Non-Euclidean Geometry: A Critical and Historical Study of Its Development

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Courier Corporation, Dec 31, 1954 - Mathematics - 389 pages
2 Reviews

This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.
Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachevski. In a discussion of later developments, the author treats the work of Riemann, Helmholtz and Lie; the impossibility of proving Euclid's postulate, and similar topics. The complete text of two of the founding monographs is appended to Bonola's study: "The Science of Absolute Space" by John Bolyai and "Geometrical Researches on the Theory of Parallels" by Nicholas Lobachevski. "Firmly recommended to any scientific reader with some mathematical inclination" Journal of the Royal Naval Scientific Service. "Classic on the subject." Scientific American.

  

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Contents

pages
1
Chapter IL
18
Chapter
64
Chapter IV
84
Chapter V
128
Appendix L
180
Appendix IL
196
Appendix
216
Appendix IV
227
Appendix V
238
Index of Authors
265
Introduction 129
iii
250
xviii
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The Shape of Space
Graham Nerlich
Limited preview - 1994
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