1

Improved Stereotype Edition.

INTRODUCTION

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.

1846.

Educ, T 118.46.435

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

BY BENJAMIN GREENLEAF,

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

STANDARD BOSTON SCHOOL BOOKS.

GREENLEAF'S 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. Twelfth improved stereotype edition. 196 pages, half bound. 3. THE NATIONAL ARITHMETIC, for advanced Scholars in Common Schools and Academies. Eighteenth improved stereotype edition. 324 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 National Arithmetic' has been extensively introduced in various sections of the United States, and is highly recommended by many distinguished teachers who have used it, for its adaptedness to give students a thorough practical knowledge of the science. It is the text-book in the Normal Schools in Massachusetts, and New York city, and the best schools in Boston, New York, Philadelphia, Richmond, Charleston, Savannah, Mobile, New Orleans, and other cities.

PARKER'S PROGRESSIVE EXERCISES

In English Composition. Forty-fifth improved stereotype edition. Price 25 cents.
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 Rev. F. W. P. Greenwood, D. D. and G. B. Emerson, A. M. of Boston. 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. Ninth stereotype edition, revised and enlarged.

A GRAMMAR OF THE GREEK LANGUAGE.
By Benjamin Franklin Fisk. Twenty-sixth improved stereotype edition. Fisk's
Greek Grammar is used in Harvard University, and in many other distinguished Col-
legiate 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. Consuetudo et exercitatio facilitatem maxime parit.'-Quintil. Adapted to the Author's Greek Grammar.' Sixteenth stereotype edition.

Fisk's Greek Exercises are well adapted to illustrate the rules of the Grammar, and constitute a very useful accompaniment thereto.

LEVERETT'S CÆSAR'S COMMENTARIES.

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

FOLSOM'S CICERO'S ORATIONS.

M. T. Ciceronis Orationes Quædam Selectæ, Notis Illustratæ. [By Charles Folsom, A. M.] In Usum Academiæ Exoniensis. Editio stereotypa, Tabulis Analyticis instructa.

I have examined with some attention Cæsar's Commentaries, edited by Leverett,
and Cicero's Orations, edited by Folsom, and am happy to recommend them to clas-
sical teachers, as being, in my estimation, far superior to any other editions of those
works to which students in this country have general access.
'JOHN J. OWEN,
Editor of 'Xenophon's Anabasis,' and Principal of Cornelius Institute, N. Y. City.
ALGER'S MURRAY'S GRAMMAR, AND EXERCISES.
ALGER'S MURRAY'S READER AND INTRODUCTION.
Published by ROBERT S. DAVIS, School-Book Publisher, BOSTON,
and sold by all the principal Booksellers throughout the United States.

Also constantly for sale, (in addition to his own publications,) a
complete assortment of School Books and Stationery, which are offered to
Booksellers, School Committees, and Teachers, on very liberal terms.
RD COLLEGE LIBRARY

GIFT OF

LuhGE ARTHUR PLIMPTON

JANUARY 20, 1924

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.

BRADFORD SEMINARY,

Nov. 1st, 1842.

THE AUTHOR.

NOTICE.

A KEY to this work, in which the method of solving the questions is fully exhibited, has just been published, for the convenience of teachers only.

October 25th, 1844.