1Qa5, c, Contt,2.b ·. ~ ·.
--.... -- \)\ ~, '-(e~\ Ccm~uno,n ~ec\co
----- --
~ s'1rnv1e \n\-e,r-~5\- -t> A. -=- ? \ , + i. n)
l .
(
(\X.'('('\
4 1-\irt \)\ll C.T'\G'x'...
"'°'\>\'-\~,
... corn9ouf"\Q ·,\'\'\ e.t t::,i' -t> A -=- Vl , t t. ) n c. orn9ou0d~ ,;>e.c 'lee\'·
('('\ '°' flO. or;:-
4> ·"n ~ IQ h O\"I
-\:> \'-=- 1"-l Hi ,-n Y> Of\0\JQ\'I =- I
1...-t>~-\-n\'-j-:. I'd.
'-1> Serf\\ / 'o\ / Q(\'('1\...\0\ 'j "" ~ 4 00\ l'I -::.. ::ib~
Lt> '::IC.l\Cl{'f \nc.teO'S\'. / Q\.".(.HClSe. . . . . . - - . . . _ .J • \
l...t> C\IJC\C '1-e-"'1 .,. 4 Lo "5d--
\f\Q\\C\G
V"('.e,~\..., -:c
Lt> 0\\1 inc.ti;:ast I C\tc.<ease.
rno.\f\S) "--...
~
Ncm\ f\Q\ e.- £ ffe<::H'le \ n ~ ' r rote, ~
1)e~r~u_Q~On :
..,_ - -
"\,f\eQ{ \on c.ast p{\u:,') ~ :i'wny\e. \C\teresi' ._ N)m\no\ : ,o\-e v-,1 <orn~uf"\CinC) ~iod Lexcep-t onf\ucu.
i< effe.c..t°i'le. :. ro'le ~I Ot\<\\.\Q\ COffi?()Ul"'Oin9 pe.noo
4 ,,._ =- Pl, - in 1
~~ ct1:.9. to e~Q '--1> O\v-..,c.,.'15 s1,9nn't "''9Y'1er tnon r,omi'0cu..
-1<- {ech.K\r-C\ bu\unc.e. -t> c.om?O\.md \t\\-tce-;\" :1<. c.Gn'-le.r<o\~ tQ{ rnu IQ C, 1-.:)0,- ON FORM \.)LA ~'t7 ct\]~
4> />\=- ?l.,-i'{'
Jf c.cm·~ ~?- -ro el':{o ltte~-=-,, +- 1 rorn
rn
)~
" c.a1c.u1m·i f'I<\ F-- \.\~i r,q rorn,na\ cote ·.
( irorn \ f'\)lm
f\-:. ? \' -\"" ~ j
-..c_a,c..u\a\\n9 f\ usi~ erfec.ti"~ cme:-.
A --=- P l , ~ i efr I'"'
, _,.,.,------
lheore.m 1 ,neorem :i
-....,___
i~ . . . it H,e of'91e made l,.. -- tne cef'tYe o~
ki ~ a \int. <ol:.O{"e('"'l't I= r om \ne. 0 \
D c,cc.1e \5 -\v-1\Ce t\.e 1:1\-ze cf;
<.en\fe. lo1f\'o TO ~ rn1d\'.x:l°1("'\\ ol= a
1 1 l) ,/
"' \ \->ne o..-,q1e moC\c ot -I-he
c.nofO ➔ ·, t ·,~ ?er?e(\C\\<.u\ac ,o \-'re
c,< c. u-rn t e.r ef"\C.G.
c.nocd. A
+ne('\ "-M ::.. M'3
------- 'B
I
i~ ...
* -.~ a \1f\e, <Secr,em tiQ'l'(I tne i'f'I .. . Cl . '>\ Cb ~ 0 -:. ?..C
I O )
0
\_ ~~~ +c:,
<.1!.n\'fe i-:, ?l:.t9tr\C.\iC.UIOt" \-Q tne
C.Y'\QI" d --t> H,e C.r\Ot"d \';) \Jie,cc.H:~O . ·c
A. I M , I"- Cl
"--._, _/
>
I
,.J converse -- o -=- J.c
+nef\ OM~ A'3 ~
A
ano ,.. "
M , ~ Mi. -= qo•
\JC\\ dtO
C.
o'C\ -\ht. f ,,? 1:>-.oe or ... 0 ~ ~c.
. -"Theo,cm 3 CJeorne\r'i
11
t'NO cro,as e,11.\-er.c.\if"IC\ ~mm \-re
-theocem '-'" - conve15e-
c.\iu1·n1~\et 1N\\1 mo"-e o C\0° \\ ... A.
