ON ARITHMETIC, DESIGNED PARTICULARLY AS A TEXT BOOK FOR CLASSES, IN WHICH THE PRINCIPLES OF THE SCIENCE ARE INDUCTIVELY DEVELOPED, AND RENDERED SIMPLE BY MODES OF ILLUSTRATION, DEVISED AFTER ACTUAL EXPERIMENT IN THE SCHOOL ROOM; COMBINING WRITTEN ARITHMETIC WITH COPIOUS AND CONTAINING A VARIETY OF USEFUL PRACTICAL ABBREVIATIONS IN CALCULATION, NOT FOUND IN ANY SIMILAR WORK: ADAPTED TO THE FEDERAL CURRENCY, AND RENDERED ENTERTAINING TO THE PUPIL, BY A GREAT VARIETY OF THE WHOLE CONSTITUTING THE MOST COMPLETE SYSTEM OF PRACTICAL ARITHMETIC, BY FREDERICK A. P. BARNARD, A. B. HARTFORD: PUBLISHED BY PACKARD & BUTLER. DISTRICT OF CONNECTICUT, ss. L. S. BE IT REMEMBERED, That on the thirteenth day of July in the fiftyfifth year of the Independence of the United States of America, Packard & Butler of the said District, have deposited in this office the title of a Book, the right whereof they claim as Proprietors in the words following, to wit: 26 "A treatise on Arithmetic, designed particularly as a text book for classes, in "which the principles of the science are inductively developed, and rendered "simple by modes of illustration, devised after careful observation, and actual "experiment in the school room; combining written arithmetic, with copious "mental exercises, and containing a variety of useful practical abbreviations in "calculation, not found in any similar work: adapted to the Federal currency, and "rendered entertaining to the pupil, by a great variety of amusing problems, "involving the principles illustrated; the whole constituting the most complete system of practical arithmetic, now before the public. By FREDERICK Å. P. "BARNARD, A. B., Mathematical Instructor in the Hartford Grammar School." In conformity to the act of Congress of the United States, entitled, "An act for "the encouragement of learning, by securing the copies of Maps, Charts and "Books, to the authors and proprietors of such copies, during the times therein "mentioned."-And also to the act, entitled, "An act supplementary to an act entitled, 'An act for the encouragement of learning, by securing the copies of 'maps, charts, and books, to the authors and proprietors of such copies during "the times therein mentioned,' and extending the benefits thereof to the arts of "designing, engraving, and etching historical and other prints." CHARLES A. INGERSOLL, Clerk of the District of Connecticut. A true copy of record, examined and sealed by me, CHARLES Á. INGERSOLL, Clerk of the District of Connecticut. PREFACE. A preface is not unfrequently made the vehicle of conveying to the public an author's apology, for having presumed to think and write upon a subject, on which many others have thought and writ. ten before him. Such an apology, however, while it betrays a want of that manly confidence, with which every one, who is conscious of having striven, with integrity of purpose, to promote the good of his fellows, should look forward to the award of an intelligent public; is in itself, unnecessary, because ineffectual to accomplish the object, for which it is intended. In the present enlightened age, works are judged of, by their own intrinsic merit, and not by what their authors may choose to say in their favor: and nothing can be more vain, than to attempt, by fair pretences, to palm off upon the public an inferior production. Influenced by considerations like these, the author of the following treatise was about to lay it before the public, without apology, and with hardly a prefatory remark; confident, that if it possess merit, this will be discovered and approved; is otherwise, that whatever he could say, would be a mere waste of breath. He deems it due, however, to those, whose interesting task it is, "to rear the tender thought," to state in what respects he has chosen to differ from other arithmeticians, and also, briefly to assign his reasons for so doing. These are the following: 1. The book commences in a style likely to attract and fix the attention of the pupil, and which, for its simplicity, is calculated to prevent the prejudices, which the young are so apt to conceive against mathematical studies. It is believed that, by commencing below the level of the pupil's capacity, and thus rendering it certain that every thing is understood in the outset, important advantages are gained; among which it is not the least, that the learner becomes encouraged to expect that he shall understand the parts which succeed. 2. In passing from the mental to the written exercises, it will be observed that the transition is so gradually made, as to render the resemblances and the differences entirely distinct. While the same general principle is seen obviously to pervade the whole of the same class of examples, the facilities of calculation afforded by the scheme of notation, which are of course mostly peculiar to written arithmetic, may easily be distinguished. 3. In developing the principles of those operations, embraced under what are usually called the ground rules, it has been on object to illustrate each step of the process separately. This is an important distinction between the present and all former treatises on the subject. Thus, in addition, the first examples only differ from the preceding mental exercises, in requiring the numbers concerned to |
