,,! ,,NEME? ,,BRL ,,CODE ,,=
,,MA!MATICS ,,& ,,SCI;E ,,NOT,N
#AIGB ,,REVI.N
,-PIL$ ,"U ! ,AU?OR;Y (!
,AM]ICAN ,ASSOCI,N ( ,"W]S =! ,BL
,ASSOCI,N = ,$UC,N (! ,VISU,Y
,H&ICAPP$ &! ,N,NAL ,BRL ,ASSOCI,N
,ADOPT$ ,JANU>Y #BJ1 #AIGB1 0!
,,AAWB-AEVH-NBA ,ADVISORY ,C\NCIL
6! ,BRL ,AU?OR;Y
,PUBLI%$1 #AIHH1 BY
,AM]ICAN ,PR9T+ ,H\SE =! ,BL
,L\ISVILLE1 ,K5TUCKY #DJBJF-JJHE
,EMBOSS$ 9 ,FIVE ,VOLUMES
,VOLUME ,,III
,BRL PAGES P#A-P#D & #BHA-DDD
,PR9T PAGES A#AAJ-A#AFJ P#A
,NEME? ,MA?4 ,CODE1 #1972
,,3T5TS
,PAGE
,,RULES (,3T4)
,,RULE ,,XVI--,,%APES
(@,S#106-@,S#115) """""""""" A#110
,,RULE ,,XVII--,,FUNC;N ,,"NS
,,& ,,_! ,,A2REVI,NS
(@,S#116-@,S#119) """"""""""" #118
,,RULE ,,XVIII--,,SIGNS ,,&
,,SYMBOLS ,,( ,,GR\P+
(@,S#120-@,S#128) """"""""""" #122
,,RULE ,,XIX--,SIGNS ,,&
,,SYMBOLS ,,( ,,OP],N
(@,S#129-@,S#138) """"""""""" #128
,,RULE ,,XX--,,SIGNS ,,& ,,SYM-
BOLS ,,( ,,-P>ISON
(@,S#139-@,S#151) """"""""""" #134
,,RULE ,,XXI--,,>R[S (@,S#152-
@,S#158) """""""""""""""""""" #145
,,RULE ,,XXII--,,MISCELLANE\S
,,SIGNS ,,& ,,SYMBOLS
(@,S#159-@,S#176) """"""""""" #152
P#C
,,RULE ,,XXIII--,,MULTIPURPOSE
,,9DICATOR (@,S#177) """""""" #158
,,! ,,NEME? ,,BRL ,,CODE A#AAJ
,,= ,,MA!MATICS
,,& ,,SCI5TIFIC ,,NOT,N
#1972 ,,REVI.N
,,RULES (,3T9U$)
,RULE ,,XVI--,%APES
,%APE ,9DICATOR $
,9T]IOR ,%APE-,MODIFIC,N ,9DICATOR _$
,/RUCTURAL ,%APE-,MODIFIC,N ,9DI-
CATOR .
,FILL$-IN ,%APE ,9DICATOR _
,%AD$ ,%APE ,9DICATOR .
,T]M9,N ,9DICATOR ]
,BASIC ,%APES
,ANGLE $[
,>C
,3CAVE UPW>D $A
,3CAVE D[NW>D $'
#BHA
,NEME? ,MA?4 ,CODE1 #1972 B#AAJ
,>R[
,LEFT-PO9T+ $[33
,"R-PO9T+
,3TRACT$ $O
,UNCONTRACT$ $33O
,D[N-PO9T+ $%33O
----------------------------------#AAA
,UP-PO9T+ $<33O
,CIRCLE $C
,DIAMOND $D
,ELLIPSE (OVAL) $E
#BHC
,NEME? ,MA?4 ,CODE1 #1972 A#AAA
,HEXAGON
,IRREGUL> $HX
,REGUL> $6
,9T]SECT+ ,L9ES $I
,IS ,P>ALLEL ,TO $L
,IS ,N ,P>ALLEL ,TO /$L
,IS ,P]P5DICUL> ,TO $P
,IS ,N ,P]P5DICUL> ,TO /$P
,P>ALLELOGRAM $G
#BHE
,NEME? ,MA?4 ,CODE1 #1972 B#AAA
,P5TAGON
,IRREGUL> $PG
,REGUL> $5
,QUADRILAT]AL $Q
,RECTANGLE $R
,RHOMBUS $H
OR
,SQU>E $4
,/> $S
,TRAPEZOID $Z
#BHG
,NEME? ,MA?4 ,CODE1 #1972 #AAB
,TRIANGLE
,9V]T$ .$
,REGUL> (EQUILAT]AL) $T
,%APES ) ,9T]IOR ,MODIFIC,N
,ANGLE
,ANGLE ) 9T]IOR >C
$[_$$A]
,ANGLE ) 9T]IOR CLOCKWISE
>R[ $[_$$[59]
,ANGLE ) 9T]IOR C.T]CLOCK-
WISE >R[ $[_$$59O]
,CIRCLE
,CIRCLE ) 9T]IOR >R[ PO9T+
"R $C_$$33O]
#BHI
,NEME? ,MA?4 ,CODE1 #1972 A#AAB
,CIRCLE ) 9T]IOR >R[ PO9T+
LEFT $C_$$[33]
,CIRCLE ) 9T]IOR >R[ PO9T+
"R OV] 9T]IOR >R[
PO9T+ LEFT
$C_$$33O$[33]
,CIRCLE ) 9T]IOR >R[ PO9T+
LEFT OV] 9T]IOR >R[
PO9T+ "R
$C_$$[33$33O]
,CIRCLE ) 9T]IOR >R[ PO9T+
UP $C_$$<33O]
,CIRCLE ) 9T]IOR >R[ PO9T+
D[N $C_$$%33O]
,CIRCLE ) 9T]IOR >R[ PO9T+
UP FOLL[$ 09T]IOR >R[
PO9T+ D[N
$C_$$<33O"$%33O]
#BIA
,NEME? ,MA?4 ,CODE1 #1972 B#AAB
,CIRCLE ) 9T]IOR >R[ PO9T+
D[N FOLL[$ 09T]IOR >R[
PO9T+ UP
$C_$$%33O"$<33O]
,CIRCLE ) 9T]IOR CROSS
$C_$@*]
,CIRCLE ) 9T]IOR DOT
$C_$*]
,CIRCLE ) 9T]IOR M9US SIGN
$C_$-]
,CIRCLE ) 9T]IOR PLUS SIGN
$C_$+]
,SQU>E
,SQU>E ) 9T]IOR DIAGONALS
$4_$5@9]
#BIC
,NEME? ,MA?4 ,CODE1 #1972 #AAC
,SQU>E ) 9T]IOR DOT
$4_$*]
,SQU>E ) 9T]IOR HORIZONTAL
B> $4_$:]
,SQU>E ) 9T]IOR V]TICAL B>
$4_$\]
,SQU>E ) 9T]IOR NOR?WE/-
S\?EA/ DIAGONAL
$4_$5]
,SQU>E ) 9T]IOR S\?WE/-
NOR?EA/ DIAGONAL
$4_$9]
,%APES ) ,/RUCTURAL ,MODIFIC,N
,ANGLE
,ADJAC5T ANGLES $[.J]
OR
#BIE
,NEME? ,MA?4 ,CODE1 #1972 A#AAC
,ALT]NATE EXT]IOR ANGLES
$[.AE]
,ALT]NATE 9T]IOR ANGLES
$[.AI]
,-PLE;T>Y ANGLES
$[.CP]
,CORRESPOND+ ANGLES
$[.C]
,EXT]IOR ANGLES
$[.E]
,9T]IOR ANGLES
$[.I]
#BIG
,NEME? ,MA?4 ,CODE1 #1972 B#AAC
,OBTUSE ANGLE $[.O]
,"R ANGLE $[.R]
,/RAI<T ANGLE $[.S]
,SUPPLE;T>Y ANGLES
$[.SP]
,V]TICAL ANGLES $[.V]
,TRIANGLE
,ACUTE TRIANGLE $T.A]
,ISOSCELES TRIANGLE
$T.I]
,OBTUSE TRIANGLE $T.O]
#BII
,NEME? ,MA?4 ,CODE1 #1972 #AAD
,"R TRIANGLE $T.R]
,SCAL5E TRIANGLE $T.S]
@,S#106_4 .,BASIC .,%APES3 ,A %APE
IS A SIGN : IS 9 G5]AL A M9IATURE PIC-
TURE OR DIAGRAM (! OBJECT : ! SIGN
REPRES5TS4
,A %APE IS REPRES5T$ 0US+ A LR1
NUM]AL1 OR EV5 A 3FIGUR,N ( DOTS : IS
SU7E/IVE (! %APE4 ,! %APE 9DICATOR M/
PREC$E ! %APE SYMBOL4 ,A SYMBOL ( %APE
M/ 2 US$ ONLY =! REPRES5T,N (! CORRE-
SPOND+ SIGN ( %APE2 X M/ N"E 2 US$ TO
REPRES5T ! ^W OR PHRASE : IS ! "N ( S*
A SIGN ( %APE4
(1) $R
(2) $C
(3) $4
(4) $6
(5) $[ #CJA
,NEME? ,MA?4 ,CODE1 #1972 A#AAD
(6) $O
(7) X^$4
(8) $[ ,A,B,C .K $[ ,D,E,F
@,S#107_4 .,O!R .,%APES3 ,SIGNS (
%APE : D N APPE> 9 ! LI/ ( ,BASIC
,%APES M/ 2 REPRES5T$ 0! USE ( "O OR M
LRS SU7E/IVE (! "N (! %APE 2+ REPRE-
S5T$4 ,C>E M/ 2 EX]CIS$ N 6USE AN
ALPHABETIC SYMBOL 6: A M1N+ IS ALR AS-
SIGN$ 9 ! ABV LI/4 ,9 A4I;N1 ! TRAN-
SCRIB] M/ SUPPLY A NOTE ( EXPLAN,N 6!
R1D] 3C]N+ ! "N ( S* A SIGN ( %APE &
M/ SUPPLY A DRAW+ (! %APE IF POSSI#4
,IF A -B9,N ( LRS SELECT$ 6REPRES5T A
SIGN ( %APE IS 3TRACTI#1 ! 3TRAC;N M/
N 2 US$4 ,! %APE 9DICATOR M/ PREC$E A
%APE SYMBOL 3/RUCT$ 9 ? WAY4
(1) $MN
(IN 9K PR9T1 ! DRAW+ (A MOON)
(2) $CH
(IN 9K PR9T1 ! DRAW+ (A *UR*)
#CJC
@,S#108_4 ..,FILL$-,IN & B#AAD
,%AD$ .,%APES3 ,ANY (! CLOS$ %APES 9 !
ABV LI/1 IF !Y >E FILL$ 9 OR %AD$1 M/
2 REPRES5T$ Z S* 0US+ _ (DOTS #4-5-6)
OR . (DOTS #4-6), RESPECTIVELY1 PREC$+
! %APE SYMBOL4 ,! %APE 9DICATOR M/1 9
TURN1 PREC$E :I*"E 9DICATOR HAS BE5
US$4
(1) $_E
(FILL$-IN ELLIPSE)
----------------------------------#AAE
(2) $.E
(%AD$ ELLIPSE)
^,S#109_4 .,POLYGONS3 ,! LI/ ( ,BAS-
IC ,%APES 3TA9S ! %APES = REGUL>
POLYGONS UP 6SIX SIDES4 ,ANY REGUL>
POLYGON ) M ?AN SIX SIDES M/ 2 REPRE-
S5T$ 9 ! MANN] SU7E/$1 T IS1 0US+ !
NUM]AL : SPECIFIES ! NUMB] ( SIDES4
,AN IRREGUL> POLYGON1 T IS1 "O : HAS
AT L1/ TWO UNEQUAL SIDES1 TWO UNEQUAL
ANGLES1 OR BO?1 M/ N 2 REPRES5T$ 9 ?
WAY4 ,X M/ 2 REPRES5T$ Z SPECIFI$ 9
,NEME? ,MA?4 ,CODE1 #1972 A#AAE
@,S#107_4
(1) $8
(REGUL> OCTAGON)
(2) $12
(REGUL> POLYGON ( #12 SIDES)
(3) $_8
(FILL$-IN REGUL> OCTAGON)
(4) $OC
(AN IRREGUL> OCTAGON2 A TRANSCRIB]'S
NOTE )A DRAW+ IS REQUIR$)
@,S#110_4 ..,%APE ) ,/RUCTURAL
.,MODIFIC,N3 ,:5 A SIGN1 : IS A SPE-
CIAL CASE (A M G5]AL SITU,N1 IS US$1
(FOR EXAMPLE1 ."R .ANGLE IS A SPECIAL
CASE ( .ANGLE), OR :5 TWO OR M SIGNS (
%APE >E -B9$ 6=M A -POSITE SIGN )A M
DETAIL$ /RUCTURE1 (FOR EXAMPLE1 TWO
.ANGLES >E -B9$ 6=M .ADJAC5T .ANGLES),
! %APE : IS =M$ 9 EI ( ^! WAYS IS
CALL$ A ..%APE ) /RUCTURAL .MODIFIC,N4
,! MODIFIC,N IS 9DICAT$ 0A LR OR
-B9,N ( LRS SU7E/IVE (! NATURE #CJE
(! MODIFIC,N4 ,! SYMBOL US$ = B#AAE
9DICAT+ ! MODIFIC,N M/ 2 PREC$$ 0!
