# Book:T. Ewan Faulkner/Projective Geometry/Second Edition

## T. Ewan Faulkner: Projective Geometry (2nd Edition)

Published $\text {1952}$, Dover Publications

ISBN 0-486-45326-X.

### Contents

PREFACE
chapter $\text {I}$ INTRODUCTION: THE PROPOSITIONS OF INCIDENCE
1. Historical note
2. The projective method
3. Desargues' theorem
4. The analytical method
5. Analytical proof of Desargues' theorem
6. Pappus' theorem
7. The fourth harmonic point

chapter $\text {II}$ 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 $\text {III}$ THE CONIC
20. Introduction
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 conics

chapter $\text {IV}$ ABSOLUTE ELEMENS: THE CIRCLE: FOCI OF CONICS
30. Introduction
31. Absolute elements
32. The circle
33. The conic and the absolute points
34. Central properties of conics; conjugate diameters
35. Foci and axes of a conic
36. The director conic
37. Confocal conics
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 $\text {V}$ THE EQUATION OF A LINE AND OF A CONIC: ALGEBRAIC CORRESPONDENCE ON A CONIC: THE HARMONIC FOCUS 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 forms 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 envelope
51. A conic associated with three conics of a pencil

chapter $\text {VI}$ METRICAL GEOMETRY
52. Introduction
53. Projective definition of distance and angle
54. The absolute conic
55. Algebraic expressions 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

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