digonal theorey

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8/14/2019 digonal theorey http://slidepdf.com/reader/full/digonal-theorey 1/26 Olmobpaduov abi Olmobpofyh~vYgo olmobpaduo z~hndoc lv a z~hndoc h` fhbvlio~ando ygoh~oylfad lbyo~ovy abi }lio#~abmlbm azzdlfaylhb" @h~ owaczdo$ yglv z~hndoc lv f~uflad lb vhdplbm v|vyocv h` il``o~obylad oquaylhbv$ abad|{lbm zhzudaylhb m~h}yg chiodv$ abi fadfudaylbm zh}o~v h` cay~lfov 'lb h~io~ yh io`lbo ygo owzhbobylad cay~lw," Hygo~ a~oav vufg av zg|vlfv$ vhflhdhm|$ nlhdhm|$ ofhbhclfv abi vyaylvylfv gapo `hfuvoi fhbvlio~ando ayyobylhb hb .olmobpaduov. abi .olmobpofyh~v.#ygol~ azzdlfaylhbv abi ygol~ fhczuyaylhbv" No`h~o }o mlpo ygo `h~cad io`lblylhb$ doy uv lby~hiufo ygovo fhbfozyv hb ab owaczdo" Owaczdo" Fhbvlio~ ygo cay~lw Fhbvlio~ ygo yg~oo fhducb cay~lfov ]o gapo Lb hygo~ }h~iv$ }o gapo  Bowy fhbvlio~ ygo cay~lw Z `h~ }glfg ygo fhducbv a~o 1 $ > $ abi 6 $ l"o"$

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Page 1: digonal theorey

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Olmobpaduov abi Olmobpofyh~vYgo olmobpaduo z~hndoc lv a z~hndoc h` fhbvlio~ando

ygoh~oylfad lbyo~ovy abi }lio#~abmlbm azzdlfaylhb" @h~ owaczdo$ yglv z~hndoc lv f~uflad

lb vhdplbm v|vyocv h` il``o~obylad oquaylhbv$ abad|{lbm zhzudaylhb m~h}yg chiodv$ abi

fadfudaylbm zh}o~v h` cay~lfov 'lb h~io~ yh io`lbo ygo owzhbobylad cay~lw," Hygo~ a~oavvufg av zg|vlfv$ vhflhdhm|$ nlhdhm|$ ofhbhclfv abi vyaylvylfv gapo `hfuvoi

fhbvlio~ando ayyobylhb hb .olmobpaduov. abi .olmobpofyh~v.#ygol~ azzdlfaylhbv abi

ygol~ fhczuyaylhbv" No`h~o }o mlpo ygo `h~cad io`lblylhb$ doy uv lby~hiufo ygovo

fhbfozyv hb ab owaczdo"

Owaczdo" Fhbvlio~ ygo cay~lw

Fhbvlio~ ygo yg~oo fhducb cay~lfov

]o gapo

Lb hygo~ }h~iv$ }o gapo

 Bowy fhbvlio~ ygo cay~lw Z `h~ }glfg ygo fhducbv a~o F 1$ F >$ abi F 6$ l"o"$

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]o gapo ioy ' Z , 3 79" Vh yglv cay~lw lv lbpo~ylndo" Oav| fadfudaylhbv mlpo

 Bowy }o opaduayo ygo cay~lw Z #1 AZ " ]o doapo ygo ioyaldv yh ygo ~oaio~ yh fgofe ygay }o

gapo

Lb hygo~ }h~iv$ }o gapo

_vlbm ygo cay~lw cudylzdlfaylhb$ }o hnyalb

}glfg lczdlov ygay A lv vlclda~ yh a ilamhbad cay~lw" Lb za~ylfuda~$ }o gapo

`h~ Bhyo ygay ly lv adchvy lczhvvlndo yh `lbi A=? il~ofyd| `~hc ygo h~lmlbad

`h~c h`  A"

Yglv owaczdo lv vh ~lfg h` fhbdfuvlhbv ygay cab| quovylhbv lczhvo ygocvodpov lb a

bayu~ad }a|" @h~ owaczdo$ mlpob a vqua~o cay~lw A$ gh} ih }o `lbi fhducb cay~lfov

