Basic Geometry (AMS Chelsea Publishing)

Offers a sound mathematical development ... and at the same time enables the student to move rapidly into the heart of geometry. —The Mathematics Teacher Should be required reading for every teacher of geometry. —The Mathematical Gazette In this highly recommended high school text by two eminent scholars, the authors deduce plane Euclidean geometry by utilizing only five fundamental postulates. Incorporation of the system of real numbers in three of the five postulates of this geometry gives these assumptions great breadth and power. They lead the reader at once to the heart of geometry. It is because of the underlying power, simplicity, and compactness of this geometry that the authors called the book Basic Geometry. The book is designed for a one-year course in plane geometry. For advanced students, the authors incorporated certain material from three-dimensional and so-called modern geometry. A rich variety of exercises as well as many illustrations applying the abstract geometrical concepts to real life provide an excellent source of teaching material. Title page......Page 1 Acknowledgements and date-line......Page 2 Preface......Page 3 Contents......Page 7 1. Reasoning. The Nature of Proof......Page 9 2. The Five Fundamental Principles......Page 38 3. The Seven Basic Theorems......Page 71 4. Parallel Lines and Networks......Page 105 5. The Circle and Regular Polygons......Page 133 6. Constructions with Straightedge and Compasses......Page 165 7. Area and Length......Page 198 8. Continuous Variation......Page 228 9. Loci......Page 242 10. Reasoning. Abstract Logical Systems......Page 268 Laws of Number......Page 284 Index......Page 289 Cover......Page 295