AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS WITH Concise and Original Methods of Solution, WHICH SIMPLIFY MANY OF THE MOST IMPORTANT RULES IN BY JOHN F. STODDARD, A.M., AUTHOR OF THE NORMAL MATHEMATICAL SERIES," ETC. NEW YORK: PUBLISHED BY SHELDON & COMPANY. CLEVELAND: INGHAM & BRAGG. CINCINNATI: APPLEGATE & Co. SHELDON & CONNOR, NORMAL MATHEMATICAL SERIES. Stoddard's Juvenile Mental Arithmetic, Stoddard's Intellectual Arithmetic, . . $0 25 0 50 0 50 1 00 1 25 1 25 2.00 0 50 1.00 1 25 2.00 Stoddard & Henkle's Elementary Algebra, Copies of the above will be promptly sent by mail, post-paid, on receipt of price by the Publishers. Entered according to Act of Congress, in the year 1849, by JOHN F. STODDARD, In the Clerk's Office of the District Court of the United States for the Southern District, of New York. Re-entered according to Act of Congress, in the year 1866, by In the Clerk's Office of the District Court of the United States for the Southern ɔtyped by SMITH & MCDOUGAL, 82 & 84 Beekman St., N. Y. PREFACE. HAVING felt the necessity of a more extended and systematic Intellectual Arithmetic for younger, as well as more advanced pupils, I prepared and used in manuscript, in my own school, for a number of years, such a series of questions as I deemed best adapted to the purpose. After observing the superior mental training derived from their use, and the ease with which pupils thus trained comprehended the more advanced branches of mathematics, I venture to submit them to the public in the following pages, hoping that they may prove as useful to other schools as they have to my own. The rule which I have observed in preparing this work is: Tell but one thing at a time, and that in its proper place. Although in many particulars the work differs from other "Mental" Arithmetics, as an examination of the "questions" will show, mention of these differences is omitted, and the following exposition of its arrangements of subjects is presented. Chapters First, Second, Third, and Fourth, from Lesson I to Lesson XV, treat respectively of Addition, Subtraction, Multiplication, and Division of simple numbers; each of which is rendered familiar by an extensive collection of practical questions. Lesson VII consists of questions which combine Addition and Subtraction; Lesson IX, of questions combining Addition, Subtraction, and Multiplication; Lesson XIII, of questions combining the twelve previous Lessons; and Lesson XIV, of questions in Proportion. Thus, an intimate connection between Lessons and even Chapters is kept up through the entire work, with the exception of Chapter Fifth, Lesson XIV to Lesson XXVII, which contains some of the most important Tables of Weights and Measures; each of which is illustrated with appropriate questions. Chapter Sixth, from Lesson XXVI to Lesson XLVI, is devoted to the subject of Fractions, in which twenty lessons are many original combinations of numbers and concise analyses. Chapter Seventh, from Lesson XLVI to Lesson LIX, consists of practical and intricate questions of various kinds, which require for their solution a thorough knowledge of the preced ing Chapters. This Chapter (perhaps not contained in any similar work), when understood, will be of great benefit to those who are studying, or who intend to study Algebra. Chapter Eighth, from Lesson LIX to the end, includes Interest, Discount, and Per Cent., in their various modifications. The method of treating these subjects is original; and renders the rules under these heads, in Written Arithmetics (which are often incomprehensible to pupils), perfectly intelligible, by reducing the whole to one continued train of reasoning. This Chapter, thoroughly taught, can not fail to quicken, strengthen, and develop the reasoning powers. Bringing into exercise, as thorough teaching of it will, nearly every principle taught in the twenty lessons of Chapter Sixth, and also the greater part of Chapter Seventh, the pupil will acquire the habit of systematically classifying his knowledge, and be enabled to call to his aid such portions of it as will assist in illustrating or demonstrating the subject under consideration. That Intellectual Arithmetic, when properly taught, is better calculated, than any other study, to invigorate and develop the reasoning faculties of the mind, to produce accurate and close discrimination, and to enable the pupil to acquire a knowledge of the Higher Mathematics with greater ease, can scarcely admit of a doubt. NEW YORK, August 1, 1860. J. F. STODDARD. PUBLISHERS' NOTE.-A new edition of this popular Intellectual Arithmetic, carefully revised by the author, is here presented in new and larger type, and on larger pages, without any changes which might interfere with its use in the same classes with previous editions. The Chapter is given at the top of each page, and the "Lessons" are numbered, in regular order, throughout the book. In Lesson XXVI are full Tables of Metrical Weights and Measures on the Decimal System, the simplicity of which is an important consideration for instructors of youth. Prof. Stoddard's new Key to this book, containing his Methods of Teaching Intellectual Arithmetic, is now published. |