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BENJAMIN GREENLEAF, A. M.

Henry B. Maglathlin

BY THE EDITOR OF “NEW ELEMENTARY ALGEBRA," "NEW HIGHER

ALGEBRA,” ETC., IN THE SERIES.

LEACH, SHEWELL AND COMPANY,

NEW YORK, BOSTON, CHICAGO.

с

GREENLEAF'S
COMPREHENSIVE SERIES.

NEW PRIMARY ARITHMETIC.
NEW ELEMENTARY ARITHMETIC.
NEW PRACTICAL ARITHMETIC.

MANUAL OF INTELLECTUAL ARITHMETIC

Supplementary to any Series.

Entered according to Act of Congress, in the year 1866, and again in the year 1867, by

HENRY B. MAGLATHLIN,
in the Clerk's Office of the District Court of Massachusetts.

Copyright, 1876, by Henry B. MAGLATHLIN.

Copyright, 1894, by Henry B. MAGLATHLIN.

The Riverside Press, Cambridge, Mass., U. S. A.
Electrotyped and Printed by H. O. Houghton & Company.

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.

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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.

In the use of the book the course may be abridged, at the discretion of the teacher, by omitting Metric Weights and Measures, Longitude and Time, Present Worth, Averaging of Accounts, Taxes, Duties, Cube Root, Medial Proportion, Series, and other parts marked by an asterisk (*).

In the Appendix may be found rules and applications of a technical nature of great value to farmers, mechanics, and other manual laborers ; also, examination problems, which have been selected largely from papers used by prominent educators.

Encouraged by the marked appreciation of this book, great care bas been taken to keep it up with the times, in all respects.

Silver LAKE, Mass., 1894.

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