,,! ,,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 ,I
,BRL PAGES P#A-P#AJ & #A-ACH
,PR9T PAGES ;I-;V & #A-B#DA P#A
,NEME? ,MA?4 ,CODE1 #1972
,,3T5TS
,VOLUME ;,I
,PAGE
,,=E^W ,,TO #1972 ,,REVI.N """""""" ;V
,,ORI5T,N (@,S#1-@,S#4) """"""""""" #1
,,RULES
,,RULE ;,I--,,BRL ,,9DICATORS
(@,S#5-@,S#6) """"""""""""""""" #3
,,RULE ,,II--,,NUM]IC ,,SIGNS
,,& ,,SYMBOLS (@,S#7-@,S#19) "" #7
,,RULE ,,III--,CAPITALIZ,N
(@,S#20-@,S#22) """""""""""""" #20
,,RULE ,,IV--,,ALPHABETS
(@,S#23-@,S#30) """""""""""""" #21
,,RULE ;,V--,,TYPE ,,=MS
(@,S#31-@,S#35) """""""""""""" #36
P#C
,VOLUME ,,II
,,RULES (,3T4)
,,RULE ,,VI--,,PUNCTU,N
,,SIGNS ,,& ,,SYMBOLS
(@,S#36-@,S#45) """"""""""""" C#41
,,RULE ,,VII--,,REF];E ,,SIGNS
,,& ,,SYMBOLS (@,S#46-
@,S#48) """""""""""""""""""""" #52
,,RULE ,,VIII--,,A2REVI,NS
(@,S#49-@,S#54) """""""""""""" #54
,,RULE ,,IX--,,3TRAC;NS ,,&
,,%ORT-=M ,,^WS (@,S#55-
@,S#56) """""""""""""""""""""" #62
,,RULE ;,X--,,OMIS.NS (@,S#57-
@,S#59) """""""""""""""""""""" #70
,,RULE ,,XI--,,C.ELL,N (@,S#60) #73
,,RULE ,,XII--,,FRAC;NS
(@,S#61-@,S#70) """""""""""""" #75
,,RULE ,,XIII--,,SUP]SCRIPTS
,,& ,,SUBSCRIPTS (@,S#71-
@,S#84) """""""""""""""""""""" #82
,,RULE ,,XIV--,,MODIFI]S
(@,S#85-@,S#102) """"""""""""" #97
,,RULE ,,XV--,,RADICALS
(@,S#103-@,S#105) """""""""" #108
,NEME? ,MA?4 ,CODE1 #1972
,VOLUCE ,,III
,,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 ,,&
,,SYMBOLS ,,( ,,-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
,,RULE ,,XXIII--,MULTIPURPOSE
P#E
,,9DICATOR (@,S#177) """""""" #158
,VOLUME ,,IV
,,RULES (,3T4)
,,RULE ,,,XXIV--,,SPATIAL
,,>RANGE;TS (@,S#178-
@,S#184) """"""""""""""""""" B#160
,,RULE ,,XXV--,,=MAT (@,S#185-
@,S#195) """""""""""""""""""" #184
,,APP5DICES
,,APP5DIX ;,A--,,COMB9,NS ,,(
,,TYPE-=M1 ,,ALPHABETIC1
,,& ,,CAPITALIZ,N ,,9DI-
CATORS """""""""""""""""""""" #208
,,APP5DIX ;,B--,,9DEX ,,(
,,BRL ,,SYMBOLS """"""""""""" #209
,VOLUME ;,V
,,9DEX """""""""""""""""""""""""" #248
,? ,BRL EDI;N 3TA9S ! 5TIRE TEXT (!
9K-PR9T EDI;N4
,NEME? ,MA?4 ,CODE1 #1972 ;V
,,=E^W ,,TO #1972 ,,REVI.N
,,! ,,NEME? ,,CODE ,,( ,,BRL ,,MA!-
MATICS ,,& ,,SCI5TIFIC ,,NOT,N1 #1965
9ITIAT$ S.D PR9CIPLES & PROC$URES =!
PRES5T,N ( BRL EQUIVAL5TS =! -PLEX
SIGNS & 3FIGUR,NS ( 9K-PR9T MA!MATICAL
& SCI5TIFIC NOT,N4 ,! E6ECTIVE;S (!
,CODE HAS BE5 AMPLY DEMON/RAT$ "? XS
APPLIC,N 0TRANSCRIB]S 9 PRODUC+ A W1L?
( TE*NICAL MAT]IAL 6MEET ! REQUIRE;TS
( /UD5TS AT ALL LEVELS ( $UC,NAL PUR-
SUITS4
,AT ! "T ( PUBLIC,N1 X 0 APP>5T T !
,CODE WD REQUIRE FUR!R UPDAT+ & RE-
F9E;T 9 ORD] 6ASSURE ! FAI?;L TRANS-
F];E F 9K PR9T 6BRL Z NEW MODES (
SCI5TIFIC NOT,N 7 9TRODUC$4 ,Z 0 AN-
TICIPAT$1 PRO#MS 9 9T]PRET,N & CL>;Y 7
5C.T]$ :5 ! ,CODE 0 PUT 96ACTUAL USE4
,! -;TS1 CRITICISMS & SU7ES;NS F /U-
D5TS1 T1*]S & TRANSCRIB]S 7 TAK5 "U
3SID],N 9 ! REVI.N (! ,CODE4 P#G
,"U ! A# TUTELAGE ( ,DR4 A;V
,ABRAHAM ,NEME?1 ! MEMB]S (!
,,AAWB-AEVH ,BRL ,AU?OR;Y & XS ,AD-
VISORY ,-MITTEE ON ,MA!MATICAL &
,SCI5TIFIC ,NOT,N 5T]$ ^U A JO9T EF=T
9 BR++ =? A ,REVIS$ ,CODE : CD )/& !
TE/ ( USE & "T4 ,Z "W PROGRESS$1 H["E1
X 2CAME 9CR1S+LY EVID5T T1 2C (! COM-
PLEX;Y (! SUBJECT MATT] & 2C (! _M
TE*NIQUES EMPLOY$ 0AU?ORS & PUBLI%]S1
SUB/ANTIAL RESE>* WD 2 REQUIR$ 9 EXP&+
! ,CODE 6XS FULLE/ E6ECTIVE;S4 ,9
RECOGNI;N ( ? FACT1 ! N,NAL ,ADVISORY
,C\NCIL 6! ,BRL ,AU?OR;Y APPLI$ =A
PLANN+ GRANT F ,SOCIAL & ,REHABILIT,N
,S]VICES (! ,DE"P;T ( ,H1L?1 ,$UC,N1 &
,WELF>E4 ,! ,AM]ICAN ,PR9T+ ,H\SE =!
,BL 0 DESIGNAT$ Z ! RECIPI5T (! GRANT1
"KN Z ! 8,BRL ,CODES ,PILOT ,PLOJECT01
: IS GE>$ 6BR+ 96FOCUS ! NE$ = FULL]
RESE>* 9 ALL BRL CODES4 ,^U ! BASIS (
? /UDY1 APPLIC,N =A RESE>* GRANT W 2
MADE &1 IF APPROV$1 ALL BRL CODES W 2
3SID]$ 9 DETAIL 9 ! 5D1VOR 6BR+ !M TO
MAXIMUM -PLETE;S & E6ICI5CY4
,NEME? ,MA?4 ,CODE1 #1972 B;V
,! #1972 REVI.N ( ,,! ,,NEME? ,,BRL
,,CODE ,,= ,,MA!MATICS ,,& ,,SCI;E
,,NOT,N PROVIDES /UD5TS & TRANSCRIB]S
)A WELL-DRAWN1 LOGICAL SY/EM ( BRL NO-
T,N : 9SURES A FAI?;L PRES5T,N ( SIGNS
& USAGES EMPLOY$ 9 TE*NICAL TEXTS4 ,!
*ANGES : H BE5 9CORPORAT$ W 3VEY 6!
R1D] A R1LI/IC PICTURE (! 9K-PR9T TEXT
& W EQUIP ! TRANSCRIB] )! NEC SIGNS &
RULES ( PROC$URE =A M EXACT BRL TRAN-
SCRIP;N4
,GRATE;L AC"KL$GE;T IS A3ORD$ ! FOL-
L[+ P]SONS = _! MAJOR 3TRIBU;N 9 !
JO9T EF=T 9 DEVELOP+ & REF9+ ! REVIS$
,CODE4
,ADVISORY ,-MITTEE ON
,MA!MATICAL & ,SCI5TIFIC ,NOT,N
,RALPH ,E4 ,MC,CRACK5
,DR4 ,ABRAHAM ,NEME?
,MRS4 ,HEL5 ,ROB]TS
P#I
,,AAWB-AEVH ,BRL ,AU?OR;Y C;V
,MRS4 ,MAX9E ,B4 ,DORF (1959-)
,M>JORIE ,S4 ,HOOP] (1959-)
,FR$A ,H5D]SON (1967-1971)
,B]N>D ,M4 ,KREBS (1959-)
,MRS4 ,ALICE ,M4 ,MANN (1967-)
,,AAWB-AEVH ,ADVISORY ,C\NCIL
6,BRL ,AU?OR;Y
,M4 ,ROB]T ,B>NETT
,DR4 ,NATALIE ,C4 ,B>RAGA
,ROB]T ,S4 ,BRAY
,DR4 ,*>LES ,E4 ,HALL5BECK
,DR4 ,B]?OLD ,L[5FELD
,DR4 ,D\GLAS ,C4 ,MAC,F>L&
,PROFESSOR ,ROB]T ,W4 ,MANN
,LORRA9E ,P4 ,MUR9
,DR4 ,ABRAHAM ,NEME?
,DR4 ,C>SON ,Y4 ,NOLAN
,DR4 ,G]ALD9E ,S*OLL
,JOSEPH9E ,L4 ,TAYLOR
,,! ,,NEME? ,,BRL ,,CODE #A
,,= ,,MA!MATICS
,,& ,,SCI;E ,,NOT,N
#1972 ,,REVI.N
,,ORI5T,N
@,S#1_4 .,DESCRIP;N3
;A_4 ,? ,BRL ,CODE = ,MA!MATICS &
,SCI;E ,NOT,N HAS BE5 PREP>$ 6PROVIDE
A SY/EM ( SYMBOLS : W ALL[ TE*NICAL
LIT]ATURE 6BE PRES5T$ & R1D 9 BRL4 ,!
,CODE IS 9T5D$ 63VEY Z A3URATE AN IM-
PRES.N Z IS POSSI# 6! BRL R1D] (!
CORRESPOND+ PR9T$ TEXT1 & ? IS "O ( XS
PR9CIPAL F1TURES4 ,:5 ! BRL R1D] HAS A
CLE> 3CEP;N (! CORRESPOND+ PR9T$ TEXT1
! >EA ( -MUNIC,N 2T HMF & 8 T1*]1 8
COLL1GUES1 8 ASSOCIATES1 &! _W AT L>GE
IS GRTLY BROAD5$4 ..,A TE/ (! A3URACY
) : ! ,CODE 3VEYS 9=M,N F ! PR9T 6!
BRL TEXT IS 6E6ECT A TRANSCRIP;N 9 !
REV]SE DIREC;N4 ,! AM.T ( AGREE;T 2T !
ORIG9AL PR9T$ TEXT & "O TRANSCRIB$ F !
BRL IS A M1SURE (! ,CODE'S .AC- #A
CURACY4 A#A
;B_4 ,A C>E;L 4T9C;N IS MA9TA9$ 2T
! M1N+ : A PR9T$ SIGN HAS &! SIGN XF4
,"S"TS ! "N (A SIGN DERIVES F ! MA!-
MATICAL M1N+ : X HAS4 ,SIMPLE EXAMPLES
>E ! .PLUS SIGN1 ! .DECIMAL .PO9T1 &!
.P]C5T SIGN4 ,O!R SIGNS H "NS : >E DE-
SCRIPTIVE (! SIGNS !MVS1 S* Z .>R[1
.V]TICAL .B>1 & .DIAGONAL .L9E4 ,/
O!RS H "NS 9 A3ORD.E )! WAY 9 : !Y >E
R1D AL\D1 S* Z ..IS LESS ?AN1 IS 3TA9$
.IN1 OR ..IS AN ELE;T .(4 ,"S SIGNS H
NO "N AT ALL4 ,( C\RSE1 ! MAJOR;Y (
SIGNS1 "PICUL>LY AT ! L[] LEVELS (
MA!MATICS1 >E SIGNS AB : "! IS UNIV]-
SAL AGREE;T Z 6_! M1N+1 & ^! 3/ITUTE !
CORE AB : HAS GR[N ! MOD]N SY/EM (
MA!MATICAL NOT,N4 ,H["E1 AT ! M ADV.ED
LEVELS1 TE*NICAL WRIT]S H1 ) 9CR1S+
FREQU5CY1 BE5 ASSIGN+ NEW & UNUSUAL
M1N+S 6_M (! SIGNS : H L;G BE5 8/&>D40
;C_4 ,AL? ! ,CODE IS 9T5D$ 6BE Z
-PLETE Z POSSI#1 F9AL;Y C N"E 2 A*IEV$
0ANY CODE4 ,9 ! C\RSE (! RAPID DEVEL-
OP;T 9 ! FIELDS ( SCI;E & TE*NOLOGY1
,NEME? ,MA?4 ,CODE1 #1972 B#A
NEW SIGNS >E 3/ANTLY 2+ DEVIS$ & OLD
"OS MODIFI$4 ,AT APPROPRIATE PLACES1
RULES & SU7ES;NS >E PRES5T$ = TRAN-
SCRIB+ SIGNS = : NO SPECIFIC PROVI.N
EXI/S AT PRES5T4
@,S#2_4 .,ORGANIZ,N3
;A_4 ,9 PRES5T+ ? ,CODE1 ! NE$S (
BO? ! TRANSCRIB] &(! R1D] H BE5 3SID-
]$4 ,:ILE ! RULES (! ,CODE H BE5 =MU-
LAT$ PRIM>ILY =! B5EFIT (! BRL R1D]1
!Y >E N"E!.S PRES5T$ 9 A MANN] DESIGN$
6EASE ! TRANSCRIB]'S TASK ( FOLL[+ ^!
