Le nombre d'or : Les propriétés esthétiques du nombre d'or sur le visage humain Mythe ou réalité?

7/31/2019 Le nombre d'or : Les proprits esthtiques du nombre d'or sur le visage humain Mythe ou ralit?

1/27

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Dgv pujpu`}v gv}n}`swgv mw

kjheug mju vwu dg |`vcbg nwhc`k 1h}ng jw ucd`} :

5? jf}jeug 5?33 ]uc|c`d mg Hc}wu`} K`kc Mhcvj

Ckcdvg mw pujl`d mwk |`vcbg pcu Djkcum mg \`kf`


2/27

5? jf}jeug 5?33 Dgv pujpu`}v gv}n}`swgv mw kjheug mju1 h}ng jw ucd`} : K`kc Mhcvj

Bhkcvg luckc`v mg E`gkkg ]uc|c`d mg hc}wu`}

5

]cedg mgv hc}`ugv

3+ @k}ujmwf}`jk ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++=

5+ Dgv ju`b`kgv mw kjheug mju ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++7

6+ Cppcu`}`jkv vwppjvgv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++2

Gk cu} g} gk cufn`}gf}wug 1 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++2

Gk vf`gkfgv 1 ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++>

=+ Dgv ugf}ckbdgv puluv mgv njhhgv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3?

7+ _ujpu`}v hc}nhc}`swgv +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 33

_ujpu`}v cdbeu`swgv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 33

c) Dc vgf}`jk mjug1 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 33

e) L`ejkcff`1 ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++ 35

f) Dgv pw`vvckfgv mw kjheug mju1+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 35

_ujpu`}v bjh}u`swgv +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 35

c) Fjkv}uwf}`jk c|gf dc ubdg g} dg fjhpcv1 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 35

e) Dg ugf}ckbdg mju1 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 36

f) Dg }u`ckbdg mju1+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 36

m) Dg pgk}cbuchhg1 +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++ 3=

g) Dg pgk}cbjkg1 ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ +++++++++++++++ +++++++++++++++++ +++++++++++++ 3=

l) Dg mjmfcmug1 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3=


3/27



6

Uvwd}c}v ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 32

\`vcbgv ckcdvv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3>

Fjkfdwv`jkv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3>

>+ Ckcdvg vgdjk mg \`kf` +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30

_ujfm ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30

Fjkfdwv`jk ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30

\`vcbgv ckcdvv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30

0+ Fjkfdwv`jk l`kcdg +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ +++++++++++++++ 55

3?+ Vjwufgv +++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ +++++++++++++++ +++++++++++++++++ ++ 56

D`|ug 1 ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++ 56

Cu}`fdgv 1 ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ +++++++++++++++ +++++++++++++++++ ++ 56

V`}gv 1 ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ ++++++++ 56

\`mjv 1 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5=

33+ Ulugkfgv pnj}jbucpn`swgv ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5=

35+ Ckkg~gv 1 ++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ +++++++++++++++++ ++++++++++++++++ ++++++++++++++++ +++++++++++++ 57

@k}gu|`gr mw Mu+ _lwdb +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 57

Kj}gv fjkv}`}wck} dc hjgkkg mg egcw} +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5


4/27



=

3+ @k}ujmwf}`jk

Gk`bhc}`swg g} hv}u`gwvg$ dc egcw} gv} wk vgfug} `hpk}ucedg+ Vjw|gk} fjkv`mug fjhhg

`kml`k`vvcedg$ gddg kgv} ub`g pcu cwfwkg kjuhg k` fu`}ug wkck`hghgk} m}guh`k+ Jk m`}

vjw|gk} swg dc egcw} gv} mckv d`d mg fgdw` sw` dc fjk}ghpdg9 vc vweagf}`|`} gv} mjkf vjwv(gk}gkmwg+ G} pjwu}ck}$ Mgdcfuj`~$ pg`k}ug luckc`v mw ^\@@@hg v+$ cllùhg swg dncuhjk`g gv}

dg~pugvv`jk dc pdwv |cv}g mw egcw+ Wkg jp`k`jk pcu}cbg pcu dg pj}g _njffd`mg sw` c|ckc`}

ma v`~ v`fdgv c|+ A+(F+ sw gk }jw}g fnjvg$ dg egcw uvwd}g mg dc awv}gvvg mgv pujpju}`jkv +

