PLANE AND SOLID GEOMETRY BY JAMES HOWARD GORE, PH.D. " PROFESSOR OF MATHEMATICS, COLUMBIAN UNIVERSITY 66 66 BIBLIOGRAPHY OF GEODESY," ETC., ETC. THIRD EDITION REVISED, WITH AN APPENDIX OF OVER 500 ADDITIONAL EXERCISES. NEW YORK LONGMANS, GREEN, AND CO. 91 AND 93 FIFTH AVENUE, NEW YORK 1908 G b 1908 COPYRIGHT, 1898, BY LONGMANS, GREEN, & CO. COPYRIGHT, 1899, BY LONGMANS, GREEN, & CO. ALL RIGHTS RESERVED. CAJORI: First edition, December, 1898. Reprinted September, 1899; Norwood Press J. S. Cushing Co. - Berwick & Smith Co. 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. 918306 |