DEPARTMENT OF EDUCATION LELAND STANFORD JUNIOR UNIVERSIT! OF PLANE GEOMETRY, ON THE HEURISTIC PLAN, WITH NUMEROUS EXTRA EXERCISES, BOTH 624597 COPYRIGHT, 1891, BY G. I. HOPKINS. TYPOGRAPHY BY J. S. CUSHING & Co., BOSTON, U.S.A. PRESSWORK BY BERWICK & SMITH, BOSTON, U.S.A. PREFACE. THIS book is published primarily for the author's pupils, and secondarily for that constantly increasing number of teachers who are getting more and more dissatisfied with the old methods of teaching geometry, but who have hitherto found no manual suited to their needs. That the reasoning faculties of a child or youth are developed by use, goes without saying; and consequently the method of teaching geometry whereby the pupil originates the demonstration, or simply demonstrates, rather than memorizes the demonstrations of another, needs no defence at my hands. This manual has stood the test of three years' work in the class-room, and differs from other geometries that provide for original work, in that the original demonstrations and constructions are not side issues, so to speak, but are required of the pupil in that sequence of theorems and problems which may be called the regular required work, and of which complete demonstrations are usually given in other manuals for the pupil to memorize. In this work demonstrations are given only where the average pupil would be at a loss to know how to proceed, and generally, as illustrative of methods, while others are partially given and left for the pupil to complete. In other cases, wherever the author has found that his own pupils were not working to advantage, he has introduced sugges tions, of which pupils may or may not avail themselves. iii |