A coordinate measuring apparatus includes probe pin(s) fixed to a probe head displaceable in coordinates. The probe pin includes probe shafts having respective ends to which probe balls are attached. At least two of the probe shafts are differently oriented when the probe pins are fixed to the probe head. A control and evaluation unit controls the course of measurement and evaluates the measuring points recorded. At least one probe shaft is determined for measuring a geometric element on a workpiece by determining at least one characteristic piece of directional information for the points to be measured of a geometric element to be measured on the workpiece, either on the basis of the measured measuring points or according to predefined nominal data of the geometric element. At least one probe shaft for measuring the measuring points is determined from the directional information.