TO FIND ANY RULE OR SUBJECT CONTAINED IN THIS TREATISE.
• The figures refer to the page.
Absolute value of figures, 15, 16; local, 11,
15, 16.
Abbreviated div. and mult., 68.
Borrow, term defined in subt., 48; explain.
ed, 49; illustrated. 49, 52.
Abstrac numbers, 28, 213; questions on, Broken numbers, 28, 111, 112, 114, 218.
28, 29.
Accepted, term explained, 224.
Acres in a mile, 234.
Addition, 30, 212; carrying in, 31; explain-
ed, 31; illustrated, 35, 36. defined, 32,
212; every principle in, 35. its use, 212;
of abstract numbers, 30, 31; proof of, 67;|
quest ons on, 36; review of, 69, 16; sup-|
plement to. 71. table of, 18. terms in
ined. 32, 33. theoretical principles of, 35.
Addition of compound numbers, 151; con-
cr te, 72, de mals, 107, 122; F. money,
88; . xed atmbers, 2, 121; sterl ng
money, 205; vulgar fractions, 111. 121.
Add ton and mult. of fractions, 220.
Adding by Das, 34; by calculat on 26.
term dein 4, 33.
A general rule or ad., 33; analysis, 102:
d v.. 65; mult.. 44; subt., 5).
Aggregate numbers, 212, 213.
Aliquot part of a dollar, 237; month, 19;
shilling powd, 237; year, 133.
Amouat. tom defined, 32; fund, in inte- j
est. 34; g.ven, to find the pr.az pal. 143.
Analysis. 96 to 105, 98; complicated exs m,
101, 102; correspondent exs. in, 132, 103.
104: cost of a quantity found by, 96. de.
fined, 98; dividing twice, to find un ty,
99; price of u ty found by. 97; illu tra.
tions in, 7, 98, 99, 103, 101, 102; intro-
duction of, annuls the rule of three, 56,
101, 179, 131, 186. questions on, 104. term
defined, 98.
Annu tes, 149.
Answer, term defined, 32.
Antecedent. 223.
Ant sur dal point, its use, 216.
Apothecaries' weight, 61, 166, 168, 172, 177;
table of, 172, 233.
Application of the first 4 rules, 82; ques
tions on, for the examination of pup.ls,
83, 4.
Arabic figures, 27; by whom invented, 28:
How long been in use, 23. lessons to be
written in, 27; questions on, 7, 8, 11, 2, 28.
Arithmetic, 210, 223; an art. 223; a science,
210. decimal, 224; its object, 210. nun-
ber of simple rules in, 210; theoretical,
224. to whom first known, 210. political,
224; vulgar, 224.
Arithinetical proportion, 184.
Arrears, 149.
[to 175.
Ascending reduction, 170, 175; exs. of, 171
Assessing town taxes, 183.
Avoirdupois weight, 161, 165, 171;
BANK discount, how found, 152
Bank note, form of, 231.
Bankrupt, term defined, 224.
Bankruptcy, exs. of, 158.
Barley corns in a mile, 234.
Barter, 155; proof of rule, 155.
Barrels in a tun, 235.
Biquadrate root, 23.
Board measure, 189, 190; wood, 190.
Bonds, interest on with indorsements, 191
to 195,
Borrowing in subt., exs. of, 49, 50; theo
retical princ.ples of, 52; table of, 21, 22
Broker described, 224.
Brokerage, 150.
Buy ng and selling of stock, 150.
CALCULATING interest on notes with in-
dorsements, 191 to 195.
Cap tal defined, 224; exs. of, 158.
Card nal numbers, 28.
Carry, term d fined, 33, 48.
Carrying in ad., 1; operation explained,
31; illustrated, 32; thoretical princ ples
of, 35, 36. in subt., 49; in mait.. 38; in
como uod ad., 61; d:v. 177; mat., 168;
sust., 165; quest ons on, 20, 52, 8, 41, 53,
165, 167, 170; table of, 19.
ha us in a mle, 234.
Caldron, bushels m, 235.
Carageable value of figures, 16.
maging of commol ties, 156, currencies,
Change of integers to fractions, 119; of
frat ons to integers, 119; of alxed aun-'
bers to tractoas, 119; of tract us to
mxd numbers, 119; vulgar to declinal
fract ous. 120; dem to valgir frac
tous, 120; from high to lower denomin3-
tous, 171; from low to he ver. 172, 175
Cpher, ts elect on integers, 13, 16; d ci-
nais, 106. ts value n ad, 2. m the
m end, 48; in the quot ent, 63; a sub-
trabend, 47, 52. how disposed of in the
mult.pl cand, 40; in the alt-pher, 4; in
both, 42. when a terminates the multipli-
cand, 45; the inult pler, 42; bot, 43;
the dv dend, 63; dv.so., 63; bota, 63
questions on, relative to the above cases,
36, 44, 64, 71.
