非欧几何，第六版（影印版）

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目录
- 前辅文
- I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY SECTION PAGE
  - 1.1 Euclid
  - 1.2 Saccheri and Lambert
  - 1.3 Gauss, Wächter, Schweikart, Taurinus
  - 1.4 Lobatschewsky
  - 1.5 Bolyai
  - 1.6 Riemann
  - 1.7 Klein
- II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS
  - 2.1 Definitions and axioms
  - 2.2 Models
  - 2.3 The principle of duality
  - 2.4 Harmonic sets
  - 2.5 Sense
  - 2.6 Triangular and tetrahedral regions
  - 2.7 Ordered correspondences
  - 2.8 One-dimensional projectivities
  - 2.9 Involutions
- III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS
  - 3.1 Two-dimensional projectivities
  - 3.2 Polarities in the plane
  - 3.3 Conies
  - 3.4 Projectivities on a conic
  - 3.5 The fixed points of a collineation
  - 3.6 Cones and reguli
  - 3.7 Three-dimensional projectivities
  - 3.8 Polarities in space
- IV. HOMOGENEOUS COORDINATES
  - 4.1 The von Staudt-Hessenberg calculus of points
  - 4.2 One-dimensional projectivities
  - 4.3 Coordinates in one and two dimensions
  - 4.4 Collineations and coordinate transformations
  - 4.5 Polarities
  - 4.6 Coordinates in three dimensions
  - 4.7 Three-dimensional projectivities
  - 4.8 Line coordinates for the generators of a quadric
  - 4.9 Complex projective geometry
- V. ELLIPTIC GEOMETRY IN ONE DIMENSION
  - 5.1 Elliptic geometry in general
  - 5.2 Models
  - 5.3 Reflections and translations
  - 5.4 Congruence
  - 5.5 Continuous translation
  - 5.6 The length of a segment
  - 5.7 Distance in terms of cross ratio
  - 5.8 Alternative treatment using the complex line
- VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS
  - 6.1 Spherical and elliptic geometry
  - 6.2 Reflection
  - 6.3 Rotations and angles Ill
  - 6.4 Congruence
  - 6.5 Circles
  - 6.6 Composition of rotations
  - 6.7 Formulae for distance and angle
  - 6.8 Rotations and quaternions
  - 6.9 Alternative treatment using the complex plane
- VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS
  - 7.1 Congruent transformations
  - 7.2 Clifford parallels
  - 7.3 The Stephanos-Cartan representation of rotations by points
  - 7.4 Right translations and left translations
  - 7.5 Right parallels and left parallels
  - 7.6 Study's representation of lines by pairs of points
  - 7.7 Clifford translations and quaternions
  - 7.8 Study's coordinates for a line
  - 7.9 Complex space
- VIII. DESCRIPTIVE GEOMETRY
  - 8.1 Klein's projective model for hyperbolic geometry
  - 8.2 Geometry in a convex region
  - 8.3 Veblen's axioms of order
  - 8.4 Order in a pencil
  - 8.5 The geometry of lines and planes through a fixed point
  - 8.6 Generalized bundles and pencils
  - 8.7 Ideal points and lines
  - 8.8 Verifying the projective axioms
  - 8.9 Parallelism
- IX. EUCLIDEAN AND HYPERBOLIC GEOMETRY
  - 9.1 The introduction of congruence
  - 9.2 Perpendicular lines and planes
  - 9.3 Improper bundles and pencils
  - 9.4 The absolute polarity
  - 9.5 The Euclidean case
  - 9.6 The hyperbolic case
  - 9.7 The Absolute
  - 9.8 The geometry of a bundle
- X. HYPERBOLIC GEOMETRY IN TWO DIMENSIONS
  - 10.1 Ideal elements
  - 10.2 Angle-bisectors
  - 10.3 Congruent transformations
  - 10.4 Some famous constructions
  - 10.5 An alternative expression for distance
  - 10.6 The angle of parallelism
  - 10.7 Distance and angle in terms of poles and polars
  - 10.8 Canonical coordinates
  - 10.9 Euclidean geometry as a limiting case
- XI. CIRCLES AND TRIANGLES
  - 11.1 Various definitions for a circle
  - 11.2 The circle as a special conic
  - 11.3 Spheres
  - 11.4 The in- and ex-circles of a triangle
  - 11.5 The circum-circles and centroids
  - 11.6 The polar triangle and the orthocentre
- XII. THE USE OF A GENERAL TRIANGLE OF REFERENCE
  - 12.1 Formulae for distance and angle
  - 12.2 The general circle
  - 12.3 Tangential equations
  - 12.4 Circum-circles and centroids
  - 12.5 In- and ex-circles
  - 12.6 The orthocentre
  - 12.7 Elliptic trigonometry
  - 12.8 The radii
  - 12.9 Hyperbolic trigonometry
- XIII. AREA
  - 13.1 Equivalent regions
  - 13.2 The choice of a unit
  - 13.3 The area of a triangle in elliptic geometry
  - 13.4 Area in hyperbolic geometry
  - 13.5 The extension to three dimensions
  - 13.6 The differential of distance
  - 13.7 Arcs and areas of circles
  - 13.8 Two surfaces which can be developed on the Euclidean plane
- XIV. EUCLIDEAN MODELS
  - 14.1 The meaning of "elliptic" and "hyperbolic"
  - 14.2 Beltrami's model
  - 14.3 The differential of distance
  - 14.4 Gnomonic projection
  - 14.5 Development on surfaces of constant curvature
  - 14.6 Klein's conformai model of the elliptic plane
  - 14.7 Klein's conformai model of the hyperbolic plane
  - 14.8 Poincaré's model of the hyperbolic plane
  - 14.9 Conformai models of non-Euclidean space
- XV. CONCLUDING REMARKS
  - 15.1 HjelmsleVs mid-line
  - 15.2 The Napier chain
  - 15.3 The Engel chain
  - 15.4 Normalized canonical coordinates
  - 15.5 Curvature
  - 15.6 Quadratic forms
  - 15.7 The volume of a tetrahedron
  - 15.8 A brief historical survey of construction problems
  - 15.9 Inversive distance and the angle of parallelism
- APPENDIX: ANGLES AND ARCS IN THE HYPERBOLIC PLANE
- BIBLIOGRAPHY
- INDEX

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非欧几何，第六版（影印版）

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