,,! ,,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 ,,IV
,BRL PAGES P#A-P#C & #DDE-FAB
,PR9T PAGES B#AFJ-BDG P#A
,NEME? ,MA?4 ,CODE1 #1972
,,3T5TS
,PAGE
,,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 ,,9DICATORS """ #208
,,APP5DIX ;,B--,,9DEX ,,( ,,BRL
,,SYMBOLS """"""""""""""""""" #209
P#C
,,! ,,NEME? ,,BRL ,,CODE B#AFJ
,,= ,,MA!MATICS
,,& ,,SCI;E ,,NOT,N
#1972 ,,REVI.N
,,RULES (,3T9U$)
,RULE ,,XXIV--
,SPATIAL ,>RANGE;TS
,DIVI.N
,CURV$ ,DIVI.N ,SIGN 333
ON ,LEFT1 ,SEP>,N O
,L9E ,ABV
,CURV$ ,DIVI.N ,SIGN 333
ON ,"R1 ,SEP>,N [
,L9E ,ABV
,CURV$ ,DIVI.N ,SIGNS 333
ON ,LEFT & ,"R1 O [
,SEP>,N ,L9E ,ABV
,/RAI<T OR ,SLANT 333
,DIVI.N ,SIGN ON _ OR
,LEFT1 ,SEP>,N
,L9E ,ABV
#DDE
,NEME? ,MA?4 ,CODE1 #1972 C#AFJ
,/RAI<T OR ,SLANT ,DI-
VI.N ,SIGN ON ,"R1 333
,SEP>,N ,L9E ,ABV _
OR
----------------------------------#AFA
,/RAI<T ,DIVI.N ,SIGNS
ON ,LEFT & ,"R1 333
,SEP>,N ,L9E ,ABV _ _
,CURV$ ,DIVI.N ,SIGN O
ON ,LEFT1 ,SEP>,N 333
,L9E ,2L
,CURV$ ,DIVI.N ,SIGN [
ON ,"R1 ,SEP>,N 333
,L9E ,2L
,CURV$ ,DIVI.N ,SIGNS O [
ON ,LEFT & ,"R1 333
,SEP>,N ,L9E ,2L
,/RAI<T OR ,SLANT ,DI- _
VI.N ,SIGN ON ,LEFT1 333 OR
,SEP>,N ,L9E ,2L
#DDG
,NEME? ,MA?4 ,CODE1 #1972 A#AFA
,/RAI<T OR ,SLANT ,DI-
VI.N ,SIGN ON ,"R1 _
,SEP>,N ,L9E ,2L 333
,/RAI<T ,DIVI.N ,SIGNS _ _
ON ,LEFT & ,"R1 333
,SEP>,N ,L9E ,2L
,V]TICAL ,L9E ,US$ 9 _
,DIVI.N ,>RANGE;TS
(V>Y+ 9 L5G?)
,SEP>,N ,L9E (V>Y+ 9 333
L5G?)
,C>RI$ ,NUMB] ,9DICATOR 777
= ,A4I;N (V>Y+ 9
L5G?)
----------------------------------#AFB
,SQU>E ,ROOT 333
>
#DDI
,NEME? ,MA?4 ,CODE1 #1972 A#AFB
,SYN!TIC ,DIVI.N
,/RAI<T ,L9E ON ,LEFT1 _
,SEP>,N ,L9E ,2L _
333
,/RAI<T ,L9E ON ,"R1 _
,SEP>,N ,L9E ,2L _
333
@,S#178_4 .,A4I;N .& .,SUBTRAC;N3
;A_4 ,9 A SPATIAL >RANGE;T = A4I-
;N OR SUBTRAC;N1 ! NUM]IC SYMBOLS1
FRAC;NS1 A2REVI,NS1 9T]IOR SIGNS (
OP],N OR -P>ISON M/ 2 V]TIC,Y ALIGN$
) DIGITS "U DIGITS1 -MAS "U -MAS1
DECIMAL PO9TS "U DECIMAL PO9TS1 FRAC-
;NS "U FRAC;NS1 A2REVI,NS "U A2REVIA-
;NS1 SIGNS ( OP],N "U SIGNS ( OP],N1 &
SIGNS ( -P>ISON "U SIGNS ( -P>ISON4
,H["E1 IF ^! >E DELIB]ATELY MISALIGN$
9 9K PR9T Z 9 AN EX]CISE REQUIR+ !
/UD5T 6MAKE A SUITA# CORREC;N1 ? MIS-
ALIGN;T M/ 2 PRES]V$ 9 ! TRANSCRIP;N4
;B_4 ,! PLUS1 M9US1 OR #DEA
,NEME? ,MA?4 ,CODE1 #1972 B#AFB
DOLL> SYMBOLS1 IF ! CORRESPOND+ SIGNS
>E PRES5T1 M/ 2 PLAC$ AT L1/ "O COLUMN
( CELLS 6! LEFT (! WIDE/ COLUMN (
NUM]IC SYMBOLS : APPE>S 9 ! "P (! >-
RANGE;T .ABV ! SEP>,N L9E4 ,SUBJECT 6!
RULES ABV1 SYMBOLS ( OP],N & DOLL>
SYMBOLS MAY 2 PLAC$ 9 ! SAME POSI;N Z
%[N 9 9K PR9T4
;C_4 ,! SEP>,N L9E : APPE>S 9 A4I-
;N OR SUBTRAC;N M/ 2 MADE "O CELL L;G]
AT EI 5D ?AN ! OV]ALL WID? (! RE/ (!
>RANGE;T4
(1) 508
2876
59
+ 427
3333333
CHGJ
(IN 9K PR9T1 ! PLUS SIGN IS FUR!R 6!
LEFT ?AN ANY T]M 9 ! PRO#M OR ! AN-
SW])
#DEC
(2) 35.50 #AFC
+77.25
--------
112.75
(IN 9K PR9T1 ! PLUS SIGN IS FUR!R 6!
LEFT ?AN ANY T]M 9 ! PRO#M OR ! AN-
SW])
(3) 3.704
- .915
--------
2.789
(IN 9K PR9T1 "P (! M9US SIGN FALLS
"U ! #3, ! RE/ EXT5DS FUR!R 6! LEFT)
(4) ?5/8#
+?3/4#
--------
(IN 9K PR9T1 ! PLUS SIGN IS FUR!R 6!
LEFT ?AN ANY T]M 9 ! PRO#M)
,NEME? ,MA?4 ,CODE1 #1972 A#AFC
(5) 1_?7/8_#
+6_?4/7_#
-----------
(IN 9K PR9T1 ! PLUS SIGN IS FUR!R 6!
LEFT ?AN ANY T]M 9 ! PRO#M)
(6) 3 LB4 12 OZ4
+1 LB4 8 OZ4
---------------
4 LB4 20 OZ4 .K #5 LB4 #4 OZ
(IN 9K PR9T1 ! PLUS SIGN IS FUR!R 6!
LEFT ?AN ANY T]M 9 ! PRO#M)
----------------------------------#AFD
(7) 4X+14Y- 3Z
17X- 9Y+20Z
- 6X - 2Z
--------------
15X+ 5Y+15Z
(IN 9K PR9T1 ! M9US SIGN IS #DEE
FUR!R 6! LEFT ?AN ANY T]M A#AFD
9 ! PRO#M)
(8) @S9.00
+1.00
---------
@S10.00
(IN 9K PR9T1 ! DOLL> SIGNS &! PLUS
SIGN O3UPY ! SAME POSI;N Z 9 BRL)
(9) @S 7.45
10.92
+ 84.00
----------
@S102.37
(IN 9K PR9T1 "! IS NO SPACE 2T !
DOLL> SIGNS &! FOLL[+ DIGITS1 &!
PLUS SIGN IS 6! LEFT (! F/ DOLL>
SIGN)
,NEME? ,MA?4 ,CODE1 #1972 B#AFD
(10) @S10,000
- 9,000
----------
@S 1,000
(IN 9K PR9T1 ! DOLL> SIGNS &! M9US
SIGN O3UPY ! SAME POSI;N Z 9 BRL)
----------------------------------#AFE
;D_4 ..,C>RI$ ,NUMB]S 9 .,A4I;N3
,:5 C>RI$ NUMB]S APPE> 9 AN A4I;N >-
RANGE;T ABV ! COLUMNS 6: !Y APPLY1 !
TRANSCRIB] M/ 9S]T ! 9DICATOR = C>RI$
NUMB]S 2T ^! C>RI$ NUMB]S &! >RANGE;T
6: !Y APPLY4 ,! C>RI$ NUMB] 9DICATOR
M/ H ! SAME L5G? Z ! SEP>,N L9E4
11
777777
(1) 254
+176
------
430
#DEG
(IN 9K PR9T1 ! C>RI$ NUMB]S A#AFE
>E 9 SMALL TYPE DIRECTLY ABV ! COL-
UMNS 6: !Y APPLY)
;E_4 ,9 AN >RANGE;T 3TA9+ FRAC;NS1
FRAC;N L9ES M/ 2 V]TIC,Y ALIGN$1 EA*
NUM]ATOR M/ 2 "R JU/IFI$ 9 ! COLUMN
RES]V$ = NUM]ATORS1 & EA* DENOM9ATOR
M/ 2 LEFT JU/IFI$ 9 ! COLUMN RES]V$ =
DENOM9ATORS4 ,FRAC;N 9DICATORS M/ AL 2
V]TIC,Y ALIGN$ & M/ 2 "R-JU/IFI$ 9 !
COLUMNS RES]V$ = BO? OP5+ & CLOS+ 9DI-
CATORS4
(1) ?3/8#
+?4/8#
33333333
?7/8#
(2) ?11/16#
+? 1/2 #
----------
,NEME? ,MA?4 ,CODE1 #1972 B#AFE
(3) ?1/5 #
-?1/10#
---------
----------------------------------#AFF
(4) 1_?5/6_#
+ ?2/3 #
-----------
;F_4 ,9 AN >RANGE;T 3TA9+ MIX$
NUMB]S1 ! :OLE-NUMB] "P M/ 2 V]TIC,Y
ALIGN$ AC TO ;A ABV4
(1) 10_?2/3_#
+ 4_?1/3_#
------------
14_?3/3_# .K #15
;G_4 ,9 AN >RANGE;T 3TA9+ POLY-
NOMIALS1 T]MS M/ 2 V]TIC,Y ALIGN$4 ,9
EA* T]M1 SYMBOLS ( OP],N1 COE6ICI5TS1
LRS1 SUP]SCRIPT 9DICATORS1 #DEI
SUP]SCRIPTS1 & BASE-L9E 9DI- A#AFF
CATORS M/ AL 2 V]TIC,Y ALIGN$4 ,:5 !
BASE-L9E 9DICATOR IS REQUIR$1 X M/ 2
PLAC$ 9 ! F/ POSSI# POSI;N 3SI/5T ) ?
REQUIR$ ALIGN;T4 ,)9 EA* COE6ICI5T &
SUP]SCRIPT1 CORRESPOND+ SYMBOLS M/ 2
V]TIC,Y ALIGN$4
(1) 2X^3"- X^2"+ X+ 1
3X^3"+4X^2"-10X+ 7
5X^2" +12
-2X^3" - 6X
---------------------
3X^3"+8X^2"-15X+20
@,S#179_4 .,MULTIPLIC,N3
;A_4 ,9 A SPATIAL >RANGE;T = MUL-
TIPLIC,N1 ! SYMBOLS -PRIS+ ! MULTIPLI]
& MULTIPLIC& M/ 2 ALIGN$ 9 ! TRAN-
SCRIP;N Z ! CORRESPOND+ SIGNS >E
ALIGN$ 9 9K PR9T4
;B_4 ,! MULTIPLIC,N SYMBOL1 IF !
CORRESPOND+ SIGN IS PRES5T 9 9K PR9T1
M/ 2 PLAC$ IMMLY 6! LEFT (! MULTIPLI]4
;C_4 ,! SEP>,N L9ES : APPE> 9 A
,NEME? ,MA?4 ,CODE1 #1972 B#AFF
MULTIPLIC,N >RANGE;T M/ 2 MADE "O CELL
L;G] AT EI 5D ?AN ! OV]ALL WID? (! RE/
(! >RANGE;T4
----------------------------------#AFG
(1) 23
@*54
------
92
115
------
1242
(2) 1704
@*5
------
8520
(3) 132
@*300
-------
39600
#DFA
(4) 2 GAL 3 QT A#AFG
@*2
------------
4 GAL 6 QT
;D_4 ,9 AN >RANGE;T 3TA9+ FRAC;NS1
MIX$ NUMB]S1 OR POLYNOMIALS1 ALIGN;T
M/ 2 G5],Y Z SPECIFI$ 9 @,S#178 ;E-
;G_4
----------------------------------#AFH
(1) 75
@*2_?3/4_#
------------
56_?1/4_#
150
------------
206_?1/4_#
,NEME? ,MA?4 ,CODE1 #1972 A#AFH
(2) 7X-3
4X+5
---------------
28X^2"-12X
+35X-15
---------------
28X^2"+23X-15
;E_4 ,9 >RANGE;TS : %[ MULTIPLIC,N
6NON-DECIMAL BASES 9 : SUBSCRIPTS AP-
PE>1 ! SUBSCRIPT 9DICATOR M/ 2 PLAC$ 9
! F/ POSSI# POSI;N 3SI/5T )! ALIGN;T
REQUIR$ =! A4I;N ( "PIAL PRODUCTS4
(1) 34;SEVEN
@*12;SEVEN
------------
101;SEVEN
34 ;SEVEN
------------
441;SEVEN
#DFC
;F_4 ,:5 -MAS OR ! DECIMAL #AFI
PO9T O3UR 9 ! ANSW] (A MULTIPLIC,N >-
RANGE;T1 A BLANK COLUMN ( CELLS M/ 2
LEFT ABV ^! 9 ! "PIAL PRODUCTS4
(1) 345.7
@*2.77
---------
24 199
241 99
691 4
---------
957.589
(2) @S18.24
@*65
------------
91 20
1 094 4
------------
@S1,185.60
,NEME? ,MA?4 ,CODE1 #1972 A#AFI
(3) 1705.00
@*4
----------
6,820.00
----------------------------------#AGJ
@,S#180_4 .,DIVI.N3
;A_4 ,9 A SPATIAL >RANGE;T = DI-
VI.N1 ! SYMBOLS -PRIS+ ! DIVID5D &!
"PIAL PRODUCTS & DI6];ES M/ 2 ALIGN$ 9
! SAME WAY Z ! CORRESPOND+ SIGNS >E
ALIGN$ 9 9K PR9T4 ,SYMBOLS 9 ! QUOTI5T
M/ 2 ALIGN$ ) _! CORRESPOND+ SYMBOLS 9
! DIVID5D UN.S !Y >E SPECIFIC,Y UN-
ALIGN$ 9 9K PR9T4
;B_4 ,! DIVI.N SYMBOL M/ 2 PLAC$ 9
! CELL DIRECTLY 2F ! DIVID5D OR DI-
RECTLY AF ! DIVID5D AC Z ! CORRESPOND+
DIVI.N SIGN O3URS 9 ! =W>D OR REV]SE
DIREC;N 9 9K PR9T4 ,! DIVISOR M/ 2
PLAC$ S T "! IS NO SPACE 2T X &! DI-
VI.N SYMBOL 6: X APPLIES4 ,IF A QUO-
TI5T AL APPLIES 6A DIVI.N SYM- #DFE
BOL 02+ PLAC$ ON ! SAME L9E A#AGJ
Z ! DIVID5D1 NO SPACE M/ 2 LEFT 2T !
QUOTI5T &! DIVI.N SYMBOL 6: X AP-
PLIES4 ,IF A HORIZONTAL L9E O3URS "U A
DIVISOR Z "P (A DIVI.N SIGN 9 9K
PR9T1 ? L9E M/ 2 IGNOR$ 9 ! TRAN-
SCRIP;N4
;C_4 ,EA* SEP>,N L9E : APPE>S 9 A
DIVI.N >RANGE;T M/ 2G9 9 ! COLUMN CON-
TA9+ A DIVI.N SYMBOL & M/ 5D 9 ! COL-
UMN 3TA9+ ! O!R DIVI.N SYMBOL1 IF !
LATT] APPE>S 9 9K PR9T4 ,O!RWISE1 EA*
SEP>,N L9E M/ 5D 9 A CELL "O COLUMN 2Y
! OV]ALL >RANGE;T4 ,H["E1 :5 ! DIVI.N
>RANGE;T 3TA9S ONLY A DIVISOR &A DIVI-
D5D1 B NO QUOTI5T & NO "PIAL PRODUCTS
& DI6];ES1 ! SEP>,N L9E1 :E!R %[N ABV
OR 2L ! DIVID5D1 M/ 2 OMITT$4 ,9 ?
