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Appendix, the theory of space /
The epoch-making work of J�anos Bolyai is presented here, together with a supplement outlining Hungarian political and science history to help the reader to get acquainted with the miserable fate of J�anos Bolyai and with his intellectual world. A facsimile of a copy of Bolyai&...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Latín |
| Publicado: |
Amsterdam ; New York : New York :
North-Holland ; Sole distributors for the U.S.A. and Canada : Elsevier Science Pub. Co.,
1987.
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| Colección: | North-Holland mathematics studies ;
138. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Appendix: The Theory of Space; Copyright Page; CONTENTS; Preface to the English edition; Part I: Evolution of the space concept up to the discovery of non-Euclidean geometry; Chapter 1. From the empirical study of space to deductive geometry; Chapter 2. Attempts to prove Postulate 5; Chapter 3. Reviving investigations at the beginning of the 19th century; Chapter 4. The meditations of Gauss and their results; Chapter 5. The geometric investigations of Lobachevsky; Chapter 6. The mathematical studies of J�anos Bolyai; Chapter 7. The discovery of absolute geometry
- Part II: The absolute geometry of J�anos Bolyai The AppendixAppendix(facsimile); Appendix (translation); Explanation of signs; Chapter I. Parallelism ( 1-10); Chapter II. The paracycle and the parasphere ( 11-24); Chapter III. Trigonometry ( 25-31); Chapter IV. Application of the methods of analysis, relation between geometry and reality (32-33); Chapter V. Constructions ( 34-43); Part III: Remarks; Chapter 1. The Hilbertian system of axioms for Euclidean geometry; Chapter 2. Remarks to 1-43; Part IV: The work of Bolyai as reflected by subsequent investigations
- Chapter I. The construction of geometry by elementary methods1. Further investigations of J�anos Bolyai in the field of absolute geometry; 2. Elliptic geometry; 3. The commentary literature; 4. Foundation of hyperbolic plane geometry without using the axioms of continuity; Chapter II. The consistency of non-Euclidean geometries; 5. On the proof of the consistency; 6. Beltrami's model; 7. The Cayley-Klein model; 8. Poincar�e's model; Chapter III. The effect of the discovery of Non-Euclidean geometry on recent evolution of mathematics
- 9. The formation and development of the concept of mathematical space10. Axiomatic method and modern mathematics; Supplement; Literature; Supplementary Literature