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INTRODUCTION

TO

ARITHMETIC;

CONTAINING

THE MOST USEFUL RULES IN COMMON ARITHMETIC, VULGAR AND
DECIMAL FRACTIONS, EXTRACTION OF THE SQUARE AND

CUBE ROOTS, PRACTICAL QUESTIONS IN MENSURATION,
AND A COLLECTION OF MISCELLANEOUS QUESTIONS.

BY JAMES GRAY,
Late of Peebles and Dundee, Author of, " A Concise Spelling-Book,

for the Use of Children," &c.

66th Edition, Stereotyped,

WITH TABLES OF MONIES, WEIGHTS, AND MEASURES,

ACCORDING TO THE IMPERIAL STANDARDB.

EDINBURGH:

FUBLISHED BY

OLIVER & BOYD, TWEEDDALE COURT ;
AND MAURICE OGLE & SON, GLASGOW.

1854.

(Price Tenpence bound. }

In offering a new and Stereotyped Edition of this Work to the public, it may be proper to state, that it has been revised with great care, and adapted, so far as its size would permit, to the present state of Arithmetical Science.

INTERMINATE DECIMALS are now introduced, for the

purpose of preparing the Student to enter with advantage upon the more complicated and abstruse rules, and the Gregorian Calendar, which was worse than useless in a School Book, has been expunged. A number of practical exercises are added to those parts which seemed most to require it; particularly to the Simple and Compound Rules, ---PRACTICE,—TARE and TRET - PARTNERSHIP, -INTEREST, FRACTIONS,--and to the EXTRACTION of the SQUARE and CUBE Roots; and, in order to insure perfect accuracy, the whole of the Exercises have been recomputed.

The phraseology, which was occasionally quaint and obsolete, has been modernized; the second Rules for Simple and Compound Proportion are struck out, as having a tendency to distract and mislead the pupil; and Explanatory Notes have been added wherever it was apprehended that the learner might feel any difficulty.

consequence of the great attention paid to the Tables of Weights and Measures at the beginning, it is hoped that they are now sufficiently adapted to all the purposes of an initiatory class-book.

Upon the whole, the Publishers trust that this Edition will be found still more worthy of that extensive encouragement which the book has so long and so deservedly enjoyed.

In

SIGNS USED IN ARITHMETIC.

+ Plus, the sign of Addition.

Minus, the sign of Subtraction.
The sign of the difference when it is not

known which is the greater.
x The sign of Multiplication.
• The sign of Division.

: The sign of Proportion.
V or The sign of the Square Root.

The sign of the Cube Root.
4. The sign of the Fourth Root..

:

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UME 3.4 1 9,8 7 6. 5 4 8, 9 8 7.6 5 4, 3 2 1

ADDITION TABLE.

| 1 2 3 4 5 6 7 | 8 9 1 2 3 41 5 6 7 8 | 9 10 2 3 4 5 6 7 8 | 9 | 10 | 11 3 | 4 | 51 6 | 7 | 8 | 9 | 10 | 11 | 12 41 5 | 6 7 8 | 9 | 10 | 11 | 12 | 13 5 6 7 8 | 9 | 10 | 11 | 12 13 6 7 8 9 10 | 11 | 12 13 14 | 15 71 8 9 10 11 | 12 13 14 15 | 16 8 9 | 10 11 12 13 14 15 16 | 17 9 10 | 11 12 13 14 15 16 | 17 | 18

| 14

SUBTRACTION TABLE.

-10

1 2 3 45 678 9 | 10 1|0|1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 2

1 | 2 3 | 4 | 5 | 6 | 7 | 8 3 -1011 2 | 3 | 4 5 6 7 4 101 2 3

4 5 1 6 5

-10112 3 | 4 | 5 6

-10 1 2 3 4 7

10 1 | 2 | 3 8

0 | 1 2 9

10 1 10

0

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