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NUMBERS SYMBOLIZED

AN

ELEMENTARY ALGEBRA

BY

DAVID M. SENSENIG, M. S.
PROFESSOR OF MATHEMATICS, STATE NORMAL SCHOOL, WEST CHESTER, PA.

NEW YORK, BOSTON, AND CHICAGO
D. APPLETON AND COMPANY

1889

EducT 128.89.780

HARVARD COLLEGE LIBRARY

BY EXCHANGE

har. 21, 1939

COPYRIGHT, 1888,
By D. APPLETON AND COMPANY.

PREFACE.

THE aim of this volume is to lay the foundation for a more extensive and philosophical treatise soon to follow, and to aid in supplying the needs of the common, high, normal, and other preparatory schools and academies, where the time allotted to this department of knowledge is necessarily limited to an elementary treatise.

In scope it includes all subjects essential to a study of higher arithmetic, elementary geometry, and the elements of physics. All matter, however, is treated in an elementary manner, so that any ordinarily intelligent student, with a fair knowledge of the principles of commonschool arithmetic, may master it. All broad generalizations and discussion of general problems have been purposely excluded.

In the earlier lessons, fundamental ideas and principles are developed inductively, and then formulated into as simple and concise statements as is consistent with truth. Further on, definitions appear at the beginning of subjects, and principles are deduced from the solutions of characteristic examples. And still later, noticeably in proportion, propositions are first enunciated and then logically proved. Thus, the pupil is led by easy transition from the more elementary forms of reasoning to pure mathematical demonstration.

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