I(+~ CIIX)le-5 ~c,e O\ -¥re
c.11'\c:i le. wneH: 't~'f mce:\.
~ c.\<c.u-rnf"eYenCe. me e.Quo1 ·,f- tne A B
c.norc.le, ('("Q't.·• ~ t'r-.e ON:)le5 cofl"e
• 5 il"ICe. ?.. 0<'9\e!i motle ore.
l=cc,...,--. me. some &ec:)rr,en~.
\-\-\en A?; ·,"' ~ 0\0l'fl e,\-e.< e.(\\JO\ on 0 \',ne '5~('{\e;l"\"I' onO
\ c.ome
·.~ ... hom
l(; ____
fue sorr-e or\c.\i0c\\
""
~ ·
\IT"le S~ffie.1"'\ I -\'l"le rou r
·,n ...
• Ir tne. Clt'C\~ rooC\e 'o'f tv-io
?Qinte, 0.1"~ COi'"\ C'f C l•C.. l 1\e on
(00(05 i'o C-\0" tr.en H,e.
1 ,. , I <:ir 1;... v,'<' Fa-enc e.
bo~• t(Ql'l"I -1-ne one c.rorct -\o B
h-en C. -= C\O" ""1e. oW'\ei ""\" be. tne
D :. C. s\'f'IC.e +~ C..'t"'(){C,\5
'-<::> <:,mc.e D O.<"lc.\ c. ote. 'oo'tl"'\ c.om\r<.)
c\iorne-\ eA •
~,o""' "e ar.O o.c ~ 'oo't\-o ~C\\l o I Oi'
s\m\\n< ''f ·.. fon·nll"IC) \-'t-lcrn 'oo~n c.o=e.
DC.. ·, A ,'o ,( O<"IC\ 1) C.111 \\e O'f"\ ~',-,e
,- converse - ~TOY'n '='eqroe'<''I' /'\t,.
c.\ rc..u'MFerence ·
, (c.oWLLAR\£ 5 ON --n1EOREM i
4 ex~ra reo~ons
- - - - - - --
\
* e.qoo\ cnorct5 f<\O\:..e. equo\ o~\e:,
0\- t\r\e cenh e .
--.... -- \)\ ~, '-(e~\ Ccm~uno,n ~ec\co
----- --
~ s'1rnv1e \n\-e,r-~5\- -t> A. -=- ? \ , + i. n)
l .
(
(\X.'('('\
4 1-\irt \)\ll C.T'\G'x'...
"'°'\>\'-\~,
... corn9ouf"\Q ·,\'\'\ e.t t::,i' -t> A -=- Vl , t t. ) n c. orn9ou0d~ ,;>e.c 'lee\'·
('('\ '°' flO. or;:-
4> ·"n ~ IQ h O\"I
-\:> \'-=- 1"-l Hi ,-n Y> Of\0\JQ\'I =- I
1...-t>~-\-n\'-j-:. I'd.
'-1> Serf\\ / 'o\ / Q(\'('1\...\0\ 'j "" ~ 4 00\ l'I -::.. ::ib~
Lt> '::IC.l\Cl{'f \nc.teO'S\'. / Q\.".(.HClSe. . . . . . - - . . . _ .J • \
l...t> C\IJC\C '1-e-"'1 .,. 4 Lo "5d--
\f\Q\\C\G
V"('.e,~\..., -:c
Lt> 0\\1 inc.ti;:ast I C\tc.<ease.
rno.\f\S) "--...
~
Ncm\ f\Q\ e.- £ ffe<::H'le \ n ~ ' r rote, ~
1)e~r~u_Q~On :
..,_ - -
"\,f\eQ{ \on c.ast p{\u:,') ~ :i'wny\e. \C\teresi' ._ N)m\no\ : ,o\-e v-,1 <orn~uf"\CinC) ~iod Lexcep-t onf\ucu.
i< effe.c..t°i'le. :. ro'le ~I Ot\<\\.\Q\ COffi?()Ul"'Oin9 pe.noo
4 ,,._ =- Pl, - in 1
~~ ct1:.9. to e~Q '--1> O\v-..,c.,.'15 s1,9nn't "''9Y'1er tnon r,omi'0cu..
