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EMBRACING A COMPLETE COURSE FOR SCHOOLS AND

ACADEMIES

BY

WILLIAM J. MILNE, Ph.D., LL.D.

LATE PRESIDENT OF NEW YORK STATE COLLEGE FOR TEACHERS

ALBANY, N.Y.

AMERICAN BOOK COMPANY
NEW YORK CINCINNATI

CHICAGO

Kanc ing.nlist

HARVARD
UNIVERSITY
LIBRARY

Copyright, 1892, 1895, and 1911, by AMERICAN BOOK COMPANY.

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PREFACE.

In the preparation of this work the author has aimed to secure two results; namely, skill in numerical computations, and a proper understanding of the reasons for the steps in the explanation of processes and the solution of problems. Skill in computing may be acquired without any intelligent apprehension of arithmetical science, and a profound insight into the truths and principles of arithmetic may be attained without much facility in using numbers. Very many people will prefer to have the student trained to be rapid and accurate in computations, and they will esteem a rapid accountant more competent in mathematics than the learned astronomers of our time; while others will prefer that training which cultivates the reasoning powers, even at the expense of practical expertness in the use of numbers. The author has endeavored to secure both these ends by embodying in the book a large number of examples upon which the pupil may be trained to accuracy and rapidity, while at the same time he has not failed to incorporate in it a large number of problems that are designed to train the analytical powers and to develop the reasoning faculties.

In practical business life, the processes learned in schools are often of very little value, because they are not the natural processes of the business man. Students who learn to work examples in a mechanical way find themselves unable to solve with certainty very simple problems, after they have left school a few weeks, because they have been taught a school method rather than a natural method. The author has, therefore, adopted business methods of computation wherever they could be wisely substituted for

the processes of the schools: he has preceded them with exercises which lead the student directly and easily to a clear apprehension of the steps in the solution and the necessity for them; and he has accompanied the solutions with explanations which enable the pupil to comprehend all that he needs to know about the operations.

By these means the student is led to employ business methods of solution because they are generally natural methods, and to understand and explain every step in the process. A student who has been trained in this manner will never forget a process or a rule, because he can devise the process and frame the rule at will.

The work is of sufficiently comprehensive scope to meet the demands of even the most advanced schools. The unusually practical character of the problems will be discerned by a very cursory examination; oral and written exercises are given in connection with each subject, and frequent and thorough reviews serve to test the pupil's proficiency, to fix the principles of the science in his mind, and to train and develop his power of reasoning.

The method exemplified in presenting the various subjects is in accord with what is deemed best in modern methods of teaching; the order and arrangement of the subjects, though they are in some respects a departure from that usually given, will hasten the pupil's progress by removing to the latter part of the book subjects too difficult for the average pupil when he reaches them, and of little practical value to any student; the explanations are thought to be conspicuously lucid, the steps logical, the definitions, principles, and rules brief and accurate.

The author desires to express his indebtedness to many educators of prominence for valuable suggestions regarding the scope

of the work and its educational character. The cordiality with which his former works have been received gives him the hope that this book also may meet with general favor.

WILLIAM J. MILNE.

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