RULES4 ,! PRO#M ( TRANSCRIP;N IS IN-
TR9SIC,Y M DI6ICULT ?AN ! PRO#M (
R1D+2 ! TRANSCRIB] M/ ACTU,Y RECALL TO
M9D ! SPECIFIC SYMBOLS : M/ 2 US$ &!
RULES : GOV]N _! USE1 ":AS ! BRL R1D]
M/ ONLY RECOGNIZE ! SYMBOLS : HE EN-
C.T]S & 2 ONLY SLI<TLY AW>E (! "ULY+
RULES4
;B_4 ,? PRES5T,N IS ORGANIZ$ 9TO
RULES4 ,": APPROPRIATE1 EA* RULE 2G9S
)A LI/ ( SIGNS & _! CORRESPOND+ SYM-
BOLS = QK REF];E4 ,! BODY (! #C
PRES5T,N IS ORGANIZ$ 96SEC;NS : C#A
>E 3SECUTIVELY NUMB]$ & CAP;N$4 ,!
SEC;NS 3TA9 RULES1 EXPLAN,NS1 & EXAM-
PLES (! USE (! ,CODE4 ,X IS 9T5D$ T !
EXAMPLES 2 SU6ICI5TLY DEF9ITIVE S T !Y
MAY 2 IMITAT$ ) 3FID;E 9 P>ALLEL SITU-
,NS4 ,! P>5!TICAL DESCRIP;NS 2L ! EX-
AMPLES >E 9T5D$ 6SUPPLE;T ! ACTUAL
SIGNS %[N 9 ! 9K-PR9T COPY4 ,! EXAM-
PLES 9 ? PRES5T,N >E DRAWN PR9CIP,Y F
! C5TRAL CORE ( PURE MA!MATICS4 ,O!R
SCI5TI/S W F9D FEW EXAMPLES F _!
FIELDS4 ,N"E!.S1 ! SYMBOLS1 RULES1 &
3/RUC;NS (! BASIC ,CODE APPLY ) EQUAL
=CE 6^? FIELDS4 ,FOLL[+ ! RULES1 "! IS
AN ..,9DEX ( ,BRL .,SYMBOLS ! 5TRIES
( : H BE5 CATEGORIZ$ 9 A3ORD.E )! /&>D
>RANGE;T (! SIXTY-?REE BRL SYMBOLS4
;C_4 ,"?\T ? PRES5T,N1 ! ^W .SIGN
IS 3SI/5TLY US$ 9 REF]R+ 6A "* OR
SEQU;E ( "*S 9 9K PR9T1 ":AS ! ^W
.SYMBOL IS US$ 9 REF]R+ 6A "* OR SE-
QU;E ( "*S 9 BRL4
;D_4 ,9 ? TEXT1 MA!MATICAL OR LIT-
]>Y MAT]IAL : (T5 APPE>S 9 ITALICS OR
,NEME? ,MA?4 ,CODE1 #1972 D#A
O!R TYPE 9 9K-PR9T TEXTBOOKS HAS BE5
PR9T$ 9 REGUL> TYPE4 ,ITALIC & O!R
TYPE =MS H BE5 US$ ONLY ": S* TYPE IS
REQUIR$ 6ILLU/RATE A RULE4
------------------------------------#B
;E_4 ,AL? #41 CELLS MAY 2 US$ 9
TRANSCRIB+ TE*NICAL "WS1 EXAMPLES 9 ?
TEXT H BE5 %ORT5$ 63=M 6! SPACE AVAIL-
A# ON ! 9K-PR9T L9ES4
@,S#3_4 .,9T]PRET,N3 ..,X IS IMPOR-
TANT T ? PRES5T,N 2 A3EPT$ Q LIT],Y &
T NO M1N+ 2 IMPUT$ 6! RULES & PR9CI-
PLES : IS N EXPRESSLY /AT$ OR DIRECTLY
IMPLI$4 ,X MAY "S"TS APPE> Q >BITR>Y
T A "PICUL> SIGN HAS BE5 CLASSIFI$ 9 A
SEC;N : ! R1D]'S PA/ EXP]I;E OR TRA9+
9DICATES IS 9APPROPRIATE4 ,=! PUR-
POSES ( ? ,CODE1 H["E1 ! TRANSCRIB] OR
T1*] M/ A3EPT ! CLASSIFIC,N Z WELL Z !
RULES "H) PRES5T$1 PA/ EXP]I;E OR TE*-
NICAL TRA9+ .NOT)/&+4
,9 C]TA9 SITU,NS X MAY 2 FELT T "S
3/RUC;NS >E EXCESSIVELY L;G & "! MAY 2
A TEMPT,N 6%ORT5 ! 3/RUC;N 0! #E
USE (A SYMBOL ( "O'S [N 9V5;N4 A#B
,H["E1 ..! TRANSCRIB] IS 5JO9$ AG/
YIELD+ 6? .TEMPT,N4 ,! ,CODE HAS BE5
=MULAT$ 9 S* A WAY T ! SAME 3/RUC;N
GIVES ! SAME 9=M,N 6! BRL R1D] F ELE-
;T>Y "? ! MO/ ADV.ED MA!MATICS4 ,"!=E1
TAMP]+ )! 3/RUC;NS PRES5T$ "H9 WD H !
E6ECT ( DE/ROY+ ? UNI=M;Y4 ,SIGNS : =
_M DECADES H BE5 EXCLUSIVELY ASSOCIAT$
) COLLEGE & GRADUATE MA!MATICS H 9 RE-
C5T YE>S BE5 FILT]+ D[N 6HI< S*OOL &
GRADE S*OOL LEVELS4 ,?US1 ! SET OP],NS
S* Z .UNION1 .9T]SEC;N1 & .9CLU.N1 : 7
TRADI;N,Y 5C.T]$ =! F/ "T 0A MA!MATICS
MAJOR 9 8 JUNIOR YE> 9 COLLEGE1 H N[
2COME FAIRLY -MONPLACE AT ! F\R? OR
FIF? GRADE LEVEL1 & >E F/ MET EV5 E>-
LI]4 ,9 A4I;N1 GRADE S*OOL & HI< S*OOL
MA!MATICS >E N[ 2+ PRES5T$ ) 3SID]ABLY
M RIGOR ?AN "HTO=E1 & %ADES 9 M1N+ >E
2+ PRES]V$ & EV5 EMPHASIZ$ 0! USE (
4T9CT SIGNS HAV+ SIMIL>1 B N EQUIVA-
L5T1 M1N+S4 ,9 KEEP+ ) ? _S1 ! ,CODE
FURNI%ES 4T9CT BRL SYMBOLS CORRESPOND+
64T9CT SIGNS 9 9K PR9T4 ,9 "PICUL>1 AT
,NEME? ,MA?4 ,CODE1 #1972 B#B
! L[] LEVELS ( MA!MATICS1 ? ,CODE MA9-
TA9S A 4T9C;N 2T ! HORIZONTAL & DIAG-
ONAL FRAC;N L9ES1 & 2T ! .DOT &!
.CROSS : SIGNIFY MULTIPLIC,N4 ,SIGNS :
H SEP>ATE ID5TITIES 9 9K PR9T %D 2
REPRES5T$ 04T9CT SYMBOLS 9 BRL4
@,S#4_4 ..,TE*NICAL & ,NON-,TE*NICAL
.,TEXTS3
;A_4 ,! DESIGN,N .NON-TE*NICAL IM-
PLIES ONLY ! ABS;E ( MA!MATICAL OR
SCI5TIFIC NOT,N2 A "W 9 LAW OR M$IC9E
MAY 2 Q TE*NICAL 9 ^? FIELDS1 B M/ 2
REG>D$ Z NON-TE*NICAL 9 ! S5SE J M5-
;N$4
;B_4 .,"PI,Y .TE*NICAL "WS 9CLUDE
SCI;E BOOKS WRITT5 =! LAYMAN OR TEXT-
BOOKS 9 O!R FIELDS : USE MA!MATICAL
T]M9OLOGY & NOT,N4 ,S* "WS >E "*IZ$ 0!
USE ( AN O3A.NAL MA!MATICAL SIGN OR A
SMALL NUMB] ( S* SIGNS4 ,9 "WS ( ?
K9D1 ! MA!MATICAL SIGNS MAY 2 TR1T$ Z
9 ,5GLI% ,BRL4 ,? PROC$URE IS "PICUL>-
LY SUITA# :5 "! IS NO 9T5;N T ! R1D]
%D MANIPULATE S* SIGNS =! PUR- #G
POSE ( SOLV+ EQU,NS OR P]=M+ C#B
-PUT,NS4 ,"S"TS1 H["E1 ! REPLACE;T (A
SIGN 0A CORRESPOND+ ^W IS N PRACTICAL1
ESPECI,Y :5 AN A7REGATE ( S* SIGNS AP-
PE>S 9 AN >RANGE;T : IS UNUSUAL F !
LIT]>Y PO9T ( VIEW4 ,9 S* CASES1 !
TRANSCRIB] %D USE ! SYMBOLS &! RULES (
? ,CODE )A NOTE 6! BRL R1D] T ? IS 2+
D"O4 ,A LI/ (! MA!MATICAL SYMBOLS 2+
US$ %D 2 9CLUD$ AT ! 2G9N+ ( ONLY !
BRL VOLUME 9 : !Y O3UR4
;C_4 .,TE*NICAL "WS >E ^? 9 !
FIELDS ( MA!MATICS1 /ATI/ICS1 PHYSICS1
OR *EMI/RY4 ,9 S* "WS ! SYMBOLS &
RULES ( ? ,CODE M/ 2 US$4 ,!Y M/ AL 2
US$ 9 "WS 9 O!R FIELDS : MAKE /R;G USE
( MA!MATICAL SIGNS & MODES ( EXPRES.N4
,9 ALL TE*NICAL "WS ! TRANSCRIB] M/
9DICATE AT ! 2G9N+ ( EA* VOLUME 0M1NS
(A TRANSCRIB]'S NOTE T ! "W HAS BE5
TRANSCRIB$ 9 ,NEME? ,CODE1 GIV+ ! YE>
! CODE 0 ADOPT$4 ,EV5 :5 ! ,NEME?
,CODE IS US$1 TITLE PAGES M/ 2 TRAN-
SCRIB$ Z 9 ,5GLI% ,BRL )\T ! USE (
,NEME? ,CODE SYMBOLS1 EXCEPT = ITEMS :
,NEME? ,MA?4 ,CODE1 #1972 D#B
3TA9 MA!MATICAL EXPRES.NS = : X WD 2
9APPROPRIATE OR IMPRACTICAL 6USE ,5G-
LI% ,BRL4
;D_4 ,X IS RECOMM5D$ T MA*9ES 2
SET =A BRL L9E ( #41 CELLS :5 TRAN-
SCRIB+ TE*NICAL "WS4
------------------------------------#C
,,RULES
,RULE ;,I--,BRL ,9DICATORS
,ALPHABETIC ,9DICATORS
,5GLI%-,LR ;
,G]MAN-,LR _
,GREEK-,LR
,= /&>D LRS .
,= ALT]NATIVE LRS .@
,HEBREW-,LR ,,
,RUSSIAN-,LR @@
,>R[ ,DIREC;N ,9DICATORS
,DEPRESSES ,NE>] ,>R[H1D BY #45
,DEGREES ;
,ELEVATES ,NE>] ,>R[H1D BY #45
,DEGREES ^ #I
,MAKES ,NE>] ,>R[H1D ,PO9T A#C
,UP <
,MAKES ,NE>] ,>R[H1D ,PO9T ,D[N %
,>R[ ,TYPES3 ,BOLDFACE _
,C.ELL,N ,9DICATORS
,OP5+ [
,CLOS+ ]
,CAPITALIZ,N ,9DICATORS
,S+LE ,
,D\# ,,
,C>RI$ ,NUMB] ,9DICATOR = ,A4I;N (V>Y+
9 L5G?) 777
------------------------------------#D
,FRAC;N ,9DICATORS
,SIMPLE
,OP5+ ?
,CLOS+ #
,-PLEX
,OP5+ ,?
,CLOS+ ,#
,HYP]COMPLEX
,OP5+ ,,?
,CLOS+ ,,#
,FRAC;NAL ,"P (A ,MIX$ ,NUMB]
,OP5+ _?
,NEME? ,MA?4 ,CODE1 #1972 A#D
,CLOS+ _#
,G5]AL ,REF];E ,9DICATOR @]
,LEVEL ,9DICATORS
,BASE ,L9E "
,SUP]SCRIPT ^
,SUP]SCRIPT ) ,SUP]SCRIPT ^^
,SUP]SCRIPT ) ,SUBSCRIPT ^;
,SUP]SCRIPT ) ,SUP]SCRIPT ) ,SUP]-
SCRIPT ^^^
,SUP]SCRIPT ) ,SUP]SCRIPT ) ,SUB-
SCRIPT ^^;
,SUP]SCRIPT ) ,SUBSCRIPT ) ,SUP]-
SCRIPT ^;^
,SUP]SCRIPT ) ,SUBSCRIPT ) ,SUB-
SCRIPT ^;;
,SUBSCRIPT ;
,SUBSCRIPT ) ,SUP]SCRIPT ;^
------------------------------------#E
,SUBSCRIPT ) ,SUBSCRIPT ;;
,SUBSCRIPT ) ,SUP]SCRIPT ) ,SUP]-
SCRIPT ;^^
,SUBSCRIPT ) ,SUP]SCRIPT ) ,SUB-
SCRIPT ;^;
#AA
,SUBSCRIPT ) ,SUBSCRIPT ) A#E
,SUP]SCRIPT ;;^
,SUBSCRIPT ) ,SUBSCRIPT ) ,SUB-
SCRIPT ;;;
,MODIFIC,N ,9DICATORS
,MULTIPURPOSE "
,DIRECTLY ,OV]
,F/ ORD] <
,SECOND ORD] <<
,DIRECTLY ,"U
,F/ ORD] %
,SECOND ORD] %%
,SUP]POSI;N @
,T]M9,N ]
,MULTIPURPOSE ,9DICATOR "
,NUM]IC ,9DICATOR #
,PUNCTU,N ,9DICATOR _
,RADICAL ,9DICATORS
,9DEX-(-,RADICAL <
,ORD]-(-,RADICAL
,F/ 9N] RADICAL .
