Studies in the History of Mathematics and Physical Sciences

A History of Non-Euclidean Geometry

Evolution of the Concept of a Geometric Space

Authors: Rosenfeld, Boris A.

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About this book

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith­ metic and algebra of real and complex numbers, and, finally, to new mathe­ matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe­ matics.

Table of contents (10 chapter)

  • Spherical Geometry

    Rosenfeld, B. A.

    Pages 1-34

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  • The Theory of Parallels

    Rosenfeld, B. A.

    Pages 35-109

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  • Geometric Transformations

    Rosenfeld, B. A.

    Pages 110-151

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  • Geometric Algebra and the Prehistory of Multidimensional Geometry

    Rosenfeld, B. A.

    Pages 152-180

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  • Philosophy of Space

    Rosenfeld, B. A.

    Pages 181-205

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Buy this book

eBook $149.00 net
( price for USA )
  • ISBN 978-1-4419-8680-1
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Hardcover $199.00 net
( price for USA )
  • ISBN 978-0-387-96458-4
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days
Softcover $189.00 net
( price for USA )
  • ISBN 978-1-4612-6449-1
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
A History of Non-Euclidean Geometry
Book Subtitle
Evolution of the Concept of a Geometric Space
Series Title
Studies in the History of Mathematics and Physical Sciences
Series Volume
12
Copyright
1988
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4419-8680-1
DOI
10.1007/978-1-4419-8680-1
Hardcover ISBN
978-0-387-96458-4
Softcover ISBN
978-1-4612-6449-1
Series ISSN
0172-570X
Edition Number
1
Topics