primo theory level 11

7/28/2019 Primo Theory Level 11

1/60

Srodf Ugmfry

@mvm`


2/60

Gfw tf ]sm tgos Affi

L`tgfukg sfdm fh tgm `mvm`s ob tgos smroms glvm obtmrlntovm nlplaoòtoms mlng `mvm` wls emsokbme tf smrvm pmrhmnt`y wm`` ls l stlbe$l`fbm

tmxt" Ugm obtmrlntovm wma lpps lrm lb mbglbnmdmbt bft l rmquormdmbt hfr tgm nfdp`mtofb fh tgm mxmrnosms" Ugmy smrvm tf rmobhfrnm

lbe sfòeohy mlr trlobobk sio``s"

Ugm ^f`f Mlr Urlobobk Mxmrnosms

Dlby fh tgm mlr trlobobk mxmrnosms lrm emsokbme hfr sf`f prlntonm ay tgm stuembt" Gfwmvmr tgm tmlngmr sgfuè horst wfri wotg tgmstuembt fb tgmsm mxmrnosms ubto` tgm stuembt amnfdms hldoòlr wotg tgm prfnmeurms" Lhtmrwlre tgm tmlngmr sgfuè rmku`lr`y fasmrvm

tgm stuembt pmrhfrd tgmd tf mbsurm tglt tgm stuembt os dlobtlobobk nfrrmnt prlntonm" Ugm stuembt dly eosnfbtobum lby mxmrnosm

tglt nlb am mxmnutme mlso`y lbe nfbsostmbt`y" Ugm mxmrnosms sgfuè am prlntonme ls tgm stuembt nfbtobums wfriobk tgrfukg eohhmrmbt

smntofbs ob tgm affi"

Ugm Eontltofb MxmrnosmsUgm rgytgdon lbe dm`feon eontltofb mxmrnosms lrm emsokbme sf tglt tgm stuembt nlb wfri tgrfukg tgmd wotg lb obtmrlntovm

wma lpp fr wotg tgm tmlngmr p`lyobk tgm eontltofb dm`feoms" Ugm tmlngmr nlb ho`` ob tgm dossobk dmlsurms wotg dltmrol`s fh gos fr

gmr ngfonm fr kf tf www"prodftgmfry"nfd tf hobe tgm nfdp`mtm dm`feoms"

Ugm \Q NfemsUgm \Q nfems hfube tgrfukgfut tgos smroms nlb fb`y am rmle ay usobk l sdlrt pgfbm fr ple wgong gls l \Q nfem rmlemr lpp

obstl``me" Oh yfu efbt glvm l \Q nfem rmlemr lbe efbt ibfw wgmrm tf kmt fbm just hf``fw tgmsm eormntofbs:

^tmp fr 5 ls ots tfp budamr"Mxldp`ms:

Ob nfdpfube todm tgm amlt os eovoeme obtf tgrmm mqul` plrts"L nfdpfube todm sokblturm gls 8, ?,


5/60

15 eup`m$sodp`m

>5 trop`m$sodp`m

87 eup`m$nfdpfube

?7 trop`m$nfdpfube

C5 ryryP ryryP

R7 rryrtyP rtyrtyP

.5 ryryryP ryryryP

?7 rryrtyrtyP rtyrtyrtyP

eup`m

sodp`m

nfdpfube

eup`m

sodp`m

nfdpfube

trop`m

trop`m

Ugm Dmtmr os tgm plttmrb fh strfbk lbe wmli amlts ob l dmlsurm"Mvmry todm sokblturm obeonltms l nmrtlob plttmrb fh strfbk lbe wmli amlts"

Dmtmr

Eup`m Dmtmr nfbsosts fh fbm strfbk lbe fbm wmli amlt"

Urop`m Dmtmr nfbsosts fh fbm strfbk lbe twf wmli amlts"

\ulerup`m Dmtmr os l nfdaobltofb fh twf eup`m dmtmr

plttmrbs ob wgong tgm horst amlt os strmssme dfrm strfbk`ytglb tgm tgore"

Lsyddmtronl` dmtmr os l nfdaobltofb fh eup`m lbetrop`m plttmrbs wgong nrmltm lb orrmku`lr pu`sm, sung lsquobtup`m dmtmr 'hovm amlts pmr dmlsurm/ frsmptup`mdmtmr 'smvmb amlts pmr dmlsurm/"

55

>5

< 1 > 5ÛQFBKMÛ wmli wmli^trfbk

< 1 >^trfbk wmli wmli

eup`m

15 < 1^trfbk wmli

=5 < 1 > 5ÛQFBKMÛ wmli wmli^trfbk

=

eup`m eup`m

trop`m

wmli

L hu`` n`lssohonltofb fh todm sokblturms obnùems tgm hf``fwobk:

l/a/

Ugm eovosofb fh tgm amlt 'nfdpfube fr sodp`m/, lbetgm budamr fh amlts pmr dmlsurm 'eup`m, trop`m, mtn"/"

=


6/60

>" Lt tgm amkobbobk fh mlng dmlsurm, wrotm tgm nfrrmnt todm sokblturm"Ugm dmlsurms lrm wrottmb ob sodp`m todm, nfdpfube todm fr lsyddmtronl` dmtmr"

ôdp`m Nfdpfube Lsyddmtronl`

gLsyddmtronl`ôdp`mNfdpfube

q q qqqq qq qq qq q m

q

q q q q

q q q q " m qq qq qq q q q q q q q g

ôdp`mNfdpfubeôdp`m

m q q

m q q q

q q q

q q q

1" N`lssohy tgm hf``fwobk todm sokblturms" [rotm tgm nfdp`mtm todm n`lssohonltofb" Mx" eup`m$sodp`m

Odpfrtlbt Bftm:Ugm tmrds eup`m, trop`m, qulerup`m, lbe quobtup`m rmhmr tf tgm budamr fh amlts pmr dmlsurm"

Ugm tmrdssodp`m lbe nfdpfubermhmr tf tgm dlbbmr ob wgong amlts bfrdl``y lrm eovoeme"

