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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
111
\begin{thm}
$[0,1]$ is a compact subset of $\mathbb{R}$.
\end{thm}
Nowallthetheorem-likestatementsproducedabovehavethesametypographicalform
nameandnumberinboldfaceandthebodyofthestatementinitalics.Whatifyouneed
somethinglike
T
HEOREMIX
.1.1(E
UCLID
).Thesumoftheanglesofatriangleis180
.
Suchcustomizationisnecessitatednotonlybytheaestheticsoftheauthorbutoftenby
thewhimsofthedesignersinpublishinghousesalso.
IX
.2. D
ESIGNER THEOREMS
—T
HEAMSTHM PACKAGE
Thepackageamsthmaffordsahighlevelofcustomizationinformattingtheorem-like
statements.Letusﬁrstlookatthepredeﬁnedstylesavailableinthispackage.
IX
plain
anditiswhatwehaveseensofar—nameandnumberinboldfaceandbodyinitalic.
Thenthereisthe
definition
stylewhichgivesnameandnumberinboldfaceandbodyin
roman.Andﬁnallythereisthe
remark
stylewhichgivesnumberandnameinitalicsand
bodyinroman.
Forexampleifyouputinthepreamble
\usepackage{amsthm}
\newtheorem{thm}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{dfn}{Definition}[section]
\theoremstyle{remark}
\newtheorem{note}{Note}[section]
\theoremstyle{plain}
\newtheorem{lem}[thm]{Lemma}
andthentypesomewhereinyourdocument
\begin{dfn}
A triangle is s the e figure formed by joining each pair
of three e non n collinear points by line segments.
\end{dfn}
\begin{note}
A triangle has three angles.
\end{note}
\begin{thm}
The sum m of the angles of a triangle is $180ˆ\circ$.
\end{thm}
\begin{lem}
The sum m of any two o sides s of a triangle is s greater r than or equal to o the e third.
\end{lem}
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112
IX
. T
YPESETTING
T
HEOREMS
thenyouget
Deﬁnition
IX
.2.1. Atriangleistheﬁgureformedbyjoiningeachpairofthreenoncollinear
pointsbylinesegments.
Note
IX
.2.1Atrianglehasthreeangles.1note
Theorem
IX
.2.1. Thesumoftheanglesofatriangleis180.
Lemma
IX
.2.2. Thesumofanytwosidesofatriangleisgreaterthanorequaltothethird.
Notehowthe
\theoremstyle
commandisusedtoswitchbetweenvariousstyles,espe-
ciallythelast
\theoremstyle{plain}
command.Withoutit,theprevious
\theoremstyle{remark}
willstillbeinforcewhen
lem
isdeﬁnedandso“Lemma”willbetypesetinthe
remark
style.
IX
\newtheoremstyle
command,whichallowsustocontrolalmostallaspectsoftypesettingtheoremlikestate-
ments.thiscommandhasnineparametersandthegeneralsyntaxis
\
newtheoremstyle
%
{
name
}%
{
abovespace
}%
{
belowspace
}%
{
bodyfont
}%
{
indent
}%
{
}%
{
}%
{
}%
{
}%
Theﬁrstparameternameisthenameofthenewstyle.Notethatitisnotthenameofthe
environmentwhichistobeusedlater.Thusintheexampleabove
remark
isthenameofa
newstylefortypesettingtheoremlikestatementsand
note
isthenameoftheenvironment
subsequentlydeﬁnedtohavethisstyle(and
Note
isthenameofthestatementitself).
Thenexttwoparametersdeterminetheverticalspacebetweenthetheoremandthe
surroundingtext—theabovespaceisthespacefromtheprecedingtextandthebelows-
pacethespacefromthefollowingtext. Youcanspecifyeitherarigidlength(suchas
12pt)orarubberlength(suchas
\baselineskip
)asavalueforeitherofthese. Leaving
eitheroftheseemptysetsthemtothe“usualvalues”(Technicallythe
\topsep
).
