CHARLES A. HOBBS, A.M., MATHEMATICAL MASTER IN THE YOLKMANN SCHOOL, NEW YORK: A. LOVELL & CO. 1899. от TYPOGRAPHY BY J. S. CUSHING & Co., NORWOOD, MASS. Plimpton Press H. M. PLIMPTON & CO., PRINTERS & BINDERS, NORWOOD, MASS., U.S.A. PREFACE. A QUARTER of a century ago, the study of Geometry consisted chiefly in memorizing the demonstrations of a certain number of propositions. This was sufficient to enable a student to pass creditably the entrance examination at any of the leading universities. At present, however, the case is very different; the papers given at the entrance examinations demand, on the part of the student, the ability to work original exercises. To the demands thus made by the universities are largely due the great advances that have been made in the methods of teaching Geometry, whereby it has become less and less a memory study, and more and more a study for the development of the reasoning faculty. To accomplish this end, we find in use two very different methods. In one method the student receives the old time drill in memorizing demonstrations, and is then required to work a greater or smaller number of original exercises. This method does not seem to be conducive to economy of time for the student, as he obtains but little development of the reasoning faculty while occupied in memorizing demonstrations. In the other method referred to, the student, is expected to consider everything as original work, and to act accordingly. The teacher suffers a loss of time by this method, as the student needs much personal assistance in his efforts to build up a series of demonstrations. The author believes that a method which lies between these extremes will afford the best results in return for the amount of energy expended. Accordingly, he presents to the teaching profession this book, the results of sixteen years' experience in teaching Geometry. At the outset, the student should understand that a demonstration is in all cases a connected series of steps, each one distinct |