Circulat ng decimals, 217, 218.
Classes, questions to be rected in, 31, 38,
40, 41, 42, 3, 44, 47, 48, 49, 59, 60, 61, 62,
64, 66.
[of, 172, 233
Cloth measure, 162, 166, 168, 172, 177; table
Column, term defined, 33.
Commission, 149
Cominon denominator, 119, 110, 220; divi.
sor, 219, 225; measure, 227.
Compos.te numbers, 44, 55.
Coinpound ad., 160; div., 176; mult. 167;
subt., 165. review of, 164, 167, 170, 178;
questions on, 165, 167, 170, 178; fellow.
sh p, 158; Interest, 195; proportion,
185.
[182
Compound terms, as yds, qurs., nails, &c.
Computing interest on notes with indorse
ments, 91 to 95; town taxes, 183.
Concrete numbers, 28.
Connected operations, 92, 93, 94.
Contractions, 44; in proportion, 185, 186.
Co-partnership, 157, 158.
Correspondent exs. in analysis, 102, 103,
14; decimals, 110 F. money, 92; re
duction, 175; vulgar fractions, 127, 128.
Cube root of decimals, 202; integers, 202;
mixed numbers 203; surds, 203; vulgar
fractions, 203.
Currency, English, 204; federal, 87; reduc
tion of each, 94, 203. table of each, 88,
89; 204, 205.
Currencies, reduction of, 207.
DAYS ma mouth, 236; year, 236: interest
for, how ouad, 137
Decimal ad. explained, 1 7; div. 139; mult.
108; subt. 107, points. 216.
Decunal fractions, 1 5, 215; changed to vul-
gar, 120; interest by, 145; the muit pl-
cand a. 110; multiplier a, 18. terimate,
217; ult.nete, 217
Decimals, 105; ciphers, after, 106; circulat
ing, 225; before, 106; decrease of, 105; de-
fined, 225; d.st.nguished from an inte
ger, 105; table of, 103. their notation, 215;
numeration, 2 5.
Definition of terms in ad., 2; div., 57;
muit., 39; subt., 48. in interest, 133; vul-
gar fractions, 11.
Demonstrations in compound rules, 161 to
164; F. money, 95; of statements in pro-
port.on, 179, IST, 185, 186. [30, 72.
Dénominat ons, derent, 160; the sum,
Denominator, common, 120; diferent, re-
duced to 120; mle for, 119; exs. necessa-
ry to be, before adding, 21. term de-
fined, 1.
Descending, reduction, 171, 175.
Dexter pont, is use, 216.
Dil relice, (see remainder.) 48.
Dg ts, the nine, way so called 28, 20.
Direct propo til, 180; inverse, 181.
Discount. 150; bank, 152.
Every principle in adding, 35; div., 64, 85;
mult., 45; subt., 50, 51.
Evolution, 197.
Example of aumer ing. 12.
Exch age, domestic, 208.
Expl nations in ad., 3, 31; div., 57, 59 60
61, 62, 67; mul., 37, 38; sub ., 6, 49. of
he signs, lus inarus, equality &c. 69;
of he terins, c rry, adding mount,
swer, &c. 32, 33; of ininuend, subtra-
hend, rem., borrow, excess, difference,
4 of multi e nd, alti lier, fc ors,
rodne, 39: of d vidend, dividu 1, divi-
sor, quotien, 56 57.
Exponent 196.
Extraction of the cube root, 2000; of an inte
ger. 20; decimal 02; m xed 'number,
203; vulgar fraction, 203; sund, an
Extremes and means, 19.
FACTOR. term defined, 39, 213.
Feder 1 money, 7 91, 161, 65; miscel
Janeous exs. in, 92 93, 94; questions on,
91; reduction of, 9, 95, 96, 171.
Fee in a mide, 234.
Fellowship, 157; compound. 15.
Figures, value not altered by ciphers, 28.
how to numerate, 12; read, 12; write, 27.
Figure defined, 33; obs on, 15; v lue of,
how deterin ned, 15, 16.
Form of orders, no es, receipts, 231.
Found ton of roportion, 1.
Divide a number into pirts, 13'.
Fractions, 111, 215; com ound, 26; deci-
Dividend, defined 57; ts place in division mal, 15; improper, 1 1, 219; mixed, 111.