/RUCTURAL %APE-MODIFIC,N 9DICATOR &
FOLL[$ 0! T]M9,N 9DICATOR4 ,? -B9,N M/
DIRECTLY FOLL[ ! SYMBOL ( BASIC %APE :
IS 2+ MODIFI$4
,%APES ) /RUCTURAL MODIFIC,N N %[N 9
! LI/ ( ,%APES ) ,/RUCTURAL ,MODIFIC,N
M/ 2 TRANSCRIB$ 9 A3ORD.E )! PR9CIPLE
SU7E/$ 0^? %APE SYMBOLS4 ,! TRANSCRIB]
M/ SUPPLY A NOTE ( EXPLAN,N 6! R1D]
3C]N+ ! "N (! /RUCTURAL MODIFIC,N & M/
SUPPLY A DRAW+ IF POSSI#4 ,IF A -B9,N
( ALPHABETIC SYMBOLS SELECT$ =A /RUC-
TURAL MODIFI] 3/ITUTES A 3TRACTI# COM-
B9,N1 ! 3TRAC;N M/ N 2 US$4
(1) $T.I]
(AN ISOSCELES TRIANGLE2 )\T MODIFI-
C,N ! %APE SYMBOL SIGNIFIES .TRI-
ANGLE)
(2) $[.J]
(ADJAC5T ANGLES2 )\T MODIFIC,N !
%APE SYMBOL SIGNIFIES .ANGLE)
,NEME? ,MA?4 ,CODE1 #1972 C#AAE
@,S#111_4 ..,%APE ) ,9T]IOR .,MODI-
FIC,N3
;A_4 ,:5 A LR1 OP],N SIGN1 OR O!R
SIGN IS PLAC$ 9SIDE ! BASIC SIGN (
%APE1 ! %APE : IS =M$ 9 ? WAY IS CALL$
A ..%APE ) 9T]IOR .MODIFIC,N4
----------------------------------#AAF
,! MODIFIC,N IS 9DICAT$ 0US+ ! SYM-
BOL : CORRESPONDS 6! MODIFY+ SIGN4 ,?
SYMBOL M/ 2 PREC$$ 0! 9T]IOR %APE-
MODIFIC,N 9DICATOR & FOLL[$ 0! T]M9,N
9DICATOR4 ,? -B9,N M/ DIRECTLY FOLL[ !
SYMBOL ( BASIC %APE : IS 2+ MODIFI$4
(1) $C_$,A]
(2) $C_$+]
(3) $R_$:]
(4) $[_$#30^.*"]
;B_4 ,IF TWO OR M 9T]IOR MODIFI]S1
>RANG$ HORIZONT,Y1 O3UR 9SIDE ! SAME
BASIC SIGN ( %APE1 ! CORRESPOND+ SYM-
BOLS M/ 2 SEP>AT$ 0! MULTIPUR- #CJG
POSE 9DICATOR1 B ! 9T]IOR A#AAF
%APE-MODIFIC,N 9DICATOR M/ 2 US$ ONLY
ONCE1 2F ! F/ MODIFY+ SYMBOL4 ,! 5TIRE
-B9,N M/ DIRECTLY FOLL[ ! BASIC SYMBOL
( %APE : IS 2+ MODIFI$4
(1) $C_$$%33O"$<33O]
;C_4 ,IF TWO OR M 9T]IOR MODIFI]S1
>RANG$ V]TIC,Y1 O3UR 9SIDE ! SAME
BASIC SIGN ( %APE1 ! CORRESPOND+ SYM-
BOLS M/ 2 TRANSCRIB$ SU3ESSIVELY1 )\T
9T]V5+ SPACES OR 9DICATORS1 2G9N+ )!
SYMBOL : CORRESPONDS 6! UPP]MO/ SIGN &
PROCE$+ 9 DESC5D+ ORD]4 ,! F/ MODIFY+
SYMBOL M/ 2 PREC$$ 0! 9T]IOR %APE-
MODIFIC,N 9DICATOR1 &! 5TIRE -B9,N M/
DIRECTLY FOLL[ ! BASIC SYMBOL ( %APE :
IS 2+ MODIFI$4 ,N"O (! 9T]IOR SIGNS
MAY 2 REG>D$ Z A MODIFI] ( ANY (!
O!RS1 &! TE*NIQUE = REPRES5T+ MODIFI$
EXPRES.NS DOES N APPLY4
(1) $C_$$33O$[33]
,NEME? ,MA?4 ,CODE1 #1972 B#AAF
@,S#112_4 ..,%APE MODIFI$ 0.,SUP]PO-
SI;N3 ,:5 A SIGN IS SUP]POS$ ^U A SIGN
( %APE1 ! %APE : IS =M$ 9 ? WAY IS
CALL$ A ..%APE MODIFI$ 0.SUP]POSI;N4
,SUP]POSI;N MAY 2 4T+UI%$ F 9T]IOR
MODIFIC,N 0NOT+ T 9 SUP]POSI;N "O (!
SIGNS EXT5DS 2Y ! B.D>Y (! O!R4 ,":AS1
9 ! CASE ( 9T]IOR MODIFIC,N1 "O (!
SIGNS IS 3F9$ )9 ! B.D>Y (! O!R (SEE
@,S#93)_4
(1) \@$C]
(A V]TICAL B> EXT5D+ 2Y ! B.D>Y (A
CIRCLE)
(2) $C_$\]
(A CIRCLE )A V]TICAL B> "? ! C5T]
EXT5D+ Z F> Z ! B.D>Y (! CIRCLE)
@,S#113_4 .,DRAWN-,IN .,%APES3 ,X IS
(T5 BETT] =! R1D] 6H %APES DRAWN 9 ?AN
6H !M REPRES5T$ 0! ELABORATE BRL CON-
/RUC;NS SPECIFI$ 9 ? RULE4 ,H["E1 X IS
N POSSI# 6=MULATE SPECIFIC #CJI
RULES 3C]N+ : =M %D 2 US$ &1 C#AAF
"!=E1 ! DECI.N IS LEFT 6! EXP]I;E &
JUDG;T (! TRANSCRIB]4
@,S#114_4 ..,PLURAL (A ,SIGN (
.,%APE3 ,! PLURAL OR ! POSSESSIVE (A
SIGN ( %APE IS "S"TS 9DICAT$ 0PLAC+ !
LR ;S ON ! 9SIDE (! SIGN ( %APE4 ,:5 ?
=M IS EMPLOY$1 ! BRL TRANSCRIP;N IS
E6ECT$ SIMPLY 0PLAC+ ! L[]-CASE LR ;S
AF ! %APE SYMBOL (SEE @,S#39)_4
(1) $TS
(IN 9K PR9T ! ;S IS 9SIDE ! TRIANGLE
%APE)
----------------------------------#AAG
@,S#115_4 ..,SPAC+ ) ,SYMBOLS (
.,%APE3
;A_4 ,:5 A SIGN ( %APE IS FOLL[$
0XS ID5TIFIC,N S* Z A LR1 SEQU;E (
LRS1 OR NUM]AL1 "! M/ 2 A SPACE 2T !
%APE SYMBOL & XS ID5TIFIC,N4 ,9 PR9-
CIPLE1 ! SPAC+ RULE : COV]S SYMBOLS (
%APE : >E ID5TIFI$ >E ! SAME Z ^? :
APPLY 6FUNC;N "NS & _! A2REVI,NS4
,NEME? ,MA?4 ,CODE1 #1972 A#AAG
(1) $[ #1
(2) $T ,A,B,C
(3) $C ,R
(4) ,9 $T ,A,B,C, $[ ,A .K #90^.*_
(5) $TS ,U,V,W & ,X,Y,Z
(6) $[.R] ,A
(7) $[_$$59O] ,A,B,C
(8) $[ X+$[ Y
(9) $[ #1+2$[ #3
(10) ?$T ,A,B,C/$T ,E,F,G#
(11) M$[ ,A,B,C
(12) $[ #90^.*"+$[ #120^.*
;B_4 ,%APE SYMBOLS : REPRES5T
OMIS.N M/ 2 SPAC$ 9 A3ORD.E )! OMITT$
ITEM : !Y REPRES5T4
(1) $4@0
(THE SQU>E REPRES5TS AN OMITT$
NUM]AL)
(2) @S$T
(THE TRIANGLE REPRES5TS AN OMITT$
NUM]AL) #CAA
(3) #6_?4/12_# B#AAG
.K #6_?$T/3_#
(THE TRIANGLE REPRES5TS AN OMITT$
NUM]AL)
(4) #1 DAY .K #24 $D
(THE DIAMOND REPRES5TS AN OMITT$ ^W
OR A2REVI,N)
----------------------------------#AAH
(5) X$4Y .K Y$4X
(THE SQU>E REPRES5TS AN OMITT$ SIGN
( OP],N)
(6) #2+4 $T #7
(THE TRIANGLE REPRES5TS AN OMITT$
-P>ISON SIGN)
(7) #2+3 .K .$
(THE 9V]T$ TRIANGLE REPRES5TS AN
OMITT$ NUM]AL)
;C_4 ,SYMBOLS ( %APE : >E EI COM-
P>ISON SYMBOLS OR OP],N SYMBOLS M/ 2
SPAC$ ACLY4
(1) F $O G
(THE >R[ IS A -P>ISON SYMBOL)
(2) "LIM%X $O ,=] F(X)
,NEME? ,MA?4 ,CODE1 #1972 A#AAH
(THE >R[ IS A -P>ISON SYMBOL)
(3) ,A,B $P ,C,D
(_8IS P]P5DICUL> TO0 IS A -P>ISON
SYMBOL)
(4) ,A,B /$L ,C,D
(_8IS N P>ALLEL TO0 IS A -P>ISON
SYMBOL)
(5) X$C_$+]Y
(THE CIRCLE ) 9T]IOR PLUS SYMBOL IS
A SYMBOL ( OP],N)
(6) X$_4Y
(THE FILL$-IN SQU>E SYMBOL IS A SYM-
BOL ( OP],N)
;D_4 ,9 ANY CASE1 A SYMBOL ( %APE
M/ 2 UNSPAC$ F ANY BRL 9DICATOR : AP-
PLIES 6X4
(1) ",A,B<$O]
(2) #1101;$D"+1000;$D
#CAC
,RULE ,,XVII--,FUNC;N B#AAH
,"NS & ,_! ,A2REVI,NS
,BRL
,A2REVI,N ,FUNC;N ,"N ,EQUIVAL5T
AMP """"""" AMPLITUDE """"" AMP
ANTILOG """ ANTILOG>I?M """ ANTILOG
----------------------------------#AAI
>C """""""" >C """""""""""" ARC
>G """""""" >GU;T """"""""" ARG
COLOG """"" COLOG>I?M """"" COLOG
COS """"""" COS9E """"""""" COS
CO% """"""" HYP]BOLIC
COS9E """""""" COSH
COT """"""" COTANG5T """""" COT
CO? """"""" HYP]BOLIC
COTANG5T """"" COTH
COV]S """"" COV]S9E """"""" COVERS
CSC """"""" COSECANT """""" CSC
CS* """"""" HYP]BOLIC
COSECANT """"" CSCH
CTN """"""" COTANG5T """""" CTN
CTNH """""" HYP]BOLIC
COTANG5T """"" CTNH
,NEME? ,MA?4 ,CODE1 #1972 A#AAI
,BRL
,A2REVI,N ,FUNC;N ,"N ,EQUIVAL5T
DET """"""" DET]M9ANT """"" DET
]F """""""" ]ROR FUNC;N """ ERF
EXP """"""" EXPON5TIAL """" EXP
EXSEC """"" EXSECANT """""" EXSEC
GRAD """""" GRADI5T """"""" GRAD
HAV """"""" HAV]S9E """"""" HAV
IM """""""" IMAG9>Y "P """" IM
9F """""""" 9FIMUM """""""" INF
LIM """"""" LIMIT """"""""" LIM
LIM """"""" UPP] LIMIT """" <LIM
----------------------------------#ABJ
LIM """"""" L[] LIMIT """"" %LIM
LN """""""" NATURAL
LOG>I?M """""" LN
LOG """"""" LOG>I?M """"""" LOG
MAX """"""" MAXIMUM """"""" MAX
M9 """""""" M9IMUM """""""" MIN
MOD """"""" MODULO """""""" MOD #CAE
A#ABJ
,BRL
,A2REVI,N ,FUNC;N ,"N ,EQUIVAL5T
RE """""""" R1L "P """""""" RE
SEC """"""" SECANT """""""" SEC
SE* """"""" HYP]BOLIC
SECANT """"""" SECH
S9 """""""" S9E """"""""""" SIN
S9H """"""" HYP]BOLIC S9E SINH
SUP """"""" SUPREMUM """""" SUP
TAN """"""" TANG5T """""""" TAN
TANH """""" HYP]BOLIC
TANG5T """"""" TANH
V]S """"""" V]S9E """"""""" VERS
@,S#116_4 ..,3TRAC;NS 9 ,FUNC;N ,"NS
& ,_! .,A2REVI,NS3 ,SEE @,S#55B &
@,S#56_4
@,S#117_4 ..,NUM]IC ,SUBSCRIPTS )
,FUNC;N ,"NS & ,_! .,A2REVI,NS3 ,SEE
@,S#77_4
@,S#118_4 ..,MODIFI]S ) ,FUNC;N ,"NS
& ,_! .,A2REVI,NS3 ,! B> : O3URS OV]
OR "U ! FUNC;N "N 8LIMIT0 OR XS A2RE-
,NEME? ,MA?4 ,CODE1 #1972 B#ABJ
VI,N 8LIM0 M/ N 2 TR1T$ Z A MODIFI]2 !
