Non-Euclidean Geometry. (Record no. 79901)
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| fixed length control field | 06895nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3330454 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729125051.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s1998 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781614445166 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780883855225 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3330454 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3330454 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr10861034 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)929120504 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA685 -- .C78 1998eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.9 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Coxeter, H.S.M. |
| 245 10 - TITLE STATEMENT | |
| Title | Non-Euclidean Geometry. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 6th ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Washington : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 1998. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©1998. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (355 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Spectrum |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Front Cover -- NON-EUCLIDEAN GEOMETRY -- Copyright Page -- PREFACE TO THE SIXTH EDITION -- CONTENTS -- CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY -- 1.1 Euclid -- 1.2 Saccheri and Lambert -- 1.3 Gauss, Wachter, Schweikart, Taurinus -- 1.4 Lobatschewsky -- 1.5 Bolyai -- 1.6 Riemann -- 1.7 Klein -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS -- 6.1 Spherical and elliptic geometry -- 6.2 Reflection -- 6.3 Rotations and angles -- 6.4 Congruence -- 6.5 Circles -- 6.6 Composition of rotations. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.7 Formulae for distance and angle -- 6.8 Rotations and quaternions -- 6.9 Alternative treatment using the complex plane -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | CHAPTER 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 -- CHAPTER 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 -- CHAPTER 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 conformal model of the elliptic plane -- 14.7 Klein's conformal model of the hyperbolic plane -- 14.8 Poincaré's model of the hyperbolic plane -- 14.9 Conformal models of non-Euclidean space -- CHAPTER XV. CONCLUDING REMARKS -- 15.1 Hjelmslev's 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Non-Euclidean. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Coxeter, H.S.M. |
| Title | Non-Euclidean Geometry |
| Place, publisher, and date of publication | Washington : American Mathematical Society,c1998 |
| International Standard Book Number | 9780883855225 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Spectrum |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330454">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330454</a> |
| Public note | Click to View |
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