1.
1710 in science
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The year 1710 in science and technology involved some significant events. The Royal Society of Sciences in Uppsala is founded in Uppsala, Sweden, edmond Halley, comparing his observations with Ptolemys catalog, discovers the proper motion of some fixed stars. Alexis Littré, in his treatise Diverses observations anatomiques, is the first physician to suggest the possibility of performing a lumbar colostomy for an obstruction of the colon, stephen Hales makes the first experimental measurement of the capacity of a mammalian heart. Jakob Christof Le Blon invents a three-color printing process with red, blue, years later he adds black introducing the earliest four-color printing process. René Antoine Ferchault de Réaumur produces a paper on the use of spiders to produce silk, john Arbuthnot publishes An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes in Philosophical Transactions of the Royal Society of London

2.
1712 in architecture
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The year 1712 in architecture involved some significant events. Castle Howard in Yorkshire, England, designed by Sir John Vanbrugh, Roehampton House in Roehampton, London, England, designed by Thomas Archer is completed. Palais Trautson in Vienna is built, st Alkmunds Church, Whitchurch, Shropshire, England, designed by John Barker, is consecrated. Construction of church of Santissimo Nome di Maria e degli Angeli Custodi, Genoa, november 7 - Antoine Choquet de Lindu, French architect and military engineer October 27 - Sir William Robinson, English architect, worked in Ireland

3.
Science
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Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The formal sciences are often excluded as they do not depend on empirical observations, disciplines which use science, like engineering and medicine, may also be considered to be applied sciences. However, during the Islamic Golden Age foundations for the method were laid by Ibn al-Haytham in his Book of Optics. In the 17th and 18th centuries, scientists increasingly sought to formulate knowledge in terms of physical laws, over the course of the 19th century, the word science became increasingly associated with the scientific method itself as a disciplined way to study the natural world. It was during this time that scientific disciplines such as biology, chemistry, Science in a broad sense existed before the modern era and in many historical civilizations. Modern science is distinct in its approach and successful in its results, Science in its original sense was a word for a type of knowledge rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other, for example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of calendars, techniques for making poisonous plants edible. For this reason, it is claimed these men were the first philosophers in the strict sense and they were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by scientists as a more appropriate interest for lower class artisans. A clear-cut distinction between formal and empirical science was made by the pre-Socratic philosopher Parmenides, although his work Peri Physeos is a poem, it may be viewed as an epistemological essay on method in natural science. Parmenides ἐὸν may refer to a system or calculus which can describe nature more precisely than natural languages. Physis may be identical to ἐὸν and he criticized the older type of study of physics as too purely speculative and lacking in self-criticism. He was particularly concerned that some of the early physicists treated nature as if it could be assumed that it had no intelligent order, explaining things merely in terms of motion and matter. The study of things had been the realm of mythology and tradition, however. Aristotle later created a less controversial systematic programme of Socratic philosophy which was teleological and he rejected many of the conclusions of earlier scientists. For example, in his physics, the sun goes around the earth, each thing has a formal cause and final cause and a role in the rational cosmic order. Motion and change is described as the actualization of potentials already in things, while the Socratics insisted that philosophy should be used to consider the practical question of the best way to live for a human being, they did not argue for any other types of applied science

4.
Technology
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Technology is the collection of techniques, skills, methods and processes used in the production of goods or services or in the accomplishment of objectives, such as scientific investigation. Technology can be the knowledge of techniques, processes, and the like, the human species use of technology began with the conversion of natural resources into simple tools. The steady progress of technology has brought weapons of ever-increasing destructive power. It has helped develop more advanced economies and has allowed the rise of a leisure class, many technological processes produce unwanted by-products known as pollution and deplete natural resources to the detriment of Earths environment. Various implementations of technology influence the values of a society and raise new questions of the ethics of technology, examples include the rise of the notion of efficiency in terms of human productivity, and the challenges of bioethics. Philosophical debates have arisen over the use of technology, with disagreements over whether technology improves the condition or worsens it. The use of the technology has changed significantly over the last 200 years. Before the 20th century, the term was uncommon in English, the term was often connected to technical education, as in the Massachusetts Institute of Technology. The term technology rose to prominence in the 20th century in connection with the Second Industrial Revolution, the terms meanings changed in the early 20th century when American social scientists, beginning with Thorstein Veblen, translated ideas from the German concept of Technik into technology. In German and other European languages, a distinction exists between technik and technologie that is absent in English, which translates both terms as technology. By the 1930s, technology referred not only to the study of the industrial arts, dictionaries and scholars have offered a variety of definitions. Ursula Franklin, in her 1989 Real World of Technology lecture, gave another definition of the concept, it is practice, the way we do things around here. The term is used to imply a specific field of technology, or to refer to high technology or just consumer electronics. Bernard Stiegler, in Technics and Time,1, defines technology in two ways, as the pursuit of life by other than life, and as organized inorganic matter. Technology can be most broadly defined as the entities, both material and immaterial, created by the application of mental and physical effort in order to some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems and it is a far-reaching term that may include simple tools, such as a crowbar or wooden spoon, or more complex machines, such as a space station or particle accelerator. Tools and machines need not be material, virtual technology, such as software and business methods. W. Brian Arthur defines technology in a broad way as a means to fulfill a human purpose

