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COMPLETE

ARITHMETIC,

UNITING

MENTAL AND WRITTEN EXERCISES

IN A

OF INSTRUCTION.

RAL SYSTEMSOME LIMENTARY Cone

VW, TEWKSBURY,

N. E. Agent,
8 HAWLEY ST., BOSTON.

By E. E. WHITE, M: A.

By E. E. VOPINION DESIRED.

VAN ANTWERP, BRAGG & CO.,
137 WALNUT STREET,

28 BOND STREET
CINCINNATI.

NEW YORK.

HARVEY'S SPELLER AND READERS.
HARVEY'S LANGUAGE COURSE.
WHITE'S ARITHMETICS.
ECLECTIC GEOGRAPHIES.
SCHUYLER'S ALGEBRA AND GEOMETRY.

HARVARD
UNIVERSITY
I LIBRI
147*1'0 .

Entered according to Act of Congress, in the year 1870, by

WILSON, HINKLE & CO., In the Clerk's Office of the District Court of the United States for PREFACE.

the Southern District of Ohio.

ECLECTIC PRESS:
VAN ANTWERP, BRAGG & CO.,

CINCINNATI.

This work is called a COMPLETE ARITHMETIC, because it embraces all the subjects which properly belong to a school arithmetic, and because it treats these subjects both analytically and inductively. It is designed to be a complete text-book for pupils who have mastered the elements of numbers.

The work is characterized by the same features as the lower books of the series, viz. :

1. It combines Mental and Written Arithmetic in a practical and philosophical manner. This is done by making the mental exercises preparatory to the written; and thus these two classes of exercises, which have been so long and so unnaturally divorced, are united as the essential complements of each other.

2. It faithfully embodies the inductive method of teaching. The written methods are preceded by the analysis of mental problems, and both the written methods and the principles which they involve, are derived inductively from the analytic processes. The successive steps of each process are mastered by the pupil through the solution of problems, and he is required to deduce and state the rules before he is confronted with the author's generalization. All definitions which are deducible from the processes, and, with few exceptions, all principles and rules, are placed after the problems-a feature peculiar to this Series.

3. It is specially adapted, both in matter and method, to the grade of pupils for which it is designed. The greater portion of the work is devoted to a progressive and thorough treatment of subjects not embraced in the lower books — an arrangement which specially meets the wants of Graded Schools. Not more than twenty pages are in any sense a repetition. The repeated matter consists of definitions, principles, and rules, all the problems being new. The subjects before treated are not only concisely reviewed, but from a higher stand-point. Of the twenty-four pages devoted to the fundamental rules, eight present new abbreviated methods; and of twenty-eight pages devoted to Denominate Numbers, simple and compound, more than sixteen discuss new topics. A sim ilar difference is observable in the treatment of Common Fractions, Decimal Fractions, United States Money, etc. Among the added articles worthy of special mention are those on Denominate Fractions, the Metric System, Longitude and Time, and Foreign Exchange.

In the number of problems, the author has aimed to hit the golden mean between a paucity and an excess, and the greatest pains have been taken to make them sufficiently progressive, varied, and difficult, to afford the requisite drill and practice. Instead of rehashing old problems, with their incorrect data and obsolete terms, the author has gone to science and history for statistical information of practical value, and he has aimed to present the current values, terms, forms, and usages of American business. The mental problems will be found as difficult and comprehensive as those which constitute the latter half of the standard Mental Arithmetics, and are sufficiently numerous to afford thorough drills in analysis.

The explanations of the written processes are not designed to serve as models for the pupil to memorize and repeat. They are intended to supplement the analysis. In some cases, a formal analysis is given; in others, a principle is deduced or demonstrated; and in others, the process is described or its principles stated. Neither teacher nor pupil is denied the privilege of determining his own explanations.

Another characteristic feature of this work is the prominence given to PRINCIPLES. A clear comprehension of the principles of arithmetic is essential to its thorough mastery, and their induction, proof, and illustration are mental exercises of great value. Until the pupil can step inductively from processes to principles, he has not a thorough knowledge of numbers. In this work the principles are concisely and formally stated in connection with the rules which are based upon them.

The author invites special attention to the sections treating of Percentage, Ratio and Proportion, and Involution and Evolution. Over eighty pages are devoted to Percentage and its applications, and it is believed that the treatment will be found not only full and thorough, but of great practical value. The student who masters these pages will certainly have a fair knowledge of the nature, laws, and usages of the business of the country. The introduction of Formulas, it is hoped, will prove a useful feature.

The thorough treatment of Ratio before Proportion, and of the latter before its application to the solution of problems, will make the mastery of this subject easy. The treatment of Involution and Evolution will not escape notice. The geometrical explanations of Square Root and Cube Root are the reverse of those usually given, and are believed to be new. They will be found both simple and natural.

All useless and obsolete subjects have been omitted; and those of interest only to more advanced students and teachers, are presented in an appendix. The typography and illustrations are beautiful and appropriate. .

The COMPLETE ARITHMETIC is submitted to American teachers in the hope that it may not only be found new in its general plans and in many of its methods and details, but that it may prove eminently adapted to the present wants and condition of GRADED SYSTEMS OF INSTRUCTION.

COLUMBUS, Ohio, July, 1870.

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