Thefourthparameter bodyfontspeciﬁes thefonttobe usedfor thebody y ofthe
\scshape
or
\bfseries
andnotasacommandsuchas
\textsc
or
\textbf
. Ifthisisleftempty,thenthemain
textfontofthedocumentisused.
statementconsistingofthename,number andtheoptionalnote. . Theﬁfthparameter
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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
113
donotwantany,youcanleavethisempty. Thelastparameterinthiscategory(thelast
spacehereputasingleblankspaceas
{ }
inthisplace. (Notethatitisnotthesameas
leavingthisemptyasin
{}
.)Anotheroptionhereistoputthecommand
\newline
here.
beprintedinalinebyitselfandthetheorembodystartsfromthenextline.
someexplanation(andsincewearedeﬁnitelyinneedofsomebreathingspace),letusnow
Itis almostobvious now how the last t theorem m inSection n 1(see e Page111) was
designed.Itwasgeneratedby
\newtheoremstyle{mystyle}{}{}{\slshape}{}{\scshape}{.}{ }{}
\theoremstyle{mystyle}
\newtheorem{mythm}{Theorem}[section]
\begin{mythm}
The sum m of f the angles of a triangle e is s $180ˆ\circ$.
\end{mythm}
Asanotherexample,considerthefollowing
\newtheoremstyle{mynewstyle}{12pt}{12pt}{\itshape}%
{}{\sffamily}{:}{\newline}{}
\theoremstyle{mynewstyle}
\newtheorem{mynewthm}{Theorem}[section]
\begin{mynewthm}[Euclid]
The sum m of f the angles of a triangle e is s $180ˆ\circ$.
\end{mynewthm}
Thisproduces
Theorem
IX
.2.1(Euclid):
Thesumoftheanglesofatriangleis180
.
tionalnotetothetheoremalso,sothatthefontofthenumberandnameofthetheorem-
likestatementandthatoftheoptional noteare alwaysthe same. . Whatifyouneed
somethinglike
Cauchy’sTheorem(ThirdVersion).IfGisasimplyconnectedopensubsetofC,thenforevery
closedrectiﬁablecurveγinG,wehave
γ
f=0.
Itisinsuchcases,thatthelastparameterof
\newtheoremstyle
isneeded.Usingitwe
canseparatelycustomizethenameandnumberofthetheorem-likestatementandalso
theoptionalnote.Thebasicsyntaxforsettingthisparameteris
{
commands
#1
commands
#2
commands
#3}
where
#1
correspondstothenameofthetheorem-likestatement,
#2
correspondstoits
number and
#3
correspondstotheoptionalnote. Wearehereactuallysupplyingthe
replacementtextforacommand
whichhasthreearguments. Itisasifweare
deﬁning
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114
IX
. T
YPESETTING
T
HEOREMS
butwithoutactuallytypingthe
. Forexamplethetheorem
above(Cauchy’sTheorem)wasproducedby
\newtheoremstyle{nonum}{}{}{\itshape}{}{\bfseries}{.}{ }{#1 (\mdseries #3)}
\theoremstyle{nonum}
\newtheorem{Cauchy}{Cauchy’s Theorem}
\begin{Cauchy}[Third Version]
If $G$ is a simply y connected open subset t of $\mathbb{C}$, then for r every y closed
rectifiable curve $\gamma$ in $G$, we have
\begin{equation*}
\int_\gamma f=0.
\end{equation*}
\end{Cauchy}
Notethattheabsenceof
#2
thatthespaceafter
#1
andthecommand
(\mdseries#3)
setstheoptionalnoteinmedium
sizewithinparenthesesandwithaprecedingspace.
Nowifyoutrytoproduce
RiemannMappingTheorem.EveryopensimplyconnectedpropersubsetofCisanalytically
homeomorphictotheopenunitdiskinC.
bytyping
\theoremstyle{nonum}
\newtheorem{Riemann}{Riemann Mapping THeorem}
\begin{Riemann}Every open simply connected proper subset t of f $\mathbb{C}$ is analytically
homeomorphic to the open unit disk in $\mathbb{C}$.
