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非欧几何，第六版（影印版）

样章
作者：
H. S. M. Coxeter
定价：
169.00元
ISBN：
978-7-04-055638-4
版面字数：
576.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-05
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
几何学
暂无
  • 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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