,,! ,,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














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