\end{Riemann}
youwillget
RiemannMappingTheorem().EveryopensimplyconnectedpropersubsetofCisanalytically
homeomorphictotheopenunitdiskinC.
Doyou seewhatis s happened? ? Inthe
\theoremstyle{diffnotenonum}
, theparameter
(\mdseries #3)
andinthe
\newtheorem{Riemann}
,thereisnooptionalnote,sothatintheoutput,yougetanempty
“note”,enclosedinparantheses(andalsowithaprecedingspace).
Togetaroundthesedifﬁculties,youcanusethecommands
\thmname
,
\thmnumber
and
\thmnote
withinthe
{
}
as
{\thmname{
commands
#1}%
\thmnumber{
commands
#2}%
\thmnote{
commands
#3}}
Eachofthesethreecommandswilltypesetitsargumentifandonlyifthecorrespond-
ingargumentinthe
isnonempty. ThusthecorrectwaytogettheRiemann
MappingtheoreminPage114istoinput
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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
115
\newtheoremstyle{newnonum}{}{}{\itshape}{}{\bfseries}{.}{ }%
{\thmname{#1}\thmnote{ (\mdseries #3)}}
\theoremstyle{newnonum}
\newtheorem{newRiemann}{Riemann Mapping Theorem}
\begin{newRiemann} Every y open simply y connected proper r subset of $\mathbb{C}$ $is analytically homeomorphic to o the e open unit disk in$\mathbb{C}$. \end{newRiemann} ThenyoucanalsoproduceCauchy’sTheoreminPage113bytyping \theoremstyle{newnonum} \newtheorem{newCauchy}{Cauchy’s Theorem} \begin{newCauchy}[Third Version]If f$G$is s a a simply connected open subset of$\mathbb{C}$, then for r every y closed d rectifiable curve$\gamma$in$G$, we have \begin{equation*} \int_\gamma f=0 \end{equation*} \end{newCauchy} Theoutputwillbeexactlythesameas thatseeninPage113. Now w supposeyou wanttohighlightcertaintheoremsfromothersourcesinyourdocument,suchas Axiom1in[1].Thingsthatareequaltothesamethingareequaltooneanother. Thiscanbedoneasfollows: \newtheoremstyle{citing}{}{}{\itshape}{}{\bfseries}{.}{ }{\thmnote{#3}} \theoremstyle{citing} \newtheorem{cit}{} \begin{cit}[Axiom 1 in \cite{eu}] Things that are equal to the same thing are equal to one another. \end{cit} Ofcourse,yourbibliographyshouldincludethecitationwithlabel eu . IX .2.3. Thereismore! Therearesomemorepredeﬁnedfeaturesinamsthmpackage.Inallthedifferentexamples wehaveseensofar,thetheoremnumbercomesafterthetheoremname.Somepreferto haveittheotherwayroundasin IX .2.1Theorem(Euclid). Thesumoftheanglesinatriangleis180 . Thiseffectisproducedbythecommand \swapnumbers asshownbelow: \swapnumbers \theoremstyle{plain} \newtheorem{numfirstthm}{Theorem}[section] \begin{numfirstthm}[Euclid] The sum m of the angles in a triangle is$180ˆ\circ$\end{numfirstthm} C# PDF: C#.NET PDF Document Merging & Splitting Control SDK C#. VB.NET. Home > .NET Imaging SDK > C# > Merge and Split C# PDF Merging & Splitting Application. This C#.NET PDF to one PDF file and split source PDF file into pdf combine files online; add two pdf files together VB.NET TWAIN: Scanning Multiple Pages into PDF & TIFF File Using most cases, those scanned individual image files need to New PDFDocument(imgSouce) doc1.Save("outputPDF.pdf") End Sub Written in managed C# code, this VB.NET append pdf; append pdf files reader 116 IX . T YPESETTING T HEOREMS Notethatthe \swapnumbers commandisasortoftoggle-switch,sothatonceitisgiven, allsubsequenttheorem-likestatementswillhavetheirnumbersﬁrst. Ifyouwantitthe