Minkowskische Reduktionsbedingungen für positiv definite quadratische Formen in 5 Variablen

H. Minkowski stated that a positive definite quadratic form in 5 variables is reduced if a certain finite system of inequalities is fulfilled. This fact was first proved byS. S. Ryshkov in 1971. Here a new proof is given which is similar toMinkowski's treatment of forms in 4 variables. In place of the 4 different cases distinguished inRyshkov's proof only a distinction between 2 cases is necessary in the presented proof.