Elementary Geometry from an Advanced Standpoint (3rd Edition)

✍ Scribed by Edwin Moise

• Publisher: Addison Wesley
• Year: 1990
• Tongue: English
• Leaves: 514
• Edition: Third Edition
• Category: Library

✦ Synopsis

  Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.

✦ Table of Contents

Cover......Page 1
Copyright......Page 3
Preface......Page 4
Contents......Page 6
1. The Algebra of the Real Numbers......Page 12
2. Incidence Geometry in Planes and Space......Page 54
3. Distance and Conguence......Page 59
4. Separation in Planes and Space......Page 83
5. Angular Measure......Page 104
6. Congruences Between Triangles......Page 111
7. Geometric Inequalities......Page 127
8. The Euclidean Program: Congruence Without Distance......Page 136
9. Three Geometries......Page 150
10. Absolute Plane Geometry......Page 159
11. The Parallel Postulate and Parallel Projection......Page 171
12. Similarities Between Triangles......Page 183
13. Polygonal Regions and Their Areas......Page 195
14. The Construction of an Area Function......Page 214
15. Perpendicular Lines and Planes in Space......Page 223
16. Circles and Spheres......Page 235
17. Cartesian Coordinate Systems......Page 254
18. Rigid Motion......Page 262
19. Constructions with Ruler and Compass......Page 275
20. From Eudexus to Dedekind......Page 306
21. Length and Plane Area......Page 331
22. Jordan Measure in the Plane......Page 347
23. Solid Mensuration: The Elementary Theory......Page 363
24. Hyperbolic Geometry......Page 381
25. The Consistency of the Hyperbolic Postulates......Page 428
26. The Consistency of Euclidean Geometry......Page 449
27. The Postulational Method......Page 466
28. The Theory of Numbers......Page 473
29. The Theory of Equations......Page 480
30. Limits of Sequences......Page 485
31. Countable and Uncountable Sets......Page 490
32. An Order Field That Is Euclidean but Not Achimedean......Page 496
Index......Page 508