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COMPILED FOR THE USE OF SCHOOLS, &c.

BY OLIVER WELCH.

SECOND EDITION,
REVISED, CORRECTED AND IMPROVED.

EXETER:

Printed by C. NORRIS & Co.

And sold at their Bookstore; sold also by most of the Booksellers and
country traders in the New-England States, and by the
Author, in Exeter. Price 62 cts. single, 6 dolls,
per. doz. and 40 dolls. per hundred.

1814.

EducT

1+8+23

1857. April. 25.
bift of

Mrs. Nathaniel A. Haven, jr.
of Portsmouth, N. H.

New-Hampshire District, to wit:

BE IT REMEMBERED, that on this thirteenth day of July, in the thirty seventh year of the Independence of the United States of America, OLIVER WELCH, of Exeter, in said district, hath deposited in this office the title of a book, whereof he claims the right as Author, in the following words, to wit: "The "American Arithmetic, adapted to the currency of the United "States, to which is added, a concise treatise on the Mensu❝ration of Planes and Solids, compiled for the use of schools, by "OLIVER WELCH." In conformity to the Act of the Congress of the United States, entitled "An Act for the encouragement of learning, by securing copies of Maps, Charts and other books, to the Authors and Proprietors therein mentioned. And also “An Act for the encouragement of learning, by securing copies of Maps, Charts and other books, to the Authors and Proprietors therein mentioned, and extending the benefit thereof to the arts of Designing, Engraving and Etching historical and other prints." R. CUTTS SHANNON, Clerk of New-Hampshire District.

A true copy of Record.
Attest....R, CUTTS SHANNON, Clerk.

PREFACE

TO THE SECOND EDITION OF WELCH'S AMERICAN ARITHMETIC.

THE sale of the first Edition of this Arithmetic has much exceeded the expectation of the Author, and the present increasing demand for them has induced him to revise, correct, and give it another impression; three thousand of the first edition have been sold in about one year, with very little exertion since this Arithmetic was first published the author has used it constantly in his school, and of course has had opportunity to discover all the crrors in the first edition, as well as to discern where any alterations could be made for the better; the errors have been corrected, and such alterations made as he thought would render the work more useful, or easy to be understood. The design of the Author, in publishing this book, is to facilitate the education of the rising generation, by furnishing them with a concise, and cheap Arithmetic, calculated in the present currency of the United States, containing all necessary rules, which are used by those who are doing busi-ness in America; having this in view he is of opinion that a book designed for a cominon school book, should contain, not only the principal rules of Arithmetic, but many other rules which are published only in books on Mathematics: Arithmetic and Mathematics are two distinct sciences, but they are so nearly connected, that it becomes necessary for every man of business to have some knowledge of Mathematics as well as of Arithmetic; Arithmetic is the art of computing by numbers; and Mathematics is the science of number and magnitude, or is numbers applied in the mensuration of superficies and solids; it is not the intention of the Author to treat of mathematics in this small treatise in its full latitude, but he only intends to treat of some of the most useful problems which often occur in business, in measuring the capacities of different bodies: to connect Arithmetic with the most useful part of Mathematics, and at the same time to comprise the whole in a book of moderate size, the Author has found it expedient to exclude many rules that are in other Arithmetics, which are of no real use in business, such as single and double Position, Arithmetical and Geometrical Progression, and several other rules which serve to amuse, rather than to give any useful information; the Author has not the least intention to censure other Arithmetics, but as he is aiming wholly at improvement, it becomes necessary to point out some of the principal deficiences of other books of this kind; the Arithmetics now extant are almost

wholly calculated in lawful money, and most of them are entirely destitute of any information on Mensuration, a subject highly necessary to be taught in every school; and the Author intends by the publication of this treatise, to furnish a great variety of useful problems in Mensuration which are not to be found in any other Arithmetic; and as the present method of computing by dollars, cents and mills is the same in all the states and is much the easiest, he is of the opinion that it ought to supersede the method of computing in pounds, shillings, pence, and farthings, and of course has calculated this book wholly in Federal money; and has only given rules to reduce the former currency of the different states into the present, and the contrary: such arrangement has been made of the rules in this book, as the Author has found by long experience in school keeping to conduce most to forward the learner; and those who are beginning to cypher in this book should follow the order of the book, observing to commit all the tables, and rules to memory before they proceed to do the questions: the Author knowing that children should be fed with milk rather than meat, has endeavoured to exclude from this treatise every thing that is intricate and hard, and has rendered the whole as simple, and easy to be understood as the nature of the work would admit of. Among the many new and useful rules in this Arithmetic is the method of making town taxes, a subject not generally understood; also many new problems in measuring timber, among which is a new and easy method of finding how much square timber is contained in any round stick, or how nuch the stick would measure if hewn square; by which an error is detected in the common method; guaging, waterleveling and tables of the monies of the world with their intrinsic value in the United States, occupy conspicuous places in this Arithmetic; and the Author flatters himself that the farmer, the mechanic, the trader, and merchant will find information in this book suited to their various occupations and while he acknowledges his grateful thanks to the generous publick, for the kind reception of the first edition of this work, he solicits that share of publick patronage which this improved edition is entitled to; and with this expectation he submits it to publick examination without any other support than its own merits; hoping that it will be highly useful in facilitating the education of youth, for whose advancement in knowledge he has spent fourteen years of the morning of his life.

Exeter, January 1, 1814.

THE AUTHOR.

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