It was an amazing geodetic instrument which was suitable for the precise measurement of horizontal, vertical and angular distances between two celestial or terrestrial points. Αccording to Heron of Alexandria with repeated use of the instrument, it was possible “in geography- to chart islands and seas, in astronomy- to calculate the distances of stars and forecast eclipses, in construction- to execute complex structures…”.
It consisted of a stand which had a horizontal toothed base that could be rotated with the help of a microwatt worm gear. A precise aiming disposition system (theodolite) could be placed on the base which consisted of a vertical (possibly calibrated) semicircular disc that could be turned in precision with the help of a worm gear and of a horizontal (possibly calibrated) disc. This disc was placed at the edge of the semicircular disc and had a cross-rotating aiming device. The operator of the instrument could aim any point in space and mark his angular coordinates.
Alternatively, a dumpy level system could be placed on the base which consisted of two vertical glass connected tubes with water that were used to determine the horizontal plane. It also consisted of an adjustable with precision aiming device. The system had, as components, two calibrated rulers each of which had a device for its vertical position and a sliding black – white disc that played the role of the target. The operator of the instrument could aim two random points where the two calibrated rulers were placed and calculate their hypsometric difference.
In solving surveying problems, using the dioptra, Heron applied the alignments, the multiple verticality and the ratios of the sides of similar triangles. It is, however, certain that at least in the calculation of astronomical sizes the protractors of the dioptra were used precisely as in the astrolabes.