VI. The Present State of Philosophy and Science

According to the Lobachevsky theory, the three angles of a triangle together are always smaller than 180 degrees, while according to the Riemann theory they are always greater than 180 degrees. According to the latter, you cannot draw a single straight line parallel to another straight line through a point, but according to the former you can draw two straight lines. And these things are not to be taken lightly. For if the mathematician sets a certain constant equal to zero in certain formulas, by which every special relationship given in the Lobachevsky theory can be expressed, he obtains Euclidean geometry as a special case of Lobachevsky geometry. You can extract Euclidean geometry from Lobachevsky geometry.