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

Subject Matter

 * Projective Geometry

Contents

 * PREFACE


 * $\text {I}$ 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


 * $\text {II}$ 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


 * $\text {III}$ 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


 * $\text {IV}$ 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


 * $\text {V}$ 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


 * $\text {VI}$ 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



Source work progress
* : Chapter $1$: Introduction: The Propositions of Incidence: $1.3$: Desargues' Theorem