A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation.
An astrolabe is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclinometer and an analog calculation device capable of working out several kinds of problems in astronomy. In its simplest form it is a metal disc with a pattern of wires, cutouts, and perforations that allows a user to calculate astronomical positions precisely. Historically used by astronomers, it is able to measure the altitude above the horizon of a celestial body, day or night; it can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate. It was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes.
Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.
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 and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.
An alidade or a turning board is a device that allows one to sight a distant object and use the line of sight to perform a task. This task can be, for example, to triangulate a scale map on site using a plane table drawing of intersecting lines in the direction of the object from two or more points or to measure the angle and horizontal distance to the object from some reference point's polar measurement. Angles measured can be horizontal, vertical or in any chosen plane.
In mathematics, a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry. In non-technical usage, the term "semicircle" is sometimes used to refer to a half-disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as all the interior points.
A circular sector, also known as circle sector or disk sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle, the radius of the circle, and is the arc length of the minor sector.
The term Jacob's staff is used to refer to several things, also known as cross-staff, a ballastella, a fore-staff, a ballestilla, or a balestilha. In its most basic form, a Jacob's staff is a stick or pole with length markings; most staffs are much more complicated than that, and usually contain a number of measurement and stabilization features. The two most frequent uses are:
The octant, also called a reflecting quadrant, is a reflecting instrument used in navigation.
Philippe Danfrie the elder, was a designer and maker of mathematical instruments in metal and paper, as well as a type-cutter, engraver, minter of coins and medals, publisher and author. Much is known about Danfrie's life and activities. He is probably best known as designer of the surveying instrument known as the graphometer.
The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. Some sectors also incorporated a quadrant, and sometimes a clamp at the end of one leg which allowed the device to be used as a gunner's quadrant.
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.
The mariner's astrolabe, also called sea astrolabe, was an inclinometer used to determine the latitude of a ship at sea by measuring the sun's noon altitude (declination) or the meridian altitude of a star of known declination. Not an astrolabe proper, the mariner's astrolabe was rather a graduated circle with an alidade used to measure vertical angles. They were designed to allow for their use on boats in rough water and/or in heavy winds, which astrolabes are ill-equipped to handle. It was invented by the Portuguese people, a nation known for its maritime prowess and dominated the sea for multiple centuries. In the sixteenth century, the instrument was also called a ring.
A plane table is a device used in surveying site mapping, exploration mapping, coastal navigation mapping, and related disciplines to provide a solid and level surface on which to make field drawings, charts and maps. The early use of the name plain table reflected its simplicity and plainness rather than its flatness. "Plane" refers to the table being both flat and levelled (horizontal).
In astronomy, sextants are devices depicting a sixth of a circle, used primarily for measuring the position of stars. There are two types of astronomical sextants, mural instruments and frame-based instruments.
A dividing engine is a device employed to mark graduations on measuring instruments to allow for reading smaller measurements than can be allowed by directly engraving them. The well-known vernier scale and micrometer screw-gauge are classic examples that make use of such graduations.
A quadrant is an instrument 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. Its earliest recorded usage was in ancient India in Rigvedic times by Rishi Atri to observe a solar eclipse. It was then proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers. Mural quadrants were important astronomical instruments in 18th-century European observatories, establishing a use for positional astronomy.
Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales. This method is based on the Intercept theorem.
Reflecting instruments are those that use mirrors to enhance their ability to make measurements. In particular, the use of mirrors permits one to observe two objects simultaneously while measuring the angular distance between the objects. While reflecting instruments are used in many professions, they are primarily associated with celestial navigation as the need to solve navigation problems, in particular the problem of the longitude, was the primary motivation in their development.
