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TO THE

NATIONAL ARITHMETIC.

ON THE

INDUCTIVE SYSTEM;

COMBINING THE

ANALYTIC AND SYNTHETIC METHODS,

IN WHICH

THE PRINCIPLES OF THE SCIENCE
ARE FULLY EXPLAINED AND ILLUSTRATED.

DESIGNED FOR COMMON SCHOOLS AND ACADEMIES.

BY BENJAMIN GREENLEAF, A. M.,

PRINCIPAL OF BRADFORD TEACHERS' SEMINARY.

NEW STEREOTYPE EDITION,
WITH ADDITIONS AND IMPROVEMENTS.

BOSTON:
PUBLISHED BY ROBERT S. DAVIS.
NEW YORK : PRATT, WOODFORD & Co., AND HUNTINGTON & SAVAGE,
PHILADELPHIA : THOMAS, COWPERTHWAIT & Co.

And sold by the trade generally.

1849.

Edellisht po 43%

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

Clerk's Office of the District Court of the District of Massachusetts.

GREENLEAFS SERIES OF ARITHMETICS. 1. MENTAL ARITHMETIC, upon the Inductive Plan, designed for Beginners. By Benjamin Greenleaf, A. M., Principal of Bradford (Mass.) Teachers' Seminary.

2. INTRODUCTION TO THE NATIONAL ARITHMETIC, designed for Common Schools. Fifteenth improved stereotype edition, revised and enlarged.

3. THE NATIONAL ARITHMETIC, for advanced Scholars in Common Schools and Academies. Twenty-fifth improved stereotype edition. 360 pages, full bound.

COMPLETE KEYS TO THE INTRODUCTION AND NATIONAL ARITHMETICS, containing Solutions and Explanations, for Teachers only. (In separate volumes.)

*** The attention of Teachers and Superintendents of Schools generally is respectfully invited to this popular system of Arithmetic, which is well adapted to all classes of students. The whole or a part of this series has been recommended and adopted by the superintending school committees of the principal towns in New England, and is also used in the best public and private schools in various sections of the United States.

GREENLEAF'S NATIONAL ARITHMETIC is now extensively used as a text-book in many distinguished seminaries of learning, including the following: - The several STATE NORMAL Schools in Massachusetts, under the direction of the State Board of Education ; the NORMAL Schools in New York city; Rutgers Female Institute, New York; Brooklyn (N. Y.) Female Academy; Abbott Female Academy, and Phillips Academy, Andover; Chauncey Hall School, Boston; Bradford Female Seminary ; Phillips Academy, Exeter ; Young Ladies' Institute, Pittsfield ; Worcester County High School, Worcester; Williston Seminary, East Hampton, Mass. ; together with the best schools in Boston, New York, Philadelphia, Richmond, Charleston, Savannah, Mobile, New Orleans, and other cities; and wherever the work has been introduced, it is still used with great success, - which is deemed a sufficient recommendation.

Parker's Progressive Exercises in English Composition. New stereotype edition, revised, enlarged, and improved. 144 pages. Price, 31 cents.

Clasg-Book of Prose and Poetry: consisting of Selections from the best English and American Authors; designed as Exercises in Parsing, for the use of Common Schools and Academies. By T. Rickard, A. M., and H. Orcutt, A. M. (Teachers). Price 124 cents single, 81 per dozen. *** A cheap work like the above (comprised in a small volume) has long been needed.

The Classical Reader: A Selection of Lessons in Prose and Verse, from the most esteemed English and American Writers. Intended for the Use of the Higher Classes in Public and Private Seminaries. By F. W. P. Greenwood, D. D., and George B. Emerson, A. M., of Bos. ton. Tenth edition, stereotyped. With an engraved frontispiece.

Smith's Class-Book of Anatomy : Explanatory of the First Principles of Human Organization as the Basis of Physical Education ; with numerous Illustrations, a full Glossary, or Explanation of Technical Terms, and Practical Questions at the Bottom of the Page. Designed for Schools and Families. Tenth stereotype edition, revised and enlarged.

A Grammar of the Greek Language. By: Benjamin Franklin Fisk, A. M. Twenty-ninth improved stereotype edition. *** Fisk's Greek Grammar is used in Harvard University, and in many other dis. tinguished collegiate and academic institutions in various parts of the United States.

Fisk's Greek Exercises. [New Edition.] Greek Exercises : containing the Substance of the Greek Syntax, illustrated by Passages from the best Greek Authors, to be written out from the Words given in their simplest Form. By Benjamin Franklin Fisk, A. M. "Consuetudo et exercitatio faci. litaiem maxime parit." —Quintil. Adapted to the Author's “Greek Grammar."

Leverett's Cæsar'g Commentaries. Caii Julii Cæsaris Commentarii de Bello Gallico ad Codices Parisinos recensiti, a N. L. Achaintre and N. E. Lemaire. Accesserunt Notulæ Anglicæ, atque Index Historicus et Geographicus. Curavit F. P. Leverett, A. M.

Folsom's Cicero'g Orations. M. T. Ciceronis Orationes Quædam Selectæ, Notis Illustratæ. (By Charles Folsom, A. M1 In Usum Academiæ Exoniensis. Editio stereoty pa, Tabulis Analyticis in. structa.

(These editions of Cæsar and Cicero are highly recommended by Prof. John J. Owen.)

Published by ROBERT S. DAVIS, 120 Washington Street, BOS. TON, and sold by all the principal Booksellers throughout the country.

L Also constantly for sale (in addition to his owon publications), a complete assortment of School-books and Stationery, which are offered to Booksellers, School Committees, and Teachers on very liberal terms.

PRE FACE.

The present edition of this work has been thoroughly revised and rewritten, and also enlarged by the addition of nearly one hundred and fifty pages of new matter; rendering it sufficiently extensive for the majority of pupils in common schools.

The arrangement is strictly progressive; no question for solution requiring the use of a rule, or the knowledge of a principle, which has not been previously explained. In this respect it is believed the work will be found to differ from most other Arithmetics.

The author has endeavored to make the language simple, precise, and accurate, and such as in all cases to render the rules, definitions, and illustrations intelligible to the pupil.

The examples are of a practical character, and adapted not only to fix in the mind the principles which they involve, but also to interest the pupil, exercise his ingenuity, and inspire a love for mathematical science.

The reasons for the operations are explained, and an attempt is made to secure to the learner a knowledge of the philosophy of the subject, and prevent the too prevalent practice of merely performing, mechanically, operations which he does not understand.

Analysis has been made a prominent subject, and employed in the solution of questions under most of the rules in which it could be used with any practical advantage; and it cannot be too strongly recommended to the pupil to make use of this mode of operation, where it is recommended by the author.

The subject of cancellation, also, is more extensively treated, it is believed, than in any other work, of the kind. The principles on which it depends, and their application, are fully developed, and the whole subject, it is thought, is made perfectly clear to the comprehension of the learner.

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