52(
)1)(1)(3)(1(
)52)(1)(52)(3(
2
2
mmm
m
mmmm
mmmm
Z> nm
nm
nmnm
nmnm
2
2
232
23222
22
nm
nm
nmnmnm
nmnmnm
2
2
)2)(2)(2(
)2)(2)(2(
Edl . nm 2
- 56 -
emeronTI5 kenSamsniTan
&> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k> a
aaaaa2
7
14
7
212
7
2
7
12
x> 714
2
14
3
14
3
14
yyyyyy
K> 1
1
1
1
1
x
x
xx
x
X> 6
3
6
2
6
b
y
b
y
b
y
g> 66666
yx
yx
yx
y
yx
x
c> 3
)(2
3333
x
ba
x
ba
x
ba
x
ba
x
ba
q> baba
baba
ba
ba
ba
b
ba
a
))((2222
C> 2
1
222222
ba
ba
ba
b
ba
a *> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k>
4
38
4
226
4
2
2
3 yxyxyxyxyx
x> 6
73
6
524
6
5
3
2 yxyxyxyxyx
K> xyz
xz
yzxy
6565
- 57 -
emeronTI5 kenSamsniTan
X> abc
ac
bc
a
ab
c
4
3
42
3 22
g> 3
32
3
3
3
2
3
3
62
4
a
a
aa
a
aa
a
c> 22
22
22 )()(
])())[((
)()( baba
bababa
ba
ba
ba
ba
)()(
42 baba
ab
q> ab
ba
ca
ac
bc
cb
00
abcabc
bcacabbcacab
C> dc
b
bc
c
36
2
510
4
)2)(2(15
)510612(2
)2)(2(15
)2(10)2(12
)2(3
2
)2(5
4
22
dcbc
bbccdc
dcbc
bcbdcc
dc
b
bc
c
Q> )4(6
75
)4(6
4233
312
2
82
1
a
a
a
aa
a
a
a
a
- 58 -
emeronTI5 kenSamsniTan
j> ))(())(())(( bcac
c
abcb
b
cbba
a
))(())()((
)())((
))()((
)()()(
cbba
a
accbba
bacbaac
accbba
bacacbaca
d> 222 1
1
5
5
4
4
a
a
aa
a
aa
a
)1)(5)(4(
20108
)1)(5)(4(
202025520164
)1)(5)(4(
)5)(4()4)(1(5)5)(1(41
1
5
5
4
4
)1)(1(
1
)5(
5
)4(
4
2
222
aaa
aa
aaa
aaaaaa
aaa
aaaaaaaaa
aa
a
aa
a
aa
a
z> )(
))((
)(
))((
abb
bybx
baa
byax
ab
xy
)(
))(())(()(
baab
bybxabyaxbbaxy
- 59 -
emeronTI5 kenSamsniTan
a
x
baab
bxxyxyba
baab
babyxbaxy
baab
abaxabbxbybaxy
)(
))((
)(
))(()(
)(
))(()(
D> 2
2
44
22
a
a
aa
a
)2()2(
1287
)2()2(
)2()2(
2
2
)2(
2
2
23
2
32
2
aa
aaa
aa
aa
a
a
a
a
Z> 12
56
127
342
2
2
2
pp
pp
pp
pp
)4)(1(
212
1
5
4
1
)1(
)5)(1(
)4)(3(
)3)(1(
2
2
pp
pp
p
p
p
p
p
pp
pp
pp
- 60 -
emeronTI5 kenSamsniTan
N> 65
107
168
432
2
2
2
nn
nn
nn
nn
)3)(4(
1752
)3)(4(
2034
3
5
4
1
)3)(2(
)5)(2(
)4(
)4)(1(
2
22
2
nn
nn
nn
nnnn
n
n
n
n
nn
nn
n
nn
t> 168
4
4
2
6
3222
xx
x
x
x
xx
x
)4)(2)(2(
124
)4)(2)(2(
4164
4
1
)2)(2(
4
4
1
2
1
2
1
)4(
4
)2)(2(
2
)2)(3(
3
22
2
xxx
xx
xxx
xx
xxxxxx
x
x
xx
x
xx
x
T> 3512
25
16
2092
2
2
2
aa
a
a
aa
)7)(5(
)5)(5(
)4)(4(
)5)(4(
aa
aa
aa
aa
)7)(4(
)5(3
7
5
4
5
aa
a
a
a
a
a
- 61 -
emeronTI5 kenSamsniTan
(> sRmYlkenSamsniTanxageRkam ³
k> 4
5
5
116
21
5
1
5
13
1
6
1
x> 10
31
4
710128
32048
4
7
2
53
8
3
2
56
K> 13
1
42
303542
3035
7
5
6
57
5
6
5
X> 0,2
313
3
3
11
3
x
x
x
xx
x
g> )3(5
2
3
)9(53
)3(2
15
3
5
23
2
2
x
x
x
x
x
x
x
x
c> 2
3
2
32
1
21
3
2
2
k
k
kk
kk
kk
k
kk
- 62 -
emeronTI5 kenSamsniTan
!!-rktémø x edIm,I[kenSamsniTan
)25)(3(2
)62)(15.03(
xx
xx
es μInwgsUnüluHRtaEt 0)62)(15.03( xx eKTaj 3,05.0 xx .
