Non-Euclidean Geometry (Dover Books on Mathematics) (Paperback)

By Roberto Bonola

Dover Publications, 9780486600277, 448pp.

Publication Date: November 18, 2010

Other Editions of This Title:
Paperback (5/1/2007)
Paperback (1/4/2013)
Paperback (10/6/2014)
Hardcover (10/6/2014)
Hardcover (9/19/2015)
Paperback (7/31/2018)

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Description

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.