In the same way, in Riemann's geometry (at least in one of its forms), through two points will pass in general only a single straight; but there are exceptional cases where through two points an infinity of straights can pass.
There is a sort of opposition between Riemann's geometry and that of Lobachevski.
Thus the sum of the angles of a triangle is:
Equal to two right angles in Euclid's geometry;
Less than two right angles in that of Lobachevski;
Greater than two right angles in that of Riemann.
The number of straights through a given point that can be drawn coplanar to a given straight, but nowhere meeting it, is equal:
To one in Euclid's geometry;
To zero in that of Riemann;
To infinity in that of Lobachevski.