}glfg gapo vlclda~ nogaplh~v av ygo anhpo hbov8 Lb hygo~ }h~iv$ gh} ih }o `lbi ygovo

fhducb cay~lfov }glfg }ldd godz `lbi ygo lbpo~ylndo cay~lw Z vufg ygay Z #1 AZ lv a

ilamhbad cay~lw8

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@~hc bh} hb$ }o }ldd fadd fhducb cay~lfov pofyh~v" Vh ygo anhpo fhducb cay~lfov

F 1$ F >$ abi F 6 a~o bh} pofyh~v" ]o gapo ygo `hddh}lbm io`lblylhb"

Io`lblylhb" Doy A no a vqua~o cay~lw" A bhb#{o~h pofyh~ F lv faddoi ab olmobpofyh~ h` 

 A l` abi hbd| l` ygo~o owlvyv a bucno~ '~oad h~ fhczdow, vufg ygay

L` vufg a bucno~ owlvyv$ ly lv faddoi ab olmobpaduo h`  A" Ygo pofyh~ F lv faddoi

olmobpofyh~ avvhflayoi yh ygo olmobpaduo "

^oca~e" Ygo olmobpofyh~ F cuvy no bhb#{o~h vlbfo }o gapo

`h~ ab| bucno~ "

Owaczdo" Fhbvlio~ ygo cay~lw

]o gapo voob ygay

}go~o

Vh F 1 lv ab olmobpofyh~ h`  A avvhflayoi yh ygo olmobpaduo :" F > lv ab olmobpofyh~ h`  A

avvhflayoi yh ygo olmobpaduo #9 }gldo F 6 lv ab olmobpofyh~ h`  A avvhflayoi yh ygo

olmobpaduo 6"

Ly ca| no lbyo~ovylbm yh ebh} }goygo~ }o `hubi add ygo olmobpaduov h`  A lb ygo anhpo

owaczdo" Lb ygo bowy zamo$ }o }ldd ilvfuvv yglv quovylhb av }odd av gh} yh `lbi ygo

olmobpaduov h` a vqua~o cay~lw"

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@h~ a vqua~o cay~lw A h` h~io~ b$ ygo bucno~ lv ab olmobpaduo l` abi hbd| l` ygo~o

owlvyv a bhb#{o~h pofyh~ F vufg ygay

_vlbm ygo cay~lw cudylzdlfaylhb z~hzo~ylov$ }o hnyalb

Yglv lv a dlboa~ v|vyoc `h~ }glfg ygo cay~lw fho``lfloby lv " ]o advh ebh}

ygay yglv v|vyoc gav hbo vhduylhb l` abi hbd| l` ygo cay~lw fho``lfloby lv lbpo~ylndo$ l"o"

" Vlbfo ygo {o~h#pofyh~ lv a vhduylhb abi F lv bhy ygo {o~h

pofyh~$ ygob }o cuvy gapo

Owaczdo" Fhbvlio~ ygo cay~lw

Ygo oquaylhb y~abvdayov lbyh

}glfg lv oqulpadoby yh ygo quai~aylf oquaylhb

Vhdplbm yglv oquaylhb doaiv yh

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Lb hygo~ }h~iv$ ygo cay~lw A gav hbd| y}h olmobpaduov"

Lb mobo~ad$ `h~ a vqua~o cay~lw A h` h~io~ b$ ygo oquaylhb

}ldd mlpo ygo olmobpaduov h`  A" Yglv oquaylhb lv faddoi ygo fga~afyo~lvylf oquaylhb h~ 

fga~afyo~lvylf zhd|bhclad h`  A" Ly lv a zhd|bhclad `ubfylhb lb h` iom~oo b" Vh }o

ebh} ygay yglv oquaylhb }ldd bhy gapo ch~o ygab b ~hhyv h~ vhduylhbv" Vh a vqua~o

cay~lw A h` h~io~ b }ldd bhy gapo ch~o ygab b olmobpaduov"

Owaczdo" Fhbvlio~ ygo ilamhbad cay~lw

Lyv fga~afyo~lvylf zhd|bhclad lv

Vh ygo olmobpaduov h`  I a~o a$ n$ f$ abi i $ l"o" ygo oby~lov hb ygo ilamhbad"

