"Between 1733 and 1740, Jacques Cassini and his son César undertook the first triangulation of France. They included a re-surveying of the meridian arc, leading to the publication in 1745 of the first map of France constructed on rigorous principles. By this time, triangulation methods were by then well established for local map-making. It was only towards the end of the 18th century that detailed triangulation network surveys mapped whole countries. In 1784, a team from General William Roy's Ordnance Survey of Great Britain began the Principal Triangulation of Britain. The first Ramsden theodolite was built for this survey. The"
"by surveyors today. Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction plots of the surrounding landscape from two separate standpoints. The two graphing papers are superimposed, providing a scale model of the landscape, or rather the targets in it. The true scale can be obtained by measuring one distance both in the real terrain and in the graphical representation. Modern triangulation as, e.g., practised by Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant. In the late 1780s, Jesse Ramsden, a"
"scale and two pivoted arms hinged at the top and bottom, the upper arm carrying sights. The two arms were joined so that their ends could slide. As a person sighted along the upper arm, the lower one changed its angle. By reading the position of the lower rod, in combination with the vertical length, the zenith distance (or, alternatively, the altitude) of a celestial object could be calculated. The triquetrum was one of the most popular astronomical instruments until the invention of the telescope, it could measure angles with a better precision than the astrolabe. Copernicus describes its use"
"for this instrument; the US used ""Panoramic Telescope""; the Russia used """". Elevations were measured by a clinometer, a device using a spirit level to measure a vertical angle from the horizontal plane. These could be separate instruments placed on a surface parallel to the axis of the bore or physically integrated into some form of sight mount. Some guns had clinometers graduated in distances instead of angles. Clinometers had several other names including ""gunner's level"", ""range scale"", ""elevation drum"" and ""gunner’s quadrant"" and several different configurations. Those graduated in ranges were specific to a type of gun. These arrangements"
"Triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points. Specifically in surveying, triangulation per se involves only angle measurements, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. Optical 3D measuring systems use this principle as well in order to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device,"
"Mural instrument A mural instrument is an angle measuring device mounted on or built into a wall. For astronomical purposes, these walls were oriented so they lie precisely on the meridian. A mural instrument that measured angles from 0 to 90 degrees was called a mural quadrant. They were utilized as astronomical devices in ancient Egypt and ancient Greece. Edmond Halley, due to the lack of an assistant and only one vertical wire in his transit, confined himself to the use of a mural quadrant built by George Graham after its erection in 1725 at the Royal Observatory, Greenwich. Bradley's"
"+ cos α sin β, this is equivalent to: therefore: From this, it is easy to determine the distance of the unknown point from either observation point, its north/south and east/west offsets from the observation point, and finally its full coordinates. Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and gun direction of weapons. In the field, triangulation methods were apparently not used by the Roman specialist land surveyors, the ""agromensores""; but were introduced into medieval Spain through Arabic treatises on the astrolabe, such as that by Ibn al-Saffar (d. 1035). Abu"
"having a telescope fixed at right angles to it, revolving freely in the plane of the meridian. At the same time Rømer invented the altitude and azimuth instrument for measuring vertical and horizontal angles, and in 1704, he combined a vertical circle with his transit instrument, so as to determine both co-ordinates at the same time. This latter idea was, however, not adopted elsewhere, although the transit instrument soon came into universal use (the first one at Greenwich being mounted in 1721), and the mural quadrant continued until the end of the century to be employed for determining declinations. The"
"Relascope The relascope, invented by Walter Bitterlich, is a multi-use instrument for forest inventory. It is primarily used to find the height of a tree, the basal area of a tree, and the diameter of a tree anywhere along the bole. This instrument is used mostly for applications involving variable radius sample plots in a forest survey. The relascope has a sight hole on the back and a clear window at the front to allow the user to sight through the tool. There are three light inlet holes which are used to light the scale. This is one of the"
"hinged above it. Pinhole sights on the upper arm allowed it to be pointed accurately at the astronomical target. Plumb bob lines descended from the scales above and intersected with linear scales marked on the horizontal scales below. These allowed measures to be read, not as angles, but as trigonometric ratios. To celebrate the 600th anniversary of the Rectangulus in 1926 a replica was constructed. This is now in the Museum of the History of Science, Oxford. Rectangulus The rectangulus was an astronomical instrument made by Richard of Wallingford around 1326. Dissatisfied with the limitations of existing astrolabes, Richard developed"
"Repeating circle Developed from the reflecting circle, the repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784, while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the equal of the great theodolite created by the renowned instrument maker, Jesse Ramsden. It was used to measure the meridian arc from Dunkirk to Barcelona by Jean Baptiste Delambre and Pierre Méchain. The repeating circle is made of two telescopes mounted on a shared axis with scales to measure the angle between the two. The instrument combines multiple measurements to"