- 63 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
lMhat; !-edaHRsaysmIkar k> 1232 x x> 67185 x K> 78299 x X> 35125 a g> 1132 x c> 120168 b q> yy 3258 C> mm 4725 Q> 3253 xx j> 2552 n d> z> aa 640 1723 x @-edaHRsaysmIkar k> 12)3(3 x x> xx 5)4(3 K> )3(5)3(5 xx X> aa 24)6(4 g> nn 18)8(9 c> )4(2)32(7 tt q> )1(3)2(4 xx C> )3(2103 zz Q> )13()3(2 xxx #-edaHRsaysmIkar k> 144
5
3x x> 8
3
1
2
3b
- 64 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
K> 3
2
2
12 x X> 9
2
3
a
g> 154
3
m c> 4
39
4
xx
$-edaHRsaysmIkar k> 0)3( xx x> 0)8(3 xx K> 0)27(12 x X> 0)82)(3( xx g> 0)1)(3( xx c> 0)7)(12( xx q> 092 x C> xx 16642 Q> mm 212 j> 04)3( 2 x
d> 08124 23 aaa z> )1(9)1(4 2 xxx
D> )1)(32()32( 2 xxx
Z> )35(7)35)(3( xxxx N> 22 )65()7( xx
5-enAeBlEdlelakRKUdak;lMhat;[sisSeFIV vibul)aneFIVlMhat;dUcteTA eK[smIkar 2510156 mm dak;GgÁTaMgBIrCaplKuNktþa )52(5)52(3 mm
- 65 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
EckGgÁTaMgBIrnwg )52( m eK)an 52
)52(5
52
)52(3
m
m
m
m
53 etIvibulmankMhusRtg;NakñúgkaredaHRsaysmIkar cUrrkkMhusenaH ? ^-plbUkR)aMcMnYnKt;bnþKñaes μInwg 520 . cUrrkR)aMcMnYnKt;enaH ? &-GayumIgsMesμInwg bIdgénGayusIuNaEdlCakUnrbs;Kat; . kalNasIuNamanGayues μInwgGayurbs;mþaynagsBVéf¶enH plbUkén GayuGñkTaMgBIresμInwg 112 qñaM .rkGayurbs;mIgsM ? *-sUpatmanGayu 51 qñaM egIyrsμImanGayu qñaM . 21
etIryHeBlb:un μanqñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgén GayursμI ?