,SECOND 9N] RADICAL ..
,?IRD 9N] RADICAL ...
,T]M9,N ]
,NEME? ,MA?4 ,CODE1 #1972 #F
,%APE ,9DICATORS
,%APE $
,/RUCTURAL ,%APE-,MODIFIC,N .
,9T]IOR ,%APE-,MODIFIC,N _$
,FILL$-,IN ,%APE _
,%AD$ ,%APE .
,T]M9,N ]
,T]M9,N ,9DICATOR ]
,TYPE-,=M ,9DICATORS = ,LRS1 ,NUM]ALS1
& ,-P.D ,EXPRES.NS
,BOLDFACE ,TYPE _
,ITALIC ,TYPE .
,SANS]IF ,TYPE ,.
,SCRIPT ,TYPE @
,TYPE-,=M ,9DICATORS = ,^WS1 ,PHRASES1
& ,MA!MATICAL ,/ATE;TS
,OP5+ ,BOLDFACE ,TYPE ,'_
,OP5+ ,ITALIC ,TYPE ,'.
,CLOS+ ,BOLDFACE ,TYPE _,'
,CLOS+ ,ITALIC ,TYPE .,'
@,S#5_4 ..,3CEPT ( ,BRL .,9DICATORS3
,MA!MATICAL EXPRES.NS >E REPRES5T$ 9
9K PR9T 0! USE ( >BITR>Y SIGNS #AC
AM;G : >E ! DIGITS1 ! L[]-CASE A#F
& CAPITALIZ$ LRS ( S"EAL ALPHABETS1 !
SCRIPT1 ITALIC1 & BOLDFACE =MS ( ^!
SAME LRS1 Z WELL Z NUM]\S SIGNS ( OP]-
,N1 SIGNS ( -P>ISON1 SIGNS ( GR\P+1 &
_M O!R SIGNS S]V+ ! MISCELLANE\S RE-
QUIRE;TS ( MA!MATICAL & SCI5TIFIC EX-
PRES.N4 ,FUR!RMORE1 MA!MATICAL SIGNIF-
IC.E IS IM"P$ N ONLY 0^! SIGNS SEPA-
RATELY1 B 0_! COLLECTIVE >RANGE;T ON
LEVELS ABV OR 2L A REF];E L9E (
WRIT+1 Z WELL Z 0_! 4POSI;N ABV OR 2L
A FRAC;N L9E4 ,) ONLY SIXTY-?REE DIS-
T9CT BRL "*S AVAILA#1 SIXTY-F\R IF !
SPACE IS C.T$1 ! A3OMPLI%;T ( ? ,CODE
IS 6MAKE PROVI.N =! REPRES5T,N ( ALL
^! SIGNS1 Z WELL Z 6GIVE AN 9DIC,N (
_! >RANGE;T4
,X IS1 ( C\RSE1 IMPOSSI# 6E/ABLI% A
"O-TO-"O CORRESPOND;E 2T ! SIXTY-?REE
BRL "*S &! HUNDR$S ( SIGNS US$ 9 MOD]N
MA!MATICS4 ,X IS AL IMPRACTICAL1 Z A
G5]AL PROC$URE1 6IMITATE ! >RANGE;T (
^! SIGNS AT V>I\S LEVELS RELATIVE 6A
REF];E L9E ( WRIT+ OR 6A FRAC;N L9E4
,NEME? ,MA?4 ,CODE1 #1972 B#F
,ACLY1 ! ,CODE PRES5T$ 9 ! FOLL[+
PAGES IS "*IZ$ 0! USE (A SY/EM ( BRL
9DICATORS4 ,! BRL 9DICATORS 9 ? ,CODE
PLAY ! SAME ROLE Z D ! -POSI;N SIGNS
------------------------------------#G
( ,5GLI% ,BRL4 ,9 BO? SY/EMS1 ! BRL
9DICATORS OR ! SIGNS ( -POSI;N CORRE-
SPOND 6NO SIGN 9 9K PR9T2 H["E1 !Y H !
P[] ( IM"P+ M1N+ 6! BRL SYMBOLS ) : !Y
>E ASSOCIAT$4 ,:ILE "! >E ONLY A FEW
SIGNS ( -POSI;N 9 ,5GLI% ,BRL1 "! >E
_M 9 ? ,CODE4 ,0_! USE X IS POSSI# TO
REPRES5T ! NUM]\S TYPE =MS & ALPHABETS
US$ 9 9K PR9T & 63VEY ! 8TWO-DIM5.NAL0
9=M,N 3TA9$ 9 9K PR9T "? ! M$IUM (!
BRL SY/EM ^: NATURE IS ESS5TI,Y 8"O-
DIM5.NAL40
@,S#6_4 ..,SPAC+ ) ,BRL .,9DICATORS3
,NO SPACE %D 2 LEFT 2T A BRL 9DICATOR
&! SYMBOL OR EXPRES.N 6: X APPLIES4 ,9
A4I;N1 ! PUNCTU,N 9DICATOR1 LEVEL 9DI-
CATORS1 & MODIFIC,N 9DICATORS APPLY
BO? 6! MAT]IAL : PREC$ES Z WELL Z 6!
MAT]IAL : FOLL[S !M4 ,"! >E #AE
SPECIAL SPAC+ RULES =! TYPE-=M A#G
9DICATORS = ^WS1 PHRASES1 & MA!MATICAL
/ATE;TS (SEE @,S#33)_4 ,EXAMPLES IL-
LU/RAT+ ? SPAC+ RULE >E F.D "?\T !
,CODE4
,NEME? ,MA?4 ,CODE1 #1972 B#G
,RULE ,,II--,NUM]IC ,SIGNS
& ,SYMBOLS
,NUM]IC ,9DICATOR #
,>ABIC ,DIGITS (,NEME? ,CODE)
#0 #1 #2 #3 #4
#5 #6 #7 #8 #9
,-MA (MA!MATICAL)
,AM]ICAN ,
,3T95TAL ,
,DECIMAL ,PO9T
,AM]ICAN .
,3T95TAL .
#AG
,NEME? ,MA?4 ,CODE1 #1972 C#G
@,S#7_4 ..,REPRES5T,N ( ,>ABIC .,NU-
M]ALS3
;A_4 ,DIGITS >E REPRES5T$ 9 TWO
WAYS3 Z 9 ,5GLI% ,BRL1 & Z 9 ! ,NEME?
,CODE4 ,! DIGITS 9 ,5GLI% ,BRL >E REP-
RES5T$ 0! LRS ;J & ;A "? ;I_4 ,! DIG-
ITS 9 ! ,NEME? ,CODE >E REPRES5T$ 0!
SYMBOLS ^: 3FIGUR,NS CORRESPOND 6^!
SAME LRS1 B : O3UPY ! L[] POR;N (! BRL
CELL4
;B_4 ,EV5 :5 A "W IS TRANSCRIB$ 9
! ,NEME? ,CODE1 :5 AT ALL PRACTICAL OR
APPROPRIATE1 ALL NUM]ALS ON TITLE
PAGES M/ 2 TRANSCRIB$ Z 9 ,5GLI% ,BRL4
,NUM]ALS AT ! CORN]S ( PAGES & AT !
5DS ( PAGE-SEP>,N L9ES M/ AL 2 TRAN-
SCRIB$ Z 9 ,5GLI% ,BRL4 ,5GLI% ,BRL
NUM]ALS M/ 2 US$ :5 ! TE*NIQUE (
8KEY+0 (@,S#187) IS EMPLOY$4 ,9 ALL
O!R CASES1 9CLUD+ 3T5TS PAGES1 =E^WS1
9TRODUC;NS1 PAGE REF];ES1 FOOTNOTES1
9DICES1 & BIBLIOGRAPHIES1 ! NUM]ALS (!
,NEME? ,CODE M/ 2 US$4 #AI
@,S#8_4 .,-MA1 .,DECIMAL D#G
.,PO9T3
;A_4 ,! TRANSCRIB] %D 2 AL]T 6!
POSSIBIL;Y T V>IANT =MS (! -MA & DEC-
IMAL PO9T >E "S"TS EMPLOY$1 "PICUL>LY
9 BOOKS PUBLI%$ \TSIDE (! ,UNIT$
,/ATES4 ,AL? ! 9K PR9T SIGNS =! -MA &
DECIMAL PO9T DI6] F
------------------------------------#H
^? US$ 9 ! ,UNIT$ ,/ATES1 ? DI6];E IS
N REFLECT$ 9 ! BRL TRANSCRIP;N4 ,H["E1
A TRANSCRIB]'S NOTE %D 2 9CLUD$ AT !
2G9N+ (! BOOK 69=M ! R1D] (! 3T95TAL
USAGE 9 ! 9K-PR9T EDI;N4
(1) #1,378
(,AM]ICAN USAGE ( -MA)
(2) #1,378
(,3T95TAL USAGE ( -MA)
(3) #3.76
(,AM]ICAN USAGE ( DECIMAL)
(4) #3.76
(,3T95TAL USAGE ( DECIMAL)
;B_4 .,! .-MA1 ,AM]ICAN OR ,3T95-
,NEME? ,MA?4 ,CODE1 #1972 A#H
TAL1 : IS 9T]IOR 6A NUM]AL1 & : IS US$
6"PI;N ! NUM]AL 96%ORT REGUL> SEG;TS1
M/ 2 REG>D$ Z A NUM]IC SYMBOL4 ,Z S*1
! -MA IS SUBJECT 6! RULES = TRAN-
SCRIB+ NUM]ALS4
(1) #1,478
(THE -MA IS A NUM]IC SYMBOL1 N A
PUNCTU,N M>K)
(2) #100, #200, #300
(THE -MAS >E PUNCTU,N M>KS1 N NUM]IC
SYMBOLS)
;C_4 .,! .DECIMAL .PO9T1 ,AM]ICAN
OR ,3T95TAL1 %D 2 REG>D$ Z A NUM]IC
SYMBOL ONLY :5 X IS ASSOCIAT$ )A NU-
M]AL4 ,AN OMIS.N SYMBOL M/ N 2 REG>D$
Z A NUM]IC SYMBOL4 ,Z A NUM]IC SYMBOL1
! DECIMAL PO9T IS SUBJECT 6! RULES =
TRANSCRIB+ NUM]ALS4
(1) #.35
(THE DECIMAL PO9T IS A NUM]IC SYM-
BOL) #BA
(2) #3.14 B#H
(THE DECIMAL PO9T IS A NUM]IC SYM-
BOL)
(3) #.2A1A2A3
(THE DECIMAL PO9T IS A NUM]IC SYM-
BOL)
(4) ."A1A2A3
(THE DECIMAL PO9T IS N A NUM]IC SYM-
BOL)
(5) #.1+.2 .K ."----
(THE F/ TWO DECIMAL PO9TS >E NUM]IC
SYMBOLS)
------------------------------------#I
@,S#9_4 ..,USE (! ,NUM]IC .,9DICA-
TOR3 ,! NUM]IC 9DICATOR M/ 2 US$ 6IN-
TRODUCE "O OR M UNSPAC$ NUM]IC SYMBOLS
"U ! FOLL[+ CIRCUM/.ES3
;A_4 ,! NUM]IC 9DICATOR M/ 2 US$
AT ! 2G9N+ (A BRL L9E OR AF A SPACE4
,X M/ AL 2 US$ AF A M9US SYMBOL : OC-
CURS AT ! 2G9N+ (A BRL L9E OR : FOLL[S
A SPACE4 ,= EXCEP;NS1 SEE @,S#11_4
(1) #27
(2) ,"! 7 #7 BALLS4
,NEME? ,MA?4 ,CODE1 #1972 A#I
(3) #1+X+Y .K #0
(1 PLUS ;X PLUS ;Y EQUALS #0)
(4) Y .K #2SIN X
(;Y EQUALS #2 S9E ;X)
(5) SIN #1
(6) SIN^2 #2X
(S9E SQU>$ ( #2X)
(7) #0.333 ''' #3 '''
(8) LOG10 #2
(LOG>I?M 6! BASE #10 ( #2)
(9) $[ #1
(ANGLE #1)
(10) (X .K #0)
(;X EQUALS #0 5CLOS$ 9 P>5!SES)
(11) #11
?333#
#5
(A SIMPLE FRAC;N)
#BC
(12) #1+3 #AJ
?3333#
#4+5
,?333333,#
#3+4
?3333#
#5+6
(A -PLEX FRAC;N)
(13)
;D ;D
(1-X)?33#(2X)-2X?33#(1-X)
DX DX
,?3333333333333333333333333,#
(1-X)^2
,,?33333333333333333333333333333,,#
#2X
#1+(?3333#)^2
#1-X
(A HYP]COMPLEX FRAC;N)
(14) -#1
(M9US #1)
,NEME? ,MA?4 ,CODE1 #1972 A#AJ
(15) -#.3
(M9US ?REE T5?S)
-----------------------------------#AA
;B_4 ,! NUM]IC 9DICATOR M/ 2 US$
AF A PUNCTU,N M>K4 ,H["E1 ! HYPH5 RE-
QUIRES SPECIAL ATT5;N (SEE SEC;N ;F
2L)_4 ,X M/ AL 2 US$ AF A M9US SYMBOL
: FOLL[S A PUNCTU,N M>K4
(1) 8#3 DOGS0
(2) ,PROBABIL;Y--#0
(3) 8#.5
(4) 8-#4
;C_4 ,! NUM]IC 9DICATOR M/ 2 US$
AF A LEFT GR\P+ SYMBOL : 9TRODUCES A
DET]M9ANT OR MATRIX4 ,X M/ AL 2 US$ AF
A M9US SYMBOL : FOLL[S S* A GR\P+ SYM-
BOL4
(1) ,\#1 #2 ,\
,\-#3 -#4,\
#BE
(2) ,\#1 #1 ,\ A#AA
,\ ?33#,\
,\ #2 ,\
,\ ,\
,\ #1 #1 ,\
,\?33# ?33#,\
,\ #2 #4 ,\
;D_4 ,! NUM]IC 9DICATOR M/ 2 US$
AF A SEC;N M>K1 P>AGRAPH M>K1 CROSS-
HAT*1 OR A/]ISK4 ,X M/ AL 2 US$ AF !
