ELEMENTS OF GEOMETRY BY GEORGE C. EDWARDS, PH.B. ASSOCIATE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. 1897 All rights reserved Eduel 148.77.345 Harvard College Library Dec 20, 1918. Transter d from COPYRIGHT, 1895, BY GEORGE C. EDWARDS. Set up and electrotyped October, 1895. Reprinted June, 1896; July, 1897. Norwood Press J. S. Cushing & Co. - Berwick & Smith PREFACE. THE large number of Geometries recently published is an indication of the fact that, so far as Geometry is concerned, there is an unsatisfied want in High Schools, Academies, and Colleges. It is in the hope of supplying this need that the book here presented has been written. Effort has been made so to frame the definitions that they will not have to be changed when the student comes to the higher reaches of the subject, or when he advances to other branches of mathematics. Effort has been made to introduce new material when needed, and not before; to appeal to the understanding; to discourage mere memorizing; and to avoid entering into confusing details. Corollaries and scholia have been in large part replaced by exercises, every one of which the student must work out as he comes to them. At the end of the Plane Geometry and at the end of the Solid Geometry there will be found a sufficiently large number of exercises to give a review of the work preceding them, and thoroughly to establish method of |