## 1st Edition

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eBook ISBN: 9781483138299
Imprint: Pergamon
Published Date: 1st January 1960
Page Count: 146
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Contents

I. Introduction

1. Point Coordinates

2. Distance Between Two Points

3. Joachimsthal's Section Formula

4. Direction-Cosines

5. Direction-Ratios

6. Angle Between Two Straight Lines

7. Projections

II. Plane—Straight Line

8. Equation of A Plane

9. Equations of A Straight Line

10. Straight Line and Plane

11. Sign of the Expression u = λx + μy + vz + ρ

12. Distance From A Point to A Plane

13. Pair of Planes

14. Bundle of Planes

15. Shortest Distance Between Two Skew Lines

16. Coplanar Lines

17. Rectangular Axes Related to Two Skew Lines

III. Sphere

18. Equation of Sphere

19. Conjugate Points

20. Pole and Polar

21. Tangent Plane and Normal Line

22. Angle of Intersection of Two Spheres

24. Coaxal Spheres

26. Cone With Vertex At The Origin

27. Circular Cone

28. Conditions That ψ(x,y,z) Be A Circular Cone

29. Angle Between Two Generators

30. Reciprocal Cone

31. Rectangular and Orthogonal Cones

34. Ellipsoid

35. Hyperboloid of One Sheet

36. Hyperboloid of Two Sheets

37. Polar Properties

38. Generators

39.Generators of Hyperboloid of One Sheet

40.Normals

41.Centre of A Section

42.Axes of Central Plane Section

43.Axes of Non-Central Plane Section

VI. Paraboloid

44.Paraboloid

45.Polar Properties

46.Generators

47.Generators of Hyperbolic Paraboloid

48.Normals

49.Centre of A Section

50.Axes of Plane Section

VII. Homogeneous Coordinates

51.Homogeneous Coordinates

52.Point At Infinity

53.Straight Line

54.Plane

55.Intersection of Three Planes

56.Circle At Infinity

58.Paraboloid

60.Cofactor Notation

61.Conjugate Points

62.Pole and Polar

63.Tangent Plane

64.Enveloping Cone

65.Generators

66.Polar of A Line

67.Conjugate Lines

68.Conjugate Diameters

69.Principal Diametral Planes

70.Discriminating Cubic

71.Circular Sections

72.Rank of Matrix Δ

IX. Transformation of Axes—Invariants

73.Translation of Axes

74.Invariants of A Quadratic Form Under Translation

75.Rotation of Axes

76.Invariants of Quadratic Form Under Rotation

77.General Transformation of Coordinates

X. Classification and Reduction of Quadric

81. Paraboloid

82. Elliptic and Hyperbolic Cylinder

83. Parabolic Cylinder and Parallel Plane-Pair

XI. Foci—Confocals

84. Focus

86. Foci of Paraboloid

88. Confocal Paraboloids

90. Self-Polar Tetrahedron of A Pencil of Quadrics

92. Associated Points

XIII. Plane-Coordinates

93. Plane-Coordinates

94. Principle of Duality

96. Conic

97. Cone

Appendices

I. Matrices

II. Solutions

Index

## Description

Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordinates. Concerns include intersection of three planes; circular sections of central quadric; straight line; and circle at infinity. The book also discusses general quadric and classification and reduction of quadric. Discussions also focus on linear systems of quadrics and plane-coordinates. The text is a valuable reference for readers interested in the analytical geometry of three dimensions.

No. of pages:
146
Language:
English
Published:
1st January 1960
Imprint:
Pergamon
eBook ISBN:
9781483138299