Table of Contents

 1. The Algebra of the Real Numbers.


 2. Incidence Geometry in Planes and Space.


 3. Distance and Congruence.


 4. Separation in Planes and Space.


 5. Angular Measure.


 6. Congruences between Triangles.


 7. Geometric Inequalities.


 8. The Euclidean Program: Congruence without Distance.


 9. Three Geometries.


10. Absolute Plane Geometry.


11. The Parallel Postulate and Parallel Projection.


12. Similarities Between Triangles.


13. Polygonal Regions and Their Areas.


14. The Construction of an Area Function.


15. Perpendicular Lines and Planes in Space.


16. Circles and Spheres.


17. Cartesian Coordinate Systems.


18. Rigid Motion.


19. Constructions with Ruler and Compass.


20. From Eudoxus to Dedekind.


21. Length and Plane Area.


22. Jordan Measure in the Plane.


23. Solid Mensuration: The Elementary Theory.


24. Hyperbolic Geometry.


25. The Consistency of the Hyperbolic Postulates.


26. The Consistency of Euclidean Geometry.


27. The Postulation Method.


28. The Theory of Numbers.


29. The Theory of Equations.


30. Limits of Sequences.


31. Countable and Uncountable Sets.


32. An Ordered Field Which Is Euclidean But Not Archimedean.


Index.