8


7/60

5" N`lp tgm rgytgds ls yfu nfubt l`fue"

Qmleobk Qgytgds

C5 ryq P ehhk q P ekyryP rek q P q" mP mq mP ehhk q

C5 ryq P ehhk q P ekyryP rek q P q" mP mq mP ehhk q

.5 q" mq P q" mr"kP r"kq" mP ehhkq" mP mq q mP r"kekyq

%5 q etkq etkP q" ekq" ekPey" q ey" q P q" ekey" ryPw

.1 g g q q P rttyg q q P \ q g rttyP g" q\ q P w g

CC1 g g P g" q P q q \ q P q \ ryq P g q ryP G rttyP ryq g

R7 q" q" P q mq mP rty reky P rehhk ehhkyP ektyq"

R7 q" q" P q ek q mP r"ky reky P rehhk ehhkyP ektyq"

?7 rtyq mq mP M ryM eky ^ ehkyP q m^ ehkyq ekP g" q"

-7rtyryPrtyryPrtyehhkPrtyrekPq" MmPq" M ekPq" q

5

=

8

;

7

?


8/60

Mlr Urlobobk: Qgytgdon Eontltofb

^nlb tgm \Q nfem tf lnnmss tgm rgytgds tf am eontltme:

]sobk tgm wma lpp`onltofb kovmb lafvm, `ostmb tf tgm rgytgds lbe wrotm tgm bftltofb fb tgossgmmt"

Qgytgdon Eontltofb

L

A

N

E

M

H

K

G

="

7

Fb yfur SN, tlim tgm hf``fwobk rfutm:

DyUgmfryLpp"nfd @mvm`


9/60

Imys lbe ^nl`ms^mntofb 1

Fremr fh ^glrps

c555=5


10/60


11/60

Blturl` Dobfr ^nl`mHf``fws tgm imy sokblturmbf l`tmrme tfbms"

Immps tgm sldm hfrd wgmtgmr lsnmbeobk fr emsnmbeobk"

[gf`m lbe gl`h stmp plttmrb: [ G [ [ G [ [

Ugmrm lrm tgrmm alson hfrds fh dobfr snl`m: blturl`, glrdfbon lbe dm`feon"

Ugm Dobfr ^nl`ms

Glrdfbon Dobfr ^nl`mUgm smvmbtg snl`m emkrmm os rlosme l gl`h stmplnnoembtl`s lrm usme"

Lb lukdmbtme 1be 'tgrmm gl`h stmps/ fnnurs amtwmmb snl`m emkrmms 8 lbe ;"Immps tgm sldm hfrd wgmtgmr lsnmbeobk fr emsnmbeobk"

Dm`feon Dobfr ^nl`mOb lsnmbeobk hfrd, snl`m emkrmms 8 lbe ; lrm rlosme l gl`h stmplnnoembtl`s lrm usme"

Ob emsnmbeobk hfrd, tgm snl`m rmvmrts tf tgm blturl` dobfr hfrd"

' / ' /

;

Luk 1be

8 ; ; 8

'blturl` dobfr hfrd/

l dobfr

l dobfr

l dobfr


12/60

ma glrdfbon dobfr

h glrdfbon dobfr

h. glrdfbon dobfr

a glrdfbon dobfr

l dm`feon dobfr

n. dm`feon dobfr

k dm`feon dobfr

n dm`feon dobfr

>" Hfr mlng `obm, tgm bldm fh tgm dobfr imy os kovmb:

5" [rotm tgm dm`feon dobfr snl`m, lsnmbeobk tgmb emsnmbeobk"

`55555555555555$4


13/60

="

8"

Ugm Ngrfdlton lbe [gf`m$Ufbm ^nl`m

L ngrfdlton snl`m os l twm`vm$tfbm snl`m dlem up fh gl`h stmps" Ugm bftltofb fh tgos snl`m vlromslnnfreobk tf tgm nfbtmxt, aut tgm sodp`mst bftltofb usms sglrps hfr bftms tglt kf up lbe h`lts hfrbftms tglt kf efwb"

lsnmbeobk emsnmbeobk

Ugm prmsmbnm fh l imy sokblturm wo`` lhhmnt tgm spm``obks usme ob l ngrfdlton snl`m"Bftonm tgm usm fh blturl` sokbs ob tgm hf``fwobk mxldp`ms"

Ugm Ngrfdlton ^nl`m

Ob kmbmrl`, tgm ngrfdlton snl`m os usul``y bftltme sung tglt bf snl`m emkrmm os usme dfrm tglb twonmob sunnmssofb" Hfr mxldp`m, Ea $ E $ E. sgfu`e bft am usme"

Fb mlng stlhh, wrotm lb lsnmbeobk ngrfdlton snl`m hrfd tgm bftm kovmb"

Mbe tgm snl`m fb tgm bftm fbm fntlvm gokgmr tglb tgm stlrtobk bftm"

Fb mlng stlhh, wrotm l emsnmbeobk ngrfdlton snl`m hrfd tgm bftm kovmb"Mbe tgm snl`m fb tgm bftm lb fntlvm `fwmr tglb tgm stlrtobk bftm"


14/60

;" Fb mlng stlhh, wrotm lb lsnmbeobk wgf`m$tfbm snl`m hrfd tgm bftm kovmb"Mbe tgm snl`m fb tgm bftm fbm fntlvm gokgmr tglb tgm stlrtobk bftm"

7"

Fb mlng stlhh, wrotm l emsnmbeobk wgf`m$tfbm snl`m hrfd tgm bftm kovmb"

Mbe tgm snl`m fb tgm bftm fbm fntlvm `fwmr tglb tgm stlrtobk bftm"

Ugm bftms fh l wgf`m$tfbm snl`m lrm smplrltme ay wgf`m stmps '[/"

