Skripta Pruznost a pevnost I

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o=l#t IN,e )
4q lsnu'tAt {t}s gu?.mar A1.usrs }c:1ug rureauq af ly qrud rafp ,r egs alolorg
jNe V''3'-) 'Ne 'Ng 'v''3 !:) ,'Ne
TV .iT +r\A'iiA'--it- += np
'Ne A.'EE 'Ne
u= ne-'lr]1#= ne
eu_ulgsop (e€-reua JupuuoJep erunmq) nm94xa nlqnrpod ord u
A''z'z tJ-T:T+=n
guroduzau fp1,r af z1y Ags glrgmau flcqsrs epod 4
eclunJ aco^l:op gqrup a? 'le'zqold as eursn{od umulurur o gupaf gupalru'p es o7 'aua791t pi(p
(zr c)
(rLe)
(or'r)
nvvlt v nHVt oHil?an]N AxJuVts AOVdlAd lHcngoN1sf 't
-69-
g zsol'f
-zn=- 8J sot ' Z _I
gl j;or . Z
zN-J e
.N I zN
I,soc'I
-zni' gl sor . a _
I
glsor.Z
zN-! I
(ZNEIINEIIN zNelNe tN ,
I'€'q8I
(fl e)
srlslo^uap uolod el e /l ar8:aua ru-ceu.lo3ap g,ro11ec eue120d,{,r arudfau e1{q npeqgd ruguapa,tn ,1
'uqua;a; u4r;faz_uqcpa;d s ppoqs a,r ef o1
'I t qeJ ^ ouapa^n at zpglpg e rp apq
'ltg , E
o=tNe 'N +
Pqpo
'Ne , '4 v'e 'Ng
tr=]-. ,li \.-=_'Ne'-i
e ne
( I I €) op orupd urluazesop lu,rodqsod ez1 rfalqcXg .zp a1p
gl ,soc-7 +J--
dsor J =
glsoc.T =LN
(4!:ie !!_) t
dzsn_.Z+l.J_zN
^ 1 ,-.. d rsot.T lv z rNeo =L"w+(1--)lz,v -rt
I; = *
l:r.ffi,1"==,n+,ne =n
aurungsop (4 9) uruqnog
qnerdg o6
EIgP E
ruolod
"'tt'\ ! ='n
t tsoNAld V tsot{znad
'n=H3Yiz ='n
fpet
'oL'
L'f 'rqo
e? '?urlrtepP ef oqer.Dl az ' L'E lqo Bu oua,^J"rzeu at Ju?qo n
:!uaIa{
9'C 'rqo
.urrxg[=rr'rxrxz=t'ultugz=zp,unng€=zo.uur00t=r,.?dllnol.s,L=z1.ururs.z=s
nlr^ez ruednots 'ruru L'91 = ,p 'EdN 9O|.Z,T, =,f ougp ef Lr:ttr^gz lll o ?tlef pnuposop od rullsur
li-+ulr?otocd 'g i lqo slpod e a3qruJ ?^olrullq ? , nqnols rne^olaco A 3rDlnz^ Il?deu o{ef
'e'e PEPUI.I
'p1n4suo1 qcr(,roFrd qsllf?lqols Juelel Hd u_e^fz^n ?q?q of dnrsod olual
d zsor.z+l .J=zN
' gl 'sot'70="N+
l_zN-
,.. . (d ,toc't \ - 'Ng t=''N*1ffi-)'=ffi''1
{pel FBId
aur-B^9sop qFq"t z
nyvlJ_ v nHVt oHjrQAn3N AXC\wLS tOValya lu)noouozre
,V
T
' ,L'
eur,Ilouuls 9'g rqo elpod arudleu fpodi{,r fqas;p o14
.Lo=zg
\Lt e)
(er e)
(sr'€)
('r'E)
()rsp)
(qsl)
='v = ro,vs
('J ?'?t| -l-_ t.J,
Vt ' 'v''t )'
(?'z ?).
\TT-T I' _
rfagnpoupaf oqau
=lg
nopnq ro e ro p?duu guepalq e?Fl
e1_unnpod yupuroyeq
v,v
(?'z ? h| ]-_- t.*
Vt tl )'
",-=ttl
,tprl
, zv.zJ \.tz-=---=--*_--
s "r'lv 'l.N
auE^slsoP (9l t)acruao:op(9J E)e (y1'g)cruror Juaz"sop o,.t. 7f
zlr -
. Lg = Zg
=!=,o U
(sz c)
\9L L)
(t+Lt)'z'tv'n
zv
i''t+'t _!=,o U
4v
E
', *!, t,
1v -!,= ll,'" =,
('t+tt)'z'tv'o
,,,\--- (9 N\zs = l.t +,t). I v. " *
lT * =t )'E
apr
oq0u
L tsoN[3d v tsoNTnad
eur-B^9lsop (ZZ'E) ,{4ryupod op (1 7 g) e (97'g) ttqqz'\ urytazssoq
- 9Z'
tl'c'rqo
'6 n$rd n alqo od nlIIe,.A oqgrlnl Eqolod gusp.Bnodp3ld ?s?^oll.s?
