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Projective geometry

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Author(s): T. Ewan Faulkner
Publisher: Dover
Year: 2006

Language: English

Cover
Title page
CHAPTER I INTRODUCTION: THE PROPOSITIONS OF INCIDENCE
1. Historical note
2. The projeotive method
3. Desargues' theorem
4. The ana1ytical method
6. Analytical proof of Deaargues' theorem
6. Pappus' theorem
7. The fourth harmonic point
8. The complete quadrangle
CHAPTER II RELATED RANGES AND PENCILS: INVOLUTIONS
9. Related ranges
10. The cross ratio
11. Cross ratio property of a(1.1) correspondence
12. Ranges in perspective
13. Related ranges on the same base; double points
14. Related pencils
15. Involution on a line
16. Cross ratio property of an involution
17. Involution property of the complete quadrangle
18. An algebraic representation of an involution
19. Pencils in involution
CHAPTER III THE CONIC
20. Introduotion
21. Projective definition of the conic
22. Related ranges on a conic
23. Involution on a conic
24. The conic as an envelope
25. Desargues' theorem
26. Pascal's theorem
27. Pole and Polar
28. Properties of two conics
29. Pencils of oonics
CHAPTER IV ABSOLUTE ELEMENTS: THE CIRCLE: FOCI OF CONICS
30. Introduotion
31. Absolute elements
32. The cirole
33. The conic and the absolute pointa
34. Central properties of conics; conjugate diameters
35. Foci and axes of a conic
36. The direotor circ1e
37. Confocal oonics
38. The auxiliary circle
39. Some properties of the parabola
40. Some properties of the rectangular hyperbola
41. The hyperbola of Apollonius
42. The Frégier point
CHAPTER V THE EQUATION OF A LINE AND OF A CONIC: ALGEBRAIC CORRESPONDENCE ON A CONIC: THE HARMONIC LOCUS AND ENVELOPE
43. The equation of a line
44. The equation of a conic
45. Tangent, pole and polar
46. The line-equation of a conic
47. Special forma for the equation of a conic
48. Correspondence between points of a conic
49. The symmetrical (2-2} correspondence of points on a conic
50. The harmonic anvelope
51. A conic associated with three oonics of a pencil
CHAPTER VI METRICAL GEOMETRY
52. Introduction
53. Projective definition of distance and angle
54. The absolute conic
55. A1gebraic expresaions for distance and angle
56. Real and complex points and lines
57. Real and complex conics
58. Metrical geometry
59. Distance and angle in Euclidean geometry
60. The Euclidean equivalents of simple projective elements
INDEX