G5]AL REF];E 9DICATOR OR ANY REF];E
SYMBOL4
(1) #3@,S#4
(3 SEC;N M>K #4)
(2) #3.##4
(3 CROSSHAT* #4)
(3) #3@##4
(3 A/]ISK #4)
-----------------------------------#AB
(4) ,SEE PAGE #15 @]#1_4
(1 FOLL[S ! G5]AL REF];E 9DICATOR2 !
#1 IS RAIS$ 9 9K PR9T)
,NEME? ,MA?4 ,CODE1 #1972 A#AB
(5) _]#3
(DA7] #3)
;E_4 ,! NUM]IC 9DICATOR M/ 2 US$
AF ANY (! TYPE-=M 9DICATORS1 OR AF
MAK+ A TRANSI;N F NON-REGUL> 6REGUL>
TYPE )9 ! SAME NUM]AL4 ,X M/ AL 2 US$
AF ! 9T]IOR %APE-MODIFIC,N 9DICATOR4
(1) .#3
(ITALICIZ$ #3)
(2) _#0
(BOLDFACE Z]O)
(3) .#.3
(ITALICIZ$ ?REE T5?S)
(4) @#2
(SCRIPT #2)
(5) _#43#56
(THE F/ TWO DIGITS 9 BOLDFACE TYPE1
! LA/ TWO 9 REGUL> TYPE)
(6) $C_$#5]
(5 5CLOS$ )9 A CIRCLE)
(7) $4_$#5]
(5 5CLOS$ )9 A SQU>E) #BG
;F_4 ,! NUM]IC 9DICATOR M/ B#AB
2 US$ AF A HYPH5 :5 ! HYPH5 FOLL[S A
^W1 AN A2REVI,N1 OR A M>K ( PUNCTU,N4
,H["E1 AL SEE @,S#11D_4
(1) #1-TO-#1 CORRESPOND;E
(2) HYDROG5-#3
(3) ,,DC-#7
(4) ;,B-#49 BOMB]
(5) ;,U-#238
(6) (287_8-#212 ,B4,C4)
-----------------------------------#AC
;G_4 ,! NUM]IC 9DICATOR M/ 2 US$
AF ! OP5+ TRANSCRIB]'S GR\P+ SYMBOL4
(1) ,9 X^2, ! #2 ,'#2 ELEVAT$ 9
PR9T,' IS ! EXPON5T4
@,S#10_4 ..,DEF9I;N ( 8,5CLOS$
.,LI/03
,AN 85CLOS$ LI/01 =! PURPOSES ( ?
,CODE1 M/ MEET ! FOLL[+ REQUIRE;TS3
;I_4 ,X M/ 2G9 & 5D )A SIGN (
GR\P+4 ,^! SIGNS ( GR\P+ D N NECESS>I-
LY H 6BE (! SAME K9D4
,NEME? ,MA?4 ,CODE1 #1972 A#AC
;II_4 ,X M/ 3TA9 NO ^W1 A2REVIA-
;N1 ORD9AL 5D+1 OR PLURAL 5D+4
;III_4 ,A FUNC;N "N1 AN A2REVI-
AT$ FUNC;N "N1 OR A SIGN ( %APE &!
SIGNS : FOLL[ !M >E REG>D$ Z A S+LE
ITEM4
;IV_4 ,AN ITEM (! LI/ MAY 2 !
ELLIPSIS OR ANY SIGN US$ = OMIS.N4
;V_4 ,NO SIGN ( -P>ISON MAY AP-
PE> ANY": )9 ! LI/4
;VI_4 ,! LI/ M/ H AT L1/ TWO
ITEMS4 ,! ITEMS (! LI/ M/ 2 SEP>AT$
ONLY 0-MAS2 ! LI/ M/ N 3TA9 ANY O!R
K9D ( PUNCTU,N M>K (EXCEPT ! ELLIPSIS
OR ! L;G DA% : IS US$ = OMIS.N) &!
SPACE _C 2 ! SOLE M1NS = SEP>AT+
ITEMS4
(1) #1, ;I, -#1, -I
(NOT AN 85CLOS$ LI/0 AC TO ;I)
(2) (A, B@)
(AN 85CLOS$ LI/02 MEETS ALL REQUIRE-
;TS)
#BI
(3) (?1/4#, ?1/2#+X, B#AC
?3/4#+X^2")
(AN 85CLOS$ LI/02 MEETS ALL REQUIRE-
;TS)
(4) (1, #2, & #3)
(NOT AN 85CLOS$ LI/0 AC TO ;II)
(5) (;H FT1 ;K IN)
(NOT AN 85CLOS$ LI/0 AC TO ;II)
(6) (1ST, #2ND, #3RD)
(NOT AN 85CLOS$ LI/0 AC TO ;II)
(7) (;X_'S, ;Y_'S, ;Z_'S)
(NOT AN 85CLOS$ LI/0 AC TO ;II)
-----------------------------------#AD
(8) @($[ #1^.*, SIN #1^.*"@)
(ANGLE #1 DEGREE1 S9E #1 DEGREE2 AN
85CLOS$ LI/02 MEETS ALL REQUIRE;TS)
(9) (A, B, ''')
(AN 85CLOS$ LI/02 MEETS ALL REQUIRE-
;TS)
(10) (X+1, X+2, =, =, X+5)
(AN 85CLOS$ LI/02 MEETS ALL REQUIRE-
;TS)
(11) (X .K #1, #2, ''', #10)
(NOT AN 85CLOS$ LI/0 AC TO ;V)
,NEME? ,MA?4 ,CODE1 #1972 A#AD
(12) (A .K #1, B .K #2, C .K -#4)
(NOT AN 85CLOS$ LI/0 AC TO ;V)
(13) (;U, ;V_2 ;X, ;Y)
(NOT AN 85CLOS$ LI/0 AC TO ;VI)
(14) (1 #2 #3)
(NOT AN 85CLOS$ LI/0 AC TO ;VI)
@,S#11_4 ..,NON-,USE (! ,NUM]IC
.,9DICATOR3 ,X M/ N 2 ASSUM$ T 2C A
SYMBOL IS NUM]IC T ! NUM]IC 9DICATOR
M/ 2 US$ ) T SYMBOL4 ,! NUM]IC 9DICA-
TOR M/ N 2 US$ PREC$+ A NUM]IC SYMBOL
"U ! FOLL[+ CIRCUM/.ES3
;A_4 ,! NUM]IC 9DICATOR M/ N 2 US$
AT ! .2G9N+ ( AN ITEM : IS "P ( AN
85CLOS$ LI/0 Z DEF9$ 9 @,S#10 ABV1 EV5
IF S* AN ITEM HAS BE5 RUN OV] 6ANO!R
L9E4 ,H["E1 IF ANY ITEM 9 AN 85CLOS$
LI/0 IS A NUM]AL 9 A TYPE =M O!R ?AN
REGUL> TYPE1 T ITEM REQUIRES ! NUM]IC
9DICATOR4
(1) @(0, 1@)
(2) (-1, -2, -3) #CA
(3) (1+H, 2+K, 0) B#AD
(4) (0, -1, +-2)
(5) (2SIN #30^.*, 3COS #60^.*")
(THE NUM]IC 9DICATOR IS REQUIR$ 2F !
#30 &! #60 2C ^! >E .N .! .2G9N+ (
_! RESPECTIVE ITEMS)
-----------------------------------#AE
(6) (1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12)
(THE NUM]IC 9DICATOR IS N REQUIR$ 2F
#10 EV5 ?\< #10 2G9S A NEW L9E)
(7) (X, 7, _#8, Y)
(THE #8 9 ? 85CLOS$ LI/0 IS 9 BOLD-
FACE TYPE)
;B_4 ,! NUM]IC 9DICATOR M/ N 2 US$
9 "W >RANG$ 9 COLUMNS & ALIGN$ = A4I-
;N1 SUBTRAC;N1 MULTIPLIC,N1 DIVI.N1 OR
ALIGN;T (A SY/EM ( EQU,NS4
,NEME? ,MA?4 ,CODE1 #1972 A#AE
(1) 273
+ 85
------
(A PRO#M ALIGN$ = A4I;N)
(2) 426
@*34
------
(A PRO#M ALIGN$ = MULTIPLIC,N)
(3) 18 R"2
---------
25O452
(A PRO#M ALIGN$ = DIVI.N)
#CC
(4) 2X- Y- 5Z+ 9 .K 0 B#AE
7Y- 5Z+28 .K 0
5Y-11Z-43 .K 0
(ALIGN;T ( ?REE EQU,NS)
;C_4 ,! NUM]IC 9DICATOR M/ N 2 US$
AF A SPACE IF ! PURPOSE (! SPACE IS TO
"PI;N A NUM]AL 96SEG;TS4
-----------------------------------#AF
(1) .P .K #3.14159 26535 '''
(2)
#947, 147, 592'
,MILLIONS ,?\S&S ,"OS OR ,UNITS
;D_4 ,! NUM]IC 9DICATOR M/ N 2 US$
AF A HYPH5 IF ! HYPH5 FOLL[S A NUM]AL1
A LR1 OR O!R MA!MATICAL EXPRES.N4
(1) #65-75
(2) #3_3#30-4_3#45
(?REE ?IRTY 6F\R =TY-FIVE)
(3) ,R1D SEC;N ;,A-12_4
;E_4 ,! NUM]IC 9DICATOR M/ N 2 US$
,NEME? ,MA?4 ,CODE1 #1972 A#AF
9 ANY SITU,N N COV]$ 9 @,S@,S#9 &
#11_4
(1) X^2
(2) ?3/X#
(3) R"5
(REMA9D] ( #5 Z 9 A DIVI.N PRO#M)
(4)
AX^3"+BX^2"Y+CXY^2"+DY^3"+EX^2"+Y^2
"-7
(5) X-5
(6) #2@*4
(7) #10,000
(IN ? NUM]AL1 ! -MA IS N A PUNCTU,N
M>K)
(8) \-3\
(THE ABSOLUTE VALUE ( M9US #3)
-----------------------------------#AG
@,S#12_4 .,L;G .,NUM]ALS3 ,L;G NU-
M]ALS T _C 2 -PLETELY A3OMMODAT$ ON "O
BRL L9E MAY 2 DIVID$ & RUN OV] 6ANO!R
L9E4 ,S* A DIVI.N M/ 2 MADE AF A -MA1
IF PRES5T1 &A HYPH5 M/ 2 SUPPLI$4 ,!
NUM]IC 9DICATOR M/ 2 US$ Z ! F/ #CE
BRL SYMBOL (! BRL L9E 6: ! A#AG
NUM]AL HAS BE5 RUN OV]4
(1) #100,000,000,000,-
#000
(2) #100000000000-
#000
@,S#13_4 ..,REPRES5T,N ( ,NUM]ALS TO
,NON-,DECIMAL .,BASES3
;A_4 ,:5 A SY/EM ( NUM],N IS 6A
BASE O!R ?AN #10, A -MON TE*NIQUE =
PROVID+ A4I;NAL DIGITS IS 6USE LRS1 EI
L[]-CASE OR CAPITALIZ$1 9 A4I;N 6! T5
,>ABIC DIGITS4 ,:5 ? TE*NIQUE IS US$1
! TRANSCRIB] M/ USE ONLY L[]-CASE LRS4
,IF CAPITALIZ$ LRS >E US$ 9 9K PR9T1 !
TRANSCRIB] M/ 9DICATE ? FACT 9 A
TRANSCRIB]'S NOTE4
(1) #13TE7
(A BASE-#12 NUM]AL 9 : ;,T REPRES5TS
#10 & ;,E REPRES5TS #11)
(2) #3FFE2
(A BASE-#16 NUM]AL 9 : ;,E REPRES5TS
,NEME? ,MA?4 ,CODE1 #1972 B#AG
#14 & ;,F REPRES5TS #15)
;B_4 ,ANO!R -MON TE*NIQUE = PRO-
VID+ A4I;NAL DIGITS IS 6USE /&>D OR
>BITR>Y SIGNS 6SUPPLE;T ! T5 ,>ABIC
DIGITS4 ,AU?ORS "S"TS GIVE "NS 6^!
SIGNS4 ,= EXAMPLE1 (DEK) REPRES5TS
#10 & (EL) REPRES5TS #11_4 ,9 ?
CASE1 ! TRANSCRIB] M/ DEVISE "O-CELL
SYMBOLS = ^! SIGNS1 PREF]ABLY *OS5 F
AM;G ! LRS (! ,5GLI% ALPHABET1 & M/
9S]T A TRANSCRIB]'S NOTE 6SPECIFY !
M1N+S : H BE5 ASSIGN$ 6^! SYMBOLS4 ,!
TRANSCRIB]'S NOTE M/ 9CLUDE A DRAW+ (
ANY SIGN = : "! IS NO EQUIVAL5T SYMBOL
9 ! ,CODE4
(1) #13DE7
(A BASE-#12 NUM]AL 9 : REPRES5TS
#CG
,NEME? ,MA?4 ,CODE1 #1972 C#AG
#10 & REPRES5TS #11_4 ,"H !