5.
John Flamsteed
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John Flamsteed FRS was an English astronomer and the first Astronomer Royal. Flamsteed was born in Denby, Derbyshire, England, the son of Stephen Flamsteed and his first wife. He was educated at the school of Derby, and was educated at Derby School, in St Peters Churchyard, Derby. At that time, most masters of the school were Puritans, Flamsteed had a solid knowledge of Latin, essential for reading the scientific literature of the day, and a love of history, leaving the school in May,1662. His progress to Jesus College, Cambridge, recommended by the Master of Derby School, was delayed by years of chronic ill health. During those years, Flamsteed gave his father some help in his business, and from his father learnt arithmetic and the use of fractions, developing a keen interest in mathematics and astronomy. In July 1662, he was fascinated by the work of Johannes de Sacrobosco, De sphaera mundi. Early in 1663, he read Thomas Fales The Art of Dialling, in the summer of 1663, he read Wingates Canon, William Oughtreds Canon, and Thomas Stirrups Art of Dialling. At about the time, he acquired Thomas Streets Astronomia Carolina. Flamsteed was greatly impressed by the work of Horrocks, in September 1670, Flamsteed visited Cambridge and entered his name as an undergraduate at Jesus College. While it seems he never took up residence, he was there for two months in 1674, and had the opportunity to hear Isaac Newtons Lucasian Lectures. Ordained a deacon, he was preparing to take up a living in Derbyshire when he was invited to London by his patron Jonas Moore, Moore had recently made an offer to the Royal Society to pay for the establishment of an observatory. Charles appointed a Royal Commission to examine the proposal in December 1674, consisting of Lord Brouncker, Seth Ward, Samuel Moreland, Christopher Wren, Silius Titus, John Pell and Robert Hooke. Having arrived in London on 2 February 1675, and staying with Jonas Moore at the Tower of London and he was subsequently admitted as an official Assistant to the Royal Commission and supplied observations in order to test St Pierres proposal and to offer his own comments. On 4 March 1675 Flamsteed was appointed by royal warrant The Kings Astronomical Observator — the first English Astronomer Royal, in June 1675, another royal warrant provided for the founding of the Royal Greenwich Observatory, and Flamsteed laid the foundation stone on 10 August. He held that office, as well as that of Astronomer Royal and he is buried at Burstow, and the east window in the church was dedicated to him as a memorial. The will of Flamsteed’s widow, Margaret, left instructions for her own remains to be deposited “in the same Grave in which Mr John Flamsteed is buryed in the Chancell of Burstow Church. It seems no such monument was created, and almost 200 years later, after his death, his papers and scientific instruments were taken by his widow

6.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers

7.
Edmond Halley
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Edmond Halley, FRS was an English astronomer, geophysicist, mathematician, meteorologist, and physicist who is best known for computing the orbit of Halleys Comet. He was the second Astronomer Royal in Britain, succeeding John Flamsteed, Halley was born in Haggerston, in east London. His father, Edmond Halley Sr. came from a Derbyshire family and was a wealthy soap-maker in London, as a child, Halley was very interested in mathematics. He studied at St Pauls School, and from 1673 at The Queens College, while still an undergraduate, Halley published papers on the Solar System and sunspots. While at Oxford University, Halley was introduced to John Flamsteed, influenced by Flamsteeds project to compile a catalog of northern stars, Halley proposed to do the same for the Southern Hemisphere. In 1676, Halley visited the south Atlantic island of Saint Helena, while there he observed a transit of Mercury, and realised that a similar transit of Venus could be used to determine the absolute size of the Solar System. He returned to England in May 1678, in the following year he went to Danzig on behalf of the Royal Society to help resolve a dispute. Because astronomer Johannes Hevelius did not use a telescope, his observations had been questioned by Robert Hooke, Halley stayed with Hevelius and he observed and verified the quality of Hevelius observations. In 1679, Halley published the results from his observations on St. Helena as Catalogus Stellarum Australium which included details of 341 southern stars and these additions to contemporary star maps earned him comparison with Tycho Brahe, e. g. the southern Tycho as described by Flamsteed. Halley was awarded his M. A. degree at Oxford, in 1686, Halley published the second part of the results from his Helenian expedition, being a paper and chart on trade winds and monsoons. The symbols he used to represent trailing winds still exist in most modern day weather chart representations, in this article he identified solar heating as the cause of atmospheric motions. He also established the relationship between pressure and height above sea level. His charts were an important contribution to the field of information visualisation. Halley spent most of his time on lunar observations, but was interested in the problems of gravity. One problem that attracted his attention was the proof of Keplers laws of planetary motion, Halleys first calculations with comets were thereby for the orbit of comet Kirch, based on Flamsteeds observations in 1680-1. Although he was to calculate the orbit of the comet of 1682. They indicated a periodicity of 575 years, thus appearing in the years 531 and 1106 and it is now known to have an orbital period of circa 10,000 years. In 1691, Halley built a bell, a device in which the atmosphere was replenished by way of weighted barrels of air sent down from the surface

