PROGRESSIVE INTELLECTUAL ARITHMETIC; ON THE INDUCTIVE PLAN. BEING A SEQUEL TO THE PROGRESSIVE PRIMARY ARITHMETIC, CONTAINING MANY ORIGINAL FORMS OF ANALYSIS APPLICABLE TO A GREAT VARIETY OF PRACTICAL QUESTIONS. AND DESIGNED FOR THE MORE ADVANCED CLASSES IN COMMON SCHOOLS AND ACADEMIES. EDITED BY DANIEL W. FISH, A.M. NEW YORK .: CINCINNATI CHICAGO ARVARD COLLEDE LIBRARY GIFT OF MRS. CHARLES S. PEIRCE Copyright, 1863, by DANIEL W. FISH. ROB, INTEL, AR. Printed by William Tvison New York, U. S. A. PREFACE. THE importance, and the practical benefit to be derived from the study of Intellectual Arithmetic, not only as a preparation for business life, but as a means of developing and strengthening the hinking and reasoning powers, and of thorough mental culture, an not be over-estimated. Not only is it a necessary study for young pupils, but indispensable to the more advanced student, as a preparation for the prompt and accurate business man. And it is believed that, as a general rule, the most critical, correct, and ready students of mathematics are those who have been most thoroughly drilled in intellectual arithmetic. This work has been prepared more especially for advanced classes, and is designed for those who have first been well taught in the primary book, and for such as are pursuing the study of written arithmetic, or algebra, and who have never been thoroughly exercised in this branch of study. Only a few of the many points of difference between this and other similar works, and which, it is believed, renders this superior to them, will be referred to. It is more complete, comprehensive, and progressive in its character. The arrangement and classification are more strictly systematic, and in accordance with the natural order of mathematical science. The development of principles, and their applications, are shown by a more numerous selection, and greater variety of appropriate examples, progressively arranged, commencing with those that are simple and easy, and advancing to those more complex and difficult. At intervals, and especially in the closing sections of each chapter, examples are given containing such a combination of principles, and forms of analysis, as to require a knowledge of almost every principle previously taught, thus affording the pupil a thorough review, as well as requiring him to classify his knowledge of what he has been over. One of the most important, and, it is thought, one of the most original and useful features of this work, is the full, concise, and uniform system of ANALYSIS it contains, the result of long expe rience in the school-room. Particular attention is invited to the subjects of Fractions, Percentage, and Interest; their treatment is peculiar, and adapted to obviate many of the difficulties, and greatly abbreviate most of the operations in them. (3) |