CASE1 ! DIVI.N >RANGE;T M/ N 2 REG>D$
Z SPATIAL4 ,9 "PICUL>1 A BLANK L9E M/
N 2 LEFT ABV OR 2L S* A DIVI.N >-
RANGE;T1 &! NUM]IC 9DICATOR M/ 2 US$ 9
! APPROPRIATE PLACE4
,NEME? ,MA?4 ,CODE1 #1972 B#AGJ
(1) 8
----
6O48
(2) ----
6O48[8
(3) 6O636
-----
106
(4) 106
-----
6_636
#DFG
(5) 644 #AGA
------
4O2576
24
------
17
16
------
16
16
------
(6) X+ 6
-------------
X+5_X^2"+11X+30
X^2"+ 5X
-------------
6X+30
6X+30
-------------
(IN 9K PR9T1 X IS CLE> T ! QUOTI5T
IS ALIGN$ )! DIVID5D1 & "! IS A
HORIZONTAL L9E "U ! DIVISOR)
,NEME? ,MA?4 ,CODE1 #1972 #AGB
(7) X+8
-------------
X+4_X^2"+12X+32
X^2"+ 4X
-------------
8X+32
8X+32
-------------
(IN 9K PR9T1 ! QUOTI5T IS CLE>LY N
ALIGN$ )! T]MS 9 ! DIVID5D)
(8) #18O452
;D_4 ,:5 -MAS OR ! DECIMAL PO9T
O3UR 9 ! DIVID5D (A DIVI.N >RANGE;T1 A
BLANK COLUMN ( CELLS M/ 2 LEFT ": ^!
O3UR 9 ! 5TIRE >RANGE;T EXCEPT 9 SEPA-
R,N L9ES4 ,:5 A C>ET O3URS 9 A DIVI-
D5D1 A BLANK COLUMN ( TWO CELLS M/ 2
LEFT ": ? O3URS 9 ! 5TIRE >RANGE;T EX-
CEPT 9 ! SEP>,N L9ES &! QUOTI5T4 ,9 !
QUOTI5T1 ! DECIMAL PO9T CORRE- #DFI
SPOND+ 6! C>ET M/ 2 "R-JU/IFI$ A#AGB
9 ! TWO CELLS ALLOTT$ 6! C>ET4
(1) @S 5.00
---------
5O@S25.00
----------------------------------#AGC
(2) 5,080.09
-----------
18O91,441.62
90
-----------
1 44
1 44
-----------
1 62
1 62
-----------
,NEME? ,MA?4 ,CODE1 #1972 A#AGC
(3) 1 2 .5
---------
6.3_<O78.7_<5
63
---------
15 7
12 6
---------
3 1 5
3 1 5
---------
----------------------------------#AGD
;E_4 ,:51 9 A DIVI.N >RANGE;T1 "!
IS A REMA9D] : IS ID5TIFI$ Z S* 0! LR
;R, L[]-CASE OR CAPITALIZ$1 ! ;R M/ 2
PREC$$ 0A SPACE4
#DGA
(1) 181 R"4 A#AGD
----------
25O4529
25
----------
202
200
----------
29
25
----------
4
----------------------------------#AGE
;F_4 ,IF A V]TICAL L9E IS "P (A
DIVI.N >RANGE;T1 X MAY 2 REPRES5T$ 0A
COLUMN ( DOTS #4-5-6 OR X MAY 2 DRAWN4
,A SPACE M/ 2 LEFT 2T ! COLUMN ( DOTS
#4-5-6 & ANY DIGIT : PREC$ES OR FOLL[S
X4
,NEME? ,MA?4 ,CODE1 #1972 A#AGE
(1) 3333333333
6O414 _
60 _ 10
33333_
354 _
120 _ 20
33333_
234 _
180 _ 30
33333_
54 _
54 _ 9
33333_3333
_ 69
#DGC
(2) 33333 #AGF
6O78 _
30 _ 5
3333_
48 _
24 _ 4
3333_
24 _
24 _ 4
3333_3333
0 _ 13
----------------------------------#AGG
@,S#181_4 .,SQU>E .,ROOT3 ,A SQU>E
ROOT >RANGE;T IS SIMIL> 6A DIVI.N >-
RANGE;T EXCEPT T NO DIVISOR IS PRES5T4
,! >RANGE;T %D 2 ADAPT$ 6RESEM# ! >-
RANGE;T 9 9K PR9T Z CLOSELY Z POSSI#4
,IF ! SQU>E ROOT SYMBOL IS US$ 9 ?
SITU,N1 ! T]M9,N 9DICATOR IS N RE-
QUIR$4
,NEME? ,MA?4 ,CODE1 #1972 A#AGG
(1) 5K 4 8
----------
>30.00 00
25
----------
104_ 5 00
@*4_ 4 16
----------
1087_ 84 00
@*7_ 76 09
--------
7 91
#DGE
(2) 2K 4 3 #AGH
---------
>5.90 49
4
---------
_1 90
44@*4_1 76
---------
_14 49
483@*3_14 49
-------
@,S#182_4 .,SYN!TIC .,DIVI.N3
;A_4 ,9 A SYN!TIC DIVI.N >RANGE;T1
! NUM]IC SYMBOLS 9 ! SYN!TIC DIVID5D1
SYN!TIC PRODUCT1 & SYN!TIC QUOTI5T M/
2 ALIGN$ 0PLACE VALUE4 ,SYMBOLS (
OP],N1 :5 PRES5T1 M/ AL 2 ALIGN$4 ,"!
M/ 2 AT L1/ "O COLUMN ( BLANK CELLS
2T ADJAC5T COLUMNS (A SYN!TIC DIVI.N
>RANGE;T4
;B_4 ,A V]TICAL L9E M/ 2 US$ 6!
LEFT OR 6! "R ( SYN!TIC DIVI.N >-
RANGE;T AC Z ! SYN!TIC DIVISOR APPE>S
6! LEFT OR 6! "R4 ,? V]TICAL L9E M/ 2
,NEME? ,MA?4 ,CODE1 #1972 A#AGH
UNSPAC$ F ! SYN!TIC DIVID5D & F !
SYN!TIC DIVISOR4 ,"O "P (! V]TICAL B>
M/ APPE> ON ! L9E 3TA9+ ! SYN!TIC
DIVID5D1 & ANO!R "P (! L9E M/ APPE> ON
! L9E 3TA9+ ! SYN!TIC PRODUCT4 ,! SEP-
>,N L9E M/ 2G9 DIRECTLY "U ! V]TICAL
L9E AT "O 5D1 & T]M9ATE "O CELL 2Y !
OV]ALL SYN!TIC >RANGE;T AT ! O!R 5D4
,IF ! SYN!TIC DIVISOR APPE>S 9 9K PR9T
Z BOX$-IN ON TWO SIDES1 ? M/ 2 IGNOR$
9 ! TRANSCRIP;N4 ,:5 A V]TICAL L9E IS
US$ 2T ! SYN!TIC QUOTI5T &! SYN!TIC
REMA9D]1 X M/ 2 PLAC$ 9 ! COLUMN (
BLANK CELLS Z %[N 9 9K PR9T4
(1) 2_1 -3 2
_ 2 -2
---------
1 -1_ 0
#DGG
(2) 1 -3 2_2 #AGI
2 -2_
---------
1 -1_ 0
(3) +2_1 +6 - 1 -30
_ +2 +16 +30
--------------
1 +8 +15 + 0
(IN 9K PR9T1 ! DIVISOR IS BOX$-IN
ON TWO SIDES2 "! IS NO V]TICAL L9E
AF ! DIVISOR)
(4) 1 -3 +4 +5_+2
+2 -2 +4_
------------
1 -1 +2_+9
(IN 9K PR9T1 ! DIVISOR IS BOX$-IN ON
TWO SIDES2 "! IS NO V]TICAL L9E AF !
DIVISOR)
,NEME? ,MA?4 ,CODE1 #1972 A#AGI
@,S#183_4 .,DET]M9ANTS .& .,MA-
TRICES3
;A_4 ,9 DET]M9ANTS OR MATRICES EA*
5TRY M/ 2 LEFT-JU/IFI$ (MOV$ Z F> LEFT
Z POSSI#) 9 ! COLUMN 6: X 2L;GS1 &
TOP-JU/IFI$ (MOV$ Z F> UP Z POSSI#) 9
! R[ 6: X APPLIES4 ,REG>D.S (! 9K-PR9T
COPY1 C5T]+ OR O!R =MS ( ALIGN;T IS N
P]MITT$4 ,"O COLUMN ( BLANK CELLS M/ 2
LEFT 2T COLUMNS4
;B_4 ,E EF=T M/ 2 MADE 63F9E ! EN-
TIRE >RANGE;T 6A S+LE BRL PAGE4 ,TO
A*IEVE ? GOAL1 ! FOLL[+ TE*NIQUES MAY
2 US$3
;I_4 ,AN 5TRY MAY 2 RUN OV] 6O!R
BRL L9ES & EA* 3T9U,N 9D5T$ TWO CELLS
F ! COLUMN M>G94 ,:5 SPACE SAV+ IS A
FACTOR1 RUNOV]S MAY 2 MADE )\T REG>D
6ANY HI]>*Y PREF];ES4 ,SU3ESSIVE R[S 9
A COLUMN M/ 2 TRANSCRIB$ )\T SKIPP+ A
L9E 2T !M4
;II_4 ,AN 5TRY MAY 2 RUN OV] TO
O!R BRL L9ES & EA* 3T9U,N LEFT- #DGI
JU/IFI$ 9 XS COLUMN4 ,:5 SPACE B#AGI
SAV+ IS A FACTOR1 RUNOV]S MAY 2 MADE
)\T REG>D 6ANY HI]>*Y PREF];ES4 ,SUC-
CESSIVE R[S 9 A COLUMN M/ 2 TRANSCRIB$
)A
----------------------------------#AHJ
SKIPP$ L9E 2T !M4 ,:5 ! TE*NIQUE DE-
SCRIB$ 9 ;I ABV IS E6ECTIVE 9 PROVID+
! REQUIR$ SPACE1 X M/ 2 US$ 9 PREF];E
6! TE*NIQUE DESCRIB$ "H4
;III_4 ,A4I;NAL SPACE MAY 2 SAV$
0DRAW+ ! 5CLOS+ GR\P+ SYMBOLS 9/1D (
US+ _! BRL EQUIVAL5TS4
;IV_4 ,:5 AN 5TRY IS A FRAC;N1 !
FRAC;N MAY 2 REPRES5T$ SPATI,Y1 IF
NEC1 6SAVE SPACE4 ,H["E1 ! R[ 3TA9+ S*
A FRAC;N M/ !N H A L9E SKIPP$ ABV & 2L
X4
;V_4 ,! TE*NIQUE ( KEY+ MAY 2
EMPLOY$ = "O OR S"EAL 5TRIES IF NO O!R
SPACE-SAV+ TE*NIQUE IS E6ECTIVE4 (,SEE
@,S#187_4)
,NEME? ,MA?4 ,CODE1 #1972 A#AHJ
(1) @,(COS A SIN A #0@,)
@,(-SIN A COS A #0@,)
@,(#0 #0 #1@,)
(IN 9K PR9T1 EA* 5TRY IS C5T]$ 9 !
COLUMN 6: X 2L;GS)
(2)
,(?1/,A# #0 #0 ,)
,(#0 ?1/,A -?COS .B/,A ,)
,( SIN^2 .B# SIN^2 .B# ,)
,(#0 -?COS .B/,A ?1/,C# ,)
,( SIN^2 .B# +?COS^2 .B,)
,( /,ASIN^2 ,)
,( .B# ,)
(IN 9K PR9T1 EA* 5TRY IS C5T]$ 9 !
COLUMN 6: X 2L;GS)
#DHA
(3) #AHA
,\,B'11- ,B'12 ,B'13 ,B'14 ,\
,\(,E- ,\
,\,E1^0") ,\
,\ ,\
,\,B'21 ,B'22- ,B'23 ,B'24 ,\
,\ (,E- ,\
,\ ,E2^0") ,\
,\ ,\
,\,B'31 ,B'32 ,B'33- ,B'34 ,\
,\ (,E- ,\
,\ ,E3^0") ,\
,\ ,\
,\,B'41 ,B'42 ,B'43 ,B'44- ,\
,\ (,E- ,\
,\ ,E4^0"),\
(IN 9K PR9T1 EA* 5TRY IS C5T]$ 9 !
COLUMN 6: X 2L;GS)
,NEME? ,MA?4 ,CODE1 #1972 #AHB
(4)
,( #1 #0 #0 ,)
,(?33# ,)
,( ,A ,)
,( ,)
,(#0 #1 COS .B ,)
,( ?3333333333# ?3333333333#,)
,( ,ASIN^2 .B ,ASIN^2 .B ,)
,( ,)
,(#0 COS .B COS^2 .B ,)
,( ?3333333333# ?3333333333#,)
,( ,ASIN^2 .B ,ASIN^2 .B ,)
(IN 9K PR9T1 EA* 5TRY IS C5T]$ 9 !
COLUMN 6: X 2L;GS)
;C_4 ,:5 A SEQU;E ( DOTS APPE>S TO
SIGNIFY ! OMIS.N ( "O OR M R[S & S*
DOTS >E 3F9$ 6EA* COLUMN (! DET]M9ANT
OR MATRIX1 A SEQU;E ( ?REE DOTS #3 M/
2 PLAC$ 9 EA* COLUMN 69DICATE ! OMIS.N
& EA* ELLIPSIS US$ 9 ? WAY M/ 2 #DHC
LEFT-JU/IFI$ 9 XS COLUMN4 ,:5 A#AHB
A SEQU;E ( DOTS APPE>S 6SIGNIFY !
OMIS.N ( "O OR M R[S & S* DOTS >E N
3F9$ 6_! COLUMNS1 OR IF "S COLUMNS
3TA9 NO DOTS1 A SEQU;E ( DOTS #3 M/ 2
US$ 2G9N+ 9 ! F/ CELL ( COLUMN "O &
EXT5D+ 6! 5D (! L;GE/ 5TRY 9 ! LA/
COLUMN4
(1) ,\A11 A12 ''' A;1N",\
,\A21 A22 ''' A;2N",\
,\''' ''' ''' ''' ,\
,\A;N1 A;N2 ''' A;NN",\
(IN 9K PR9T1 "O DOT IS %[N 9 ! F/1
SECOND1 & F\R? COLUMNS1 RESPECTIVE-
LY)
----------------------------------#AHC
(2) @,(A11 A12 ''' A;1N"@,)
@,(A21 A22 ''' A;2N"@,)
@,('''''''''''''''''''@,)
@,(A;N1 A;N2 ''' A;NN"@,)
(IN 9K PR9T1 ! SEQU;E ( DOTS 9 !
,NEME? ,MA?4 ,CODE1 #1972 A#AHC
?IRD R[ IS N 3F9$ 6SPECIFIC COLUMNS)
(3) ,\A11 A12 ''' A;1N",\
,\A21 A22 ''' A;2N",\
,\''''''''''''''''''',\
,\A;M1 A;M2 ''' A;MN",\
(IN 9K PR9T1 ?REE DOTS >E V]TIC,Y
ALIGN$1 "O "U ! O!R 9 ! F/ & F\R?
COLUMNS2 NO S* DOTS APPE> 9 ! SECOND
OR ?IRD COLUMNS)
@,S#184_4 .,UNIFI$ .,EXPRES.NS3
;A_4 ,:5 5L>G$ GR\P+ SYMBOLS >E
US$ 6UNIFY AN EXPRES.N : IS NEI A
DET]M9ANT NOR A MATRIX1 EA* ITEM M/
2G9 9 ! CELL : IMMLY FOLL[S ! LEFT EN-
L>G$ GR\P+ SYMBOL & M/ 5D 9 ! CELL :
IMMLY PREC$ES ! "R 5L>G$ GR\P+ SYMBOL4
,X IS ADVANTAGE\S 6DRAW ^! 5L>G$ GR\P+
SYMBOLS :5 SPACE SAV+ IS A FACTOR4
,H["E1 ^! REQUIRE;TS M/ 2 WAIV$ :5"E
V]TICAL ALIGN;T M/ 2 9DICAT$4 ,9 ?