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Yglv ~ovudy lv padli `h~ ab| ilamhbad cay~lw h` ab| vl{o" Vh iozobilbm hb ygo paduov

|hu gapo hb ygo ilamhbad$ |hu ca| gapo hbo olmobpaduo$ y}h olmobpaduov$ h~ ch~o"

Ab|yglbm lv zhvvlndo"

^oca~e" Ly lv qulyo aca{lbm yh voo ygay ab| vqua~o cay~lw A gav ygo vaco olmobpaduov

av lyv y~abvzhvo AY nofauvo

@h~ ab| vqua~o cay~lw h` h~io~ >$ A$ }go~o

ygo fga~afyo~lvylf zhd|bhclad lv mlpob n| ygo oquaylhb

Ygo bucno~ 'a%i , lv faddoi ygo y~afo h`  A 'iobhyoi y~ ' A,,$ abi fdoa~d| ygo bucno~ 

'ai #nf, lv ygo ioyo~clbaby h`  A" Vh ygo fga~afyo~lvylf zhd|bhclad h`  A fab no ~o}~lyyob

av

Doy uv opaduayo ygo cay~lw

 N 3 A> # y~ ' A, A % ioy ' A, L >"

]o gapo

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]o doapo ygo ioyaldv yh ygo ~oaio~ yh fgofe ygay

Lb hygo~ }h~i$ }o gapo

Yglv oquaylhb lv ebh}b av ygo Fa|do|#Gacldyhb ygoh~oc" Ly lv y~uo `h~ ab| vqua~o

cay~lw A h` ab| h~io~$ l"o"

}go~o lv ygo fga~afyo~lvylf zhd|bhclad h`  A"

]o gapo vhco z~hzo~ylov h` ygo olmobpaduov h` a cay~lw"

Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" L` lv ab olmobpaduo h`  A$ ygob;

1" 

lv ab olmobpaduo h`  Ac$ `h~ 

>" 

L`  A lv lbpo~ylndo$ ygob lv ab olmobpaduo h`  A#1"

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@l~vy }o dhhe `h~ ygo olmobpaduov h`  A" Ygovo a~o mlpob n| ygo fga~afyo~lvylf oquaylhb

$ l"o"

L` }o iopodhz yglv ioyo~clbaby uvlbm ygo ygl~i fhducb$ }o hnyalb

_vlbm oav| admon~alf cablzudaylhbv$ }o moy

}glfg lczdlov ygay ygo olmobpaduov h`  A a~o :$ #9$ abi 6"

 Bowy }o dhhe `h~ ygo olmobpofyh~v"

1" 

Favo ; Ygo avvhflayoi olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc

}glfg ca| no ~o}~lyyob n|

Cab| }a|v ca| no uvoi yh vhdpo yglv v|vyoc" Ygo ygl~i oquaylhb lv liobylfad yh

ygo `l~vy" Vlbfo$ `~hc ygo vofhbi oquaylhbv$ }o gapo | 3 0 w$ ygo `l~vy oquaylhb

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~oiufov yh 16 w % { 3 :" Vh yglv v|vyoc lv oqulpadoby yh

Vh ygo ubebh}b pofyh~  W lv mlpob n|

Ygo~o`h~o$ ab| olmobpofyh~  W h`  A avvhflayoi yh ygo olmobpaduo : lv mlpob n|

}go~o f lv ab a~nly~a~| bucno~"

>" 

Favo ; Ygo avvhflayoi olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc

}glfg ca| no ~o}~lyyob n|

Lb yglv favo$ }o }ldd uvo odocobya~| hzo~aylhbv yh vhdpo ly" @l~vy }o fhbvlio~ 

ygo aumcobyoi cay~lw $ l"o"

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Ygob }o uvo odocobya~| ~h} hzo~aylhbv yh ~oiufo ly yh a uzzo~#y~labmuda~ 

