PRINCIPLES 15- OF PLANE GEOMETRY ames allace BY J. W. MACDONALD, 1843 – PRINCIPAL OF THE STONEHAM (MASS.) HIGH SCHOOL Let him know a thing because he has found it out for himself, and not Boston ALLYN AND BACON 1889 QA 462 .M135P Copyright, 1889, University Press: JOHN WILSON AND SON, CAMBRIDGE. Library of W.W. Bəman, 02-17-45BHP. PREFACE. THE most appropriate preface for a book of this kind would be an exposition of the principles of psychology pertaining to the development and training of the reasoning and linguistic faculties. As such a preface, however, would be more pretentious than the book proper, and as these principles have been so well expounded by many eminent writers, I must content myself by merely urging studious investigation upon all teachers who are ambitious to practise the best methods. If teachers will do this, of one thing I am confident, they will grant that the purpose of this book is right in theory, even if in practice certain difficulties may seem to them insurmountable. As a help, however, to teachers who may wish it, I have thought it advisable to publish as a companion to this book a monograph on teaching geometry,* illustrating actual class-work, and showing in detail how some of the most difficult topics may be mastered, not, let me add, as a * Geometry in the Secondary School. Willard Small, Publisher, 24 Franklin Street, Boston, Mass. dogmatic declaration of the method of development, but only as a suggestive illustration of a method. The earnest teacher, who thoroughly understands the subject he is teaching, and who has a purpose clear in his mind, will make his own, and for him the best method. It cannot be said of this Geometry, as I have heard it said of others, that it is designed to aid inefficient teachers. The teacher who does not thoroughly understand elementary geometry, who is not sharp to detect inaccuracies in definitions and arguments,who, in short, is dependent on the written text for what he teaches, should not undertake to use this book. I have thought it best to publish the books in an inexpensive form, so that, where the free text-book system exists, it would be as economical to purchase them new each year as to transmit a more expensive volume from pupil to pupil, with much distasteful accumulation. They will be furnished in a more durable form, if desired. In conclusion, I wish to thank the publishers and the proof-reader, by whose suggestions and watchfulness the text has been much improved and saved from numerous errors. STONEHAM, August 1, 1889. J. W. M. |