8.
John Arbuthnot
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John Arbuthnot, often known simply as Dr Arbuthnot, was a Scottish physician, satirist and polymath in London. He is best remembered for his contributions to mathematics, his membership in the Scriblerus Club, Alexander Pope noted to Joseph Spence that Arbuthnot allowed his infant children to play with, and even burn, his writings. Throughout his professional life, Arbuthnot exhibited a strong humility and conviviality, Arbuthnot was born in Kincardineshire, on the north-eastern coast of Scotland, son of Rev Alexander Arbuthnot, an Episcopalian priest and Margaret, née Lammie. He may have graduated with a degree from Marischal College in 1685. Where Johns brothers took part in Jacobite causes in 1689, he remained with his father and these brothers included Robert, who fled after fighting for King James VII in 1689 and became a banker in Rouen and half-brother George, who fled to France and became a wine merchant. However, when William and Mary came to the throne and the new Act of Settlement required all ministers to swear allegiance to them as heads of the Church of England, Arbuthnots father did not comply. As a non-conformist, he was removed from his church, and John was there to care of affairs when. Arbuthnot went to London in 1691, where he is supposed to have supported himself by teaching mathematics and he lodged with William Pate, whom Swift knew and called a bel esprit. He published Of the Laws of Chance in 1692, translated from Christiaan Huygenss De ratiociniis in ludo aleae and this was the first work on probability published in English. The work, which applied the field of probability to common games, was a success, and Arbuthnot became the tutor of one Edward Jeffreys, son of Jeffrey Jeffreys. However, Arbuthnot lacked the money to be a student and was already well educated. He went to the University of St Andrews and enrolled as a student in medicine on 11 September 1696. The very same day he defended seven theses on medicine and was awarded the doctorate and he first wrote satire in 1697, when he answered Dr John Woodwards An essay towards a natural history of the earth and terrestrial bodies, especially minerals. With An Examination of Dr Woodwards Account &c and he poked fun at the arrogance of the work and Woodwards misguided, Aristotelian insistence that what is theoretically attractive must be actually true. In 1701, Arbuthnot wrote another work, An essay on the usefulness of mathematical learning. The work was successful, and Arbuthnot praises mathematics as a method of freeing the mind from superstition. In 1702, he was at Epsom when Prince George of Denmark, according to tradition, Arbuthnot treated the prince successfully. According to tradition again, this treatment earned him an invitation to court, also around 1702, he married Margaret, whose maiden name is possibly Wemyss

9.
Seki Takakazu
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Seki Takakazu, also known as Seki Kōwa, was a Japanese mathematician in the Edo period. Seki laid foundations for the subsequent development of Japanese mathematics known as wasan and he created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. A contemporary of Gottfried Leibniz and Isaac Newton, Sekis work was independent and his successors later developed a school dominant in Japanese mathematics until the end of the Edo period. While it is not clear how much of the achievements of wasan are Sekis, since many of them only in writings of his pupils. For example, he is credited with the discovery of Bernoulli numbers, the resultant and determinant are attributed to him. This work was an advance on, for example, the comprehensive introduction of 13th-century Chinese algebra made as late as 1671. Not much is known about Kōwas personal life and his birthplace has been indicated as either Fujioka in Gunma prefecture, or Edo. His birth date ranges from 1635 to 1643 and he was born to the Uchiyama clan, a subject of Ko-shu han, and adopted into the Seki family, a subject of the Shogun. While in Ko-shu han, he was involved in a project to produce a reliable map of his employers land. He spent many years in studying 13th-century Chinese calendars to replace the accurate one used in Japan at that time. His mathematics was based on knowledge from the 13th to 15th centuries. This consisted of algebra with numerical methods, polynomial interpolation and its applications, Sekis work is more or less based on and related to these known methods. Chinese algebra discovered numerical evaluation of arbitrary degree algebraic equation with real coefficients, by using the Pythagorean theorem, they reduced geometric problems to algebra systematically. The number of unknowns in an equation was, however, quite limited and they used notations of an array of numbers to represent a formula, for example, for a x 2 + b x + c. Later, they developed a method that uses two-dimensional arrays, representing four variables at most, hence, a target of Seki and his contemporary Japanese mathematicians was the development of general multi-variable algebraic equations and elimination theory. In the Chinese approach to interpolation, the motivation was to predict the motion of celestial bodies from observed data. The method was applied to find various mathematical formulas. Seki learned this technique, most likely, through his examination of Chinese calendars

