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ARITHMETIC

SIMPLIFIED AND IMPROVED

ACCORDING TO MODERN ADVANCEMENT IN

ARITHMETICAL SCIENCE,

CONTAINING

I. ARITHMETIC in WHOLE NUMBERS; or a brief Explanation of all its

Rules, in a new and short method, with an Application to each Rule, consisting
of a large variety of Questions applicable to Business transactions, with their

Answers annexed.
II. VULGAR FRACTIONS, which are treated with great Plainness and

Perspicuity.
III. DECIMALS, with the Extraction of the Square, Cube, and Biquadrate Roots,

after a very plain and familiar manner; in which are set down Rules for the easy
Calculation of Interest, Annuities, Pensions in Arrears, the Present Worth of

Annuities, &c., by Compound Interest.
IV. DUODECIMALS, or MULTIPLICATION of Feet and Inches, with Exam-

ples applied to measuring and working by Multiplication, Practice and Decimals.
V. A COLLECTION of QUESTIONS set down promiscuously, for the greater
trial of the foregoing Rules.

ALSO,

Shart Berkanings, Mental Calculations,

AND A COMPENDIUM OF BOOK-KEEPING.

BY FRANCIS WALKINGAME.

A NEW EDITION,
SIMPLIFIED AND IMPROVED,

BY W. NICHOLSON.

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Entered at Stationers Wall.

PREFACE.

HAVING some time ago drawn up a set of Arithmetical rules and questions, with answers annexed, for the use of my school, and divided them into several books, for more ease to myself, and the readier improvement of my scholars, I found them of great use : for when a master takes upon him the laborious, yet necessary, method of writing out the rules and questions in the children's books, he must either be toiling after the duties of the school are over, to get ready the books for the next day, or else he must lose that time which would be much better spent in instructilig his pupils.—But I had not the satisfaction I at first expected, for where there are several boys in a class, one must wait till the boy who first has the book finishes writing out those rules and questions he wants; to remedy which, I was prompted to compile a book, and have it printed, that it might not only be of use to my own school, but to such others as would have their scholars make a quick progress. It will also be of great use to such gentlemen as have acquired some knowledge of numbers at school, to make them more perfect. I shall not presume to say any more in favour of this work, but refer the reader to the remark of a certain author,* concerning compositions of this nature :

"It is possible that some who like best to tread the old beaten path, and to sweat at their business, when they may do it with pleasure, may start an objection " against this well intended ASSISTANT, because the course of ARITHMETIC is "always the same; and therefore say, That some boys, lazily inclined, when they "see another at work upon the same question, will be apt to make his operation "pass for their own. But these little forgeries are soon detected by the diligence “of the TUTOR: Therefore, as different questions to different boys do not promote "their improvement, so neither do the questions hinder it. Neither is it in the power of any master, how full of spirits soever he be, to frame new questions at "pleasure, in any rule; but the same question will frequently occur in the same rule, notwithstanding his greatest care and skill to the contrary.

“It may also be objected, That to teach by a printed book is an argument of "ignorance and incapacity; which is no less trifling than the former. He, indeed, "who is afraid his scholars will improve too fast, will undoubtedly decry this method: "But that master's ignorance can never be brought in question who can begin and "end it readily: and most certainly, that scholar's non-improvement can be as little "questioned, who makes a much greater progress by this than by the common " method."

I shall now give a general idea of the nature of this work. The rules follow according to the table of contents. I have gone through the four fundamental rules in Integers first, before those of the several denominations, in order that they being well understood, the latter will be performed with much more ease and dispatch, according to the rule shown, than by the customary method of dotong. In Multiplication I have shown its beauty and use, in resolving most questions that occur

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* MR. THOMAS DILWORTH.

in merchandizing, and have prefixed before Reduction several Bills of Parcels, applicable to real business. In working Interest by Decimals, I have added tables to the rules for the readier calculating annuities, &c., and have shown the method of making them. I have also added a NEW RULE for extracting the Cube Root, shorter than any already published; also an Interest Table, calculated for the easier finding the Interest of any sum of money, at any rate per cent. by Multiplication and Addition only: It is also useful in calculating rents, incomes, and servants' wages, for any number of months, weeks, or days.

I return my most sincere thanks to the Gentlemen, Schoolmasters, and others, whose kind patronage have established the use of this book in almost every school of eminence throughout the kingdom; and also those who have favoured me with their remarks. And I beg of every candid reader, that if he should find any error, to excuse it; for, notwithstanding great care in correcting, errors of the press may have escaped my observation; in which case, the admonition of a good natured reader will be acceptable to his

much obliged,

and most obedient,

humble servant,

F. WALKINGAME.

In this Edition it has been my object to advance the utility of a work so popular. In the commencement of this Arithmetic directions are introduced by which the teacher may instruct his pupils in the rudiments of Arithmetic by a reference to objects, and by means of the Black Board, a method which cannot fail to secure improvement. In the four fundamental rules of Arithmetic, Addition, Subtraction, Multiplication, and Division, great simplification has been adopted, and in learning that department, the junior pupils may first go through the Simple Exercises, and then through the General or Slate Exercises. It will also be seen that Short Reckonings and Mental Calculations have been introduced. Simple Propor. tion, Compound Proportion, Fractions, &c., have been greatly simplified, and a Compendium of Book-keeping has been added.

1852

WILLIAM NICHOLSON.

..

ib.

:::

ib.

PART I.

Page

Page Progression Geometrical

110

Introduction

7

Permutation

113

Preliminary Exercises in Numera-

PART II.

tion

ib.

Notation and Numeration

9 Vulgar Fractions

114

12

Simple Addition

Reduction

116

Subtraction

15

Addition

121

Multiplication

17 Subtraction

122

Division

23 Multiplication

ib.

28

Table of Composite numbers

Division

123

Moneys, Weights and Measures.. 29 Proportion

Addition of ditto

36

Rule of Three

124

Subtraction of ditto

41

Double Rule of Three

ib.

Multiplication of ditto

44

PART III.

Short Reckonings 46

Decimal Fractions

125

Compound Multiplication

47

Addition

126

Division of Money, &c. ..

48

Subtraction

ib.

Short Reckonings 51

ib.

Bills of Parcels

Multiplication

52

Short Reckonings

Contracted Multiplication

127

54

128

Reduction

Division of Decimals

56

Short Reckonings

Contracted

65

Reduction

129

Proportion, or Rule of Three

66

Rule of Three Inverse ..

72

Decimal Tables

132

Double Rule of Three

Rule of Three

135

73

Practice

136

Involution

75

ib.

Simple Interest

Evolution

81

Short Reckonings

84

Extraction of the Square Root

Cube Root

140

Compound Interest

86

Commission

87

Biquadrate Root 143

Purchasing of Stock

ib.

145

Simple Interest

Annuities or Pensions

147

Brokerage

88

Discount

Rebate or Discount

149

89

151

Equation of Payments

90

Equation of Payments

Barter

91 Compound Interest

ib.

Profit and Loss

153

93

Annuities, Pensions, &c.

Fellowship

94

in Reversion

156

with Time

158

95

Purchasing Freehold Estates

Rebate or Discount

159

Alligation

96

Position

100

PART IV.

Double Position

101

Duodecimals

161

Exchange

103

Compari of eights & Measures 106

PART V

Conjoined Proportion

107 Promiscuous Questions

164

Progression Arithmetical 108 Book-keeping ..

178

..

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ib.

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