CASE1 AT L1/ "O ITEM M/ EI 2G9 #DHE
9 ! CELL : IMMLY FOLL[S ! LEFT B#AHC
5L>G$ GR\P+ SYMBOL OR M/ 5D 9 ! CELL :
IMMLY PREC$ES ! "R 5L>G$ GR\P+ SYMBOL4
(1) .,(4X-Y .K 3.,)
.,(3X-Y .K 1.,)
(2) .,(3X+15Y-2Z .K #64 .,)
.,( X+12Y+ Z .K #51 .,)
.,(7X- 8Y+2Z .K -#16.,)
----------------------------------#AHD
;B_4 ,:5 AN EXPLAN,N OR -;T REF]S
6M ?AN "O 9K PR9T L9E 6: NO GR\P+ SIGN
Z A :OLE APPLIES1 ! IMPLI$ GR\P+ M/ 2
9DICAT$ 0US+ A TRANSCRIB]'S 5L>G$
GR\P+ SYMBOL4 ,IF ! EXPLAN,N O3URS 6!
LEFT1 ! LEFT TRANSCRIB]'S 5L>G$ GR\P+
SYMBOL M/ 2 US$2 IF X O3URS 6! "R1 !
"R TRANSCRIB]'S 5L>G$ GR\P+ SYMBOL M/
2 US$4 ,"! M/ 2 AT L1/ "O CLE> COLUMN
( SPACES 2T EI ( ^! TRANSCRIB]'S 5L>G$
GR\P+ SYMBOLS &! ASSOCIAT$ EXPLAN,N4
,IF ! EXPLAN,N REQUIRES M BRL L9ES ?AN
:AT IS 2+ EXPLA9$1 ! TRANSCRIB]'S EN-
,NEME? ,MA?4 ,CODE1 #1972 A#AHD
L>G$ GR\P+ SYMBOL M/ 2 EXT5D$ 6COV] !
EXPLAN,N1 & EA* RUNOV] (! EXPLAN,N M/
2 9D5T$ TWO CELLS F ! COLUMN 9 : ! EX-
PLAN,N 2G9S4
(1)
A .K ?X+Y/X-Y#,') -#1 "K X "K #1,
B .K ?X-Y/X+Y#,') -#1 "K Y "K #1
(IN 9K PR9T1 ! EXPLAN,N IS C5T]$ 6!
"R (! TWO EQU,NS 6: X APPLIES)
,RULE ,,XXV--,=MAT
@,S#185_4 .,SPATIAL .,>RANGE;T3
;A_4 ,:5 ! TRANSCRIP;N IS 9 ! =M (
A SPATIAL >RANGE;T1 A BLANK L9E M/ 2
LEFT BO? ABV & 2L ! SPATIAL >RANGE;T
EV5 IF ! SPATIAL >RANGE;T DIRECTLY
PREC$ES OR FOLL[S ! PAGE-*ANGE L9E IN-
DICAT+ A NEW 9K-PR9T PAGE4 ,TRANSI;N
6A NEW BRL PAGE 2F 2G9N+ OR AF 5D+ !
TRANSCRIP;N (A SPATIAL >RANGE;T #DHG
TAKES ! PLACE (! REQUIR$ BLANK B#AHD
L9E4 ,H["E1 :5 A RUNN+ H1D IS US$1 A
L9E M/ 2 SKIPP$ 2T ! RUNN+ H1D &A
SPATIAL >RANGE;T4 ,:5 A SPATIAL >-
RANGE;T 2G9S ON ! F/ OR SECOND L9E (A
BRL PAGE OR 5DS ON ! TW5TY-F\R? OR !
TW5TY-FIF? L9E (A BRL PAGE1 "! M/ ALW
2 AT L1/ ?REE CLE> COLUMNS ( CELLS 2T
! LA/ SYMBOL ON ANY L9E (! >RANGE;T1
9CLUD+ ANY SEP>,N L9ES1 &! F/ SYMBOL (
A PAGE NUMB]4 ,IF ? _C 2 A*IEV$1 ! >-
RANGE;T M/ 2G9 ON L9E #3 OR 5D ON L9E
#23, RESPECTIVELY4 ,! 5TIRE SPATIAL
>RANGE;T %D 2 3F9$ 6"O BRL PAGE4
(1) EFGH #AJF
432
+ 10
-------
;B_4 ,:5 A SPATIAL >RANGE;T IS
ID5TIFI$ 0A NUMB] OR A LR1 S* Z 9 A
SET ( EX]CISES1 ! ID5TIFI] M/ 2 PLAC$
Z 9DICAT$ 2L4 ,9 ALL CASES1 "! M/ 2 "O
COLUMN ( BLANK CELLS 2T ! ID5TIFI] &!
,NEME? ,MA?4 ,CODE1 #1972 C#AHD
LEFT-MO/ SYMBOL (! >RANGE;T Z A :OLE1
9CLUD+ ANY SEP>,N L9ES4
;I_4 ,! ID5TIFI] M/ 2 PLAC$ ON !
TOP L9E ( AN A4I;N1 SUBTRAC;N1 OR
MULTIPLIC,N >RANGE;T4 ,H["E1 :5 ! C>-
RI$-NUMB] 9DICATOR HAS BE5 US$ 9 AN
A4I;N >RANGE;T OR :5 NUMB]S H BE5
C.EL$ \ 9 A SUBTRAC;N >RANGE;T1 !
ID5TIFI] M/ 2 PLAC$ ON ! L9E : 3TA9S !
F/ T]M (! A4I;N >RANGE;T OR ! M9U5D (!
SUBTRAC;N >RANGE;T4
----------------------------------#AHE
(1) #1_4 4956
789
+ 31
-------
#DHI
(2) #2_4 @S18.24 A#AHE
@*65
------------
91 20
1 094 4
------------
@S1,185.60
,
77777
(3) #3_4 27
+ 5
-----
32
----------------------------------#AHF
(4) 2 16 16
#4_4 [3][ 7][ 6]
- 1 9 8
--------------
1 7 8
;II_4 ,! ID5TIFI] M/ 2 PLAC$ ON
! L9E : 3TA9S ! DIVID5D 9 A DIVI.N >-
,NEME? ,MA?4 ,CODE1 #1972 A#AHF
RANGE;T1 ON ! L9E : 3TA9S ! RADIC& 9 A
SQU>E ROOT >RANGE;T1 & ON ! L9E : CON-
TA9S ! SYN!TIC DIVID5D 9 A SYN!TIC DI-
VI.N >RANGE;T4
(1) 4947
-------
#5_4 5O24735
;III_4 ,9 ! CASE ( SPATIAL FRAC-
;NS1 ID5TIFI]S & C5T]$ -P>ISON SYM-
BOLS1 SYMBOLS ( OP],N1 PUNCTU,N1 & O!R
APPLICA# SYMBOLS M/ 2 PLAC$ ON ! PR9-
CIPAL FRAC;N L9E4 ,H["E1 ID5TIFI]S M/
2 PLAC$ ON ! TOP L9E (A 3T9U$ FRAC;N4
(1) #1 #3
#6_4 ?33#+?33# .K #1_?1/4_#
#2 #4
;IV_4 ,9 ! CASE ( DET]M9ANTS1
MATRICES1 & UNIFI$ EXPRES.NS1 ID5TI-
FI]S1 -P>ISON SYMBOLS1 SYMBOLS ( OP]-
,N1 PUNCTU,N1 & O!R APPLICA# #DIA
SYMBOLS M/1 IF !Y APPE> ON ! B#AHF
SAME SIDE (! EXPRES.N Z ! 5L>G$ GR\P+
SYMBOL1 2 PLAC$ ON ! TOP L9E EV5 ?\<
!Y >E C5T]$ 9 9K PR9T4
(1) #7_4 ,D .K ,\A11 A12,\ .K #100
,\A21 A22,\
(IN 9K PR9T1 ! MAT]IAL \TSIDE !
DET]M9ANT IS C5T]$)
----------------------------------#AHG
(2) #8_4 @,(#1 #3@,)*@,(C1@,)
@,(#2 #1@,) @,(C2@,)
@,(#1 #0@,)
.K @,(#15@,)_4
@,(#10@,)
@,(#3@,)
(IN 9K PR9T1 ! EXAMPLE NUMB]1 !
MULTIPLIC,N DOT1 ! SECOND MATRIX1 !
EQUALS SIGN1 &! P]IOD >E ALL C5T]$
V]TIC,Y 9 REL,N 6! F/ & LA/
MATRICES)
,NEME? ,MA?4 ,CODE1 #1972 A#AHG
(3) #9_4 (-#1 #4 #2),(#5,)_4
,(#1,)
,(#3,)
(IN 9K PR9T1 ! EXAMPLE NUMB]1 F/
MATRIX1 & P]IOD >E V]TIC,Y C5T]$ 9
REL,N 6! SECOND MATRIX)
(4) #10_4 .,(X+3Y+Z .K #5 .,)_4
.,(2X+Y+2Z .K #5.,)
.,(7X+8Y+Z .K #7.,)
(IN 9K PR9T1 ! EXAMPLE NUMB] &! P]I-
OD >E V]TIC,Y C5T]$ 9 REL,N 6! UNI-
FI$ SY/EM)
----------------------------------#AHH
;C_4 ,:5 SPATIAL >RANGE;TS >E
PLAC$ SIDE-BY-SIDE "! M/ 2 AT L1/ "O
CLE> COLUMN ( BLANK CELLS 2T ! 5D ( "O
SEP>,N L9E &! 2G9N+ (! NEXT4 ,9 ANY
CASE1 NO SYMBOL 9 "O SPATIAL >RANGE;T
MAY 2 LESS ?AN ?REE CELLS 4TANT F ANY
SYMBOL ON ANY L9E IN1 OR AS- #DIC
SOCIAT$ )1 A NEI<BOR+ >RANGE;T A#AHH
O!R ?AN NEI<BOR+ 5DS ( SEP>,N L9ES4
(1) 27 15
+ 7 +23
----- -----
(IN 9K PR9T1 ! EXAMPLES >E SIDE-BY-
SIDE)
(2) #1_4 42 #2_4 100
-23 - 91
----- ------
(IN 9K PR9T1 ! EXAMPLES >E SIDE-BY-
SIDE)
@,S#186_4 .,TRANSCRIB]'S .,NOTES3
;A_4 ,TRANSCRIB]'S NOTES M/ 2 EN-
CLOS$ 0! TRANSCRIB]'S GR\P+ SYMBOLS4
;B_4 ,A TRANSCRIB]'S NOTE 3SI/+ (
SEV5 ^WS OR LESS MAY 2 9S]T$ DIRECTLY
96! TEXT AT ! PO9T ": X APPLIES4 ,L;G]
NOTES M/ 2 PLAC$ AT ! NE>E/ 3V5I5T
PO9T RELATIVE 6! MAT]IAL 6: !Y APPLY &
,NEME? ,MA?4 ,CODE1 #1972 B#AHH
M/ 2 PLAC$1 9D5T$1 & RUN OV] 9 A3ORD.E
)! RULES (! ..,CODE ( ,BRL ,TEXTBOOK
,=MAT & .,TE*NIQUES4
(1) ,9 X^2, ! #2 ,'THE #2 IS ELE-
VAT$ 9 9K PR9T,' IS ! EX-
PON5T4
@,S#187_4 .,KEY+ .,TE*NIQUE3
;A_4 ,:5 SPACE DOES N P]MIT ! IN-
CLU.N ( LABELS1 COLUMN H1D+S1 5TRIES1
ETC41 9 A FIGURE1 DET]M9ANT1 MATRIX1
OR TA# Z %[N 9 9K PR9T1 "O OR M (!
LABELS1 H1D+S1 5TRIES1 ETC4 MAY 2 RE-
PLAC$ 0A NUM]IC OR ALPHABETIC KEY4 ,A
NUM]IC KEY %D 3SI/ (A NUM]AL WRITT5 9
! UPP] "P (! BRL CELL4 ,? NUM]AL M/ 2
PREC$$ 0! NUM]IC 9DICATOR & M/ N 2
PUNCTUAT$4 ,AN ALPHABETIC KEY M/ 3SI/
( TWO L[]-CASE ,5GLI% LRS &1 IF POS-
SI#1 ! -B9,N %D 2 SU7E/IVE (! ITEM X
REPRES5TS4 ,AN ALPHABETIC KEY MAY ONLY
2 US$ :5 ! AU?OR'S 5TRIES >E N"E -POS$
( TWO L[]-CASE LRS4 ,TWO #DIE
ITEMS : >E ID5TICAL %D H ! C#AHH
SAME KEY ASSIGN$ 6!M4
;B_4 ,IF A LI/ ( NUM]IC KEYS IS
US$1 X M/ 3SI/ ( 3SECUTIVE NUM]ALS BE-
G9N+ ) NUMB] #1, & ^! NUM]ALS %D 2
PLAC$ 9 ! FIGURE1 DET]M9ANT1 MATRIX1
OR TA# 9 ! SAME POSI;N Z ! MAT]IAL :
!Y REPLACE4
----------------------------------#AHI
;C_4 ,A LI/ ( NUM]IC OR ALPHABETIC
KEYS & _! M1N+S M/ 2 5CLOS$ 9 TRAN-
SCRIB]'S GR\P+ SYMBOLS & M/ PREC$E !
MAT]IAL 6: X APPLIES4 ,KEY ITEMS MAY 2
>RANG$ V]TIC,Y AT ! M>G91 OR !Y MAY 2
>RANG$ 9 COLUMNS 6SAVE SPACE4 ,A KEY
LI/+ M/ 2 PREC$$ & FOLL[$ 0A BLANK
L9E4 ,IF POSSI#1 ? LI/ M/ 2 PLAC$ ON !
SAME BRL PAGE Z ! MAT]IAL 6: X AP-
PLIES4
,NEME? ,MA?4 ,CODE1 #1972 A#AHI
(1)
,',KEY 6ITEMS 9 ! TA# 2L3
#A ,S\RCE ( ,V>I,N
#B ,SUMS ( ,SQU>ES
SI ,S,S;I .K #2
SJ ,S,S;J .K #26
IJ ,S,S;IJ .K #10
SS ,S,S .K #38
#C ,D4,F4
#D ,M1N ,SQU>E
ML ?2/2# .K #1
MM ?26/2# .K #13
MN ?10/4# .K #2.5
----------------------------------#AIJ
#E ,,EMS
EO .S^2"+?3/2#.,S.A;I^2
EP .S^2"+?3/2#.,S.B;J^2
EQ .S^2
#F ;,F-,RATIO
FT ?1/2.5# .K #.4
FU ?13/2.5# .K #5.2,'
#DIG
A#AIJ
-------------------------------
#A #B #C #D #E #F
7777777777777777777777777777777
,2T BLOCKS SI #2 ML EO FT
-------------------------------
,2T TR1T;TS SJ #2 MM EP FU
-------------------------------
,]ROR IJ #4 MN EQ
7777777777777777777777777777777
,TOTAL SS #8
-------------------------------
@,S#188_4 ..,4PLAY$ & ,EMB$D$ .,EX-
PRES.NS3
;A_4 ,:5"E AN EXPRES.N IS SET A"P
F ! BODY (! TEXT 0SKIPP$ L9ES1 9D5T,N1
OR "S O!R M1NS1 X W 2 REF]R$ TO Z A
.4PLAY$ .EXPRES.N4 ,03TRA/1 AN EXPRES-
.N : IS N SET A"P F ! BODY (! TEXT BY
ANY (! ABV M1NS W 2 REF]R$ TO Z AN
.EMB$D$ .EXPRES.N4
,NEME? ,MA?4 ,CODE1 #1972 #AIA
(1) ,! EQU,N
X^2"-3X+1 .K #0
IS A QUADRATIC EQU,N 2C X IS (
! =M AX^2"+BX+C .K #0_4
(THE F/ EQU,N IS A 4PLAY$ EXPRES.N2
! SECOND EQU,N IS AN EMB$D$ EXPRES-
.N)
;B_4 ,IF AN ID5TIFY+ NUMB] OR LR
IS ASSOCIAT$ )A 4PLAY$ EXPRES.N1 ?
NUMB] OR LR IS "P (! 4PLAY$ EXPRES.N &
M/ 2G9 9 ! APPROPRIATE CELL 9 A3ORD.E
)! RULES = 4PLAY$ EXPRES.NS 9
@,S@,S#190-191_4 ,9 9K PR9T1 ID5TIFY+
NUMB]S OR LRS >E "S"TS AT ! "R4 ,9
BRL1 NUMB]S OR LRS M/ 2 PLAC$ UNI=MLY
AT ! LEFT4 ,H["E1 IF ID5TIFY+ NUMB]S
OR LRS O3UR AT ! "R 9 9K PR9T1 A TRAN-
SCRIB]'S NOTE 3C]N+ ! TRANSPOSI;N ( S*
NUMB]S OR LRS M/ 2 PLAC$ AT ! 2G9N+ (!
