321 BROADWAY, NEW YORK,

PUBLISH

THE AMERICAN EDUCATIONAL SERIES

A FULL COURSE

OF PROGRESSIVE TEXT-BOOKS,

FROM THE INITIAL SCHOOL BOOK TO

THE HIGHEST MANUAL USED IN COLLEGES, ON UNIFORM PRINCIPLES,

AND WHOLLY BY PRACTICAL TEACHERS.

This series is the result of twenty-five years' experience on the part of its Authors and Publishers, and the several works in it are believed to excel in their progressIve character-their attractiveness and adaptation to the young-their pure and elevated moral character-their conformity to the highest literary authoritiestheir superior mechanical execution, as regards distinct type, white paper, pleasing and appropriate engravings, tasteful and durable binding—and as the result of all, the COMPARATIVE EASE AND PLEASURE with which they are taught and learned

II. DAY AND THOMSON'S ARITHMETICS, INTRODUCTORY

TO THE MATHEMATICAL SERIES.

BY JAMES B. THOMSON, LL.D.,

AUTHOR OF MENTAL ARITHMETIO; EXERCISES IN ARITHMETICAL ANALYSIS,
PRACTICAL ARITHMETIO; EDITOR OF DAY'S SCHOOL ALGEBRA;
LEGENDRE'S GEOMETRY, ETC.

ONE HUNDRED AND TWENTIETH EDITION.

NEW YORK:

IVISON & PHINNEY, 321 BROADWAY,

(SUCCESSORS OF MARK H. NEWMAN & Co.)

CHICAGO: S. C. GRIGGS & CO., 39 & 41 LAKE ST.
BUFFALO: PHINNEY & Co.

ners.

I. MENTAL ARITHMETIC; or, First Lessons in Numbers;—for BeginThis work commences with the simplest combinations of numbers, and gradually advances to more difficult combinations, as the mind of the learner expands and is prepared to comprehend them.

II. PRACTICAL ARITHMETIC; - Uniting the Inductive with the Synthetic mode of Instruction; also illustrating the principles of CANCELATION. The design of this work is to make the pupil thoroughly acquainted with the reason of every operation which he is required to perform. It abounds in examples, and is eminently practical.

III. KEY TO PRACTICAL ARITHMETIC;-Containing the answers, with numerous suggestions, &c.

IV. HIGHER ARITHMETIC; or, the Science and Application of Numbers;-For advanced Classes. This work is complete in itself, commencing with the fundamental rulés, and extending to the highest department of the

science.

V. KEY TO HIGHER ARITHMETIC;-Containing all the answers, with many suggestions, and the solution of the more difficult questions.

VI. THOMSON'S DAY'S ALGEBRA;-This work is designed to be a ucid and easy transition from the study of Arithmetic to the higher branches of Mathematics. The number of examples is much increased; and the work is every way adapted to the improved methods of instruction in Schools and Academies.

VII. KEY TO THOMSON'S DAY'S ALGEBRA;-Containing the answers, the solution of the more difficult problems, &c.

VIII. THOMSON'S LEGENDRE'S GEOMETRY;-With practical notes and illustrations. This work has received the approbation of many

of the most eminent Teachers and Practical Educators.

IX. PLANE TRIGONOMETRY, AND THE MENSURATION OF HEIGHTS AND DISTANCES; with a summary view of the Nature and Use of Logarithms;-Adapted to the method of instruction in Schools and Academies

X. ELEMENTS OF SURVEYING;—Adapted both to the wants of the learner and the practical Surveyor. (Published soon.)

Entered according to Act of Congress, in the year 1847,
BY JAMES B. THOMSON,

in the Clerk's Office of the Northern District of New York.

PREFACE.

THE Higher Arithmetic which is now presented to the public, is the third and last of a series of Arithmetics adapted to the wants of different classes of pupils in Schools and Academies. The title of each explains the character of the work. The series is constructed upon the principle, that "there is a place for everything, and everything should be in its proper place." Each work forms an entire treatise in itself; the examples in each are all different from those in the others, so that pupils who study the series, will not be obliged to purchase the same matter twice, nor to solve the same problems over again.

The Mental Arithmetic, is designed for children from six to eight years of age. It is divided into progressive lessons of convenient length, beginning with the simplest combinations of numbers, and advancing by gradual steps, to more difficult operations, as the mind of the learner expands and is prepared to comprehend them.

The Practical Arithmetic embraces all the subjects requisite for a thorough business education. The principles and rules are carefully analyzed and demonstrated; the examples for practice are numerous, and the observations and notes contain much information pertaining to business matters, not found in other works of the kind. This is the FIRST SCHOOL BOOK in which the Standard Units of Weights and Measures adopted by the Government in 1834, were published.

The Higher Arithmetic is designed to give a full development of the philosophy of Arithmetic, and its various applications to commercial purposes. Its plan is the following:

1. The work is complete in itself. It commences with notation, and illustrating the different properties of numbers, the principles of Cancelation, and various other methods of contraction, extends to the higher operations in mercantile affairs, and the more abstruse departments of the science.

2. Great pains have been taken to render the definitions and rules clear, concise, exact, comprehensive.

3. It has been a cardinal point never to anticipate a principle; and never to use one principle in the explanation of another, until it has itself been explained or demonstrated.

4. Nothing is taken for granted which requires proof. Every principle therefore has been reinvestigated, and carefully analyzed.