TRANSCRIB] HAS ASSIGN$ D TO
& E TO )
;C_4 ,ANO!R -MON TE*NIQUE IS 6USE
AN >BITR>Y SET ( SIGNS : D N 9CLUDE
,>ABIC DIGITS4 ,9 ? CASE1 ! TRANSCRIB]
M/ PROCE$ Z 9 ;B ABV4
(1) #APD
(A BASE-#3 NUM]AL ( ?REE DIGITS2 "H
! TRANSCRIB] HAS ASSIGN$ A TO ,
P TO , & D TO )
;D_4 ,! "O-CELL SYMBOLS : ! TRAN-
SCRIB] USES 6REPRES5T ! DIGITS ( #CI
,NEME? ,MA?4 ,CODE1 #1972 D#AG
A NON-DECIMAL NUM],N SY/EM M/ 2 REG>D$
Z NUM]IC SYMBOLS4 ,Z S*1 ^! NUM]IC
SYMBOLS >E SUBJECT 6! RULES = TRAN-
SCRIB+ NUM]ALS4
-----------------------------------#AH
(1) #T2E4
(A BASE-#12 NUM]AL2 ;T & ;E >E L[]
CASE 9 9K PR9T)
(2) #3T.T8
(A BASE-#12 NUM]AL 3TA9+ A DECIMAL
PO9T 2T ! SECOND & ?IRD DIGITS2 ;T
IS L[] CASE 9 9K PR9T)
(3) #FA9,B7C.0A
(A BASE-#16 NUM]AL 3TA9+ A -MA &A
DECIMAL PO9T2 ;,F, ;,A, ;,B & ;,C >E
CAPITALIZ$ 9 9K PR9T)
@,S#14_4 .,ORD9AL .,5D+S3 (,SEE
@,S#55D_4)
@,S#15_4 ..,PLURAL & ,POSSESSIVE
.,5D+S3 (,SEE @,S#39_4)
@,S#16_4 .,NUM]ALS .9 .,DIAGRAMS3 ,9
DIAGRAMS : 3TA9 NUM]IC LABELS1 ! NU-
M]IC 9DICATOR M/ 2 US$4 ,! #DA
SPACE 6A3OMMODATE ! NUM]IC 9DI- A#AH
CATOR MAY (T5 2 GA9$ 0A SU6ICI5T EN-
L>GE;T (! DIAGRAM4
@,S#17_4 .,NUM]ALS 9 ,TA# .,5TRIES3
,9 TA#S ^: 5TRIES 3SI/ 5TIRELY ( NU-
M]ALS1 ! NUM]IC 9DICATOR M/ 2 OMITT$4
,H["E1 9 TA#S ^: 5TRIES >E A MIXTURE (
^WS1 NUM]ALS1 LRS1 OR O!R MA!MATICAL
SIGNS1 ! NUM]IC 9DICATOR M/ 2 US$4 ,?
RULE APPLIES ONLY 6! BODY (A TA# & N
6! H1D+S4 ,DET]M9ANTS & MATRICES >E N
6BE REG>D$ Z TA#S4 ,! M9US SYMBOL IS N
NUM]IC S T1 IF X O3URS 9 A TA#1 !
NUM]IC 9DICATOR M/ 2 US$ "?\T ! TA#4
@,S#18_4 .,ROMAN .,NUM]ALS3
;A_4 ,CAPITALIZ$ ,ROMAN NUM]ALS M/
2 TRANSCRIB$ US+ ! S+LE CAPITAL SIGN
2F "O LR &! D\# CAPITAL SIGN 2F M ?AN
"O LR4 ,=! USE (! ,5GLI%-LR 9DICATOR )
,ROMAN NUM]ALS1 SEE @,S#28C_4
(1) ;,I, ,,II, ,,III, ,,IV, ;,V_4
(2) ,! LRS ;,I, ;,V, ;,X, ;,L,
;,C, ;,D, ;,M >E ! SYMBOLS
WE USE 6WRITE ,ROMAN NU-
,NEME? ,MA?4 ,CODE1 #1972 B#AH
M]ALS4
(3) ,,VII+,V .K ,,XII
(4) (,I+,,II)+,,III
.K ,I+(,,II+,,III)
-----------------------------------#AI
(5) ,,II'
(PRIME SIGN FOLL[S ! ,ROMAN NUM]AL)
(6) ,M:
(B> OV] ;,M)
(7) ,V .K #5, ,L .K #50_4
(8) ,R1D *APT]S ;,I-;,V &
,,XI-,,XV_4
(9) #1_4
(,I)
(,,II)
(10) #1_4
;,I_4
,,II_4
;B_4 ,:5 A ,ROMAN NUM]AL 3SI/S (
"O OR M L[]-CASE LRS X M/ 2 TR1T$ Z
?\< X 7 A 8S+LE LR0 &1 Z S*1 ! ,5GLI%-
LR 9DICATOR M/ 2 US$ OR N US$ 9 A3ORD-
.E )! RULES GOV]N+ ! ,5GLI%-LR #DC
9DICATOR (SEE @,S@,S#26-28)_4 A#AI
(1) ;I, ;II, ;III, ;IV, ;V_4
(2) ,SEE PAGES ;V & ;VI_4
(3) @,PA, @,SI & @,SII_4
(4) VI+IV .K X
(5) I .K #1, V .K #5, & X .K #10_4
-----------------------------------#BJ
(6) ,R1D PAGES ;I-;V & ;XI-;XV_4
(7) #1_4
(I)
(II)
(8) #1_4
;I_4
;II_4
;C_4 ,:5 X IS "QA# T A LR -B9,N IS
A ,ROMAN NUM]AL1 TR1T ! -B9,N Z IF X
IS N A ,ROMAN NUM]AL4
(1) ,C,L
(THIS -B9,N O3URS 9 A 3TEXT F : X _C
2 ASC]TA9$ :E!R ,C,L IS A ,ROMAN
NUM]AL)
,NEME? ,MA?4 ,CODE1 #1972 A#BJ
(2) MIX
(THIS -B9,N O3URS 9 A 3TEXT F : X _C
2 ASC]TA9$ :E!R MIX IS A ,ROMAN NU-
M]AL)
;D_4 ,= PUNCTU,N ( ,ROMAN NUM]ALS1
SEE @,S#37, ;III_4
@,S#19_4 .,SPAC+ .) .,NUM]ALS3
,SPACES )9 NUM]ALS M/ 2 LEFT :5 X IS
NEC 6"PI;N A NUM]AL 96%ORT REGUL> SEG-
;TS1 OR 6A*IEVE ALIGN;T4 (,FOR EXAM-
PLES SEE @,S#11B & ;C_4)
,RULE ,,III--,CAPITALIZ,N
,CAPITALIZ,N ,9DICATORS
,S+LE ,
,D\# ,, (,FOR -B9,NS ( CAPITALIZ,N1
ALPHABETIC1 & TYPE-=M 9DI-
CATORS1 SEE ,APP5DIX1 PAGE
#208)
#DE
@,S#20_4 ..,USE (! ,CAPI- #BA
TALIZ,N .,9DICATOR3
;A_4 ,! CAPITALIZ,N 9DICATOR M/ 2
US$ 69DICATE ! CAPITALIZ,N (A LR F ANY
(! ALPHABETS LI/$ 9 .,RULE .,,IV,
EXCEPT ! ,HEBREW ALPHABET ^: LRS D N
POSSESS A CAPITALIZ$ =M4 ,? 9DICATOR
M/ PREC$E ! LR 3C]N$4
(1) _,A
(,G]MAN CAPITALIZ$ @H)
(2) .,G
(,GREEK CAPITALIZ$ GAMMA)
;B_4 ,= CAPITALIZ$ ,ROMAN NUM]ALS1
SEE A,S#18A_4
;C_4 ,=! CAPITALIZ,N ( A2REVI,NS1
SEE A,S#50_4
A,S#2"_4 ..,NON-,USE (! ,CAPITALIZ,N
.,9DICATOR3 ,CAPITALIZ,N M/ N 2 US$ )A
LR J ;C X 2G9S A S5T;E1 IF ! CORRE-
SPOND+ LR 9 9K PR9T IS UNCAPITALIZ$4
(1) ;X IS A NUMB] 2T #2 & #3_4
,NEME? ,MA?4 ,CODE1 #1972 A#BA
@,S#22_4 ..,E6ECTIVE;S (! ,CAPITALI-
Z,N .,9DICATOR3
;A_4 ,! E6ECTIVE;S (! S+LE CAPI-
TALIZ,N 9DICATOR EXT5DS ONLY 6! LR :
FOLL[S X1 S T IF EA* LR 9 A SEQU;E RE-
QUIRES CAPITALIZ,N1 ! CAPITALIZ,N 9DI-
CATOR M/ 2 US$ ) EA* ( ^! LRS 9DIVID-
U,Y4
(1) $T ,A,B,C
(TRIANGLE ,A,B,C)
;B_4 ,! E6ECTIVE;S (! D\# CAPI-
TALIZ,N 9DICATOR 9 ,ROMAN NUM]ALS & 9
A2REVI,NS EXT5DS 6ALL (! LRS : IMMLY
FOLL[ X4 ,H["E1 A SYMBOL O!R ?AN A LR
T]M9ATES XS E6ECT4
(1) ,,LL4,D4
(2) ,,III+,V
#DG
,RULE ,,IV--,ALPHABETS B#BA
,ALPHABETIC ,9DICATORS
,5GLI% (,ROMAN) ,LR ;
,G]MAN-,LR _
-----------------------------------#BB
,GREEK-,LR
,= ,/&>D ,LRS .
,= ,ALT]NATIVE ,=MS ( ,LRS .@
,HEBREW-,LR ,,
,RUSSIAN (,CYRILLIC) ,LR @@
(,FOR -B9,NS ( CAPITALIZ,N1 AL-
PHABETIC1 & TYPE-=M 9DICATORS1
SEE ,APP5DIX1 PAGE #208)
,ALPHABETS
,5GLI% (,ROMAN) ,ALPHABET
,',COLUMN H1D+S 9 ! FOLL[+ TA#
>E LABEL$ ?US3
;,A--,ORD9>Y L[]-CASE
;,B--,ORD9>Y CAPITALIZ$
;,C--,SCRIPT L[]-CASE
;,D--,SCRIPT CAPITALIZ$
;,E--,SANS]IF CAPITALIZ$
,NEME?,MA?4 ,CODE1#1972 A#BB
;,F--,BRL EQUIVAL5T,'
;,A ;,B ;,C ;,D ;,E ;,F
A
B
C
D
E
#DI
,NEME? ,MA?4 ,CODE1 #1972 B#BB
;,A ;,B ;,C ;,D ;,E ;,F
F
G
H
I
0
#EA
,NEME? ,MA?4 ,CODE1 #1972 C#BB
;,A ;,B ;,C ;,D ;,E ;,F
K
L
M
N
O
#EC
,NEME? ,MA?4 ,CODE1 #1972 D#BB
;,A ;,B ;,C ;,D ;,E ;,F
P
Q
R
S
T
#EE
,NEME? ,MA?4 ,CODE1 #1972 E#BB
;,A ;,B ;,C ;,D ;,E ;,F
U
V
W
X
Y
#EG
,NEME? ,MA?4 ,CODE1 #1972 F#BB
;,A ;,B ;,C ;,D ;,E ;,F
Z
-----------------------------------#BC
,G]MAN ,ALPHABET
,',COLUMN H1D+S 9 ! FOLL[+ TA#
>E LABEL$ ?US3
;,A--,"N ( LR
;,B--,ORD9>Y L[]-CASE
;,C--,ORD9>Y CAPITALIZ$
;,D--,SCRIPT L[]-CASE
;,E--,SCRIPT CAPITALIZ$
;,F--,BRL EQUIVAL5T,'
#EI
,NEME? ,MA?4 ,CODE1 #1972 A#BC
;,A ;,B ;,C ;,D ;,E ;,F
AH A
BEH B
TSEH C
DEH D
EH E
#FA
,NEME? ,MA?4 ,CODE1 #1972 B#BC
;,A ;,B ;,C ;,D ;,E ;,F
EFF F
<EH G
HAH H
OR
EE I
#FC
,NEME? ,MA?4 ,CODE1 #1972 C#BC
;,A ;,B ;,C ;,D ;,E ;,F
YAHT J
OR
KAH K
ELL L
EM M
#FE
,NEME? ,MA?4 ,CODE1 #1972 D#BC
;,A ;,B ;,C ;,D ;,E ;,F
EN N
OH O
PEH P
KOO Q
]R R
#FG
,NEME? ,MA?4 ,CODE1 #1972 E#BC
;,A ;,B ;,C ;,D ;,E ;,F
ESS S
OR
TEH T
OO U
FAO V
#FI
,NEME? ,MA?4 ,CODE1 #1972 F#BC
;,A ;,B ;,C ;,D ;,E ;,F
VEH W
IKS X
YPSILON Y
TSET Z
,GREEK ,ALPHABET (,/&>D)
,',COLUMN H1D+S 9 ! FOLL[+ TA#
>E LABEL$ ?US3
;,A--,"N ( LR #GA
,NEME? ,MA?4 ,CODE1 #1972 G#BC
;,B--,ORD9>Y L[]-CASE
;,C--,ORD9>Y CAPITALIZ$
;,D--,SCRIPT L[]-CASE
;,E--,SCRIPT CAPITALIZ$
;,F--,BRL EQUIVAL5T,'
;,A ;,B ;,C ;,D ;,E ;,F
ALPHA A
2TA B
GAMMA G
DELTA D
#GC
,NEME? ,MA?4 ,CODE1 #1972 H#BC
;,A ;,B ;,C ;,D ;,E ;,F
EPSILON E
ZETA Z
ETA :
!TA ?