F/ VOLUME4 ,PAGE REF];ES : >E ASSOCI-
AT$ ) AN EXPRES.N M/ IMMLY FOLL[ T
#DII
EXPRES.N4 A#AIA
(1) ,9 ? SEC;N1 FUNC;NS (! TYPE
(1) H(X1, X2, ''', X;N")
>E 6BE 3SID]$4
(IN 9K PR9T1 ! ID5TIFY+ NUMB] O3URS
AT ! "R)
(2) ,! 9EQUAL;Y SYMBOLS
"K AND .1 (98-99)
>E US$ 6/ATE ! ORD] ( NUMB]S4
(IN 9K PR9T1 ! PAGE NUMB]S O3UR AT !
"R-H& M>G9 (! PAGE)
@,S#189_4 .,L9K$ .,EXPRES.NS3
;A_4 ,A L9K$ EXPRES.N M/ 3TA9 AT
L1/ "O SIGN ( -P>ISON4 ,! -PON5T :
PREC$ES ! F/ SIGN ( -P>ISON IS CALL$
! .AN*OR4 ,EA* (! REMA9+ -PON5TS1 2G9-
N+ )A -P>ISON SIGN B N 9CLUD+ ! NEXT
-P>ISON SIGN1 IS CALL$ A .L9K4
----------------------------------#AIB
;B_4 ,:5 A L9K$ EXPRES.N MEETS !
FOLL[+ CRIT]IA1 X IS SUBJECT 6! SPE-
CIAL M>G9 REQUIRE;TS SET =? 9
@,S#190C, @,S#191A (IV) & ;B (V)_4
,NEME? ,MA?4 ,CODE1 #1972 A#AIB
;I_4 ,! EXPRES.N M/ 2 4PLAY$ &
N EMB$D$ )9 TEXT4
;II_4 ,XS SIGNS ( -P>ISON M/ 2
V]TIC,Y ALIGN$ 9 PR9T1 EXCEPT POSSIBLY
=! LA/ FEW : MAY O3UR ON ! LA/ PR9T
L9E (! EXPRES.N4
;III_4 ,NO SIGN ( -P>ISON1 EX-
CEPT POSSIBLY ! F/ "O1 MAY 2 PREC$$ BY
ANY EXPRES.N ON XS LEFT4
(1) #12_?1/2_#@0
.K #12.5@0
.K #.125
.K ?125/1000#
.K ?1/8#
(IN 9K PR9T1 ! F/ EQUALS SIGN APPE>S
6! "R ( #12_?1/2@0 & ALL O!R EQUALS
SIGNS EXCEPT ! LA/ "O >E ALIGN$ 2N
IT)
(2) #12_?1/2_#@0 .K #12.5@0
.K #.125 .K ?125/1000#
.K ?1/8# #EJA
(A L9K$ EXPRES.N : DOES N B#AIB
REQUIRE SPECIAL M>G9 PROVI.NS2 9 9K
PR9T ! 5TIRE EXPRES.N APPE>S ON "O
L9E)
@,S#190_4 ..,M>G9S = ,N>RATIVE ,POR-
;NS ( .,TEXT3
;A_4 ,9 N>RATIVE POR;NS ( TEXT1
M>G9S %D 2 MA9TA9$ Z 9 ,5GLI% ,BRL2
P>AGRAPHS M/ 2G9 9 CELL #3 & M/ 2 RUN
OV]1 IF NEC1 9 CELL #1_4
(1) X+2 & X+5 >E FACTORS (
X^2"+7X+10 2C (X+2)(X+5)
.K X^2"+7X+10_4
,? IS SIMIL> 6>I?METIC ": #5
& #3 >E FACTORS ( #15 2C #5@*3
.K #15_4
----------------------------------#AIC
;B_4 ,:5 ! SPECIAL M>G9 REQUIRE;TS
= L9K$ EXPRES.NS D N APPLY1 A 4PLAY$
EXPRES.N M/ 2G9 9 CELL #3 & M/ 2 RUN
OV]1 IF NEC1 9 CELL #5_4
,NEME? ,MA?4 ,CODE1 #1972 A#AIC
(1) ,! PRODUCT ( TWO MONOMIALS IS
A MONOMIAL4 ,= EXAMPLE
(3X^2")^3 .K (3X^2")(3X^2")
(3X^2") .K (9X^4")(3X^2")
.K #27X^6_4
;C_4 ,:5 ! SPECIAL M>G9 REQUIRE;TS
= L9K$ EXPRES.NS D APPLY1 ! AN*OR M/
2G9 9 CELL #3 & M/ 2 RUN OV]1 IF NEC1
9 CELL #7_4 ,EA* L9K M/ 2G9 9 CELL #5
ON A NEW BRL L9E & M/ 2 RUN OV]1 IF
NEC1 9 CELL #7_4
(1) #8X^3"+125Y^3 C 2 FACTOR$ 9 !
FOLL[+ WAY3
#8X^3"+125Y^3
.K (2X)^3"+(5Y)^3
.K (2X+5Y)@((2X)^2"-(2X)(5Y)
+(5Y)^2"@)
.K (2X+5Y)(4X^2"-10XY
+25Y^2")_4
(IN 9K PR9T1 ! F/ EQUALS SIGN #EJC
APPE>S 6! "R ( #8X^3"+125Y^3 B#AIC
& ALL O!R EQUALS SIGNS >E ALIGN$ 2N
IT)
@,S#191_4 ..,M>G9S = ,NON-,SPATIAL
,ITEMIZ$ .,MAT]IALS3 ,:5 MAT]IAL IS
ID5TIFI$ SEQU5TI,Y 0NUMB] OR LR1 Z 9
EX]CISES OR \TL9ES1 X W 2 REF]R$ TO Z
.ITEMIZ$ .MAT]IAL4
;A_4 ,:5 NON-SPATIAL ITEMIZ$ MA-
T]IAL 3TA9S MA9 DIVI.NS ONLY (NO SUB-
DIVI.NS) ! FOLL[+ RULES 3C]N+ M>G9S M/
2 OBS]V$3
;I_4 ,! MA9 DIVI.N NUMB]S OR LRS
M/ 2G9 9 CELL #1 &! ASSOCIAT$ MAT]IAL
M/ 2 RUN OV]1 IF NEC1 9 CELL #3_4
----------------------------------#AID
;II_4 ,SU3E$+ P>AGRAPHS1 IF ANY1
M/ 2G9 9 CELL #5 & M/ 2 RUN OV]1 IF
NEC1 9 CELL #3_4
;III_4 ,:5 ! SPECIAL M>G9 RE-
QUIRE;TS = L9K$ EXPRES.NS D N APPLY1 A
4PLAY$ EXPRES.N M/ 2G9 9 CELL #5 & M/
2 RUN OV]1 IF NEC1 9 CELL #7_4
;IV_4 ,:5 ! SPECIAL M>G9 RE-
,NEME? ,MA?4 ,CODE1 #1972 A#AID
QUIRE;TS = L9K$ EXPRES.NS D APPLY1 !
AN*OR M/ 2G9 9 CELL #5 & M/ 2 RUN OV]1
IF NEC1 9 CELL #9_4 ,EA* L9K M/ 2G9 9
CELL #7 & M/ 2 RUN OV]1 IF NEC1 9 CELL
#9_4
;V_4 ,9/RUC;NS : APPLY 6A GR\P
( PRO#MS : FOLL[ M/ 2G9 9 CELL #5 & M/
2 RUN OV]1 IF NEC1 9 CELL #3_4 ,"! M/
2 A BLANK L9E ABV S* 9/RUC;NS1 B N 2L4
,H["E1 A PAGE-*ANGE L9E MAY TAKE !
PLACE ( ? REQUIR$ SKIPP$ L9E4 ,! LA/
L9E ( AN 9/RUC;N &! F/ L9E (A PRO#M 6:
X APPLIES M/ 2 ON ! SAME BRL PAGE4
(1) #1_4 ,IS (Y-3) A FACTOR (
Y^3"+3Y^2"-7Y-33_8 ,IF S1 :AT IS
! O!R FACTOR8
,*ECK 0DIVI.N1 OR Z %[N 9
,*APT] #9_4
#EJE
(2) #2_4 ,WRITE ! S+LE NUM]AL B#AID
T "NS ! SAME NUMB] Z
(3@*10^4")+(4@*10^3")
+(5@*10^2")+(6@*10)+(7@*1)_4
----------------------------------#AIE
(3) #3_4 ,US+ ! BINOMIAL !OREM 6F9D
#1.1^5 6?REE DECIMAL PLACES1 WE
SEE T
#1.1^5
.K (1+0.1)^5
.K #1^5"+5(1^4")(0.1)
+10(1^3")(0.1)^2
"+10(1^2")(0.1)^3
"+5(1)(0.1)^4"+(0.1)^5
.K #1+0.5+0.1+0.01+0.0005
+0.00001
.K #1.61051
(IN 9K PR9T1 ! F/ EQUALS SIGN IS 6!
"R ( #1.1^5 & ALL O!R EQUALS SIGNS
>E ALIGN$ 2N IT)
(4) ,USE ! SUMM,N SIGN 6WRITE EA*
S]IES4
#1_4 #6+10+14+18
,NEME? ,MA?4 ,CODE1 #1972 A#AIE
#2_4 A1B1+A2B2+A3B3
#3_4 X1^2"+X2^2"+X3^2"+X4^2"+X5^2
;B_4 ,:5 NON-SPATIAL ITEMIZ$ MA-
T]IAL 3TA9S BO? MA9 DIVI.NS & SUBDI-
VI.NS 6:AT"E DEP?1 ! FOLL[+ RULES CON-
C]N+ M>G9S M/ 2 OBS]V$3
;I_4 ,! MA9 DIVI.N NUMB]S OR LRS
M/ 2G9 9 CELL #1 &! ASSOCIAT$ MAT]IAL
M/ 2 RUN OV]1 IF NEC1 9 CELL #5_4
;II_4 ,SUBDIVI.N NUMB]S OR LRS1
REG>D.S ( DEP?1 M/ 2G9 9 CELL #3 & M/
2 RUN OV]1 IF NEC1 9 CELL #5_4
----------------------------------#AIF
;III_4 ,SU3E$+ P>AGRAPHS1 IF
ANY1 M/ 2G9 9 CELL #7 & M/ 2 RUN OV]1
IF NEC1 9 CELL #5_4
;IV_4 ,:5 ! SPECIAL M>G9 RE-
QUIRE;TS = L9K$ EXPRES.NS D N APPLY1 A
4PLAY$ EXPRES.N M/ 2G9 9 CELL #7 & M/
2 RUN OV]1 IF NEC1 9 CELL #9_4
;V_4 ,:5 ! SPECIAL M>G9 REQUIRE-
;TS = L9K$ EXPRES.NS D APPLY1 ! AN*OR
M/ 2G9 9 CELL #7 & M/ 2 RUN #EJG
OV]1 IF NEC1 9 CELL #11_4 A#AIF
,EA* L9K M/ 2G9 9 CELL #9 & M/ 2 RUN
OV]1 IF NEC1 9 CELL #11_4
;VI_4 ,9/RUC;NS : APPLY 6A GR\P
( PRO#MS : FOLL[ M/ 2G9 9 CELL #5 & M/
2 RUN OV]1 IF NEC1 9 CELL #3_4 ,"! M/
2 A BLANK L9E ABV S* 9/RUC;NS1 B N 2L4
,H["E1 A PAGE-*ANGE L9E MAY TAKE !
PLACE ( ? REQUIR$ SKIPP$ L9E4 ,! LA/
L9E ( AN 9/RUC;N &! F/ L9E (A PRO#M 6:
X APPLIES M/ 2 ON ! SAME BRL PAGE4
(1) #1_4 ,F9D ! REPLACE;T = ;,N T W
MAKE EA* S5T;E TRUE4
;A_4 (3@*5)@*2 .K #3@*(,N@*2)
;B_4 #3@*(5@*2) .K (3@*5)@*,N
,DID Y USE ! SAME NUM]AL Z A
REPLACE;T 9 EA* S5T;E8 ,IS ?
S5T;E TRUE3
(3@*5)@*2 .K #3@*(5@*2)_8
(2) #2_4
;A_4 X(A+1)-Y(A+1)
;B_4 X^2"-2X+1-4A^2
"-12A-9
,NEME? ,MA?4 ,CODE1 #1972 B#AIF
(IN 9K PR9T1 ! ;A IS ON ! SAME L9E
Z ! PRO#M NUMB]1 &! ;B IS ALIGN$ 2N
;A)
----------------------------------#AIG
(3) #3_4 ,9 FACTOR+ AB+C^2"+AC+BC_3
(A) ,! T]MS MAY 2 GR\P$ 9 PAIRS
)A -MON FACTOR4
AB+C^2"+AC+BC
.K (AB+AC)+(BC+C^2")
.K A(B+C)+C(B+C)
.K (A+C)(B+C)
(B) ,RE>RANGE ! T]MS & GR\P !M
ANO!R WAY4
;I_4 ,D ! T]MS FIT ANY (! PAT-
T]NS /UDI$ 2F8
;II_4 ,9 FACTOR+1 C BINOMIAL &
POLYNOMIAL EXPRES.NS 2 TR1T$ L
MONOMIAL FACTORS8
(IN 9K PR9T1 ! MA9 PRO#M NUMB]1 !
(A) &! (B) >E V]TIC,Y ALIGN$2 !
,ROMAN NUM]ALS >E 9D5T$ FUR!R 6! "R)
#EJI
(4) ,ADD4 ,*ECK YR A4I;N #AIH
0A4+ ! O!R WAY4
#4_4
;A_4 #118+37+66
;B_4 #123+159+92
;C_4 #146+192
(IN 9K PR9T1 ! PRO#M NUMB] &! F/ TWO
SUBDIVI.NS >E ON ! SAME L9E2 ! ?IRD
SUBDIVI.N IS 2N ! F/)
;C_4 ,:5 NON-SPATIAL ITEMIZ$ MA-
T]IAL 3TA9S BO? MA9 DIVI.NS & SUBDI-
VI.NS1 X IS P]MISSI# 6PLACE ALL SUBDI-
VI.NS ON A S+LE BRL L9E IF T BRL L9E
C A3OMMODATE ALL ! SUBDIVI.NS4
(1) #1_4 ,SUBTRACT3
(A) #10-3 (B) #15-4 (C) #21-19
(THE BRL & 9K PR9T >E ! SAME)
----------------------------------#AII
@,S#192_4 ..,M>G9S = ,SPATIAL ,ITEM-
IZ$ .,MAT]IALS3 ,SPATIAL ITEMIZ$ MA-
T]IAL MAY 2 TRANSCRIB$ US+ ! SAME M>G9
,NEME? ,MA?4 ,CODE1 #1972 A#AII
RULES Z >E 3TA9$ 9 @,S#191_4 ,H["E1 =
SPACE-SAV+ PURPOSES ! FOLL[+ ALT]NA-
TIVES >E AVAILA#3
;A_4 ,:5 SPATIAL ITEMIZ$ MAT]IAL
3TA9S MA9 DIVI.NS ONLY (NO SUBDI-
VI.NS), ! F/ DIVI.N NUMB] 2G9S 9 CELL
#1_4 ,SUBSEQU5T DIVI.N NUMB]S MAY 2G9
6! "R (! PREC$+ SPATIAL >RANGE;T RE-
G>D.S ( H[ !Y O3UR 9 9K PR9T4 ,Z _M
MA9 DIVI.N NUMB]S & _! ASSOCIAT$ SPA-
TIAL >RANGE;TS MAY O3UR ACR ! PAGE Z C
2 A3OMMODAT$4 ,IF A4I;NAL MA9 DIVI.N
NUMB]S REMA91 ! F/ ( ^! 2G9S AG 9 CELL
#1, AF HAV+ LEFT A BLANK L9E 2L !
L;GE/ (! SPATIAL >RANGE;TS : O3UR ABV4
#EAA
(1) ,SUBTRACT4 B#AII
#1_4 76 #2_4 9,674
-43 - 476
----- --------
#3_4 2.31 #4_4 6.97
- .04 -6.07
------- -------
(IN 9K PR9T1 EXAMPLES #1 & #2 APPE>
9 ! F/ COLUMN1 EXAMPLES #3 & #4 AP-
PE> 9 ! SECOND COLUMN)
----------------------------------#BJJ
;B_4 ,:5 SPATIAL ITEMIZ$ MAT]IALS
3TA9 BO? MA9 DIVI.NS & SUBDIVI.NS1 !
