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

Εξώφυλλο
Courier Corporation, 1 Ιαν 1955 - 389 σελίδες

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

The Attempts to prove Euclids Parallel Postulate
1
Chapter II
22
S 1822 JOHANN HEINRICH LAMBERT 17281777
44
S 2728 ADRIEN MARIE LEGENDRE 17521833
60
Chapter IV
84
Chapter V
128
Principles of RIEMANNs Solid Geometry
151
Representation of RIEMANNs Elliptic Geometry
175
CLIFFORDS Parallels and Surface Sketch of CLIFFORD
200
Appendix III
216
Appendix IV
227
Complete Projective Space
233
S 27 The System of Circles passing through
239
129
265
The Science of Absolute Space
271
The Theory of Parallels
273

Appendix I
181
Appendix II
194
Construction of the Common Parallel to
5
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