Axiomatic projective geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Groningen [u.a.]
Noordhoff [u.a.]
1980
|
| Edition: | 2. ed. |
| Series: | Bibliotheca mathematica
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 150 S. graph. Darst. |
| ISBN: | 0444854312 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002264270 | ||
| 003 | DE-604 | ||
| 005 | 20121005 | ||
| 007 | t | ||
| 008 | 890928s1980 d||| |||| 00||| eng d | ||
| 020 | |a 0444854312 |9 0-444-85431-2 | ||
| 035 | |a (OCoLC)5946638 | ||
| 035 | |a (DE-599)BVBBV002264270 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-739 |a DE-355 |a DE-29T |a DE-19 |a DE-703 |a DE-706 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA554 | |
| 082 | 0 | |a 516/.5 |2 18 | |
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a 51M35 |2 msc | ||
| 100 | 1 | |a Heyting, Arend |e Verfasser |4 aut | |
| 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 | ||
| 490 | 1 | |a Bibliotheca mathematica |v 5 | |
| 650 | 7 | |a Axiomatique |2 ram | |
| 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 | |
| 650 | 0 | 7 | |a Projektive Geometrie |0 (DE-588)4047436-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Axiomatik |0 (DE-588)4004038-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologie |0 (DE-588)4060425-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Projektive Geometrie |0 (DE-588)4047436-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Projektive Geometrie |0 (DE-588)4047436-7 |D s |
| 689 | 2 | 1 | |a Axiomatik |0 (DE-588)4004038-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 830 | 0 | |a Bibliotheca mathematica |v 5 |w (DE-604)BV001887077 |9 5 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001487986 | ||
Record in the Search Index
| _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
|
| any_adam_object | 1 |
| author | Heyting, Arend |
| author_facet | Heyting, Arend |
| author_role | aut |
| author_sort | Heyting, Arend |
| author_variant | a h ah |
| building | Verbundindex |
| bvnumber | BV002264270 |
| callnumber-first | Q - Science |
| callnumber-label | QA554 |
| callnumber-raw | QA554 |
| callnumber-search | QA554 |
| callnumber-sort | QA 3554 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)5946638 (DE-599)BVBBV002264270 |
| dewey-full | 516/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.5 |
| dewey-search | 516/.5 |
| dewey-sort | 3516 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01988nam a2200541 cb4500</leader><controlfield tag="001">BV002264270</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20121005 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1980 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444854312</subfield><subfield code="9">0-444-85431-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)5946638</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002264270</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA554</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.5</subfield><subfield code="2">18</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">51M35</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Heyting, Arend</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Axiomatic projective geometry</subfield><subfield code="c">by A. Heyting</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Groningen [u.a.]</subfield><subfield code="b">Noordhoff [u.a.]</subfield><subfield code="c">1980</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">150 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Bibliotheca mathematica</subfield><subfield code="v">5</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Axiomatique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Grondslagen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Géométrie projective</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Géométrie projective</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Projectieve meetkunde</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Projective</subfield><subfield code="x">Foundations</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Projektive Geometrie</subfield><subfield code="0">(DE-588)4047436-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Axiomatik</subfield><subfield code="0">(DE-588)4004038-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Projektive Geometrie</subfield><subfield code="0">(DE-588)4047436-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Projektive Geometrie</subfield><subfield code="0">(DE-588)4047436-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Axiomatik</subfield><subfield code="0">(DE-588)4004038-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Bibliotheca mathematica</subfield><subfield code="v">5</subfield><subfield code="w">(DE-604)BV001887077</subfield><subfield code="9">5</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001487986</subfield></datafield></record></collection> |
| 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 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-703 DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-703 DE-706 DE-83 DE-188 |
| 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 |
| volume_link | (DE-604)BV001887077 |
| work_keys_str_mv | AT heytingarend axiomaticprojectivegeometry |