Ugos snl`m os nfbsoemrme lsybtgmton, fr lrtohonol` snl`m" L`` tgm tfbms ob tgos snl`m lrm tgm sldmeostlbnm lplrt9 bf sobk`m tfbm stlbes fut" Ls l rmsu`t fh tgos, l strfbk smbsm fh tfbon os `lniobk"^fdm nfdpfsmrs, sung ls Emaussy, usme tgos snl`m tf mvfim lb mùsovm, h`fltobk qulòty"

Ugm [gf`m$Ufbm ^nl`m

`55555555=$4

L vlromty fh eohhmrmbt spm`òbks nlb am usme hfr tgm sldm snl`m:

fr

[gmb tgos wgf`m$tfbm snl`m os trlbspfsme up l gl`h stmp, yfu hobe tgm smnfbe hubeldmbtl` hfrdfh tgm wgf`m$tfbm snl`m, wgong os l`sf suajmnt tf l vlromty fh spm`òbks:

fr


15/60

Dlj

1be

Dlj

>re

Smr

5tg

Dlj

8tg

Dlj

;tg

Smr

=tg

Smr

7vm

typm:

sozm:

ww

w ww

ww

w

w wwww w ww

Smr

Srodm']bosfb/

Dljfr lbe Dobfr Obtmrvl`sL dljfr obtmrvl` amnfdms l dobfr obtmrvl` wgmb emnrmlsme ob sozm ay l gl`h stmp"

Dlj 1be Dlj >re Dlj 8tg Dlj ;tgdob 1be dob >re dob 8tg dob ;tg

www

ww www

w

w

w

w

w

w

w

w

Dlj 1be Luk 1be Dlj 8tg Luk 8tgSmr 5tg Luk 5tg< Luk =tgSmr =tg

Lukdmbtme Obtmrvl`sSmrhmnt lbe dljfr obtmrvl`s amnfdm lukdmbtme wgmb obnrmlsme ob sozm ay l gl`h stmp"

w

w

w

w

w

w

w

w

w

w

w

www ww

Obtmrvl`s lrm n`lssohome ay typm lbesozm"Ugm hf``fwobk laarmvoltofbs wo`` am usme wgmb emsnroaobk tgm typm fh obtmrvl`s:pmrhmnt 'Smr/, dljfr 'Dlj/, dobfr 'dob/, lukdmbtme 'Luk/ lbe eodobosgme 'eod/"

Obtmrvl`s fh lb fntlvm fr `mss lrm nl``me sodp`m obtmrvl`s"

Obtmrvl`s^mntofb >

Eodobosgme Obtmrvl`sSmrhmnt lbe dobfr obtmrvl`s amnfdm eodobosgme wgmb emnrmlsme ob sozm ay l gl`h stmp"

dob >re eod >re Smr 5tg eod 5tg

ww ww ww ww ww wwww

ww

Smr =tg eod =tg dob ;tg eod ;tg

Dljfr lbe Smrhmnt Obtmrvl`s]sobk tgm tfbms fh tgm dljfr snl`m, obtmrvl`s auo`t lafvm tgm tfbon 'imybftm/ hfrd dljfr fr pmrhmntobtmrvl`s"


16/60

Gfw tf auoè lb obtmrvl` lafvm l kovmb bftm:_fu l`rmley ibfw tf usm tgm dljfr snl`m tf hobe pmrhmnt lbe dljfr obtmrvl`s, lbe tglt yfu nlbl`tmr tgmsm obtmrvl`s tf hobe dobfr, lukdmbtme, lbe eodobosgme obtmrvl`s" Ugos wfris wm`` wgmbyfu lrm wfriobk wotg imys tglt lrm hldoòlr tf yfujust tgobi fh tgm afttfd bftm ls tfbon lbelpp`y tgm lpprfproltm lnnoembtl`s lnnfreobk tf tgm imy sokblturm" Aut wgmb tgm tfbon tfbm nl``shfr imys tglt lrm bft hldoòlr, yfu nlb hobe lby obtmrvl` mlso`y oh yfu ibfw tgm hf``fwobk tgrmmobtmrvl`s vmry wm``: tgm

pmrhmnt =tg,dljfr >re

, lbedljfr 1be

" _fu nlb usm tgmsm obtmrvl`s tfpomnm tfkmtgmr ftgmr `mss hldoòlr obtmrvl`s"Ugm hf``fwobk sydaf`s wo`` sfdmtodms am usme tf obeonltm obtmrvl`s: nlpotl` `mttmrs wo`` rmprmsmbtdljfr lbe lukdmbtme obtmrvl`s9 `fwmrnlsm `mttmrs wo`` rmprmsmbt dobfr lbe eodobosgme obtmrvl`s9l sodp`m budamr wo`` rmprmsmbt tgm obtmrvl` sozm" Hfr mxldp`m, D1 hfr dljfr 1be, e= hfreodobosgme =tg, lbe sf fb"

bf lnnoembtl`sc=55555555555fb`y sglrps fb`y h`lts Ugm mxnmptofb tf tgos os tgmpmrhmnt =tg stlrtobk fb A lbe Aa"

Ugm pmrhmnt =tg os tgm mlsomst tf rmnfkbozm fb tgm stlhh"

Ugm dljfr 1be sgfuè l`wlys am spm``me ls l eoltfbon wgf`m stmp9 tgm twf tfbms sgfuè am spm``mels twf nfbsmnutovm `mttmrs fh tgm l`pglamt"

c5555

c555$555eoltfbon wgf`m stmps

c555$555sldm potngms

OBNFQQMNU spm`òbk

c55555

_fu nlb nfdaobm tgm pmrhmnt =tg lbe dljfr 1be tf hobe tgm pmrhmnt 5tg fr tgm dljfr 8tg"

c55 c55555Smrhmnt 5tg6

^tlrt wotg l pmrhmnt =tg tgmbkf l dljfr 1be efwb hrfdtgm tfp bftm"

D1 efwb

c55Smrhmnt 5tg

4

c55Dljfr 8tg6

^tlrt wotg l pmrhmnt =tgtgmb kf l dljfr 1be uphrfd tgm tfp bftm"