56; wha i expresses 214. when r- no ation of, 15; proper, 111; vulgar, 218.
min ed by ciphers 63; questions reh-GALLONS in tun, 235; chaldron, 235.
tive o 64.
Grams in a lb. troy, 233.
173, 174, 175.
Hogsheads in tun, 2 5.
ours in a year, 235.
ILLUSTRATION » in ad., 32; analysis, 97
0 1 3; d.v. 56; mult., 39: numeration,
13. 15; ro ort on, 179, 184; subt., 49.
Improper fractions, 11; defined, 15, 219.
Inches i inile, 4.
Ind x is use, 19.
Dividing integer by a fraction, 103 124; HIGH d nominat ons brought to lower; 172,
a frac ion by fr etion, 122. 222;
tion by n reger, 19, 123 221; n in e-
ger by an integer 57; n integer by aj
mixed number, 125; a mixed mumber by
an integer, 11; mixed number by he
ine 109 126. lus rion of hese o e-
rat ons, 122, to 127. Iso, 1 8, 109.
Div du 1, wh pr of division, 56 ques-
tions relt ve 0, 60. erm defined, 57.
Divis on. 53; com osed of sever I figures,
69; defined, 69; expl :ned, 59; llustrated
7. exs. of every princi le in, 64, 65. su
pleinen o 78 o 82. table of, 23 6 27.
terms in, defined nd lustr ed 56; heo-
retic Irinciles of. 70; ques ions on, 71.
proof of d.vision 68, 214
Division,
con rc ion of sub. 53; finding
how inany nes numberc n be subt'd.
from not her, 55; nd ha here is
mainder, 56: shows h one number is
con ained in no her, 53.
Division of decim is, 18
Indorseme o otes &c. 191 to 195.
Insolve cy, exs. of 58.
Interes to 47;t to 12 per cent. 134;
thlf &c. er ce t, 4:a. 6 nd 7 per
cet 34. for dys 197; months, 136;
ye rs 5. ye rs ad mon hs, 1:7 years,
in s. d ys, 128; for v rious r tes per
ce t nd time 14. amou in how found,
15; ri ci, al, '4; rate, 144; ime, 144.
questions on, 147, 8.
In roductory lessons designed to tea h new
beginners how o read figures 7 o 12, 13,
5 ad., 26; numerate 12, 13, 14; write 27.
Divisor defined, 6, 57. rules to determine Inverse pro orton 13.
how m ny mes i will go, when divid-Involve unber, 196, 197.
ing, GO o 64, 65.
Involution, 6 98.
Divisor a decim 1 109; a mixed number, Isnur nee, 48.
125; a vulg r fr e ion, 124. what i ex-JOIS, rule o measure 190.
presses, 211.
Dry me sure, 163; t ble of, 173.
LAND measure, 6., 166, 169, 174, 177; ta-
ble of. 7, 24.
Lw of our umer tio, 211.
Duodecim Is, 187, d. of, 188; mul. of, 18; Let ers, used to express numbers, 16, 17.
Equation of aynen s, 156,
Even numbers, 23, 214,
Liquid measure, 10, 766, 165, 7, 177; ta-
ble of 7, 5.
Local value of figures 15, 1, 27; sim le, 16.
Long ine sure, 12, 166, 1 9. 17; table of
57, 24.
Loss on he whole, how found, 155; per
ce t, 54
[172, 175.
Lower denominations brought to higher.
MEANS and extremes, 184.
Mensuration, 190.
Minue d, terin defined, 48.
Minutes in a year, 235.
Mixed numbers, 111; ad., 112; div. 126;
mult., 117; reduced, 119; sub'., 113.
Motion, 164, 167, 70, 178; table of, 236.
Multi licend, a decimal, 108. defied, 39; an
integer, 7; a mixed number, 117; a vul-
gr frac ion, 114.
Multipliction 37, 213; carry in, 38; defi
ed, 39; every principle in, 44, 45; gene-
ral rule for, 44; explined, 38; illustra ed,
39; proof of. 6; questio s on. 46; terms
in defined, 39; theoretical principles of,
45, 4.
Multiplication table, 0.
Recapitulation, 25, 86, 87.
Reduction scendi g. 171; descending, 175
Reduction 170; of currencies, 20; sci-
mals, 09; F. mo ey, 9; mixed umbers,
119;s erling :noney 20; vulgar fractions,
118. questions on 6, 175.
Remainder, term defined. 48
Review of ad., 154; div., 178; mult 170;
subt.. 167; reduction, 175; vulg..r frae
jons, 129.
Roma table 16.
Roods in a mile 24.
Row, erm deuned 33.