-B9,N M/ 2 TRANSCRIB$ 0M1NS ( SPECIAL
SYMBOLS = .UPP] .LIMIT <LIM OR <LIMIT
OR .L[] .LIMIT %LIM OR %LIMIT_4 ,O!R
MODIFI]S1 H["E1 M/ 2 TRANSCRIB$ 9
A3ORD.E )! TE*NIQUES =! REPRES5T,N (
MODIFI$ EXPRES.NS4
----------------------------------#ABA
(1) "<LIM%N $O ,=] F;N"(X)
(2) "%LIM%N $O ,=] F;N"(X)
(3) "LIM%X $O #0] F(X)
@,S#119_4 ..,SPAC+ ) ,FUNC;N ,"NS &
,_! .,A2REVI,NS3
;A_4 ,A SPACE M/ 2 LEFT AF AN UN-
MODIFI$ FUNC;N "N OR XS A2REVI,N4 ,IF
! FUNC;N "N OR XS A2REVI,N C>RIES A
SUP]SCRIPT1 SUBSCRIPT1 OR MODIFI]1 !
SPACE M/ FOLL[ ! SUP]SCRIPT1 SUB-
SCRIPT1 OR T]M9,N ( MODIFI]4
(1) SIN X
(2) COS^2 X
(3) E^SIN X #CAG
(4) ARC ,A,O,B A#ABA
(5) LOG;A X
(6) "LIM%X $O #0] F(X)
;B_4 ,IF TWO OR M 3SECUTIVE FUNC;N
"NS OR _! A2REVI,NS O3UR1 ! SPACE 2T
!M MAY EI 2 OMITT$ OR 9CLUD$ 9 A3ORD.E
)! 9K PR9T COPY4 ,:5 "! IS D\BT 3C]N+
! PRES;E (A SPACE 9 9K PR9T 2T ! FUNC-
;N "NS OR _! A2REVI,NS1 A SPACE %D 2
LEFT 9 ! TRANSCRIP;N4
(1) ARCSIN X
(NO SPACE 9 9K PR9T 2T >C & SIN)
(2) ARC SIN X
(SPACE 2T >C & S9 CLE>LY %[N 9 9K
PR9T)
;C_4 ,! EXPRES.N : FOLL[S OR PRE-
C$ES ! FUNC;N "N OR XS A2REVI,N M/ 2
SPAC$ 9 A3ORD.E )! O!R SPAC+ RULES ( ?
,CODE4
(1) SIN X+Y
(IN 9K PR9T1 "! IS A SPACE ON BO?
,NEME? ,MA?4 ,CODE1 #1972 B#ABA
SIDES (! PLUS SIGN)
(2) SIN .P_/3
(IN 9K PR9T1 "! IS NO SPACE ON EI
SIDE (! DIAGONAL L9E)
----------------------------------#ABB
(3) SIN #30^.*"COS #45^.*
"+COS #30^.*"SIN #45^.*
(IN 9K PR9T1 COS #45^.* & COS #30^.*
>E PREC$$ & FOLL[$ 0SPACES)
(4) #2SIN X+3COS Y
(IN 9K PR9T1 "! IS NO SPACE AF ! #2
&! #3, & "! IS A SPACE ON BO? SIDES
(! PLUS SIGN)
(5) SIN ACOS Y
(IN 9K PR9T1 "! IS A SPACE ON BO?
SIDES (! ;A &! ;Y)
(6) >1-COS^2 X]
(IN 9K PR9T1 "! IS A SPACE ON BO?
SIDES (! M9US SIGN &! ;X)
(7) ?1/COS#-COS .K TAN *SIN
(8) #1_/COS -COS .K TAN *SIN
#CAI
,NEME? ,MA?4 ,CODE1 #1972 A#ABB
,RULE ,,XVIII--,SIGNS
& ,SYMBOLS ( ,GR\P+
,NORMAL ,5L>G$
,P>5!SES (R.D BRACKETS)
,LEFT ( """""" ,(
,"R ) """""" ,)
,BRACKETS (SQU>E BRACKETS)
,LEFT @( """"" @,(
"@F @) """"" @,)
,BOLDFACE ,LEFT _@(
#CBA
,NEME? ,MA?4 ,CODE1 #1972 B#ABB
,NORMAL ,5L>G$
,BOLDFACE ,"R _@)
----------------------------------#ABC
,BRACES (CURLY BRACKETS)
,LEFT .( """""" .,(
,"R .) """""" .,)
,V]TICAL ,B>
,S+LE \ """"""" ,\
,D\# \\ """""" ,\,\
,BOLDFACE ,S+LE _\
#CBC
,NEME? ,MA?4 ,CODE1 #1972 A#ABC
,NORMAL ,5L>G$
,BOLDFACE ,D\# _\_\
,ANGLE ,BRACKETS (ANGUL> P>5!SES)
,LEFT ..( """"" ..,(
,"R ..) """"" ..,)
,B>R$ ,BRACKETS
,LEFT @_( """"" @_,(
,"R @_) """"" @_,)
,B>R$ ,BRACES
,LEFT ._( """"" ._,(
#CBE
,NEME? ,MA?4 ,CODE1 #1972 B#ABC
,NORMAL ,5L>G$
,"R ._) """"" ._,)
,HALF ,BRACKETS
,UPP] ,LEFT @^( """"" @B,(
OR
,UPP] ,"R @^) """"" @^,)
OR
,L[] ,LEFT @;( """"" @;,(
OR
,L[] ,"R @;) """"" @;,)
OR
#CBG
,NEME? ,MA?4 ,CODE1 #1972 C#ABC
,NORMAL ,5L>G$
,TRANSCRIB]'S ,GR\P+ ,SYMBOLS
,LEFT """"""""""""" ,' """""" ,'(
,"R """"""""""""""" ,' """""" ,')
----------------------------------#ABD
@,S#120_4 .,SYMBOLS .( .,GR\P+3
;A_4 ,! GR\P+ SYMBOLS LI/$ ABV M/
2 US$ "EY": 9 ! TRANSCRIP;N1 :E!R =
LIT]>Y OR MA!MATICAL PURPOSES4 ,!
GR\P+ SYMBOLS ( ,5GLI% ,BRL M/ N"E 2
US$ EXCEPT 65CLOSE LIT]>Y MAT]IAL ON
TITLE PAGES4 ,IF A GR\P+ SIGN O3URS :
IS N LI/$ ABV1 !N 9 ! _S (! ,CODE1 !
TRANSCRIB] M/ DEVISE A SYMBOL ^: F/
-PON5T IS ( =! OP5+ GR\P+ SYMBOL &
M/ USE ! SAME DEVICE B ) LA/ -PON5T )
=! CLOS+ SYMBOL4
(1) (I4E4)
(2) (S4A4S4 .K S4A4S4)
(3) (,,LCM M1NS .L[E/ .-MON
.MULTIPLE) #CBI
(4) .(,W$41 ,?URS41 A#ABD
,FRI4.)
(5) .(,M>Y1 ,S,Y1 ,J1N.)
(6) (SEV5)^2"+1
(7) (LI<T-YE>)
(8) (;X-9T]CEPT), (XY-PLANE)
(9) (_8,TWO0 IS N ! SAME Z TWO4)
(10) (5-9* /ICK)
(11) (,B>-;X)
(12) (1-TO-#1)
(13) (RATE)@*("T) .K (4T.E)
(14) (DIVISOR)("PIAL QUOTI5T)
+(REMA9D]) .K (DIVID5D)
----------------------------------#ABE
(15) (;A-;Z)
(16) (,,VI-,,IX)
(17) (X+Y)(X-Y)
;B_4 ,AL? SIGNS ( GR\P+ MO/ -MONLY
O3UR 9 PAIRS1 ? IS N ALW S4 ,IF AN
OP5+ GR\P+ SIGN O3URS )\T 2+ FOLL[$
LAT] 0! CORRESPOND+ CLOS+ SIGN1 OR IF
! CLOS+ SIGN O3URS )\T HAV+ BE5 PREC$$
0! CORRESPOND+ OP5+ SIGN1 ? SITU,N M/
2 PRES]V$ 9 ! TRANSCRIP;N4
,NEME? ,MA?4 ,CODE1 #1972 A#ABE
(1) @);0^1
(CLOS+ BRACKET ) #0 Z SUBSCRIPT & #1
Z SUP]SCRIPT)
@,S#121_4 .,HORIZONTAL .,GR\P+
.,SIGNS3 ,:5 A HORIZONTAL GR\P+ SIGN
O3URS OV] OR "U A MA!MATICAL EXPRES.N1
X M/ 2 REG>D$ Z A MODIFI]4 ,X IS REC-
OMM5D$ T ! HORIZONTAL GR\P+ SYMBOLS 2
DRAWN4 ,H["E1 :5 !Y >E 6BE REPRES5T$ 9
BRL1 ! MODIFI$ EXPRES.N M/ 2 TRAN-
SCRIB$ AC TO @,S#86A_4 ,! LEFT GR\P+
SYMBOL M/ 2 US$ :5 ! MODIFI] IS .DI-
RECTLY .OV] &! "R GR\P+ SYMBOL :5 !
MODIFI] IS .DIRECTLY ."U4
(1) "X+Y<.(]
(2) "X+Y%.)]
(3) "X+Y<@(]
(4) "X+Y%@)]
634 ,'BRACKET OV] 9 PR9T,'
(5) X+Y
#CCA
9E5 ,'BRACE OV] 9 PR9T,' B#ABE
(6) X+Y
@,S#122_4 .,BOLDFACE .,BRACKETS3
,BOLDFACE BRACKETS >E (T5 US$ 6DESIG-
NATE ! .9TEG] .FUNC;N4
(1) _@(X_@)
@,S#123_4 .,HALF-,BRACKETS3 ,! UPP]
HALF-BRACKETS (LEFT & "R) >E -MONLY
US$ 6REPRES5T ! .CEIL+ .FUNC;N4 ,! L[]
HALF-BRACKETS (LEFT & "R) >E -MONLY
US$ 6REPRES5T ! .FLOOR .FUNC;N4 ,^!
SIGNS >E AL US$ = MISCELLANE\S PUR-
POSES 9 _M FIELDS ( MA!MATICS & SCI;E4
(1) ,IF X .K #3.5, !N A;(X@;)
.K #3 & @^(X@^) .K #4_4
----------------------------------#ABF
(2) ,A;N@^)I
(3) @^(A1 A2 ''' A;N"@;)
@,S#124_4 .,V]TICAL .,B>S3
;A_4 ,D\# BOLDFACE V]TICAL B>S >E
,NEME? ,MA?4 ,CODE1 #1972 A#ABF
USU,Y R1D Z .! .NORM .(4
(1) _\_\F_\_\
;B_4 ,S+LE V]TICAL B>S >E (T5 R1D
Z ..! ABSOLUTE VALUE .(1 B >E US$ =
O!R PURPOSES4
(1) \X\
(2) \;0^1
(3) \;X ;.K #0
@,S#125_4 .,TRANSCRIB]'S .,GR\P+
.,SYMBOLS3 ,! REGUL> TRANSCRIB]'S
GR\P+ SYMBOLS 9 ! ABV LI/ M/ 2 US$ TO
5CLOSE ANY TRANSCRIB]'S NOTE : HAS BE5
9S]T$ 96! TEXT (SEE @,S#186B)_4 ,^! M/
N 2 US$ 65CLOSE A LI/ ( TRANSCRIB]'S
NOTES : APPE>S AT ! 2G9N+ (A BRL VOL-
UME4 ,! SAME RULES : GOV]N PUNCTU,N &
3TRAC;N ( EXPRES.NS 3TA9+ GR\P+ SYM-
BOLS AL GOV]N TRANSCRIB]'S NOTES4 ,=
USE ( 5L>G$ TRANSCRIB]'S GR\P+ SYMBOLS
SEE @,S#184B_4 #CCC
@,S#126_4 ..,USE ( ,5L>G$ B#ABF
,GR\P+ .,SYMBOLS3 ,:5 A SY/EM ( MA!-
MATICAL EXPRES.NS IS >RANG$ ON TWO OR
M L9ES ( 9K PR9T1 &A SIGN ( GR\P+ IS
US$ 6UNIFY ! SY/EM1 ! CORRESPOND+
GR\P+ SYMBOL 9 ! TRANSCRIP;N M/ 2 9DI-
CAT$ Z 5L>G$ 0! USE ( DOT #6 69DICATE
! 5L>GE;T4 ,AM;G S* SY/EMS ( MA!MATI-
CAL EXPRES.NS >E3 SY/EMS ( EQU,NS1
DET]M9ANTS1 & MATRICES4 ,EA* BRL L9E :
3TA9S ANY "P (! TRANSCRIP;N ( S* A
SY/EM M/ AL 3TA9 ! 5L>G$ GR\P+ SYMBOL
& ^! M/ 2 V]TIC,Y ALIGN$4 ,IF ONLY !
