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PLANE AND SOLID GEOMETRY

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PLANE AND SOLID

GEOMETRY

BY

JAMES HOWARD GORE, PH.D.
PROFESSOR OF MATHEMATICS, COLUMBIAN UNIVERSITY

ELEMENTS OF GEODESY,' HISTORY OF GEODESY,"
BIBLIOGRAPHY OF GEODESY," ETC., ETC.

AUTHOR OF

NEW YORK

LONGMANS, GREEN, AND CO.

LONDON AND BOMBAY

1898

HARVARD COLLEGE LISR17

GIFT OF
GINN AND COMPANY

DEC. 26, 1923

COPYRIGHT, 1898,
By LONGMANS, GREEN, AND CO.

ALL RIGHTS RESERVED.

INTRODUCTION.

The study of Geometry is pursued with a threefold purpose. 1. To aid in the development of logical reasoning.

2. To stimulate the use of accurate and precise forms of expression.

3. To acquire facts and principles that may be of practical value in subsequent life.

The first two purposes are advocated because of their disciplinary importance; and when mathematics, because of its exactness, was the only science which furthered to a high degree these purposes, it was necessary for the student to devote a large part of his time to their study. But now other sciences, and even the languages and philosophy, claim disciplinary merit equal to that possessed by mathematics, although differing somewhat in the character of the training.

Hence it appears that the time has come when we can afford to hearken to the demands of the utilitarians, and give up those refinements in mathematics which have been retained for the mental discipline they bring about, but which are wholly lacking in practical application.

I have therefore, out of an experience as a computer and worker in applied mathematics, as well as a teacher, eliminated from this treatise all propositions that are not of practical value or needed in the demonstration of such propositions.

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