In addition to straight edge and compasses, the classical instruments of Euclidean geometry, we have in hyperbolic geometry the horocompass and the hypercompass. By a straight edge, or ruler, we draw the line joining any two distinct points, and by the compasses we construct a circle with given center and radius. The horocompass is used to draw a horocycle through a given point when its diameter through the point with its direction are given. If the central line and radius of a hypercycle are given, we can draw it by the hypercompass. Although ruler and compasses have been generally used in the solutions of construction problems in hyperbolic geometry [1; 2, p. 191, pp. 204-206; 3, p. 394], other instruments have been introduced, and the relationships among these instruments, together with some restrictions, have been studied in recent years [2, pp. 289-291]. An important result in this connection is the following theorem [2, p. 290].