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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.

HARVARD
UNIVERSITY

LIBRARY
JUN 1 1957

5671

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

LANE S. HART,
PRINTER AND BINDER,

HARRISBURG, PA.

[graphic][subsumed]

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 steadily 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 (249-257) 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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