F/ MA9 DIVI.N NUMB] 2G9S 9 CELL #1 &!
F/ SUBDIVI.N FOLL[S ON ! SAME BRL L9E
IF "! IS NO MAT]IAL 2T ! MA9 DIVI.N
NUMB] &! SUBDIVI.N NUMB]4 ,Z _M A4I-
;NAL SUBDIVI.NS MAY 2 TRANSCRIB$ ACR !
L9E Z C 2 A3OMMODAT$4 ,IF A4I;NAL SUB-
DIVI.NS REMA91 !Y >E />T$ 9 CELL #3 AF
HAV+ LEFT A BLANK L9E 2L ! L;GE/ (!
SPATIAL >RANGE;TS : O3UR ABV4
,NEME? ,MA?4 ,CODE1 #1972 A#BJJ
(1) #1_4 ;A_4 462 ;B_4 1,763
@*30 @*142
------ -------
;C_4 51.986 ;D_4 .67
@*7.3 @*.92
-------- -------
#2_4 ;A_4 712 ;B_4 2,547
@*430 @*3
------- -------
;C_4 8.69 ;D_4 200.2
@*.03 @*100.0
------- ---------
(IN 9K PR9T1 ALL F\R SUBDIVI.NS (
EA* PRO#M APPE> ACR ! PAGE 9 COLUMN>
=M)
#EAC
(2) #2_4 ,MULTIPLY4 #BJA
;A_4 94621 ;B_4 43290
567 380
------- -------
;C_4 1,000,000
432
-----------
(IN 9K PR9T1 ALL ! SUBDIVI.NS >E ON
! SAME L9E)
@,S#193_4 ..,M>G9S = ,SPATIAL &
,NON-,SPATIAL ,ITEMIZ$ ,MAT]IALS ,>-
RANG$ 9 ,TABUL> .,=M3
;A_4 ,:5 ITEMIZ$ MAT]IAL IS >RANG$
9 TABUL> =M S T R[S >E ID5TIFI$ 0NUMB]
& COLUMNS >E ID5TIFI$ 0LR1 ! FOLL[+
TE*NIQUE M/ 2 US$ PROVID$ T ! .5TIRE
TABUL,N C 2 3TA9$ ACR ! BRL PAGE4
;I_4 ,! LRS : ID5TIFY ! COLUMNS
M/ 2 LEFT-JU/IFI$ 9 ! COLUMNS 6: !Y
APPLY4
;II_4 ,A BLANK L9E M/ 2 LEFT ABV
,NEME? ,MA?4 ,CODE1 #1972 A#BJA
& 2L ! COLUMN H1D+S4
;III_4 ,R[ NUMB]S M/ 2G9 9 CELL
#1_4
;IV_4 ,AT L1/ TWO SPACES %D 2
LEFT 2T ! "R-H& M>G9 ( "O COLUMN &!
LEFT-H& M>G9 (! NEXT COLUMN4
----------------------------------#BJB
(1) ;A ;B
#1_4 #1745-431 .K ,N ,N .K -#5+2
#2_4 ,N .K #18+(-9) -#7+14 .K ,N
(INK PR9T & BRL >E ! SAME)
#EAE
A#BJB
(2) ;A ;B ;C
#1_4 4396 6010 73.01
+ 873 - 809 @*.62
------- ------- -------
#2_4 37,285 48,063 69.35
+ 9,476 - 1,741 @*.04
--------- --------- -------
(INK PR9T & BLL >E ! SAME)
;B_4 ,IF ! 5TIRE TABUL,N _C 2 CON-
TA9$ ACR ! BRL PAGE US+ ! TE*NIQUE (
;A ABV1 ! TRANSCRIP;N %D PROCE$ Z IF !
R[ NUMB]S 7 MA9 H1D+S &! COLUMN LRS 7
SUBDIVI.N H1D+S = EA* MA9 DIVI.N NUM-
B]4 ,9 S* CASES1 ! M>G9 RULES (
@,S#191B & @,S#192B !N APPLY4
,NEME? ,MA?4 ,CODE1 #1972 #BJC
(1) ,FACTOR3
#1_4
;A (X-Y)^2"-(A+B)^2
;B M(P-Q)-N(Q-P)
#2_4
;A #1-(X+1)^2
;B #4AB+4X^2"-A^2"-4B^2
(IN 9K PR9T1 ! SUBDIVI.NS >E PLAC$
ACR ! PAGE & >E ALIGN$ 2N LR$ COLUMN
H1D+S)
(2) #1_4 ;A 7238 ;B 4231
+ 457 +1389
------- -------
;C 2643 ;D 75,011
+ 52 + 96
------- ---------
(IN 9K PR9T1 ! SUBDIVI.NS >E PLAC$
ACR ! PAGE & >E ALIGN$ 2N LR$ COLUMN
H1D+S) #EAG
@,S#194_4 ..,=MAT = ,=MAL #BJD
.,PRO(S3
;A_4 ,A =MAL PRO( IS USU,Y 9TRO-
DUC$ 0A ^W S* Z .,!OREM1 .,PROPOSI;N1
OR .,LEMMA4 ,! FOLL[+ =MAT IS RECOM-
M5D$ =! TRANSCRIP;N ( S* =MAL PRO(S3
;I_4 ,A L9E M/ 2 SKIPP$ 2F ! BE-
G9N+ (! =MAL PRO(4
;II_4 ,! FULLY CAPITALIZ$ ^W
.,!OREM1 .,PROPOSI;N1 OR .,LEMMA M/
2G9 9 CELL #3 &! /ATE;T FOLL[+ ? ^W %D
2 RUN OV]1 IF NEC1 6CELL #1_4
;III_4 ,AUXILI>Y CAP;NS S* Z
.,GIV51 .,HYPO!SIS1 .,PROVE1 OR .,CON-
CLU.N M/ FOLL[1 )\T A SKIPP$ L9E1 & M/
2G9 9 CELL #3_4 ,^! CAP;NS %D 2 CAPI-
TALIZ$ OR ITALICIZ$ 9 A3ORD.E )! PR9T
TEXT4 ,IF !Y >E 9 BOLDFACE TYPE1 !Y
%D 2 WRITT5 Z FULLY CAPITALIZ$ 9 BRL4
,MAT]IAL ASSOCIAT$ ) ^! CAP;NS %D FOL-
L[ ! CAP;NS & %D 2 RUN OV]1 IF NEC1 TO
CELL #1_4 ,H["E1 :5 A PRO( IS PRES5T$
0/EP NUMB]1 A L9E %D 2 LEFT BLANK AF !
CAP;N .PRO( &! =MAT 9 ;B 2L M/ 2 FOL-
L[$4
,NEME? ,MA?4 ,CODE1 #1972 A#BJD
;IV_4 ,:5 ! =MAL PRO( IS -PLETE1
A L9E M/ 2 LEFT BLANK 2F 3T9U+ )!
TEXT4
(1) ,,!OREM #4_4 ,'. ,IF TWO L9ES >E
CUT 0A TRANSV]SAL &A PAIR ( ALT]-
NATE 9T]IOR ANGLES >E EQUAL1 ! TWO
L9ES >E P>ALLEL4 .,'
.,GIV53 ,L9ES ,A,B & ,C,D CUT BY
TRANSV]SAL ,R,S AT PO9TS ;,E & ;,F
RESPECTIVELY2 $[ X .K $[ Y_4
.,TO .,PROVE3 ,A,B $L ,C,D_4
;B_4 ,:5 A =MAL PRO( IS PRES5T$ BY
/EP NUMB] & IS DIVID$ 96TWO COLUMNS
H1D$ 8,/ATE;T0 & 8,R1SON01 ! FOLL[+
TE*NIQUE M/ 2 US$3
;I_4 ,ALL /EP NUMB]S M/ 2G9 AT !
M>G94
;II_4 ,! /EP NUMB] M/ 2 FOLL[$
0! LR ;,S OR ;,R AC Z ! TRANSCRIP;N TO
FOLL[ IS F ! ,/ATE;T OR ! ,R1SON COL-
UMN4 ,! TRANSCRIP;N M/ 2G9 ON ! SAME
L9E Z ! /EP NUMB] & RUNOV]S1 IF #EAI
NEC1 M/ 2G9 9 CELL #3_4 ,IF A B#BJD
CAP;N O!R ?AN 8,/ATE;T0 OR 8,R1SON0 IS
US$1 A SUITA# LR %D 2 US$ = ;,S OR
;,R_4
----------------------------------#BJE
;III_4 ,A TRANSCRIB]'S NOTE M/ 2
9CLUD$ 6CALL ATT5;N 6? BRL =MAT & TO
SPECIFY ! M1N+ ( ;,S, ;,R, OR O!R LRS
: MAY H BE5 US$4 ,? NOTE M/ 2 PLAC$ AT
! 2G9N+ ( EA* BRL VOLUME 9 : ? TE*-
NIQUE IS US$4
(1) #1,S_4 ,D,E BISECTS $[ ,A,C,B_4
#1,R_4 ,GIV54
#2,S_4 $[ A .K $[ B_4
#2,R_4 ,A BISECTOR DIVIDES AN AN-
GLE 96TWO EQUAL ANGLES4
#3,S_4 ,F,C,B & ,D,C,E >E /RAI<T
L9ES4
#3,R_4 ,GIV54
#4,S_4 $[ X .K $[ B_4
#4,R_4 ,IF TWO /RAI<T L9ES 9T]-
SECT1 ! V]TICAL ANGLES >E EQUAL4
#5,S_4 $[ X .K $[ A_4
#5,R_4 ,SUB/ITU;N PO/ULATE4
,NEME? ,MA?4 ,CODE1 #1972 A#BJE
(IN 9K PR9T1 "! IS A ,/ATE;T COLUMN
&A ,R1SON COLUMN)
----------------------------------#BJF
@,S#195_4 .,RUNOV]S3 ,! RUNOV] (A
MA!MATICAL EXPRES.N 6ANO!R BRL L9E M/
2 AVOID$ SUBJECT 6! M>G9 REQUIRE;TS :
>E 9 E6ECT AT ! "T ( TRANSCRIB+ ! EX-
PRES.N4
;A_4 ,Z M* (A BRL L9E M/ 2 LEFT
BLANK Z NEC 9 ORD] 6KEEP ALL (A MA!-
MATICAL EXPRES.N ON A S+LE BRL L9E4
(1) ,WE C %[ T
#2+4+6+ ''' +2N .K N(N+1)+(N-1) IS
TRUE = N .K #1_4
;B_4 ,A SEQU;E ( MA!MATICAL EX-
PRES.NS : O3URS 9 AN 85CLOS$ LI/0 M/ N
2 DIVID$ 2T BRL L9ES IF ALL (! 8EN-
CLOS$ LI/0 C 2 KEPT ON A S+LE BRL L9E4
#EBA
(1) ,! ELE;TS (! SEQU;E A#BJF
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) C 2
C.T$4
;C_4 ,AN A2REVI,N M/ N 2 PLAC$ ON
A DI6]5T BRL L9E F XS PREC$+ OR FOLL[+
NUM]AL OR LR4
(1) #4 IN
(2) #3 P4M4
(3) #30^.* ;,C
(4) ;,N #30^.* ;,W
(5) ,FIG4 #6.10
(6) ;X FT4
;D_4 ,A HYPH5AT$ EXPRES.N ( : "O
-PON5T (! EXPRES.N IS MA!MATICAL M/ N
2 DIVID$ 2T BRL L9ES4
(1) #6-9* RUL]
(2) #4-SID$ FIGURE
----------------------------------#BJG
(3) ;X-9T]CEPT
(4) XY-PLANE
,NEME? ,MA?4 ,CODE1 #1972 A#BJG
;E_4 ,:5 A MA!MATICAL EXPRES.N _C
2 KEPT ON "O BRL L9E & M/ 2 DIVID$ 2T
L9ES1 ! DIVI.N M/ 2 MADE GIV+ PRIOR;Y
6! FOLL[+ ITEMS 9 DESC5D+ ORD]3
;I_4 ,AF A -MA : O3URS 2T ITEMS
9 AN 85CLOS$ LI/40
;II_4 ,2F A SYMBOL ( -P>ISON4
;III_4 ,2F A SYMBOL ( OP],N4
;IV_4 ,2F A FRAC;N L9E4
;V_4 ,2F ! BASE-L9E 9DICATOR4
;VI_4 ,2F A *ANGE-(-LEVEL 9DI-
CATOR OR )9 A SUP]SCRIPT OR SUBSCRIPT
2F "O (! SYMBOLS LI/$ ABV4
;VII_4 ,2T FACTORS : >E 5CLOS$
)9 GR\P+ SYMBOLS4
;VIII_4 ,AF A T]M9,N 9DICATOR4
#EBC
,NEME? ,MA?4 ,CODE1 #1972 #BJH
,,APP5DIX ;,A
,,-B9,NS ,,( ,,TYPE-=M1
,,ALPHABETIC1 ,,&
,,CAPITALIZ,N ,,9DICATORS
,',COLUMN H1D+S 9 ! FOLL[+ TA#
>E LABEL$ ?US3
;,A--,TYPE-=M
;,B--,5GLI% LRS
;,C--,G]MAN LRS
;,D--,GREEK LRS
;,E--,GREEK ,LR ,ALT]NATIVE
;,F--,HEBREW LRS
;,G--,RUSSIAN LRS,'
,L[]-,CASE ,LRS
;,A ;,B ;,C ;,D ;,E ;,F ;,G
,BOLDFACE _; __ _. _@@
,ITALIC .; ._ .. .@@
,ORD9>Y ; _ . .@ ,, @@
#EBE
A#BJH
;,A ;,B ;,C ;,D ;,E ;,F ;,G
,SANS]IF ,.
,SCRIPT @; @_ @. @,, @@@
,CAPITALIZ$ ,LRS
,BOLDFACE _;, __, _., _@@,
,ITALIC .;, ._, .., .@@,
,ORD9>Y ;, _, ., @@,
,SANS]IF ,.,
,SCRIPT @;, @_, @., @@@,
,NEME? ,MA?4 ,CODE1 #1972 #BJI
,,APP5DIX ;,B
,,9DEX ,,( ,,BRL ,,SYMBOLS
,! FOLL[+ IS ! LI/ ( #63 BRL SYMBOLS
>RANG$ 9 _! /&>D ORD]4 ,! SEP>,N ( ^!
SYMBOLS 96! USUAL SEV5 L9ES ( BRL IS
IGNOR$1 B EA* SYMBOL IS NUMB]$ 9 AC-
CORD.E ) XS RANK 9 ! LI/4
#1 A #15 O
#2 B #16 P
#3 C #17 Q
#4 D #18 R
#5 E #19 S
#6 F #20 T
#7 G #21 U
#8 H #22 V
#9 I #23 X
#10 J #24 Y
#11 K #25 Z
#12 L #26 &
#13 M #27 =
#14 N #28 ( #EBG
#29 ! #54 > A#BJI
#30 ) #55 '
#31 * #56 -
#32 < #57 @
#33 % #58 ^
#34 ? #59 _
#35 : #60 "
#36 $ #61 .
