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A CORRECT and accurate knowledge of Arithmetic is one of the most importànt elements of a liberal or practical education. The public should, therefore, receive with indulgence every attempt that may be made to improve this department of instruction.

The Elementary Treatise, which is here presented, is an enlarged, and it is hoped, an improved edition of the Common School Arithmetic, published in 1833. The suggestions of several experienced teachers have been incorporated with the body of the work in its new form, and, indeed, nothing has been omitted which it was thought would give it value to those for whose use it is designed. It has been the intention to render the whole subject as plain as it is capable of being made, and at the same time, to treat it as concisely as possible.

The reasons for most of the rules are given. It was not, however, thought best to demonstrate the rules for the extraction of roots, nor that for finding the sum of a geometrical series.

The name, Compound Numbers, which has heretofore been given to all numbers in which the kind of unit is expressed, has been changed to that of Denominate Numbers. This change has not been made with

any

ambitious spirit of innovation, but because it is deemed an improvement

It is not easy to form an idea of what is meant by the term, Compound Number, and especially so, when we find it applied to such numbers as 3 pounds, 3 dollars, 3 shillings, &c. Why is 3 pounds a compound number any more than 3? If it be answered, that 3 pounds is composed or compounded of three single pounds, that does not remove the difficulty, for 3 is also composed of three units 1. Is it not then the better way to call the first a denominate number, and the other a simple number, as is done in 45.

Mr. Hasler, in his Arithmetic, has called this class of numbers, Denominate Fractions.

In the present edition, the questions referring to each section are arranged directly after the section, which generally brings the question and answer on the same page. This alteration will, no doubt, be found convenient to teachers.

A Key has also been prepared, in which all the questions contained in the Arithmetic are resolved, and in such a manner, that the particular methods of solution can be fully understood. Many examples, not in the Arithmetic, have been imbodied in the Key, in order that the pupils may be exercised in questions not found in the books before them.

Hartford, Connecticut, March, 1838.

MENTAL ARITHMETIC.

PART I.

are.?

1. How many eyes have you? How many ears have you? How many hands have you? How

many

thumbs have you? How many fingers have you on each hand ? How many fingers have you on both hands ?

If you have one apple and Charles gives you one, how many will you

have ? One and one are how many ? If you have one apple and Charles gives you two, how many will you have ? One and two are how many ? If he gives you three, how many will you have ? One and three are how many ? If he gives you four, how many will you have? One and four are ? One and five are? One and six are ? One and seven are ? One and eight

One and nine are ? 2. If you have two nuts in one hand and one in the other, how many have you in both ? Two and one are how many ? If you have two nuts in one hand and two in the other, how many have you in both ? Two and two are how many ? If you have two nuts in one hand and three in the other, how many have you in both ? Two and three are how many? If you have two nuts in one hand and four in the other, how many

have
you

in both ? Two and four are? Two and five are? Two and six

Two and seven are? Two and eight are ? Two and nine are ?

3. If you have three peaches in one basket and one in another, how many have you in both? Three and one are ? If you have three in one basket and two in the other, how many? Three and two are ? If

you

have three in one basket and three in the other, how many ? Three and three are? Three and four are ? Three and five

are ?

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