| PART I. GENERAL CONCEPTS AND ONE-DIMENSIONAL GEOMETRY CHAPTER I. GENERAL CONCEPTS SECTION 1. CoSrdinates 2. The principle of duality 3. The use of imaginaries 4. Infinity 5. Transformations 6. Groups CHAPTER II. RANGES AND PENCILS 7. Cartesian coordinate of a point on a line 8. Projective coSrdinate of a point on a line 9. Change of coSrdinates 10. CoSrdinate of a line of a pencil 11. CoSrdinate of a plane of a pencil CHAPTER III. PROJECTIVITY 12. The linear transformation 13. The cross ratio 14. Harmonic sets 15. Projection 16. Perspective figures 17. Other one-dimensional extents PART II. TWO-DIMENSIONAL GEOMETRY CHAPTER IV. POINT AND LINE COORDINATES IN A PLANE 18. Homogeneous Cartesian point coSrdinates 19. The straight line 20. The circle points at infinity 21. The conic 22. Trilinear point co6rdinates 23. Points on a line 24. The linear equation in point co6rdinates 25. Lines of a pencil 26. Line co6rdinates in a plane 27. Pencil of lines and the linear equation in line coordinates 28. Dualistic relations 29. Change of co6rdinates 30. Certain straight-line configurations 31. Curves in point coordinates 32. Curves in line coordinates CHAPTER V. CURVES OF SECOND ORDER AND SECOND CLASS 33. Singular points of a curve of second order 34. Poles and polars with respect to a curve of second order 35. Classification of curves of second order 36. Singular lines of a curve of second class 37. Classification of curves of second class 38. Poles and polars with respect to a curve of second class 39. Projective properties of conics CHAPTER VI. LINEAR TRANSFORMATIONS 40. Collineations 41. Types of nonsingular collineations 42. Correlations 43. Pairs of conies 44. The projective group 45. The metrical group 46. Angle and the circle points at infinity CHAPTER VII. PROJECTIVE MEASUREMENT 47. General principles 48. The hyperbolic case 49. The elliptic case 50. The parabolic case CHAPTER Vlll. CONTACT TRANSFORMATIONS IN THE PLANE 51. Point-point transformations 52. Quadric inversion 53. Inversion 54. Point-curve transformations 55. The pedal transformation 56. The line element CHAPTER XIII SURFACES OF SECOND ORDER AND OF SECOND CLASS CHAPTER XIV TRANSFORMATIONS CHAPTER XV THE SPHERE IN CARTESIAN COORDINATES CHAPTER XVI PENTASPHERICAL COORDINATES PART IV GEOMETRY OF FOUF AND HIGHER DIMENSIONS CHAPTER XVII LINE COORDINATS IN THREE DIMENSIONAL SPACE CHAPTER XVIII SPHERE COORDINATES CHAPTER XIX FOUR DIMENSIONAL POINT COORDINATES CHAPTER XX GEOMETRY OF N DIMENSIONS INDEX |
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