Cu`v}j}g ml`k`} swck} dw` dc egcw} gk }uj`v hj}v1 puf`v`jk$ vh}u`g g} fjjum`kc}`jk+

_cu c`ddgwuv$ pdwv`gwuv }wmgv jk} mhjk}u swg fgu}c`kgv fjkv}ck}gv$ pculj`v fn`llugv$ kjwv

}jwfnc`gk} pcu}`fwdùghgk}+ Fgv} dg fcv mwkg |cv}g }wmg eu`}ckk`swg j$ dc`mg mwk

pujbuchhg `kljuhc}`swg$ mgv |`vcbgv mnjhhgv jk} } hjm`l`v mcpuv mgv c|`v lh`k`kv cl`kmcppujfngu dc pgulgf}`jk hcvfwd`kg$ g} |`fg |guvc+ @d uvwd}c swg dg hdg ùuv`v}èdg vguc`}

fcucf}u`v pcu wkg hfnjùg g} wk hgk}jk pw`vvck}$ mgv vjwuf`dv hcuswv$ wk }juvg hwvfd$ mgv

pj`bkg}v vh}u`swgv$ g} wk }jwu mg }c`ddg 3?' `klu`gwu cw }jwu mg nckfngv+ Swck} dc lghhg

`mcdg$ gddg vguc`} mj}g mg buckmv gw~$ mwk pg}`} kgq$ mg d|ugv pwdpgwvgv$ mwkg hfnjùg g}

mwk hgk}jk md`fc}v$ mwkg pj`}u`kg lguhg g} vh}u`swg$ mwkg pgcw d`vvg vckv `hpgulgf}`jkv$ g}

mwk }jwu mg }c`ddg ugpuvgk}ck} 2?' mw }jwu mg nckfngv+ Dc vgfjkmg gksw}g vgv} fjkfgk}ug vwu

dg ucppju} }c`ddg*nckfngv mgv lghhgv+ Dg _u+ Mg|gkmuc V`kbn c `k}guujb pdwv mwk h`dd`gu

mnjhhgv bv mg 3> >< ckv$ `vvwv mg fwd}wug g} mg h`d`gw~ vjf`jpujlgvv`jkkgdv m`llugk}v cw~

swc}ug fj`kv mw hjkmg+ Dc fjkfdwv`jk lw} vckv cppgd$ dg awu hcvfwd`k cck} wkck`hghgk} dw dgv

lghhgv mjk} dg ucppju} }c`ddg*nckfngv vg v`}wc`} gk}ug


5/27



7

5+ Dgv ju`b`kgv mw kjheug mju

Mgpw`v mgv v`fdgv$ dg kjheug mju$ sw` gv} dc fjkv}ck}g 8 .37)*583$?6 lc`} pcudgu mg dw`+

@d `k}gu|`gk} mckv dc pujpju}`jk m`|`kg$ cwvv` cppgdg vgf}`jk mjug$ sw` djk pu}g mgv

pujpu`}v gv}n}`swgv g} hc}nhc}`swgv fjkv`mugv fjhhg hv}`swgv+

Dg pugh`gu sw` v `k}ugvvc lw} Gwfd`mg$ sw`$ }uj`v v`fdgv c|ck} kj}ug ug$ }wm`c dg pcu}cbg mwk

vgbhgk} CE pcu wk pj`k} F dg fjwpck} gk g~}uhg g} hjgkkg uc`vjk$ dg pj`k} F }ck} ml`k`

pcu dswc}`jk CE*CF8CF*FE .fl+ p+33 c)vgf}`jk mjug)+ @d vgk vgu|c`} mckv dc fjkv}uwf}`jk mgv

pgk}cbjkgv g} dgv ljuhwdgv ml`k`vvck} dgv pujpu`}v mw mjmfcmug .fl+ p+3=) g} mg d`fjvcmug+