- 66 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
- 67 -
dMeNaHRsay !-edaHRsaysmIkar k> 1232 x
2
9
92
3122
x
x
x
x> 67185 x
5
49
495
18675
x
x
x
K> 78299 x
9
49
499
29789
x
x
x
X> 35125 a b¤ 475 a
5
47a
emeronTI6 smIkardWeRkTI1manmYyGBaØat
g> 1132 x
7
142
3112
x
x
x
c> 120168 b
13
1048
161208
b
b
b
q> yy 3258
5
255
2538
y
y
yy
C> mm 4725
1
99
2745
m
m
mm
Q> 3253 xx
8
5323
x
xx
- 68 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
j> 2552 n
10
202
5252
n
n
n
d> aa 640
8
405
406
a
a
aa
z> 1723 x
5
153
2173
x
x
x
@-edaHRsaysmIkar k> 12)3(3 x
7
43
x
x
x> xx 5)4(3
6
1253
5123
x
xx
xx
- 69 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
K> )3(5)3(5 xx
3
62
33
x
x
xx
X> aa 24)6(4
5
6
66
66
a
aa
aa
g> nn 18)8(9
3
8
83
28
n
n
nn
c> )4(2)32(7 tt
12
29
2912
822114
t
t
tt
- 70 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
- 71 -
q> )1(3)2(4 xx
11
3384
x
xx
C> )3(2103 zz
4
62103
z
zz
#-edaHRsaysmIkar k> 144
5
3x
30
903
70203
x
x
x
x> 83
1
2
3b
9
44
449
4629
b
b
b
K> 3
2
2
12 x
12 43 x b¤ 12
1x
emeronTI6 smIkardWeRkTI1manmYyGBaØat
X> 92
3
a
63
18
a
a
g> 154
3
m
203
60
m
m
c> 4
39
4
xx
9
364
336
x
x
xx
$-edaHRsaysmIkar k> 0)3( xx eK)an 3,0 xx x> 0)8(3 xx eK)an 8,0 xx K> 0)27(12 x naM[ 27x
- 72 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
X> 0)82)(3( xx ebI 03 x enaH 3x ebI 082 x enaH 4x g> 0)1)(3( xx eK)an 1,3 xx c> 0)7)(12( xx eK)an 7,12 xx q> 092 x b¤ 0)3)(3( xx eK)an 3,3 xx C> xx 16642 eK)an b¤ 0)8(6416 22 xxx 8x Q> mm 212 eK)an b¤ 0)1(12 22 mmm 1m j> 04)3( 2 x
eK)an 0)1)(5( xx naM[ 1,5 xx
- 73 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
d> 08124 23 aaa 0)2)(1(4 aaa
eKTaj 2,1,0 aaa z> )1(9)1(4 2 xxx
0)32)(32)(1(
0)94)(1( 2
xxx
xx
eK)an 2
3,
2
3,1 xxx
D> )1)(32()32( 2 xxx
0)4)(32(
0)132)(32(
0)1)(32()32( 2
xx
xxx
xxx
eK)an 4,2
3 xx
N> 22 )65()7( xx
0)14)(136(
0)657)(657(
0)65()7( 22
xx
xxxx
xx
eK)an 4
1,
6
13 xx
- 74 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
5-enAeBlEdlelakRKUdak;lMhat;[sisSeFIV vibul)aneFIVlMhat;dUcteTA eK[smIkar 2510156 mm dak;GgÁTaMgBIrCaplKuNktþa )52(5)52(3 mm EckGgÁTaMgBIrnwg )52( m eK)an
52
)52(5
52
)52(3
m
m
m
m
53 etIvibulmankMhusRtg;NakñúgkaredaHRsaysmIkar cUrrkkMhusenaH ? kMhusEdlvibulmanenARtg;karEcksmIkarCamYyktþa 52 m
BIeRBaHkñúgdMeNaHRsaysmIkareKminGacsRmYl b¤EckktþaEdlman GBaØat)aneTeRBaHvaGacnaM[)at;b¤ssmIkar . ^-plbUkR)aMcMnYnKt;bnþKñaes μInwg 520 . cUrrkR)aMcMnYnKt;enaH ? tag 4,3,2,1, xxxxx CaR)aMcMnYnKt;bnþKñaEdlRtUvrk eK)an 5204321 xxxxx
102
5105
520105
x
x
x
dUcenH CaR)aMcMnYnKt;EdlRtUvrk . 106,105,104,103,102
- 75 -
emeronTI6 smIkardWeRkTI1manmYyGBaØat
&-GayumIgsMesμInwg bIdgénGayusIuNaEdlCakUnrbs;Kat; . kalNasIuNamanGayues μInwgGayurbs;mþaynagsBVéf¶enH plbUkén GayuGñkTaMgBIresμInwg 112 qñaM .rkGayurbs;mIgsM ? tag x CaGayurbs;mIgsMbc©úb,nñ nig
3
x CaGayurbs;sIuNaCakUn
kalNasIuNamanGayues μImþaysBVéf¶enaHmIgsMnwgmanGayu 3
4x
tamsmμtikmμeK)ansmIkar 112)3
(3
4
xx
x
42
1123
8
x
x
dUcenHmIgsMmanGayu 42qñaM nigsIuNamanGayu 14qñaM . *-sUpatmanGayu 51 qñaM ehIyrsμImanGayu qñaM . 21
etIryHeBlb:un μanqñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgén GayursμI ? tag x CacMnYnqñaMeTAmuxeTot eK)ansmIkar )21(251 xx eK)an 9x qñaM dUcenH 9qñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgénGayursμI.
