  Certain topics on polygons are extended from Euclidean to hyperbolic
geometry. This first part deals with uniqueness and existence of cocyclic
polygons with prescribed sidelengths. The non-Euclidean versions are more
difficult due to the existence of three different types of circles in the
hyperbolic plane. The second part will be concerned with the problem of
maximizing the area of polygons with fixed sidelengths. By the metric character
of these problems it is necessary to dispense to a certain extent with
classical hyperbolic trigonometry because angles must be replaced by length
quantities. So this first part also takes regard of this technical aspect.