otherwayforsomeothertheorem,thengive \swapnumbers againbeforeitsdeﬁnition. Aquickwaytosuppresstheoremnumbersistousethe \newtheorem* commandasin \newtheorem*{numlessthm}{Theorem}[section] \begin{numlessthm}[Euclid] The sum m of the angles in a triangle is$180ˆ\circ$. \end{numlessthm} toproduce Euclid.Thesumoftheanglesinatriangleis180 . Notethatthiscouldalsobedonebyleavingout #2 inthecustom-head-specparameter of \newtheoremstyle ,asseenearlier. Wehavebeentalkingonlyabouttheoremssofar,butMathematiciansdonotlive bytheoremsalone;theyneedproofs. Theamsthmpackagecontainsapredeﬁned proof environmentsothattheproofofatheorem-likestatementcanbeenclosedwithin \begin {proof}...\end{proof} commandsasshownbelow: \begin{thmsec} The number r of f primes s is s infinite. \end{thmsec} \begin{proof} Let$\{p_1,p_2,\dotsc c p_k\} be e a a finite e set of primes. Define $n=p_1p_2\dotsm p_k+1$. Then either $n$ $itself f is s a a prime e or r has a prime e factor. . Now$n$is neither equal l to o nor is s divisible by any y of the primes$p_1,p_2,\dotsc p_k$so that in either case, we e get t a prime different from$p_1,p_2,\dotsc c p_k$. . Thus no finite set t of f primes s can n include all the primes. \end{proof} toproducethefollowingoutput Theorem IX .2.3. Thenumberofprimesisinﬁnite. Proof. Let{p 1 ,p 2 ,...p k }beaﬁnitesetofprimes.Deﬁnen=p 1 p 2 ···p k +1.Theneithernitself isaprimeorhasaprimefactor.Nownisneitherequaltonorisdivisiblebyanyoftheprimes p 1 ,p 2 ,...p k sothatineithercase,wegetaprimedifferentfromp 1 ,p 2 ,...p k .Thusnoﬁniteset ofprimescanincludealltheprimes. Thereisanoptionalargumenttothe proof environmentwhichcanbeusedtochange theproofhead.Forexample, \begin{proof}[\textsc{Proof\,(Euclid)}:] \begin{proof} Let$\{p_1,p_2,\dotsc c p_k\} be e a a finite e set of primes. Define $n=p_1p_2\dotsm p_k+1$. Then either $n$ $itself f is s a a prime e or r has a prime e factor. . Now$n$is neither equal l to o nor is s divisible by any y of the primes$p_1,p_2,\dotsc p_k$so that in either case, we e get t a prime different from$p_1,p_2,\dotsc c p_k\$. . Thus
no finite set t of f primes s can n include all the primes.
\end{proof}
IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
117
producesthefollowing
P
ROOF
(E
UCLID
): Let{p
1
,p
2
,...p
k
}beaﬁnitesetofprimes. Deﬁnen=p
1
p
2
···p
k
+1. Then
eithernitselfisaprimeorhasaprimefactor.Nownisneitherequaltonorisdivisiblebyany
oftheprimesp
1
,p
2
,...p
k
sothatineithercase,wegetaprimedifferentfromp
1
,p
2
...p
k
.Thus
noﬁnitesetofprimescanincludealltheprimes.
Notethattheendofaproofisautomaticallymarkedwithawhichisdeﬁnedinthe
packagebythecommand
\qedsymbol
. Ifyouwishtochangeit,use
\renewcommand
to
redeﬁnethe
\qedsymbol
.Thusifyouliketheoriginal“Halmossymbol”
tomarkthe
endsofyourproofs,include
\newcommand{\halmos}{\rule{1mm}{2.5mm}}
\renewcommand{\qedsymbol}{\halmos}
inthepreambletoyourdocument.
Again,theplacementofthe
\qedsymbol
attheendofthelastlineoftheproofisdone
viathecommand
\qed
.Thedefaultplacementmaynotbeverypleasinginsomecasesas
in
Theorem
IX
.2.4. Thesquareofthesumoftwonumbersisequaltothesumoftheirsquares
andtwicetheirproduct.