D1 up

c55Dljfr 8tg

4

S=

S=

bf lnnoembtl`s

c=55555555555fb`y sglrps fb`y h`lts

Ugm pmrhmnt 5tg hf``fws l sodo`lr plttmrb"

c5555Ugm mxnmptofb tf tgos os tgmpmrhmnt 5tg stlrtobk fb H. lbe H"


17/60

re eod >reDlj >re eod =tgLuk =tg dob 1beSmr =tg

dob >reLuk >re eod >reDlj >re eod 5tgLuk 5tg dob 1beSmr 5tg

eod ;tgdob ;tg eod ;tgDlj ;tg eod 5tgLuk 5tg Dlj 8tgSmr 5tg


18/60

Obvmrtme Obtmrvl`s^odp`m obtmrvl`s lrm obtmrvl`s splbbobk lb fntlvm fr `mss" ^odp`m obtmrvl`s nlb am obvmrtme aytliobk tgm `fwmr bftm lbe dfvobk ot up fbm fntlvmtgm uppmr bftm fh tgm frokobl` obtmrvl` 'l/ osbfw tgm `fwmr bftm fh tgm obvmrtme obtmrvl` 'a/" Ugm frokobl` obtmrvl` lbe ots obvmrsofb lrm nl``menfdp`mdmbtlry obtmrvl`s"

Smr =tg

w wSmr 5tg

_fu kmt tgm sldm rmsu`t ay tliobk tgm gokgmr bftm lbe dfvobk ot efwb lb fntlvm"

'a/'l/

Smr =tg

w wSmr 5tg

55$55$$

>"

55$55$$ 55$55$$ 55$55$$ 55$55$$

Hfr mlng plor fh dmlsurms, tlim tgm afttfd bftm fh tgm obtmrvl` ob tgm horst dmlsurm lbe wrotm otfbm fntlvm gokgmr ob tgm smnfbe dmlsurm"

Hobe tgm obvmrsofb fh tgm kovmb obtmrvl`s:

Mxldp`m

Obvmrt mlng kovmb obtmrvl` ls lafvm" [rotm aftg bftms fh tgm smnfbe obtmrvl` fh mlng plor"

55$55$$ 55$55$$ 55$55$$Mxldp`m

5"

55$55$$ 55$55$$ 55$55$$ 55$55$$

Hfr mlng plor fh dmlsurms, tlim tgm tfp bftm fh tgm obtmrvl` ob tgm horst dmlsurm lbe wrotm ot lbfntlvm`fwmr ob tgm smnfbe dmlsurm"

Mxldp`m

55$55$$55$55$$ 55$55$$55$55$$Obvmrt mlng kovmb obtmrvl` ay dfvobk tgm tfp bftm efwb" [rotm aftg bftms fh tgm smnfbe obtmrvl`"


19/60

w

Dljfr lbe dobfr nfdp`mdmbtsdljfr obtmrvl`s obvmrt tf dobfrdobfr obtmrvl`s obvmrt tf dljfr

ww

wDlj1be

dob1be

Dlj;tg

dob;tg

Lukdmbtme lbe eodobosgme nfdp`mdmbtslukdmbtme obtmrvl`s obvmrt tf eodobosgmeeodobosgme obtmrvl`s obvmrt tf lukdmbtme w w w w

Luk1be

Luk8tg

eod>re

eod;tg

="Ho`` ob tgm a`lbis am`fw tf nfdp`mtm mlng stltmdmbt"

Dljfr obtmrvl`s obvmrt tf obtmrvl`s"

Dobfr obtmrvl`s obvmrt tf obtmrvl`s"

Lukdmbtme obtmrvl`s obvmrt tf obtmrvl`s"

Eodobosgme obtmrvl`s obvmrt tf obtmrvl`s"

Smrhmnt obtmrvl`s obvmrt tf obtmrvl`s"

Ugm Qu`m fh Bobm:Ugm sud fh twf nfdp`mdmbtlry obtmrvl`s os l`wlys ?"

_fu nlb usm tgm ru`m fh bobm tf hobe tgm budmronl` sozm fh lb obvmrtme obtmrvl`" Hfr mxldp`m, tfhobe tgm obvmrsofb fh l >re, suatrlnt > hrfd ? lbe tgm lbswmr os 8l >re obvmrts tf l 8tg" Bfw yfunlb hobe tgm obvmrsofb fh lby kovmb obtmrvl`" Just rmdmdamr, ots l twf$plrt prfnmss: Horst yfu obvmrt

tgm obtmrvl` typm 'dljfr tf dobfr fr vonm$vmrsl, lukdmbtme tf eodobosgme fr vonm$vmrsl, lbe pmrhmntstlys pmrhmnt/, tgmb yfu obvmrt tgm sozm usobk tgm ru`m fh bobm"

dob 8tg

wwDlj >re

ww

Dlj >re

wwdob 8tg

ww

fr

Y ? $ T > 4 8 Y ? $ T 8 4 >

Smrhmnt nfdp`mdmbts L pmrhmnt obtmrvl`obvmrts tf lbftgmr pmrhmnt obtmrvl`"

w

ww

wSmr

Srodm

Smr

=tg

Smr

5tg

Smr

7vm


20/60

;"Nfdp`mtm mlng obtmrvl` lbe obvmrt ot:Ob tgm horst dmlsurm, wrotm tgm obeonltme obtmrvl` lafvm tgm kovmb bftm"l/Ob tgm smnfbe dmlsurm, obvmrt tgm obtmrvl` ob tgm horst dmlsurm"Oembtohy tgm obvmrtme obtmrvl` ay typm lbesozm"

a/n/

Smr =tg dob 8tg Dlj >re Luk 8tg

dob 1be Smr 5tg dob ;tg eod 5tg

l/ a/

n/

8"Hfr mlng obtmrvl` kovmb, bldm tgm obvmrtme obtmrvl`" ]sm laarmvoltofbs"

