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

Subject Matter

• Projective Geometry

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

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Further Editions

• 1948: T. Ewan Faulkner: Projective Geometry

Source work progress

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