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THE

ELEMENTS OF ARITHMETIC;

FOR

SCHOOLS AND ACADEMIES.

IN WHICH

DECIMAL AND INTEGRAL ARITHMETIC ARE COMBINED,

AND TAUGHT INDUCTIVELY,

ON THE SYSTEM OF PESTALOZZI.

PART FIRST.

BY PLINY E. CHASE.

PHILADELPHIA:

URIAH HUNT AND SON.
1844.

Entered, according to the Act of Congress, in the year 1844, by

PLINY E. CHASE,

in the clerk's office of the district court of the United States in and for the eastern district of Pennsylvania.

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PREFACE.

THE following work is the First Part of a treatise on Arithmetic, the plan of which is in many respects entirely new.

The book commences with Mental Questions, designed to illustrate all the fundamental principles of the science, and of such a character as to be understood by children at a very early age. The addition, subtraction, multiplication and division, of units and tens, the reason for carrying the tens in each operation, the principles of simple and compound, proper and improper fractions, and the various operations that may be performed upon them, are all taught in the most simple and concise manner.

After the pupil has become accustomed to exercise his judgment in the solution of these questions, he is allowed to read and write numbers embracing many denominations, and to perform examples on the slate. The assistance of the teacher is then required, to explain clearly and fully on the board, each new principle that is introduced, and with little further aid, the pupil will be able to go through the remaining chapters.

The boy who can read and write integers as high as millions, may be taught, with equal facility, to read and write decimals as low as millionths; and if Numeration be properly inculcated at first, no more difficulty will be found in the operations on decimals, than in those on whole numbers. The two are therefore very properly combined,-the necessity of a separate and unintelligible series of rules, is obviated,—and the scholar learns readily to solve all questions that may be proposed to him.

No rules are given to be learned by rote, but the parts that are of most importance are printed in italics. The teacher should assure himself, by frequent questioning, that every principle is fully understood,-the pupil being required to tell not only how, but why, every thing is done.

The remarks given under the head of Examples for the Board, are designed as a guide to the teacher in his explanations to the class. If the scholar be left entirely to himself, he will not understand any assistance the book may give, nearly so well as if it were communicated verbally by his instructor.

The difference between abstract and concrete numbers will be early perceived by the pupil, and it will be well for the teacher to (5)

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