INTRODUCTION.

CULTURE is progressive in its nature. Higher, still higher, is the true educational spirit.

Advance in methods of instruction makes new, improved text-books a necessity; and, to subserve wants apparently not heretofore fully provided for, this work has been carefully prepared.

Without being in any respect redundant, it is intended to be complete in details and comprehensive in scope; Combining with processes the most scientific the greatest simplicity;

Developing principles by inductive methods, deducing rules from rational solutions, and encouraging self-reliance and originality by numerous exercises in analysis;

Making written arithmetic in all its steps intellectual; and

Keeping prominently in view the practical uses of numbers, by various applications of a business character.

While it avoids obsolete or useless material, it properly treats new topics requiring attention, such as the Metric System of Weights and Measures, Annual Interest, Internal Revenue, etc.; and

Enforces thorough educational results, by orderly arrangement of subjects, and by systematic review questions and exercises.

(III)

The prominence given in this book to the enunciation of Principles, will, it is believed, commend itself to the enlightened educator, since, without a knowledge of these principles, the art of using numbers becomes mere mechanical ciphering.

Multiplication and Division of Decimal Fractions have been much simplified by assimilating their processes to those of like cases in Common Fractions, and by making the corresponding rules substantially the same.

By treating of Fractions before Compound Denominate Numbers, the Reduction of the latter is made more thorough, and a number of special rules is avoided.

Many rules of limited application are also dispensed with, by analyzing single examples, of some anomalous kind, as a guide to the solution of all others of its class.

The examples have been selected with special reference to their adaptation to the present wants of active life.

Grateful expression of indebtedness is due to Hon. John A. Kasson of Iowa, to Prof. H. A. Newton of Yale College, and to many others, for favors received while preparing this volume.

PERMANENT EDITION.

The generous favor extended to this book, and its wide introduction into the best schools, have led to the sale of several large editions, in a few months. Encouraged by this marked appreciation, the work has been critically re-examined, and put in a permanent form.

KINGSTON, MASS., March, 1867.

H. B. MAGLATHLIN.

PRACTICAL ARITHMETIC.

DEFINITIONS.

1. A Unit is a single thing, or one. Thus, A dollar is a unit, an apple is a unit, etc.

2. Quantity is any thing that can be measured, or computed. Thus,

Distance is quantity, since it can be measured, so as to be named miles, rods, etc.

3. A Number is a unit, or a collection of units of the same kind.

One, two, three, four, etc., which show how many units there are of any quantity, express numbers.

4. The Unit of a Number is one of that number. Thus, One dollar is the unit of three dollars, and one the unit of five.

5. Like Numbers are such as have the same unit. Thus, Five dollars and seven dollars are like numbers.

6. A Concrete Number is a number in which some kind of unit is named.

Thus,

Two books, five days, seven dollars, are concrete numbers.

What is a Unit? A Quantity? A Number? The Unit of a Number? Like Numbers? A Concrete Number?