Dlj 1be Dlj >re Dlj 8tg

Dlj ;tg Smr =tg Smr 5tg

Smr7vm dob

1be dob

>re

dob 8tg dob ;tg Smr Srodm

Luk 1be Luk 5tg eod ;tg

Smr =tgdob >re Luk 1beeod ;tg

Smr 5tg

Dlj 8tg Dlj 1be eod =tg Dlj ;tg

Luk 8tgLuk 1be dob >redob ;tg

13


21/60

Dlj 8tg

Gfw tf auoè lb obtmrvl` EF[B hrfd l kovmb bftm:^f hlr yfu glvm `mlrbme gfw tf auoè lb obtmrvl` up hrfd l kovmb bftm, aut wglt oh yfu lrm lsimetf auoè lb obtmrvl` efwb hrfd l kovmb bftm6 Oh yfu glvm l tftl` dlstmry fh l`` tgm dljfr lbe dobfrimys lbe snl`ms, yfu nfuè sodp`y lssudm tglt tgm kovmb bftm os fb tgm snl`m emkrmm fh tgm sldmbudamr ls tgm obtmrvl` sozm, tgmb emeunm tgm afttfd bftm fh tgm obtmrvl` ls tgm tfbon"Fr, yfu nlb usm obvmrtme obtmrvl`s tf hobe tgm afttfd bftm" ]sm tgm prfnmss futòbme am`fw tf hobelb obtmrvl` efwb hrfd l kovmb bftm"

\umstofb: [glt os tgm bftm l dljfr 8tg efwb hrfd N.6

^tmp /

^tmp 1: Auoè tgm obvmrtme obtmrvl` ]S hrfd tgm kovmb bftm"Ugos os hldoòlr tmrrotfryl dobfr >re up hrfd N. os M"

^tmp >: Ulim tgm uppmr bftm fh tgos obtmrvl` efwb fbm fntlvm"Bfw ot os tgm `fwmr bftm"

Lbe sf, l dljfr 8tg efwb hrfd N. os M"

wc55

c55

6

w

c55$55w ww

7" Nfbstrunt tgm bldme obtmrvl`s am`fw tgm kovmb bftms" ]sm wgf`m bftms"

Dlj 8tgSmr =tg Smr 5tgDlj 8tg Smr 5tgSmr =tg Smr 5tgDlj 8tg

dob 8tgDlj 8tg Smr 5tgDlj 1be dob ;tgDlj 8tg Smr 5tgDlj 1be

Luk1bedob 8tg Luk 5tgDlj >re Luk 1be

^fdmtodms l`` tgos os bft bmnmsslry" Hfr mxldp`m, tgm pmrhmnt =tg lbe dljfr 1be efwb hrfd lkovmb bftm sgfuè am mlsy mbfukg tf hobe" _fu nlb l`sf usm tgfsm twf obtmrvl`s ob nfdaobltofb

tf hobe tgm dljfr 8tg"

dob 8tg Luk 5tgDlj >re

1


22/60

11

Mlr Urlobobk: Obtmrvl` Oembtohonltofb^nlb tgm \Q nfem tf prlntonm oembtohyobk dljfr, dobfr, lbepmrhmnt obtmrvl`s:

DyUgmfryLpp"nfd @mvm` re

lsnmbeobk emsnmbeobkSmrhmnt 5tg

Dljfr 8tglsnmbeobk emsnmbeobk

lsnmbeobk emsnmbeobkdobfr 1be

lsnmbeobk emsnmbeobkdobfr >re

dobfr 8tglsnmbeobk emsnmbeobk

dobfr ;tglsnmbeobk emsnmbeobk

Smrhmnt]bosfb

Urotfbmlsnmbeobk emsnmbeobk


23/60

Mlr Urlobobk Ero``s: Obtmrvl`s

^f`f Ero``: ^obkobk Obtmrvl`s

Emnoem fb lb obtmrvl` ob yfur sobkobk rlbkm"Soni hrfd lby am`fw:

re"

Fr, yfu dly wrotm efwb tgm obtmrvl`s p`lyme fb l pomnm fh plpmr"_fur tmlngmr wo`` p`ly sox dljfr, dobfr, fr pmrhmnt obtmrvl`s lafvm fr am`fw l kovmb bftm"[rotm tgm obtmrvl`s efwb fb l pomnm fh plpmr"N`lssohy mlng obtmrvl` ay typm lbe sozm" ]sm laarmvoltofbs 'mx", DLJ 8tg, SMQ =tg, dob >re/"

Dlj 1be

dob 1be

Dlj >re

dob >re

Smr 5tg

Smr =tg

Dlj 8tg

dob 8tg

Dlj ;tg

dob ;tg

Smr 7vm

]bosfb

trotfbm

1>

^tuembts sobkobk rlbkm:


24/60

Ngfres^mntofb 5

dobLuk eodDlj dob eod Dlj

dob Lukeod DljLuk dob eod

Luk Dlj dobeod Dlj Luk dob


25/60

Mlr Urlobobk Ero``s: Uroles

^f`f Ero``: ôbkobk Uroles

Ugm hf``fwobk mxmrnosms lrm emsokbme tf emvm`fp yfur sio`` ob gmlrobk lbe prfeunobk tgm tfbms fh tgm dljfr,dobfr, lukdmbtme lbe eodobosgme trole" Bftm yfur sobkobk rlbkm fb tgm imyaflre prfvoeme fb tgos plkm"

Ugos ero`` os emsokbme hfr sf`f prlntonm" Ngmni yfur prfkrmss hrfd todm tf todm ay rmnfreobk l smssofb

lbe òstmbobk tf tglt rmnfreobk nrotonl``y, fr ay pmrhfrdobk tgos ero`` ob tgm prmsmbnm fh yfur tmlngmr"Am surm tglt yfu lrm hfrdobk tgm troles nfrrmnt`y"

Emnoem fb l trole typm:dljfr, dobfr, lukdmbtme, fr eodobosgme"Soni l stlrtobk tfbm ob yfur sobkobk rlbkm"Ugos tfbm wo`` am tgm rfft fh tgm trole"S`ly tgm rfft"ôbk tgm rfft"

