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L

HARVARD
UNIVERSITY
LIBRARY

COPYRIGHT, 1899,

BY
J. B. LIPPINCOTT COMPANY.

ELECTROTYPED AND PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA, U. S. A.

PREFACE.

swer.

“In all the affairs of life, the arithmetical part of the business is the dominant one." How many and how much have we? How many and how much do we want? are questions that constantly obtrude themselves for an

« Arithmetic is the conclusive science that men have to apply, all their days, to all their affairs.” Of all the sciences, therefore, with which men have to do, none deserves more intelligent study or more prudent application than the arithmetical one. Memory alone cannot deal with it or comprehend it. Pupils must be trained to see, to hear, to think, in order to grasp its truths and learn to apply them. We dare say that the philosophical study of no other subject will impart to the mind of youth a higher degree of acuteness and penetration. “It makes men subtile," said Lord Bacon.

Very few pupils, we presume, enter school for the first time who have not some idea of number and of numerical combinations; but this knowledge, incidentally gathered here and there, necessarily lies in the mind in no definite or connected order. It is important, therefore, that when pupils begin the systematic study of Arithmetic, they begin with the very first lesson, so that what they already know may be set in order and be made the basis of what is next to be learned. Beginners should be

led without delay to perceive that the lesson learned today is little more than the cultivated ground out of which is to grow the lesson of to-morrow.

It is a fatal error, only too common, to start a child to study where that which he is asked to learn is out of touch with that which he already knows. Pupils should be taught very early to keep an accurate separation of the known from the unknown, and “ to be careful not to stamp a thing as known” until they have fully mastered it in all its relations to that which they know, and have done so " in that way which conscience calls honest.

The following Elementary Treatise on Arithmetic has been prepared with the view of presenting to both teacher and pupil a thoroughly systematic and gently graded scheme in which they may together make daily progress in scientific knowledge of the subject, and by a mutual interest in the work gather by diligence many of the best fruits of industry.

Nothing, from beginning to end, has been written as mere verbiage, undeserving of attention. Every word has a measure of significance, and every sentence in the book is there for the single purpose of being understood.

J. M. R.

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