Metrical Conception of the Space-Time Geometry

Primordially a geometry was a science on properties of geometrical objects and their mutual disposition. A use of the proper Euclidean geometry generated the axiomatic conception of geometry, where the geometry is considered as a logical construction. There is the metrical conception of a geometry, where the geometry is considered as a science on properties of geometric objects. In the framework of metrical conception the space-time geometries form a more powerful set of geometries, than those do in the framework of the axiomatic conception. It is important at the construction of the general relativity.