A dioptra (sometimes also named dioptre or diopter, from el, διόπτρα) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure

angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles a ...

Use

Greek astronomers used the dioptra to measure the positions of stars; both

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...

and

Geminus Geminus of Rhodes ( el, Γεμῖνος ὁ Ῥόδιος), was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the ''Introduction to the Phenomena'', still survives; it was intended as an int ...

refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the

theodolite A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building an ...

, or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma. There is some speculation that it may have been used to build the Eupalinian aqueduct. Called "one of the greatest engineering achievements of ancient times," it is a tunnel 1,036 meters (4,000 ft) long, "excavated through Mount Kastro on the Greek island of

Samos Samos (, also ; el, Σάμος ) is a Greece, Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, from which it is separated by the -wide Mycale Strait. It is also a se ...

, in the 6th century BCE" during the reign of

Polycrates Polycrates (; grc-gre, Πολυκράτης), son of Aeaces, was the tyrant of Samos from the 540s BC to 522 BC. He had a reputation as both a fierce warrior and an enlightened tyrant. Sources The main source for Polycrates' life and activit ...

. Scholars disagree, however, whether the dioptra was available that early. An entire book about the construction and surveying usage of the dioptra is credited to

Hero of Alexandria Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He ...

(also known as Heron; a brief description of the book is available online; see Lahanas link, below). Hero was "one of history’s most ingenious

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limit ...

s and applied

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

s." The dioptra was used extensively on aqueduct building projects. Screw turns on several different parts of the instrument made it easy to calibrate for very precise measurements The dioptra was replaced as a surveying instrument by the

References

External links

* Michael Lahanas
Heron of Alexandria, Inventions, Biography, Science
* Nathan Sidoli (2005)
Heron's Dioptra 35 and Analemma Methods: An Astronomical Determination of the Distance between Two Cities
''Centaurus'', 47(3), 236-258 *

Bamber Gascoigne Arthur Bamber Gascoigne (24 January 1935 – 8 February 2022) was an English television presenter and author. He was the original quizmaster on ''University Challenge'', which initially ran from 1962 to 1987. Early life and education Gasco ...

History of Measurement
historyworld.net * Tom M. Apostol (2004)
The Tunnel of Samos
''Engineering and Science'', 64(4), 30-40 {{Use dmy dates, date=August 2019 Ancient Greek astronomy Astrometry Astronomical instruments Historical scientific instruments Angle measuring instruments Surveying instruments

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External links