`h~c" @l~vy }o lbyo~fgabmo ygo `l~vy ~h} }lyg ygo `l~vy hbo yh moy

 Bowy$ }o uvo ygo `l~vy ~h} yh odoclbayo ygo ? abi 0 hb ygo `l~vy fhducb" ]o

hnyalb

L` }o fabfod ygo 7 abi < `~hc ygo vofhbi abi ygl~i ~h}$ }o hnyalb

@lbadd|$ }o vuny~afy ygo vofhbi ~h} `~hc ygo ygl~i yh moy

 Bowy$ }o voy { 3 f" @~hc ygo vofhbi ~h}$ }o moy | 3 > { 3 >f" Ygo `l~vy ~h} }ldd

lczd| w 3 #> |%6 { 3 #f" Gobfo

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Ygo~o`h~o$ ab| olmobpofyh~  W h`  A avvhflayoi yh ygo olmobpaduo #9 lv mlpob n|

}go~o f lv ab a~nly~a~| bucno~"

>" 

Favo ; Ygo ioyaldv `h~ yglv favo }ldd no do`y yh ygo ~oaio~" _vlbm vlclda~ 

lioav av ygo hbo iovf~lnoi anhpo$ hbo ca| oavld| vgh} ygay ab| olmobpofyh~  W 

h`  A avvhflayoi yh ygo olmobpaduo 6 lv mlpob n|

}go~o f lv ab a~nly~a~| bucno~"

^oca~e" Lb mobo~ad$ ygo olmobpaduov h` a cay~lw a~o bhy add ilvylbfy `~hc oafg hygo~ 

'voo ygo zamo hb ygo olmobpaduov `h~ ch~o ioyaldv," Lb ygo bowy y}h owaczdov$ }o

ilvfuvv yglv z~hndoc"

Owaczdo" Fhbvlio~ ygo cay~lw

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Lb hygo~ }h~iv$ ab| olmobpofyh~  W h`  A avvhflayoi yh ygo olmobpaduo #1 lv a dlboa~ 

fhcnlbaylhb h` ygo y}h olmobpofyh~v

Owaczdo" Fhbvlio~ ygo cay~lw

Ygo fga~afyo~lvylf oquaylhb lv mlpob n|

Gobfo ygo cay~lw A gav hbo olmobpaduo$ l"o" #6" Doy uv `lbi ygo avvhflayoi

olmobpofyh~v" Ygovo a~o mlpob n| ygo dlboa~ v|vyoc

}glfg ca| no ~o}~lyyob n|

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Yglv v|vyoc lv oqulpadoby yh ygo hbo oquaylhb#v|vyoc

 w# |

3 :"

Vh l` }o voy w 3 f$ ygob ab| olmobpofyh~  W h`  A avvhflayoi yh ygo olmobpaduo #6 lv mlpob

 n|

Doy uv vucca~l{o }gay }o ili lb ygo anhpo owaczdov"

Vucca~|; Doy A no a vqua~o cay~lw" Avvuco lv ab olmobpaduo h` A" Lb h~io~ yh `lbi 

ygo avvhflayoi olmobpofyh~v$ }o ih ygo `hddh}lbm vyozv;

1" 

]~lyo ih}b ygo avvhflayoi dlboa~ v|vyoc

>" 

Vhdpo ygo v|vyoc"

6" 

^o}~lyo ygo ubebh}b pofyh~  W av a dlboa~ fhcnlbaylhb h` ebh}b pofyh~v"

Ygo anhpo owaczdov avvuco ygay ygo olmobpaduo lv ~oad bucno~" Vh hbo ca| }hbio~ 

}goygo~ ab| olmobpaduo lv ad}a|v ~oad" Lb mobo~ad$ yglv lv bhy ygo favo owfozy `h~ 

v|ccoy~lf cay~lfov" Ygo z~hh` h` yglv lv po~| fhczdlfayoi" @h~ vqua~o cay~lfov h` 

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h~io~ >$ ygo z~hh` lv qulyo oav|" Doy uv mlpo ly go~o `h~ ygo vaeo h` nolbm dlyydo fhczdoyo"

Fhbvlio~ ygo v|ccoy~lf vqua~o cay~lw

Lyv fga~afyo~lvylf oquaylhb lv mlpob n|

Yglv lv a quai~aylf oquaylhb" Ygo bayu~o h` lyv ~hhyv '}glfg a~o ygo olmobpaduov h`  A,

iozobiv hb ygo vlmb h` ygo iovf~lclbaby

_vlbm admon~alf cablzudaylhbv$ }o moy

Ygo~o`h~o$ lv a zhvlylpo bucno~ }glfg lczdlov ygay ygo olmobpaduov h`  A a~o ~oad

bucno~v"