Rule of three, 1.8 180, 182; 96, 101.
SECONDS in a year, 237.
Se ara rix, is use, 15.
Scruples in lb., 33.
Shilling table, 2 7.
Sin.ster point, 215.
S lid measure, 234
Square root, 1.8; of decimals, 20; integers,
99; mixed Nos. 2. surds, 2 0; vulgar
f actions, 20
Multipher, decimal, 108; defined, 39; a
i.teger, 7; a mixed number, 116; a vul-Short division, 66.
gar fr ction 114.
Multiply, trin defined, 39.
Multiplying n integer by a fraction, 114;
by a mixed No., 16; by a decim 1, 2'7.
a decin I by a decimal. 1. 8. a frac ion
by an integer, 10; by a mixed No. 121;Statements in proporti n, 179, 181, 185, 86.
by a fraction, 114. a mixed No. by the subtraction, 6; carrying in, 48, 49; com
s me, 18.
pound, 165; of concrete Nos. 4; deci
mals, 107. defined, 48; every principle in,
5,5; explained, 49. f F. mo ey, 98. il-
lus ra ed, 49, 50. of mixed N 6., 13, 121;
proof of 8. review of, 9, 170. of sterling
money, 20; supplement to, 78. theoreti
cal principles of, 52. of vulgar fractions,
NOTATI N. 16; by figures, 27; by letters,
16; quest ons on. 16, 17, 28.
Notes, forms of, 231; indorseme: ts o, 191.
Numbers, bsr ct, 2; com, osi e, 44; cr
dil, 28; concre e, 28; divided in o pe-
riods, 14; even, 28; odd 2 ; ordinal. 2;
prime 28; square 22; whole 28. how
many w ys expressed 15; written, 211.
Numeration, 1; illustrati ns in 13; bs. on
15; questions on, 11, 12, 2; rem. on,
tables of 13 14.
ODD numbers, 28, 214; ordinal, 28.
Oral lessons, 18 19 20 23.
Origin of our figures, 28.
Ounces in a lb. troy 233.
PACE in a mile. 234.
Pecks in a chaldr n. 235.
Subtraction table, 21, 22; questions on, 23
Subtrahend, term defined. 48.
25;ummary, view of ad. subt. mult. and div.
69; definitions, 19.
Period definit n of a, 28; Nes pointed off
into, 14; t ble of 15.
Pints in a un 25; chaldron, 235.
Poles in a mile 24.
Sup lement to ad., 71; div., 78; mult., 76;
subt., 74.
Surd, 9.; cube of 203; square, 200.
urdal oin, 216.
Table of ad.,18; ap th. w, 233; avoird., 16;
cloth m., 233. c rrying, 19; div., 23; dry
m. 2 5. Eng. mo ey, 204, 237; federal 88,
8, 160, 237: land, m. 131; liquid, 235;
long, 234. motio, 236; months, 19; 236
mul, 2. numeration, 13. par iculars,:26;
pence, 27, r ti s, 145; Roman, 16; shil
lings, 23; sterling money, 2 4, 2 7. subt,
2. time, 25; troy w.,1, 25; years, 139
Taxes, 83; assessmen of, 83
en, sta dard of numeration, 211.
Terminate decimal, 17.
Theoretical ri ciples of, ed., 35; div., 70;
mult., 45; subt., 52. questions on each, 36,
53, 46, 70, 71.
Prime Nos.. 28, 213, 2'4.
Product defined 29, 213.
Proof of d., sub. mult., div., 68; barter
discoun 5; equio of ayments,
; fellowshin, 158; loss and gain 52
153, 154; propor.ion, by analysis, 179, 181,
186.
Proportion, 178; compound 185; demo.
stratio s in, 8; illustrations. 179, 184;
obs. on, 179, 180. questions n, 187.
QUARTSi a tun, 235; ch Idron, 2 5.
Questions on ad., 36; able, 18; an lysis
104; barter, 16; broker ge, 19; com-
mission 15; compound rules. 15, 67, Tr y weight, 165, 168, 172, 176; table of
170, 178; discount. 59; div. 70; equation 12, 233.
Time, 164,167,170, 174,178; tab'e of, 172, 233.
erms, in ad. explained, 32 33; in div., 56,
5.; mult., 39; subt., 48; vulgar fractions,
111; interest, 133.
of payments 6); F. money, 91; fellow-ULTIMATE fraction, 2'7; in eger, 217.
ship, t0; figures, 7, 8, 11; insurance, 5;Unit, 12, 1-
35, 36, 46, 210, 229,
interest, 147; loss and gain, 160; mult. 46; And, 33, 28, 128.
nota ion, 16, 17; numera ion, 2; propor
tin, 18; reduction, 95, 175, stock, 5. to
be answered orally, 18, 19, 202; in
classes, 31. 32. 33, 8, 40 41, 42, 43, 44, 47,
48, 49, 59, 60 61, (2, 64. 66. on the firs
four rules 83, 8'; on the ables of weights
and measures, 23 to 236.
