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QA 103 P728

1848

DEDICATION.

TO TEACHERS, ACCOUNTANTS, MECHANICS, and the PRIVATE StuDENT OF ARITHMETIC, THE AMERICAN EQUATER

is respectfully dedicated by

THE AUTHOR.

1. TEACHERS, it is believed, will find THIS an ASSISTANT, adapted, in a peculiar manner, to facilitate the business of instruction. The mode of solving problems in the PRIMARY RULES, has been furnished at LENGTH, so that scholars may learn, with comparatively little assistance. For such calculations as involve the ratio of numbers, a minute ANALYSIS has been given, WHICH, it is hoped, will be followed in every case, in preference to the RULE. The process for analyzing questions of this kind has been fully explained, under the head of MENTAL ARITHMETIC, and applied more generally in the "EXAMPLES FOR ILLUSTRATION," (page 103,) and also throughout the remainder of the

BOOK.

2. ACCOUNTANTS, will be greatly assisted in their calculations, by making themselves acquainted with the RULES, which have been given with special reference to THEIR accommodation.

3. MECHANICS will find EQUATIONS decidedly the most simple and convenient MODE for the mensuration of SURFACES and SOLIDS WHICH has yet been suggested, and finally,

4. The PRIVATE STUDENT of ARITHMETIC, will be able to prosecute his studies successfully, without other assistance, by giving a careful attention to the explanations which accompany each particular SUBJECT.

Entered according to Act of Congress, in the year 1847, by
CONLEY PLOTTS,

in the Office of the Clerk of the District Court for the Eastern District
of Pennsylvania.

Stereotyped by

S. DOUGLAS WYETH, No. 7 Pear St., Philadelphia.

Printed by I. ASHMEAD & CO.

PREFACE.

THE present is peculiarly an age of BOOKS, and no where is this evinced more clearly than in the endless variety of school books, which literally crowd themselves upon the notice of teachers, from almost every quarter; for which cause the author feels that an apology is due to the fraternity, for asking their perusal of the following pages.

The mode of teaching Arithmetic, has been much improved within the last few years, by the introduction of an analytical system of instruction by which the mind of the pupil has been gradually led to realize those elementary principles, without which it is impossible to become interested in the study of that useful science.

The most approved method of teaching, at the present time, comprises a course of mental and written ARITHMETIC, the former of which may be considered as an introduction to the latter.

This system of instruction has been attended with a single difficulty, that has greatly enhanced the labor of teachers, and had a tendency to retard the progress of the pupil; for, while the MENTAL EXERCISES, previously studied, have prepared the mind for the more advanced operations of WRITTEN ARITHMETIC, no plan has been suggested by which the quantities may be arranged so as to be read intelligently.

The PROPORTIONATE ARRANGEMENT of numbers, so generally resorted to by former authors, has been found unavailing in a system of pure analysis, and has, therefore, been omitted by this class of teachers, as unsuited to their purpose. These difficulties, so manifest to all reflecting teachers, have presented themselves to the WRITER, and, for a time, seemed almost insurmountable, till at length the idea of EQUATIONS, (as explained in Articles XIII. and XIV. of

1 *

(v)

the AMERICAN EQUATER,) presented itself. This arrangement was immediately adopted and carried into execution, and the experiment has proved ENTIRELY SUCCESSFUL.

By the use of an EQUATION a solution in Arithmetic may be performed without losing sight of the numbers which enter into IT. This is a decided advantage, for by such a process, a principle may be illustrated without the use of literal quantities, as clearly as it could be explained by algebraic formulæ.

Another advantage of the equating system over all others, consists in the facility which it affords for correcting errors in calculation. By the old system, the original numbers are lost, in the course of a demonstration, and if an error has been committed, by multiplying or dividing by the wrong quantity, it cannot be detected till we have arrived at the conclusion; but by the use of equations, the terms are all preserved till they have been brought into a simple formula, constituting the right hand member of the last EQUATION, and hence, an error is easily detected.

A third advantage consists in the ease with which PROPORTIONATE QUANTITIES may be arranged, without losing sight of THEIR peculiar character, whether as DIMENSIONS of a surface or solid, or as FACTORS representing time, quantity, &c.; and,

Lastly, an EQUATION is the most natural form under which Arithmetical quantities can be arranged.

Great pains have been taken to illustrate every PRINCIPLE by numerous EXAMPLES, and to furnish the most concise rules which the nature of the case will admit.

With these remarks, the SYSTEM is submitted to teachers for their impartial decision, in the hope that it may prove to them as EFFICIENT an AUXILIARY as it has already been to THE AUTHOR.

Camden, (N. J.) January, 1848.

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