DECIMAL ARITHMETIC, ON A NEW AND IMPROVED PLAN THROUGHOUT, COMPRISING SEVERAL NEW METHODS OF COMPUTING SIMPLE INTEREST, DUODECIMALS, AND A GREAT IMPROVEMENT IN MULTIPLICATION AND DIVISION, NOT FOUND IN ANY OTHER WORK EXTANT. BY OSMAN CALL. L. A. FLETCHER, HAN COCK FACTORY, N.H. ...... 1842. Entered according to act of Congress, in the year 1842, By OSMAN CALL, in the Clerk's Office of the District Court of the United States for the Vermont District. STEREOTYPED AND PRINTED BY MORRILL, SILSBY, & CO. CONCORD, N. H. 06-21-377 6-18-37 PREFACE. In presenting to the public a new School-Book, it may be proper to state the circumstances which have led to its publication. The author, Mr. Osman Call, having prepared manuscripts on REDUCTION, REDUCTION OF CURRENCIES, DECIMALS, INTEREST, and SQUARE AND CUBIC MEASURE, in which he had given new rules and new methods of performing arithmetical questions, wished to present his system to the public. Knowing that a complete system of arithmetic would be required, in order to render his book useful and acceptable to the public, he engaged the subscriber to act as editor in preparing a book for the press, in which his peculiar method should be found. In engaging in this enterprise, we felt our incompetency to do justice to the science of arithmetic. And the farther we proceeded, the more clearly did we see the wide field, which we had not explored, rising to our vision. But unlike many other subjects, arithmetic cannot lead one far astray, if a close adherence be maintained to the exact course indicated by figures. Hence, we have ventured to depart from the beaten path of arithmeticians, and mark out a new arrangement, new rules, and a new method of operation peculiar to this work. The subscriber made use of Mr. Call's manuscripts in preparing those articles in which his peculiar method is given. He made such selections from these manuscripts as he thought proper; added such new matter as, in his opinion, would be useful to the student, and labored to make that portion of the work as intelligible as possible. Throughout other parts of the work, the subscriber has made his own selections and arrangement, and readily assumes whatever responsibility rests upon an author. He has not confined himself to the "old method" in any article in the work. We have depended mostly upon our own resources for rules and illustrations throughout the book; yet we have not hesitated to insert questions found in other books, whenever we thought proper. The following authors have been consulted in our preparation, from each of whom we have derived greater or less aid: Pike, Lacroix, Stevens, Montgomery, Greenleaf, Adams, Little, Walsh, Euler, Allen, Day, American Encyclopedia, and Edinburgh Encyclopedia. We have aimed to make our book a useful school-book; how far we have succeeded, we shall leave to the public to judge. The Editor feels it due to himself to state, that, residing at so great a distance from the press, and thus being unable to review his proof sheets, many more errors may be found in the work, than would otherwise have escaped notice. The attention of teachers, and others, is requested in relation to points of improvement, any suggestions from whom will be thankfully received by the Editor, that any errors that may occur in this edition may be corrected in the next, and such other new matter inserted, as shall be useful in advancing the knowledge of arithmetic. ZEBULON JONES, Peterborough, N. H., Jan. 3, 1842. EDITOR, INTRODUCTION. THE importance of the science of Arithmetic to the people of the United States, is easily understood. The possession and transfer of property, a knowledge of the mechanic arts, and especially an acquaintance with the higher branches of science, make a previous understanding of this science indispensably necessary. Great advancement in the arts, or great progress in civilization, cannot be made without it. Hence, savage and barbarous people only, those unacquainted with the habits of civilized life, and destitute of the means of acquiring a knowledge of arts and sciences, will be found without any system of computing by numbers. If Arithmetic is important as a branch of education, it is not an unimportant point, what system is adopted in our schools. In decimals by inspection, our common systems adopt rules that only approximate to the true answers; while the exposition of the rules is long and difficult. In the Square and Cube Roots, rules are generally so constructed, as not to develop the true principles of the process of performing problems. This kind of frame-work in rules, carries the scholar over his work, rather than into it. Another fault is bad arrangement. Most authors agree in placing Decimal Fractions in the body of their works. Hence the student is induced to believe that, as he has ciphered so far without the use of Decimals, he may now safely go on without any knowledge of them. To show the absurdity of this arrangement, I need only say, that books, thus constructed, necessarily contradict themselves. One author goes through one hundred and thirty pages of |