#37 ] #62 ;
#38 \ #63 ,
#39 [
#40 W
#41 1
#42 2
#43 3
#44 4
#45 5
#46 6
#47 7
#48 8
#49 9
#50 0
#51 /
#52 +
#53 #
,NEME? ,MA?4 ,CODE1 #1972 #BAJ
,! ITEMS 9 ! ,,9DEX ,,( ,,BRL ,,SYM-
BOLS >E 8ALPHABETIZ$0 9 A3ORD.E )! LI/
(! #63 BRL SYMBOLS ABV4
,',9 ! FOLL[+ 9DEX ! BRL SYMBOL
IS FOLL[$ 0M1N+1 0PAGE REF];ES,'
#1 A (DOT #1)
A ,5GLI% ;A #22
,G]MAN AH #23
,GREEK ALPHA #23
,HEBREW ALEPH #24
,RUSSIAN AH #25
AMP AMP (AMPLITUDE) #118
ANTILOG ANTILOG (ANTILOG>I?M)
#118
ARC >C (>C) #119
ARG >G (>GU;T) #119
#2 B (DOTS #1-2)
B ,5GLI% ;B #22
,G]MAN BEH #23
,GREEK 2TA #23
#1 A--#2 B #EBI
,RUSSIAN BEH #25 A#BAJ
#3 C (DOTS #1-4)
C ,5GLI% ;C #22
,G]MAN TSEH #23
,GREEK SAMPI #23
,RUSSIAN TSEH #25
----------------------------------#BAA
COLOG COLOG (COLOG>I?M) #119
COS COS (COS9E) #119
COSH CO% (HYP]BOLIC COS9E)
#119
COT COT (COTANG5T) #119
COTH CO? (HYP]BOLIC COTANG5T)
#119
COVERS COV]S (COV]S9E) #119
CSC CSC (COSECANT) #119
CSCH CS* (HYP]BOLIC COSECANT)
#119
CTN CTN (COTANG5T) #119
CTNH CTNH (HYP]BOLIC COTANG5T)
#119
,NEME? ,MA?4 ,CODE1 #1972 A#BAA
#4 D (DOTS #1-4-5)
D ,5GLI% ;D #22
,G]MAN DEH #23
,GREEK DELTA #23
,RUSSIAN DEH #25
DET DET (DET]M9ANT) #119
#5 E (DOTS #1-5)
E ,5GLI% ;E #22
,G]MAN EH #23
,GREEK EPSILON #23
,RUSSIAN YEH #25
----------------------------------#BAB
ERF ]F (]ROR FUNC;N) #119
EXP EXP (EXPON5TIAL) #119
EXSEC EXSEC (EXSECANT) #119
#6 F (DOTS #1-2-4)
F ,5GLI% ;F #22
,G]MAN EFF #23
,GREEK PHI #24
,HEBREW FEH #24
#2 B--#6 F #ECA
,RUSSIAN EFF #25 A#BAB
#7 G (DOTS #1-2-4-5)
G ,5GLI% ;G #22
,G]MAN <EH #23
,GREEK GAMMA #23
,HEBREW GIMEL #24
,RUSSIAN <EH #25
GRAD GRAD (GRADI5T) #119
#8 H (DOTS #1-2-5)
H ,5GLI% ;H #22
,G]MAN HAH #23
,HEBREW HEH #24
----------------------------------#BAC
,RUSSIAN KHAH #25
HAV HAV (HAV]S9E) #119
#9 I (DOTS #2-4)
I ,5GLI% ;I #22
,G]MAN EE #23
,GREEK IOTA #24
,RUSSIAN EE #25
IM IM (IMAG9>Y "P) #119
INF 9F (INFIMUM) #119
,NEME? ,MA?4 ,CODE1 #1972 A#BAC
#10 J (DOTS #2-4-5)
J ,5GLI% ;J #22
,G]MAN YAHT #23
,HEBREW YOD #24
,RUSSIAN ZHEH #25
#11 K (DOTS #1-3)
K ,5GLI% ;K #22
,G]MAN KAH #23
,GREEK KAPPA #24
,RUSSIAN KAH #25
----------------------------------#BAD
#12 L (DOTS #1-2-3)
L ,5GLI% ;L #22
,G]MAN ELL #23
,GREEK LAMBDA #24
,HEBREW LAM$ #24
,RUSSIAN ELL #25
LIM LIM (LIMIT) #119
LN LN (NATURAL LOG>I?M) #120
LOG LOG (LOG>I?M) #120
#6 F--#12 L #ECC
#13 M (DOTS A#BAD
#1-3-4)
M ,5GLI% ;M #22
,G]MAN EM #23
,GREEK MU #24
,HEBREW MEM #24
,RUSSIAN EM #25
MAX MAX (MAXIMUM) #120
MIN M9 (M9IMUM) #120
MOD MOD (MODULO) #120
#14 N (DOTS #1-3-4-5)
N ,5GLI% ;N #22
,G]MAN EN #23
----------------------------------#BAE
,GREEK NU #24
,HEBREW NUN #24
,RUSSIAN EN #25
#15 O (DOTS #1-3-5)
O B>B$ "R FULL >R[H1D
#146
,5GLI% ;O #22
,G]MAN OH #23
,GREEK OMICRON #24
,NEME? ,MA?4 ,CODE1 #1972 A#BAE
,RUSSIAN OH #25
333 CURV$ DIVI.N SIGN ON
O LEFT1 SEP>,N L9E ABV
#160
O CURV$ DIVI.N SIGN ON
333 LEFT1 SEP>,N L9E 2L
#161
O [ CURV$ DIVI.N SIGNS ON
333 LEFT & "R1 SEP>,N L9E
2L #161
#16 P (DOTS #1-2-3-4)
P ,5GLI% ;P #22
,G]MAN PEH #23
----------------------------------#BAF
,GREEK PI #24
,RUSSIAN PEH #25
#13 M--#16 P #ECE
#17 Q (DOTS #1-2- A#BAF
#3-4-5)
Q ,5GLI% ;Q #22
,G]MAN KOO #23
,GREEK KOPH (OR QOPH) #26
,HEBREW KOPH #24
,RUSSIAN *EH #25
#18 R (DOTS #1-2-3-5)
R ,5GLI% ;R #22
,G]MAN ]R #23
,GREEK RHO #24
,HEBREW RE% #25
,RUSSIAN ]R #25
RE RE (R1L "P) #120
#19 S (DOTS #2-3-4)
S ,5GLI% ;S #22
,G]MAN ESS #23
,GREEK SIGMA #24
,HEBREW SAMEKH #24
----------------------------------#BAG
,RUSSIAN ESS #25
,NEME? ,MA?4 ,CODE1 #1972 A#BAG
SEC SEC (SECANT) #120
SECH SE* (HYP]BOLIC SECANT)
#120
SIN S9 (S9E) #120
SINH S9H (HYP]BOLIC S9E) #120
SUP SUP (SUPREMUM) #120
#20 T (DOTS #2-3-4-5)
T ,5GLI% ;T #22
,G]MAN TEH #23
,GREEK TAU #24
,HEBREW TE? #24
,RUSSIAN TEH #25
TAN TAN (TANG5T) #120
TANH TANH (HYP]BOLIC TANG5T)
#120
#21 U (DOTS #1-3-6)
U ,5GLI% ;U #22
,G]MAN OO #23
,GREEK UPSILON #24
,RUSSIAN OO #25
#17 Q--#21 U #ECG
#22 V (DOTS #1-2- #BAH
#3-6)
V ,5GLI% ;V #22
,G]MAN FAO #23
,GREEK VAU #26
,HEBREW VE? #24
VERS V]S (V]S9E) #120
#23 X (DOTS #1-3-4-6)
X ,5GLI% ;X #22
,G]MAN IKS #23
,GREEK XI #24
,HEBREW *E? #24
,RUSSIAN %*AH #25
#24 Y (DOTS #1-3-4-5-6)
Y ,5GLI% ;Y #22
CURV$ "R FULL >R[H1D
#146
,G]MAN YPSILON #23
,GREEK PSI #24
#25 Z (DOTS #1-3-5-6)
Z ,5GLI% ;Z #22
,NEME? ,MA?4 ,CODE1 #1972 A#BAH
,G]MAN TSET #23
,GREEK ZETA #23
----------------------------------#BAI
,HEBREW ZAY9 #23
,RUSSIAN ZEH #25
#26 & (DOTS #1-2-3-4-6)
& CURV$ LEFT FULL >R[H1D
#146
FACTORIAL #152
,GREEK *I #24
#27 = (DOTS #1-2-3-4-5-6)
= BLUNT$ LEFT FULL >R[H1D
JADF
BLUNT$ "R FULL >R[H1D
#146
#22 V--#27 = #ECI
G5]AL OMIS.N SYMBOL A#BAI
#70
#28 ( (DOTS #1-2-3-5-6)
( LEFT P>5!SIS #122
#29 ! (DOTS #2-3-4-6)
! ,GREEK /IGMA #26
,HEBREW TSADI #24
S+LE 9TEGRAL #152
,RUSSIAN Y]IH #25
!! D\# 9TEGRAL #152
!!! TRIPLE 9TEGRAL #153
----------------------------------#BBJ
!@$C] 9TEGRAL ) SUP]POS$
CIRCLE #153
,NEME? ,MA?4 ,CODE1 #1972 A#BBJ
!@$R] 9TEGRAL ) SUP]POS$
RECTANGLE #153
!@$4] 9TEGRAL ) SUP]POS$
SQU>E #153
!@,=] 9TEGRAL ) SUP]POS$
9F9;Y #153
#30 ) (DOTS #2-3-4-5-6)
) "R P>5!SIS #122
#31 * (DOTS #1-6)
* DOT1 & "TS #128, #129
,HEBREW *APH #24
*@_"K] DOT )9 9CLU.N SIGN
#140
#27 =--#31 * #EDA
*@_.1] DOT )9 REV]SE B#BBJ
9CLU.N SIGN #140
*@.K] DOT 2T B>S ( EQUALS
SIGN #140
#32 < (DOTS #1-2-6)
< DIRECTLY-OV] 9DICATOR
(F/ ORD]) #97
9DEX-(-RADICAL 9DICATOR
#108
MAKES NE>] >R[H1D PO9T
UP #145
<< DIRECTLY-OV] 9DICATOR
(SECOND ORD]) #97
<LIM UPP] LIMIT #119
<! UPP] 9TEGRAL #153
,NEME? ,MA?4 ,CODE1 #1972 #BBA
#33 % (DOTS #1-4-6)
% DIRECTLY-"U 9DICATOR (F/
ORD]) #97
MAKES NE>] >R[H1D PO9T
D[N #145
%LIM L[] LIMIT #120
%! L[] 9TEGRAL #153
%% DIRECTLY-"U 9DICATOR
(SECOND ORD]) #97
#34 ? (DOTS #1-4-5-6)
? ,GREEK !TA #23
,HEBREW ?AV #24
OP5+ SIMPLE-FRAC;N 9DICATOR
#75
#31 *--#34 ? #EDC
#35 : (DOTS A#BBA
#1-5-6)
: ,GREEK ETA #23
,HEBREW S9 #24
HORIZONTAL B> (MACRON)
#98
,RUSSIAN %AH #25
:@% B> OV] LOGICAL PRODUCT
#138
:@%: B> OV] & B> "U LOGICAL
PRODUCT #138
:@%.K B> OV] & EQUALS SIGN
"U LOGICAL PRODUCT
#138
:@: B> OV] S+LE TILDE
#139
:@:@: B> OV] D\# TILDE
#139
,NEME? ,MA?4 ,CODE1 #1972 #BBB
:@+ B> OV] LOGICAL SUM
#139
:@+: B> OV] & B> "U LOGI-
CAL SUM #139
:@+.K B> OV] & EQUALS SIGN
"U LOGICAL SUM #139
:@_"K] B> "? 9CLU.N SIGN
#141
:@_.1] B> "? REV]SE 9CLU.N
SIGN #141
:_"K B> OV] 9CLU.N SIGN
#138
:_.1 B> OV] REV]SE 9CLU.N
SIGN #138
#35 : #EDE
A#BBB
:"K B> OV] LESS ?AN SIGN
#138
OR
:.1 B> OV] GRT] ?AN SIGN
#137
OR
#36 $ (DOTS #1-2-4-6)
$ ,HEBREW AY9 #24
,RUSSIAN YAH #25
%APE 9DICATOR #110
$A >C 3CAVE UPW>D #110
$C CIRCLE #111
$C_$*] CIRCLE ) 9T]IOR
DOT #112
,NEME? ,MA?4 ,CODE1 #1972 B#BBB
$C_$$<33O] CIRCLE ) IN-
T]IOR >R[ PO9T+ UP
#112
$C_$$<33O"$%33O] CIRCLE
) 9T]IOR >R[ PO9T+
UP FOLL[$ 09T]IOR
>R[ PO9T+ D[N #112
$C_$$%33O] CIRCLE ) IN-
T]IOR >R[ PO9T+ D[N
#112
$C_$$%33O"$<33O] CIRCLE
) 9T]IOR >R[ PO9T+
D[N FOLL[$ 09T]IOR
>R[ PO9T+ UP #112
----------------------------------#BBC
$C_$$[33] CIRCLE ) IN-
T]IOR >R[ PO9T+ LEFT
#112
#35 :--#36 $ #EDG
$C_$$[33$33O] CIRCLE A#BBC
) 9T]IOR >R[ PO9T+
LEFT OV] 9T]IOR >R[
PO9T+ "R #112
$C_$$33O] CIRCLE ) IN-
T]IOR >R[ PO9T+ "R
#112
$C_$$33O$[33] CIRCLE )
9T]IOR >R[ PO9T+ "R
OV] 9T]IOR >R[ PO9T+
LEFT #112
$C_$+] CIRCLE ) 9T]IOR
PLUS SIGN #112
$C_$-] CIRCLE ) 9T]IOR
M9US SIGN #112
,NEME? ,MA?4 ,CODE1 #1972 B#BBC
$C_$@*] CIRCLE ) 9T]IOR
CROSS #112
$D DIAMOND #111
$E ELLIPSE (OVAL) #111
$G P>ALLELOGRAM #111
$H RHOMBUS #111
$HX IRREGUL> HEXAGON
JAAA
$I 9T]SECT+ L9ES #111
#36 $ #EDI
C#BBC
$L IS P>ALLEL TO #111
$O >R[ B>B$ AT "R (CON-
TRACT$ =M) #98, #135
"R-PO9T+ >R[ (CON-
TRACT$ =M) #110
$P IS P]P5DICUL> TO #111
$PG IRREGUL> P5TAGON
#111
$Q QUADRILAT]AL #111
$R RECTANGLE #111
,NEME? ,MA?4 ,CODE1 #1972 D#BBC
$S /> #52, #111, #130
----------------------------------#BBD
$T REGUL> TRIANGLE
(EQUILAT]AL) #112
$T.A] ACUTE TRIANGLE #113
$T.I] ISOSCELES TRIANGLE
#113
$T.O] OBTUSE TRIANGLE
#113
$T.R] "R TRIANGLE #114
#36 $ #EEA
A#BBD
$T.S] SCAL5E TRIANGLE
#114
$Z TRAPEZOID #111
$*33 >R[ DOTT$ AT LEFT
(NO B>B) #98
$*33O >R[ DOTT$ AT LEFT
& B>B$ AT "R #98
$*33* >R[ DOTT$ AT BO?
5DS #98
$<[33O V]TICAL TWO-WAY
>R[ #135
$<33O >R[ PO9T+ UP #135
,NEME? ,MA?4 ,CODE1 #1972 B#BBD
$<33O"$%33O >R[ PO9T+ UP
FOLL[$ 0>R[ PO9T+ D[N
#140
$<33O"$%_33O >R[ PO9T+ UP
FOLL[$ 0BOLDFACE >R[
PO9T+ D[N #140
$<_33O"$%33O BOLDFACE >R[
PO9T+ UP FOLL[$ 0>R[
PO9T+ D[N #140
$<_33O"$%_33O BOLDFACE
>R[ PO9T+ UP FOLL[$
0BOLDFACE >R[ PO9T+
D[N #140
#36 $ #EEC
C#BBD
$%33O >R[ PO9T+ D[N #135
$%33O"$<33O >R[ PO9T+
D[N FOLL[$ 0>R[
PO9T+ UP #140
$%33O"$<_33O >R[ PO9T+
D[N FOLL[$ 0BOLDFACE
>R[ PO9T+ UP #140
$%_33O"$<33O BOLDFACE
>R[ PO9T+ D[N FOLL[$
0>R[ PO9T+ UP #140
----------------------------------#BBE
$%_33O"$<_33O BOLDFACE
>R[ PO9T+ D[N FOLL[$
0BOLDFACE >R[ PO9T+
UP #140
,NEME? ,MA?4 ,CODE1 #1972 A#BBE
$[ ANGLE #110
$[33 >R[ B>B$ AT LEFT
#98
LEFT-PO9T+ >R[ #110
$[33O >R[ B>B$ AT BO?
