basic surveying instrument of unknown origin but going back to the 16th-century English mathematician Leonard Digges; it is used to measure horizontal and vertical angles. In its modern form it consists of a telescope mounted to swivel both horizontally and vertically. Leveling is accomplished with the aid of a spirit level; crosshairs in the telescope permit accurate alignment with the object sighted. After the telescope is adjusted precisely, the two accompanying scales, vertical and horizontal, are read.

Mounted on a tripod with adjustable legs, the theodolite is used in the field to obtain precise angular measurements for triangulation in road building, tunnel alignment, and other civil-engineering work. The transit is a variety of theodolite that has the telescope so mounted that it can be completely reversed, or transited. The phototheodolite, a combination camera and theodolite mounted on the same tripod, is used in terrestrial photogrammetry for mapmaking and other purposes.