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

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Courier Corporation, 1 Ιαν 1955 - 389 σελίδες
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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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Περιεχόμενα

Chapter
1
Chapter II
22
S 2728 ADRIEN MARIE LEGENDRE 17521833
60
Chapter IV
84
Chapter V
128
Representation of RIEMANNs Elliptic Geometry
175
SI3 On the Principle of the Lever
181
Appendix II
194
Appendix III
216
Appendix IV
227
Index of Authors
233
Introduction
239
S 812 The System of Circles orthogonal to
250
224
265
2244
266
239250
xviii

CLIFFORDS Parallels and Surface Sketch of CLIFFORD
200

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