systems. As decimal fractions may be learneu much easier than vulgar, and are more simple, useful, and necessary;

and soonest wanted in more useful branches of Arithmetic, they ought to be learned first, and Vulgar Fractions omitted, until further progress in the science shall make them necessary. It may be well to obtain a general idea of them, and to attend to two or three easy problems therein: after which, the scholar may learn decimals, which will be necessary in the reduction of currencies, computing interest and many other branches.

Besides, to obtain a thorough knowledge of Vulgar Fractions, is generally a task too hard for young

scholars who have made no further progress in Arithmetic than Reduction, and often discourages them.

I have therefore placed a few problems in Fractions, according to the method above hinted ; and after going through the principal mercantile rules, have treated upon Vulgar Fractions at large, the scholar being now capable of going through them with advantage and ease.

In Simple Interest, in Federal Money, I have given several new and concise rules ; some of which are particularly designed for the use of the compting-house.

The Appendix contains a variety of rules for casting Interest, Rebate, &c. together with a number of the most easy and useful problems, for measuring superficies and solids, examples of forms commonly used in transacting business, useful tables, &c. which are designed as aids in the common business of life.

Perfect accuracy, in a work of this nature, can hardly be expected ; errors of the press, or perhaps of the au thor, may have escaped correction. If any such are point ed out, it will be considered as a mark of friendship and favor, by

The public's most humble
and obedient Servant,

NATHAN DABOLL.

TABLE OF CONTENTS.

PAGE

17

22

40

189

205

194

138

125

14

124

149
232

34

37

57

188

228

138

09

151

ADDITION, Simple

-of Federal Money

-Compound

Alligation

Annuities or Pensions, at Compound Interest

Arithmetical Progression .

Barter

Brokerage

Characters, Explanation of

Commission

Conjoined Proportion
Coins of the United States, Weights of

Division of Whole Numbers.

Contractions in

Compound .

Discount

Duodecimals.

Equation of Payments

Esolution, or Extraction of Roots

Exchange

Federal Money

Subtraction of

Fellowship

Compound

Fractions, Vulgar and Decimals

Insurance

Interest, Simple

- by Decimals

Compound

by Decimals

Inverse Proportion

Involution

Loss and Gain

Multiplication, Simple

application and use of

Supplement to

Compound

Numeration :

Practice

Position

Permutation of Quantities

27

144

146

74, 155

126

120

169

134

177

167

178

140

23

32

38

31

15

109

200

204

• 98

9

Questions for Exercise

200

Reduction

63

of Currencies, do. of Coins

. 89, 93

Rule of Three Direct, do. Inverse

100, 108

Double

148

Rules for reducing the different currencies of the several

United States, also Canada and Nova Scotia, each

to the par of all others

96, 97

Application of the preceding

Short Practical, for calculating Interest

126

for casting interest at 6 per cent

215

- for finding the contents of Superfices and Solids

220

to reduce the currencies of the different states to Federal

Money

218

Rebate, a short method of finding the, of any given sum for

months and days

217

Subtraction, Simple

25

Compound

45

Table, Numeration and Pence

Addition, Subtraction and Multiplication

10

of Weight and Measure

of Time and Motion

13

- showing the number of days from any day of one month,
to the same day in any other month

172
showing the amount of ll. or one dollar, at 5 and 6 per
cent. Compound Interest, for 20 years

232
showing the amount of 11. annuity, forborne for 31 years or
under, at 5 and 6 per cent. Compound Interest

233
showing the present worth of 11. annuity, for 31 years, at
5 and 6 per cent. Compound Interest

ib.
of cents, answering to the currencies of the United States,
with Sterling, &c.

236
showing the value of Federal Money in other currencies 237
Tare and Trett

11

DABOLL'S

SCHOOL MASTER's ASSISTANT.

AKITHMETICAL TABLES.

Numeratiun Tabie.

Pence dable.

coHundreds of Millions,

0 Tens of Millions.
coo Millions
coco y Hundreds of Thousands

o voor Tens of Thousands.

co voor A Thousands. woo yoor A co Hundreds.

s. d. d. is 18 12 is ? 30 6

2 40 s 4 S6 50 4 2 45 4 60 5 0 60 5 70) 5 10 72 80 6

84 T 90 They 6 96 8 100 8

108 110

9 2 120

120 10 O 192
9 8 7 6 5 4 2
9 8 6 5 4 S
9 8 7 6 5 4
9 8 7 6 5
9 8 7 6

make
9 8 7 4 farthings 1 penny, il
9 8 112 pence,

ADDITION AND SUBTRACTION TABLE.

13

14

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 11 12 2 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 13 14 3 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12

15. 41 617| 8 | 9 | 10 | 11 | 12 | 13 14 15 16 51 71 81 9 | 10 | 11 | 12 | 13 | 14 15 16 17

| 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 17 18 7 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 17 18 19 8 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 19 | 20 I| 11 | 19 | 13 | 14 | 15 | 16 | 17 | 18 19 20 21 10 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 21 22

MULTIPLICATION TABLE.

1 2 3; 4; 5; 6; 7; 8; 9 101 111 12 2; 4; 6; 8; 10 ; 12 | 14 | 16; 18 201 221 24 SI 6.1 9;12; 15:18; 21; 24; 27; 30 331 36 + 1 8:12 | 16 | 20 | 24 : 28 | 52 | 56 401 441 48 5 : 10 ; 15 ; 20; 25 | 30 | 55 40 | 45 ;

50 55 60 6 : 12 18 : 24 | 30 | 36 ; 42 | 48 ; 54 | 601 66| 721 7 14; 21 | 28 | 55 | 42 | 49 | 56 ; 63 ; 701 771 84 8 | 16 | 34 | 32 40 | 48 | 56 64 ; 72 ; 801 88 96 9 18 : 27 | 56 | 45 | 54 | 63 | 72 ; 81 901 99|108 10 | 20 | 50 | 40 | 50 00 70 90 | 100110120 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 _99 | 1101121|132 12 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120/132|144

To learn this 'Table : Find your multiplier in the left hand coluinn, and the multiplicand a-tor, and in the common angle of meeting, or against your multiplier, along at the right hand, and under your multiplicand, you will find the product.