Nicolaus Mercator
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Nicolaus Mercator
Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician. He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he lived from 1642 to 1648 in the Netherlands. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). On 3 May 1661 he observed a transit of Mercury with Christiaan Huygens and Thomas Streete from Long Acre, London. On 14 November 1666 he was elected a Fellow of the Royal Society. He designed a marine chronometer for Charles II. In 1682 Jean Colbert invited Mercator to assist in the design and construction of the fountains at the Palace of Versailles, so he relocated there, but a falling-out with Colbert followed. Mathematically, he ...
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Nicolaus Mercator Logarithmotechnia
Nicolaus is a masculine given name. It is a Latin, Greek and German form of Nicholas. Nicolaus may refer to: In science: * Nicolaus Copernicus, a Polish astronomer who provided the first modern formulation of a heliocentric theory of the Solar System * Nicolaus Otto (1832 – 1891), a German engineer In mathematics: * Nicolaus I Bernoulli, a Swiss mathematician * Nicolaus II Bernoulli, a Swiss mathematician * Nicolaus Rohlfs, an 18th-century German mathematics teacher who wrote astronomical calendars In literature: * Nicolaus Becker, a German lawyer and writer, the author of the '' Rheinlied'' * Nicolaus of Damascus, a Greek historical and philosophical writer who lived in the Augustan age In music: * Nicolaus Bruhns, a German composer * Nicolaus Zacharie, an Italian composer of the early Renaissance In Christianity: * Nicolaus Ludwig Zinzendorf, a German religious and social reformer and bishop of the Moravian Church * Nicolaus Taurellus, a German philosopher and theolo ...
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Sussex
Sussex (Help:IPA/English, /ˈsʌsɪks/; from the Old English ''Sūþseaxe''; lit. 'South Saxons'; 'Sussex') is an area within South East England that was historically a kingdom of Sussex, kingdom and, later, a Historic counties of England, county. It includes the Ceremonial counties of England, ceremonial counties of East Sussex and West Sussex. The area borders the English Channel to the south, and the Ceremonial counties of England, ceremonial counties of Surrey to the north, Kent to the north-east, and Hampshire to the west. Sussex contains the city of Brighton and Hove and its wider Greater Brighton City Region, city region, as well as the South Downs National Park and the National Landscapes of the High Weald National Landscape, High Weald and Chichester Harbour. Its coastline is long. The Kingdom of Sussex emerged in the fifth century in the area that had previously been inhabited by the Regni tribe in the Roman Britain, Romano-British period. In about 827, shortly a ...
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Natural Logarithm
The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if the base is implicit, simply . Parentheses are sometimes added for clarity, giving , , or . This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity. The natural logarithm of is the exponentiation, power to which would have to be raised to equal . For example, is , because . The natural logarithm of itself, , is , because , while the natural logarithm of is , since . The natural logarithm can be defined for any positive real number as the Integral, area under the curve from to (with the area being negative when ). The simplicity of this definition, which is matched in many other formulas ...
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Mercator Series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural logarithm (shifted by 1) whenever -1 .


History

The series was discovered independently by Johannes Hudde (1656) and (1665) but neither published the result. Nicholas Mercator also independently discovered it, and included values of the series for small values in his 1668 treatise ''Logarithmotechnia''; the general series was included in