Buelsa.r{ez et }t € rqo eN'g^oIutlld {p7,r g4u1,{ls qc;qop ecrufods ePnq Jue?gvz tu?qo^oqll ud
'nur-e"q ur?qru epuolop eu nosf gn-rd ,{sg,rp Jr4op a7 'oqo1 aurafz-n'{'r ql4urPod lu?suroJaP org
(q ez e) 0=e.eN+e'e'tN
o=eN-'N+'N
af 7 npoq 1 e4ryurPod elolueuroru B
(e 9z'L)
J€Al eur ru?uls ulruE{gxt^ aA e3mAOJ 9AO{?OIS
'n-1ultupod nonoluaruoru nuPaf s rcru ol nolo>Vols
nupaf rgsd aue?r.lur n^etsnos olru old ?ur^oJ A Is qc{'?9qou'ror n^slsnos o '{ps} es guPaf zA,
? ,rV .{lls a,roqa aurep-e1lodpe$ Z 'L qratrud qc;crfe,rdqz aA 'ri, nolts no^oIBIl uazvrqeu ?A?$nos A
af lourqg Toqef 'g urud rulugue.4spo af aursf lpe^ord'€I e 'lqo 3u ouaiermu a[ f^elmos ;u?ulo^n
:luapa
ct'f rqo zI'c'rqo
'nur-s.q rrraqu epuolop eu Xu2tsJum nosf grud 'Gqne-z Juloq 'y nzer-n:d oqgufap J
9qno1p qufals 'edlnl sol.Z'Z =Z=cA =23 = tl9,ro1aro nosf ,fin:6 1-J.s-0I'Sl'I =n:Jo0L=lV oc
qn:d uruuqqo Z l 'C rqo atpod sc{n-qsuol altlrnau flcqels qtolud ^ norqnz'r' ppdeu 91eJ 'anSl[Z
'9'e pspuld
'1[e4u,lau ,t1;s g,roso ap 're,u |[af ual rueE |ne^algo as ?l!?m
Alcuels f,lElmos n ocurFn ',{,reFnos qralrud ,r ,(1;s g'roso flelsnos ?lao rue^elqo oqau qrud oqEaqqu
€rt
lv
h
r+4 fqrl tlu'o)loP
tadJHsnooNoT'e
. LL-
(q?l) ed!t. 6'91= z o
ot B Z ? nlud uleryIloeu ^ epnq lu,I"qeureu r$^^fau e? .lp^olgtsuol orqoru ef r,r1p-a1s{a 7
\LL L' ,lv_rlv- tlv_ttv
n4_unupod ;upuuuoyap rysd aurs7r.rur g1Jr4eq4fo4 qsouqopod 7 .qcru
,r rure|s nu-f,roqel rur,(uepepodpa;d s ?poqs e^ g^oqBt o4ef,{ualsarleu nosfT e ;, glrud eozuuo;aq
L tsoNAsd v JsoNznad
(ryn) [ean]q'oE = t,sz.. =to.7=1.7r.".:=?=t" "1,
Z
(qer) [ean]o'sr = {sz..E =to.s=3.7v.".1=J='o r -rv
({ep) [ear\] e'sz = -0t.2.2.0r.._0,.r,,,.f =a., o.".+=+='" t'N
nopnq uolod qce1rud ,r uqdeu guepelg .(- o4uaureuz) ryp nqPl olslu apnq
I nrn:d ,1 6 e 7 rurud n gu,re:ds ,{1Xq Fs f1s.{urs auepgqodpa;d aq .gufep ef g4pa1sf,r olqcpr 7
t^v.J.tv.D.Z='N
(ogs) I 'v.1.rv.D.i= "N
Iv.3.rv.nj_=
N
qcaln:d,r Xlrs o:d fqelz,r arueue$op (62.t) .(q .e 97.g) cru,ror laalsnos umrasaa
(6zi) V.3'lV.D.Z=tN.Z+rN.€+tN-
a,rerdn od aurauelsop (LZ t),(ry1upod op (g7 g) cruaor qc;u19ry2,! ur;uezesoq
'(lry Alls a^o{en auspeqodpqd po ruatg.rlz az s n^e{uo po Jue^mopord z gpegs es 6 ntrud eceuuoJaq)
(8zE) V'.3 -,.rv.p=trv : V'? =r,o v'1
t."N ='rv i-N=-tv , ^=',,
nopnq $ru^ol JurBTz,(C
e'e e.€
-82-
tae(l=-
-ne
{por 'f.,ro1nu ay Xlls ?lpqosBd
.rnsod gurfap ef q 7 g :qo ap gpedgd L'tt?^ lhounlpltsD) u4r!?n ll;el a4 ,(ped;4d or,{1 1
