1. A method for determining corrections for artillery fire toward a fixed target using a fixed optronic geographical positioning system which can be oriented and equipped with a device for measuring the orientation of the line of sight thereof, a laser rangefinder, system positioning means, a display screen provided with a fixed crosshair and harmonized with the axis of the rangefinder, and means for displaying and moving another crosshair on the screen, which method includes the following step: orienting the observation system so as to display the central crosshair on the image of the target on the display screen and calculating geographical coordinates of the target as a function of the distance provided by the rangefinder, the orientation provided by the orientation-measuring device, and the position of the optronic system provided by the positioning means, wherein, in the event that, after firing, the impact of this firing and the target do not coincide, it includes the following steps: the orientation of the system being fixed: displaying on the display screen a second crosshair on the image of the impact and measuring on the display screen the offset between the two crosshairs, displaying a third crosshair on the display screen at a position that is symmetrical to that of the second crosshair relative to the first crosshair, orienting the optronic system in order to position the third crosshair on the image of the target, the first crosshair then coinciding with the image of the impact point, and actuating the rangefinder in order to obtain the distance between the system and the impact.