IOTA I
#GE
,NEME? ,MA?4 ,CODE1 #1972 I#BC
;,A ;,B ;,C ;,D ;,E ;,F
KAPPA K
-----------------------------------#BD
LAMBDA L
MU M
NU N
XI X
#GG
,NEME? ,MA?4 ,CODE1 #1972 A#BD
;,A ;,B ;,C ;,D ;,E ;,F
OMICRON O
PI P
RHO R
SIGMA S
TAU T
#GI
,NEME? ,MA?4 ,CODE1 #1972 B#BD
;,A ;,B ;,C ;,D ;,E ;,F
UPSILON U
PHI F
*I &
PSI Y
OMEGA W
#HA
,NEME? ,MA?4 ,CODE1 #1972 C#BD
,HEBREW ,ALPHABET
,HEBREW LRS D N POSSESS A CAPITALIZ$
=M4
,"N ( ,BRL
LR ,ORD9>Y ,SCRIPT EQUIVAL5T
ALEPH 1
VE? V
GIMEL G
DALE? D
#HC
,NEME? ,MA?4 ,CODE1 #1972 D#BD
,"N ( ,BRL
LR ,ORD9>Y ,SCRIPT EQUIVAL5T
858 8
VAV W
ZAY9 Z
*E? X
TE? T
#HE
,NEME? ,MA?4 ,CODE1 #1972 E#BD
,"N ( ,BRL
LR ,ORD9>Y ,SCRIPT EQUIVAL5T
YOD 0
*APH *
LAM$ L
MEM M
NUN N
#HG
,NEME? ,MA?4 ,CODE1 #1972 F#BD
,"N ( ,BRL
LR ,ORD9>Y ,SCRIPT EQUIVAL5T
SAMEKH S
AY9 $
658 6
TSADI !
KOPH Q
#HI
,NEME? ,MA?4 ,CODE1 #1972 G#BD
,"N ( ,BRL
LR ,ORD9>Y ,SCRIPT EQUIVAL5T
RE% R
S9 :
?AV ?
-----------------------------------#BE
,RUSSIAN ,ALPHABET
,! ,RUSSIAN ALPHABET IS "S"TS REF]R
TO Z ! .,CYRILLIC .ALPHABET4
,',COLUMN H1D+S 9 ! FOLL[+ TA#
>E LABEL$ ?US3
;,A--,"N ( LR
;,B--,ORD9>Y L[]-CASE
;,C--,ORD9>Y CAPITALIZ$
;,D--,SCRIPT L[]-CASE #IA
,NEME? ,MA?4 ,CODE1 #1972 A#BE
;,E--,SCRIPT CAPITALIZ$
;,F--,BRL EQUIVAL5T,'
;,A ;,B ;,C ;,D ;,E ;,F
AH A
BEH B
VEH W
<EH G
#IC
,NEME? ,MA?4 ,CODE1 #1972 B#BE
;,A ;,B ;,C ;,D ;,E ;,F
DEH D
OR
YEH E
ZHEH J
#IE
,NEME? ,MA?4 ,CODE1 #1972 C#BE
;,A ;,B ;,C ;,D ;,E ;,F
ZEH Z
OR
EE
I
KAH K
ELL L
#IG
,NEME? ,MA?4 ,CODE1 #1972 D#BE
;,A ;,B ;,3 ;,D ;,E ;,F
EM M
EN N
OH O
PEH P
]R R
#II
,NEME? ,MA?4 ,CODE1 #1972 E#BE
;,A ;,B ;,C ;,D ;,E ;,F
ESS S
TEH T
OO U
566 F
KHAH H
#AJA
,NEME? ,MA?4 ,CODE1 #1972 F#BE
;,A ;,B ;,C ;,D ;,E ;,F
TSEH C
*EH Q
%AH :
%*AH X
Y]IH !
#AJC
,NEME? ,MA?4 ,CODE1 #1972 G#BE
;,A ;,B ;,C ;,D ;,E ;,F
EH [
YU \
YAH $
-----------------------------------#BF
@,S#23_4 .,ALPHABETS3
;A_4 ,SPECIFIC PROVI.N IS MADE 9 ?
CODE = FIVE ALPHABETS--,5GLI%1 ,G]MAN1
,GREEK1 ,HEBREW1 & ,RUSSIAN4 ,! LRS (!
,5GLI% ALPHABET >E (T5 CALL$ .,ROMAN1
& ^? (! ,RUSSIAN ALPHABET .,CYRILLIC4
;B_4 ,"S (! LRS (! ORD9>Y L[]-CASE
,GREEK ALPHABET POSSESS AN #AJE
,NEME? ,MA?4 ,CODE1 #1972 A#BF
ALT]NATIVE =M4 ,! M -MON "OS >E3
,"N ( ,BRL
LR ,SIGN EQUIVAL5T
ALPHA .@A
2TA .@B
!TA .@?
SIGMA .@S
PHI .@F
,:5 ^! ALT]NATIVE =MS O3UR .9/1D .(!
/&>D =MS "?\T A TEXT1 ! SYMBOLS =! /&-
>D =MS %D 2 US$ 9 BRL1 &! TRANSCRIB]
%D CALL ATT5;N 6? USAGE 0A #AJG
,NEME? ,MA?4 ,CODE1 #1972 B#BF
TRANSCRIB]'S NOTE4 ,! ALT]NATIVE =MS
%D 2 US$ ONLY :5 ! AU?OR HAS ASSIGN$
4T9CT M1N+S 6! /&>D & ALT]NATIVE =MS (
! SAME LR4
;C_4 ,"S ,GREEK LRS US$ 9 TEXT-
BOOKS >E OBSOLETE4 ,! M -MON "OS >E3
,"N ( ,BRL
LR ,SIGN EQUIVAL5T
/IGMA .!
VAU .V
KOPH (OR QOPH) .Q
SAMPI .C
@,S#24_4 .,ALPHABETIC .,9DICATORS3
;A_4 ,EXCEPT =! ,5GLI%-LR #AJI
,NEME? ,MA?4 ,CODE1 #1972 C#BF
9DICATOR (SEE @,S@,S#26-28), ! APPRO-
PRIATE ALPHABETIC 9DICATOR M/ 2 US$ TO
SPECIFY ! ALPHABET 6: A LR 2L;GS4 ,IF
! LR IS L[] CASE1 ! CORRESPOND+ ALPHA-
BETIC 9DICATOR M/ PREC$E ! LR DIRECT-
LY2 IF ! LR IS CAPITALIZ$1 S T ! CAPI-
TALIZ,N 9DICATOR IS AL REQUIR$1 !
ALPHABETIC 9DICATOR M/ PREC$E ! CAPI-
TALIZ,N 9DICATOR4
(1) .A
(,GREEK L[]-CASE ALPHA)
(2) .,S
(,GREEK CAPITALIZ$ SIGMA)
-----------------------------------#BG
(3) .P
(,GREEK L[]-CASE PI)
(4) .@F
(ALT]NATIVE =M ( ,GREEK L[]-CASE
PHI)
(5) .!
(,GREEK /IGMA2 OBSOLETE)
(6) _A
(,G]MAN L[]-CASE AH) #AAA
(7) _,A A#BG
(,G]MAN CAPITALIZ$ AH)
(8) ,,A0
(,HEBREW ALEF SUB Z]O)
(9) @@A
(,RUSSIAN L[]-CASE AH)
(10) @@,A
(,RUSSIAN CAPITALIZ$ AH)
;B_4 ,! E6ECTIVE;S ( AN ALPHABETIC
9DICATOR EXT5DS ONLY 6! LR OR1 9 !
CASE (! ,5GLI%-LR 9DICATOR1 6A 8%ORT-
=M -B9,N0 OR A L[]-CASE ,ROMAN NUM]AL
: FOLL[S X4 ,:5 AN ALPHABETIC 9DICATOR
IS REQUIR$1 X M/ 2 US$ ) EA* 9DIVIDUAL
LR (A SEQU;E ( LRS OR1 9 ! CASE (!
,5GLI%-LR 9DICATOR1 )! 8%ORT-=M -B9,N0
: FOLL[S X4 (,SEE @,S#25_4)
(1) .A.B
(,GREEK L[]-CASE ALPHA FOLL[$ BY
,GREEK L[]-CASE 2TA)
(2) _,A.A+_,B.B
(,G]MAN CAPITALIZ$ AH FOLL[$ 0,GREEK
L[]-CASE ALPHA PLUS ,G]MAN CAPITAL-
,NEME? ,MA?4 ,CODE1 #1972 B#BG
IZ$ BEH FOLL[$ 0,GREEK L[]-CASE
2TA)
(3) ;AB IS P>ALLEL TO ;CD
(4) ;IV
@,S#25_4 8..,S+LE ,LRS0 & 8,%ORT-,=M
,LR .,-B9,NS0 (,SEE @,S#26)_3
;A_4 ,A 8S+LE LR01 =! PURPOSES ( ?
,CODE1 M/ MEET ! FOLL[+ REQUIRE;TS3
-----------------------------------#BH
;I_4 ,! LR M/ 2 F ! ,5GLI%
ALPHABET4
(1) ;A CORRESPONDS TO .A & ;,D
CORRESPONDS TO .,D_4
(;A & ;,D >E 8S+LE LRS02 .A & .,D
>E NOT)
;II_4 ,X M/ 2 9 REGUL> TYPE4
(1) _;,X IS A VECTOR2 ;X IS A
SCAL>
(_;,X IS N A 8S+LE LR02 ;X IS A
8S+LE LR0) #AAC
;III_4 ,X M/ 2 UNMODIFI$4 A#BH
(1) X', X'', X1, X;A, X^2, X:
(N"O ( ^! ITEMS IS A 8S+LE LR0)
;IV_4 ,X M/ N 2 AN A2REVI,N OR
ANY (! ^WS 8A01 8,A01 8,I01 OR 8,O04
(1) #1 L4 .K #1000 CC4
(THE L4 IS N A 8S+LE LR0)
(2) ,F #11 A4M4 TO #2 P4M4
(THE LRS 9 A4M4 & P4M4 >E N 8S+LE
LRS0)
(3) ,IF ,I TAKE ;I Z A V>IA# '''
(THE ^WS 8,I0 & 8A0 >E N 8S+LE LRS0)
;V_4 ,X M/ 2 PREC$$ 0A SPACE OR
0"O OR M PUNCTU,N M>KS 9 9K PR9T4 ,IF
? SPACE IS N %[N 9 BRL1 ! LR IS NO
L;G] A 8S+LE LR40 ,:E!R ^! PUNCTU,N
M>KS >E PREC$$ 0A SPACE OR N IS IRREL-
EVANT4 ,A GR\P+ SIGN IS N A M>K (
PUNCTU,N4
,NEME? ,MA?4 ,CODE1 #1972 B#BH
(1) ;X 8;X (_8;X (;X
(OF ! ABV ITEMS1 ! F/ ?REE >E 8S+LE
LRS02 ! LA/ IS NOT)
-----------------------------------#BI
(2) X+Y
(;Y IS N A 8S+LE LR0 S9CE X IS N
PREC$$ 0A SPACE OR PUNCTU,N)
;VI_4 ,X M/ 2 FOLL[$ 0A SPACE OR
0"O OR M PUNCTU,N M>KS 9 9K PR9T4 ,IF
? SPACE IS N %[N 9 BRL1 ! LR IS NO
L;G] A 8S+LE LR40 ,:E!R ^! PUNCTU,N
M>KS >E FOLL[$ 0A SPACE OR N IS
IRRELEVANT4 ,A GR\P+ SIGN IS N A M>K (
PUNCTU,N4
(1) ;X_0 ;X_0) ;X)
(OF ! ABV ITEMS1 ! F/ TWO >E 8S+LE
LRS02 ! LA/ IS NOT)
(2) ,ACOS B
(;,A IS N A 8S+LE LR0 S9CE NO SPACE
W 2 LEFT AF ! ;,A 9 BRL)
#AAE
(3) X+Y A#BI
(;X IS N A 8S+LE LR0 S9CE X IS N
FOLL[$ 0A SPACE OR PUNCTU,N)
;B_4 ,A 8%ORT-=M LR -B9,N01 M
BRIEFLY REF]R$ TO Z A 8%ORT-=M -B9,N01
=! PURPOSES ( ? ,CODE M/ MEET ! FOLL[+
REQUIRE;TS3
;I_4 ,X M/ 2 A LR -B9,N : CORRE-
SPONDS 6A %ORT-=M ^W ( ,5GLI% ,BRL4
;II_4 ,ALL ( XS LRS M/ 2 L[]
CASE4
;III_4 ,X M/ MEET ! REQUIRE;TS
( ;II-;VI ( ;A ABV4
(1) ;CD IS P>ALLEL TO EF_4
(;CD IS A 8%ORT-=M -B9,N02 EF IS
NOT)
(2) 6! ;NTH DEGREE
(;NTH IS N A 8%ORT-=M -B9,N0 AC TO
;I)
(3) ,A,B IS P]P5DICUL> TO ,C,D
(NEI ,A,B NOR ,C,D >E 8%ORT-=M -B9A-
;NS0 AC TO ;II)
,NEME? ,MA?4 ,CODE1 #1972 B#BI
(4) #1 YR4 .K #12 MO4
(YR4 IS N A 8%ORT-=M -B9,N0 AC TO
;IV ( ;A ABV)
@,S#26_4 ..,USE (! ,5GLI%-,LR .,9DI-
CATOR3 ,EA* (! FOLL[+ RULES APPLIES1
SUBJECT 6! 3DI;NS ( @,S#27_4
;A_4 ,! ,5GLI%-LR 9DICATOR M/ 2
US$ ) ,5GLI% LRS1 :E!R L[] CASE OR
CAPITALIZ$1 IF ! TYPE =M IS O!R ?AN
REGUL> TYPE4
-----------------------------------#CJ
(1) _;,A_;,B
(BOLDFACE CAPITALIZ$ ;A FOLL[$ BY
BOLDFACE CAPITALIZ$ ;B)
(2) .;A.;B
(ITALIC L[]-CASE ;A FOLL[$ 0ITALIC
L[]-CASE ;B)
(3) @;E@;F
(SCRIPT L[]-CASE ;E FOLL[$ 0SCRIPT
L[]-CASE ;F)
;B_4 ,! ,5GLI%-LR 9DICATOR M/ 2
US$ ) 8S+LE LRS0 OR 8%ORT-=M #AAG
-B9,NS0 UN.S SPECIFIC,Y PRO- A#CJ
HIBIT$ 0O!R RULES ( ? ,CODE4
(1) $[_'S ;,A & ;,B >E ACUTE4
(2) ,! 9T]SEC;N ( ;AB & ;CD
IS ;,O_4
(3) ,F9D ! SUM (! ;N $[_'S_4
("H ! %APE SIGN = .ANGLE IS N AN
OMIS.N SIGN S T ! ,5GLI%-LR 9DICATOR
IS REQUIR$)
(4) (;H FT1 ;K FT)
(THIS IS N AN 85CLOS$ LI/02 "!=E1 !
