CORRELATED MATHEMATICS FOR SECONDARY SCHOOLS PLANE GEOMETRY BY EDITH LONG DEPARTMENT OF MATHEMATICS, HIGH SCHOOL, LINCOLN, NEBRASKA PREFACE In this text, as in the "Algebra," the authors have attempted to present the subject-matter in a way more suitable to beginners than is the case in most of the modern books. Brief and concise methods of exposition are therefore largely avoided, especially at the start, and much space is given to the explanation and analysis of theorems and problems, in order to bring out clearly the plan of attack and the method of proof. In the presentation of theorems, where complete proofs are given, the following plan has been adopted: 1. Statement of theorem. 2. Figure. 3. Statement of what is given. (Hypothesis.) 4. Statement of what is to be proved. (Conclusion.) 5. Analysis. 6. Proof. Special attention is called to the analyses. If the student can be taught to analyze a problem clearly, he has taken a long step in its solution. It is at this point that the logical faculties, and the ability to co-ordinate and apply information previously acquired, receive their chief development, and too much emphasis can hardly be placed on this point. The proof then consists merely in establishing the steps marked out in the analysis. In a number of theorems and problems, only the statement and analysis are given; in others the statement alone. These should be assigned as exercises, the student being required to work out complete proofs and to file them in a carefully kept note-book. There is no better way to vivify the treatment of Algebra than through geometric interpretation of its magnitudes; likewise, Geometry can, and does, borrow much from Algebra V M306195 |