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Od geometrii syntetycznej do teorii struktur geometrycznych. Przemianyw geometrii a rozwój teorii mnogości

Gruszecki Lech

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

173-181

This article is a short outline of the history of synthetic geometry, particularly in the nineteenth century. The development of geometry in that period was based on the extension of projective notions due to Poncelet, Chasles, Mobius, Steiner and von Standt. The second half of the nineteenth century, however, brought decline of the classical geometry. New ideas introduced by Riemann in his qualifying lecture (1854) and by Klein in the called Eriangen Programme (1872) turned geometry into the theory of geometrical structures. Evolution of projective geometry was important for the theory of sets as in both theories one-to-one correspondences play essential role and both theories there exists problem of actual infinity.