systems. As decimal fractions may be learned much easier than vulgar, and are more simple, useful, and necessary, and soonest wanted in more useful branches of Arith metic, 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 Re' duction, 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 author, may have escaped correction. If any such are pointed out, it will be considered as a mark of friendship and favour, by

The public's most humble
and obedient Servant,

NATHAN DABQLL.

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

Evolution or Extraction of Roots

Exchange

Federal Money

Subtraction of

Fellowship

Compound

Fractions, Vulgar and Decimal

Ensurance

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

Page

17
22

40

- 189

205

· 194

138

- 125

14

124

149

232

34

37

57

131

22

138

179

- 151

21
27

144

146

74, 155

126

120

· 169

134

- 177

1 67

· 178

140

28

32

38

51

15
109

- 200

204

Questions for Exercise

Page 209

Reduction

63

of Currencies, do. of Coin

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 No-

va-Scotia, each to the par of all others 96, 97

Application of the preceding

98

Short Practical, for calculating Interest

126

for casting interest at 6 per cent.

215

for finding the contents of Superfices & Solids 220

to reduce the currencies of the different

States, to Federal Money

218

Rebate, A short method of finding the, of any giv-

en sum for months and days

217

Subtraction, Simple

25

Compound

45

Table, Numeration and Pence

9

Addition, Subtraction, and Multiplication 10

Of Weight and Measure

11

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 1l. or 1 dollar, at 5 &

6 per cent. Compound Interest, for 20 years - 232

showing the amount of 1l. annuity, forborne

for 31 years or under, at 5 and 6 per cent.

Compound Interest

233

showing the present worth of il. annuity, for

31 years, at 5 & 6 per cent. Compound Int.
of cents, answering to the currencies of the

United States, with Sterling, &c.

236

showing the value of Federal Money in oth-

er currencies

237

Tare and Tret

114

Useful Forins in transacting business

238

Weights of several pieces of English, Portuguese, &

French, gold coins, in dollars, cents, & mills 234

- of English & Portuguese gold, do. do. 235

of French and Spanish gold, do. do. ib.

50

Hundreds of Millions. o co Tens of Millions.

os Millions.
ovo Hundreds of Thousands.
ooo voo Tens of Thousands

ovosen A Thousands.
© voer A c Hundreds.

d. s. d. d.
20 is 1 8 12 is 1
30 2 6 24
40 3 4 36 S

4 2 48 4
60 5 0 60 5
70 5 10 72 C
80 6 8 84
90 7 6 96 8
100 8 4 108 9

1 110 9 2 120 10 8 7 6 5 4 3 2 120 10 0 132 9 87 6 5 4

3 9. 8 7 6 5 4 9 8 7 6 5 9 8 7 6

make 9 8 7 4 farthings 1 penny, d. 9 8 12 pence 1 shilling,

9 20 shillings, 1 pound, £.1

ADDITION AND SUBTRACTICN TABLE.

1 2 3 4 | 5 | 6 | 7 8 9 10 11 12 2 | 4 5 | 6 | 7 | 8 | 9 10 11 | 12 13 14 31 51 61 7 | 8 | 9 | 10 11 12 | 13 14 15 4 1 6 7 | 8 | 9 | 10 | 11 | 12 13 | 14

15 | 16 5 1 7

8 | 9 | 10 | 11 12 13 | 14 | 15 | 16 |17 6 1 8 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 17 | 18 71 9 10 | 11 | 12 | 13 | 14 | 15 16 | 17 18 | 19 8 | 10 | 11 | 12 | 13 14 | 15 | 16 17 18 19 20 9 | 11 | 12 | 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 31 41 51617181 9 10 11 12 2 | 41 61.8

| 10 | 12 | 14 | 16 18| 20 22 24 3 161 97 12 | 15 | 18 | 21 | 24 | 271 30 331 38 41 81 12 16 | 20 | 24 | 28 / 32 36| 40 441 48 5 | 10 | 15 | 20 | 2 | 30 35 | 40 45 50 55 60 6 | 12 | 18 24 | 30 | 36 | 42 | 48 | 54 601 661 72 7 | 14 | 21 28 | 35 | 42 | 49 | 56 | 631 701 771 84 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 72 801 881 96

9 | 18 | 27 | 36 | 45 54 | 63 | 72 | 81| 901 99|108 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90/100/110/120 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99|110|121|132 112 24 / 36 | 48 60 | 72 | 84 96 | 108/120/132:144]

To learn this Table : Find your multiplier in the left hand column, and the multiplicand a.top, and in the como mon angle of meeting, or against your multiplier, along at the right hand, and under your multiplicand, you will find the product, or answer.