-1<- {ech.K\r-C\ bu\unc.e. -t> c.om?O\.md \t\\-tce-;\" :1<. c.Gn'-le.r<o\~ tQ{ rnu IQ C, 1-.:)0,- ON FORM \.)LA ~'t7 ct\]~
4> />\=- ?l.,-i'{'
Jf c.cm·~ ~?- -ro el':{o ltte~-=-,, +- 1 rorn
rn
)~
" c.a1c.u1m·i f'I<\ F-- \.\~i r,q rorn,na\ cote ·.
( irorn \ f'\)lm
f\-:. ? \' -\"" ~ j
-..c_a,c..u\a\\n9 f\ usi~ erfec.ti"~ cme:-.
A --=- P l , ~ i efr I'"'
, _,.,.,------
lheore.m 1 ,neorem :i
-....,___
i~ . . . it H,e of'91e made l,.. -- tne cef'tYe o~
ki ~ a \int. <ol:.O{"e('"'l't I= r om \ne. 0 \
D c,cc.1e \5 -\v-1\Ce t\.e 1:1\-ze cf;
<.en\fe. lo1f\'o TO ~ rn1d\'.x:l°1("'\\ ol= a
1 1 l) ,/
"' \ \->ne o..-,q1e moC\c ot -I-he
c.nofO ➔ ·, t ·,~ ?er?e(\C\\<.u\ac ,o \-'re
c,< c. u-rn t e.r ef"\C.G.
c.nocd. A
+ne('\ "-M ::.. M'3
------- 'B
I
i~ ...
* -.~ a \1f\e, <Secr,em tiQ'l'(I tne i'f'I .. . Cl . '>\ Cb ~ 0 -:. ?..C
I O )
0
\_ ~~~ +c:,
<.1!.n\'fe i-:, ?l:.t9tr\C.\iC.UIOt" \-Q tne
C.Y'\QI" d --t> H,e C.r\Ot"d \';) \Jie,cc.H:~O . ·c
A. I M , I"- Cl
"--._, _/
>
I
,.J converse -- o -=- J.c
+nef\ OM~ A'3 ~
A
ano ,.. "
M , ~ Mi. -= qo•
\JC\\ dtO
C.
o'C\ -\ht. f ,,? 1:>-.oe or ... 0 ~ ~c.
. -"Theo,cm 3 CJeorne\r'i
11
t'NO cro,as e,11.\-er.c.\if"IC\ ~mm \-re
-theocem '-'" - conve15e-
c.\iu1·n1~\et 1N\\1 mo"-e o C\0° \\ ... A.
I(+~ CIIX)le-5 ~c,e O\ -¥re
c.11'\c:i le. wneH: 't~'f mce:\.
~ c.\<c.u-rnf"eYenCe. me e.Quo1 ·,f- tne A B
c.norc.le, ('("Q't.·• ~ t'r-.e ON:)le5 cofl"e
• 5 il"ICe. ?.. 0<'9\e!i motle ore.
l=cc,...,--. me. some &ec:)rr,en~.
\-\-\en A?; ·,"' ~ 0\0l'fl e,\-e.< e.(\\JO\ on 0 \',ne '5~('{\e;l"\"I' onO
\ c.ome
·.~ ... hom
l(; ____
fue sorr-e or\c.\i0c\\
""
~ ·
\IT"le S~ffie.1"'\ I -\'l"le rou r
·,n ...
• Ir tne. Clt'C\~ rooC\e 'o'f tv-io
?Qinte, 0.1"~ COi'"\ C'f C l•C.. l 1\e on
(00(05 i'o C-\0" tr.en H,e.
1 ,. , I <:ir 1;... v,'<' Fa-enc e.
bo~• t(Ql'l"I -1-ne one c.rorct -\o B
h-en C. -= C\O" ""1e. oW'\ei ""\" be. tne
D :. C. s\'f'IC.e +~ C..'t"'(){C,\5
'-<::> <:,mc.e D O.<"lc.\ c. ote. 'oo'tl"'\ c.om\r<.)
c\iorne-\ eA •
~,o""' "e ar.O o.c ~ 'oo't\-o ~C\\l o I Oi'
s\m\\n< ''f ·.. fon·nll"IC) \-'t-lcrn 'oo~n c.o=e.
DC.. ·, A ,'o ,( O<"IC\ 1) C.111 \\e O'f"\ ~',-,e
,- converse - ~TOY'n '='eqroe'<''I' /'\t,.
c.\ rc..u'MFerence ·
, (c.oWLLAR\£ 5 ON --n1EOREM i
4 ex~ra reo~ons
- - - - - - --
\
* e.qoo\ cnorct5 f<\O\:..e. equo\ o~\e:,
0\- t\r\e cenh e .