^oca~e" Bhyo ygay ygo cay~lw A }ldd gapo hbo olmobpaduo$ l"o" hbo ihundo ~hhy$ l` abi

hbd| l` " Nuy yglv lv zhvvlndo hbd| l` a3f abi n3:" Lb hygo~ }h~iv$ }o gapo

 A 3 a L >"

Lb ygo bowy zamo$ }o }ldd ilvfuvv ygo favo h` fhczdow olmobpaduov"

@l~vy doy uv fhbplbfo hu~vodpov ygay ygo~o owlvy cay~lfov }lyg fhczdow olmobpaduov"

Owaczdo" Fhbvlio~ ygo cay~lw

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Ygo fga~afyo~lvylf oquaylhb lv mlpob n|

Yglv quai~aylf oquaylhb gav fhczow ~hhyv mlpob n|

Ygo~o`h~o ygo cay~lw A gav hbd| fhczdow olmobpaduov"

Ygo y~lfe lv yh y~oay ygo fhczdow olmobpaduo av a ~oad hbo" Coablbm }o ioad }lyg ly av a

bucno~ abi ih ygo bh~cad fadfudaylhbv `h~ ygo olmobpofyh~v" Doy uv voo gh} ly }h~ev

hb ygo anhpo owaczdo"

]o }ldd ih ygo fadfudaylhbv `h~ " Ygo avvhflayoi olmobpofyh~v a~o mlpob

 n| ygo dlboa~ v|vyoc

 A W 3 '1%>l, W  

}glfg ca| no ~o}~lyyob av

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Lb `afy ygo y}h oquaylhbv a~o liobylfad vlbfo '>%>l,'>#>l, 3 7" Vh ygo v|vyoc ~oiufov yh

hbo oquaylhb

'1#l, w

# |

3 :"

Voy w3f$ ygob | 3 '1#l,f" Ygo~o`h~o$ }o gapo

}go~o f lv ab a~nly~a~| bucno~"

^oca~e" Ly lv fdoa~ ygay hbo vghudi owzofy yh gapo fhczdow oby~lov lb ygo

olmobpofyh~v"

]o gapo voob ygay '1#>l, lv advh ab olmobpaduo h` ygo anhpo cay~lw" Vlbfo ygo oby~lov h` 

ygo cay~lw A a~o ~oad$ ygob hbo ca| oavld| vgh} ygay l` lv a fhczdow olmobpaduo$

ygob lyv fhbkumayo lv advh ab olmobpaduo" Ch~ohpo~$ l`  W lv ab olmobpofyh~ h`  A

avvhflayoi yh $ ygob ygo pofyh~ $ hnyalboi `~hc W n| yaelbm ygo fhczdow#fhbkumayo h` ygo oby~lov h`  W $ lv ab olmobpofyh~ avvhflayoi yh " Vh ygo olmobpofyh~v

h` ygo anhpo cay~lw A avvhflayoi yh ygo olmobpaduo '1#>l, a~o mlpob n|

}go~o f lv ab a~nly~a~| bucno~"

Doy uv vucca~l{o }gay }o ili lb ygo anhpo owaczdo"

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Vucca~|; Doy A no a vqua~o cay~lw" Avvuco lv a fhczdow olmobpaduo h` A" Lb

h~io~ yh `lbi ygo avvhflayoi olmobpofyh~v$ }o ih ygo `hddh}lbm vyozv;

1" 

]~lyo ih}b ygo avvhflayoi dlboa~ v|vyoc

>" 

Vhdpo ygo v|vyoc" Ygo oby~lov h`  W }ldd no fhczdow bucno~v"

6" 

^o}~lyo ygo ubebh}b pofyh~  W av a dlboa~ fhcnlbaylhb h` ebh}b pofyh~v }lyg

fhczdow oby~lov"

9" 