C dc l`k mw 37hg v`fdg$ wk hj`kg luckf`vfc`k$

Dwfc _cf`jd`$ pwed`c H`dck gk 3=0> wk jw|ucbg

kjhhMg m`|`kc pujpju}`jkg }uc`}ck} mw

lchgw~ pcu}cbg gk g~}uhg g} hjgkkg

uc`vjk + Dgv pugh`guv vjwpjkv swck} cw~

pujpu`}v gv}n}`swgv pujecedgv mw kjheug

mju kcsw`ugk} mw lc`} swg dg }njdjb`gk vjwdg|c

dc puvgkfg mg mckv dg mjmfcmug sw`$ vgdjk

_dc}jk$ ugpuvgk}c`} dwk`|guv+ Fg lw} Djkcum

mg \`kf` swg ug|`k} dc }fng mg mgvv`kgu wkgvj`~ck}c`kg mg pjdmugv pjwu dg pugh`gu

|jdwhg$ Fjhpgkm`j mg M`|`kc _ujpju}`jkg$ mg

Dwfc _cf`jd`$ sw`d fjhpd}c pcu dc vw`}g pcu mgw~

ckkg~gv$ dwk fjkfgukck} dcufn`}gf}wug g} dcw}ug

dgv pujpju}`jkv mw fjupv nwhc`k$ mckv dgvswgdv

`d kg lw} cwfwkghgk} swgv}`jk mwkg gv}n}`swg

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnk`pcu}`fwd`ug mwg dc m`|`kg pujpju}`jk+

_dwv }cum$ cw ^@^hgv`fdg$ Cmjdl Qg`v`kb.3>3?(3>2


6/27




7/27



2

_ uch mg mg Ingj v

vcfughgk} mg dc mgukùg fkg mg Mcd`

6+ Cppcu`}`jkv vwppjvgv

Gk cu} g} gk cufn`}gf}wug 1

Cl`k mg pujw|gu dgv pjw|jùv gv}n}`swgv mw kjheug mju$ fgu}c`kv vf`gk}`l`swgv vg vjk} pgkfnv

vwu vc puvgkfg gk cu}$ gk cufn`}gf}wug g} gk vf`gkfgv+ C`kv`$ `dv jk} mfjw|gu} sw`d c } w}`d`v

pjwu dc pughùg lj`v pcu dgv bp}`gkv |guv 57


8/27



>

Vpùcdg djbcu`}nh`swg

Dg Fjuewv`gu$ cufn`}gf}g vw`vvg mw ^^hg$ gw

bcdghgk} ugfjwuv cw kjheug mju mckv vgv

fjkv}uwf}`jkv+ @d v`kvpùc mgv `mgv mg \`}uw|g$

cufn`}gf}g ujhc`k cck} |fw wk v`fdg c|+ A+F+$

sw` mjkkc`} cw~ e}`hgk}v dgv m`hgkv`jkv mw

fjupv nwhc`k+ Gk 307?$ Dg Fjuewv`gu pwed`c dg

Hjmwdju$ jw|ucbg mckv dgswgd `d g~pd`swg mg

swgddg hckùg `d fngufng kjuhcd`vgu

dwueck`vhg dc`mg mw kjheug mju mckv wk ew}

mncuhjk`g g} mgv}n}`swg+ Fg vv}hg gv}

puvgk} mckv dc f`} ucm`gwvg Hcuvg`ddg$ g}

dc fncpgddg Kj}ug(Mchg(mw(Ncw} mg

Ujkfnchpv+

Gk vf`gkfgv 1

@d vgv} c|u swg dg kjheug mju gv} puvgk} mckv dc kc}wug+ _cu g~ghpdg$ jk ug}ujw|g dc vpùcdg

djbcu`}nh`swg mckv dgv chhjk`}gv g} dgv fjsw`ddgv mgvfcubj}v+ Dg kjheug mg p}cdgv mgv ldgwuv

vguc`} dw` }uv }uj`}ghgk} d` c|gf dc vw`}g mg Lèjkcff`+ Gk gllg}$ ucugv vjk} dgv gvpfgv kcck}

cwfwk ucppju} c|gf gddg+ @d vg pjwuuc`} mc`ddgwuv swg fgf` g~pd`swg dc ucug} mgv }uldgv swc}ug+

