Coordinate measuring device having at least one measuring carriage (15, 3, 4), via which a sensor for scanning the surface of a workpiece is mounted such that it can be displaced in at least one coordinate direction (x, y, z) relative to a workpiece resting on a workpiece support, the measuring carriage (15, 3, 4) for this purpose being guided movably in the coordinate direction (x, y, z) relative to a component supporting the measuring carriage via a fluid bearing guide, and this fluid bearing guide comprising a flat guide (60, 63, 64, 67, 68) and a fluid pressure bearing (31; 31') cooperating with the guide (60, 63, 64, 67, 68), the fluid pressure bearing (31; 31') being a constituent part of a bearing assembly (59; 59') which, in addition to the fluid pressure bearing (31; 31'), additionally comprises a spring system (55; 55') having two regions sprung relative to each other, the fluid pressure bearing (31; 31') being fixed to a first region and its second region being fixed to a bearing base body (21; 35; 57), and either the bearing base body being arranged on the supporting component and the flat guide (67, 68) being arranged on the measuring carriage, or the bearing base body (35; 57) being arranged on the measuring carriage (15, 3) and the flat guide (60, 63, 64) being arranged on the supporting component (15, 18), the spring system being a gas pressure spring, characterized in that a) the gas pressure spring (55; 55') comprises the following: - a piston (32; 32'), to which the fluid pressure bearing (31; 31') is fixed, - a pressure chamber housing (34; 34'), - a rolling diaphragm (33; 33'), which connects the piston (32; 32') and the pressure chamber housing (34; 34') to each other and which supports the piston (32; 32') movably with respect to the pressure chamber housing (34; 34'), wherein the pressure chamber housing (34; 34') and the rolling diaphragm (33; 33') form a pressure chamber (53; 53'), and b) in that the flat guide (60, 63, 64, 67, 68) is arranged on a guide body (18, 15, 4) with a rectangular or square cross section, wherein the guide body (18, 15, 4) has at least one further guide (62, 65, 66, 69, 70) on the side opposite the guide, wherein the bearing base body (21, 35, 57) at least partly encloses the guide body (18, 15, 4), and wherein, in addition, at least one further fluid pressure bearing, which rests directly on the bearing base body (21, 35, 57), is fixed to the bearing base body (21, 35, 57) in the region of the further guide (62, 65, 66, 69, 70). a) the gas pressure spring (55; 55') comprises the following: - a piston (32; 32'), to which the fluid pressure bearing (31; 31') is fixed, - a pressure chamber housing (34; 34'), - a rolling diaphragm (33; 33'), which connects the piston (32; 32') and the pressure chamber housing (34; 34') to each other and which supports the piston (32; 32') movably with respect to the pressure chamber housing (34; 34'), wherein the pressure chamber housing (34; 34') and the rolling diaphragm (33; 33') form a pressure chamber (53; 53'), and - a piston (32; 32'), to which the fluid pressure bearing (31; 31') is fixed, - a pressure chamber housing (34; 34'), - a rolling diaphragm (33; 33'), which connects the piston (32; 32') and the pressure chamber housing (34; 34') to each other and which supports the piston (32; 32') movably with respect to the pressure chamber housing (34; 34'), wherein the pressure chamber housing (34; 34') and the rolling diaphragm (33; 33') form a pressure chamber (53; 53'), and b) in that the flat guide (60, 63, 64, 67, 68) is arranged on a guide body (18, 15, 4) with a rectangular or square cross section, wherein the guide body (18, 15, 4) has at least one further guide (62, 65, 66, 69, 70) on the side opposite the guide, wherein the bearing base body (21, 35, 57) at least partly encloses the guide body (18, 15, 4), and wherein, in addition, at least one further fluid pressure bearing, which rests directly on the bearing base body (21, 35, 57), is fixed to the bearing base body (21, 35, 57) in the region of the further guide (62, 65, 66, 69, 70).