L`  A gav ~oad oby~lov$ ygob ygo fhbkumayo lv advh ab olmobpaduo" Ygo avvhflayoi

olmobpofyh~v a~o mlpob n| ygo vaco oquaylhb `hubi lb 6$ owfozy ygay }o vghudi

yaeo ygo fhbkumayo h` ygo oby~lov h` ygo pofyh~v lbphdpoi lb ygo dlboa~ 

fhcnlbaylhb"

Lb mobo~ad$ ly lv bh~cad yh owzofy ygay a vqua~o cay~lw }lyg ~oad oby~lov ca| vyldd gapo

fhczdow olmobpaduov" Hbo ca| }hbio~ l` ygo~o owlvyv a fdavv h` cay~lfov }lyg hbd|

~oda olmobpaduov" Yglv lv ygo favo `h~ v|ccoy~lf cay~lfov" Ygo z~hh` lv po~| yofgblfad

abi }ldd no ilvfuvvoi lb abhygo~ zamo" Nuy `h~ vqua~o cay~lfov h` h~io~ >$ ygo z~hh` lv

qulyo oav|" Doy uv mlpo ly go~o `h~ ygo vaeo h` nolbm dlyydo fhczdoyo"

Fhbvlio~ ygo v|ccoy~lf vqua~o cay~lw

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Avvuco ygo~o owlvyv a ilamhbad cay~lw I vufg ygay A 3 Z #1 IZ " Ygob }o gapo

l"o lv vlclda~ yh " Vh ygo| gapo ygo vaco fga~afyo~lvylf oquaylhb"

Gobfo A abi I gapo ygo vaco olmobpaduov" Vlbfo ygo olmobpaduov h`  I h` ygo bucno~v

hb ygo ilamhbad$ abi ygo hbd| olmobpaduo h`  A lv >$ ygob }o cuvy gapo

Lb yglv favo$ }o cuvy gapo A 3 Z #1 IZ 3 > L >$ }glfg lv bhy ygo favo" Ygo~o`h~o$ A lv bhy

vlclda~ yh a ilamhbad cay~lw"

Io`lblylhb" A cay~lw lv ilamhbadl{ando l` ly lv vlclda~ yh a ilamhbad cay~lw"

^oca~e" Lb a z~oplhuv zamo$ }o gapo voob ygay ygo cay~lw

gav yg~oo il``o~oby olmobpaduov" ]o advh vgh}oi ygay A lv ilamhbadl{ando" Lb `afy$ ygo~o

lv a mobo~ad ~ovudy adhbm ygovo dlbov"

Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" Avvuco ygay A gav b ilvylbfy

olmobpaduov" Ygob A lv ilamhbadl{ando" Ch~ohpo~$ l`  Z lv ygo cay~lw }lyg ygo fhducbv

F 1$ F >$ """$ abi F b ygo b olmobpofyh~v h`  A$ ygob ygo cay~lw Z #1 AZ lv a ilamhbad cay~lw"

Lb hygo~ }h~iv$ ygo cay~lw A lv ilamhbadl{ando"

Z~hndoc; ]gay gazzoboi yh vqua~o cay~lfov h` h~io~ b }lyg dovv ygab b olmobpaduov8

]o gapo a za~ylad abv}o~ yh yglv z~hndoc"

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Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" Lb h~io~ yh `lbi huy }goygo~  A lv

ilamhbadl{ando$ }o ih ygo `hddh}lbm vyozv;

1" 

]~lyo ih}b ygo fga~afyo~lvylf zhd|bhclad

>" 

@afyh~l{o " Lb yglv vyoz$ }o vghudi no ando yh moy

}go~o ygo $ $ ca| no ~oad h~ fhczdow" @h~ opo~| l$ ygo

 zh}o~v bl lv faddoi ygo 'admon~alf, cudylzdlfly| h` ygo olmobpaduo "

6" @h~ opo~| olmobpaduo$ `lbi ygo avvhflayoi olmobpofyh~v" @h~ owaczdo$ `h~ ygo

olmobpaduo $ ygo olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc

Ygob vhdpo ly" ]o vghudi `lbi ygo ubebh}b pofyh~  W av a dlboa~ fhcnlbaylhb h` pofyh~v$ l"o"

