The foundations of geometry and the non-Euclidean plane/
George E. Martin
- New York: Springer, 1975.
- xvi, 509 p. : ill. ; 25 cm.
- (Undergraduate texts in mathematics) .
1. Equivalence relations -- 2. Mappings -- 3. The real numbers -- 4. Axiom systems -- Part 1. Absolute geometry -- 5. Models -- 6. Incidence axiom and ruler postulate -- 7. Betweenness -- 8. Segments, rays, and convex sets -- 9. Angles and triangles -- 10. The golden age of Green mathematics -- 11. Euclid's elements -- 12. Pasch's postulate and plane separation postulate -- 13. Crossbar and quadrilaterals -- 14. Measuring angles and the protractor postulate -- 15. Alternative axiom systems -- 16. Mirrors -- 17. Congruence and the penultimate postulate -- 18. Perpendiculars and inequalities -- 19. Reflections -- 20. Circles -- 21. Absolute geometry and Saccheri quadrilaterals -- 22. Saccheri's three hypotheses -- 23. Euclid's parallel postulate -- 24. Biangles -- 25. Excursions -- Part 2. Non-Euclidean geometry -- 26. Parallels and the ultimate axiom -- 27. Brushes and cycles -- 28. Rotations, translations, and horolations -- 29. The classification of isometries -- 30. Symmetry -- 31. Horocircles -- 32. The fundamental formula -- 33. Categoricalness and area -- 34. Quadrature of the circle.