Dioptrae

Dioptrae are ancient surveying and astronomical instruments used to measure angles and lines of sight. The dioptra, from Greek dia- “through” and optr- “sight,” was employed by Greek and Roman engineers to determine the relationships between objects in the field and in the sky.

Design and use: A dioptra comprises a rigid frame with a baseline, an alidade or sighting rod that could pivot about horizontal and vertical axes, and a graduated scale. By aligning its sights with two points and reading the angular measurements, a user could determine elevations, azimuths, and, with a known distance, distances and heights through triangulation.

History: The instrument is described in ancient sources such as Hero of Alexandria and Vitruvius, who note its use for surveying, construction, and astronomical observation. Variants differ in details, but the core concept—measuring angles via a sighting line on a graduated frame—remained constant. The dioptra influenced later Islamic and European surveying instruments and contributed to the evolution of the alidade-based theodolite.

Legacy: The dioptra’s naming influenced later optical terms; the word diopter in modern optics derives from the same root indicating a device for measuring angles.