LEFT OR ONLY ! "R MEMB] (A PAIR (
GR\P+ SIGNS IS PRES5T 9 9K PR9T1 ONLY
! CORRESPOND+ GR\P+ SYMBOL M/ 2 REPRE-
S5T$ 9 ! TRANSCRIP;N4 ,H["E1 :5 X IS
ADVISA# = ANY R1SON 6D S1 = EXAMPLE1
6SAVE SPACE 0AVOID+ RUNOV]S1 ! 5L>G$
GR\P+ SYMBOLS MAY 2 DRAWN4
(1) .,(X+Y .K #2.,)_4
.,(X-Y .K #0.,)
(A TWO-L9E SY/EM ( EQU,NS 5CLOS$ )9
,NEME? ,MA?4 ,CODE1 #1972 C#ABF
BRACES1 EQU,NS >E A3ID5T,Y ALIGN$2 9
9K PR9T1 P]IOD IS C5T]$)
(2) ,\A B,\ .K AD-BC_4
,\C D,\
(A TWO-BY-TWO DET]M9ANT 5CLOS$ )9
V]TICAL B>S2 ! EQUALS SIGN &! AD-BC
>E C5T]$ 9 9K PR9T)
(3) Y .K @,(;X, IF X "K.K #0
@,(0, IF X .1 #0_4
(A TWO-L9E SY/EM UNIFI$ ON ! LEFT 0A
LEFT BRACKET)
----------------------------------#ABG
(4) X .K @,(COS .A SIN .A #0@,)
@,(-SIN .A COS .A #0@,)
@,(#0 #0 #1@,)
(A ?REE-BY-?REE MATRIX 5CLOS$ )9
L>GE BRACKETS)
#CCE
(5) A#ABG
,\,\#1 #0 #0,\,\ .K ,I_4
,\,\#0 #1 #0,\,\
,\,\#0 #0 #1,\,\
(A ?REE-BY-?REE MATRIX 5CLOS$ )9 D\#
V]TICAL B>S)
@,S#127_4 ..,NON-,USE ( ,5L>G$
,GR\P+ .,SYMBOLS3 ,SIGNS ( GR\P+ M/ N
2 9DICAT$ Z 5L>G$ 9 ! TRANSCRIP;N :5 !
CORRESPOND+ SIGNS 9 9K PR9T >E MADE
L>GE S* Z =! PURPOSE ( COV]+ A FRAC;N1
BINOMIAL COE6ICI5T OR O!R MAT]IAL O3U-
PY+ A L>GE AM.T ( V]TICAL SPACE4 ,NO
SIGNS1 EXCEPT GR\P+ SIGNS1 MAY "E 2
%[N Z 2+ 5L>G$4
(1) (?X+Y/U+V)^2
(2) (N+K%K)
(3) >.>X.]]
(4) !?F(X)DX/(X-T)^N"#
,NEME? ,MA?4 ,CODE1 #1972 B#ABG
@,S#128_4 ..,SPAC+ ) ,SYMBOLS (
.,GR\P+3
;A_4 ,SPACES MAY 2 REQUIR$ 6BE
LEFT AF AN OP5+ 5L>G$ GR\P+ SYMBOL OR
2F A CLOS+ 5L>G$ GR\P+ SYMBOL 6PRES]VE
! V]TICAL ALIGN;T ( S* SYMBOLS REQUIR$
9 @,S#126_4
(1) .,(2X+ Y .K 9.,)
.,( X-3Y .K 11.,)
(A UNIFI$ SY/EM ( TWO EQU,NS 9 :
V]TICAL ALIGN;T IS REQUIR$)
----------------------------------#ABH
;B_4 ,A SPACE M/ 2 LEFT 2T AN OP5+
& CLOS+ GR\P+ SYMBOL :5 "! IS A BLANK1
N REPRES5T+ OMIS.N1 2T ! CORRESPOND+
SIGNS 9 9K PR9T4
(1) .( .)
(THE EMPTY SET)
#CCG
,NEME? ,MA?4 ,CODE1 #1972 A#ABH
,RULE ,,XIX--,SIGNS
& ,SYMBOLS ( ,OP],N
,AMP]S& (AND1 LOGICAL PRODUCT) _&
,A/]ISK @#
,BACK ,SLA% (DIVIDES1 IS A FACTOR
OF) _*
,CIRCLE ) ,9T]IOR ,DOT $C_$*]
,CIRCLE ) ,9T]IOR ,PLUS $C_$+]
,CIRCLE ) ,9T]IOR ,M9US $C_$-]
#CCI
,NEME? ,MA?4 ,CODE1 #1972 B#ABH
,DA7]
,S+LE _]
,D\# __]
,DIVI.N (DIVID$ BY) ./
,DOT (AND) *
,FRAC;N ,L9E (OV])
,DIAGONAL _/
,SIMPLE /
,DIAGONAL ,-PLEX ,_/
,-PLEX ,/ "33
#CDA
,NEME? ,MA?4 ,CODE1 #1972 C#ABH
,HYP]COMPLEX ,,/
,HOLL[ ,DOT .*
----------------------------------#ABI
,9T]SEC;N (CAP) .%
,LOGICAL ,PRODUCT (AND1 MEET) @%
,LOGICAL ,SUM (JO91 OR) @+
,M9US
,REGUL> -
,BOLDFACE _-
,M9US ,FOLL[$ 0,PLUS
,BOLDFACE ,M9US ,FOLL[$ 0,BOLDFACE
,PLUS _-"_+
,BOLDFACE ,M9US ,FOLL[$ 0,REGUL>
,PLUS _-"+
#CDC
,NEME? ,MA?4 ,CODE1 #1972 A#ABI
,REGUL> ,M9US ,FOLL[$ 0,REGUL>
,PLUS -"+
,REGUL> ,M9US ,FOLL[$ 0,BOLDFACE
,PLUS -"_+
,M9US OR ,PLUS -+
,M9US ) ,DOT OV] (PROP] DI6];E)
.-
,MULTIPLIC,N ("TS)
,CROSS (C>TESIAN PRODUCT) @*
,DOT *
,NUMB] ,SIGN2 ,CROSSHAT*2
,TIC-TAC-TOE2 ,P.DS (WEI<T) .#
#CDE
,NEME? ,MA?4 ,CODE1 #1972 B#ABI
,P>AGRAPH ,M>K @,P
,PLUS
,REGUL> +
,BOLDFACE _+
,PLUS ,FOLL[$ 0,M9US
,BOLDFACE ,PLUS ,FOLL[$ BY
,BOLDFACE ,M9US _+"_-
,BOLDFACE ,PLUS ,FOLL[$ BY
,REGUL> ,M9US _+"-
----------------------------------#ACJ
,REGUL> ,PLUS ,FOLL[$ BY
,REGUL> ,M9US +"-
,REGUL> ,PLUS ,FOLL[$ BY
,BOLDFACE ,M9US +"_-
,PLUS OR ,M9US +-
#CDG
,NEME? ,MA?4 ,CODE1 #1972 A#ACJ
,SEC;N ,M>K @,S
,SLA% (P]1 OV]1 DIVID$ BY) _/
,SQU>E
,FILL$-,IN ,SQU>E $_4
,HOLL[ ,SQU>E $4
,/> $S
,TILDE
,EXT5D$ @,:
,SIMPLE @:
,UNION (CUP) .+
,V]TICAL ,B> (IS A FACTOR1
DIVIDES) \
#CDI
,NEME? ,MA?4 ,CODE1 #1972 B#ACJ
@,S#129_4 .,AMP]S&3 ,:5 ! AMP]S& IS
US$ 9 LIT]>Y 3TEXT1 & )\T REF];E 6!
SPECIFIC NATURE (! SIGN XF1 X %D N 2
REG>D$ Z A SIGN ( OP],N1 &1 ACLY1 !
RULES ( ,5GLI% ,BRL APPLY4 ,O!RWISE1 !
SYMBOL 9 ! ABV LI/ M/ 2 US$4
(1) ,,AT&,T
(LIT]>Y 3TEXT)
(2) ,! _& (T5 DENOTES LOGICAL
3JUNC;N4
(SPECIFIC ATT5;N IS CALL$ 6! NATURE
(! SIGN)
(3) ,A_&,B
(MA!MATICAL 3TEXT)
----------------------------------#ACA
@,S#130_4 ..,A/]ISK1 ,DA7]1 ,D\#
,DA7]1 ,NUMB] ,SIGN1 ,P>AGRAPH ,M>K1
,SEC;N ,M>K1 .,/>3 ,! A/]ISK1 DA7]1
D\# DA7]1 NUMB] SIGN1 P>AGRAPH M>K1
SEC;N M>K1 & /> M/ 2 REPRES5T$ 0! SYM-
BOLS PROVID$ = !M 9 ? ,CODE2 ! ,5GLI%
,BRL SYMBOLS M/ 2 AVOID$ EV5 #CEA
:5 ! CORRESPOND+ SIGNS >E US$ A#ACA
= PURPOSES ( REF];E4
(1) F@#G
(2) #3@##4
(3) X^@#
(4) X.#Y
(5) #2.##3
(6) ,R^.#
(7) ,A@,P,B
(8) ,A@,S,B
(9) ,A$S,B
@,S#131_4 .,FRAC;N .,L9ES3 ,=A COM-
PLETE 4CUS.N (! RULES GOV]N+ FRAC;NS
SEE ,RULE ,,XII_4
@,S#132_4 .,9T]SEC;N1 .,UNION3 ,:5 !
9T]SEC;N SIGN OR ! UNION SIGN IS MODI-
FI$ 0A SUP]SCRIB$ B>1 A SUBSCRIB$ B>1
OR BO?1 ! -B9,N IS NO L;G] A SIGN (
OP],N B A SIGN ( -P>ISON -P.D$ V]TI-
C,Y (SEE @,S#147)_4
,^! SIGNS >E FREQU5TLY MODIFI$ 2L1 &
>E 3SEQU5TLY PR9T$ WIDE 5 6A3OMMODATE
! MODIFI]4 ,! V>IA# WID? ( ^! SIGNS M/
,NEME? ,MA?4 ,CODE1 #1972 B#ACA
2 IGNOR$ 9 ! TRANSCRIP;N4 ,SUP]SCRIPTS
OR SUBSCRIPTS : >E "S"TS ATTA*$ 6^!
SIGNS M/ 2 TR1T$ 9 ! USUAL MANN] =
H&L+ SUP]SCRIPTS & SUBSCRIPTS4
(1) ,A.%,B
(2) ".%%.A @E .,A]X;.A
(3) ,A.+,B
@,S#133_4 ..,LOGICAL ,PRODUCT1 ,LOG-
ICAL .,SUM3 ,:5 ! SIGNS = .LOGICAL
.PRODUCT OR .LOGICAL .SUM >E MODIFI$
0A SUP]SCRIB$ B>1 A SUBSCRIB$ B>1 OR
BO?1 ! -B9,N IS NO L;G] A SIGN ( OP],N
B A SIGN ( -P>ISON -P.D$ V]TIC,Y (SEE
@,S#147)_4
(1) X@%Y
(2) X@+Y
----------------------------------#ACB
@,S#134_4 ..,M9US ,FOLL[$ 0,PLUS1
,PLUS ,FOLL[$ 0,M9US1 ,M9US OR ,PLUS1
,PLUS OR .,M9US3 ,:5 ! SIGNS = .PLUS &
.M9US >E -B9$ EI V]TIC,Y OR #CEC
HORIZONT,Y1 ! -B9,N M/ 2 RE- A#ACB
G>D$ Z A S+LE SIGN ( OP],N4 ,XS COM-
PON5TS M/ N 2 DIVID$ 2T BRL L9ES 9 !
TRANSCRIP;N4
(1) +2-"+3
(2) -#3+"-5
(3) X-+Y
(4) X+-Y
@,S#135_4 .,MULTIPLIC,N3 ,! TWO COM-
MON MULTIPLIC,N SIGNS1 .CROSS & .DOT1
M/ N 2 US$ 9T]*ANGEABLY 9 ! TRANSCRIP-
;N4 ,! CROSS IS "S"TS MODIFI$ 2L4
(1) #3@*10
(2) X*Y
(3) "@*%.A @E .,A],A;.A
@,S#136_4 .,SLA%3 ,! SLA% M/ 2 REP-
RES5T$ 0! SYMBOL PROVID$ = X 9 ?
,CODE4 ,! ,5GLI% ,BRL SYMBOL M/ N 2
US$4
(1) AND_/OR
,NEME? ,MA?4 ,CODE1 #1972 B#ACB
(2) ,! RISE_/RUN RATIO IS #3_4
(3) #1 WATT .K #1 JOULE_/SEC4
(4) ;C_/;O
(A2REVI,N M1N+ 8C>E OF_0)
(5) VOLT_/AMP
(6) #60 MI_/HR
(7) #7_/4_/76
(A DATE)
----------------------------------#ACC
@,S#137_4 .,TILDE3 ,? SIGN ( OP],N
IS US$ PREDOM9ANTLY 9 LOGIC )! M1N+ (
.N4
(1) @:P
(2) @:P@+@:Q@+@:R
(3) @:"@:,T@+,R
@,S#138_4 ..,SPAC+ ) ,SYMBOLS (
.,OP],N3
;A_4 ,A SPACE M/ 2 LEFT ON EI SIDE
( AN OP],N SYMBOL "U ANY (! CIRCUM/.ES
LI/$ 2L4
;I_4 ,2T A -P>ISON SYMBOL & AN
OP],N SYMBOL4 #CEE
(1) X .K -Y A#ACC
;II_4 ,AF A FUNC;N "N OR XS
A2REVI,N & 2F A SYMBOL ( OP],N4
(1) SIN -X
;III_4 ,2T AN ELLIPSIS OR DA% &A
SYMBOL ( OP],N4
(1) #1+2+ ''' +N
(2) #10- ---- .K #8
;IV_4 ,2T AN A2REVI,N &A SYMBOL
( OP],N O!R ?AN ! FRAC;N L9E OR SLA%4
(1) #1 YD +2 YD .K #3 YD
(IN 9K PR9T1 "! IS A SPACE ON BO?