- 76 -
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 77 -
lMhat; !-edaHRsayvismIkar k> 153 xx x> 52710 xx K> 1565 xx X> 1667 xx g> 75 xx c> 12)3(2 xx q> C> 2.475.03.2 m 05.53.14.4 t @-edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> x> 063217 a x K> 3 51 x X> 127
4
256
x
x
g> 3 4720 xx c> 63
1
m
q> 125
8
5
68
mm C> 54
22
54
63
xx #- edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 2 237 xx x>
31
23
xxx
K> 3232
mmm X>
8
)1(33
4
1
mm
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 78 -
g> 4
18
3
191
6
)1(5
xxx
c> 4
13
8
)1(32
mm
q> 6
)3(11
3
7
2
13
4
13
xxxx
C> 157
5
21
13
25
9
25
2 xxx
$- edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 73 x x> 55 x K> 5030 x X>
4
3
4
3x
g> 7
2
7
2 t c>
22
3
11
3 q
q> 155352 xxx C> yyy 12)12(3 Q> 5.05.1 x j> 200100 x d> 1232 xx z> 2565 mm D> 21287253 aaaa %-pldkrvag nigmYycMnYnFMCagplbUkrvag nig dgcMnYnenaH. 2 3 2
cUrrkcMnYnTaMgGs;EdlepÞógpÞat;bRmab;xagelI ?
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
dMeNaHRsay !-edaHRsayvismIkar k> 153 xx
2
3
64
513
x
x
xx
x> 52710 xx
2
38
12
128
75210
x
x
x
xx
K> 1565 xx
50
6155
x
xx
vismIkarKμancemøIy . X> 1667 xx 80 x KμancemøIy
- 79 -
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 80 -
g> 75 xx 20 x KμancemøIuy c> 12)3(2 xx
50
1262
x
xx
KμancemøIy . q> 2.475.03.2 m
5.1
45.33.2
75.02.43.2
m
m
m
C> 05.53.14.4 t
5.0
65.03.1
4.405.53.1
t
t
t
@-edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 217 a
37
21
a
a
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 81 -
x> 063 x
23
6
63
x
x
x
K> 513 x
2
63
x
x
X> 1276 x 4
25 x
11
8
2433
2448285
48282524
x
x
xx
xx
g> 47203 xx
64
24
244
20473
x
x
x
xx
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 82 -
c> 63
1
m
19
181
m
m
q> 125
8
5
68
mm
10
202
406086
608640
m
m
mm
mm
C> 54
22
54
63
xx
8
6223
2263
x
xx
xx
#- eda bHRsayvismIkarrYc kRsaycemøIyelIbnÞat;cMnYn k> 2372 xx
9x
9
7232
x
xx
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 83 -
x> 3
12
3xx
x
13
6
613
26318
x
x
xxx
K> 3232
mmm
17
18
1817
181223
m
m
mmm
X> 8
)1(33
4
1
mm
29
332422
m
mm
g> 4
18
3
191
6
)1(5
xxx
2
3
32
211210
112210
3244361210
10
x
x
xx
xx
xxx
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 84 -
c> 4
13
8
)1(32
mm
5
7
75
22243316
m
m
mm
q> 6
)3(11
3
7
2
13
4
13
xxxx
3
5
159
6668115
66222867839
x
x
xx
xxxx
$-edaHRs nayvismIkarrYcbkRsaycemøIyelIb Þat;cMnYn k> 73 x 10x x> 55 x 10x K> 5030 x 0 2x
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
- 85 -
X> 4
3
4
3x
0x g>
7
2
7
2t
1
t c>
22
3
11
3 q
2
1q
q> 155352 xxx
2
2010
5 1555
x
x
xx
C> yyy 1212( )3
2
3
96
1236
y
y
yyy
Q> 5.05.1 x 1x
emeronTI7 vismIkardWeRkTI1manmYyGBaØat
j> 200100 x 300x d> 1232 xx 1x
7m z> 265 m 5m
D> 753 21282 aaa a
- 86 -
2
1
24 109125
a
aa
nigmYycMnYnFMCagplbUkrvag nig dgcMnYnenaH. kcMnYnTaMgGs;EdlepÞógpÞat;bRmab;xag lI ?