5DS #98
HORIZONTAL TWO-WAY >R[
#135
$[33* >R[ B>B$ AT LEFT &
DOTT$ AT "R #98
$[33$_33O >R[ PO9T+ LEFT
OV] BOLDFACE >R[
PO9T+ "R #137
#36 $ #EEE
$[33.* >R[ ) HOLL[ B#BBE
DOT AT "R & B>B$ AT
LEFT #98
$[.AE] ALT]NATE EXT]IOR
ANGLES #113
$[.AI] ALT]NATE 9T]IOR
ANGLES #113
$[.CP] -PLE;T>Y ANGLES
#113
$[.C] CORRESPOND+ ANGLES
#113
,NEME? ,MA?4 ,CODE1 #1972 C#BBE
$[.E] EXT]IOR ANGLES
#113
$[.I] 9T]IOR ANGLES
#113
$[.J] ADJAC5T ANGLES
#113
$[.O] OBTUSE ANGLE #113
$[.R] "R ANGLE #113
$[.S] /RAI<T ANGLE #113
#36 $ #EEG
$[.SP] SUPPLE;T>Y AN- D#BBE
GLES #113
$[.V] V]TICAL ANGLES
#113
----------------------------------#BBF
$[_$$A] ANGLE ) 9T]IOR
>C #112
$[_$$[59] ANGLE ) 9T]IOR
CLOCKWISE >R[ #112
$[_$$59O] ANGLE ) 9T]IOR
C.T]CLOCKWISE >R[
#112
,NEME? ,MA?4 ,CODE1 #1972 A#BBF
$3O$[333 %ORT >R[ PO9T+
"R OV] L;G >R[ PO9T+
LEFT #137
$33O >R[ B>B$ AT "R (UN-
3TRACT$ =M) #98
$33O$[33 >R[ PO9T+ "R OV]
>R[ PO9T+ LEFT #137
$33O$_[33 >R[ PO9T+ "R
OV] BOLDFACE >R[
PO9T+ LEFT #137
$33* >R[ DOTT$ AT "R (NO
B>B) #98
$333O$[3 L;G >R[ PO9T+ "R
OV] %ORT >R[ PO9T+
LEFT #137
#36 $ #EEI
$33@O$,[33 >R[ ) UPP] B#BBF
B>B PO9T+ "R OV] >R[
) L[] B>B PO9T+ LEFT
#137
$33.* >R[ ) HORL[ DOQ AT
"R (NO B>B) #98
$4 SQU>E #111
$4_$*] SQU>E ) 9T]IOR DOT
#113
$4_$:] SQU>E ) 9T]IOR
HORIZONTAL B> #113
$4_$\] SQU>E ) 9T]IOR
V]TICAL B> #113
$4_$5] SQU>E ) 9T]IOR
NOR?WE/-S\?EA/ DIAG-
ONAL #113
,NEME? ,MA?4 ,CODE1 #1972 C#BBF
$4_$5@9] SQU>E ) 9T]IOR
DIAGONALS #112
$4_$9] SQU>E ) 9T]IOR
S\?WE/-NOR?EA/ DIAG-
ONAL #113
$5 REGUL> P5TAGON #111
$6 REGUL> HEXAGON #111
----------------------------------#BBG
$' >C 3CAVE D[NW>D #110
$_[33$33O BOLDFACE >R[
PO9T+ LEFT OV] >R[
PO9T+ "R #137
#36 $ #EFA
$_[33$_33O BOLDFACE >R[ A#BBG
PO9T+ LEFT OV] BOLD-
FACE >R[ PO9T+ "R
#137
$_33O$[33 BOLDFACE >R[
PO9T+ "R OV] >R[
PO9T+ LEFT #137
$_33O$_[33 BOLDFACE >R[
PO9T+ "R OV] BOLD-
FACE >R[ PO9T+ LEFT
#137
$_4 FILL$-IN SQU>E #130
$.*33 >R[ ) HOLL[ DOT AT
LEFT (NO B>B) #98
$.*33O >R[ ) HOLL[ DOT AT
LEFT & B>B$ AT "R
#98
,NEME? ,MA?4 ,CODE1 #1972 B#BBG
$.*33.* >R[ ) HOLL[ DOT
AT BO? 5DS #98
#37 ] (DOTS #1-2-4-5-6)
] CLOS+ C.ELL,N 9DICATOR #73
T]M9,N 9DICATOR #5, #6
#38 \ (DOTS #1-2-5-6)
\ ,RUSSIAN YU #25
/RAI<T LEFT FULL >R[H1D
#146
/RAI<T "R FULL >R[H1D
#146
V]TICAL B> Z A SIGN (
GR\P+ #123
V]TICAL B> (IS A FACTOR1
DIVIDES) #130
V]TICAL B> (S* THAT)
#136
#36 $--#38 \ #EFC
C#BBG
\\ D\# V]TICAL B> #123
----------------------------------#BBH
\@$[33] V]TICAL B> "?
%AFT ( >R[ PO9T+ LEFT
#141
\@$33O] V]TICAL B> "?
%AFT ( >R[ PO9T+ "R
#141
#39 [ (DOTS #2-4-6)
[ B>B$ LEFT FULL >R[H1D
#145
3TRAC;N = -MA & OP;NAL
SPACE AT SUP]SCRIPT OR
SUBSCRIPT LEVEL #82
OP5+ C.ELL,N 9DICATOR #73
,RUSSIAN EH #25
[ CURV$ DIVI.N SIGN ON "R1
333 SEP>,N L9E 2L #161
,NEME? ,MA?4 ,CODE1 #1972 A#BBH
#40 W (DOTS #2-4-5-6)
W ,5GLI% ;W #22
,G]MAN VEH #23
,GREEK OMEGA #24
,HEBREW VAV #24
,RUSSIAN VEH #25
#41 1 (DOT #2)
1 NUM]AL #1 #7
LIT]>Y -MA #42
111 DOTT$ >R[ %AFT #145 111
----------------------------------#BBI
#42 2 (DOTS #2-3)
2 NUM]AL #2 #7
SEMICOLON #42
#38 \--#42 2 #EFE
#43 3 (DOTS #2-5) B#BBI
3 COLON #41
NUM]AL #3 #7
%ORT S+LE >R[ %AFT #145
33 ORD9>Y S+LE >R[ %AFT
#145
333 L;G S+LE >R[ %AFT
#145
SEP>,N L9E (V>Y+ 9
L5G?) #161
3 3 DA%$ >R[ %AFT #145
33333 HORIZONTAL FRAC;N
L9E 9 SPATIAL >RANGE;T
(V>Y+ 9 L5G?) #76
,NEME? ,MA?4 ,CODE1 #1972 C#BBI
333 CURV$ DIVI.N SIGN ON
O LEFT1 SEP>,N L9E
ABV #160
333 CURV$ DIVI.N SIGNS ON
O [ LEFT & "R1 SEP>,N
L9E ABV #160
333 CURV$ DIVI.N SIGN ON
[ "R1 SEP>,N L9E
ABV #160
333 /RAI<T OR SLANT DI-
_ VI.N SIGN ON LEFT1
SEP>,N L9E ABV
#160
----------------------------------#BCJ
/RAI<T DIVI.N SIGNS
333 ON LEFT & "R1 SEPA-
_ _ R,N L9E ABV #161
#43 3 #EFG
333 /RAI<T OR SLANT A#BCJ
_ DIVI.N SIGN ON "R1
SEP>,N L9E ABV
#160 OR
#44 4 (DOTS #2-5-6)
4 NUM]AL #4 #7
P]IOD #42
#45 5 (DOTS #2-6)
5 NUM]AL #5 #7
59 CURV$ >R[ %AFT #145
OR
,NEME? ,MA?4 ,CODE1 #1972 B#BCJ
#46 6 (DOTS #2-3-5)
6 EXCLAM,N PO9T #42
NUM]AL #6 #7
#47 7 (DOTS #2-3-5-6)
7 NUM]AL #7 #7
%ORT D\# >R[ %AFT #145
77 ORD9>Y D\# >R[ %AFT
#145
----------------------------------#BCA
777 L;G D\# >R[ %AFT
#145
77777 C>RI$-NUMB] 9DICATOR
= A4I;N (V>Y+ 9 L5G?)
#161
#43 3--#47 7 #EFI
#48 8 (DOTS #2-3- A#BCA
#6)
8 LEFT \T] QUOT,N M>K #42
NUM]AL #8 #7
"Q M>K #42
#49 9 (DOTS #3-5)
9 NUM]AL #9 #7
935 WAVY >R[ %AFT #145
#50 0 (DOTS #3-5-6)
0 NUM]AL #0 #7
"R \T] QUOT,N M>K #42
0' "R 9N] QUOT,N M>K #42
,NEME? ,MA?4 ,CODE1 #1972 B#BCA
#51 / (DOTS #3-4)
/ NEG,N SIGN #141
HORIZONTAL SIMPLE FRAC;N
L9E #75
/$L IS N P>ALLEL TO #111
/$P IS N P]P5DICUL> TO
#111
/,* X DOES N FOLL[ T
#153
----------------------------------#BCB
#52 + (DOTS #3-4-6)
+ REGUL> PLUS #129
+- PLUS OR M9US #130
#48 8--#52 + #EGA
+"- REGUL> PLUS FOLL[$ A#BCB
0REGUL> M9US #130
+"_- REGUL> PLUS FOLL[$
0BOLDFACE M9US #130
#53 # (DOTS #3-4-5-6)
# CLOS+ SIMPLE-FRAC;N 9DICATOR
#75
NUM]IC 9DICATOR #7
#54 > (DOTS #3-4-5)
> RADICAL (SQU>E ROOT)
#108
#55 ' (DOT #3)
' APO/ROPHE #41
PRIME #153
''' ELLIPSIS #42
,NEME? ,MA?4 ,CODE1 #1972 B#BCB
#56 - (DOTS #3-6)
- HYPH5 #42
REGUL> M9US #129
-+ M9US OR PLUS #129
-- %ORT DA% #42
----------------------------------#BCC
---- L;G DA% #42
-"+ REGUL> M9US FOLL[$
0REGUL> PLUS #129
-"_+ REGUL> M9US FOLL[$
0BOLDFACE PLUS #129
#57 @ (DOT #4)
@ SCRIPT-TYPE 9DICATOR #36
SUP]POSI;N 9DICATOR #97
#52 +--#57 @ #EGC
A#BCC
@A AT #152
@C C5T #152
@D "PIAL DERIVATIVE (R.D
;D) #153
@E MEMB]%IP (IS AN ELE;T
OF) #135
@H CROSS$ ;H #152
@L P.D /]L+ #153
,NEME? ,MA?4 ,CODE1 #1972 B#BCC
@O B>B$ "R UPP] >R[H1D
#146
@S DOLL> SIGN #142
@Y CURV$ "R UPP] >R[H1D
#146
@& CURV$ LEFT UPP] >R[H1D
#146
UNIV]SAL QUANTIFI]
(FOR ALL1 = EA*1
= EVERY) #143
@= BLUNT$ LEFT UPP] >R[H1D
#146
BLUNT$ "R UPP] >R[H1D
#146
#57 @ #EGE
EXI/5TIAL QUANTIFI] C#BCC
(THERE EXI/S1 =
"S) #143
@=\ EXI/5TIAL QUANTIFI]
(THERE EXI/S UNIQUELY
= EXACTLY "O) #143
----------------------------------#BCD
@( LEFT SQU>E BRACKET
#122
@) "R SQU>E BRACKET
#122
@* CROSS (,C>TESIAN PROD-
UCT1 MULTIPLIC,N SIGN)
#137
@<,< EQUIVAL;E #129
@% LOGICAL PRODUCT (AND1
MEET) #129
,NEME? ,MA?4 ,CODE1 #1972 A#BCD
@%: B> "U LOGICAL PRODUCT
#138
@%.K EQUALS SIGN "U LOGI-
CAL PRODUCT #138
@: SIMPLE TILDE (IS RELAT$
TO1 IS SIMIL>) #136
@:: B> "U S+LE TILDE #139
@:@: D\# TILDE #139
@:@:: B> "U D\# TILDE #139
@:@:.K EQUALS SIGN "U D\#
TILDE #139
#57 @ #EGG
@:.K EQUALS SIGN "U B#BCD
S+LE TILDE #139
@$ CROSS$ ;D #152
@] G5]AL REF];E 9DICATOR
#52
@\ /RAI<T LEFT UPP] >R[H1D
#146
/RAI<T "R UPP] >R[H1D
#146
@[ B>B$ LEFT UPP] >R[H1D
#146
@5 REV]SE MEMB]%IP (CON-
TA9S ! ELE;T) #136
,NEME? ,MA?4 ,CODE1 #1972 C#BCD
@0 P]C5T SIGN #153
@/ S9CE (BECAUSE) #153
----------------------------------#BCE
@+ LOGICAL SUM (JO91 OR)
#129
@+: B> "U LOGICAL SUM #139
@+.K EQUALS SIGN "U LOGI-
CAL SUM #139
@# A/]ISK #52, #128
@> *ECK M>K #152
@@ ,RUSSIAN-LR 9DICATOR #22
#57 @ #EGI
@@@ L[]-CASE SCRIPT A#BCE
,RUSSIAN-LR 9DICATOR
#208
@@, CAPITAL ,RUSSIAN-LR
9DICATOR #208
@@@, CAPITAL SCRIPT ,RUSSIAN-LR
9DICATOR #208
@^( UPP] LEFT HALF-BRACKET
#123
@^) UPP] "R HALF-BRACKET
#123
@^,( UPP]-LEFT 5L>G$ HALF-
BRACKET #123
@^,) UPP]-"R 5L>G$ HALF-
BRACKET #123
@_ L[]-CASE SCRIPT ,G]MAN-LR
9DICATOR #208
,NEME? ,MA?4 ,CODE1 #1972 B#BCE
@_( LEFT B>R$ BRACKET #123
@_) "R B>R$ BRACKET #123
@_, CAPITAL SCRIPT ,G]MAN-LR
9DICATOR #208
@_,( LEFT 5L>G$ B>R$ BRACKET
JABC
@_,) "R 5L>G$ B>R$ BRACKET
#123
@. L[]-CASE SCRIPT ,GREEK-LR
9DICATOR #208
@.L CROSS$ LAMBDA #152
#57 @ #EHA
@., CAPITAL SCRIPT #BCF
,GREEK-LR 9DICATOR #208
@; L[]-CASE SCRIPT ,5GLI%-LR
9DICATOR #208
@;( L[] LEFT HALF-BRACKET
#123
@;) L[] "R HALF-BRACKET
#123
@;,( L[]-LEFT 5L>G$ HALF-
BRACKET #123
@;,) L[]-"R 5L>G$ HALF-
BRACKET #123
@,A ANG/ROM UNIT #152
,NEME? ,MA?4 ,CODE1 #1972 A#BCF
@,P P>AGRAPH M>K #52, #129
@,R CROSS$ ;,R #152
@,S S+LE SEC;N M>K #52,
#130
@,S@,S D\# SEC;N M>K #52
@,( 5L>G$ LEFT SQU>E BRACKET
#122
@,) 5L>G$ "R SQU>E BRACKET
#122
@,: EXT5D$ TILDE #136
#57 @ #EHC
@,, L[]-CASE SCRIPT ,HE- B#BCF
BREW-LR 9DICATOR #208
#58 ^ (DOTS #4-5)
^ ELEVATES NE>] >R[H1D BY #45
DEGREES #145
SUP]SCRIPT 9DICATOR #82
^^ SUP]SCRIPT ) SUP]SCRIPT 9DI-
CATOR #82
^^^ SUP]SCRIPT ) SUP]SCRIPT )
SUP]SCRIPT 9DICATOR #82
----------------------------------#BCG
^^; SUP]SCRIPT ) SUP]SCRIPT )
SUBSCRIPT 9DICATOR #82
^; SUP]SCRIPT ) SUBSCRIPT 9DI-
CATOR #82
^;^ SUP]SCRIPT ) SUBSCRIPT )
SUP]SCRIPT 9DICATOR #82
^;; SUP]SCRIPT ) SUBSCRIPT )
SUBSCRIPT 9DICATOR #82
#59 _ (DOTS #4-5-6)
_ BOLDFACE-TYPE 9DICATOR #36
FILL$-IN %APE 9DICATOR #110
,G]MAN-LR 9DICATOR #21
,NEME? ,MA?4 ,CODE1 #1972 A#BCG
PUNCTU,N 9DICATOR #110
T,Y M>K #153
V]TICAL L9E US$ 9 DIVI.N
>RANGE;TS (V>Y+ 9 L5G?)