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Logarithms
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base . The logarithm base is called the ''decimal'' or ''common'' logarithm and is commonly used in science and engineering. The ''natural'' logarithm has the number  as its base; its use is widespread in mathematics and physics because of its very simple derivative. The ''binary'' logarithm uses base and is widely used in computer science, information theory, music theory, and photography. When the base is unambiguous from the context or irrelevant it is often omitted, and the logarithm is written . Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. ...
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Encyclopedia
An encyclopedia is a reference work or compendium providing summaries of knowledge, either general or special, in a particular field or discipline. Encyclopedias are divided into article (publishing), articles or entries that are arranged Alphabetical order, alphabetically by article name or by thematic categories, or else are hyperlinked and searchable. Encyclopedia entries are longer and more detailed than those in most dictionary, dictionaries. Generally speaking, encyclopedia articles focus on ''factual information'' concerning the subject named in the article's title; this is unlike dictionary entries, which focus on Linguistics, linguistic information about words, such as their etymology, meaning, pronunciation, use, and grammar, grammatical forms.Béjoint, Henri (2000)''Modern Lexicography'', pp. 30–31. Oxford University Press. Encyclopedias have existed for around 2,000 years and have evolved considerably during that time as regards language (written in a major inte ...
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Palace Of Versailles
The Palace of Versailles ( ; ) is a former royal residence commissioned by King Louis XIV located in Versailles, Yvelines, Versailles, about west of Paris, in the Yvelines, Yvelines Department of Île-de-France, Île-de-France region in France. The palace is owned by the government of France and since 1995 has been managed, under the direction of the Ministry of Culture (France), French Ministry of Culture, by the Public Establishment of the Palace, Museum and National Estate of Versailles. About 15,000,000 people visit the palace, park, or gardens of Versailles every year, making it one of the most popular tourist attractions in the world. Louis XIII built a hunting lodge at Versailles in 1623. His successor, Louis XIV, expanded the château into a palace that went through several expansions in phases from 1661 to 1715. It was a favourite residence for both kings, and in 1682, Louis XIV moved the seat of his court and government to Versailles, making the palace the ''de fact ...
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Jean Colbert
Jean-Baptiste Colbert (; 29 August 1619 – 6 September 1683) was a French statesman who served as First Minister of State from 1661 until his death in 1683 under the rule of King Louis XIV. His lasting impact on the organization of the country's politics and markets, known as Colbertism, a doctrine often characterized as a variant of mercantilism, earned him the nickname ''le Grand Colbert'' (; "the Great Colbert"). A native of Reims, he was appointed Intendant of Finances on 4 May 1661. Colbert took over as Controller-General of Finances, a newly created position, in the aftermath of the arrest of Nicolas Fouquet for embezzlement, an event that led to the abolishment of the office of Superintendent of Finances. He worked to develop the domestic economy by raising tariffs and encouraging major public works projects, as well as to ensure that the French East India Company had access to foreign markets, so that they could always obtain coffee, cotton, dyewoods, fur, pepper, ...
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Thomas Birch
Thomas Birch (23 November 17059 January 1766) was an English historian. Life He was the son of Joseph Birch, a coffee-mill maker, and was born at Clerkenwell. He preferred study to business but, as his parents were Quakers, he did not go to the university. Notwithstanding this circumstance, he was ordained deacon in the Church of England in 1730 and priest in 1731. As a strong supporter of the Whigs, he gained the favour of Philip Yorke, afterwards Lord Chancellor and first Earl of Hardwicke, and his subsequent preferments were largely due to this friendship. He held successively a number of benefices in different counties, and finally in London. He was noted as a keen fisherman during the course of his lifetime, and devised an unusual method of disguising his intentions. Dressed as a tree, he stood by the side of a stream in an outfit designed to make his arms seem like branches and the rod and line a spray of blossom. Any movement, he argued, would be taken by a fish to ...
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Charles II Of England
Charles II (29 May 1630 – 6 February 1685) was King of Scotland from 1649 until 1651 and King of England, Scotland, and King of Ireland, Ireland from the 1660 Restoration of the monarchy until his death in 1685. Charles II was the eldest surviving child of Charles I of England, Scotland and Ireland and Henrietta Maria of France. After Charles I's execution at Palace of Whitehall, Whitehall on 30 January 1649, at the climax of the English Civil War, the Parliament of Scotland proclaimed Charles II king on 5 February 1649. However, England entered the period known as the English Interregnum or the English Commonwealth with a republican government eventually led by Oliver Cromwell. Cromwell defeated Charles II at the Battle of Worcester on 3 September 1651, and Charles Escape of Charles II, fled to mainland Europe. Cromwell became Lord Protector of England, Scotland and Ireland. Charles spent the next nine years in exile in France, the Dutch Republic and the Spanish Netherlands. ...
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Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, including mathematics, engineering science, and medical science". Overview Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to :Fellows of the Royal Society, around 8,000 fellows, including eminent scientists Isaac Newton (1672), Benjamin Franklin (1756), Charles Babbage (1816), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Jagadish Chandra Bose (1920), Albert Einstein (1921), Paul Dirac (1930), Subrahmanyan Chandrasekhar (1944), Prasanta Chandra Mahalanobis (1945), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955), Satyendra Nath Bose (1958), and Francis Crick (1959). More recently, fellow ...
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Long Acre
Long Acre is a street in the City of Westminster in central London. It runs from St Martin's Lane, at its western end, to Drury Lane in the east. The street was completed in the early 17th century and was once known for its Coach_(carriage), coach-makers, and later for its car dealers. History After the dissolution of the Monasteries in 1540, Henry VIII of England, Henry VIII confiscated the land belonging to Westminster Abbey, including the convent garden of Covent Garden and land to the north originally called the Elms and later Seven Acres. In 1552, his son, Edward VI of England, Edward VI, granted it to John Russell, 1st Earl of Bedford. The Russell family, who in 1694 were advanced in their peerage from Earl to Duke of Bedford, held the land from 1552 to 1918. At the time of Charles I of England, Charles I it was renamed Long Acre after the length of the first pathway constructed across the land. Charles took offence at the condition of the road and houses along it, which ...
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