A COMPLETE ARITHMETIC, ORAL AND WRITTEN. PART SECOND. BY MALCOLM MACVICAR, PH. D., LL.D., PRINCIPAL STATE NORMAL SCHOOL, POTSDAM, N. Y. PUBLISHED BY TAINTOR BROTHERS, MERRILL & CO., HARVARD COPYRIGHT BY TAINTOR BROTHERS, MERRILL & CO., 1879. Electrotyped by SMITH & MCDOUGAL, 82 Beckman St., N. Y. PREFACE. T HE aim of the author in the preparation of this work may be stated as follows: 1. To present each subject in arithmetic in such a manner as to lead the pupil by means of preparatory steps and propositions which he is required to examine for himself, to gain clear perceptions of the elements necessary to enable him to grasp as a reality the more complex and complete processes. 2. To present, wherever it can be done, each process objectively, so that the truth under discussion is exhibited to the eye and thus sharply defined in the mind. 3. To give such a systematic drill on oral and written exercises and review and test questions as will fix permanently in the mind the principles and processes of numbers with their applications in practical business. 4. To arrange the pupil's work in arithmetic in such a manner that he will not fail to acquire such a knowledge of principles and facts, and to receive such mental discipline, as will fit him properly for the study of the higher mathematics. The intelligent and experienced teacher can readily determine by an examination of the work how well the author has Special attention is invited to the method of presentation given in the teacher's edition. This is arranged at the beginning of each subject, just where it is required, and contains definite and full instructions regarding the order in which the subject should be presented, the points that require special attention and illustration, the kind of illustrations that should be used, a method for drill exercise, additional oral exercises where required for the teacher's use, and such other instructions as are necessary to form a complete guide to the teacher in the discussion and presentation of each subject. The plan adopted of having a separate teacher's edition avoids entirely the injurious course usually pursued of cumbering the pupil's book with hints and suggestions which are intended strictly for the teacher. Attention is also invited to the Properties of Numbers, Greatest Common Divisor, Fractions, Decimals, Compound Numbers, Business Arithmetic, Ratio and Proportion, Alligation, and Square and Cube Root, with the belief that the treatment will be found new and an improvement upon former methods. The author acknowledges with pleasure his indebtedness to Prof. D. H. MACVICAR, LL.D., Montreal, for valuable aid rendered in the preparation of the work, and to CHARLES D. MCLEAN, A. M., Principal of the State Normal and Training School, at Brockport, N. Y., for valuable suggestions on several subjects. POTSDAM, September, 1877. M. MACVICAR. |