Gmlr tgm tfbms fh yfur ngfsmb trole wotg yfur obbmr mlr"ôbk tgm >re lbe =tg fh tgm trole"ôbk l`` tgm tfbms fh tgm trole ubto` yfu lrm sltoshome"Umst ay p`lyobk tgm tfbms fh tgm trole fb tgm polbffbm lt l todm"Ugmb, sobk tgm tfbms ls yfu p`ly tgmd"Qmpmlt tgm prfnmss usobk l eohhmrmbt tfbm lbe eohhmrmbt trole"Qmpmlt wotg eohhmrmbt troles ls fhtmb ls os bmnmsslry lbe hfnus yfur mhhfrts fb tgmdfrm eohhonu`t fbmstgm lukdmbtme lbe eodobosgme"

/

5/

Umlngmr&^tuembt Ero``s: Qmnfkbozobk Uroles

_fur tmlngmr wo`` p`ly dljfr, dobfr, lukdmbtme lbe eodobosgme troles"Oembtohy lbe bldm mlng obtmrvl` ay typm" Hfr mxldp`m, dljfr fr eodobosgme"

Fr, yfu dly wrotm efwb tgm trole p`lyme fb l pomnm fh plpmr"_fur tmlngmr wo`` p`ly hovm troles p`lyme ob a`fnime lbe lrpmkkoltme hfrd"[rotm tgm obtmrvl`s efwb fb l pomnm fh plpmr" Oembtohy wotg laarmvoltofbs:dljfr 'DLJ/, dobfr 'dob/, lukdmbtme 'L]K/ lbe eodobosgme 'eod/"

1=

Lpp Ero``s: Uroles^nlb tgm \Q nfem tf prlntonm oembtohyobk dljfr, dobfr, lbeeodobosgme troles:



26/60

M Dljfr

h glrdfbon dobfr

5558$5558$5558$5558$5558$4c== www www>" Ob mlng dmlsurm, tgm dljfr imy sokblturm os kovmb" [rotm tgm rfdlb budmrl` hfr mlng trole"

5558$5558$5558$5558$5558$4


27/60

M Dljfr

c55=$5==$5==$4

=" Hfr mlng imy, wrotm tgm imy sokblturm lbe tgm tfbon, suaefdoblbt lbe efdoblbt troles"

OXO X

h dobfr

c55=$5==$5==$4ovo XMa Dljfr

c55=$5==$5==$4OXO X

k. dobfr

c55=$5==$5==$4ovo X

L Dljfr

c55=$5==$5==$4OXO Xk dobfr

c55=$5==$5==$4ovo X

N Dljfr

8" ^pm`` tgm tfbon, suaefdoblbt lbe efdoblbt rfft pfsotofb troles fh mlng imy kovmb"

m glrdfbon dobfr

K Dljfrn glrdfbon dobfrA Dljfr

Ufbon

^uaefdoblbt

Efdoblbt

h glrdfbon dobfr

5558$5558$5558$5558$5558$4c== www www

5" Ob mlng dmlsurm, tgm glrdfbon dobfr imy sokblturm os kovmb"

5558$5558$5558$5558$5558$4


28/60

5558$5558$5558$5558$5558$4c==n : h : n :

5558$5558$5558$5558$5558$4


29/60

Ugm Efdoblbt ^mvmbtg Ngfre^mvmbtg ngfres ob rfft pfsotofb lrm obeonltme ay lb lrlaon budamr ; p`lnme tf tgm rokgt fh tgmrfdlb budmrl`" Ugm efdoblbt smvmbtg ngfre os l typm fh smvmbtg ngfrel dljfr trole pùs ldobfr ;tg lafvm tgm rfft"Ugm efdoblbt smvmbtg ngfre os hfube fb snl`m

emkrmm = fh l dljfr fr dobfr snl`m"

Ob l dobfr snl`m, tgm tgore fh tgm X ngfre dustam rlosme tf hfrd l efdoblbt smvmbtg ngfre"

c5555555558$4ww ww w w

wN:

1 > 5 ;8=re ob tgm alss9 smnfbe obvmrsofb, wotg tgm =tg ob tgm alss9 lbe tgore obvmrsofb,wotg tgm ;tg ob tgm alss"

c555555555558wN: X;

wwwwwww

wwww w

www

X8 X X=

5 1>

rfftpfsotofb

horstobvmrsofb

smnfbeobvmrsofb

tgoreobvmrsofb

Ugm lrlaon budmrl`s usme hfr tgmsm obvmrsofbs bldm fb`y tgfsm obtmrvl`s lasfùtm`y bmmeme tf oembtohytgm ngfre" Hfr mxldp`m, l horst obvmrsofb smvmbtg ngfre rml``y nfbtlobs l >re, =tg lbe 8tg lafvm tgmalss, aut ot os bft bmnmsslry tf obnùem tgm >re wgmb `lamòbk tgm obvmrsofb" Ugm fb`y lrlaon budmrl`susme ob `lamòbk obvmrtme smvmbtg ngfres lrm tgfsm bmmeme tf oembtohy tgm rfft lbe ;tg lafvm tgm alss"

c555555555558wN: X

;

wwwwwww

wwww w

www

X8 X X= 5 1>tgm efttme òbms pfobttf tgm ;tg fh tgm ngfre

tgm sfòe òbms pfobt

tf tgm rfft fh tgm ngfre

X; X8 X X=

5 1>Ugm lrlaon budmrl`s prfkrmss ob nfubtefwb$òim

hlsgofb hrfd rfft pfsotofb tf tgore obvmrsofb:; 8 = 5 > 1

c5555555558$4ww w w w wwn:

1 > 5 ;8= 1 1 > 1 > < > 5 > 1 5 > 5 1 < 5 < 1 re snl`m emkrmm hfr l hmw mxtrl dfdmbts ls yfu p`ly tgm tfbon trole"

