A method of producing a tapered surface by a lathe, comprising: a main spindle driven by a first drive device for rotating the workpiece, a feed spindle driven by a second drive device, a main slide movable in a z direction on a machine bed by the feed spindle, a cross slide manually movable on the main slide in an x direction perpendicular to the z direction, a position measuring and display device for measuring an xz coordinate of a cutting edge of a tool mounted on the cross slide and displaying the xz coordinate on a screen, and a control device for controlling the second drive device, the method comprising the following steps: transferring a data set describing the course of the tapered surface to the control device, moving the cutting edge by device of the main slide and/or the cross slide to a position with predetermined starting coordinates, rotating the workpiece by the main spindle, and manually moving the cross slide in an x direction predetermined by the course of the tapered surface and, simultaneously, automatically tracking the main slide in the z direction by the second drive device controlled by the control device such that the cutting edge of the tool is moved according to the course of the tapered surface to be produced, wherein z coordinates for automatically tracking the main slide in the z direction will be calculated. a main spindle driven by a first drive device for rotating the workpiece, a feed spindle driven by a second drive device, a main slide movable in a z direction on a machine bed by the feed spindle, a cross slide manually movable on the main slide in an x direction perpendicular to the z direction, a position measuring and display device for measuring an xz coordinate of a cutting edge of a tool mounted on the cross slide and displaying the xz coordinate on a screen, and a control device for controlling the second drive device, the method comprising the following steps: transferring a data set describing the course of the tapered surface to the control device, moving the cutting edge by device of the main slide and/or the cross slide to a position with predetermined starting coordinates, rotating the workpiece by the main spindle, and manually moving the cross slide in an x direction predetermined by the course of the tapered surface and, simultaneously, automatically tracking the main slide in the z direction by the second drive device controlled by the control device such that the cutting edge of the tool is moved according to the course of the tapered surface to be produced, wherein z coordinates for automatically tracking the main slide in the z direction will be calculated. transferring a data set describing the course of the tapered surface to the control device, moving the cutting edge by device of the main slide and/or the cross slide to a position with predetermined starting coordinates, rotating the workpiece by the main spindle, and manually moving the cross slide in an x direction predetermined by the course of the tapered surface and, simultaneously, automatically tracking the main slide in the z direction by the second drive device controlled by the control device such that the cutting edge of the tool is moved according to the course of the tapered surface to be produced, wherein z coordinates for automatically tracking the main slide in the z direction will be calculated.