#161
_L ID5TIFY (IS 3GRU5T TO1
IS ID5TICAL WITH) #135
_& AMP]S& (AND1 LOGICAL
PRODUCT) #128
_= V>I,N (V>IES AS) #136
_* BACK SLA% (DIVIDES1 IS
A FACTOR OF) #128
#57 @--#59 _ #EHE
_< C>ET (CIRCUMFLEX) B#BCG
#99, #152
_% 9V]T$ C>ET #99
_? OP5+ FRAC;NAL-"P-(-
MIX$-NUMB] 9DICATOR #75
_$ 9T]IOR %APE-MODIFIC,N 9DI-
CATOR #110
_] S+LE DA7] #52, #128
----------------------------------#BCH
_\ BOLDFACE S+LE V]TICAL B>
#123
BOLDFACE V]TICAL B> (5D
( PROOF) #153
_\_\ BOLDFACE D\# V]TICAL
B> #123
,NEME? ,MA?4 ,CODE1 #1972 A#BCH
_ /RAI<T OR SLANT OR
333 DIVI.N SIGN ON
LEFT1 SEP>,N L9E
2L #161
_ _ /RAI<T DIVI.N SIGNS
333 ON LEFT & "R1
SEP>,N L9E 2L #161
_ /RAI<T OR SLANT OR
333 DIVI.N SIGN ON
"R1 SEP>,N L9E
2L #161
_ SYN!TIC DIVI.N )
_ /RAI<T L9E ON
333 LEFT1 SEP>,N L9E
2L #162
#59 _ #EHG
SYN!TIC DIVI.N ) B#BCH
_ /RAI<T L9E ON "R1
_ SEP>,N L9E 2L
333 #162
_8 "Q M>K (AS A MODIFI])
#99
_0 EMPTY SET (REPRES5T$
0Z]O ) V]TICAL OR OR
OBLIQUE B> "? IT)
#152
_/ DIAGONAL L9E OR SLA%
#75
DIAGONAL FRAC;N L9E
#128
----------------------------------#BCI
_+ BOLDFACE PLUS #129
,NEME? ,MA?4 ,CODE1 #1972 A#BCI
_+"- BOLDFACE PLUS FOLL[$
0REGUL> M9US #129
_+"_- BOLDFACE PLUS FOL-
L[$ 0BOLDFACE M9US
#129
_# CLOS+ FRAC;NAL-"P-(-MIX$-
NUMB] 9DICATOR #75
_- BOLDFACE M9US #129
_-"+ BOLDFACE M9US FOLL[$
0REGUL> PLUS #129
_-"_+ BOLDFACE M9US FOL-
L[$ 0BOLDFACE PLUS
#129
_@( BOLDFACE LEFT SQU>E
BRACKET #122
#59 _ #EHI
_@) BOLDFACE "R SQU>E B#BCI
BRACKET #122
_@@ L[]-CASE BOLDFACE ,RUSSIAN-
LR 9DICATOR #208
_@@, CAPITAL BOLDFACE ,RUSSIAN-
LR 9DICATOR #208
__ L[]-CASE BOLDFACE ,G]MAN-LR
9DICATOR #208
__] D\# DA7] #52
__, CAPITAL BOLDFACE ,G]MAN-LR
9DICATOR #208
_"K 9CLU.N SIGN (IS 3TA9$
IN1 IS A SUBSET OF)
#135
_"K: B> "U 9CLU.N SIGN (IS
A SUBSET OF) #138
,NEME? ,MA?4 ,CODE1 #1972 C#BCI
_"K@.K] 9CLU.N SIGN "?
EQUALS SIGN #141
_"K.K EQUALS SIGN "U IN-
CLU.N SIGN (IS A SUB-
SET OF) #138
_K L[]-CASE BOLDFACE ,GREEK-LR
9DICATOR #208
_.K BOLDFACE EQUALS SIGN
#A35
_.1 REV]SE 9CLU.N SIGN
(3TA9S1 IMPLIES) #136
----------------------------------#BDJ
_.1: B> "U REV]SE 9CLU.N
SIGN #139
_.1@.K] REV]SE 9CLU.N
SIGN "? EQUALS SIGN
#141
#59 _ #EIA
_.1.K EQUALS SIGN "U A#BDJ
REV]SE 9CLU.N SIGN
#139
_., CAPITAL BOLDFACE
,GREEK-LR 9DICATOR #208
_; L[]-CASE BOLDFACE ,5GLI%-LR
9DICATOR #208
_;, CAPITAL BOLDFACE ,5GLI%-LR
9DICATOR #208
_, CAPITAL ,G]MAN-LR 9DICATOR
#208
_,' CLOS+ BOLDFACE TYPE 9DICATOR
= ^WS1 PHRASES1 & MA!MATICAL
/ATE;TS #36
#60 " (DOT #5)
" BASE-L9E 9DICATOR #82
MULTIPURPOSE 9DICATOR
#158
"K LESS ?AN SIGN (REGUL>)
#135
,NEME? ,MA?4 ,CODE1 #1972 B#BDJ
"K: B> "U LESS ?AN SIGN
(IS LESS ?AN OR
EQUAL TO) #138
"K@"K] NE/ ( TWO LESS ?AN
SIGNS ) /RAI<T SIDES
(IS SMALL -P>$ WITH)
#141
"K".K".1 LESS ?AN SIGN
FOLL[$ 0EQUALS SIGN
FOLL[$ 0GRT] ?AN
SIGN #140
"K".1 LESS ?AN SIGN
FOLL[$ 0GRT] ?AN
SIGN #140
"K.K EQUALS SIGN "U LESS
?AN SIGN (IS LESS ?AN
OR EQUAL TO) #138
#59 _--#60 " #EIC
":<_<] C>ET OV] HORI- C#BDJ
ZONTAL B> #136
":%*] DOT "U HORIZONTAL
B> #137
":%_<] C>ET "U HORIZONTAL
B> (IS P]SPECTIVE TO1
P]SPECTIVE CORRE-
SPOND;E) #138
"1 RATIO SIGN (IS TO) #135
----------------------------------#BDA
"@:%*] DOT "U SIMPLE TILDE
#137
".K<*] DOT OV] EQUALS SIGN
(IS APPROXIMATELY EQUAL
TO) #136
".K<$T] EQUILAT]AL TRIANGLE
OV] EQUALS SIGN #136
,NEME? ,MA?4 ,CODE1 #1972 A#BDA
".K<\] V]TICAL B> OV]
EQUALS SIGN #136
".K<_<] C>ET OV] EQUALS
SIGN #136
".K<_%] 9V]T$ C>ET OV]
EQUALS SIGN #136
".K<_8] "Q M>K OV] EQUALS
SIGN #136
".K<.*] DEGREE SIGN OV]
EQUALS SIGN (IS
EQUAL 9 DEGREES TO)
#136
#60 " #EIE
".K<;<] LEFT-PO9T+ C>ET B#BDA
OV] EQUALS SIGN #136
".K<;%] "R-PO9T+ C>ET OV]
EQUALS SIGN #136
".K%**<**] TWO DOTS OV] &
TWO DOTS "U EQUALS
SIGN #136
".K%*<*] DOT OV] & DOT "U
EQUALS SIGN #136
".K%_<] C>ET "U EQUALS
SIGN (IS PROJECTIVE
TO1 PROJECTIVE CORRE-
SPOND;E) #136
#61 . (DOTS #4-6)
. DECIMAL PO9T (,AM]ICAN
& ,3T95TAL) #7
F/ 9N] RADICAL 9DICATOR #108
,NEME? ,MA?4 ,CODE1 #1972 C#BDA
,GREEK-LR 9DICATOR = /&>D
LRS #22
,GREEK-LR 9DICATOR #22
ITALIC-TYPE 9DICATOR #36
%AD$ %APE 9DICATOR #110
/RUCTURAL %APE-MODIFIC,N 9DI-
CATOR #110
----------------------------------#BDB
.K REGUL> EQUALS SIGN (IS
EQUAL TO) #135
.K@% EQUALS SIGN OV] LOG-
ICAL PRODUCT #138
.K@%: EQUALS SIGN OV] &
B> "U LOGICAL PRODUCT
#138
#60 "--#61 . #EIG
.K@%.K EQUALS SIGN OV] A#BDB
& EQUALS SIGN "U
LOGICAL PRODUCT #138
.K@: EQUALS SIGN OV] S+LE
TILDE #139
.K@:@: EQUALS SIGN OV] D\#
TILDE #139
.K@+ EQUALS SIGN OV] LOG-
ICAL SUM #139
.K@+: EQUALS SIGN OV] &
B> "U LOGICAL SUM
#139
.K@+.K EQUALS SIGN OV] &
EQUALS SIGN "U LOGI-
CAL SUM #139
,NEME? ,MA?4 ,CODE1 #1972 B#BDB
.K@_"K] EQUALS SIGN )
SUP]POS$ 9CLU.N SIGN
#141
.K@_.1] EQUALS SIGN )
SUP]POS$ REV]SE IN-
CLU.N SIGN #141
.K_"K EQUALS SIGN OV] IN-
CLU.N SIGN (IS A SUB-
SET OF) #141
.K_.1 EQUALS SIGN OV] RE-
V]SE 9CLU.N SIGN #139
.K"K EQUALS SIGN OV] LESS
?AN (IS EQUAL TO OR
LESS ?AN) #138
#61 . #EII
.K.1 EQUALS SIGN OV] C#BDB
GRT] ?AN (IS EQUAL TO
OR GRT] ?AN) #137
.( LEFT CURLY BRACE #123
.( .) EMPTY SET (REPRES5T$
0FAC+ BRACES) #152
.) "R CURLY BRACE #123
.* DEGREE SIGN #152
HOLL[ DOT #128
,NEME? ,MA?4 ,CODE1 #1972 #BDC
.% 9T]SEC;N SIGN (CAP)
#129
.%: B> "U 9T]SEC;N SIGN
#137
.%.K EQUALS SIGN "U 9T]-
953,4 9974 #138
.$ DEL (NABLA1 GRADI5T),
9V]T$ TRIANGLE #152
.1 GRT] ?AN SIGN (REGUL>)
#135
.1: B> "U GRT] ?AN SIGN
(IS GRT] ?AN OR OR
EQUAL TO) #137
#61 . #FJA
.1""K GRT] ?AN SIGN A#BDC
FOLL[$ 0LESS ?AN SIGN
#140
.1".K""K GRT] ?AN SIGN
FOLL[$ 0EQUALS SIGN
FOLL[$ 0LESS ?AN
SIGN #140
.1@.1] NE/ ( TWO GRT] ?AN
SIGNS ) /RAI<T SIDES
(IS L>GE -P>$ WITH)
#141
.1.K EQUALS SIGN "U GRT]
?AN (IS GRT] ?AN OR
EQUAL TO) #137
./ DIVI.N SIGN (DIVID$
BY) #128
.+ UNION SIGN (CUP) #130
,NEME? ,MA?4 ,CODE1 #1972 B#BDC
.+: B> "U UNION SIGN #140
.+.K EQUALS SIGN "U UNION
SIGN #140
.# NUMB] SIGN2 CROSSHAT*2
TIC-TAC-TOE2 P.DS
GD@AEFG JABI
.- M9US ) DOT OV] (PROP]
DI6];E) #129
.@ ,GREEK-LR 9DICATOR = ALT]NA-
TIVE LRS #22
.@@ L[]-CASE ITALIC ,RUSSIAN-LR
9DICATOR #208
.@@, CAPITAL ITALIC ,RUSSIAN-LR
9DICATOR #208
._ L[]-CASE ITALIC ,G]MAN-LR
9DICATOR #208
#61 . #FJC
C#BDC
._( B>R$ LEFT BRACE #123
----------------------------------#BDD
._) B>R$ "R BRACE #123
._, CAPITAL ITALIC ,G]MAN-LR
9DICATOR #208
._,( 5L>G$ LEFT B>R$ BRACE
#123
._,) 5L>G$ "R B>R$ BRACE
#123
."K LESS ?AN SIGN ) CURV$
SIDES #135
,NEME? ,MA?4 ,CODE1 #1972 A#BDD
."K@."K] NE/ ( TWO LESS
?AN SIGNS ) CURV$
SIDES #141
.. SECOND 9N] RADICAL 9DICATOR
#108
L[]-CASE ITALIC ,GREEK-LR
9DICATOR #208
..( LEFT ANGLE BRACKET
(ANGUL> P>5!SIS) #123
..) "R ANGLE BRACKET
(ANGUL> P>5!SIS) #123
..1 GRT] ?AN SIGN ) CURV$
SIDES #135
..1@..1] NE/ ( TWO GRT]
?AN SIGNS ) CURV$
SIDES #141
... ?IRD 9N] RADICAL 9DICATOR
#108
#61 . #FJE
.., CAPITAL ITALIC B#BDD
,GREEK-LR 9DICATOR #208
..,( LEFT 5L>G$ ANGUL>
P>5!SIS #123
..,) "R 5L>G$ ANGUL>
P>5!SIS #123
.; L[]-CASE ITALIC ,5GLI%-LR
9DICATOR #208
.;, CAPITAL ITALIC ,5GLI%-LR
9DICATOR #208
., CAPITAL ,GREEK-LR 9DICA-
TOR #208
.,( LEFT 5L>G$ CURLY BRACE
#123
.,) "R 5L>G$ CURLY BRACE
#123
,NEME? ,MA?4 ,CODE1 #1972 #BDE
.,' CLOS+ ITALIC-TYPE 9DICATOR =
^WS1 PHRASES1 & MA!MATICAL
/ATE;TS #36
#62 ; (DOTS #5-6)
; DEPRESSES NE>] >R[H1D BY #45
DEGREES #145
,5GLI%-LR 9DICATOR #21, #208
SUBSCRIPT 9DICATOR #82
;< LEFT-PO9T+ C>ET #99
;% "R-PO9T+ C>ET #99
;2 PROPOR;N SIGN (AS) #135
;^ SUBSCRIPT ) SUP]SCRIPT 9DICA-
TOR #82
;^^ SUBSCRIPT ) SUP]SCRIPT )
SUP]SCRIPT 9DICATOR #82
#61 .--#62 ; #FJG
;^; SUBSCRIPT ) SUP]- A#BDE
SCRIPT ) SUBSCRIPT 9DICATOR
#82
;; SUBSCRIPT ) SUBSCRIPT 9DICA-
TOR #82
;;^ SUBSCRIPT ) SUBSCRIPT )
SUP]SCRIPT 9DICATOR #82
;;; SUBSCRIPT ) SUBSCRIPT )
SUBSCRIPT 9DICATOR #82
;, CAPITAL ,5GLI%-LR 9DICATOR
#208
#63 , (DOT #6)
, S+LE CAPITALIZ,N 9DICATOR #20
MA!MATICAL -MA (,AM]ICAN
& ,3T95TAL) #7
,O B>B] "R L[] >R[H1D #146
----------------------------------#BDF
,R REL,N (IS RELAT$ TO)
#136
,NEME? ,MA?4 ,CODE1 #1972 A#BDF
,Y CURV$ "R L[] >R[H1D
#146
,& CURV$ LEFT L[] >R[H1D
#146
,= BLUNT$ LEFT L[] >R[H1D
#146
BLUNT$ "R L[] >R[H1D
#146
9F9;Y #152
,( LEFT 5L>G$ P>5!SIS
#122
,) "R 5L>G$ P>5!SIS #122
#62 ;--#63 , #FJI
B#BDF
,* "!=E (REGUL>) #153
,? OP5+ -PLEX-FRAC;N 9DICATOR
#75
,\ S+LE 5L>G$ V]TICAL B>
#123
/RAI<T LEFT L[] >R[H1D
#146
/RAI<T "R L[] >R[H1D
#146
,\,\ D\# 5L>G$ V]TICAL B>
#123
,[ B>B$ LEFT L[] >R[H1D
#145
,8 LEFT 9N] QUOT,N M>K
#42
,NEME? ,MA?4 ,CODE1 #1972 C#BDF
,/ HORIZONTAL -PLEX FRAC;N
L9E #75
,# CLOS+ -PLEX-FRAC;N 9DI-
CATOR #75
,' DITTO M>K #152
LEFT & "R TRANSCRIB]'S GR\P+
SYMBOL #123
,'( "R 5L>G$ TRANSCRIB]'S
GR\P+ SYMBOL #123
----------------------------------#BDG
,') LEFT 5L>G$ TRANSCRIB]'S
GR\P+ SYMBOL #123
,'_ OP5+ BOLDFACE-TYPE 9DICATOR
= ^WS1 PHRASES & MA!MATICAL
/ATE;TS #36
,'. OP5+ ITALIC-TYPE 9DICATOR =
^WS1 PHRASES & MA!MATICAL
/ATE;TS #36
,_/ DIAGONAL -PLEX FRAC;N
L9E #75
#63 , #FAA
,. SANS]IF TYPE 9DICATOR A#BDG
#208
,.; L[]-CASE SANS]IF ,5GLI%-LR
9DICATOR #208
,.;, CAPITAL SANS]IF ,5GLI%-LR
9DICATOR #208
,, D\# CAPITALIZ,N 9DICATOR
#20
,HEBREW-LR 9DICATOR #208
,,? OP5+ HYP]COMPLEX-FRAC;N 9DI-
CATOR #75
,,/ HORIZONTAL HYP]COMPLEX
FRAC;N L9E #75
,,# CLOS+ HYP]COMPLEX-FRAC;N
9DICATOR #75
,,5D ,,( ,,VOLUME ,,IV