a
%-pldkrvag 2 3 2
cUrr e tag x CacMn eK)an
YnEdlRtUvrk x23 x2
3
1x
13
x
emeronTI8 bøg;kUGedaen nig Rkab
lMhat; !-edayyk CargVas;ÉktaelIGkS½TaMgBIr cm1 oxx' nig oyy' edAcMnucEdlmankUGredaendUcteTA ³ 5,3: yxA 4,3: yxB 3,4: yxC 6,0: yxD 2,5: yxE 4,1: yxF 3,2: yxG 0,3: yxH 6,
2
1: yxI
- 87 -
emeronTI8 bøg;kUGedaen nig Rkab
@-KUsRtIekaN EdlmankMBUl ABC )3,6(;)2,8(;)5,4( CBA . #-KUsctuekaNEkg EdlmankMBUl ABCD )6,10(;)8,3( BA )5,5( C nig )4,7( D . $-kñúgtMruykUGredaeb yk CargVas;Ékta edAcMnucdUctetA ³ cm1
)0,3(:
)6,6(:
)4,1(:
)5,0(:
yxD
yxC
yxB
yxA
P¢ab; nig . etIGñksegáteXIjy:agdUcemþc ? BDACBC ,, AD
%-sg;RkabénsmIkarxageRkam ³ k> 53 xy x> 42 xy K>
2
12 yx X> 23 yx
g> yx 33 c> yx 1593
- 88 -
emeronTI8 bøg;kUGedaen nig Rkab
- 89 -
dMeNaHRsay !- edAcMnucEdlmankUGredaendUcteTA ³ 5,3: yxA 4,3: yxB 3,4: yxC 6,0: yxD 2,5: yxE 4,1: yxF 3,2: yxG 0,3: yxH 6,
2
1: yxI
2 3 4 5 6-1-2-3-4-5-6-7-8
2
3
4
5
6
7
-1
-2
-3
-4
-5
70 1
1
x
y
A
B
C
D
E
F
G
H
I
emeronTI8 bøg;kUGedaen nig Rkab
@-KUsRtIekaN EdlmankMBUl ABC )3,6(;)2,8(;)5,4( CBA .
2 3 4 5 6 7 8 9 10 11-1-2-3-4-5-6-7
2
3
4
5
6
-1
0 1
1
x
y
A
B
C
- 90 -
emeronTI8 bøg;kUGedaen nig Rkab
- 91 -
#-KUsctuekaNEkg EdlmankMBUl ABCD )6,10(;)8,3( BA )5,5( C nig )4,7( D . $-kñúgtMruykUGredaeb yk CargVas;Ékta edAcMnucdUctetA ³ cm1
)0,3(:)6,6(:
)4,1(:)5,0(:
yxDyxC
yxByxA
P¢ab; BDACBC ,, nig . etIGñksegáteXIjy:agdUcemþc ? AD
2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7
2
3
4
5
6
7
8
-1
-2
-3
-4
-5
0 1
1
x
yA
B
CD
emeronTI8 bøg;kUGedaen nig Rkab
- 92 -
2 3 4 5 6 7 8-1-2
2
3
4
5
6
-1
-2
0 1
1
x
y
C
D
A
B
%-sg;RkabénsmIkarxageRkam ³ k> 53 xy ebI 5,0 yx ebI
3
5,0 xy
2 3 4 5-1-2-3-4
2
3
4
5
6
-1
0 1
1
x
y
emeronTI8 bøg;kUGedaen nig Rkab
- 93 -
x> 42 xy ebI 4,0 yx ebI 2,0 xy
K>
2
12 yx ebI
2
1,0 yx ebI
4
1,0 xy
2 3 4 5-1-2-3-4
2
3
4
5
6
-1
0 1
1
x
y
2 3 4 5 6-1-2-3-4
2
3
-1
-2
0 1
1
x
y
emeronTI8 bøg;kUGedaen nig Rkab
- 94 -
X> 23 yx ebI 2,0 yx ebI 3
2,0 xy
g> yx 33 ebI 1,0 yx ebI 3,0 xy
2 3 4 5-1-2-3-4 6-5
2
3
4
5
-1
-2
0 1
1
x
y
2 3 4 5 6-1-2-3-4-5
2
3
4
5
-1
-2
0 1
1
x
y
emeronTI8 bøg;kUGedaen nig Rkab
c> yx 1593 ebI
5
3,0 yx
ebI 3,0 xy
2 3 4 5 6-1-2-3-4-5
2
3
4
5
-1
-2
0 1
1
- 95 -
x
y
emeronTI9 RbU)ab
