摘要：On the Klein's model of the hyperbolic plane the harmonic homology is defined. This collineation maps absolute points of the h-plane onto absolute points, real points onto real points and ideal points onto ideal points. It is called line symmetry if the center of collineation is ideal point and point symmetry if the center is real point, because described mappings have equal properties as the analogues mappings in the Euclidean plane. By using point and line symmetries, symmetric images of the lines, points and triangles, bisectors of the angles and perpendicular bisectors of the segments are constructed. At the end one complicated metric problem is solved.
关键词：hyperbolic plane; Klein's model of the hyperbolic plane; central involutory collineation
