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AMERICAN PROGRESSIVE SERIES.

THE

COMPLETE

ARITHMETIC.

BY

MILTON B. GOFF, A.M.,

PROFESSOR OF MATHEMATICS IN THE WESTERN UNIVERSITY OF PENNSYLVANIA,

PITTSBURGH:

PUBLISHED BY H. I. GOURLEY, Agt.

98 FOURTH AVENUE.

G6

Copyright, 1876. A. H. ENGLISH & CO.

LANE S. HART,
PRINTER AND BINDER,

HARRISBURG, PA.

CAJORI

an

PREFACE

BY

an experience of over twenty years in the class-room, the author has been convinced of these three things: 1. That both in our public schools and academies too many books have been used and too much time has been spent in the study of Arithmetic.

2. That while the study of Intellectual Arithmetic, as such, is doubtless beneficial, the greatest good results from its study in close connection with Written Arithmetic; indeed, that the two cannot be separated.

3. That while it is impossible from any text-book, to teach a pupil allthat he is to practice as a man,” it is possible to comprise in less space than is usually done, and in a manner that will serve to strengthen the reasoning powers, many of the facts with which our youth will have to deal in after life.

The aim, therefore, in the following pages has been to present in a form compact, but not obscure, all that is necessary for the instruction of youth in the science of Arithmetic, whether as a preparation for the ordinary vocations of life, or as a preliminary training for a course in Mathematics.

The First BOOK IN ARITHMETIC is intended for the younger pupils, and may be placed in their hands at a very early stage of advancement in their education. And it is safe to say, that those finishing the First Book will readily master the second, or COMPLETE ARITHMETIC. It is believed, however, that in the rural districts, as children do not enter school at as tender an age as in the cities, the present work will be found sufficiently elementary in the first part, even for beginners; and although in the body of the work the matter is often as difficult, and quite as extensive, as in the Higher Arithmetic, the whole is arranged in so progressive a manner, that the natural and necessary development of the mind of the pupil will enable him to master every difficulty.

We cannot see why Oral Arithmetic and Written Arithmetic should be separated; for every process in the latter includes, more or less, the former. Yielding, therefore, to what seemed to be a necessity, we have made the “Oral” and “ Written" alternate in every case where it was deemed judicious, presenting as great a variety of examples as is usually found in works devoted exclusively to the Intellectual, and better adapted, in our opinion, for teaching the pupil to think. At the same time, the “Oral" part can, if desired, be omitted without destroying connection between subjects. The third object has been kept

in view. Examples and problems have been chosen with special reference to the wants of our American youth. And while we do not claim perfection in this matter, we do think we have taken a step in the right direction. We believe that no man whose son is to engage in any

mechanical pursuit, will begrudge the space (219-257) given to the computation of carpenters', bricklayers’, painters', and stonemasons' work. Nor will any one having to do with lands in the Western States, regard the time devoted to Government

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Lands (211, 248) as time poorly spent. These articles we regard as being “ for the greatest good of the greatest number”; since their position, somewhat early in the work, serves the purpose of giving to many who would never see them if placed on the last pages with Mensuration, an idea of what they shall have to labor at in after years. Besides, the rules may be laid by for future use and reference.

In addition to the points named, we wish to call attention to our Outlines. It will be observed that we have a General Outline and for each chapter a Sub-outline. And although these may not be all that the heart could desire, we do think that every teacher may make them a valuable aid in the prosecution of his labors. We like them better than synopses placed at the close of the chapter ; for the mind, like the eye, takes in an object as a whole, then separates it into parts, then sub-divides each part, and so proceeds, until all the minutiæ are, in turn, examined. This is the principal object of the Outlines; though they also serve the purpose of a ready index.

In the arrangements of subjects, deviation has been made from the “beaten track”; but only with great caution. The placing of Decimals immediately after Division of Integers was decided upon only after careful experiment by many of our most experienced educators.

And last, though, perhaps, to some, not least, is the fact that although the publishers have spared neither pains nor expense (as the most casual examination of the books themselves shows) to make this series, consisting of the First BOOK IN ARITHMetic and THE COMPLETE ARITHMETIC, second to none, they propose to offer to their customers in these two volumes, what is usually found in from three to five, and at correspondingly low prices; and thus relieve our humble poor," as well as those of moderate means, of much of the expense they can so ill afford in the procuring of text-books for their children. They do not expect, however, to change in a day the habits strengthened by years. There will be men who will differ from them and us in opinion, and who will think, despite what has been said, that two books are not enough; that Intellectual and Written Arithmetic should be separate works. With these the publishers have no quarrel, but, having acted in accordance with their best judgment, now submit to an intelligent public for their decision this question so important to all interested in the subject of education.

One word to our fellow-teachers. We have made an earnest effort to present such a work as will meet with your approval and suit your wants. From comments of some of you on portions of the manuscript and proof-sheets that you have seen, we have reason to believe that you will be pleased with the result of our labors. But we cannot, and do not, expect you all to agree with us in all points. You have minds of your own; and we are glad to know that you have not only the independence to think for yourselves, but that you possess that liberality of view, that grants others the privileges you claim for yourselves. Therefore, while we do not hope to escape your criticism, we do look for that honest, straightforward expression of opinion that becomes those who are engaged in a profession which, when properly pursued, develops the noblest qualities of mind and heart.

In the preparation of this work, we have been greatly aided and encouraged by many friends, whose kind suggestions have been thankfully received and freely used. To all we return our best thanks, as well as to our co-laborers, Messrs. J. M. LOGAN and H. I. GOURLEY, of the Pittsburgh Schools, to whose superior taste we are indebted for the neat arrangement of headings, plates, and outlines, and by whose care and vigilance many errors and crudities have been avoided. WESTERN UNIVERSITY OF Pa., June, 1876.

M. B. G.

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