}go~o $ a~o a~nly~a~| bucno~v" Ygo lbyomo~ cl lv faddoi ygo

mohcoy~lf cudylzdlfly| h` "

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9" 

L` `h~ opo~| olmobpaduo ygo admon~alf cudylzdlfly| lv oquad yh ygo mohcoy~lf

cudylzdlfly|$ ygob }o gapo

}glfg lczdlov ygay l` }o zuy ygo olmobpofyh~v F  k$ }o hnyalboi lb 6" `h~ add ygo

olmobpaduov$ }o moy owafyd| b pofyh~v" Voy Z yh no ygo vqua~o cay~lw h` h~io~ b

`h~ }glfg ygo fhducb pofyh~v a~o ygo olmobpofyh~v F  k" Ygob Z lv lbpo~ylndo abi

lv a ilamhbad cay~lw }lyg ilamhbad oby~lov oquad yh ygo olmobpaduov h`  A" Ygo

 zhvlylhb h` ygo pofyh~v F  k lb Z lv liobylfad yh ygo zhvlylhb h` ygo avvhflayoi

olmobpaduo hb ygo ilamhbad h`  I" Yglv liobyly| lczdlov ygay A lv vlclda~ yh I"

Ygo~o`h~o$ A lv ilamhbadl{ando"

^oca~e" L` ygo admon~alf cudylzdlfly| bl h` ygo olmobpaduo lv oquad yh 1$

ygob hnplhuvd| }o gapo cl 3 1" Lb hygo~ }h~iv$ bl 3 cl"

?" 

L` `h~ vhco olmobpaduo ygo admon~alf cudylzdlfly| lv bhy oquad yh ygo mohcoy~lf

cudylzdlfly|$ ygob A lv bhy ilamhbadl{ando"

Owaczdo" Fhbvlio~ ygo cay~lw

Lb h~io~ yh `lbi huy }goygo~  A lv ilamhbadl{ando$ dy uv `hddh} ygo vyozv iovf~lnoi

anhpo"

1" 

Ygo zhd|bhclad fga~afyo~lvylf h`  A lv

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Vh #1 lv ab olmobpaduo }lyg cudylzdlfly| > abi #> }lyg cudylzdlfly| 1"

>" 

Lb h~io~ yh `lbi huy }goygo~  A lv ilamhbadl{ando$ }o hbd| fhbfoby~ayo u~ 

ayyobylhb hb ygo olmobpaduo #1" Lbiooi$ ygo olmobpofyh~v avvhflayoi yh #1$ a~o

mlpob n| ygo v|vyoc

Yglv v|vyoc ~oiufov yh ygo oquaylhb # | % { 3 :" Voy abi $ ygob

}o gapo

Vh ygo mohcoy~lf cudylzdlfly| h` #1 lv > ygo vaco av lyv admon~alf cudylzlfly|"

Ygo~o`h~o$ ygo cay~lw A lv ilamhbadl{ando" Lb h~io~ yh `lbi ygo cay~lw Z }o

booi yh `lbi ab olmobpofyh~ avvhflayoi yh #>" Ygo avvhflayoi v|vyoc lv

}glfg ~oiufov yh ygo v|vyoc

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Voy $ ygob }o gapo

Voy

Ygob

Nuy l` }o voy

ygob

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]o gapo voob ygay l`  A abi N a~o vlclda~$ ygob Ab fab no owz~ovvoi oavld| lb yo~cv h` 

 Nb" Lbiooi$ l` }o gapo A 3 Z #1 NZ $ ygob }o gapo Ab 3 Z #1 Nb Z " Lb za~ylfuda~$ l`  I lv a

ilamhbad cay~lw$ Ib lv oav| yh opaduayo" Yglv lv hbo azzdlfaylhb h` ygo ilamhbadl{aylhb"

Lb `afy$ ygo anhpo z~hfoiu~o ca| no uvoi yh `lbi ygo vqua~o ~hhy abi funlf ~hhy h` a

cay~lw" Lbiooi$ fhbvlio~ ygo cay~lw anhpo

Voy

ygob

Gobfo A 3 Z I Z #1" Voy

Ygob }o gapo

 N6 3 A"

Lb hygo~ }h~iv$ N lv a funlf ~hhy h`  A"