,5GLI%-LR 9DICATOR IS REQUIR$ )! ;H
&! ;K)
(5) (;A, #2X, Y .K Z)
(THIS IS N AN 85CLOS$ LI/02 "!=E1 !
,5GLI%-LR 9DICATOR IS REQUIR$ )! ;A
B IS N REQUIR$ )! ;Y OR ;Z, Z WD 2 !
CASE IF ! P>5!SES 7 N PRES5T)
(6) ;X-9T]CEPT
(7) ;N-TUPLE
(8) N-;P
(9) ,EX]CISES ;,A-;,F
(10) ,EX]CISE #1-;A
(11) ;,X-, ;,Y-, & ;,Z-AXES4
,NEME? ,MA?4 ,CODE1 #1972 #CA
(12) @> ;A
(13) ;A
?333#
;AB
(14) #1_4
;A_4
;B_4
(15) ,IF ;N, N1, N2, >E '''
(16) 8;X_0 .K 8;Y_0
(17) (;P IS A POSITIVE 9TEG])
(;P IS 9 DIRECT 3TACT ) XS LEFT
GR\P+ SIGN2 ? LR WD REQUIRE ! ,5G-
LI%-LR 9DICATOR IF ! P>5!SIS 0 RE-
MOV$)
(18) (;P & ;Q)
(;P & ;Q >E 9 DIRECT 3TACT ) _! RE-
SPECTIVE GR\P+ SIGNS2 ^! LRS WD RE-
QUIRE ! ,5GLI%-LR 9DICATOR IF ! P>5-
!SES 7 REMOV$)
(19) (;L, ;M, ;N >E 9 SET ;,R)
(;L IS 9 DIRECT 3TACT ) XS LEFT
GR\P+ SIGN & ;,R IS 9 DIRECT #AAI
3TACT ) XS "R GR\P+ SIGN2 ^! A#CA
LRS WD REQUIRE ! ,5GLI%-LR 9DICATOR
IF ! P>5!SES 7 REMOV$)
(20) (;X-9T]CEPT)
(THE ;X WD REQUIRE ! ,5GLI%-LR 9DI-
CATOR IF ! P>5!SIS 0 REMOV$)
(21) (;AB & ;CD)
(THESE 8%ORT-=M -B9,NS0 WD REQUIRE
,5GLI%-LR 9DICATORS IF ! P>5!SES 7
REMOV$)
-----------------------------------#CB
;C_4 ,= USE (! ,5GLI%-LR 9DICATOR
) A2REVI,NS1 SEE @,S#51_4
;D_4 ,= O!R SITU,NS 9 : ! ,5GLI%-
LR 9DICATOR MAY AL 2 US$1 SEE @,S#28_4
@,S#27_4 ..,NON-,USE (! ,5GLI%-,LR
.,9DICATOR3 ,X M/ N 2 ASSUM$ T 2C A
SYMBOL IS A 8S+LE LR0 OR A 8%ORT-=M
-B9,N0 T ! ,5GLI%-LR 9DICATOR M/ 2
US$4
;A_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N0 T
FOLL[S A FUNC;N "N OR XS A2REVI,N4
(1) COS ,A
,NEME? ,MA?4 ,CODE1 #1972 A#CB
(2) ARC AB
(3) E^SIN X
;B_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N0 T
FOLL[S A SIGN ( %APE1 PROVID$ T ! SIGN
( %APE DOES N H A PLURAL OR A POSSES-
SIVE 5D+4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N0 :
PREC$ES A SIGN ( %APE :5 T SIGN ( %APE
IS AL A SIGN ( OMIS.N4
(1) $[ A
(2) $T ACR
(3) X $4 Y
(THE .SQU>E IS A SIGN ( %APE : IS AL
A SIGN ( OMIS.N)
(4) ,F9D ! SUM (! ;N $[_'S_4
("H ! %APE SIGN = .ANGLE IS N AN
OMIS.N SIGN S T ! ,5GLI%-LR 9DICA-
TOR IS REQUIR$)
;C_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ 2F ANY LR OR -B9,N ( TWO OR M LRS
9 A DET]M9ANT OR MATRIX4 #ABA
(1) ,\A B C,\ B#CB
,\D E F,\
,\G H I,\
-----------------------------------#CC
(2) ,\ D D ,\
,\?33# ?33#"\
,\ DU DV ,\
,\ ,\
,\ D D ,\
,\?33# ?33#"\
,\ DX DY ,\
;D_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N0 :
IS AN ITEM 9 AN 85CLOS$ LI/40 (,FOR
DEF9I;N ( 85CLOS$ LI/0 SEE @,S#10_4)
(1) (0, A, 1, B, 2)
(2) .(A, B, C, D.)
(3) (AB, CD, EF)
(4) (A, 2X, B)
;E_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
,NEME? ,MA?4 ,CODE1 #1972 A#CC
US$ )! LR ;S :5 ? ;S IS "P (! APOS-
TROPHE-;S -B9,N4
(1) ;X_'S, ;Y_'S, & ;Z_'S_4
;F_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N0 :
IS PREC$$ OR FOLL[$ 0A -P>ISON SIGN4
(1) ,IF A .K B, !N AC .K BC_4
(2) A .K B, BUT C /.K B_4
(3) #30@0 ( ,N .K #63
(4) 8X .K Y_0
-----------------------------------#CD
(5) ,9 X .K #5, ;X IS ! UN"KN4
(6) ,= "S VALUE ( ;S, D .K ST_4
(7) ;A, ;B, & C .K #10
(8) I .K #1, #2, ''', ;N
(9) ;N_3V $O R
(10) E@*E .K E-SQU>$
(11) ;P_3R .K Q_3;S
;G_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ ) ANY LR OR -B9,N ( LRS : #ABC
>E NEI 8S+LE LRS0 NOR 8%ORT-=M A#CD
-B9,NS0 9 SITU,NS N SPECIFIC,Y COV]$
(SEE @,S@,S#26, #27, #28, & #51)_4
(1) X+Y & -A
(2) PQR & ,A,B,C
(3) X@0
(4) ACOS ,B
(5) M$[ B
(6) ,IF ;N, N1, N2, >E '''
(7) $TS ,A,B,C & ,A',B',C' >E
SIMIL>4
;H_4 ,= O!R SITU,NS 9 : ! ,5GLI%-
LR 9DICATOR IS N REQUIR$1 SEE @,S#28_4
@,S#28_4 ..,O!R ,3SID],NS ,3C]N+ !
,5GLI%-,LR .,9DICATOR3
;A_4 ,! ,5GLI%-LR 9DICATOR M/ N 2
US$ :5 ONLY "O LR OR ANY -B9,N ( UN-
SPAC$ LRS IS 9 DIRECT 3TACT ) BO? XS
OP5+ & CLOS+ GR\P+ SIGNS1 PROVID$ T !Y
>E ,5GLI% LRS 9 REGUL> TYPE4 ,:5 ONLY
"O LR OR ANY
-----------------------------------#CE
-B9,N ( UNSPAC$ LRS IS 9 DIRECT 3TACT
,NEME? ,MA?4 ,CODE1 #1972 A#CE
) ONLY XS OP5+ OR ONLY XS CLOS+ GR\P+
SIGN1 ! ,5GLI%-LR 9DICATOR M/ 2 US$
(SEE @,S#26) OR M/ N 2 US$ (SEE
@,S#27) Z ?\< ! GR\P+ SIGNS 7 N PRES-
5T4 ,H["E1 IF ! GR\P+ SIGN HAS A
PRIME1 SUBSCRIPT OR SUP]SCRIPT1 !
,5GLI%-LR 9DICATOR M/ N 2 US$4
(1) #1_4
(A)
(B)
(2) \X\, @(X@), \\F\\
(3) (AB)+(CD)
(4) (;P IS A POSITIVE 9TEG])
(5) (;P & ;Q)
(6) (;L, ;M, ;N >E 9 SET ;,R)
(7) (;X-9T]CEPT)
(8) (;AB & ;CD)
(9) .(X \ X HAS ! PROP]TY ;,R.)
(BECAUSE (! .S* .T SIGN1 : IS A COM-
P>ISON SIGN1 ! ;X_'S D N REQUIRE !
,5GLI%-LR 9DICATOR)
(10) (_8X .K Y_0)
(11) ,SOLVE = ;X (X .1 Y)_4 #ABE
(12) (J .K #1, #2, ''', ;N) B#CE
(13) (AB .K CD)
(14) S@);A^B
(CLOS+ BRACKET HAS A SUBSCRIPT &A
SUP]SCRIPT2 "!=E1 ! ,5GLI%-LR 9DI-
CATOR IS N REQUIR$ )! ;S)
-----------------------------------#CF
;B_4 ,:5 ONLY "O LR OR ANY -B9,N (
UNSPAC$ LRS HAS A PLURAL1 POSSESSIVE
OR ORD9AL 5D+1 ! ,5GLI%-LR 9DICATOR M/
2 US$ (SEE @,S#26) OR M/ N 2 US$ (SEE
@,S#27) Z ?\< S* 5D+S 7 N PRES5T4
(1) ;XS
(2) ;X_'S
(3) ;NTH
(4) #2NTH
(WITHOUT ! TH ORD9AL 5D+ ! ,5GLI%-
LR 9DICATOR WD N 2 REQUIR$ 2F ! ;N)
;C_4 ,A L[]-CASE ,ROMAN NUM]AL M/
2 TR1T$ Z 3SI/+ ( "O LR EV5 :5 X 3SI/S
( M ?AN "O LR4 ,! ,5GLI%-LR 9DICATOR
M/ 2 US$ OR M/ N 2 US$ 9 A3ORD.E )!
RULES = ANY LR (SEE @,S@,S#26-28)_4 ,A
,NEME? ,MA?4 ,CODE1 #1972 A#CF
CAPITALIZ$ ,ROMAN NUM]AL ( "O LR IS
SUBJECT 6^! SAME RULES4 ,= CAPITALIZ$
,ROMAN NUM]ALS ( M ?AN "O LR ! ,5GLI%-
LR 9DICATOR M/ N 2 US$4
@,S#29_4 .,LRS .9 .,DIAGRAMS3 ,:5 A
S+LE ,5GLI% LR 9 REGUL> TYPE IS US$ Z
A LABEL 9 A DIAGRAM1 ! ,5GLI%-LR 9DI-
CATOR IS REQUIR$ IF ! LR IS 9 L[]
CASE1 B M/ 2 OMITT$ IF ! LR IS CAPI-
TALIZ$4
@,S#30_4 .,LRS .9 .,TA#S3 ,:5 LRS
APPE> 9 TA#S1 :E!R Z 5TRIES OR H1D+S1
! ,5GLI%-LR 9DICATOR M/ 2 US$ OR M/ N
2 US$ 9 A3ORD.E )! RULES 3TA9$ 9
@,S@,S#26-28_4
,RULE ;,V--,TYPE ,=MS
,TYPE-,=M ,9DICATORS = ,LRS1 ,NUM]ALS1
& ,-P.D ,EXPRES.NS
,BOLDFACE-,TYPE _
,ITALIC-,TYPE .
,SANS]IF-,TYPE ,.
,SCRIPT-,TYPE @ #ABG
,TYPE-,=M ,9DICATORS = ,^WS1 B#CF
,PHRASES1 & ,MA!MATICAL ,/ATE;TS
,OP5+ ,BOLDFACE-,TYPE ,'_
,OP5+ ,ITALIC-,TYPE ,'.
,CLOS+ ,BOLDFACE-,TYPE _,'
,CLOS+ ,ITALIC-,TYPE .,'
(,FOR -B9,NS ( CAPITALIZ,N1 ALPHA-
BETIC1 & TYPE-=M 9DICATORS1 SEE
,APP5DIX1 PAGE #208)
-----------------------------------#CG
@,S#31_4 .,TYPE .,=MS3 ,SPECIFIC
PROVI.N IS MADE 9 ? ,CODE = FIVE TYPE
=MS--BOLDFACE1 ITALIC1 REGUL>1 SANS]-
IF1 & SCRIPT4 ,EXCEPT = REGUL> TYPE1
^! TYPE =MS M/ 2 SPECIFI$ 0! APPROPRI-
ATE TYPE-=M 9DICATOR4
@,S#32_4 ..,USE ( ,TYPE-,=M ,9DICA-
TORS ) ,LRS1 ,NUM]ALS1 & ,-P.D .,EX-
PRES.NS3
;A_4 ,SUBJECT 6! PROVI.NS (
@,S#34, ! APPROPRIATE TYPE-=M 9DICATOR
M/ 2 US$ 6EXPRESS ! TYPE =M (A LR4 ,!