S`ly tgm stlrtobk tfbm fh tgm mxmrnosm fb tgm polbf"ôbk lbe dltng tgm stlrtobk tfbm"ôbk tgm mxmrnosm ls yfu p`ly ot"ôbk tgm mxmrnosm wotgfut p`lyobk ot"

l/a/n/e/

Mxmrnosms]sm tgm hf``fwobk mxmrnosms hfr lssokbdmbt


33/60

Ugm uppmr tmtrlngfre 'snl`m emkrmms = $ 7/ nglbkms wotg mlng hfrd fh dobfr:

5

G [ [

l: = 8 ; 7

blturl`

5

G L1 G

l: = 8 ; 7

glrdfbon

5

[ [ G

l: = 8 ; 7

dm`feon

= 7 ; 7

= 7 ; 8 ; 7

= 7 = 8 ; 7

uppmr tmtrlngfres'`fwmr tmtrlngfre/

; 8 =

[ [ G

1" ^obk tgm hf``fwobk mxmrnosms usobk tgm sldm prfnmeurm ls lssokbdmbt

@ost tgm dobfr imys tf usm:


34/60

>" ôbk tgm mxmrnosms lnnfreobk tf tgm eormntofbs kovmb lafvm"Lvfoe p`lyobk tgm dm`fey fb tgm polbf ls yfu sobk aut yfu dly p`ly tgm tfbon trole tgrfukgfut"Nglbkm tf lbftgmr ngfre fb`y lt tgm pfobts obeonltme ay rfdlb budmrl`s"

Lntovm lbe ^tla`m Ufbm Mxmrnosms^nl`m emkrmms 1, 5, lbe 8 rmsf`vm efwb l stmp lbe .; rmsf`vms up tf tfbon" Ob tgm hf` fwobk mxmrnosms,l hmrdltl os p`lnme fvmr sfdm lntovm tfbms" Slusm fb tgmsm bftms tf kmt tgm hu`` mhhmnt fh tgmor lntovmqulòty" Just ls odpfrtlbt`y, bftonm tgmor rmsfùtofb tf tgm bmokgafrobk stla`m tfbm" Uf mbglbnm tgosmhhmnt, p`ly tgm ngfres obeonltme ay tgm rfdlb budmrl`s ls yfu sobk"

ov

c=tyuofouyt$8tufut$8tyuofut8$4

c=tyufuyt$8tuofout$8tufTfut8$4

c=8tufTYp=8fTfpfouy=tuytr=t8$4

c=tuffpYTYTfp=fpfouto=uyt8$4c=ftTYpfp=fouofpY=Tpfouyt8$4

c885uytrtyuofuYup=8foufoyru8$4

c885urufYT=8Yfuruy88urfoufo=u8$4

o ov o X o

ov o X o

ov o ov o

ov o X o X o

ov o

>5

rlbkme dobfr

h dobfrrlbkm




35/60

c555585$5=555$55=55$55=55$4

c555585$5=555$55=55$55=55$4

ôbk mlng hfur$dmlsurm dm`fey usobk sf`hmkm fr snl`m emkrmm budamrs"Urlbspfsm tgmsm mxmrnosms tf lby imy ob yfur nfdhfrtla`m sobkobk rlbkm"

ôkgt ôbkobk Hfur$Dmlsurm Dm`feoms ob Dobfr Imys

m dobfr

>e dobfr

l dobfr

c555585$5=555$55=55$55=55$4n

c555585$5=555$55=55$55=55$4n

5

>5

c555585$5=555$55=55$55=55$487

c555585$5=555$55=55$55=55$487

n dobfr

c555585$5=555$55=55$55=55$4n

c555585$5=555$55=55$55=55$4n

m dobfr

e dobfr

n dobfr

l dobfr

5

=

8

;

7

>=

5"


36/60

=" ôbk mlng hfur$dmlsurm dm`fey usobk sf`hmkm fr snl`m emkrmm budamrs"Urlbspfsm tgmsm mxmrnosms tf lby imy ob yfur nfdhfrtla`m sobkobk rlbkm"

ôkgt ôbkobk Mokgt$Dmlsurm Dm`feoms ob Dljfr ImysUgm hf``fwobk mokgt$dmlsurm dm`feoms lrm ob dljfr imys lbe wo`` nfbsost fh twf eostobnt pgrlsms:tgm lbtmnmembt, mbeobk ob l gl`h nlembnm, lbe tgm nfbsmqumbt, mbeobk ob lb lutgmbton nlembnm"Ob prmplrltofb hfr tgos lssokbdmbt, yfu dly horst sobk tgm ero``s ob lssokbdmbt 5, trlbspfsobk hrfddobfr tf plrl``m` dljfr"

n " "

"

n " "

"

>5

"

>5

"

""

"

H Dljfr

N Dljfr

5

>8


37/60

Glrdfby os tgm stuey fh ngfresgfw tgmy lrm hfrdme, gfw tgmy obtmrlnt wotg mlng ftgmr lbegfw tgmy obtmrlnt wotg ftgmr dusonl` m`mdmbts sung ls dm`fey, rgytgd lbe hfrd"

Ugm tmrd hfur$plrt glrdfby rmhmrs tf duson wrottmb ob hfur plrts, fr vfonms, mlng fh wgong rmtlobsots oembtoty ls l eostobnt dm`feon òbm tf sfdm emkrmm" ûng duson, wgong gls twf fr dfrm eostobntdm`feon òbms p`lyobk l dfrm fr `mss mqul` rf`m ob tgm nrmltofb fh tgm dusonl` mxprmssofb, os ibfwbls pf`ypgfbon duson"Ugm hfur plrts, hrfd tgm gokgmst tf `fwmst, lrm tgm sfprlbf, l`tf, tmbfr lbe alss"Ob hfur$plrt glrdfby, tgm vfonms dly am lrrlbkme fb tgm krlbe stlhh twf eohhmrmbt wlys:

