Book:T. Ewan Faulkner/Projective Geometry/Second Edition
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T. Ewan Faulkner: Projective Geometry (2nd Edition)
Published $\text {1952}$, Dover Publications
- ISBN 0-486-45326-X
Subject Matter
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
- 8. The complete quadrangle
- 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
Further Editions
Source work progress
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