SIDES (! PLUS SIGN)
;V_4 ,": REQUIR$ AC 6,RULE
,,XXII_4
(1) ____ + ____
,NEME? ,MA?4 ,CODE1 #1972 B#ACC
;B_4 ,A SPACE M/ N 2 LEFT ON EI
SIDE (A SYMBOL ( OP],N 9 ANY O!R SITU-
,N4
(1) A_*B
(2) X$C_$+]Y
(3) #12./3
----------------------------------#ACD
(4) F.*G
(5) SIN X-SIN Y
(IN 9K PR9T1 "! IS A SPACE ON BO?
SIDES (! M9US SIGN)
(6) X$4Y
(7) $4+$T
(8) RATE@*TIME
(9) MILES_/HOUR
(10) QUOTIENT@*DIVISOR+REMAINDER
.K DIVIDEND
(11)
#3@*SEVEN^2"+4@*SEVEN^1"+5@*SEVEN^0
.K #345;SEVEN
(12) (2N+3)\3
#CEG
(13) A#ACD
#3 FT^2"+3 FT^2 .K #6 FT^2
,NEME? ,MA?4 ,CODE1 #1972 B#ACD
,RULE ,,XX--,SIGNS &
,SYMBOLS ( ,-P>ISON
,SIMPLE ,-P>ISON ,SIGNS
,>C
,3CAVE UPW>D $A
,3CAVE D[NW>D $'
,>R[
,LEFT-PO9T+ $[33
----------------------------------#ACE
,"R-PO9T+
,3TRACT$ $O
,UNCONTRACT$ $33O
,D[N-PO9T+ $%33O
,UP-PO9T+ $<33O
#CEI
,NEME? ,MA?4 ,CODE1 #1972 A#ACE
,TWO-WAY
,HORIZONTAL $[33O
,V]TICAL $<[33O
,EQUALS (IS EQUAL TO)
,NORMAL .K
,BOLDFACE _.K
,GRT] ,?AN (IS GRT] ?AN)
,NORMAL .1
,) CURV$ SIDES ..1
,ID5T;Y (IS 3GRU5T TO2 IS ID5TICAL
TO _L
,9CLU.N (IS 3TA9$ IN2 IS A SUBSET
OF) _"K
,LESS ,?AN (IS LESS ?AN)
,NORMAL "K
#CFA
,NEME? ,MA?4 ,CODE1 #1972 B#ACE
,) CURV$ SIDES ."K
,MEMB]%IP (IS AN ELE;T (2 2L;GS TO)
@E
,P>ALLEL ,TO (IS P>ALLEL TO) $L
,P]P5DICUL> ,TO (IS P]P5DICUL> TO)
$P
,PROPOR;N (AS) ;2
,RATIO (IS TO) "1
----------------------------------#ACF
,REL,N (IS RELAT$ TO) ,R
,REV]SE ,9CLU.N (3TA9S2 9 LOGIC1
IMPLIES) _.1
,REV]SE ,MEMB]%IP (3TA9S ! ELE;T)
@5 OR
#CFC
,NEME? ,MA?4 ,CODE1 #1972 A#ACF
,TILDE
,SIMPLE (IS RELAT$ TO1 IS SIMIL>
TO) @:
,EXT5D$ (IS RELAT$ TO) @,:
,V>I,N (V>IES AS) _=
,V]TICAL ,B> (S* THAT) \
,MODIFI$ ,-P>ISON ,SIGNS
,EQUALS ,SIGN
,C>ET OV] ".K<_<]
,C>ET "U (IS PROJECTIVE
TO1 PROJECTIVE CORRE-
SPOND;E) ".K%_<]
,DEGREE SIGN OV] (IS EQUAL
9 DEGREES TO)
".K<.*]
,DOT OV] (IS APPROXIMATELY
EQUAL TO) ".K<*]
#CFE
,NEME? ,MA?4 ,CODE1 #1972 B#ACF
,DOT OV] & DOT "U ".K%*<*]
,EQUILAT]AL TRIANGLE OV]
".K<$T]
,9V]T$ C>ET OV] ".K<_%]
,LEFT-PO9T+ C>ET OV]
".K<;<]
,"Q M>K OV] ".K<_8]
,"R-PO9T+ C>ET OV]
".K<;%]
,TWO DOTS OV] & TWO DOTS "U
".K%**<**]
,V]TICAL B> OV] ".K<\]
#CFG
,NEME? ,MA?4 ,CODE1 #1972 C#ACF
,HORIZONTAL ,B>
,C>ET OV] ":<_<]
----------------------------------#ACG
,C>ET "U (IS P]SPECTIVE TO1
P]SPECTIVE CORRE-
SPOND;E) ":%_<]
,DOT "U ":%*]
,SIMPLE ,TILDE1 ,DOT ,"U
"@:%*]
,-P>ISON ,SIGNS ,-P.D$ ,V]TIC,Y
,>R[ ,-B9,NS
,"R-PO9T+ OV] LEFT-PO9T+
$33O$[33
,"R-PO9T+ ) UPP] B>B OV]
LEFT-PO9T+ ) L[] B>B
$33@O$,[33
,"R-PO9T+ OV] BOLDFACE
LEFT-PO9T+
$33O$_[33
#CFI
,NEME? ,MA?4 ,CODE1 #1972 A#ACG
,LEFT-PO9T+ OV] BOLDFACE
"R PO9T+ $[33$_33O
,BOLDFACE "R-PO9T+ OV]
LEFT PO9T+ $_33O$[33
,BOLDFACE LEFT-PO9T+ OV]
"R-PO9T+ $_[33$33O
,BOLDFACE "R-PO9T+ OV]
BOLDFACE LEFT-PO9T+
$_33O$_[33
,BOLDFACE LEFT-PO9T+ OV]
BOLDFACE "R-PO9T+
$_[33$_33O
,L;G "R-PO9T+ OV] %ORT
LEFT-PO9T+ $333O$[3
,%ORT "R-PO9T+ OV] L;G
LEFT-PO9T+ $3O$[333
#CGA
,NEME? ,MA?4 ,CODE1 #1972 B#ACG
,EQUIVAL;E (IS EQUIVAL5T TO)
@<,<
,GRT] ,?AN
,B> OV] GRT] ?AN (IS EQUAL
TO OR GRT] ?AN)
:.1 OR
,B> "U GRT] ?AN (IS GRT]
?AN OR EQUAL TO) OR
.1:
,EQUALS SIGN OV] GRT] ?AN
(IS EQUAL TO OR
GRT] ?AN) .K.1 OR
,EQUALS SIGN "U GRT] ?AN
(IS GRT] ?AN OR
EQUAL TO) .1.K OR A
----------------------------------#ACH
,9CLU.N
,B> OV] 9CLU.N (IS A
SUBSET OF) :_"K
,B> "U 9CLU.N (IS A
SUBSET OF) _"K:
#CGC
,NEME? ,MA?4 ,CODE1 #1972 A#ACH
,EQUALS SIGN OV] 9CLU.N
(IS A SUBSET OF) .K_"K
,EQUALS SIGN "U 9CLU.N (IS
A SUBSET OF) _"K.K
,9T]SEC;N (CAP)
,B> "U 9T]SEC;N .%:
,EQUALS SIGN "U 9T]SEC;N
.%.K
,LESS ,?AN
,B> OV] LESS ?AN (IS
EQUAL TO OR LESS ?AN)
:"K OR
,B> "U LESS ?AN (IS
LESS ?AN OR EQUAL TO) OR
"K:
,EQUALS SIGN OV] LESS ?AN
(IS EQUAL TO OR LESS
?AN) .K"K OR
#CGE
,NEME? ,MA?4 ,CODE1 #1972 B#ACH
,EQUALS SIGN "U LESS ?AN
(IS LESS ?AN OR OR
EQUAL TO) "K.K
,LOGICAL ,PRODUCT (MEET)
,B> OV] LOGICAL PRODUCT
:@%
,B> OV] & B> "U LOGICAL
PRODUCT :@%:
,B> OV] & EQUALS SIGN "U
LOGICAL PRODUCT
:@%.K
,B> "U LOGICAL PRODUCT @%:
,EQUALS SIGN OV] LOGICAL
PRODUCT .K@%
,EQUALS SIGN OV] & B> "U
LOGICAL PRODUCT .K@%:
,EQUALS SIGN OV] & EQUALS
SIGN "U LOGICAL PROD-
UCT .K@%.K
#CGG
,NEME? ,MA?4 ,CODE1 #1972 C#ACH
,EQUALS SIGN "U LOGICAL
PRODUCT @%.K
----------------------------------#ACI
,LOGICAL ,SUM (JOIN)
,B> OV] LOGICAL SUM :@+
,B> OV] & B> "U LOGICAL
SUM :@+:
,B> OV] & EQUALS SIGN "U
LOGICAL SUM :@+.K
,B> "U LOGICAL SUM @+:
,EQUALS SIGN OV] LOGICAL
SUM .K@+
,EQUALS SIGN OV] & B> "U
LOGICAL SUM .K@+:
,EQUALS SIGN OV] & EQUALS
SIGN "U LOGICAL SUM
.K@+.K
#CGI
,NEME? ,MA?4 ,CODE1 #1972 A#ACI
,EQUALS SIGN "U LOGICAL
SUM @+.K
,REV]SE ,9CLU.N
,B> OV] REV]SE 9CLU.N
:_O
,B> "U REV]SE 9CLU.N
_.1:
,EQUALS SIGN OV] REV]SE
9CLU.N .K_.1
,EQUALS SIGN "U REV]SE
9CLU.N _.1.K
,TILDE (IS RELAT$ TO)
,B> OV] D\# TILDE :@:@:
,B> OV] S+LE TILDE :@:
,B> "U D\# TILDE @:@::
#CHA
,NEME? ,MA?4 ,CODE1 #1972 B#ACI
,B> "U S+LE TILDE @::
,D\# TILDE @:@:
,EQUALS SIGN OV] D\# TILDE
.K@:@:
,EQUALS SIGN OV] S+LE TILDE
.K@:
,EQUALS SIGN "U D\# TILDE
@:@:.K
,EQUALS SIGN "U S+LE TILDE
@:.K
----------------------------------#ADJ
,UNION (CUP)
,B> "U UNION .+:
,EQUALS SIGN "U UNION .+.K
#CHC
,NEME? ,MA?4 ,CODE1 #1972 A#ADJ
,-P>ISON ,SIGNS ,-P.D$ ,HORIZONT,Y
,>R[ ,-B9,NS
,UP-PO9T+ FOLL[$ 0D[N-
PO9T+ $<33O"$%33O
,D[N-PO9T+ FOLL[$ 0UP-
PO9T+ $%33O"$<33O
,UP-PO9T+ FOLL[$ 0BOLD-
FACE D[N-PO9T+
$<33O"$%_33O
,D[N-PO9T+ FOLL[$ 0BOLD-
FACE UP-PO9T+
$%33O"$<_33O
,BOLDFACE UP-PO9T+ FOLL[$
0D[N-PO9T+
$<_33O"$%33O
,BOLDFACE D[N-PO9T+ FOLL[$
0UP-PO9T+
$%_33O"$<33O
#CHE
,NEME? ,MA?4 ,CODE1 #1972 B#ADJ
,BOLDFACE UP-PO9T+ FOLL[$
0BOLDFACE D[N-PO9T+
$<_33O"$%_33O
,BOLDFACE D[N-PO9T+ FOLL[$
0BOLDFACE UP-PO9T+
$%_33O"$<_33O
,GRT] ,?AN
,FOLL[$ 0LESS ?AN .1""K
,FOLL[$ 0EQUALS SIGN FOL-
L[$ 0LESS ?AN
.1".K""K
,LESS ,?AN
,FOLL[$ 0GRT] ?AN "K".1
,FOLL[$ 0EQUALS SIGN FOL-
L[$ 0GRT] ?AN
"K".K".1
#CHG
,NEME? ,MA?4 ,CODE1 #1972 C#ADJ
,-P>ISON ,SIGNS ,-P.D$ 0,SUP]POSI;N
,DOT
,2T B>S ( EQUALS SIGN
*@.K]
,)9 9CLU.N SIGN *@_"K]
,)9 REV]SE 9CLU.N SIGN
*@_.1]
----------------------------------#ADA
,EQUALS ,SIGN
,"? 9CLU.N SIGN
.K@_"K] OR _"K@.K]
,"? REV]SE 9CLU.N SIGN
.K@_.1] OR _.1@.K]
,GRT] ,?AN
,NE/ ( TWO ) /RAI<T SIDES
(IS L>GE -P>$ WITH)
.1@.1]
,NE/ ( TWO ) CURV$ SIDES
..1@..1]
#CHI
,NEME? ,MA?4 ,CODE1 #1972 A#ADA
,HORIZONTAL ,B>
,"? 9CLU.N SIGN :@_"K]
,"? REV]SE 9CLU.N SIGN
:@_.1]
,LESS ,?AN
,NE/ ( TWO ) /RAI<T SIDES
(IS SMALL -P>$ WITH)
"K@"K]
,NE/ ( TWO ) CURV$ SIDES
."K@."K]
,V]TICAL ,B>
,"? %AFT ( "R-PO9T+ >R[
\@$33O]
,"? %AFT ( LEFT-PO9T+ >R[
\@$[33]
#CIA
,NEME? ,MA?4 ,CODE1 #1972 B#ADA
@,S#139_4 .,NEG,N3 ,-P>ISON SIGNS
MAY 2 NEGAT$ 0A V]TICAL /ROKE OR 0AN
OBLIQUE /ROKE 9 EI DIREC;N4 ,H["E !