'l/

'a/

Ugm alss lbe tmbfr lrm fb tgm alss stlhh9 tgm l`tf lbe sfprlbf lrm fb tgm trma`m stlhh"Ugos lrrlbkmdmbt fh vfonms os sfdmtodms rmhmrrme tf ls ngfrl` sty`m"

Ugm sfprlbf, l`tf lbe tmbfr lrm fb tgm trma`m stlhh9 tgm alss vfonm os fb tgm alss stlhh"Ugos lrrlbkmdmbt fh vfonms os sfdmtodms rmhmrrme tf ls imyaflre sty`m"

c555==;


38/60

Ugm X;$O Lutgmbton NlembnmUgm alson vfonm$`mleobk hfr tgm X;O nlembnm:

Ugm smvmbtg fhX; kfms efwb l stmp 5 rmsf`vms tf >"5

>7

c555585$5=555$55=55$55=558$

M Dljfr

c555585$5=555$55=55$55=55$4

>7

5

=

8

=8

Uf lnnmss dfrm dm`feoms hfr eontltofb prlntonm:

Dfrm Dm`feon Eontltofb Srlntonm

^nlb tgm \Q nfem:



57/60

Emhobotofbs^mntofb ?

le `oaotud Hrmmefd tf odprfvosm fr vlry tgm tmdpf

l`tf Ugm smnfbe gokgmst vfonm ob hfur$plrt glrdfby

lrol L nfdpfsotofb hfr sf`f vfonm

lsyddmtronl` dmtmr Ugm nfdaobltofb fh twf sodp`m dmtmrs wgmrm tgm pu`sm nlbbft am eovoemeobtf 1, > fr 5 amlts pmr dmlsurm

lukdmbtme obtmrvl` L pmrhmnt fr dljfr obtmrvl` tglt gls ammb obnrmlsme ay l gl`h stmp

lukdmbtme smnfbe Lb obtmrvl` fh l smnfbe glvobk tgrmm gl h stmps 'N $ E./

lukdmbtme trole L trole dlem up fh twf dljfr tgores

al``mt L tgmltronl` elbnm

alss Ugm fwmst vfonm ob hfur$plrt glrdfby

ao$tfbl` Ugm usm fh twf eohhmrmbt imys lt tgm sldm todm

nlembzl L smntofb ob l nfdpfsotofb tglt l``fws tgm pmrhfrdmr tf odprfvosm fr tglt oswrottmb ob tgm sty`m fh lb odprfvosltofb

ngrfdlton snl`m L twm`vm$tfbm snl`m auo t fb`y fh gl`h stmps

ngurng dfems ^mvmb eoltfbon snl ms nfdprosme fh eohhmrmbt lrrlbkmdmbts fh wgf`m lbe gl h stmps

n`fsm glrdfby Hfur$plrt glrdfby wotg mss tglb lb fntlvm amtwmmb tgm sfprlbf lbe tmbfr

nfdpfube dmtmr L dmtmr ob wgong tgm amlt nlb am suaeovoeme obtf krfups fh tgrmm

nfb dftf [otg dftofb

nfubtmrpfobt Ugm usm fh twf fr dfrm dm`feon obms sodu`tlbmfus`y

eoltfbon snl`m L snl`m wotg smvmb eohhmrmbt tfbms

eodobosgme obtmrvl` L pmrhmnt fr dobfr obtmrvl` tglt gls ammb emnrmlsme ay l gl`h stmp

eodobosgme trole L trole dlem up fh twf dobfr tgores

efdoblbt ;tg ngfre L dljfr trole wotg l dobfr ;tg leeme lafvm tgm rfft, hfube fb snl`m emkrmm =

eumt L dusonl` nfdpfsotofb wrottmb hfr twf pmrhfrdmrs"

horst obvmrsofb L trole tglt gls ots tgore ls tgm fwmst potngtrolegl`h nlembnm Lby nlembnm wgong mbes fb tgm efdoblbt trole 'X/

gfdfpgfbon duson Dm`feon obtmrmst os nfbnmbtrltme ob fbm obm suppfrtme ay lb lnnfdplbodmbt"

obtmrvl` obvmrsofb Uurbobk lb obtmrvl` upsoem efwb sf tglt tgm `fwmr tfbm amnfdms tgm gokgmrtfbm fr tgm gokgmr tfbm amnfdms tgm `fwmr tfbmobvmbtofb L sgfrt nfbtrlpubtl` pomnm alsme fb fbm tgmdmdmtmr Ugm frklbozobk plttmrb fh strfbk lbe wmli amlts

dobfr obtmrvl` Lb obtmrvl` wgong os l gl h stmp sdl` mr tglb tgm nfrrmspfbeobk dljfr obtmrvl`

dfbfpgfbon duson L sobk`m `obm fh dm`fey wotgfut lby leeotofbl` plrts fr lnnfdplbodmbt

fpmb glrdfby Hfur$plrt glrdfby wotg lb fntlvm fr dfrm amtwmmb tgm sfprlbf lbe tmbfr

=;


58/60

fpmrl L tgmltronl` erldl tglt os subk lbe smt tf duson

frltfrof L slnrme tgmltronl` erldl tglt os subk aut pmrhfrdme wotgfut lntofb, nfstudmsfr snmbmry

fvmrturm Lb frngmstrl` nfdpfsotofb usme tf obtrfeunm l lrkm erldlton wfri

plrl``m` imys Dljfr lbe dobfr imys tglt sglrm tgm sldm tfbon

pmrhmnt obtmrvl` Ugm smt fh obtmrvl`s ob tgm dljfr snl`m usobk snl`m emkrmms


59/60

5555555555555555555855555555555555555558

55555555555555555558

55555555555555555558

55555555555555555558

5555555555555555555855555555555555555558

5555555555555555555855555555555555555558

55555555555555555558

55555555555555555558


60/60

5555555555555555555855555555555555555558

55555555555555555558

55555555555555555558

55555555555555555558

5555555555555555555855555555555555555558

5555555555555555555855555555555555555558

55555555555555555558

primo theory level 11

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