"of the earth (meaning there were more than 180 degrees in a triangle) were all allowed for. Principal Triangulation of Great Britain The Principal Triangulation of Britain was the first high-precision trigonometric survey of the whole of Great Britain (including Ireland), carried out between 1791 and 1853 under the auspices of the Board of Ordnance. The aim of the survey was to establish precise geographical coordinates of almost 300 significant landmarks which could be used as the fixed points of local topographic surveys from which maps could be drawn. In addition there was a purely scientific aim in providing precise"
"errors related to determining the horizon and from refraction, the preferred method in surveying was to use well known stars located closer to the zenith, such as Aldebaran for India, whose declination from the pole-star had been pre-established. Lambton's assistant John Warren investigated the effect of refraction on errors in calculating the latitudes.). The main survey instrument from 1802 for the primary triangles was a Great Theodolite made by William Cary. This was very similar to the instruments used in France and Britain for previous trigonometrical surveys. It had a horizontal circle that was 36 inches wide and the readings"
"Circumferentor A circumferentor, or surveyor's compass, is an instrument used in surveying to measure horizontal angles. It was superseded by the theodolite in the early 19th century. A circumferentor consists of a circular brass box containing a magnetic needle, which moves freely over a brass circle, or compass divided into 360 degrees. The needle is protected by a glass covering. A pair of sights is located on the North-South axis of the compass. Circumferentors were typically mounted on tripods and rotated on ball-and-socket joints. Circumferentors were made throughout Europe, including in England, France, Italy, and Holland. By the early 19th"
"Rectangulus The rectangulus was an astronomical instrument made by Richard of Wallingford around 1326. Dissatisfied with the limitations of existing astrolabes, Richard developed the rectangulus as an instrument for spherical trigonometry and to measure the angles between planets and other astronomical bodies. This was one of a number of instruments he created, including the ""Albion"", a form of equatorium, and a famously complicated and expensive horologium (astronomical clock). His ""Tractus Rectanguli"", describing the rectangulus, was an influential text in medieval astronomy and at least thirty copies were known to survive. His ""Quadripartitum"" was the first text on spherical trigonometry to"
"objects ranging from small nails driven into the ground to large beacons that can be seen from long distances. The surveyors can set up their instruments on this position and measure to nearby objects. Sometimes a tall, distinctive feature such as a steeple or radio aerial has its position calculated as a reference point that angles can be measured against. ""Triangulation"" is a method of horizontal location favoured in the days before EDM and GPS measurement. It can determine distances, elevations and directions between distant objects. Since the early days of surveying, this was the primary method of determining accurate"
"surveying, and in 1828 headed up a machine-shop in Fall River. In 1830 Bordon invented a new apparatus for accurately measuring the base line for the upcoming Massachusetts' Trigonometrical Survey. It was 50 feet long, enclosed in a tube, and used with four compound microscopes. The tube and microscopes were mounted on trestles, and adjustable to any direction. Borden's equipment was judged to be more accurate and convenient than any instrument available, and thus he assisted in measuring the Massachusetts base line (now known as the Borden Base Line) to a remarkable accuracy in 1831, and afterwards led the triangulation"
"triangulation station on the Starkey property. The tower was built of wood and stood 100 ft (30 m) with a 36×36 ft (11×11 m) base. The tower was located on the highest point of the property which is also the highest point in Puslinch township. The purpose of the tower was for triangulation surveying. There were hundreds of towers constructed for this purpose in North America. Most of the work was done at night and lamps were placed in towers and sighted from ground locations. The information gathered from this project formed the basis for topographic mapping used today. These"
"Triquetrum (astronomy) The triquetrum (derived from the Latin ""tri-"" [""three""] and ""quetrum"" [""cornered""]) was the medieval name for an ancient astronomical instrument first described by Ptolemy (""c."" 90–""c."" 168) in the ""Almagest"" (V. 12). Also known as ""Parallactic Rulers"", it was used for determining altitudes of heavenly bodies. Ptolemy calls it a """"parallactic instrument"""" and seems to have used it to determine the zenith distance and parallax of the Moon. The triquetrum performed the same function as the quadrant and was devised to overcome the difficulty of graduating arcs and circles. It consisted of a vertical post with a graduated"
"He created a design with three index arms and verniers. This permitted three simultaneous readings to average out the error. As a navigation instrument, the reflecting circle was more popular with the French navy than with the British. One instrument derived from the reflecting circle is the repeating circle. Invented by Lenoir in 1784, Borda and Lenoir developed the instrument for geodetic surveying. Since it was not used for the celestial measures, it did not use double reflection and substituted two telescope sights. As such, it was not a reflecting instrument. It was notable as being the equal of the"
"Tripod (surveying) A surveyor's tripod is a device used to support any one of a number of surveying instruments, such as theodolites, total stations, levels or transits. The modern sturdy, but portable, tripod stand with three leg pairs hinged to a triangular metal head was invented and first manufactured for sale by Sir Francis Ronalds in the late 1820s in Croydon. He sold 140 of the stands in the decade 1830-40 and his design was soon imitated by others. Older surveying tripods had slightly different features compared to modern ones. For example, on some older tripods, the instrument had its"
"with a compass and a physical metal chain – the unit of length also being the chain. Compass bearings were taken of the lines measured. He also created a triangulation network over the entire area to be covered by taking readings from church towers and similar high places using a theodolite made by Jonathan Sisson (inventor of the telescopic-sighted theodolite) to measure the observed angle between two other prominent locations. The process was repeated from point to point. The two methods needed to be reconciled and at the start of his work Rocque relied too much on his ground surveys,"
"Principal Triangulation of Great Britain The Principal Triangulation of Britain was the first high-precision trigonometric survey of the whole of Great Britain (including Ireland), carried out between 1791 and 1853 under the auspices of the Board of Ordnance. The aim of the survey was to establish precise geographical coordinates of almost 300 significant landmarks which could be used as the fixed points of local topographic surveys from which maps could be drawn. In addition there was a purely scientific aim in providing precise data for geodetic calculations such as the determination of the length of meridian arcs and the figure"
"unique types of instruments. There was interest in much larger instruments for special purposes. In particular a number of full circle instruments were made, categorized as reflecting circles and repeating circles. The reflecting circle was invented by the German geometer and astronomer Tobias Mayer in 1752, with details published in 1767. His development preceded the sextant and was motivated by the need to create a superior surveying instrument. The reflecting circle is a complete circular instrument graduated to 720° (To measure distances between heavenly bodies, there is no need to read an angle greater than 180°, since the minimum distance"
"instrument to be able to measure the spherical excess of large survey triangles. After completion of the Anglo-French survey this instrument was stored at the Royal Society but in 1799 the Board of Ordnance requested its use for the Principal Triangulation of Great Britain. On completion of the Survey the theodolite was stored in the headquarters of the Ordnance Survey at Southampton where it was destroyed in the bombing raids of 1941. In his report to the Royal Society in 1775 William Roy had noted the suitability of India as a location for both meridian arc and parallel arc measurements."
"the stadia allow range-finding; stadia are usually at ratios of 100:1, in which case one metre between the stadia marks on the levelling staff repesents 100 metres from the target. The complete unit is normally mounted on a tripod, and the telescope can freely rotate 360° in a horizontal plane. The surveyor adjusts the instrument's level by coarse adjustment of the tripod legs and fine adjustment using three precision levelling screws on the instrument to make the rotational plane horizontal. The surveyor does this with the use of a bull's eye level built into the instrument mount. The surveyor looks"
"Triangulation (surveying) In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side and two known angles. Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of Willebrord Snell in 1615–17, who showed how a point could be located from the"
"Yorkshireman from Halifax, England who had developed the dividing engine for dividing angular scales accurately to within a second of arc (≈ 0.0048 mrad or 4.8 µrad), was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation. In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-millimeter precision. Nowadays GPS antennas used for geodetic"
"angles subtended from ""three"" known points, but measured at the new unknown point rather than the previously fixed points, a problem called resectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s. Triangulation may be used to find the position of the ship when the positions of A and B are known. An observer at ""A"" measures"
"Gyrotheodolite In surveying, a gyrotheodolite (also: surveying gyro) is an instrument composed of a gyroscope mounted to a theodolite. It is used to determine the orientation of true north. It is the main instrument for orientation in mine surveying and in tunnel engineering, where astronomical star sights are not visible and GPS does not work. In 1852, the French physicist Léon Foucault discovered that a gyro with two degrees of freedom points north. This principle was adapted by Max Schuler in 1921 to build the first surveying gyro. In 1949, the gyro-theodolite – at that time called a ""meridian pointer"""
"the stadia marks on the levelling staff represents 100 metres from the target. The complete unit is normally mounted on a tripod, and the telescope can freely rotate 360° in a horizontal plane. The surveyor adjusts the instrument's level by coarse adjustment of the tripod legs and fine adjustment using three precision levelling screws on the instrument to make the rotational plane horizontal. The surveyor does this with the use of a bull's eye level built into the instrument mount. The surveyor looks through the eyepiece of telescope while an assistant holds a vertical level staff which is a graduated"
"Quadrant (instrument) A quadrant is an instrument that is used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings, such as longitude, latitude, and time of day. It was originally proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers. The term “quadrant”, meaning one fourth, refers to the fact that early versions of the instrument were derived from astrolabes. The quadrant condensed the workings of the astrolabe into an area one fourth the size of the astrolabe face;"
"move laterally by a large distance in the optical plummet as the tribrach level is adjusted. Tribrachs are precision instruments and should be checked regularly to ensure they do not become a source of error. Tribrach (instrument) A tribrach is an attachment plate used to attach a surveying instrument, for example a theodolite, total station, GNSS antenna or target to a tripod. A tribrach allows the survey instrument to be repeatedly placed in the same position over a surveying marker point with sub-millimetre precision, by loosening and re-tightening a lock to adjust the instrument base in a horizontal plane. The"