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in addition to which, they seldom occur to any one who is not engaged in Scientific Speculations, or in Professional Calculations.

A Second Appendix of Miscellaneous Questions, (many of which have been taken from the Examination Papers given in the University during the last few years) has been added to the present edition of this work, which the Author considers will conduce greatly to its practical utility, especially for those who are intended for mercantile pursuits.

CAMBRIDGE,

January, 1856.

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The Rule of Three

CHAPTER IV.

Notation and Numeration of Fractions

Transformation of Fractions.....

Addition of Fractions

Subtraction of Fractions

Multiplication of Fractions

Division of Fractions.....

Reduction of Fractions

Rules of Practice

Miscellaneous Questions

61

63

73

76

77

79

82

89

93

CHAPTER V.

Notation and Numeration of Decimals

Addition of Decimals

Subtraction of Decimals

Multiplication of Decimals

Division of Decimals

Reduction of Decimals

Recurring Decimals........

101

104

105

106

107

109

112

CHAPTER VI.

Ratio

Proportion.

The Rule of Proportion.

Simple and Compound Interest

The Natures and Transfers of Stocks....

119

122

126

133

139
CHAPTER IX.

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The Application of Arithmetic to Geometry..

The Theory of Lineal or Long Measure..

The Theory of Superficial or Square Measure

The Theory of Solid or Cubic Áleasure.

The Practice of Lineal Measure

The Practice of Superficial Measure

The Practice of Solid Measure...

The Computations of Artificers

The Computations of Gagers.........

The Computations of Land-Surveyors ................

Imperial Weights and Measures

The Calendar

French Impe Measures, &c.

Problems

194

195

197

201

203

205

208

210

216

218

220

224

227

230

APPENDIX I.

Notation and Numeration

Addition and Subtraction

Multiplication and Division

Involution and Evolution

Ratio and Proportion .....

Approximate Dimensions and Contracted Decimal Operations

Different Scales of Notation

235

236

239

245

246

248

251

APPENDIX II.

Miscellaneous Questions for Practice in all the Rules of Arithmetic 257

TABLES

OF

MONEY, WEIGHTS AND MEASURES,

WITH SOME OBSERVATIONS RESPECTING THEM.

.

0

I. TABLE OF MONEY OR VALUE.

A Farthing is written or marked d. 2 Farthings are · 1 Halfpenny

d. 4. Farthings i Penny

1d. 12 Pence . 1 Shilling

1s. 20 Shillings....1 Pound

. . £i. Money as expressed by means of these denominations is called Sterling money, in order to distinguish it from Stocks, Shares, &c.

The Standard gold coin of this Kingdom is made of a metal consisting of 22 parts of pure gold, and 2 parts of copper. The Pound sterling is represented by a gold coin called a Sovereign, and from a pound troy of standard gold are coined 4628 sovereigns, so that the weight of each is 5dwts. 317} grs., or 123.274 grs.; and the value, of gold of the Mint-Fineness, called 22 Carat gold, is £3. 17s. 10 d. per ounce. The Standard silver coin consists of 37 parts of

pure silver, and 3 parts of copper : and a pound troy of this metal furnishes 66 shillings, so that the weight of a shilling is 3dwts. 1511 grs., and the Mint-Price of standard silver is 5s. 6d. per ounce. The silver coinage is not a legal tender for more than 40s., the gold coinage being the general standard of value.

In the Copper Coinage, 24 pence are made from an avoirdupois pound of copper, so that a penny should weigh io drs. avoirdupois, or 291?grs. troy: and this coin is not a legal tender for more than 12d.

A Farthing, or if., is the lowest denomination above mentioned: but farthings and all other subdivisions of a penny are in practice, denoted by Fractions of a penny.

1

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The Coins now current are the following, constituting what is called The Circulating Medium.,

Copper.
A Half-farthing 4.f. = d.
A Farthing

if. = 1d.
A Half-penny 2 f. = įd.
A Penny

4 f. = 1d.
Silver.

S. d.
A Fourpence

= 0.4.
A Sixpence

0.6. A Shilling

1.0. A Half-Crown

2.6. A Crown

5.0.

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Gold.

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A Half-sovereign

0.10. A Sovereign ... 1. 0.

A Double-sovereign. = 2. 0. The following coins, no longer in circulation, are frequently mentioned, and their values are subjoined. £. d.

£. d. A Groat. = 0. 0. 4. | An Angel = 0. 10. 0. A Tester. D. 0.6. | A Mark

0.13. 4. A Guinea

-1: 1.0. A Carolus 1. 3. 0. A Half-guinea = 0.10.6. A Jacobus . . =1. 5.0. A Noble .. = 0. 6.8. | A Moidore.. =1. 7.0.

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II. TABLE OF AVOIRDUPOIS WEIGHT.

A Dram is written i dr. 16 Drams are

1 Ounce

1 oz. 16 Ounces .

1 Pound

1 lb. 14 Pounds..

1 Stone ..

1 st. 2 Stone or 28lbs .. 1 Quarter 4 Quarters or 112lbs 1 Hundredweight. 1 cwt. 20 Hundredweight. 1 Ton

1 ton.

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