TYPE-=M 9DICATOR =A LR M/ ALW 2 FOLL[$
0AN ALPHABETIC 9DICATOR4
,NEME? ,MA?4 ,CODE1 #1972 A#CG
(1) .;A
(ITALIC ,5GLI% L[]-CASE ;A)
(2) .;,A
(ITALIC ,5GLI% CAPITALIZ$ ;A)
(3) ._A
(ITALIC ,G]MAN L[]-CASE AH)
(4) _;A
(BOLDFACE ,5GLI% L[]-CASE ;A)
(5) _;,A
(BOLDFACE ,5GLI% CAPITALIZ$ ;A)
(6) _.A
(BOLDFACE ,GREEK L[]-CASE ALPHA)
(7) __A
(BOLDFACE ,G]MAN L[]-CASE AH)
(8) _@@A
(BOLDFACE ,RUSSIAN L[]-CASE AH)
(9) @;A
(SCRIPT ,5GLI% L[]-CASE ;A)
(10) @;,A
(SCRIPT ,5GLI% CAPITALIZ$ ;A)
(11) @_A
(SCRIPT ,G]MAN L[]-CASE AH)
#ABI
(12) @,,A B#CG
(SCRIPT ,HEBREW ALEF)
-----------------------------------#CH
(13) ,.;H
(SANS]IF ,5GLI% L[]-CASE ;H)
(14) ,.;,H
(SANS]IF ,5GLI% CAPITALIZ$ ;H)
(15) A.;B_;C@;D
(REGUL> ;A, ITALIC ;B, BOLDFACE ;C,
SCRIPT ;D)
;B_4 ,SUBJECT 6! PROVI.NS (
@,S#34, ! APPROPRIATE TYPE-=M 9DICATOR
M/ 2 US$ 6EXPRESS ! TYPE =M (A NUM]AL4
,! TYPE-=M 9DICATOR =A NUM]AL M/ ALW 2
FOLL[$ 0! NUM]IC 9DICATOR4 ,IF A NUM]-
AL 6BE TRANSCRIB$ 0US+ TYPE-=M 9DICA-
TORS 3TA9S M ?AN "O DIGIT1 & IS ALL (
"O TYPE =M1 ! TYPE-=M 9DICATOR &!
NUM]IC 9DICATOR M/ 2 US$ ONLY 2F ! F/
DIGIT4 ,IF "! IS A TRANSI;N F "O TYPE
=M 6ANO!R NON-REGUL> TYPE =M )9 ! SAME
NUM]AL1 ! NEW TYPE-=M 9DICATOR FOLL[$
0! NUM]IC 9DICATOR M/ 2 US$ 2F ! F/
DIGIT (! NEW TYPE =M4 ,IF ! TRANSI;N
,NEME? ,MA?4 ,CODE1 #1972 A#CH
IS 6REGUL> TYPE1 ONLY ! NUM]IC 9DICA-
TOR M/ 2 US$4
(1) _#0
(BOLDFACE Z]O)
(2) @#2
(SCRIPT #2)
(3) _#345
(345 9 BOLDFACE TYPE)
(4) .#3.5
(3.5 9 ITALIC TYPE)
(5) .#3_#4@#5
(ITALIC #3, BOLDFACE #4, SCRIPT #5)
(6) _#4#35
(BOLDFACE #4, REGUL> #3 & #5)
;C_4 ,SUBJECT 6! PROVI.NS (
@,S#34, :5 A NUM]AL IS JO9$ 6A ^W OR
AN A2REVI,N 0A HYPH5 &! :OLE EXPRES.N
IS PR9T$ 9 NON-REGUL> TYPE1 ! APPRO-
PRIATE TYPE-=M 9DICATOR M/ 2 US$ 2F !
NUM]AL ONLY1 B A6ECTS ! 5TIRE -P.D EX-
PRES.N4 ,IF "! IS A *ANGE 9 TYPE =M AF
! HYPH5 6REGUL> TYPE1 ! HYPH5 #ACA
M/ 2 PREC$$ 0! LIT]>Y T]M9,N B#CH
SYMBOL ,' (DOTS #6, #3)_4 ,IF "! IS A
*ANGE 9 TYPE =M AF ! HYPH5 6NON-REGUL>
TYPE1 ONLY ! APPROPRIATE TYPE-=M 9DI-
CATOR M/ 2 US$ AF ! HYPH54
(1) .#45-OHM
(THE :OLE EXPRES.N IS 9 ITALIC TYPE)
-----------------------------------#CI
(2) _#45-FT
(THE :OLE EXPRES.N IS 9 BOLDFACE
TYPE)
(3) .#45,'-OHM
(45 9 ITALIC TYPE1 OHM 9 REGUL>
TYPE)
(4) .#45-_OHM
(45 9 ITALIC TYPE1 OHM 9 BOLDFACE
TYPE)
;D_4 ,:5 A TYPE-=M 9DICATOR IS US$
) LRS1 XS E6ECTIVE;S EXT5DS ONLY 6!
LR : FOLL[S X4 ,?US1 EXCEPT = REGUL>
TYPE1 A TYPE-=M 9DICATOR M/ 2 US$ )
EA* 9DIVIDUAL LR (A SEQU;E ( LRS4 ,:5
A TYPE-=M 9DICATOR IS US$ ) NUM]ALS
,NEME? ,MA?4 ,CODE1 #1972 A#CI
ONLY1 X IS E6ECTIVE UNTIL T]M9AT$ 0A
SPACE1 A NUM]IC 9DICATOR1 OR ANY NON-
NUM]IC SYMBOL4 ,:5 A TYPE-=M 9DICATOR
IS US$ )A -P.D EXPRES.N1 X IS E6ECTIVE
=! 5TIRE -P.D EXPRES.N UN.S T]M9AT$ 0!
LIT]>Y T]M9,N SYMBOL ,' (DOTS #6, #3),
OR ANO!R TYPE-=M 9DICATOR4
@,S#33_4 ..,USE ( ,TYPE-,=M ,9DICA-
TORS ) ,^WS1 ,PHRASES1 & ,MA!MATICAL
.,/ATE;TS3
;A_4 ,:5 ! 9K-PR9T TEXT USES !
3V5;N ( %[+ .LABEL$ ./ATE;TS S* Z
!OREMS1 DEF9I;NS1 AXIOMS1 LEMMAS1 ETC4
9 NON-REGUL> TYPE =M1 ! BODY ( S* AN
ITEM M/ 2 TRANSCRIB$ US+ ! CORRESPOND+
TYPE-=M 9DICATORS1 B ! LABELS !MVS M/
2 TRANSCRIB$ Z ?\< !Y 7 5TIRELY CAPI-
TALIZ$4 ,IF1 9 ! BODY (! LABEL$ /ATE-
;T1 A ^W OR PHRASE IS S+L$ \ = SPECIAL
ATT5;N 0US+ A NON-REGUL> TYPE =M =!
PURPOSE ( DEF9I;N OR O!R ELABOR,N1 S*
A /ATE;T M/ AL 2 TRANSCRIB$ US+ ! COR-
RESPOND+ TYPE-=M 9DICATORS4 ,:5 ! PAS-
SAGE 6BE TRANSCRIB$ IS 5TIRELY #ACC
(! SAME NON-REGUL> TYPE =M1 X B#CI
M/ 2 PREC$$ 0! APPROPRIATE OP5+ TYPE-
=M 9DICATOR & FOLL[$ 0! CORRESPOND+
CLOS+ TYPE-=M 9DICATOR4 ,^! TYPE-=M
9DICATORS M/ 2 SEP>AT$ F ! 5CLOS$ MA-
T]IAL 0"O SPACE4 ,IF MAT]IAL 9 NON-
REGUL> TYPE O!R ?AN LRS OR =MULAS
3/ITUT+ A MA!MATICAL EXPRES.N IS EM-
B$D$ )9 A L>G] BODY (A DI6]5T NON-
REGUL> TYPE1 ! EMB$D$ MAT]IAL M/ 2
TRANSCRIB$ US+ ! APPROPRIATE TYPE-=M
9DICATORS 9 A3ORD.E )! PROC$URE DE-
SCRIB$ ABV4 ,IF X 2COMES NEC 6USE TWO
( ^! TYPE-=M 9DICATORS 3SECUTIVELY1 !Y
M/ 2 UNSPAC$ F EA* O!R4
(1) ,,!OREM #15_4 ,'. ,A TRIANGLE
IS ISOSCELES IF XS BASE
ANGLES >E EQUAL4 .,'
(IN 9K PR9T1 8,!OREM #15_0 IS 9
BOLDFACE TYPE & ONLY ! F/ LR (
8,!OREM0 IS CAPITALIZ$)
(2) ,,DEF9I;N4 ,'_ X+YI .K A+BI,
IF & ONLY IF X .K A &
Y .K B_4 _,'
,NEME? ,MA?4 ,CODE1 #1972 C#CI
(IN 9K PR9T1 8,DEF9I;N0 IS 9 BOLD-
FACE TYPE & ONLY XS F/ LR IS CAPI-
TALIZ$)
-----------------------------------#DJ
(3) ,,DEF9I;N4 ,'. ,WE SAY T Z0 IS
A ,'_ Z]O ( ORD] ;N _,' (!
POLYNOMIAL F(Z) IF & ONLY IF
''' .,'
(IN 9K PR9T1 8,DEF9I;N0 IS 9 BOLD-
FACE TYPE & ONLY XS F/ LR IS CAPI-
TALIZ$)
(4) ,,DEF9I;N4 ,'. ,A SET : C 2
PUT 96"O-TO-"O CORRESPOND;E
)! NATURAL NUMB]S IS CALL$ A
,'_ C.TA# SET4 _,'.,'
(IN 9K PR9T1 8,DEF9I;N0 IS ITALICIZ$
& ONLY XS F/ LR IS CAPITALIZ$)
;B_4 ,SUBJECT 6! PROVI.NS (
@,S#34, :5 ! 9K-PR9T TEXT %[S A BOLD-
FACE ^W OR PHRASE )9 AN UNLABEL$ ITEM1
OR :5 X %[S AN ITALICIZ$ PHRASE : EI
2G9S OR 5DS )A MA!MATICAL EXPRES.N1 !
APPROPRIATE TYPE-=M 9DICATORS #ACE
M/ 2 US$ AC 6! RULES 9 ;A ABV4 A#DJ
,:5 ! 9K PR9T %[S AN ITALICIZ$ ^W OR
AN ITALICIZ$ PHRASE : BO? 2G9S & 5DS )
A ^W1 ! RULES ( ,5GLI% ,BRL 3C]N+
ITALICS M/ 2 OBS]V$4 ,H["E1 ? DOES N
APPLY 6A -P.D EXPRES.N (SEE @,S#32C)_4
(1) ,L4,C4,D4 /&S = ,'_ ,L1/ ,-MON
,DENOM9ATOR4 _,'
(2) ,'. ,! ANGLE ,A,O,B IS SD 6H A
V]TEX ;,O_4 .,'
(3) ,G4,C4,M4 /&S = .GRTE/ .-MON
.MULTIPLE4
-----------------------------------#DA
(4) ..,! ORD9>Y OP],NS ( A4I;N &
MULTIPLIC,N >E ASSOCIATIVE 9
! SET ( R1L .NUMB]S4
(5) ..,IF A.*B .K B.*A, !N ! OP],N
IS .-MUTATIVE4
@,S#34_4 ..,NON-,USE ( ,TYPE-,=M
.,9DICATORS3
;A_4 ,A TYPE-=M 9DICATOR M/ N 2
US$ :5 A LR OR A NUM]AL IS PR9T$ 9
REGUL> TYPE4
,NEME? ,MA?4 ,CODE1 #1972 A#DA
;B_4 ,:5 ANY MAT]IAL1 MA!MATICAL
OR LIT]>Y1 IS PR9T$ 9 NON-REGUL> TYPE
T HAS NO MA!MATICAL SIGNIFIC.E1 !
V>IANT TYPE =M M/ N 2 REPRES5T$ 9 !
TRANSCRIP;N4 ,FREQU5TLY1 X IS ! PRAC-
TICE 6PR9T ! LRS ( ALL =MULAS "?\T A
BOOK 9 ITALICIZ$ TYPE4 ,? PRACTICE M/
N 2 C>RI$ OV] 6! TRANSCRIP;N UN.S !
AU?OR HAS SPECIFIC,Y 4T+UI%$ 2T TWO
M1N+S (! SAME LR1 ASSIGN+ "O M1N+ 6!
LR 9 REGUL> TYPE & ANO!R 6! LR 9 ITAL-
IC TYPE4 ,9 A4I;N1 A V>IANT TYPE =M IS
(T5 US$1 "PICUL>LY AT ! L[] GRADE LEV-
ELS1 =! SOLE PURPOSE ( ATTRACT+ !
R1D]'S ATT5;N4 ,S* V>IANT TYPE =MS M/
AL N 2 REPRES5T$ 9 ! TRANSCRIP;N4
@,S#35_4 .,BOLDFACE .,TYPE3
;A_4 ,:5 C]TA9 SIGNS ( OP],N OR
-P>ISON >E PR9T$ 9 BOLDFACE TYPE1 ?
,CODE EMPLOYS ! DEVICE ( PLAC+ DOTS
#4-5-6 2F ! CORRESPOND+ SYMBOL4 ,!
SPECIFIC SIGNS 6: ? TE*NIQUE APPLIES
>E LI/$ 9 APPROPRIATE SEC;NS "?\T !
,CODE1 &! TRANSCRIB] M/ N USE ? #ACG
TE*NIQUE ) ANY O!R SIGN4 ,:5 B#DA
US$ 9 ? WAY1 DOTS #4-5-6 M/ N 2 REG>D$
Z ! BOLDFACE TYPE-=M 9DICATOR B Z AN
9TEGRAL "P (! SYMBOL 6: X 2L;GS4 ,?
TE*NIQUE HAS BE5 US$ ONLY :5 ! 4T9C;N
2T ! REGUL> & BOLDFACE =MS (! SAME
SIGN HAS MA!MATICAL SIGNIFIC.E4 ,DOTS
#4-5-6 >E AL US$ Z "P (! TE*NIQUE =
REPRES5T+ FILL$-IN %APES (SEE
@,S#108)_4
;B_4 ,BOLDFACE TYPE1 US$ 9 _M
TEXTS 6ID5TIFY LRS Z VECTORS1 M/ 2
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