'llue|'uz sU e lfl?^z qoupoq olnl o eE rU ec{Rau '9 ttsoTte^ nolu?rll9 luoupoq noulels o Ju?trE
rs ?r{Eer 1upo4d a7 '9ur[ap a[ 1'g npegl;d n acluar ord,tqeP,\ os plPals4^ olqc?l ulrugu orod
(ze e) #r_Tr=aa
#n.T.!='a ruc,r1 aA atlsar ord {qep,r nopf,h nolqrupod pleuuoJeP onoi
s ltsd 'Sl e rqo elpod rclear,(lsftus ll-aullo^Z'eU lJlsar plond,l ryt e g n:odo;upods eu t lpasop
lednols 3 A11s urJuaqosgd ,{qe gIBu IBl af g sloupoq a7 'eurgp-cgodpeld gufapoures ruolqg
(rr s) g=lv -alv
apnq ppedgd olurot ,r greq 'ulu,nupoci
lupuuoJep oznod es tu?uz l e npe14;d n olXq nrnol oryf 4uqopqo el3cz ePnq ;ueqe1 dqsog
sl'e 'rqo
'qdnols qratEl qcdalpoupaf ,r Sopfdeu r
gulaldoqcod ?{el urp3 ru e su lclBar qsoTle^ es lu?trE'(sI'€ rqo) 9 ruosPoq noleul o l[uau n)II9P
no^o{loc tlur ePnq hp"dlld oq?lQmeu flcqels Juogo; dn6od {uceqo quirozuln eursf ul.'rol{ zu 'I €
npe14;d z ladnols ';deu 7fp; ,{,rupnos ,lt4euloa8 gnzp frpuzol 9usald guau d,rsFnos p,rrd {ragpu
e? trlr ?{sl ,{u2u,r11ao I4ur2r,r 9,rops ,lhu I Frnlu p,{q noqou qca{1t1mau {IcEe$ ^"Fnos n
ltsouso;ldeu - !llt^ qtlu?gluour ^ll^ s'e
'6/'
Lt'f 'rqo 9t'f 'rqo
'N
'nure.q rx?qu epuolop eu nosflsprgz lulo6 "0e =d'.SV=o lrnu969=graf
{sd app ?dlll 501.2'Z=ll =zj1 = 13 npuepur oqgufap ez luaqor,{,r nostey -zyr = ryzaptd {uQrs;.feur
,{lrud.{urlcoiA ^A?tsnos nqauroa? opp;,rodpo ,{q r17eu 'unu g'0: g o y;tzq af {.laq ? ntrud q4uour
,,arqrseu,, od 9l t lqo apod ,{.te1snos a,rotrud gtqmsu,{1cqqs qcolrud A notqnul nqdvu eryt eleg;1
9'f pBpl;{il
'qrud yuaqruod 1 ?upadgd 'p-uqgureu oq?uelo^op
lue?oqald I tlfop nrrud trraraDl?u ^ eqlua 'lre{gvz oqnzoaord po qsoEfdsu s e?g-luoru po lsopfdeo
rupo,rr;d ofnuod:edns as fp1 'ao{n4suol tu:lTovz lurnrzolotd urylszl,r r;d e .oJe1;pdau urepa;d Ju s
es e4olord ?u?edzeqau l4q e?Brx l?_?tuout ,,noqrs_Eur eJ{n-qsuol op guasau,r lsopldeli .ppdeu qcoln:d I
nosf ac4n4suo1 u\ueVgzgz umlsel,r pald p1;:f Ipal '^ slsnos qca1rud qc{,rrpoupaf n f1;s 9,loso g1o,,r,{n
?_?luotu ,,eulrsgu. olBAo{"I rs_eu prTnod zaq treqoqdz umjl?uuotr e3{n-qsuo\ zauoru pa,rotd a4eu
(lsousaldau ruqo:,f,r) rElep oqeu rll?q 1rud {:at11u gtu FelI .X,relsnos e,rolud 911meu ^rtrpets n
q+e.a_q+e.t=a>t
v'?" ct - lpdo fpal e
ef
V.1'Z v'3'z
tl"ylD*E7g= n af ayz qo4t1e1
(€r'r) o- ="ag-ne
re4 qceped;.r^d oqcgt ^grn Dqtr ndou41317so3 .7
{pal e g usolqa,r uanol ef ,r.nsod ?U flF nlsfus gord g npoq,rnsod "f St.S .rqo apod ppedgd I
L tsoNA?d v tsoNTnad
-08-
glsoz-V.J V.J
E:z'|=zizi="tv psoc.v.l
V.J--;ji-=Tzi='tv
(8e E)
(e''c)
(se e)
(" r)
