Dioptra
Encyclopedia
A dioptra is a classical
astronomical and surveying instrument, dating from the 3rd century BCE. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractor
s, it could be used to measure angles
.
used the dioptra to measure the positions of stars
; both Euclid
and Geminus
refer to the dioptra in their astronomical works. By the time of Ptolemy
(2nd century CE), it was obsolete as an astronomical instrument, having been replaced by the armillary sphere
.
It continued in use as an effective surveying
tool. Adapted to surveying, the dioptra is similar to the theodolite
, or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma
.
The dioptra may have been sophisticated enough, for example, to construct a tunnel through two opposite points in a mountain. 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
, in the 6th century BCE" during the reign of Polycrates
. Scholars disagree 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
(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
s and applied mathematician
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 theodolite
.
Hellenistic civilization
Hellenistic civilization represents the zenith of Greek influence in the ancient world from 323 BCE to about 146 BCE...
astronomical and surveying instrument, dating from the 3rd century BCE. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractor
Protractor
In geometry, a protractor is a circular or semicircular tool for measuring an angle or a circle. The units of measurement utilized are usually degrees.Some protractors are simple half-discs; these have existed since ancient times...
s, it could be used to measure angles
Angles
The Angles is a modern English term for a Germanic people who took their name from the ancestral cultural region of Angeln, a district located in Schleswig-Holstein, Germany...
.
Use
Greek astronomersGreek astronomy
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the...
used the dioptra to measure the positions of stars
Astrometry
Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of our Solar System and our Galaxy, the Milky...
; both Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
and Geminus
Geminus
Geminus of Rhodes , 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 introductory astronomy book for students. He also wrote a work on mathematics, of which only...
refer to the dioptra in their astronomical works. By the time of Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
(2nd century CE), it was obsolete as an astronomical instrument, having been replaced by the armillary sphere
Armillary sphere
An armillary sphere is a model of objects in the sky , consisting of a spherical framework of rings, centred on Earth, that represent lines of celestial longitude and latitude and other astronomically important features such as the ecliptic...
.
It continued in use as an effective surveying
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...
tool. Adapted to surveying, the dioptra is similar to the theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...
, or surveyor's transit, which dates to the sixteenth century. It is a more accurate version of the groma
Groma surveying
The Groma or gruma was the principal Roman surveying instrument. It comprised a vertical staff with horizontal cross pieces mounted at right-angles on a bracket. Each cross piece had a plumb line hanging vertically at each end...
.
The dioptra may have been sophisticated enough, for example, to construct a tunnel through two opposite points in a mountain. There is some speculation that it may have been used to build the Eupalinian aqueduct
Eupalinian aqueduct
The Tunnel of Eupalinos or Eupalinian aqueduct is a tunnel of length in Samos, Greece, built in the 6th century BC to serve as an aqueduct. The tunnel is the second known tunnel in history which was excavated from both ends , and the first with a geometry-based approach in doing so...
. 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 Island
Samos is a Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of Asia Minor, from which it is separated by the -wide Mycale Strait. It is also a separate regional unit of the North Aegean region, and the only municipality of the regional...
, in the 6th century BCE" during the reign of Polycrates
Polycrates
Polycrates , son of Aeaces, was the tyrant of Samos from c. 538 BC to 522 BC.He took power during a festival of Hera with his brothers Pantagnotus and Syloson, but soon had Pantagnotus killed and exiled Syloson to take full control for himself. He then allied with Amasis II, pharaoh of Egypt, as...
. Scholars disagree 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
Hero of Alexandria was an ancient Greek mathematician and engineerEnc. Britannica 2007, "Heron of Alexandria" who was active in his native city of Alexandria, Roman Egypt...
(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
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
s and applied mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s."
The dioptra was used extensively on aqueduct
Aqueduct
An aqueduct is a water supply or navigable channel constructed to convey water. In modern engineering, the term is used for any system of pipes, ditches, canals, tunnels, and other structures used for this purpose....
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 theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...
.
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 GascoigneBamber GascoigneBamber Gascoigne, FRSL is a British television presenter and author, most known for being the original quizmaster on University Challenge.-Biography:...
, History of Measurement, historyworld.net - Tom M. ApostolTom M. ApostolTom Mike Apostol is a Greek-American analytic number theorist and professor at the California Institute of Technology.He was born in Helper, Utah in 1923. His parents, Emmanouil Apostolopoulos and Efrosini Papathanasopoulos, originated from Greece. Mr...
(2004), The Tunnel of Samos, Engineering and Science, 64(4), 30-40