NEG,N IS E6ECT$ 9 9K PR9T1 ! SYMBOL /
(DOTS #3-4) M/ 2 PLAC$ UNSPAC$ 2F !
-P>ISON SYMBOL 2+ NEGAT$4
(1) /.K
(OBLIQUE NEG,N SIGN 9 9K PR9T1 F L[]
LEFT 6UPP] "R)
(2) /.K
(V]TICAL NEG,N SIGN 9 9K PR9T)
(3) /@E
(OBLIQUE NEG,N SIGN 9 9K PR9T1 F
UPP] LEFT 6L[] "R)
(4) /$L
(OBLIQUE NEG,N SIGN 9 9K PR9T1 F L[]
LEFT 6UPP] "R)
----------------------------------#ADB
(5) /"K
(OBLIQUE NEG,N SIGN 9 9K PR9T1 F
UPP] LEFT 6L[] "R)
#CIC
(6) /.1.K A#ADB
(V]TICAL NEG,N SIGN 9 9K PR9T)
@,S#140_4 .,>R[S3 ,A DETAIL$ 4CUS.N
(! 3/RUC;N ( >R[S ( _M TYPES IS PRE-
S5T$ 9 ,RULE ,,XXI_4 ,! >R[S 9 ! LI/ (
SIMPLE -P>ISON SIGNS >E ^? : O3UR )!
GRTE/ FREQU5CY4
,IF A "R-PO9T+ >R[ HAS A FULL B>B &A
S+LE %AFT ( ORD9>Y L5G?1 IS 9 REGUL>
TYPE1 & O3URS 0XF1 X M/ 2 REPRES5T$ 9
XS 3TRACT$ =M4 ,IF S* AN >R[ IS 9 NON-
REGUL> TYPE1 IS XF MODIFI$ OR O3URS Z
"P (A M -PLEX MODIFIC,N1 X M/ 2 REPRE-
S5T$ 9 XS UNCONTRACT$ =M4
(1) ,B $[33 ,A
(2) ,A $O ,B
(3) ,A $[33O ,B
(4) ,X "$33O<F.*G] ,Y
@,S#141_4 .,ID5T;Y3 ,? SIGN M/ N 2
US$ = .IS .3GRU5T .TO 9 GEOMETRY IF
ANO!R SIGN IS EMPLOY$ = ? PURPOSE 9 9K
PR9T4
,NEME? ,MA?4 ,CODE1 #1972 B#ADB
(1) F(X) _L #0
(2) #2 _L #5(MOD #3)
@,S#142_4 .,MEMB]%IP3 ,? SIGN M/ N 2
MISTAK5 =! ,GREEK L[]-CASE EPSILON1
EV5 ?\< X IS "S"TS REF]R$ TO 0T V "N4
,? SIGN IS G5],Y US$ :5 SP1K+ AB SETS
&! ELE;TS ( : !Y >E -POS$4 ,:5 !
,GREEK L[]-CASE EPSILON IS US$ 9 !
SAME TEXTBOOK1 ! PUBLI%] USU,Y MAKES A
SU6ICI5T 4T9C;N 2T ! TWO SIGNS 6PREV5T
? 3FU.N4
(1) X @E ,A
(;X IS AN ELE;T ( ;,A)
@,S#143_4 .,REL,N3 ,:5 A LR OR O!R
SIGN IS US$ 2T TWO EXPRES.NS 6%[ T !Y
>E RELAT$1 ! LR OR SIGN US$ 9 ? WAY M/
2 REG>D$ Z A -P>ISON SIGN4 ,Z S*1 X IS
SUBJECT 6ALL ! RULES GOV]N+ -P>ISON
SIGNS & SYMBOLS4 ,! LR ;,R IS FRE-
QU5TLY US$ 9 ? SITU,N4 #CIE
(1) A ,R B C#ADB
(2) A .? B
----------------------------------#ADC
@,S#144_4 .,TILDE3 ,:5 ! TILDE1 SIM-
PLE OR EXT5D$1 O3URS )A DOT OR C>ET
DIRECTLY OV] OR DIRECTLY "U X1 ! -B9,N
IS A MODIFI$ SIGN ( -P>ISON (SEE
@,S#146)_4 ,:5 X O3URS DIRECTLY OV] OR
DIRECTLY "U ANO!R SIMPLE -P>ISON SIGN1
! -B9,N IS A -P>ISON SIGN -P.D$ V]TI-
C,Y (SEE @,S#147)_4
(1) X @: Y
(2) X @,: Y
@,S#145_4 .,V]TICAL .,B>3 ,9 A4I;N
6XS USE Z A -P>ISON SIGN M1N+ 8S* T10
! V]TICAL B> IS US$ 9 S"EAL O!R WAYS 9
MA!MATICS4 ,X HAS ALR BE5 LI/$ Z A
SIGN ( GR\P+ & Z A SIGN ( OP],N4 ,X IS
HELP;L 6"K T :5 ! V]TICAL B> M1NS 8S*
T0 X IS USU,Y "P ( AN EXPRES.N )9
BRACES US$ = SET NOT,N1 OR 9 ASSOCI,N
) "O (! QUANTIFI]S4 ,H["E1 X MAY AL
APPE> 9 O!R SITU,NS4
,NEME? ,MA?4 ,CODE1 #1972 A#ADC
(1) .(X \ \X\ "K #10.)
(2) ,*OOSE X \ X .K Y^2_4
(3) @=\;X \ X .K -X
@,S#146_4 .,MODIFI$ .,-P>ISON
.,SIGNS3 ,! MODIFI$ -P>ISON SIGNS 9 !
ABV LI/ >E 3/RUCT$ 9 A3ORD.E )! RULES
=! REPRES5T,N ( MODIFI$ EXPRES.NS (SEE
,RULE ,,XIV)_4 ,MODIFI$ SIGNS ( -P>I-
SON O!R ?AN ^? 9 ! ABV LI/ M/ 2 CON-
/RUCT$ 9 A3ORD.E )! SAME PR9CIPLES4
@,S#147_4 ..,-P>ISON ,SIGNS ,-P.D$
.,V]TIC,Y3 ,! TRANSCRIB] M/ REPRES5T A
V]TICAL >RANGE;T ( SIMPLE -P>ISON
SIGNS Z AN UNSPAC$ HORIZONTAL SU3ES.N
(! CORRESPOND+ SIMPLE -P>ISON SYMBOLS1
! F/ SYMBOL CORRESPOND+ 6! UPP]MO/
SIGN4 ,! BRL R1D] M/ 9T]PRET A SU3ES.N
( UNSPAC$ SIMPLE -P>ISON SYMBOLS Z
REPRES5T+ ! FACT T ! CORRESPOND+ SIGNS
>E >RANG$ V]TIC,Y 9 9K PR9T1 9 DESC5D+
ORD]1 ! UPP]MO/ SIGN CORRESPOND+ 6! F/
SYMBOL4 ,-P>ISON SIGNS -P.D$ #CIG
V]TIC,Y N %[N 9 ! LI/ M/ 2 B#ADC
TRANSCRIB$ 9 A3ORD.E )! ABV PR9CIPLES4
@,S#148_4 ..,9T]SEC;N1 ,UNION1
,LOGICAL ,PRODUCT1 ,LOGICAL .,SUM3 ,!
9T]SEC;N1 UNION1 LOGICAL PRODUCT1 &
LOGICAL SUM SIGNS1 :5 UNMODIFI$1 >E N
SIMPLE -P>ISON SIGNS1 B OP],N SIGNS
(SEE @,S#132 & @,S#133, RESPECTIVE-
LY)_4
@,S#149_4 ..,-P>ISON ,SIGNS ,-P.D$
.,HORIZONT,Y3 ,! TRANSCRIB] M/ REPRE-
S5T A HORIZONTAL SU3ES.N ( -P>ISON
SIGNS 0PLAC+ ! MULTIPURPOSE 9DICATOR
2T ! UNSPAC$ CORRESPOND+ -P>ISON SYM-
BOLS4 ,-P>ISON SIGNS -P.D$ HORIZONT,Y
: >E N %[N 9 ! LI/ M/ 2 TRANSCRIB$ 9
A3ORD.E )! ABV PR9CIPLE4
@,S#150_4 ..,-P>ISON ,SIGNS ,-P.D$
0.,SUP]POSI;N3 ,-P>ISON SIGNS -P.D$ BY
SUP]POSI;N 9 ! ABV LI/ >E 3/RUCT$ 9
A3ORD.E )! RULES = REPRES5T+ SUP]POSI-
;N (SEE @,S#93)_4 ,-P>ISON SIGNS -P.D$
0SUP]POSI;N O!R ?AN ^? 9 ! ABV LI/ M/
2 3/RUCT$ 9 A3ORD.E )! SAME PR9CIPLES4
@,S#151_4 ..,SPAC+ ) ,SYMBOLS (
,NEME? ,MA?4 ,CODE1 #1972 C#ADC
.,-P>ISON3 ,A SPACE M/ 2 LEFT ON EI
SIDE (A -P>ISON SYMBOL4 ,H["E1 A SPACE
M/ N 2 LEFT 2T ! -P>ISON SYMBOL & ANY
PUNCTU,N SYMBOL1 GR\P+ SYMBOL1 OR 9DI-
CATOR : APPLIES 6X4
----------------------------------#ADD
(1) X $A Y
(2) X .K Y
(3) ".,S%N .K #0<,=]A;N
(4) (A, B) _.K (C, D) IF & ONLY IF
A .K C & B .K D_4
(5) X .1 Y
(6) ,X _"K ,Y
(7) ".+%,A _"K ,F],A
(8) ".,S%I "K J]A;IJ
(9) ,A @5 X
(10) #1 "1 #2 ;2 #3 "1 #6
(11) A+B "1 B ;2 C+D "1 D
(12) X _= Y
(13) .(ALL X \ EACH X "K #6.)
(14) ,! UNIT INTERVAL
.K .(X \ #0 "K: X "K: #1.)
(15) ,! SYMBOL = .LESS .?AN IS
8"K_40 #CII
(16) ("K, .K, .1) A#ADD
(17) !;X ;.K A^X ^.K B"F(X)DX
,NEME? ,MA?4 ,CODE1 #1972 #ADE
,RULE ,,XXI--,>R[S
,>R[ ,-PON5TS
,>R[ ,DIREC;N ,9DICATORS
,DEPRESSES NE>] >R[H1D BY #45
DEGREES ;
,ELEVATES NE>] >R[H1D BY #45
DEGREES ^
,MAKES NE>] >R[H1D PO9T UP <
,MAKES NE>] >R[H1D PO9T D[N %
,>R[ ,%AFTS
,CURV$ 59
,DA%$ 3 3
,DOTT$ 111
,L;G D\# 777
,L;G S+LE 333
,ORD9>Y D\# 77
#DJA
,NEME? ,MA?4 ,CODE1 #1972 A#ADE
,ORD9>Y S+LE 33
,%ORT D\# 7
,%ORT S+LE 3
,WAVY 935
,>R[ ,TYPES
,BOLDFACE _
,REGUL> (NO 9DICATOR)
,>R[H1DS
,B>B$ LEFT FULL [
,B>B$ LEFT L[] ,[
----------------------------------#ADF
,B>B$ LEFT UPP] @[
,B>B$ "R FULL O
,B>B$ "R L[] ,O
,B>B$ "R UPP] @O
#DJC
,NEME? ,MA?4 ,CODE1 #1972 A#ADF
,BLUNT$ LEFT FULL =
,BLUNT$ LEFT L[] ,=
,BLUNT$ LEFT UPP] @=
,BLUNT$ "R FULL =
,BLUNT$ "R L[] ,=
,BLUNT$ "R UPP] @=
,CURV$ LEFT FULL &
,CURV$ LEFT L[] ,&
#DJE
,NEME? ,MA?4 ,CODE1 #1972 B#ADF
,CURV$ LEFT UPP] @&
,CURV$ "R FULL Y
,CURV$ "R L[] ,Y
,CURV$ "R UPP] @Y
,/RAI<T LEFT FULL \
,/RAI<T LEFT L[] ,\
,/RAI<T LEFT UPP] @\
,/RAI<T "R FULL \
#DJG
,NEME? ,MA?4 ,CODE1 #1972 C#ADF
,/RAI<T "R L[] ,\
,/RAI<T "R UPP] @\
----------------------------------#ADG
@,S#152_4 ..,3TRACT$ ,=M ( ,"R-
,PO9T+ .,>R[3 ,:5 A "R-PO9T+ >R[ 9
REGUL> TYPE1 )A S+LE %AFT ( ORD9>Y
L5G? &A FULL B>B1 O3URS 0XF1 X M/ 2
REPRES5T$ 9 XS 3TRACT$ =M $O_4 ,IF S*
AN >R[ IS 9 NON-REGUL> TYPE1 IS MODI-
FI$1 OR O3URS Z "P (A M -PLEX MODIFI-
C,N1 X M/ 2 REPRES5T$ 9 XS UNCONTRACT$
=M $33O_4
@,S#153_4 .,>R[ .,-PON5TS3 ,"! IS A
L>GE CLASS ( SIGNS 9 ! =M ( >R[S :
DI6] F EA* O!R 9 S"EAL WAYS4 ,9 ! ABV
LI/1 "! IS PRES5T$ AN ASSORT;T ( >R[
-PON5TS F : S* SIGNS >E 3/RUCT$4 ,!