e.z e-7r =r7
nopnq acrurror pp4tzfg
d urs
-" = zA"tv-9 nu$' ---- = Li,IV
eP,l
(rr'r)
9,r{1df,r g 1 'g :qo 7
8I'e 'rqo
.(Z.e peplu^d A^) nueqoyod
rurrupo,rgd s alq?qou ol nosf q-aluoru od prud {qo1od aq .Jua;npoupafz e (9,ro1u4;d auelsgz g4u2,{rs
acrufods) nure..q ur?qnl opuolop eu qr1up,{ts ;ug1s;um o1r7nX,l o1,{q ruo11;4 .17_uluour od nrrrB-q oqaqnt
sl€uoTop e grud uqolod aoe?evnu flra o1rg? af n-122. rqo n .gl.e .lqo apod eure;ydeu qu;upod
IrpeuuoJaq (9e t) lcTu or emod eurelpnod;uaqsl 1;Jup o.rd e (9g.g) .(1E.g) ecplor 6urllsnd.{A hrnp,.u
oqaqnl al"uolop g nda2 u9u1o1o n lU oU 6go1s seu yfeurrlezau e ,zN e tN {Us tlrslfz .{pe1 lca1rud
^ u?deu lr?m eqap af ru_epe'z alpod o? ?truol I urepe1F1 .auprzou r.gig nosf qc;cnnol qcas eA
3
3
3nre
t a Alqrupod e{cqels 1esd
ezl nlelsnos nolrpm {1cr1u1s noppz^ oDlst ord .(LI.t .:qo) 161 nps no^olsp eulgpgplodpo;d 1 rurud
A W nolls no^orlBl etxlperlPu laurpg Toqel I run:d ur;upuetspo aurapelord ,itulmos ;ugqo,rg
:luaraa
g = gl uts. e. 7. rN - nr1t. s. rf
g = gluls . zy + nuts. tN - ^d
: BI
T
:.N
g=glsoc..1t1 -nsoc.tN+'A : "N
nyvlt v nHVt oHil?AnfN AyCttvts Aovdlad THcnooNoJre
'L8-
'd rrcryp oua{pgfX^ aqes "u r.r:gnorl ;ueqosld gnurafgz,r af cp)t .02.€ .rqo eu oue*uzuu
af rupulo,rg .rgruolod 4u[ap la^moq eqo ord p,role,rn ;uaqnpoupafz o.rd orqour ef , ru?ruolod
I?tl^ ?Ptu nosl ts 3 rs ,,fu?uzo: a7oto.r6 frprnau X1oqe6 pedu^d o es gupef 1r' ;tso1qc,{r no,rolqr,r
s rcelo: euaqo.rpod (6t [ 4o) ^lnrmssu ?ulo^ nprn Ez oqas eu nosf 9:at1 Tl_pFepur q34uz[l z BT{noq
nolp Blelsnos rt-apng 'nT^morl oqlc;fn1or tsopfdeu eus;ag u1,{q qc{rpm ,t1cqe1s r.lpedHd n
A47nor1!r!Jnfo1 9't
'FroTltrl"z w.vzo^ord gd eclnusuol
lu-Dqgurpu ;q19,rru4;d ef ua1y3 gqsXurg l,relsnos op ;rpdeu 14_utuour eu4;9ua ,(p191r1 :Drlwpuzod
'Bln:d Fr-uqgu?u ?uqerz rTpuoru od ;qosgdz
(rurr gE11 qnrd ac19p eu uru g'g) lsousa;dau Fqo4fu gleul ?ur?ruod e? .gtlla;z at 41pe1sair 7
o0gsoc-+
I
ostsoc.o9t zurs
.0t zuls'Z
(qer) leawl r'zr =
()pI1) lsawl s'os =
e}t.z'z 9'0
O0S'Z z
o0gso3.o0turs ostso3.ostuls
.sluls .0Euls. z
sot.z'7
p so). D z! s
d ,uts'7
v'!l
aur-?^9lsop ruolod ruazesop u.rgulesl? od
V=_ =,o',
nosf pgdeu guepalg
00S t
s'0
Y =,o.N
gl soc '.+
I
ff='*6lsoc.glurs Dsoz. Du,s+_-,_a uls
d uls .Z
v'3
e':=,^,
c
eu,{1d (69 g) e (9g E) cruor uryraqag
(6e'E) gl uts . gl soc---T- d uts e-e
v'1 I
DU|S.pSOs
,^,
g-rerd9 od aueuelsop (ag.g) nqqz,r op (gg.g)
tru or rfsJul_ellp.! ur,ruezesog '$rld) + o{u?uretz al Lw otd rcrurror ;q.e4z$ e^ e?Jel tpelnos ^
