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TO THE

NATIONAL ARITHMETIC,

ON THE

INDUCTIVE SYSTEM;

COMBINING THE

ANALYTIC AND SYNTHETIC METHODS

WITH THE

CANCELLING SYSTEM;

IN WHICH

THE PRINCIPLES OF ARITHMETIC ARE EXPLAINED

AND ILLUSTRATED IN A FAMILIAR MANNER.

DESIGNED FOR COMMON SCHOOLS.

BY BENJAMIN GREENLEAF, A. M.,

PRINCIPAL OF BRADFORD TEACHERS' SEMINARY.

BOSTON:
ROBERT S. DAVIS, AND GOULD, KENDALL, & LINCOLN.
N. YORK: ROBINSON, PRATT, & Co., AND COLLINS, BROTHER, & Co.
PHILADELPHIA : THOMAS, COWPERTHWAIT, & Co.

BALTIMORE: CUSHING & BROTHER.

And sold by the trade generally.

1842.

Eauit 118,42,435

Entered according to Act of Congress, in the year 1842, by

BENJAMIN GREEN LEAF, in the Clerk's Office of the District Court of the District of Massachusetts.

GREENLEAF'S NATIONAL ARITHMETIC,
TWELFTH IMPROVED STEREOTYPE EDITION,

For the more advanced Scholars, forming a volume of upwards of 300 pages, handsomely printed on fine paper, and bound in leather._Also, a COMPLETE KEY to this work, designed exclusively for Teachers. Fourth Edition.

PUBLISHED BY ROBERT S. DAVIS, BOSTON, and sold by all the principal booksellers throughout the United States.

I This work, having been extensively adopted in various sections of the country, is highly commended by all intelligent Teachers who have tested it, for its practical adaptation to make thorough scholars in this department of science.

The publishers have recently received the following letter from Rev. G. B. Perry, one of the Superintending Committee of Bradford.

“Bradford, Mass., January 1, 1842. "Gentlemen : The National Arithmetic, by Benjamin Greenleaf, Esq., after having been pretty thoroughly examined by those intrusted with the superintendence of the Public Schools, was introduced into them very soon after its first publication, and has been constantly used from that time; and, after so long and extended experiment, 1 have no hesitancy in saying, the best expectations of the Committee have been fully met. A new and increased interest was thereby given to that part of Education, which has been constantly increasing in most or all of our schools, – a spirit of perseverance excited, which has carried a considerable number of our youth through the whole book, and there are now a still greater number, who are going on with a determination to perform every question. Having formerly recommended the work, as, in my opinion, possossing great merit, from the lucid and scientific manner in which its parts are arranged, and the rules of operation expressed, I have thought the above statement would afford the best testimony, that I could now give of its practical worth, and of the benefits likely to result from its introduction into other places.

“ Very respectfully, (Signed.)

“GARDNER B. PERRY." From H. Morison, Esq., of Baltimore, President, and Professor of Mathematics, in the University of Maryland.

“This is one of the most complete books of its kind, both in the extent and arrangement of its matter, that has yet appeared. Combining, as it does, the Analytic and Synthetic methods, and abounding in familiar examples, it is admirably calcu. lated to interest the pupil, and lead him, by easy and progressive steps, through the difficulties of the science, to its complete mastery, and full comprehension. To make the work more perfect, than a treatise on Arithmetic merely could be, the author has added many geometrical, mechanical, philosophical, and astronomical problems, and a concise system of Book-keeping, so that, without the aid of any other book, it is calculated to make the perfect business man, in all his various departments.

(Signed.)

“H. MORISON." Other testimonials to the merits of this work, will be found in the advertising sheet, at the end of the volume.

CAMBRIDGE:
METCALF, KEITH, AND NICHOLS, PRINTERS TO THE UNIVERSITY.

PREFACE.

The following treatise is intended for that class of pupils, who may not have sufficient time to read the larger work on this science, published by the author a few years since, and which has had extensive circulation.

It is believed, that this book contains all, that is necessary to prepare the young for the common avocations of life.

If the student wishes to obtain an extensive and full knowledge of this science, he can consult the National Arithmetic.

It has been a great object with the author to render the work practical ; how far he has succeeded, the public must judge.

The questions are original, although there may be a similarity between some of these and others, which are before the public, and which could not be well avoided.

Although the author has carefully examined every question, yet, it is possible, some few mistakes may be found in this work. These, however, will be corrected in a future edition.

With these few prefatory remarks, the author commends this small volume to the candor of an enlightened Public.

THE AUTHOR. BRADFORD SEMINARY,

Nov. 1st, 1842.

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