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AN

ELEMENTARY TREATISE

ON

ARITHMETIC,

IN

THEORY AND PRACTICE:

ADAPTED TO THE INSTRUCTION OF YOUTH IN SCHOOLS AND

ACADEMIES IN THE UNITED STATES.

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AUTHOR OF AN ELEMENTARY TREATISE ON ALGEBRA,” THE NEW

AMERICAN GRAMMAR OF ASTRONOMY," &c. &c.

NEW-YORK:

PUBLISHED BY COLLINS & HANNAY.

J. & J. Harper, Printers.

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SOUTHERN DISTRICT OF NEW-YORK, ss. BE IT REMEMBERED, that on the 15th day of May, in the fiftyfirst year of the Independence of the United States of America, COLLINS AND HANNAY, of the said District, have deposited in this office the title of a book, the right whereof they claim, as Proprietors, in the words folloring, tó wit:

56 An Elementary Treatise on Arithmetic, in Theory and Practice: adapted to the Instruction of Youth in Schools and Academies in the United States. By JAMES RYAN, anthor of an Elementary Treatise on Algebra, the New American Grammar of Astronomy, &c. &c."

In conformity to the Act of the 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 an Act, entitled, “An Act, supplementary to an Act, entitled an Act for the encouragement of Learn ing, 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."

FREDERICK J. TTS,
Clerk of the Southern District of New-York.

012-2-41 LEC

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ADVERTISEMENT.

012-2-4MEC

As UTILITY is the great object of the following Treatise, I have spared no pains to make a careful selection of materials from the most approved sources, which may tend to elucidate, in a full and clear manner, whatever is useful in the Elements of Arithmetic, both in theory and practice.

Those authors, of whose labours I have principally availed myself, are Walker's Philosophy of Arithmetic, and Professor Thomson's Treatise on Arithmetic.

The definitions and rules which it may, perhaps, be proper for the learner to commit to memory, are in the largest type employed in the work. The examples and exercises, and the principal illustrations, are in a character somewhat smaller; and the notes at the bottom of the pages, being in a type still smaller, contain several important illustrations and remarks, which may often be very interesting to those students who have made some progress in the science of Arithmetic.

The reasons of the rules and operations are explained, not in strict, formal demonstrations, but generally by simple and easy illustrations of particular cases and examples ; and it is hoped that the subject will thus be rendered as intelligible and attractive as possible. This part of Arithmetic, as has been very justly observed by Professor Thomson, is too generally neglected in treatises on this subject, and thus one of the principal divisions of Mathematical Science is converted into a mere practical art, and what is calculated to call forth and improve the reasoning power of the pupil, is degraded into a dry exercise of memory.

Of the examples and exercises, some are proposed in purely abstract terms, being intended merely to afford practice to the learner in the rules and modes of calculation. To these are subjoined, in those parts of the work in which it could be conveniently done, other questions, which will not only afford

the pupil further exercise on the rules which precede them, but will also furnish him with many important facts in Commerce, Geography, Astronomy, Chronology, Chemistry, and other departments of knowledge.

As-the information contained in these questions has been all derived from authentic sources, its correctness may be depended on; and, it is hoped, that what is thus presented, may excite, in the young reader, a desire to enrich his mind by the acquisition of further information of a similar nature.

J. R.

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