ef?oc?'?nrrudpacgrlzue>pc1s1iraf91'6.rqoapod€nltsno^oleFogupates,rZrc?uuoJepn
L tsoN(sd v tsoNznad
- z8-
'(dlo g2&u gt'opo^qo ?uspelq epnq rDF-noq qrezol ^ B ol n)pp po pp ecrupelsl0r lrqoqd apnq
f.nq zu
dp urelq4 ur,{,ropags 4ur?ruenro (q 12.g .:qo) tuoruala auaurf,{,r nT^moq Z (s I Z.€ rqo) d ryF {uappzor
?ueulou^oJ nlu sz lqoqtd FaLI eu ? ,Clll 's ^lUnon r nryrolod u!runru o {o.^moq aIlrQN
'd nI?[ po n2deu g,ropo,rqo ord
tptz^ lrpo^po eqag e[ arudfau ep .d n4ep po ruquolod nu?u.v trpo^po az1 uraqosgdz u-r{uqopqg
(sr e)
@v s)
aJBlor lulsgl^ po
(€r'E)
\(9 L'
(r'.s)
(0t'f)
ord aura;yd nluJurpod
I
zort'o
=(o))V
J =(o)'3
z(D.zJ.d
eceror po ru?uJolod euguz uolod e
n{?noDl
(n:?rus u.r9^opo^qo ,r paTrolpord 9u:purod) ac"urroJap glopo qo gmgruod epnq
zo. z!.d = (to ),o
et (7 e1o1rde1) qTnoq u4.f trqol ^ Indeu grr.opo,rqo a1o1or6
-n4ep paqosgd po wgntolod euVtn . . (d)tV
e."tor Fqs?l^ po ru?wopd evTtn ... (to)tV
(d)rrtV+(to)t)V=r!V
(d)rtv-(ro)rrV= lV
epr
?ulo?qo
ttv = /v
nre,g e,r 1 rgurolod {up{p ord fpat .Ju?qo^n olsrur
ru?BrruoJaq 'eur?llan elr?mou ,{1cuu1s geno_rgz e eurywz.tt uulpef ef d ry11
0z'f zqo 6t'f,'rqo
nyvlt v nHVt oHtrlQan3N Aycuvls AowNetHSnooNojFT
-88-
,1 .rS t1 .tS
+ -- ---
(8t e)
(0t t) Jcru^or op ruluazssop
\Ln t)
(9r's)
('a ?t
l.a -,a )' ,' '
fi=ror'
dtp. t. q. d = Op = dtp. s. q. (d ), o
=d
'a ''s
nre,r1 a.,\ tupgf ^ ecru,ro.r olgl z ez1 d ryn 4uryuzaN
'? '3''s 'z-j:{+
/n-ra=7-d
-- o'-iE
surerjulsop
qclfaf e (7y g) e (tt e) r,rqplz^ op (w 0 e (sy'g) cru,ror ulruazesoc
f.s=
.=(d)tv
,J .d
d rupl po ru?ruotod eupnrz molod u
3'szt = (d )te
t'd (d)'o (d)tv
apnq d qen po ug^oponqo ru?urs aA peTnolpotd grugruo6
EoqQz
'r 17 9 rqo apod 1ge1d lsnu: nluarualo Bu lrs qrlug - rrr--
I qcllhu nrlB^ou^or ot4 s.g.(d)to usoTla^ o nlls le^gp s.q alold eu apng ugdeu 9^opo^qo
q.dtp-t.d =6p
a7 'gufay at nnzetqo 7
I Z'C 'rqo
(a(q(r
J,Pq.,d =
L tsoNAsd v tsoNznad
(rle)
(gg g) ecru,ro: op ruruazesop qcrfaf z
\Ln t)
(9? S)
(t
'88 -
'z.'s '1 .ts- -+
II _=d
('z ?\I z4 - t; l' ,to't
\- -./
nre^l e4 lqDgl ^ a cnttot o1g1z ezl d {ell 4ur-EuzeN
'Z ''s 'J 'J.'s 'z--------------
-
,J.d ,o.rJ.zd ,J.d ,to. rJ.Ld
eureu?Nop
(Zn t) u (IyO r"rqep op (tt t) e (SV.O rruAor rrrruazeso(l
f.s:
.-(d)tv
,l .o
d nl1ell po ru?tnolod euquz ruolod e
3's?t
t.d (d)'o (d)tv
apnq d rupp po ue^opo^qo ru?us e,r paTnolpord 9u:pruo6
j 6=ror'
dtp - t' q. d = Op = dtp. s. q. (d )to
?oqe? z
'c 17 g 'rqo alpod 1qu1d 1mu: nluauale Eu lrs qclulrrr,:.
