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ARITHMETIC,

IN WHICH THB

PRINCIPLES OF OPERATING BY NUMBERS

ARE

ANALYTICALLY EXPLAINED

AND

SYNTHETICALLY APPLIED.

ILLUSTRATED BY COPIOUS EXAMPLES

DESIGNED FOR THE USE OF SCHOOLS AND ACADEMIES.

BY DANIEL ADAMS, M. D.,
AUTHOR OF THE SCHOLAR'S ARITHMETIC, SCHOOL GEOGRAPHY, ETC.

KEENE, N. H.
PUBLISHED BY J. W. PRENTISS & CO.

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Entered according to Act of Congress, in the year 1848, by

DANIEL ADAMS, M. D. la the Clerk's Office of the District Court of the District of New Hampshire.

Stereotyped by
GEORGE A. CURTIS;
NEW ENGLAND TYPE AND STEREOTYPE POUNDRY,

BOSTON.

PREFACE.

THE "Scholar's Arithmetic,” by the author of the present work, was first published in 1801. The great favor with which it was received is an evidence that it was adapted to the wants of schools at the time.

At a subsequent period the analytic method of instruction was applied to arithmetic, with much ingenuity and success, by our late lamented countryman, WARREN COLBURN. This was the great improvement in the modern method of teaching arithmetic. The author then yielded to the solicitations of numerous friends of education, and prepared a work combining the analytic with the synthetic method, which was published in 1827, with the title of “ Adams' New Arithmetic."

Few works ever issued from the American press have acquired so great popularity as the “ New Arithmetic." It is almost the only work on arithmetic used in extensive sections of New England. It has been re-published in Canada, and adapted to the currency of that province. It has been translated into the language of Greece, and published in that country. It has found its way into every part of the United States. In the state of New York, for example, it is the text-book in ninetythree of the one hundred and fifty-five academies, which reported to the regents of the University in 1847. And, let it bé remarked, it has secured this extensive circulation solely by its merits. Teachers, superintendents, and committees have adopted it because they have found it fitted to its purpose, not because hired agents have made unfair representations of its merits, and, of the defects of other works, seconding their arguments by liberal pecuniary offers – - a course of dealing recently introduced, as unfair as it is injurious to the cause of education. The 'merits of the “New Arithmetic" have sustained it very successfully against such exertions. Instances are indeed known, in which it has been thrown out of schools on account of the “liberal offers” of those interested in other works, but has subsequently been readopted without any efforts from its publishers or author.

The “ New Arithmetic” was the pioneer in the field which it has occupied. It is not strange, then, that teachers should find defects and deficiencies in it which they would desire to see removed, though they might not think that they would be profited by exchanging it for any other work. The repeated calls of such have induced the author to undertake a revision, in which labor he would present acknowledgments to numerous friends for important and valuable suggestions. Mr. J. Homer French, of Phelps, N. Y., well known as a teacher, has been engaged with the author in this revision, and has rendered important aid. Mr. W. B. BUNNELL, also, principal of Yates Academy, N. Y., formerly principal of an academy in Vermont, has assisted throughout the work, having prepared many of the articles. The revision after Percentage is mostly his work.

The characteristics of the “New Arithmetic,” which have given the work so great popularity, are too well known to require any notice here. These, it is believed, will be found in the new work in an improved form.

One of the peculiar characteristics of the new work is a more natural and philosophical arrangement. After the consideration of simple whole numbers, that of simple fractional numbers should evidently be introduced, since a part of a thing needs to be considered quite as frequently as a whole thing. Again; since the money unit of the federal currency is divided decimally, Federal Money certainly ought not to precede Decimal Fractions. It has been thought best to consider it in connection with decimals. Then follow Compound Numbers, both integral and fractional, the reductions preceding the other operations, as they necessarily must. Percentage is made a general subject, under which are embraced many particulars. The articles on Proportion, Alligation, and the Progressions will be found well calculated to make pupils thoroughly acquainted with these interesting but difficult subjects.

Care has been taken to avoid an arbitrary arrangement, whereby the processes will be purely mechanical to the learner. If, for instance, all the reductions in common fractions precede the other operations, the pupil will have occasion to divide one fraction by another long before he shall have learned the method of doing it, and must proceed by a rule, to himself perfectly unintelligible. The studied aim has been through out the entire work to enable the ordinary pupil to understand every thing as he advances. The author is yet to be convinced that mental discipline will be promoted, or any desirable end be subserved, by conducting the pupil through blind, mechanical processes. Just so far as he can understand, and no farther, is there prospect of benefit. No good results from presenting things, however excellent in themselves, if they are beyond the comprehension of the learner.

Those teachers who prefer to examine their classes by questions, will find that little will escape the pupil's attention, who shall correctly answer all those in the present work, while teachers who practise the far superior method of recitation by analysis, will find the work admirably adapted to their purpose.

The examples, it is hoped, will require very full applications of the principles.

Many antiquated things, which it has been fashionable to copy in arithmetics, from time immemorial, have been omitted or improved, while new and practical matter has been introduced. A Key to this revision is in progress.

With these remarks, the work is submitted to the candid examination of the public, by

THE AUTHOR. Keene, N. H., February, 1848.

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SUGGESTIONS TO TEACHERS.

The writer complies with the request of the venerable author of " Adams' Arithmetic," to preface the new work with a few suggestions to his associates in the work of instruction. Though he has been engaged for sometime past in assisting to make the work better fitted to accomplish its design, he is perfectly satistied that improvement in school education is rather to be sought in improved use of the books which we now have, than in making better books. Better arithmeticians would be made by the book as it was before the present revision, using it as it might be used, than will probably be made in most cases with the new work, even though the former were very defective, the latter perfect. Exertion, then, to bring teachers to a higher standard, will be more effective in improving school education, than any efforts at improving school books can possibly be. It is here where the great improvement must be sought. Without the cooperation of competent teachers, the greatest excellences in any book will remain unnoticed, and unimproved. Pu. pils will frequently complain that they have never found one that could explain some particular thing, of which a full explanation is given in the book which they have ever used, and their attention only needed to have been called to the explanation.

Then let teachers make themselves, in the first place, thoroughly acquainted with arithmetic. The idea that they can a study and keep ahead of their classes,” is an absurd one. They must have surveyed the whole field in order to conduct inquirers over any part, or there will be liability to ruinous misdirection. Young teachers are little aware of their deficiencies in knowledge, and still less aware of the injurious effects which these deficiencies exert upon pupils, who are often disgusted with school education, because they are made to see in it so little that is meaning.

In the next place, let no previous familiarity with the subject excuse teachers from carefully preparing each lesson before meeting their classes. Thereby alone will they feel that freshness of interest, which will awaken a kindred interest among their pupils; and if on any occasion they are compelled to omit such preparation, they will discover a declining of interest with their classes. Teachers who are obliged to have their books open, and watch the page while their classes recite, are unfit for their work.

Pupils should be taught how to study. That, after all, is the great object of educating. The facilities for merely acquiring knowledge are abundant, if persons know how to improve them. The members of classes will often fail in recitation, not because they have not tried, but have not known how to get their lesson. They neglect trying, because they can do so little to advantage. They may read over a statement in their book a dozen times, they say, but cannot remember it, - because they do not understand it.' An hour spent with each pupil individually

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