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101117s1973 nyua ob 001 0 eng d |
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1 |
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|a Gans, David,
|d 1907-1999.
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| 245 |
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|a An introduction to non-Euclidean geometry.
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| 260 |
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|a New York,
|b Academic Press
|c [1973]
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| 300 |
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|a 1 online resource (xii, 274 pages)
|b illustrations
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| 336 |
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|a text
|b txt
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|a computer
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|a online resource
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| 504 |
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|a Includes bibliographical references (page 263).
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| 506 |
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|3 Use copy
|f Restrictions unspecified
|2 star
|5 MiAaHDL
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| 533 |
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|a Electronic reproduction.
|b [Place of publication not identified] :
|c HathiTrust Digital Library,
|d 2010.
|5 MiAaHDL
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| 538 |
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|a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
|u http://purl.oclc.org/DLF/benchrepro0212
|5 MiAaHDL
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|a digitized
|c 2010
|h HathiTrust Digital Library
|l committed to preserve
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|5 MiAaHDL
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|a Print version record.
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|a Front Cover -- An Introduction to Non-Euclidean Geometry -- Copyright Page -- Table of Contents -- Dedication -- Preface -- PART I: HISTORICAL INTRODUCTION -- Chapter I. Euclid's Fifth Postulate -- 1. Introduction -- 2. Euclid's Stated Assumptions -- 3. The Extent of a Straight Line -- 4. Euclid's Theory of Parallels -- 5. Further Consequences of Postulate 5 -- 6. Substitutes for Postulate 5 -- Chapter II. Attempts to Prove the Fifth Postulate -- 1. Introduction -- 2. Euclid's Choices -- 3. Posidonius and His Followers -- 4. Ptolemy and Proclus
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|a 5. Saccheri6. Lambert -- 7. Legendre -- 8. The Discovery of Non-Euclidean Geometry -- PART II: HYPERBOLIC GEOMETRY -- Chapter III. Parallels With a Common Perpendicular -- 1. Introduction -- 2. The Basis E -- 3. The Initial Theorems of Hyperbolic Geometry -- 4. The Hyperbolic Parallel Postulate -- 5. Immediate Consequences of the Postulate -- 6. Further Properties of Quadrilaterals -- 7. Parallels With a Common Perpendicular -- 8. The Angle-Sum of a Triangle -- 9. The Defect of a Triangle -- 10. Quadrilaterals Associated with a Triangle
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|a 11. The Equivalence of Triangles12. Area of a Triangle -- 13. Implications of the Area Formula -- 14. Circles -- Chapter IV. Parallels Without a Common Perpendicular -- 1. Introduction -- 2. Parallels Without a Common Perpendicular -- 3. Properties of Boundary Parallels -- 4. Trilateral -- 5. Angles of Parallelism -- 6. Distance between Two Lines -- 7. The Uniqueness of Parallels Without a Common Perpendicular -- 8. Perpendicular Bisectors of the Sides of a Triangle -- Chapter V. Horocycles -- 1. Introduction -- 2. Corresponding Points
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| 505 |
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|a 3. Definition of a Horocycle4. Arcs and Chords of a Horocycle -- 5. Codirectional Horocycles -- 6. Arc Length on a Horocycle -- 7. Formulas Related to k-Arcs -- Chapter VI. Triangle Relations -- 1. Introduction -- 2. Associated Right Triangles -- 3. Improved Angle of Parallelism Formulas -- 4. Remarks on the Trigonometric Functions -- 5. Right Triangle Formulas -- 6. Comparison with Euclidean Formulas -- 7. Formulas for the General Triangle -- 8. Hyperbolic Geometry in Small Regions -- 9. Hyperbolic Geometry and the Physical World
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| 505 |
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|a PART III: ELLIPTIC GEOMETRYChapter VII. Double Elliptic Geometry -- 1. Introduction -- 2. Riemann -- 3. The Elliptic Geometries -- 4. Geometry on a Sphere -- 5. A Description of Double Elliptic Geometry -- 6. Double Elliptic Geometry and the Physical World -- 7. An Axiomatic Presentation of Double Elliptic Geometry -- Chapter VIII. Single Elliptic Geometry -- 1. Introduction -- 2. Geometry on a Modified Hemisphere -- 3. A Description of Single Elliptic Geometry -- 4. An Axiomatic Presentation of Single Elliptic Geometry
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| 546 |
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|a English.
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| 650 |
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|a Geometry, Non-Euclidean.
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| 650 |
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|a G�eom�etrie non-euclidienne.
|0 (CaQQLa)201-0005575
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| 650 |
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|a MATHEMATICS
|x Geometry
|x General.
|2 bisacsh
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| 650 |
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|a Geometry, Non-Euclidean
|2 fast
|0 (OCoLC)fst00940928
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| 650 |
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|a Einf�uhrung
|2 gnd
|0 (DE-588)4151278-9
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| 650 |
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|a Nichteuklidische Geometrie
|2 gnd
|0 (DE-588)4042073-5
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| 650 |
1 |
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|a Niet-Euclidische meetkunde.
|2 gtt
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| 776 |
0 |
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|i Print version:
|a Gans, David, 1907-1999.
|t Introduction to non-Euclidean geometry.
|d New York, Academic Press [1973]
|w (DLC) 72009326
|w (OCoLC)590719
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| 856 |
4 |
0 |
|u https://sciencedirect.uam.elogim.com/science/book/9780122748509
|z Texto completo
|
