Miquel Sätze in Minkowski—Ebenen I

Summary For the coordinization of axiomatically given nonlinear incidence structures, the theorem of Miquel acts as a powerful tool. In the literature there exist many different versions of this theorem, especially in the most complicated area of Minkowski geometries. In three papers (this one and the following parts II, III) all possibilities to formulate Miquelian theorems are discussed. This part I and the first half of part II mainly deal with conditions which are necessary to get interesting results. Having done this troublesome job we are able to present a big number of Miquelian theorems which can be used to coordinize Minkowski geometries, too. At the end of part III we present a peculiar version of a nontrivial theorem of Miquelian type. Up to now this is the only one which is not equivalent to the other interesting theorems of Miquel.