Qu tien figure, rules to find, 60, 61; table
to find 23 to 27.
REASONS for carrying for ten, 32, 49, 52.
fr ctions, 11, 218; added, 111, 220.
chinged t decimals, 20; ai teger, 119:
mixed, No. 119. dv. 122, 132, 221.
explained, 28 to 1 3; 210 to 22. inverted,
114, 122, 132. mult 114, 13, 13, 221. no-
Latin of, 15, 29. questio so. 123 to 132.
reduced to lowes terms, 1 9: one com.
non denominator, 120. reduction of, 118.
VALUE of ciphers, 7, 11, 13, 16, 28, 106,
216; figures, 11, 15, 16, 28, 129,
THE lessons that follow the figures that have their amount expressed in words, are to be read by the pupils in classes. The questions at the foot of each page, are for examination and to be answered by the pupil at recitation.
8 7 9 3 2 14 20 5 4 7 9 6 8 12 10 11 12 13
10 16 10 11 14 18 18 12 13 16 18 14 10 11 12
seventeen.
fifteen.
nineteen.
twenty-three.
twenty-six.
twenty-one.
twenty-five.
twenty-four.
twenty-eight.
twenty-seven.
twenty-two.
twenty-nine.
twenty.
14 15 17 19 20 23 26 21 25 24 28 27 22 29 30
26 19 14 17 15 20 24 28 25 27 22 21 23 14 29
30 17 19 20 15 25 28 24 22 27 21 14 29 26 23
Name the nine figures that stand for numbers; and the character which of itself is of no value. A. One, Two, Three, Four, Five, Six, Seven, Fight, Nine, and a Cipher.-What figures stand for ten? What for thirteen? For Eighteen? Foi Eleven? What figures stand for thirty? For forty? For thirty-five? For twenty ?-Two fours express what number? Four and aine express what number?
Read the figures, one and naught are ten; one and three are thirteen ; &c.
thirty-four.
thirty-three.
thirty-six.
thirty-five.
thirty-one.
thirty-seven.
thirty-two.
thirty-eight.
forty.
forty-one.
forty-five.
forty-eight.
forty-four.
forty-nine.
forty-three.
34 33 36 35 31 37 32 38 40 41 45 48 44 49 43
32 33 36 35 34 38 41 36 40 31 40 43 49 45 44
34 35 33 35 31 48 44 45 41 43 36 40 37 43 41
forty-two.
forty-six.
forty-seven.
fifty-three.
fifty-six.
fifty-two.
fifty.
fifty-nine.
fifty-one.
fifty-four.
fifty-eight.
fifty-five.
fifty-seven.
sixty-one.
sixty.
42 46 50 47 53 56 52 59 51 54 58 55 57 61 60
46 42 47 50 56 52 53 57 59 57 55 51 61 60 54
50 60 42 46 56 47 61 53 55 52 58 51 59 54 57
sixty-two.
sixty-nine.
sixty-three.
sixty-one.
sixty-eight.
sixty-four.
sixty-seven.
sixty-five.
seventy.
sixty-six.
seventy-three.
seventy-eight.
seventy-two.
seventy-nine.
seventy-one.
62 69 63 61 68 64 67 65 70 66 73 78 72 79 71
61 62 63 69 64 68 65 79 66 73 79 72 71 70 64
72 70 61 66 73 64 67 65 70 73 78 71 79 69 68
seventy-six.
seventy-five.
eighty.
eighty-three.
eighty-five.
eighty-one.
O eighty-four.
eighty-two.
seventy-seven.
eighty-six.
eighty-nine.
eighty-seven.
ninety.
eighty-eight.
74 76 75 80 83 85 81 84 82 77 86 89 87 90 88
Three and two express what number?-Name the figures that stand for thirty-cne;-for twenty-one- for forty-one-fortwelve. &c. Which is the most, five and six, or five and two? What figures stand for eightyeight? What do five and nine stand for?-five and four? Two fives stand for what number? Six and two express what number? Six and seven what? Seven and one express what number? Seve before a 0 express what number? Seven and nine express what number? Nine and a 0 make what number? A0 placed after eight are how many? Two uines are for what number?-two eights?-two sevens? two sixes? two threes? two twos?
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