I q.ltFu nrle^ou^ol ord 's.q.(d)to Dsolrle^ o nlls p^9p s.q e;o1d eu apnq pgdeu ?^opo^qo
(q
q.6p-t.d=6p
I Z'C 'rqo
aq'ql.ufag. al rrytqo 7
(r
: q(d)h
$pq.,d=
- v8-
{qe1z,r ppdeu ord JlaryWf,^ (gp.g) ,(9y.0 4qey^ e 97.g
'rqo u41?nod rlcp?noq qr4^rpoupaf ^ pgdeu 9upe1s{,r lgsrlz ez1 d n:pp oq?u.l?odd^ ?pe1lgz eN
n0l.z'2. f_0I.t 0I.z't. r-0I.9
lualrrl ls'o - [ea] lturgs = ,l I =d
(uot'E'z rr0l.z'r) / ot \| -_- _ __-_ l. |_ l.2.0
( for.8'r ror.6'8, .\ooot.tl ) - -
,{1^znor4 rzeur ruaqosnd 9rro1e1l 1ut;2od,,tr oqoru af (gg.g) nqelz,r epo4
:!uaraa
.uIuI 002 :J .ulu/ro 000, : u ^pI .rrslor rld
unu t : zs 'edl{ sOl.Z'Z - z3 'rur781 ,91.9'4: zfiuru 9:,s .EdIAI e0I.Z.I :,J.€ur/EI e01.6.8: rcl
:oupo
(r) raz-noq rus$ !r-ef ,6r., .rqo apod q.!'?no-Dr 0",",r*",T"jlffil';Hift1"",rifit-
z'e pEptlld
{,{toldor) n rago po ruguo1od lopnrud af 4V.n = (|ry ap1
(d)rrtV+(lrrV=utV
(d)rtV -(lrtV = ,tV
e4 'olueyd .{q ap1 '(Zl e) '(t I g) qclcruor rr e1,{q ,(q eugur2
'3. 37 o fig;qo eqo glod e ,$nunseu aqos eu nosf groq lpFepu:
qcAuzy z 4a^moq qc{uqopqo no^p ped;;d 1 1y;a; as {q uaqosgdz rrfuqopod :olwpuzod
';ualqppo qcrfaf l rceror gd,(q olgop
',{uafods qu,rod (1,(qeu ,(rynor1 ,(q e7r11so1 '(uere,,rs 'gdau 'yuafods oqgusd qcrfaf npegodpqd rz)
qat e[ II 1 i$gznoq zaur e p I a -rrta '] r
']4i(p:J
pu2euo;
? = d urotod r" =
t+a7'ppedsd
1
'{?ll af ll I ^Tznoq .,au a p 4 y' urolo o'
r?.
tE
uo*,
nvvlt v nHVt oHilQansN AyJuvts AovdlHd lHcnooNosr 'e
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luawts'rs = [ear ror.qr'a = -i:t':-*.(on#t) iZ'o',0r'8'L =,,'o
leawf s'ut = [ea] ror'sr'r = # ,(rn#t) 7z'o'r0t'6'8 = ,'o
epnq Jueze sop ul?qasl? od
zs
fi * rr' rt' zd = (d ) rr'o + ( ro ) rr' o = rto
-L- rr-rt.Ld =(d)rto-(to)rto= r'o
L tsoNAld v tsoNTnad
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p?deu qcf^ol^urs lua?Btz llgpoupafz aua74u >7el e fil =^xt ldeu a7 'aua4-u1op lQPzod
.xA| ,'122 ,zx| 'n2 'zA, 'Att e zg tt, 'xg ppdeu 1a^zo1s 6 ?uceqo euryIsF {eI ru oIIDJq oq]uJ-?lueul3la
q39u?ls qcal^ al auspo.,ro:d pePlzol olual ( glzjqou^or ppdeu oq9,ro1,{rus eryo1s -eue,ro7e.m a[ 7,m
s '^so r?urs qqerz xapur i(qnrp s pel p?dsu e^ol,{rus o1o1 4u ,r '.{ur,ror npuuou 1lerz 99duu qc{,ro1^urs
n xspur !u^ld) 'zx7 e ax, !t?d?u ?^ol^urs aureu?Nop ,el e 2 e,( nrjeso s qcfqgqouor le?ots op
eu!?olzor ?UO[ d etlelsou "u ppdeu 9,ro1,{rug I aq*o.t rr rcp.a1 d ,{4uqd op e (xo p?dsu ?^olBuuou)
u .{puuou op,^ F?dBu ?upels4^ eul?olzor (qI t lqo 21 ) x 3so { ?lt{olt pur,ror 'r ';de11
'lqosgd
?ru A 'nour^oJ s -e4,rs pgdau o1o1 ,{:aq lxelqrl ?ltef le^4qsz as.er4nu ol,{q fq,{p1
'a uppdzu uta{meqo
s rJe,rorado uroqc{qfP)t 7eu '1;fgopoq{,r uaqorrur qcetpda{,r ud o1 e1 'p^a1 ?m or olgl ^ Frp " ?uqol
;qosgd nu ^ ?rIr^or r?g^ of 9ru4 pqdeu e,ro1,{uls a ?Aol-?uuou Bu arugoFoJ ;ufu p2duu o{el z^ e
tA 'xA tf?deu;qosgd z1 y Jqo 3u nlouejq qtqu.l or A lsouloz-su nolorolso.td }Fdel old smod ul8u4^
lleur nllouurq ,&?uzor gu?ouol 3 ssal?l npoq lu?uloz-unz ol ef a? lnnop?^n IBI^ Is ?qon 9f
l't 'rqo
(E(q
tA tA
z
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,l
na ?A A I'(e1 9 rqo) lalouurq yupuaurala fiao 1r1se-q qclclqoqd qcm ,r opdzu qcfiryqq d e rnao: 1p
olqo?t lu?uloz-eu u.{Jgerfl ud uelA^z gMg uapoq orup qc{ue7o1ord qcgur,ror qc,(ur1o19uuefirzr qcep
e,r lcrqosld pgdzu q-eum-rz 'EUa?m ?u$rzoupel "sepl ?poq u?I?m ^ af $op[deu o? @Top .fe,Q
$opfdeu (esooupaf) g,ro1urg^d u 6opldeu (gsoto,tp) guur,ror nosf llsolgfdBu ?,roroFord .eueqo '(pedu^d
rurnq$Bl^z 'osalfl ?u r.qu1pr,r qc,,&rop u4uaqoeld -s-rl.IE 4rtDl '?sel?l ^sF frgm eru.e,{zuu Fsop[dsN
llsol8JdBr ,(qn.rp - fsofBfd8N I''
INsuo^rsud v IrgdYN'?
