Elementary Geometry, WITH PRACTICAL APPLICATIONS. A SHORTER COURSE, UPON THE BASIS OF THE LARGER WORK: BY BENJAMIN GREENLEAF, A.M., AUTHOR OF A MATHEMATICAL SERIES. BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: BAKER, PRATT, & CO., 142 & 144 GRAND STREET. ST. LOUIS: GRAY, BAKER, & COMPANY. CHICAGO: JANSEN, MCCLURG, & CO. 1875. BARVARD COLLEGE LIBRARY FROM THE GIFT OF CHARLES HERBERT THURBER Mar 7, 1926 New Comprehensive Series; AN ENTIRELY NEW MATHEMATICAL COURSE, Fully adapted to the best methods of modern instruction. NEW PRIMARY ARITHMETIC. NEW ELEMENTARY ARITHMETIC. NEW INTELLECTUAL ARITHMETIC. NEW PRACTICAL ARITHMETIC. NEW ELEMENTARY ALGEBRA. NEW ELEMENTARY GEOMETRY. NEW HIGHER ALGEBRA, ELEMENTS OF GEOMETRY. ELEMENTS OF TRIGONOMETRY. GEOMETRY AND TRIGONOMETRY, in one volume. COMMON SCHOOL ARITHMETIC. NATIONAL ARITHMETIC. Entered according to Act of Congress, in the year 1873, by ROBERT S. DAVIS & COMPANY, In the office of the Librarian of Congress, at Washington. PREFACE. E amount of time usually devoted to the study of THE Geometry in High Schools and Academies is not sufficient for the mastery of a lengthy treatise. The present edition of Greenleaf's Elements of Geometry has been prepared to meet the wants of such institutions. It consists of all the more important theorems and problems of the science, and contains, therefore, all the Geometry required for admission into the best Scientific Schools and Colleges of the country. The arrangement and language of the "Elements" having been commended by the best mathematical teachers, no change has been made in either, except as appeared absolutely necessary to adapt the same to the proper character of a briefer and more elementary work. This book is, then not wholly a new work; but a more compendious edition of a standard manual that has proved its excellence by standing the test of the school-room. The exercises which have been freely introduced are intended to test the thoroughness of the learner's geometrical knowledge, besides being especially adapted to develop skill and discrimination in the demonstration of theorems, |