THE A M E R I CAN INTELLECTUAL ARITHMETIC, DESIGNED FOR SCHOOLS AND ACADEMIES; CONTAINING AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS, WITH CONCISE AND ORIGINAL METHODS OF SOLUTION, WHICH SIMPLIFY MANY OF THE MOST IMPORTANT RULES IN WRITTEN ARITHMETIC. BY JOHN F. STODDARD, A.M., NEW YORK: CLEVELAND: INGHAM & BRAGG, OINOINNATI: APPLEGATE de Co. DETROIT: E. B. SMITH & Co. STODDARD'S JUVENILE MENTAL ARITHMETIC. 25 conts. INTELLECTUAL ARITHMETIC. Entered, according to Act of Congress in the year 1849, by JOHN F. STODDARD, the Southern Distriot of New York. Ro-entered, according to Act of Congress, in the year 1860, by SHELDON & COMPANY, the Southern District of New York, Electrotyped by SMITH & MODOUGAL, 82 & 84 Boekman St, N. Y. PREFACE. NEITHER a desire of pecuniary gain, nor a wish to appear as an author, prompted the presentation of this work to the public. Having felt the necessity of a more extended and systematic Intellectual Arithmetic for the 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 its preparation is to tell but one thing at a time, and that in its proper place. It would be laborious to point out all the particulars in which this work differs from others of a similar character; I shall, therefore, give only a brief exposition of its general plan, leaving the other differences (which, doubtlessly, will be considered of importance) to be found by those who study the book. Chapters First, Second, Third, and Fourth, treat respectively of Addition, Subtraction, Multiplication, and Division of simple numbers; each of which is rendered familiar by an extensive collection of practical questions. The last Lesson in Chapter Second, consists of questions, which combine Addition and Subtraction; the last Lesson in Chapter Third, of questions combining Addition, Subtraction, and Multiplication. Thus, an intimate connection between Lessons and even Chapters is kept up through the entire work, with the exception of Chapter Fifth, which contains a few of the most important tables of Weights and Measures ; each of which is illustrated with appropriate questions. Chapter Sixth is devoted to the subject of Fractions, and contains twenty lessons, in which many original combinations and concise solutions occur. Chapter Seventh consists of practical and intricate questions of various kinds, which require for their solution a thorough knowledge of the preceding Chapters. This Chapter (which, it is believed, is not contained in any similar work,) when thoroughly understood, will be of incalculable benefit to those who are studying, or intend to study Algebra. Chapter Eighth includes Interest, Discount, and per cent. of every description, in their various modifications. The method of treating these subjects is original; and renders the rules in Written Arithmetics, under these heads (which are often incomprehensible to pupils) perfectly intelligible by reducing the whole to one continued train of reasoning. It is believed that this Chapter, if thoroughly taught, can not fail to quicken, strengthen and develop the reasoning powers; bringing into exercise, as it does, nearly every principle taught in the twenty lessons of Chapter Sixth, and also, the greater part of Chapter Seventh, it must of necessity cause the pupil to acquire the habit of systematically classifying his knowledge, that he may, at any time, be able to call to his aid, such portions of it as will assist him in illustrating or demonstrating the subject under consideration. The mind is composed of a variety of faculties which require for their development appropriate and constant exercise. That Intellectual Arithmetic, when properly taught, is better calculated, than any other study, to invigorate and develop these faculties, to produce accurate and close discrimination, and, to enable the pupil to acquire a knowl. edge of the Higher Mathematics with greater ease, can not for a moment admit of a doubt. J. F. STODDARD. NEW YORK, August 1, 1860. |