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LOBACHEVSKY, Nikolai Ivanovich. Nouveaux principes de la géométrie avec une théorie complète des parallèles.

Bruxelles, Hayez, 1901.

8vo (230x154 mm), (2)-132 pages and 8 plates. binding : Modern full green cloth. Spine a little faded.

First edition in french of this the "New Foundations of Geometry with a Complete Theory ol Parallels".

references: Popov ['Lobachevsky Geometry and Modern Nonlinear Problems', p.4 : "This is the largest work of N.I. Lobachevsky, which sums up in detail, and in the necessary cases develops, the results of his earlier work. It is from this memoir that one can draw the most completely information on the global scientific, worldoutlook and philosophical views of this great mathematician.

In this work the fundamental notions of geometry are discussed in detail: adjacency, cuts and the definition of the notions of the notion of point connected with them, lines, surfaces, and also the basic theorems on perpendicular straight lines and planes, relations in triangles, linear and angular measures, measuring of areas, an others. Starting from more general fundamental premises (compared with earlier works), a theory of parallel straight lines is constructed in detail. The fundamental equations of the imaginary geometry are introduced. As a whole, in this work Lobachecsky establishes the precise axiomatic foundations of geometry and defines the principles of its logical development, accompanying them with the corresponding foundational results in each of the fields he considered"], Kline [p. 873 : "He presented his views on the foundations of geometry in a paper before the department of mathematics and physics of the University in 1826. However, the paper was never printed and was lost. He gave his approach to non-Euclidean geometry in a series of papers, the first two of which were published in Kazan journals. The first was entitled " On the Foundations of Geometry" and appeared in 1829-30. The second, entitled "New Foundations of Geometry with a Complete Theory ol Parallels" (1835-37), is a better presentation of Lobatchevsky's ideas"].

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