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MATHEMATICS FOR COMMON SCHOOLS

PART III

HIGHER ARITHMETIC

INCLUDING

EASY ALGEBRAIC EQUATIONS AND SIMPLE

GEOMETRICAL PROBLEMS

BY

JOHN H. WALSH

ASSOCIATE SUPERINTENDENT OF PUBLIC INSTRUCTION,

BROOKLYN, N.Y.

REVISED

BOSTON, U.S.A.
D. C. HEATH & CO., PUBLISHERS

NGARI

COPYRIGHT, 1893,
BY JOHN H. WALSH.

Norwood Press :
J. S. Cushing & Co. – Berwick & Smith.

Boston, Mass., U.S.A.

PREFACE.

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MATHEMATICS FOR COMMON SCHOOLS is a one-book arithmetic in three parts. Part I., an ELEMENTARY ARITHMETIC, contains those portions of the subject needed by all pupils of the common schools : addition, subtraction, multiplication, and division of whole numbers; simple fractions; and the most commonly used denominations of compound numbers.

Part II., an INTERMEDIATE ARITHMETIC, intended for pupils of the fifth and sixth school years, gives a sufficiently full treatment of common and decimal fractions, and of compound numbers, and takes up the simpler and more practical parts of percentage and interest. A short chapter on easy algebraic equations of one unknown quantity is added, to be used whenever it is deemed advisable.

Part III., a HIGHER ARITHMETIC, completes the ordinary grammar school course in this subject, and contains, in addition thereto, a chapter on algebraic equations and one on elementary constructive geometry, with applications. These two chapters are placed, for convenience, at the end of the work; but it is intended that suitable parts of each be taught from time to time throughout the last two years of the grammar school.

The special features of the work are its division of the arithmetical portion into half-yearly chapters, instead of the ordinary arrangement by topics; the omission, as far as possible, of rules and definitions; the very great number and variety of the examples ; the use of the equation in the solution of arithmetical problems, especially in those of percentage and interest; and the introduction of the elements of algebra and geometry.

Believing that there is some foundation for the complaints frequently made by business men and high-school teachers that grammar-school graduates are too often slow and inaccurate in ordinary computations, the author has furnished throughout the entire work systematic drills and reviews in the addition, subtraction, multiplication, and division of ordinary numbers and of fractions.

In this endeavor to enrich the grammar school course in mathematics the attempt has not been made to shorten it so much as some may desire. The intelligent teacher can and should do the remainder for himself, by rigorously omitting all such topics as he finds unnecessary.

J. H. W.

BROOKLYN, N.Y., December, 1893.

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