Dividing Engine
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Dividing Engine
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. History There has always been a need for accurate measuring instruments. Whether it is a linear device such as a ruler or vernier or a circular device such as a protractor, astrolabe, sextant, theodolite, or setting circles for astronomical telescopes, the desire for ever greater precision has always existed. For every improvement in the measuring instruments, such as better alidades or the introduction of telescopic sights, the need for more exact graduations immediately followed. In early instruments, graduations were typically etched or scribed lines in wood, ivory or brass. Instrument makers devised various devices to perform such tasks. Early Islamic instrument makers must have had tec ...
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Quadrant (instrument)
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. Etymology 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; it was essentially a quarter of an astrolabe. History During Rigvedic times in ancient India, quadrants called 'Tureeyam's were used ...
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Limb
Limb may refer to: Science and technology *Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, the border or upper spreading part of a petal or sepal *Limb, in a measuring instrument, the graduated edge of a circle or arc Music * ''Limb'' (album), by Foetus, 2009 *''Limb'', an album by Justin Clayton, 1999 *"Limbs", a song by Emma Pollock from ''Watch the Fireworks'', 2007 *Limb Music, a German record label Other uses * Limb (surname), a list of people * Limb McKenry (1888–1956), American baseball pitcher *Limb Brook, a stream in Sheffield, South Yorkshire, England * Limbs Dance Company, in Auckland, New Zealand *Limbs, in archery, the upper and lower working parts of the bow; see recurve bow * Bresso Airfield, Bresso, Italy (ICAO code) *Limbu script (ISO 15924 code) See also * Limb darkening Limb darkening is an optical e ...
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George Graham (clockmaker)
George Graham, FRS (7 July 1673, maybe 1675 – 16 November 1751) was an English clockmaker, inventor, and geophysicist, and a Fellow of the Royal Society. He was born in Kirklinton, Cumberland. A Friend (Quaker) like his mentor Thomas Tompion, Graham left Cumberland in 1688 for London to work with Tompion. He later married Tompion's niece, Elizabeth Tompion. Career Graham was partner to the influential English clockmaker Thomas Tompion during the last few years of Tompion's life. Graham is credited with inventing several design improvements to the pendulum clock, inventing the mercury pendulum and also the orrery. He was made Master of the Worshipful Company of Clockmakers in 1722. Between 1730 and 1738, Graham had as an apprentice Thomas Mudge, who went on to be an eminent watchmaker in his own right, and invented the lever escapement, an important development for pocket watches.Harold Bagust, "The Greater Genius?", 2006, Ian Allan Publishing, (page 15) He was widely ...
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Gear
A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic principle behind the operation of gears is analogous to the basic principle of levers. A gear may also be known informally as a cog. Geared devices can change the speed, torque, and direction of a power source. Gears of different sizes produce a change in torque, creating a mechanical advantage, through their ''gear ratio'', and thus may be considered a simple machine. The rotational speeds, and the torques, of two meshing gears differ in proportion to their diameters. The teeth on the two meshing gears all have the same shape. Two or more meshing gears, working in a sequence, are called a gear train or a '' transmission''. The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is tha ...
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Pierre Vernier
Pierre Vernier (19 August 1580 at Ornans, Franche-Comté (at that time ruled by the Spanish Habsburgs, now part of France) – 14 September 1637, same location) was a French mathematician and instrument-inventor. He was the inventor and eponym of the vernier scale used in measuring devices. Life He was born in Ornans, France, in 1580. He was taught science by his father. He became captain and castellan of the castle at Ornans, for the King of Spain. He was also later councillor and director general of economy in the County of Burgundy. In Brussels, in the year 1631, Vernier published his treatise ''La construction, l'usage, et les propriétés du quadrant nouveau de mathématique'', and dedicated it to the Infanta. In it, he described the ingenious device which now bears his name, the vernier scale. To a quadrant with a primary scale in half degrees Vernier proposed to attach a movable sector, thirty-one half degrees in length but divided into thirty equal parts (each pa ...
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Jacob Curtius
Jacob (; ; ar, يَعْقُوب, Yaʿqūb; gr, Ἰακώβ, Iakṓb), later given the name Israel, is regarded as a patriarch of the Israelites and is an important figure in Abrahamic religions, such as Judaism, Christianity, and Islam. Jacob first appears in the Book of Genesis, where he is described as the son of Isaac and Rebecca, and the grandson of Abraham, Sarah, and Bethuel. According to the biblical account, he was the second-born of Isaac's children, the elder being Jacob's fraternal twin brother, Esau. Jacob is said to have bought Esau's birthright and, with his mother's help, deceived his aging father to bless him instead of Esau. Later in the narrative, following a severe drought in his homeland of Canaan, Jacob and his descendants, with the help of his son Joseph (who had become a confidant of the pharaoh), moved to Egypt where Jacob died at the age of 147. He is supposed to have been buried in the Cave of Machpelah. Jacob had twelve sons through four women, his ...
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Christopher Clavius
Christopher Clavius, SJ (25 March 1538 – 6 February 1612) was a Jesuit German mathematician, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by Aloysius Lilius, that is known as the Gregorian calendar. Clavius would later write defences and an explanation of the reformed calendar, including an emphatic acknowledgement of Lilius' work. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in and even out of Europe. Early life Little is known about Clavius' early life other than the fact that he was born in Bamberg in either 1538 or 1537. His given name is not known to any great degree of certainty—it is thought by scholars to have perhaps been ''Christoph Clau'' or ''Klau''. There are also some who think that his taken name, ''Clavius'', may be a Latinization of his original Ge ...
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Concentric
In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center point), as may cylinders (sharing the same central axis). Geometric properties In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere. By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the cir ...
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Nonius (device)
Nonius is a measuring tool used in navigation and astronomy named in honour of its inventor, Pedro Nunes (Latin: Petrus Nonius), a Portuguese author, mathematician and navigator. The nonius was created in 1542 as a system for taking finer measurements on circular instruments such as the astrolabe. The system was eventually adapted into the Vernier scale in 1631 by the French mathematician Pierre Vernier. Technical features The nonius was used to improve the astrolabe's accuracy. This consisted of a number of concentric circles traced on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. On a standard scale of 90 degrees, there are an additional 44–45 concentric circles, with each divided into a specific unit size such that a scale unit on position n had an arc of 90/n degrees. Thus, the outermost quadrant would comprise 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle ...
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Pedro Nunes
Pedro Nunes (; Latin: ''Petrus Nonius''; 1502 – 11 August 1578) was a Portuguese mathematician, cosmographer, and professor, from a New Christian (of Jewish origin) family. Considered one of the greatest mathematicians of his time, Nunes is best known for his contributions to the nautical sciences (navigation and cartography), which he approached, for the first time, in a mathematical way. He was the first to propose the idea of a loxodrome, and was the inventor of several measuring devices, including the nonius (from which Vernier scale was derived), named after his Latin surname. Life Little is known about Nunes' early education, life or family background, only that he was born in Alcácer do Sal, his origins are Jewish and that his grandchildren spent a few years behind bars after they were accused by the Portuguese Inquisition of professing and secretly practicing Judaism. He studied at the University of Salamanca, maybe from 1521 until 1522, and at the University o ...
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