Lobatschewsky-Bolyai Geometry in Euclidean Geometry can be extend into by solid geometry by:
Space = Region of points inside a sphere.
Point = Point inside of a Sphere
Strait Line = Chord in the Sphere (i.e. Volume Cap is Pi*h^2*(3r-h)/3 and the spherical cap is 2*Pi*r*h)
Plane = Points of a plane section which are inside of the Sphe
Displacements = Projective transformation in the space (i.e. dot products, cross product and linear mapping), which change the region of the point inside the sphere itself
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