lNlUOMsHdv UldvN',
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rlsolrls^ o (qz t rqo) ro u?deu ?^oBrruou apnq lunjd oso gulgpod { rll?ullol
'nzel tuguall^u ^ urolod ?z t lqo J nolls no^oso u-Eqetueu apnq v nzellljd owr4e$uol lrud ?fp)
(gsoouPo$ g,ro4u;;d 1so1u[duP X'7
'nosooupe! oqau nosofo,rP
ru olzf tsotufdeu uu lazqqod lugqgtuuu qraprd;.^ld qlflo;19u a azl nrlouurq oqJul9lueuale
nqo;od nolrrn oJd omod 'eso[o:; J1;1 'eaorolsord lsolnldsu ^!lotlgJ,l{ af Euraqg
:larrzod {tr7e1gp lsaln nPoAn,r pauq Xpet aura4lp1 g,ro:olsord
rlsop1efdeu ,{pedpd ruryularcads nosf lsotefdeu 9,to1urHd ? guuhol eq 'gasfap ef oq91;epe;d 7
'(nosooupaf) noaoluqd
lsolefdeu o gupef urotod es ePZ '^ = ro ,t17ols e^oplluou nolunffl s ?^o1nu 't>go1s fuqceg'r
nopnq'x noso s atq?qou ol af0+x^ eg=za =Aa p?deu guoaqo ldeu,{p1 !ed;;d Jrqarcads o:6
'(asoto,tp) 9uqr,ro.r usolefdeu o eur,'tn1rr epz ?^oFu nopnq fryz.o1s ;ureno
e,x e Ao'xo ,Cvols nopnq ol cl ? lqo n ,tx nour.to: s 7qu,ro: grqgqouaoj ,(ryo1s Xuqca;'r nopnq
'0 :z^ e Ax norn^or s ?tq?qou o.l ?ul^ol ^ I?al'{^ e x^ (vl l rqo) pqdeu gucaqo ,{p4 'ppedgd n
'qsotefdeu (gsofon) 9,roro1so.rd o e{urlnlul ',{1nu po 9tzg gureqo gqdau Xryo1s fuqca;'r
nosl aTrpsel rlgpzod ouqupo,rgPz apnq ?oc lqtouerq uryuerq I ?uolser{eu nosf ppdau g^o{^us
rI'' 'rqo
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LI'''rqo
'r Aso n1s,{urs urgurodgz ^ nusrEsrp ?Aorqohl

p?deu ?^o{^rus au4p_"uA ryd '(q11'7 'rqo) r
urg?deu s rl-au,tlds a {o?r?n: qc{^oulpoq Jue?ol nlsfus uord 3pr laqqr o noJerurou ladoeu q-au4?olood
'urpoq {a?r?utt: nqfqod nF,(us e^ Zpr o;u,otood u"d nrppdeu otrrrrt s auflds (e11'1 'tqo) u elgrruou
!!Qu e4l$et ',{pqs1 r ,{so n1s,{urs urgupe1:1 ^ mue.r3?p s^orqol l op eu}lguf^ F?dBu ?^oI{ES
'nunferp e,rorqor{ op F?dsu qc4^o+(us
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eF9al ?)pq?ulelstu olsrPaFl z nost?qo e p?d?u g^olflls gue?ups tltosf L e, qrgul^or ^ t, p?d?u ryf^
(r(q
NIAOM1UdV ttldvN ''
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6I't'rqo
'2, ury?duu ur,fiolfus e ro urJpd?u
udropuuou :nlacrups{nos eu_pp ("61.t lqo) rcn&nrx ?^olrlol,{ Bu ot(gl.} .rqo) | uur,roX .lsopfdsu
nouep o:d lrnqrrDt n^olqot\ aunfo4sas eagple5l .e61 g .Jqo BU oua?Btzpu af rua;e; 91cr-p.rg
:1ua;a4 mc{ntg
8I't'rqo
'?qe?od e iq.rJprS
e1.pa,r.ord ruele1 sdl4l 0S- = z, ?d14i 0e- : ,o .Bdl,\ 69 = ro lpaf (g 1 I .rqo 2r,.,) 1aprpru qcf,rourpoq
Iue?elo ru?urs qold o6t =, loqg o I finror po ?ua?olo d ?ul,rol t dt e do fryo1s a1ag3
I't pBptlid
'rJlqqrr.ot ?^orqol4l Bu poq 4tl?m uazEud pqazoupef ry1etd llzelwe;,J:cqo ^dt edo g;ldea
