These two cases are mentioned also by Riemann in Goethes Romantechnik.
Riemann and Beltrami are chief among those whose labors characterize the scope of this period.
In his revision of the chapter before us, Dr. Riemann proceeded from an entirely different point of view.
There is a sort of opposition between Riemann's geometry and that of Lobachevski.
Well, Riemann's geometry is spherical geometry extended to three dimensions.
The two-dimensional geometries of Riemann and Lobachevski are thus correlated to the Euclidean geometry.
The geometry of these surfaces reduces itself therefore to the spherical geometry, which is that of Riemann.
If Lobachevski's geometry is true, the parallax of a very distant star will be finite; if Riemann's is true, it will be negative.
Who would venture to say whether he preferred that Weierstrass had never written or that there had never been a Riemann?
He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws.