The ''torquetum'' or turquet is a medieval

astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxi ...

instrument designed to take and convert measurements made in three sets of coordinates: Horizon, equatorial, and ecliptic. It is said to be a combination of

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...

's astrolabon and the plane astrolabe. In a sense, the ''torquetum'' is an

analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...

Invention

The origins of the ''torquetum'' are unclear. The earliest account of the ''torquetum'' appear in the writings of Bernard of Verdun and Franco of Poland. Franco of Poland's work was published in 1284; however, Bernard of Verdun's work does not contain a date. Therefore, it is impossible to know which work was written first. Franco's work was more widely known and is credited with the distribution of knowledge about the ''torquetum''. The first ''torquetum'' is thought to have been built by Jabir ibn Aflah (more commonly known as Geber). However, there is conflicting evidence that suggests that Jabir simply inspired the invention of the torquetum. One of the reasons is that little evidence exists to suggest that it was created by Jabir. However, it is equally likely to be the invention of either Bernard of Verdun, Franco of Poland, or Jabir ibn Aflah. The instrument was first created sometime in the 12th or 13th century. However, the only surviving examples of the ''torquetum'' are dated from the 16th century. In the middle of the 16th century, the ''torquetum'' had numerous structural changes to the original design. The most important change was by instrument-maker, Erasmus Habermel. His alteration allowed for astronomers to make observations to all three of the scales. A ''torquetum'' can be seen in the famous portrait '' The Ambassadors'' (1533) by Hans Holbein the Younger. It is placed on the right side of the table, next to and above the elbow of the ambassador clad in a long brown coat or robe. The painting shows much of the details of the inscriptions on the disk and half disk, which make up the top of this particular kind of torquetum. A 14th century instrument, the rectangulus, was invented by

Richard of Wallingford Richard of Wallingford (1292–1336) was an English mathematician, astronomer, horologist, and cleric who made major contributions to astronomy and horology while serving as abbot of St Albans Abbey in Hertfordshire. Biography Richard was bor ...

. This carried out the same task as the torquetum, but was calibrated with linear scales, read by plumb lines. This simplified the

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

by resolving the polar measurements directly into their Cartesian components.

Notable historic uses

Following the conception of the ''torquetum'', the device had been put through many of the following uses. The astronomer,

Peter of Limoges Peter of Limoges ( la, Petrus Lemovicensis or '; french: Pierre de Limoges; – 1306) was the author of ''A Moral Treatise on the Eye'' ( la, Tractatus Moralis de Oculo) or ''On the Moral Eye'' ('), a popular guide for Catholic priests, composed ...

, used this device for his observation of what is known today as

Halley's Comet Halley's Comet or Comet Halley, officially designated 1P/Halley, is a short-period comet visible from Earth every 75–79 years. Halley is the only known short-period comet that is regularly visible to the naked eye from Earth, and thus the on ...

at the turn of the 14th century. In the early 1300s, John of Murs mentions the ''torquetum'' as his defence "of the reliability of observational astronomy", thus further solidifying its practicality and viability in ancient astronomy. Additionally, Johannes Schoner built a torquetum model for his own personal use in the observation of Halley's Comet in the 1500s. The best-documented account of the ''torquetum'' was done by Peter Apian in 1532. Peter Apian was a German humanist, specializing in astronomy, mathematics, and cartography. In his book ''

Astronomicum Caesareum ''Astronomicum Caesareum'' (''Astronomy of the Caesars''; also translated as ''The Emperor's Astronomy'') is a book by Petrus Apianus first published in 1540. ''Astronomicum'' was initially published in 1540. Charles V, Holy Roman Emperor, and ...

'' (1540), Apian gives a description of the ''torquetum'' near the end of the second part. He also details how the device is used. Apian explains that the ''torquetum'' was used for astronomical observations and how the description of the instrument was used as a basis for common astronomical instruments. He also notes the manufacturing process of the instrument and the use of the torquetum for astronomical measurements.

Components

The torquetum is a complex medieval analog computer that measures three sets of astronomical coordinates: the horizon, equatorial, and ecliptic. One of the defining attributes of the torquetum is its ability to interconvert between these three sets of coordinate dimensions without the use of calculations, as well as to demonstrate the relationship between the same coordinate sets. However, it is a device that requires a thorough understanding of the components and how they work together to make relative positional measurements of certain celestial objects. The anatomy of the torquetum involves many different components, which can be grouped into subdivisions of the torquetum structure, those being: the base, the midframe, and the upperframe. The base starts with the tabula orizontis, which is the bottommost rectangular piece in contact with the ground, and this component represents the horizon of the Earth, relative to the point of measurement. Hinged to the tabula orizontis is a similarly shaped component, the tabula quinoctialis, which represents the latitude of the Earth. This piece can rotate up to 90 degrees, coinciding with the latitudinal lines of the Earth from the equator to the poles. This angle of rotation is created by the stylus, which is an arm mechanism that pins to the slotted holes, which are part of the tabula orizontis. The midframe of the torquetum consists of a free-spinning disk (unnamed) that can be locked into place, and the tabula orbis signorum, directly hinged to it above. The angle between these two pieces is defined by the basilica, a solid stand piece, which is used to either set the draft angle at 0 degrees (Where the basilica is removed) or 23.5 degrees, representing the off-set of the axis of rotation of the Earth. Whether or not the basilica is included depends on the point of measurement either below or above the tropical latitudinal lines. Inscribed on the tabula equinoctialis along, although separate from, the outer perimeter of the bottom disk is a 24-hour circle, which is used to measure the angle between the longitudinal line facing the poles, and the line to the object being measured. Lastly, the upper frame is made up of the crista, the semis and the perpendiculum. The base of the crista is joined to another free-spinning disk directly above the tabula orbis signorum. Similarly, on the outer edge of the tabula orbis signorum is a zodiacal calendar and degree scale, with each of the 12 signs divided amongst it. This scale measures the zodiacal sector of the sky the object being measured is in. The crista itself is a circular piece that corresponds with the meridian of the celestial sphere, which has four quadrants inscribed along the edges, each starting at 0 degrees along the horizontal, and 90 degrees along the vertical. Adjacent, and locked with the crista at 23.5 degrees angle is the semis, which is a half-circle composed of two quadrants starting at 0 degrees along the vertical (relative to 23.5-degree placement) and 90 degrees at the horizontal. Finally, the last major component is the perpendicular, a free-hanging pendulum which measures the angle between the radial line of the Earth and the measured object using the semis.

Parts and configurations

The base of the instrument represents the horizon and is built on a hinge and a part known as the stylus holds the instrument up to the viewer's complementary latitude. This represents the celestial equator and the angle varies depending on where the view is located on Earth. The several plates and circles that make up the upper portion of the instrument represent the celestial sphere. These parts are built on top of the base and above the basilica, which rotates on a pin to represent the axis of the Earth. The zodiac calendar is inscribed on the tabula orbis signorum this is part of the mechanical aspects of the instrument that take away the tedious calculations required in previous instruments. The versatility of the "torquetum" can be seen in its three possible configurations for the measuring. The first method used lays the instruments flat on a table with no angles within the instrument set. This configuration gives the coordinates of celestial bodies as related to the horizon. The basilica is set so that 0 degree mark faces north. The user can now measure altitude of the target celestial body as well as use the base as a compass for viewing the possible paths they travel. The second configuration uses the stylus to elevate the base set at co-latitude of 90 degrees. The position of the celestial bodies can now be measured in hours, minutes, and seconds using the inscribed clock on the almuri. This helps give the proper ascension and decline coordinates of the celestial bodies as they travel through space. The zero point for ascension and decline coordinates of the celestial bodies as they travel through space. The zero point for ascension is set to the vernal equinox while the end measurement (decline) is the equator, this would put the North Pole at the 90 degree point. The third and most commonly seen configuration of the "torquetum" uses all its assets to make measurements. The upper portion is now set at an angle equal to the obliquity of the ecliptic, which allows the instrument to give ecliptic coordinates. This measures the celestial bodies now on celestial latitude and longitude scales which allow for greater precision and accuracy in making measurements. These three differing configurations allowed for added convenience in taking readings and made once tedious and complicated measuring more streamlined and simple.

Notes and references

* Ralf Kern: Wissenschaftliche Instrumente in ihrer Zeit. Vom 15. – 19. Jahrhundert. Verlag der Buchhandlung Walther König 2010,

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