Kcw}`dg


9/27



0

Fjkfgukck} dc _nddj}c~`g$ mjhc`kg }uc`}ck}

mg dc m`vpjv`}`jk mgv lgw`ddgv vwu wkg }`bg$ jk

fjkv}c}g swg fngq dgv }jwukgvjdv jw gkfjug

dgv pswgug}}gv$ dgv pcucv`}`swgv

vgk}ugfuj`vgk}$ }ugk}g(swc}ug }jwukgk} mckv dg

vgkv mgv c`bw`ddgv mwkg hjk}ug$ g} |`kb}(g}(

wkg mckv dg vgkv `k|guvg+ Ju$ 6=*538

3+


10/27



3?

Ugf}ckbdg mju

=+ Dgv ugf}ckbdgv puluv mgv njhhgv

Mgv }wmgv jk} } gllgf}wgv mckv dg ew} mg pujw|gu dgv pujpu`}v gv}n}`swgv mg dc vgf}`jk

mjug+ Fgpgkmck}$ dgv uvwd}c}v mg Bgjubg Hcuijrvi`

pcu g~ghpdg$ pujlgvvgwu mg hc}nhc}`swgv mckv dgvckkgv 302? mckv dgv pugv}`b`gwvgv wk`|guv`}v

chu`fc`kgv mg Ncu|cum g} Fjdwhe`c$ vg vjk} hjk}uv

mfg|ck}v$ `d c puvgk} wk awu swcuck}g(nw`}

ugf}ckbdgv g} dw` c mghckm mg dgv fdcvv`l`gu mw pdwv

egcw cw pdwv hjfng vgdjk dgwu c|`v+ @d gv} cuu`| dc fjkfdwv`jk swg dg pulu }c`} fgdw` mg 3+>6*3+

Kckhj`kv$ gk 3>26

Fcu}g mg fum`}


11/27



33

7+ _ujpu`}v hc}nhc}`swgv

Fg kgv} pcv wk ncvcum v` fg kjheug vwvf`}g wk }gd gkbjwghgk} g} sw`d gv} dc fèdg mg }ck}

m`k}guujbc}`jkv+ Gk gllg}$ v` dgv |gu}wv gv}n}`swgv g} hv}`swgv swjk dw` c}}uèwg vjk} vjw|gk}

swcd`l`gv m`hcb`kcùgv$ vgv pujpu`}v cdbeu`swgv g} bjh}u`swgv vjk} swck} gddgv ugddgv+ Gk|j`f` swgdswgv wkgv+

_ujpu`}v cdbeu`swgv

c) Dc vgf}`jk mjug1 Wk vgbhgk} gv} fjkv`mu fjwp gk g~}uhg g} hjgkkg uc`vjk djuvswg

CE*CF 8 CF*FE8 ^

C ^ 3 F 3 E

Mjkf 1

t ~

``

Ljuhwdg mg \`}g 1

C|gf 1 3 8 hh

V` $ cdjuv mg|`gk} t 1 k

Jk ughcuswg swg v` djk cmm`}`jkkg 3 $ jk je}`gk} vjk fcuu$ g} v` djk vjwv}uc`} 3$ dg uvwd}c}

kgv} cw}ug swg vjk `k|guvg+


12/27



35

e) Lèjkcff`1 Dc vw`}g mg Lèjkcff` vg ljuhg gk cajw}ck} fncswg lj`v dg uvwd}c} mg dcmm`}`jk mgv

