Appendix, the theory of space
The epoch-making work of János 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 János Bolyai and with his intellectual world. A facsimile of a copy of Bolyai's original 1831 S...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
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Amsterdam
North-Holland
1987, 1987
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| Series: | North-Holland mathematics studies
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- Includes bibliographical references (pages 238-239)
- Part II: The absolute geometry of János 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
- 9. The formation and development of the concept of mathematical space10. Axiomatic method and modern mathematics; Supplement; Literature; Supplementary Literature
- 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 János Bolyai; Chapter 7. The discovery of absolute geometry
- Chapter I. The construction of geometry by elementary methods1. Further investigations of János 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. Poincaré's model; Chapter III. The effect of the discovery of Non-Euclidean geometry on recent evolution of mathematics