1. A geodetic surveying appliance for fine sighting of a target defining a surveying point which is indicated with a high level of precision in space by a known target mark with an external form designed for this purpose, comprising: a targeting device, wherein the targeting device can swivel in motorized fashion relative to a base of the surveying appliance in order to change the orientation thereof, and includes: an objective-lens unit which defines an optical target axis; and a fine targeting camera sensor for acquiring a camera image of the sighted target mark; an angle sensor for the high-precision capture of the orientation of the target axis, and electronic data processing unit configured to perform image processing, data storage and control of the orientation of the targeting device, wherein: a set of different target marks, which each define a target defining a surveying point with a high level of precision, is known, for each of which a target mark pattern database in the electronic data processing unit stores corresponding target mark patterns, whereby automatically or by the user of the surveying appliance the respective target mark used is selectable and the corresponding target mark pattern for an automatic target fine sighting functionality from the target mark pattern database is called up and whereby each target mark pattern corresponds to the external form of one of the known target marks, each target mark pattern is embodied as a target mark template, and a main point in each target mark patter is defined as indicating the target, and in that the electronic data processing unit is designed to execute the automatic fine target sighting functionality after execution of a manual or automatic coarse target sighting whereby the coarse target sighting is executed without the fine targeting camera and in the course of the coarse target sighting the targeting device is oriented to the target mark at least with such accuracy that the target mark is in the field of vision of the camera sensor, whereby the start of the automatic fine target sighting functionality is automatically followed by performance of the following steps: taking a camera image of the target mark; matching the target mark pattern to the target mark in the camera image by means of image processing, wherein the target mark pattern in the camera image is made consistent with the target mark, such that it is aligned with the depiction of the target mark in the camera image; determining a position of the main point of the target mark pattern in the camera image in the matched state of the target mark pattern; and changing the orientation of the targeting device in a motorized fashion on the basis of the determined position of the main point in the camera image such that the optical target axis is oriented with a high level of precision to the target.