Theodolite,

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.

This article was most recently revised and updated by Amy Tikkanen, Corrections Manager.

surveying: History

…were called topographic instruments, or theodolites. They included pivoted arms for sighting and could be used for measuring both horizontal and vertical angles. Magnetic compasses may have been included on some.…

triangulation

…surveying device known as a theodolite, and the entire triangle is established. By constructing a series of such triangles, each adjacent to at least one other triangle, values can be obtained for distances and angles not otherwise measurable. Triangulation was used by the ancient Egyptians, Greeks, and other peoples at…

Triangulation

, in navigation, surveying, and civil engineering, a technique for precise determination of a ship’s or aircraft’s position, and the direction of roads, tunnels, or other structures under construction. It is based on the laws of plane trigonometry, which state that, if one side and two angles of a triangle are known, the other two sides and angle can be readily calculated. One side of the selected triangle is measured; this is the baseline. The two adjacent angles are measured by means of a surveying device known as a theodolite, and the entire triangle is established. By constructing a series of such triangles, each adjacent to at least one other triangle, values can be obtained for distances and angles not otherwise measurable.