mgw~ mguk`guv kjheugv+

3 93 95 96 97 9> 936 953 96= 977 9>0 93== 9

Vc pcu}`fwdcu`} gv} swg v` djk m`|`vg dg mguk`gu kjheug pcu dc|ck} mguk`gu$ dg uvwd}c} je}gkw vg

ucppujfng mg pdwv gk pdwv mw kjheug mju cw lwu g} hgvwug swg dgv kjheugv cwbhgk}gk}+ C`kv`$

djuvswg }gkm |guv d`kl`k`$ dc d`h`}g mg dc vw`}g mgv swj}`gk}v gv} dg kjheug mju+

f) Dgv pw`vvckfgv mw kjheug mju1

8

Jk fjkv}c}g swg dgv fjgll`f`gk}v kg vjk} cw}ugv swg dgv kjheugv mg Lèjkcff`+

_ujpu`}v bjh}u`swgv

c) Fjkv}uwf}`jk c|gf dc ubdg g} dg fjhpcv1

3

F8 8 8 8

3*5

F


13/27



36

e) Dg ugf}ckbdg mju1 fncswg lj`v swjk dw` gkd|g wk fcuu$ jk je}`gk} wk kjw|gcw ugf}ckbdg mju+

Dc d`h`}g }ck} dg ugf}ckbdg pj`k}+

^(3

M F

3 (~ 8 3

^

C ^ L E

f) Dg }u`ckbdg mju1Fgv} wk }u`ckbdg sw`dc}ucd mjk} wk ckbdg |cw} 6


14/27



3=

m) Dg pgk}cbuchhg1

g) Dg pgk}cbjkg1

C

l) Dg mjmfcmug1 `d lc`} pcu}` mgv f`ks vjd`mgv mg _dc}jk g} ugpuvgk}g mcpuv fgdw`(f` dwk`|guv+

Vgv mjwqg lcfgv vjk} }jw}gv mgv pgk}cbjkgv ubwd`guv$ fg sw`g~pd`swg vjk ucppju} c|gf dg kjheug mju+

Dg ucppju} gk}ug dgv vgbhgk}v cefm mckv wk

jumug mg djkbwgwuv mfuj`vvck}gv fjuugvpjkm cw

kjheug mju+

E

FM

G

6


15/27



37

_ujl`d mg Ic}g Hjvv ckcdv pcu dg Mu+ _lwdb pjwu dg hcbcv`kg \jbwg


16/27



3


17/27



32

V` fgdw`(f` gv} bcd 3+


18/27



3>

\`vcbgv ckcdvv

\`vcbg k3 \`vcbg k5 \`vcbg k6

\`vcbg k= \`vcbg k7

Fjkfdwv`jkv

V` djk pcu} mw pu`kf`pg swg hc h}njmg mckcdvg gv} fjuugf}g g} kg fjhpju}g pcv mg lc`ddgv$ dc

fjkfdwv`jk gv} vckv cppgdv$ dg kjheug mju kc v}u`f}ghgk} cwfwkgv pujpu`}v gv}n}`swgv cw

k`|gcw mw |`vcbg nwhc`k+ @d hgv} `hpjvv`edg mg }ujw|gu wk d`gk gk}ug vc puvgkfg g} dc|`v mw awu+


19/27



30

>+ Ckcdvg vgdjk mg \`kf`

_ujfm

C dc vw`}g mgv fjkfdwv`jkv }ùgv mg hc pughùg h}njmg mckcdvg$ ac` mf`m mcppd`swgu dc

hhg }gfnk`swg swg dg Mu+ _lwdb$ sw` gv} fgddg mg mg \`kf`+ Mckv wk pugh`gu }ghpv$ ac|c`v fnj`v`

mg kg pcv dw}`d`vgu fcu ag kg vw`v pcv gk hgvwug mg~pd`swgu vjk d`gk c|gf dc vgf}`jk mjug+

