HARVARD COLLEGE LIBRARY GIFT OF THE GRADUATE SCHOOL OF EDUCATION 7 Entered according to Act of Congress, in the year 1901, by J. H. DUNBAR, in the Office of the Librarian of Congress at Washington. Preface. Shall arithmetic be taught as a science or as an art? Shall its principal aim be to aid in developing a trained and logical brain or to produce an expert accountant? It is the theory of the author of this book that the subject should be regarded as equally important from both stand-points, and that both aims should be kept in view alike by those who write textbooks and those who teach them. In spite of the fact that the statement is that of one who has written an arithmetic issued by a large publishing house, and of one who is adorned with the degree LL. D., it is rather less than a half-truth to assert that "In the extending of taxes, or the finding of interest in banks, or in making bills for lumber, for excavations, for mechanics' work, etc.-the results are not obtained by computation; they are taken from prepared tables." The statement may apply in certain sections of our country, but in New England, at least, the carpenter is as little troubled at being called upon to make out a bill of lumber as he would be at being required to repeat the easier portions of the multiplication table, and the bank cashier or clerk names the interest on any ordinary principal, for 60 days, or any convenient part or multiple of that number, in less time than he could open the pages of the book with prepared tables. What characterizes the real student of arithmetic is not a pocket filled with printed technical tables, but a head filled with thoroughly comprehended principles, and with the necessary number, always small, of essential facts. A young man thus endowed need have no anxiety in whatever field of arithmetic work he may chance to be placed. As may be assumed from the preceding remarks, the author will endeavor in the remaining parts of his arithmetic to give a clear and comprehensive treatment, with numerous concrete illustrations, of practical measurements and the problems of commercial arithmetic. The plan of this book may be stated in a few words. It is to guide the mental efforts of the pupil instead of performing the work for him, and to guide them along the most direct and natural path, whether this be the beaten track followed through many generations, or some hitherto unexplored way which serves to straighten and shorten a crooked portion of the regular road. In other words the two-fold aim kept constantly in view is that the pupil should follow the most direct path, and know his exact bearings at every point. To make the attainment of this end absolutely certain, every page of the book has been developed and tested in the class room, and every principle has been demonstrated to be within the ready comprehension of any average pupil. That it will be as favorably received by the progressive teachers of New England, and prove as satisfactory to them, as the part that preceded it, is the hope and confident belief of its author. Contents. Development of terms Addition, Addend, Sum or Amount 19 Problems in Addition and Subtraction, including Dia-. 38 Development of terms Multiplication, Multiplicand, 43 Development of terms Division, Dividend, Divisor, Abstract Numbers, Factors, Square, Cube, Exponent, Products where neither Factor is Greater than 12 Complete and Test Tables in Multiplication and Division To Multiply when the Multiplicand is Greater than 12 To Divide when the Quotient is to be Greater than 12 To Multiply when the Multiplier is Greater than 12. To Divide when the Divisor is Greater than 12. To Prove Multiplication and Division Principles of Multiplication and Division |