lMhat; !-kñúgRbGb;mYymansársUkULa 24 RKab; kñúgenaHman 10RKab;mansñÚl ERkm 8RKab;KμansñÚl nigenAsl;mansñúlsENþk . sársUkULa ! RKab;RtUveRCIserIsedayécdnü . KNnaRbU)abEdlsársUkULa³ k>mansñÚlERkm x> mansñÚlsENþk K> minmansñÚlERkm. @-eKe)aHRKab;LukLak;mYyRKab . rkRbU)abénRBwtþikarN_xageRkam ³ k> e)aH)anelxess x> e)aH)anelxFMCag # K> e)aH)anelxEckdac;nwg % X> e)aH)anelxFMCag ! . #-rdæamaneRsameCIgBN’épÞemXcMnYn* BN’exovcMnYn & BN’sUkULa cMnYn !# nig BN’RkhmcMnYn^ .rdæaeRCIserIseRsameCIgmYyeday écdnü . KNnaRbU)abEdleRsameCIgman ³
- 96 -
emeronTI9 RbU)ab
k> BN’épÞemX x> BN’exov K> minEmnBN’sUkULa X> minEmnBN’sUkULa b¤ BN’Rkhm g> BN’épÞemX b¤ BN’exov . $-eKe)aHkak;mYycMnYnbIdg . k> KNnacMnYnkrNIGac x> KNnaRbU)abénRBwtþikarN_e)aHkak;)anxagrUbBIr nig xagelxmYy
- 97 -
emeronTI9 RbU)ab
dMeNaHRsay !-kñúgRbGb;mYymansársUkULa 24 RKab; kñúgenaHman 10RKab;mansñÚl ERkm 8RKab;KμansñÚl nigenAsl;mansñÚlsENþk . sársUkULa ! RKab;RtUveRCIserIsedayécdnü . KNnaRbU)abEdlsársUkULa³ k>mansñÚlERkm cMnYnkrNIGa
sbcMnYnkrNIRcP
42.012
5
24
10
x> mansñÚlsENþk cMnYnkrNIGa
sbcMnYnkrNIRcP
25.024
6
24
81024
K> minmansñÚlERkm cMnYnkrNIGa
sbcMnYnkrNIRcP
33.03
1
24
8
- 98 -
emeronTI9 RbU)ab
@-eKe)aHRKab;LukLak;mYyRKab . rkRbU)abénRBwtþikarN_xageRkam ³ k> e)aH)anelxess RBwtþikarN_Gac cMnYnkrNIGacesμI ^ . }6,5,4,3,2,1{
cMnYnkrNIRsb cMnYnkrNIRsbesμI # . }5,3,1{
cMnYnkrNIGasbcMnYnkrNIR
cP
5.06
3
x> e)aH)anelxFMCag # cMnYnkrNIRsb cMnYnkrNIRsbesμI # . }6,5,4{
cMnYnkrNIGasbcMnYnkrNIR
cP
5.06
3
K> e)aH)anelxEckdac;nwg % cMnYnkrNIRsb cMnYnkrNIRsbesμI!. }5{
6
1 cMnYnkrNIGa
sbcMnYnkrNIRcP
- 99 -
emeronTI9 RbU)ab
X> e)aH)anelxFMCag ! cMnYnkrNIRsb cMnYnkrNIRsbesμI % . }6,5,4,3,2{
6
5 cMnYnkrNIGa
sbcMnYnkrNIRcP
#-rdæamaneRsameCIgBN’épÞemXcMnYn* BN’exovcMnYn & BN’sUkULa cMnYn !# nig BN’RkhmcMnYn^ .rdæaeRCIserIseRsameCIgmYyeday écdnü . KNnaRbU)abEdleRsameCIgman ³ k> BN’épÞemX cMnYnkrNIGac 3461378 cMnYnkrNIRsb 8 .
17
4
34
8 cMnYnkrNIGa
sbcMnYnkrNIRcP
x> BN’exov cMnYnkrNIRsb 7 .
34
7 cMnYnkrNIGa
sbcMnYnkrNIRcP
- 100 -
emeronTI9 RbU)ab
X> minEmnBN’sUkULa b¤ BN’Rkhm
34
15
34
7
17
4P
g> BN’épÞemX b¤ BN’exov
34
15
34
7
17
4P
$-eKe)aHkak;mYycMnYnbIdg . k> KNnacMnYnkrNIGac RBwtþikarGac },,,,,,,{ TTTHTTTHTTTHTHHHTHHHTHHH cMnYnkrNIGacesμI 8 . x> KNnaRbU)abénRBwtþikarN_e)aHkak;)anxagrUbBIr nig xagelxmYy cMnYnkrNIRsb },,{ THHHTHHHT cMnYnkrNIRsbesμInwg # . 375.0
8
3 cMnYnkrNIGa
sbcMnYnkrNIRcP .
- 101 -