_jwu}ck}$ fgv} pcu}ù mgv uvwd}c}v je}gkwv dc vw`}g mg fg}}g }gfnk`swg mckcdvg swg dg kjheug

mju vgv} |w c}}uèwgu dc fcpcf`} mghegddù wk |`vcbg+ G} v` hjk vjwnc`} gv} mg dc fjklùhgu$ `d hg

vghedg db`}`hg mg pujfmgu mg dc hhg hckùg swg hgv pumfgvvgwuv+

Ac` mjkf }gkw fjhp}g$ }jw} fjhhg mg \`kf`$ mgv }uj`v fu`}ugv

vw`|ck}v 1 v` dg |`vcbg gv} m`|`v gk }uj`v pcu}`gv bcdgv$ dwkg cddck}

mw vjhhg} mw lujk} cw~ vjwuf`dv$ dc vgfjkmg mgv vjwuf`dv dc ecvg

mw kgq$ g} dc mgukùg mg dc ecvg mw kgq dc pj`k}g mw hgk}jk 9 v`

dc m`v}ckfg vpcuck} dg hgk}jk mg dc lgk}g dce`cdg gv} mgw~ lj`v

bcdg dc m`v}ckfg gk}ug dc ecvg mw kgq g} dc lgk}g dce`cdg 9 g} v` dgv

gw~ vjk} `kfd`kv |guv dg ncw}

Fjkfdwv`jk

kjw|gcw$ ag kg kj}g cwfwkv ucppju}v pcu}`fwd`guv gk}ug dc|`v mw awu g} dgv pujpju}`jkv m`|`kgv mg

mg \`kf`+

\`vcbgv ckcdvv

\`vcbg k3

c8e8f kjk

58 kjkPgw~ mg v}cu jw`

Ckcdvg lc`}g pcu mg \`kf`


20/27



5?

\`vcbg k5

\`vcbg k6

c8e8f kjk

58 jw`Pgw~ mg v}cu kjk

c8e8f kjk



21/27



53

\`vcbg k=

\`vcbg k 7

c8e8f kjk


c8e8f jw`

58 jw`Pgw~ mg v}cu jw`


22/27



55

0+ Fjkfdwv`jk l`kcdg

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26/27



5 < < 7 2 = 6 < < < 2 >

< > < 7 > > < 7 < = = 7

= 7 6 7 < < 2 > 7 = > 67 = < < 2 7 < < = < 7 7 < > = = 7 < 7 < 7

6 7 < 2 < > 2 < = < 2

2 < 7+

5 7 6 = 5 7 = 5 7 < 2 7 =

7 7 2 5 7 2 < 5 7 < = 7

7 6 6 6 7 2 7 6 = 5 = 5

= 7 < > 7 < 7 = 7 < 6 57 = 5 = 5 3 = 7 > 7 < =

> = 5 6 2 = 5 = 5 6 7 5

= 5 = 2 = > 5 < 5 =+==

6 6 6 5 = 5 5 5 = 7 5 = 6

< 6 3 3 2 = 5 6 5 5 6 6

= 5 6 5 7 7 < 3 3 3 6 7

5 6 5 3 = 3 5 6 5 5 3 5

6 7 5 6 = = = 5 3 = 3 =

6 5 7 3 5 = < 3 5 5 = 5

6 6 < 6 = 7 6 7 5 = 6 =

3 7 7 7 6 6+?=

= 7 7 0 > 2 < 3? > 2 > 5 >

= = > > > 2 2 > 7 7 < 2

= > > 2 5 < < 7 = < < 7

= < < < 2 2 2 > > < 7 7

< < > > = 7 7 < 2 0 < 3?

< > < < > 3? > 6 > > > 2

7 > > 2 3? < 3? 7 < = > >

7 >

7 6 3? 2 2 3? 7 < 2 6 2 2 >

= 6 2 7 = = < 7 = = = 6

5 3 7 5 7 < < > 0 > 2 0

0 2 7 2 7 > 2 > < > > 0

= > 2 2 2 < > < > < = 2

2 2 > < 7 = > 0 0 7 > 2

7 < 7 = > = > > 6 7+07


27/27


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