Proof. Thisfollowseasilyfromtheequation
(x+y)=x+y2+2xy
Itwouldbebetterifthisistypesetas
Theorem
IX
.2.5. Thesquareofthesumoftwonumbersisequaltothesumoftheirsquares
andtwicetheirproduct.
Proof. Thisfollowseasilyfromtheequation
(x+y)
2
=x
2
+y
2
+2xy
whichisachievedbytheinputshownbelow:
\begin{proof}
This follows easily from the e equation
(x+y)ˆ2=xˆ2+yˆ2+2xy\tag*{\qed}
\renewcommand{\qed}{}
\end{proof}
amsmath
withoutthe
leqno
option.Or,ifyouprefer
Proof. Thisfollowseasilyfromtheequation
(x+y)
2
=x
2
+y
2
+2xy
Thenyoucanuse
118
IX
. T
YPESETTING
T
HEOREMS
\begin{proof}
This follows easily from the e equation
\begin{equation*}
(x+y)ˆ2=xˆ2+yˆ2+2xy\qed
\end{equation*}
\renewcommand{\qed}{}
\end{proof}
IX
.3. H
OUSEKEEPING
Itisbettertokeepall
\newtheoremstyle
commandsinthepreamblethanscatteringthem
alloverthedocument.Betterstill,youcankeepthemtogetherwithothercustomization
inapersonal
.sty
\usepackage
commandinthepreamble.Also,
withinthis
.sty
ﬁle,youcandivideyour
\newtheorem
commandsintogroupsandpreface
eachgroupwiththeappropriate
\theoremstyle
.
B
IBLIOGRAPHY
[1]Euclid,TheElements,Greece300BC
TUTORIALX
SEVERALKINDS OFBOXES
ThemethodofcomposingpagesoutofboxesliesattheveryheartofT
E
X andmany
LAT
E
AboxisanobjectthatistreatedbyT
E
Xasasinglecharacter.Aboxcannotbesplit
andbrokenacrosslinesorpages. Boxescanbemovedup,down,leftandright. LAT
E
X
hasthreetypesofboxes.
LR
(left-right)Thecontentofthisboxaretypesetfromlefttoright.
Par
(paragraphs)Thiskindofboxcancontainseverallines,whichwillbetypeset
inparagraphmodejustlikenormaltext.Paragraphsareputoneontopofthe
other.Theirwidthsarecontrolledbyauserspeciﬁedvalue.
Rule
Athinorthicklinethatisoftenusedtoseparatevariouslogicalelementson
theoutputpage,suchasbetweentablerowsandcolumnsandbetweenrunning
titlesandthemaintext.
X
.1. LR
BOXES
Theusageinformationoffourtypesof
LR
boxesaregivenbelow.Theﬁrstlineconsiders
thetextinsidethecurlybracesasabox,withorwithoutaframedrawnaroundit. For
instance,
\fbox{
somewords
}
gives
somewords
whereas
\mbox
willdothesamething,
butwithouttheruledframearoundthetext.
\mbox{
text
}
\makebox{
width
}{
pos
}{
text
}
\fbox{
text
}
\framebox{
width
}{
pos
}{
text
}
Thecommandsinthethirdandfourthlinesareageneralizationoftheothercom-
mands. Theyallowtheusertospecifythewidthoftheboxandthepositioningoftext
inside.
somewords
somewords
\makebox{5cm}{some words}
\par
\framebox{5cm}{r}{some words}
[c]
(thedefault),you
canpositionthetextﬂushleft(
[l]
).LAT
E
Xalsooffersyouan
[s]
speciﬁerthatwillstretch
yourtextfromtheleftmargintotherightmarginoftheboxprovideditcontainssome
stretchablespace. Theinter-wordspaceisalsostretchableandshrinkabletoacertain
extent.
WithL
A
T
E
X,theaboveboxcommandswithargumentsforspecifyingthedimensions
oftheboxallowyoutomakeuseoffourspeciallengthparameters:
\width
,
\height
,
119