1a7o1s rcrforrp gpge;1 (17 1aqr.r o ;ua^rorood) rcrz-rurf noleJ euqiqo qcgqr^or olqc?l ^ I?dRu ^{?ots rcrtn?m
1cntrn-u ?^orqol,\ su poq ruollld I 1aq4 o d za; os q-poio lfudra?,{^ es pag ,{qo1od grqou ,{uqcal1
'quamala ,r d eur,to.l o1e[
nls/(u$ ur?ufo$ en afnq{qod as lcn4nDt ?^oJqo}\ w ,l pog .llsou?olDF e^ zel }?-?lo os 7eu 1fa1qcf.r
(B(q
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epnq urolod nls,tus oq?u?€do ?pol ef leqB 4up"u
',{u:odez oryf z ItW} lu^ozvsop ?pedgd olurot,l eu4snu tI t t g1 7 r.up-e.rqo epod
(qgt l)'(egt l) dt edo \ldeu A17o1s ord lqBlz^ Iuazo^po I ruaparfz eE 'l\T,e^n;uapel ur;rqa2od IJd
arulsnru '(0z t rqo) {opr?n: qclirourpoq lue?glo nls^urs a^ eryqoluel .08 = z Iar{B {ufats o | .{ut,tor
op ?ua?olo n Qurnor A " B io i{-Vols 1r?rn 1sopfdeu noufa;s ord ll?ur uoqc^q .T!1ls6l :o4upuzod
'urrua;e; uqtlcr.pr? s 2Poqs e,r af o1
lea^l ls = "ngror. (os-)-"ot u,r. ffi = o "
/ \ L L og
led t^ l 8'S- = o09J S . 10 9- )+ o09 sor ' - * -:------:----------- =(ot-)- ot
lot-'1+ 6e
(qgt t) '(egt l) BrPtz^ op loupoq q3^uepez ur,ruazsop euePe^ord
:lual24 !ula?o .o > eo gutdv) 9^oIeD nosf Fd"u Iu sH ?qo 'z
st't 'rqo
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a^ 'ullo-l ,{qo1od ale2rg 'ngduu oqe,rolfrus oq1rprurx?ur ruoupoq " ppdeu qcJu,rqq qso) la^ ete?m
(e S t rqo) sdhl 0Z- = r, e Edt\ 9g =,to t4y1 S9 = ro ml?vols guepez qsopfdeu ?uuhor f)
t't pBFU{d
'(egg t'rqo) 6 ?w^or I ?u{ol
Aur,ro.r Xuqoaq,l. nosf rulelq a1 .gutfapoureg .poq ^ rr{ acnqnu ace:eua8ap qpalsBp A or{ouur
?u?auo{au l?do ef unol olqr?I }nt laqr,r g nouhoJ s lfer;,rs 9ra1:1 q._?ur^ol qcapr o,r yqosgd
os't 'rqo
0 =?D
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pgdeu g,ro1,{rus lul_"uuxet^l lu?otoE e6 rrt e crt rJlr&nq e poq ^ afiuaus8op ,,ry acnz-nry
'q6S t lqo uu ou?uon, uz at 1ef.;cnz-rur noulpaf ualm urer€elp ^Erqon
af '(sos t .rqo) o = ro = ,o Bupoqs psopfdeu armnor u^d ppduu ;uqq gqo nosf ag .?pedHd A.t
''p i$lB t B , rununor s yfe4,rs graq !c,er4,ror ,r ;qosgd e
z _,o,,,
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=
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aur_B^s-lsop ('l i) e5ru^or lr4ll?nod
:tuata{ }uta?od
IS'' 'rqo
'fll loqr,l I 'r'lcnutlor nuluaelq s lleryrs ae o Aw'ot eq"g.uu lap al q $ t'!qoZ
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nous^olr-p? ,{uapeuzeu nosl ruIz-erqo a7u91 n usorfdeu A{?ols gutoqo euupez ;qosgd qcgu?ls ?oqef
^ 'DllotrBJq oq;upolgd eqolod eueqeueu of mrerel u.{aue1 'nueral nu,.fups t IS't 'qo rr '{u+leueu
nost g e I . ur,ro: lurrelq $tnlsF^d 6 n1q1 ;coruod our?m ?o l? ro nqduu qcJuirelq m,ror '(q