Philosophy of mathematics and deductive structure in Euclid's "Elements":
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass.
MIT Press
1981
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 378 S. graph. Darst. |
| ISBN: | 0262131633 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804117770291380224 |
|---|---|
| adam_text | Contents
Acknowledgments vii
Introduction viii
Bibliographical Note xiv
1 Plane Rectilineal Geometry 1
1.1 Hilbert s Geometry and Its Interpretation 1
1.2 Book I of the Elements 11
1.3 Geometry and Algebra: Book II, Propositions 1-7 41
Notes 52
O Euclidean Arithmetic 58
2.1 Book VII 58
2.2 Books VIII and IX 83
2.3 Arithmetic and Algebra; Applications of Arithmetic
in Book X 107
Notes 113
Q Magnitudes in Proportion 118
3.1 BookV 118
3.2 Problems in the Interpretation of Book V 134
Notes 148
A Proportion and the Geometry of Plane Rectilineal
*^ Figures 152
Notes 174
£ The Circle and Its Relation to the Triangle,
*- the Square, and the Regular Pentagon, Hexagon,
and Petitekaidehagon 177
5.1 The Circle 177
5.2 Rectilineal Figures and the Circle 189
Notes 205
vi Contents
6 Elementary Solid Geometry and the Method of
Exhaustion 207
6.1 The Foundations 207
6.2 Solids and Their Volumes 216
6.3 The Method of Exhaustion 230
Notes 247
H The Investigation of the Platonic Solids 251
7.1 Pyramid, Cube, Octahedron, Icosahedron 251
7.2 The Edge Value of the Icosahedron and Book X 260
7.3 The Dodecahedron 295
Notes 303
Appendix 1 Symbols and Abbreviations 307
Appendix 2 Euclidean Assumptions 312
Appendix 3 Additional Propositions 315
Appendix 4 The Contents of the Elements 317
Notes 370
Bibliography 371
Index 377
|
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| discipline | Mathematik Philosophie |
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| spelling | Mueller, Ian 1938- Verfasser (DE-588)1225703654 aut Philosophy of mathematics and deductive structure in Euclid's "Elements" Cambridge, Mass. MIT Press 1981 XV, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Euclide / Éléments Euclid Elements Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 gnd rswk-swf Elementen (Euclides) gtt Euclide Jussieu Filosofie van de wiskunde gtt Géométrie Hilbert Jussieu Logique symbolique et mathématique Logique symbolique et mathématique ram Mathématiques - Philosophie Mathématiques - Philosophie ram Philosophie mathématiques Jussieu Théorie démonstration Jussieu Mathematik Philosophie Logic, Symbolic and mathematical Mathematics Philosophy Logik (DE-588)4036202-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Griechenland Altertum (DE-588)4093976-5 gnd rswk-swf Griechenland Altertum (DE-588)4093976-5 g Logik (DE-588)4036202-4 s DE-604 Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 u Axiomatik (DE-588)4004038-0 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002165076&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mueller, Ian 1938- Philosophy of mathematics and deductive structure in Euclid's "Elements" Euclide / Éléments Euclid Elements Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 gnd Elementen (Euclides) gtt Euclide Jussieu Filosofie van de wiskunde gtt Géométrie Hilbert Jussieu Logique symbolique et mathématique Logique symbolique et mathématique ram Mathématiques - Philosophie Mathématiques - Philosophie ram Philosophie mathématiques Jussieu Théorie démonstration Jussieu Mathematik Philosophie Logic, Symbolic and mathematical Mathematics Philosophy Logik (DE-588)4036202-4 gnd Mathematik (DE-588)4037944-9 gnd Axiomatik (DE-588)4004038-0 gnd Philosophie (DE-588)4045791-6 gnd |
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| title | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_auth | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_exact_search | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_full | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_fullStr | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_full_unstemmed | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_short | Philosophy of mathematics and deductive structure in Euclid's "Elements" |
| title_sort | philosophy of mathematics and deductive structure in euclid s elements |
| topic | Euclide / Éléments Euclid Elements Euclides ca. v3. Jh. Elementa (DE-588)4266253-9 gnd Elementen (Euclides) gtt Euclide Jussieu Filosofie van de wiskunde gtt Géométrie Hilbert Jussieu Logique symbolique et mathématique Logique symbolique et mathématique ram Mathématiques - Philosophie Mathématiques - Philosophie ram Philosophie mathématiques Jussieu Théorie démonstration Jussieu Mathematik Philosophie Logic, Symbolic and mathematical Mathematics Philosophy Logik (DE-588)4036202-4 gnd Mathematik (DE-588)4037944-9 gnd Axiomatik (DE-588)4004038-0 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Euclide / Éléments Euclid Elements Euclides ca. v3. Jh. Elementa Elementen (Euclides) Euclide Filosofie van de wiskunde Géométrie Hilbert Logique symbolique et mathématique Mathématiques - Philosophie Philosophie mathématiques Théorie démonstration Mathematik Philosophie Logic, Symbolic and mathematical Mathematics Philosophy Logik Axiomatik Griechenland Altertum |
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