Well, Riemann's geometry is spherical geometry extended to three dimensions.
The geometry of these surfaces reduces itself therefore to the spherical geometry, which is that of Riemann.
Indeed, it is very easily calculated by means of spherical geometry, what a great extent of the earth's area I beheld.
If we call the disc-shadows rigid figures, then spherical geometry holds good on the plane E with respect to these rigid figures.
They founded and largely constructed both plane and spherical geometry on the lines which best suit our practical intelligence.
|spherical geometry |
The geometry of circles, angles, and figures on the surface of a sphere.