5TIRE 3/RUC;N IS A SIMPLE -P>ISON
SYMBOL4
@,S#154_4 ..,SIX ,/EPS = ,3/RUC;N (
.,>R[S3 ,>R[ -PON5TS M/ 2 #DJI
,NEME? ,MA?4 ,CODE1 #1972 A#ADG
TRANSCRIB$ 9 ! FOLL[+ ORD]3
;I_4 ,! %APE 9DICATOR4
;II_4 ,! >R[ DIREC;N1 IF X M/ 2
9DICAT$4
;III_4 ,! >R[ TYPE1 IF X M/ 2
9DICAT$4
;IV_4 ,! LEFT >R[H1D1 IF ANY4
;V_4 ,! >R[ %AFT1 IF REQUIR$4
;VI_4 ,! "R >R[H1D1 IF ANY4
(1) $<_[33O
(>R[1 TWO-WAY V]TICAL1 BOLDFACE1
B>B$ >R[H1DS AT BO? 5DS)
(2) $&33Y
(>R[1 TWO-WAY HORIZONTAL1 REGUL>
TYPE1 CURV$ >R[H1DS AT BO? 5DS)
(3) $^=77
(SPE>1 NOR?WE/1 BLUNT$ >R[H1D)
@,S#155_4 .,>R[ .,DIREC;NS3 ,X IS
POSSI# 6REPRES5T EI<T >R[ DIREC;NS BY
MAK+ PROP] USE (! DIREC;N 9DICATORS4
;A_4 ,! TWO HORIZONTAL DIREC;NS1
."R & .LEFT1 REQUIRE NO 9DI- #DAA
CATOR4 B#ADG
(1) $O
("R-PO9T+ >R[1 3TRACT$ =M)
(2) $33O
("R-PO9T+ >R[1 UNCONTRACT$ =M)
----------------------------------#ADH
(3) $[33
(LEFT-PO9T+ >R[)
(4) $[33O
(TWO-WAY HORIZONTAL >R[)
;B_4 ,! TWO V]TICAL DIREC;NS1 .UP
& .D[N1 REQUIRE ! DIRECTLY-OV] 9DI-
CATOR OR ! DIRECTLY-"U 9DICATOR1 RE-
SPECTIVELY4 ,! DIRECTLY-OV] 9DICATOR
8MAKES ! >R[H1D PO9T UP02 ! DIRECTLY-
"U 9DICATOR 8MAKES ! >R[H1D PO9T
D[N04 ,IF A V]TICAL >R[ IS PR9T$ ) "O
>R[H1D1 X M/ 2 TRANSCRIB$ 0US+ ! AP-
PROPRIATE SYMBOL =A ."R >R[H1D1 & N A
LEFT "O4
(1) $<33O
(>R[ PO9T+ UP)
,NEME? ,MA?4 ,CODE1 #1972 A#ADH
(2) $%33O
(>R[ PO9T+ D[N)
(3) $<[33O
(V]TICAL TWO-WAY >R[)
;C_4 ,! F\R OBLIQUE DIREC;NS RE-
QUIRE ! SUP]SCRIPT 9DICATOR OR ! SUB-
SCRIPT 9DICATOR4 ,! SUP]SCRIPT 9DI-
CATOR 8ELEVATES ! NE>] >R[H1D (IF "!
>E TWO) BY #45 DEGREES F ! HORIZONTAL
POSI;N02 ! SUBSCRIPT 9DICATOR 8DE-
PRESSES ! NE>] >R[H1D (IF "! >E TWO)
BY #45 DEGREES F ! HORIZONTAL POSI;N04
(1) $^33O
(>R[1 NOR?EA/)
(2) $^[33
(>R[1 NOR?WE/)
(3) $;33O
(>R[1 S\?EA/)
(4) $;[33
(>R[1 S\?WE/)
(5) $^[33O
(>R[1 NOR?WE/-S\?EA/) #DAC
(6) $;[33O B#ADH
(>R[1 S\?WE/-NOR?EA/)
----------------------------------#ADI
@,S#156_4 .,>R[ .,%AFTS3 ,AN >R[
%AFT MAY 2 CURV$1 DA%$1 DOTT$1 /RAI<T
OR WAVY1 S+LE OR D\#1 L;G OR %ORT4
;A_4 ,IF AN >R[ %AFT IS CURV$1 !
DIREC;N ( CURVATURE IS 9DICAT$ 0A LEFT
>R[H1D OR A "R >R[H1D4 ,A CURV$ >R[
%AFT FOLL[$ 0A "R >R[H1D REPRES5TS A
C.T]CLOCKWISE >R[2 A CURV$ >R[ %AFT
PREC$$ 0A LEFT >R[H1D REPRES5TS A
CLOCKWISE >R[4
(1) $59O
(>R[1 C.T]CLOCKWISE)
(2) $[59
(>R[1 CLOCKWISE)
;B_4 ,MO/ >R[ %AFTS >E S+LE4 ,AN
>R[ )A D\# >R[ %AFT IS "S"TS CALL$ A
.SPE>4
(1) $77O
(SPE>1 "R-PO9T+)
,NEME? ,MA?4 ,CODE1 #1972 A#ADI
(2) $[77
(SPE>1 LEFT-PO9T+)
(3) $[77O
(SPE>1 HORIZONTAL TWO-WAY)
;C_4 ,": ! L5G? ( AN >R[ %AFT HAS
SIGNIFIC.E1 ! L5G? IS 9DICAT$ 0! NUMB]
( REPETI;NS (! BRL >R[ %AFT SYMBOL4 ,!
LI/ 4T+UI%ES ?REE L5G?S1 B O!R L5G?S
MAY 2 9DICAT$ 0REP1T+ ! BRL >R[-%AFT
SYMBOL A SUITA# NUMB] ( "TS4
(1) $3O
(%ORT >R[1 "R-PO9T+)
(2) $[3
(%ORT >R[1 LEFT-PO9T+)
(3) $[3O
(%ORT >R[1 HORIZONTAL TWO-WAY)
(4) $333O
(L;G >R[1 "R-PO9T+)
(5) $[333
(L;G >R[1 LEFT-PO9T+#
(6) $[333O
(L;G >R[1 HORIZONTAL TWO-WAY) #DAE
@,S#157_4 .,>R[ .,TYPES3 #AEJ
,MO/ >R[S >E PR9T$ 9 REGUL> TYPE4 ,9 T
CASE1 NO 9DICATOR IS REQUIR$4 ,IF AN
>R[ IS PR9T$ 9 BOLDFACE TYPE1 ! BOLD-
FACE TYPE 9DICATOR IS REQUIR$4
(1) $_33O
(BOLDFACE >R[1 "R-PO9T+)
(2) $_[33
(BOLDFACE >R[1 LEFT-PO9T+)
(3) $_[33O
(BOLDFACE >R[1 HORIZONTAL TWO-WAY)
@,S#158_4 .,>R[H1DS3
;A_4 ,MO/ >R[H1DS >E B>B$4 ,H["E1
>R[H1DS AL O3UR Z BLUNT$1 CURV$1 OR
/RAI<T4 ,!Y MAY O3UR AT ! LEFT 5D1 "R
5D1 OR AT BO? 5DS1 (! >R[ %AFT4
(1) $33=
(>R[1 "R-PO9T+2 BLUNT$ >R[H1D)
(2) $=33
(>R[1 LEFT-PO9T+2 BLUNT$ >R[H1D)
(3) $=33=
(>R[1 HORIZONTAL TWO-WAY2 BLUNT$
,NEME? ,MA?4 ,CODE1 #1972 A#AEJ
>R[H1DS)
(4) $33Y
(>R[1 "R-PO9T+2 CURV$ >R[H1D)
(5) $&33
(>R[1 LEFT-PO9T+2 CURV$ >R[H1D)
(6) $&33Y
(>R[1 HORIZONTAL TWO-WAY2 CURV$ >R[-
H1DS)
(7) $33\
(>R[1 "R-PO9T+2 /RAI<T >R[H1D)
(8) $\33
(>R[1 LEFT-PO9T+2 /RAI<T >R[H1D)
(9) $\33\
(>R[1 HORIZONTAL TWO-WAY1 /RAI<T
>R[H1DS)
----------------------------------#AEA
;B_4 ,AN >R[H1D ) XS UPP] HALF
ONLY1 OR XS L[] HALF ONLY1 MAY AL 2
PRES5T4 ,ANY -B9,N ( >R[H1DS--B>B$1
BLUNT$1 CURV$1 /RAI<T1 LEFT OR "R1
FULL1 L[] HALF1 OR UPP] HALF--MAY OC-
CUR4
#DAG
(1) $@[33 A#AEA
(>R[1 LEFT UPP] B>B ONLY)
(2) $,[33
(>R[1 LEFT L[] B>B ONLY)
(3) $33@O
(>R[1 "R UPP] B>B ONLY)
(4) $33,O
(>R[1 "R L[] B>B ONLY)
(5) $@[33@O
(>R[1 UPP] B>BS ONLY)
(6) $,[33,O
(>R[1 L[] B>BS ONLY)
(7) $@[33,O
(>R[1 LEFT UPP] B>B & "R L[] B>B)
(8) $,[33@O
(>R[1 LEFT L[] B>B & "R UPP] B>B)
(9) $@[33O
(>R[1 LEFT UPP] B>B & FULL "R B>B)
(10) $,[33O
(>R[1 LEFT L[] B>B & FULL "R B>B)
(11) $[33@O
(>R[1 FULL LEFT B>B & "R UPP] B>B)
(12) $[33,O
(>R[1 FULL LEFT B>B & "R L[] B>B)
(13) $[33O
,NEME? ,MA?4 ,CODE1 #1972 B#AEA
(>R[1 FULL LEFT & "R B>BS)
----------------------------------#AEB
,RULE ,,XXII--,MISCELLANE\S
,SIGNS & ,SYMBOLS
,ANG/ROM ,UNIT @,A
,AT @A
,C>ET (CIRCUMFLEX) _<
,C5T @C
,*ECK ,M>K @>
,CROSS$ ;D @$
,CROSS$ ;H @H
,CROSS$ ,LAMBDA @.L
#DAI
,NEME? ,MA?4 ,CODE1 #1972 A#AEB
,CROSS$ ;,R @,R
,DEGREE .*
,DEL (NABLA1 GRADI5T) .$
,DITTO ,M>K ,'
,DOLL> @S
,EMPTY ,SET
,REPRES5T$ 0,Z]O ) ,V]TICAL
OR ,OBLIQUE ,B> ,"? ,X
_0
OR
,REPRES5T$ 0,FAC+ ,BRACES
.( .)
,FACTORIAL &
,9F9;Y ,=
#DBA
,NEME? ,MA?4 ,CODE1 #1972 B#AEB
,9TEGRAL
,S+LE !
,D\# !!
----------------------------------#AEC
,TRIPLE !!!
,L[] %!
,UPP] <!
,9TEGRAL ) ,SUP]POS$ ,CIRCLE
!@$C]
,9TEGRAL ) ,SUP]POS$ ,9F9;Y
!@,=]
#DBC
,NEME? ,MA?4 ,CODE1 #1972 A#AEC
,9TEGRAL ) ,SUP]POS$
,RECTANGLE !@$R]
,9TEGRAL ) ,SUP]POS$ ,SQU>E
!@$4]
,"PIAL ,DERIVATIVE (R.D ;D) @D
,P]C5T @0
,P.D (/]L+) @L
,PRIME '
,QUANTIFI]S
,EXI/5TIAL ,QUANTIFI]
,"! EXI/S1 = "S @=
OR
,"! EXI/S UNIQUELY = EX-
ACTLY "O @=\
OR
#DBE
,NEME? ,MA?4 ,CODE1 #1972 B#AEC
,UNIV]SAL ,QUANTIFI] (FOR
ALL1 = EA*1 = EVERY)
@&
,S9CE (BECAUSE) @/
,T,Y _
,"!=E
,NORMAL ,*
,NEGAT$ (IT DOES N FOLL[
THAT) /,*
,V]TICAL ,B> (5D ( PROOF) _\
----------------------------------#AED
@,S#159_4 .,ANG/ROM .,UNIT3 ,!
ANG/ROM UNIT M/ 2 TR1T$ Z AN A2REVI,N
& SPAC$ ACLY4
(1) #1_/10,000 .M .K #1 @,A
@,S#160_4 .,AT3 ,EXCEPT = PUNCTU,N1
9DICATORS1 OR SYMBOLS ( GR\P+ : #DBG
,NEME? ,MA?4 ,CODE1 #1972 A#AED
APPLY 6X1 A SPACE M/ 2 LEFT ON BO?
SIDES (! .AT SYMBOL4
(1) #3 BOXES @A #27@C
@,S#161_4 .,C>ET3 ,A C>ET M/ 2 UN-
SPAC$ F ! SYMBOLS 6: X APPLIES4
(1) #.35_<73
@,S#162_4 ..,C5T1 ,DOLL>1 ,P]C5T1
,P.D (,/]L+)_3 ,9 TRANSCRIB+ ^! SIGNS1
! CORRESPOND+ SYMBOLS M/ O3UPY ! SAME
POSI;N1 LEFT OR "R1 RELATIVE 6! SYM-
BOLS 6: !Y APPLY Z IS ! CASE 9 9K
PR9T4 ,^! SYMBOLS M/ 2 UNSPAC$ F !
