PREFACE In the First and Second Books the pupil has become familiar with all the common notions of geometry and has learned many of the theorems through the construction work and the many problems of mensuration. In the demonstrative geometry offered in this book the purpose is to give an understanding of the nature of a proof and to develop some power and skill in proving geometric theorems. The theorems selected are the fundamental theorems of plane geometry whose proofs are simple and direct. Complete proofs are given for all the earlier theorems and for the more difficult theorems throughout the book. But an effort is made to have the pupil see how the proof was arrived at through an analysis which is meant to suggest to the pupil a method for discovering the proof. As theorems are proved they are classified on the basis of the way in which they may be used to prove other theorems, and summaries of the different ways of proving certain facts are given frequently. Every effort is made to have pupils discover proofs rather than memorize proofs which are given them. It is thought that this course, preceded by the work in geometry in the First and Second Books, will give the pupils by the end of the ninth year a course in geometry that has all the values of the more extended course involving the more intricate methods of proof and less used theorems which are usually memorized and seldom really mastered by the pupil. For those who are to continue a study of mathematics this course should be followed by a summing up course in plane and solid geometry of a half year, organized on the basis of method of proof. The other half of the tenth year should be devoted to a similar summing up course in algebra. |