Axiomatic projective geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Groningen [u.a.]
Noordhoff [u.a.]
1980
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Bibliotheca mathematica
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 150 S. graph. Darst. |
| ISBN: | 0444854312 |
Internformat
MARC
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| 245 | 1 | 0 | |a Axiomatic projective geometry |c by A. Heyting |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Groningen [u.a.] |b Noordhoff [u.a.] |c 1980 | |
| 300 | |a 150 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 7 | |a Grondslagen |2 gtt | |
| 650 | 4 | |a Géométrie projective | |
| 650 | 7 | |a Géométrie projective |2 ram | |
| 650 | 7 | |a Projectieve meetkunde |2 gtt | |
| 650 | 4 | |a Geometry, Projective |x Foundations | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001487986 | ||
Datensatz im Suchindex
| _version_ | 1804116721912512512 |
|---|---|
| adam_text | CONTENTS
List of symbols ix
Chapter I. Introduction.
§ 1.1. The axiomatic method 1
1.2. Notions from set theory 8
1.3. Notions from algebra 10
1.4. Analytic projective geometry 13
1.5. Analytic solid projective geometry 20
1.6. Vector spaces over a division ring 21
Chapter II. Incidence Propositions in the Plane.
§ 2.1. Trivial axioms, duality 24
2.2. Desargues proposition 28
2.3. Collineations 41
2.4. The first quadrangle proposition, harmonic pairs . . 46
2.5. Projectivities between lines 56
2.6. Pappos proposition 60
Chaptfr III. Coordinates in the Plane.
§ 3.1. Ternary fields attached to a given projective plane . 70
3.2. Ternary field and axiom system 74
3.3. Some complementary results 78
3.4. The geometry over a given ternary field 84
3.5. Independence results 90
3.6. Homogeneous coordinates 91
Chapter IV. Incidence Propositions in Space.
§ 4.1. Trivial axioms and propositions 93
4.2. The sixteen points proposition 96
Chapter V. Coordinates in Space.
§ 5.1. Coordinates of a point 100
5.2. Equation of a plane 102
5.3. Homogeneous coordinates 104
5.4. The geometry over a given division ring 106
Chapter VI. The Fundamental Proposition of
Projective Geometry.
§ 6.1. The fundamental proposition 107
6.2. Summary of results Ill
Chapter VII. Order.
§ 7.1. Cyclically ordered sets 113
7.2. Cyclical order of a projective line lx
7.3. Order and coordinates 121
7.4. The geometry over an ordered ternary field .... 127
7.5. A counterexample 136
7.6. The axiom of Archimedes 140
7.7. The axiom of continuity 143
Appendices 147
Index 149
|
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| ctrlnum | (OCoLC)5946638 (DE-599)BVBBV002264270 |
| dewey-full | 516/.5 |
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| edition | 2. ed. |
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| id | DE-604.BV002264270 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:01Z |
| institution | BVB |
| isbn | 0444854312 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001487986 |
| oclc_num | 5946638 |
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| physical | 150 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Noordhoff [u.a.] |
| record_format | marc |
| series | Bibliotheca mathematica |
| series2 | Bibliotheca mathematica |
| spelling | Heyting, Arend Verfasser aut Axiomatic projective geometry by A. Heyting 2. ed. Groningen [u.a.] Noordhoff [u.a.] 1980 150 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bibliotheca mathematica 5 Axiomatique ram Grondslagen gtt Géométrie projective Géométrie projective ram Projectieve meetkunde gtt Geometry, Projective Foundations Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Topologie (DE-588)4060425-1 s DE-604 Projektive Geometrie (DE-588)4047436-7 s Axiomatik (DE-588)4004038-0 s Bibliotheca mathematica 5 (DE-604)BV001887077 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heyting, Arend Axiomatic projective geometry Bibliotheca mathematica Axiomatique ram Grondslagen gtt Géométrie projective Géométrie projective ram Projectieve meetkunde gtt Geometry, Projective Foundations Projektive Geometrie (DE-588)4047436-7 gnd Topologie (DE-588)4060425-1 gnd Axiomatik (DE-588)4004038-0 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4060425-1 (DE-588)4004038-0 |
| title | Axiomatic projective geometry |
| title_auth | Axiomatic projective geometry |
| title_exact_search | Axiomatic projective geometry |
| title_full | Axiomatic projective geometry by A. Heyting |
| title_fullStr | Axiomatic projective geometry by A. Heyting |
| title_full_unstemmed | Axiomatic projective geometry by A. Heyting |
| title_short | Axiomatic projective geometry |
| title_sort | axiomatic projective geometry |
| topic | Axiomatique ram Grondslagen gtt Géométrie projective Géométrie projective ram Projectieve meetkunde gtt Geometry, Projective Foundations Projektive Geometrie (DE-588)4047436-7 gnd Topologie (DE-588)4060425-1 gnd Axiomatik (DE-588)4004038-0 gnd |
| topic_facet | Axiomatique Grondslagen Géométrie projective Projectieve meetkunde Geometry, Projective Foundations Projektive Geometrie Topologie Axiomatik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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