SYMBOLS 6: !Y APPLY4
(1) #10@C
(2) X@C
(3) @S2.98
(4) @SX
(5) #7@0
(6) X@0 #DBI
(7) @L5 B#AED
(8) @LX
@,S#163_4 .,*ECK .,M>K4 ,MULTIPLE
*ECK M>KS M/ 2 WRITT5 UNSPAC$ F EA*
O!R4 ,EXCEPT = PUNCTU,N1 9DICATORS1 OR
SYMBOLS ( GR\P+ : APPLY 6X1 A SPACE M/
2 LEFT 2F & AF A S+LE *ECK M>K OR A
SEQU;E ( TWO OR M *ECK M>KS4
(1) @> MILK
(2) (@>) E7S
(3) @>@> BR1D
----------------------------------#AEE
@,S#164_4 ..,CROSS$ ;D, ,CROSS$ ;H,
,CROSS$ ,LAMBDA1 ,CROSS$ ;,R, ,"PIAL
.,DERIVATIVE3 ,^! SYMBOLS M/ 2 UNSPAC$
F EA* O!R & F O!R MA!MATICAL SYMBOLS &
SYMBOLS ( GR\P+ UN.S RULES : GOV]N ^!
O!R SYMBOLS REQUIRE A SPACE4
(1) @,R(,P1,P2, ,P3,P4)
(2) ?@D/@DX#F(X, Y)
(3) ?@D^2"U/@DX@DY#
,NEME? ,MA?4 ,CODE1 #1972 A#AEE
@,S#165_4 .,DEGREES3 ,:5 ! HOLL[ DOT
IS US$ )! M1N+ .DEGREES1 XS POSI;N AT
! SUP]SCRIPT LEVEL M/ 2 9DICAT$ 9 !
TRANSCRIP;N4
(1) #90^.*"+90^.* .K #180^.*
@,S#166_4 .,DEL3 ,:5 DEL IS US$ Z AN
OMIS.N SYMBOL1 ! SPAC+ REQUIR$ IS !
SAME Z ! SYMBOL X REPLACES4 ,O!RWISE1
! DEL IS SUBJECT 6! SPAC+ RULE (
@,S#164_4
(1) .$U+.$V
@,S#167_4 .,DITTO .,M>K3 ,DITTO
M>KS M/ 2 C5T]$ 2L ! MAT]IAL : !Y
DUPLICATE4 ,EXCEPT = PUNCTU,N1 9DICA-
TORS1 OR SYMBOLS ( GR\P+ : APPLY 6X1 A
SPACE M/ 2 LEFT ON BO? SIDES (A DITTO
M>K4
#DCA
,NEME? ,MA?4 ,CODE1 #1972 B#AEE
(1) #2 GOES 9TO #2, #1
,' ,' ,' #4, #2
,' ,' ,' #6, #3
@,S#168_4 ..,EMPTY ,SET (NULL SET1
VOID .SET)_3 ,! TRANSCRIB] M/ N MIS-
TAKE ! Z]O )A V]TICAL OR OBLIQUE B>
( OR ), M1N+ .EMPTY .SET1 =! L[]-
CASE ,GREEK LR PHI ( ) 6: X IS SIM-
IL>4 ,:5 ! EMPTY SET IS REPRES5T$ 0!
Z]O )A V]TICAL OR OBLIQUE B> 9 9K
PR9T1 ! CORRESPOND+ BRL SYMBOL _0 M/
2 US$ & IS SUBJECT 6! SPAC+ RULE (
@,S#164_4 ,:5 FAC+ BRACES >E US$ TO
REPRES5T ! EMPTY SET 9 9K PR9T1 ! COR-
RESPOND+ BRL SYMBOLS .( .) M/ 2 US$
& ^! >E SPAC$ Z GR\P+ SYMBOLS4
(1) ,A.+_0 .K ,A #DCC
,NEME? ,MA?4 ,C9DE1 #1972 C#AEE
(2) .(EV5 9TEG]S.).%.(ODD 9TEG]S.)
.K .( .)
----------------------------------#AEF
@,S#169_4 .,FACTORIAL3 ,! FACTORIAL
SYMBOL M/ 2 UNSPAC$ F ! QUANT;Y 6: X
APPLIES4
(1) N&
(2) (N-K)&
@,S#170_4 .,9F9;Y3 ,! 9F9;Y SYMBOL
IS SUBJECT 6! SPAC+ RULE ( @,S#164_4
(1) "LIM%X $O ,=] F(X)
(2) !;0^,="F(X)DX
@,S#171_4 .,9TEGRAL3 ,! B> OV] !
9TEGRAL SIGN1 OR ! B> "U ! 9TEGRAL
SIGN1 M/ 2 TRANSCRIB$ Z %[N 9 ! ABV
LI/4 ,! TE*NIQUE =! REPRES5T,N ( MODI-
FI$ EXPRES.NS M/ N 2 US$ 9 ^! CASES2
O!R MODIFI]S1 H["E1 M/ 2 TRANSCRIB$ 9
A3ORD.E )! TE*NIQUE =! REPRES5T,N (
MODIFI$ EXPRES.NS (SEE ,RULE #DCE
,,XIV)_4 ,! 9TEGRAL1 MODIFI$ A#AEF
OR UNMODIFI$1 M/ 2 UNSPAC$ F ! SYMBOL
6: X APPLIES4
(1) !;A^B"F(X)DX
(2) "!%0<,=]F(X)DX
(3) <!;A^B"F(X)DX .K #0
(4) %!;A^B"F(X)DX .K #0
(5) "!%X .K A<X .K B]F(T)DT
(6) "!!%,R]F(X, Y)D,A
(7) "!!!%,R]F(X, Y, Z)D,V
@,S#172_4 .,PRIME3 ,! S+LE & D\#
PRIMES >E (T5 US$ 6DENOTE .FEET &
.9*ES1 RESPECTIVELY4 ,!Y >E AL US$ TO
DENOTE .M9UTES & .SECONDS1 RESPECTIVE-
LY1 :E!R ( "T OR ( ANGLE4 ,PRIME SYM-
BOLS M/ 2 UNSPAC$ F EA* O!R1 & F !
QUANT;Y 6: !Y APPLY4
(1) X'
(2) X''
----------------------------------#AEG
(3) X'''
(4) X'^2
,NEME? ,MA?4 ,CODE1 #1972 A#AEG
(5) X';I
(6) X'1
(7) (U+V)' .K U'+V'
(8) X:'
(9) #5'8''
(10) #20^.*"30'10''
@,S#173_4 .,QUANTIFI]S3 ,! EXI/5TIAL
& UNIV]SAL QUANTIFI]S M/ 2 UNSPAC$ F !
QUANTITIES 6: !Y APPLY4
(1) @=X, X "K ?1/N#
(2) @=\;X \ X .K -X
(3) @&X @E ,A
(4) @&;X"@&;Y"-?Y-X/X+Y#
.K ?X-Y/X+Y#
@,S#174_4 .,S9CE1 .,"!=E3 ,EXCEPT =
PUNCTU,N1 9DICATORS1 & GR\P+ SYMBOLS1
! SYMBOL = .S9CE & SYMBOLS = ."!=E1 9
XS NORMAL OR NEGAT$ =M1 M/ 2 SPAC$ F !
MAT]IAL 6: !Y APPLY4
(1) @/ ,A,B .K ,A,C #DCG
(2) ,* ,A,B .K ,A,C B#AEG
@,S#175_4 .,T,X .,M>KS3 ,T,Y M>KS M/
2 GR\P$ 9 BRL Z !Y >E GR\P$ 9 9K PR9T4
,H["E1 ! CROSS T,Y : "S"TS APPE>S 9 9K
PR9T M/ 2 TR1T$ Z J ANO!R T,Y M>K4
,GR\PS ( T,Y M>KS M/ 2 SEP>AT$ 0A S+LE
SPACE F EA* O!R &1 EXCEPT = PUNCTU,N1
9DICATORS1 & GR\P+ SYMBOLS1 F SURR.D+
MAT]IAL4 ,H["E1 TRANSI;N 6ANO!R BRL
L9E TAKES ! PLACE ( ? REQUIR$ SPACE4
,TRANSI;N 6ANO!R L9E ( BRL M/ N"E 2
MADE F "O T,Y M>K 6ANO!R )9 ! SAME
GR\P4
----------------------------------#AEH
(1) ___
(IN 9K PR9T1 "! IS NO CROSS T,Y)
(2) _____ ____
(IN 9K PR9T1 ! F/ GR\P ( TALLIES HAS
A CROSS T,Y)
(3) ______ ______ ___
(IN 9K PR9T1 "! >E NO CROSS TALLIES)
(4) _____ _____ _____ _____ __
(IN 9K PR9T1 ! F/ F\R GR\PS (
TALLIES H CROSS TALLIES)
,NEME? ,MA?4 ,CODE1 #1972 A#AEH
@,S#176_4 .,BOLDFACE .,V]TICAL .,B>3
,! S+LE BOLDFACE V]TICAL B> M1N+ .5D
.( .PRO( M/ 2 SPAC$ F ANY SURR.D+ MA-
T]IAL4
(1) ,,PRO(4 (B+C)-(A+C) .K B-A
IS POSITIVE4 _\
,RULE ,,XXIII--
,MULTIPURPOSE ,9DICATOR
.,MULTIPURPOSE .,9DICATOR "
@,S#177_4 ..,USE (! ,MULTIPURPOSE
.,9DICATOR3 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 9 ! SITU,NS 2L =! SPECIFIC
PURPOSES DESCRIB$ &1 :5 US$ 9 ^! SITU-
,NS1 X M/ N 2 REG>D$ Z ! BASE-L9E 9DI-
CATOR3
;I_4 ,! MULTIPURPOSE 9DICATOR M/
2 US$ 2F A MODIFI$ EXPRES.N Z AN 9DI-
C,N 6! R1D] ( IMP5D+ MODIFIC,N4 ,SEE
,RULE ,,XIV = A4I;NAL 9=M,N & #DCI
EXAMPLES4 B#AEH
;II_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T A LR &A SU3E$+ NUM]IC SYM-
BOL 69DICATE T ! CORRESPOND+ NUM]AL IS
N A SUBSCRIPT 6! CORRESPOND+ LR4 ,H[-
"E1 :5 ! LR REPRES5TS A NUM]AL 9 A
NUM],N SY/EM 6A BASE O!R ?AN #10, X M/
2 REG>D$ Z A NUM]AL &1 ACLY1 ! MULTI-
PURPOSE 9DICATOR M/ N 2 US$4
(1) X"5
(2) X".6
----------------------------------#AEI
(3) .,S"2
(4) #T1E4
(A BASE-#12 NUM]AL2 9 9K PR9T1 ;,T &
;,E >E CAPITALIZ$)
;III_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T A NUM]IC SUBSCRIPT &A
NUM]AL1 IF ! LATT] IS ON ! BASE L9E4
(1) C0"10^2"+C1"10+C2
(2) #2N1"5^-3_/2"-N2"5^-1_/2
,NEME? ,MA?4 ,CODE1 #1972 A#AEI
;IV_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T TWO SYMBOLS ( -P>ISON 6IN-
DICATE T ! CORRESPOND+ SIGNS ( -P>ISON
>E PR9T$ HORIZONT,Y & N V]TIC,Y (SEE
@,S#149)_4
;V_4 ,! MULTIPURPOSE 9DICATOR M/
2 US$ AF ! DECIMAL PO9T SYMBOL 69DI-
CATE T ! SYMBOL : FOLL[S X IS N NUM]IC
UN.S T SYMBOL IS ! -MA OR ! PUNCTU,N
9DICATOR4
(1) #0."A1A2 '''
(2) #0.".A1.A2 '''
(3) ?1/3# .K ."=
(THE G5]AL OMIS.N SYMBOL REPRES5TS A
"Q M>K OV] A DA% 9 9K PR9T)
(4) #3."+.4 .K #3.4
(5) (3.")
(6) ?1."/2."#
;VI_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T A T,Y M>K &! PUNCTU,N 9DI-
CATOR4 #DDA
(1) _____, ____"_4 B#AEI
(IN 9K PR9T1 ! F/ GR\P ( TALLIES HAS
A CROSS T,Y)
;VII_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T TWO V]TICAL B>S ( : ! F/
IS A CLOS+ GR\P+ SYMBOL &! SECOND IS
AN OP5+ GR\P+ SYMBOL4 ,X M/ AL 2 US$
2T TWO V]TICAL B>S : >E GR\P+ SYMBOLS
( : "O IS %ORT] AND_/OR ?ICK] ?AN !
O!R4
(1) \X\"\Y\
(2) \\X\\"\\Y\\
----------------------------------#AFJ
(3) \\"\X\"\\
(4) \X\"\;X ;.K #0
;VIII_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T AN OP],N SYMBOL :5 X IS
REPRES5T$ 0A SYMBOL =A REGUL> POLYGON
&A NUM]AL : FOLL[S4
(1) #9$4"14 .K #23
(2) #9;7"$_4"13;7
,NEME? ,MA?4 ,CODE1 #1972 A#AFJ
;IX_4 ,! MULTIPURPOSE 9DICATOR
M/ 2 US$ 2T TWO SYMBOLS =! TILDE 69DI-
CATE T !Y >E WRITT5 HORIZONT,Y1 "O AF
! O!R4
(1) @:"@:,T
,,5D ,,( ,,VOLUME ,,III
#DDC