Surveying instrument to measure position angles and distances simultaneously. These operations are performed by means of a graduated horizontal disk fitted with a magnetic compass. The center of the disk holds a rotating support for a graduated vertical semicircle carrying a sight. When the sight is pointed toward a particular spot, the measurer can read the azimuth angle (or position angle) with respect to the direction of magnetic north on the horizontal disk, and the zenith angle or altitude on the vertical semicircle. Distances can be calculated using the rules of trigonometry. A theodolite of this type was described by Leonard (c. 1520 - c. 1559) and Thomas Digges (c. 1546-1595) in 1571. In more modern designs, the sight is replaced by a telescope.