10.
Bernoulli number
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In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers with deep connections to number theory. The values of the first few Bernoulli numbers are B0 =1, B±1 = ±1/2, B2 = 1/6, B3 =0, B4 = −1/30, B5 =0, B6 = 1/42, B7 =0, B8 = −1/30. The superscript ± is used by this article to designate the two conventions for Bernoulli numbers. They differ only in the sign of the n =1 term, B−n are the first Bernoulli numbers, in this convention, B−1 = −1/2. B+n are the second Bernoulli numbers, which are called the original Bernoulli numbers. In this convention, B+1 = +1/2, since Bn =0 for all odd n >1, and many formulas only involve even-index Bernoulli numbers, some authors write Bn to mean B2n. This article does not follow this notation, the Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and independently by Japanese mathematician Seki Kōwa. Sekis discovery was published in 1712 in his work Katsuyo Sampo, Bernoullis, also posthumously. Ada Lovelaces note G on the Analytical Engine from 1842 describes an algorithm for generating Bernoulli numbers with Babbages machine, as a result, the Bernoulli numbers have the distinction of being the subject of the first published complex computer program. Bernoulli numbers feature prominently in the form expression of the sum of the mth powers of the first n positive integers. For m, n ≥0 define S m = ∑ k =1 n k m =1 m +2 m + ⋯ + n m and this expression can always be rewritten as a polynomial in n of degree m +1. The coefficients of polynomials are related to the Bernoulli numbers by Bernoullis formula, S m =1 m +1 ∑ k =0 m B k + n m +1 − k. For example, taking m to be 1 gives the triangular numbers 0,1,3,6, … A000217,1 +2 + ⋯ + n =12 =12. Taking m to be 2 gives the square pyramidal numbers 0,1,5,14,12 +22 + ⋯ + n 2 =13 =13. Some authors use the convention for Bernoulli numbers and state Bernoullis formula in this way. Bernoullis formula is sometimes called Faulhabers formula after Johann Faulhaber who also found ways to calculate sums of powers. Faulhabers formula was generalized by V. Guo and J. Zeng to a q-analog, many characterizations of the Bernoulli numbers have been found in the last 300 years, and each could be used to introduce these numbers. Here only four of the most useful ones are mentioned, an equation, an explicit formula, a generating function

11.
Brook Taylor
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Brook Taylor FRS was an English mathematician who is best known for Taylors theorem and the Taylor series. Brook Taylor was born in Edmonton to John Taylor of Bifrons House in Patrixbourne, Kent and he entered St Johns College, Cambridge, as a fellow-commoner in 1701, and took degrees of LL. B. and LL. D. in 1709 and 1714, respectively. Taylors Methodus Incrementorum Directa et Inversa added a new branch to higher mathematics, among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. From 1715 his studies took a philosophical and religious bent and he corresponded in that year with the Comte de Montmort on the subject of Nicolas Malebranches tenets. Unfinished treatises, On the Jewish Sacrifices and On the Lawfulness of Eating Blood, written on his return from Aix-la-Chapelle in 1719, were afterwards found among his papers. His marriage in 1721 with Miss Brydges of Wallington, Surrey, led to an estrangement from his father, which ended in 1723 after her death in giving birth to a son, by the date of his fathers death in 1729 he had inherited the Bifrons estate. Taylors fragile health gave way, he fell into a decline and he was buried in London on 2 December 1731, near his first wife, in the churchyard of St Annes, Soho. A posthumous work entitled Contemplatio Philosophica was printed for private circulation in 1793 by Taylors grandson, Sir William Young, prefaced by a life of the author, and with an appendix containing letters addressed to him by Bolingbroke, Bossuet, and others. Several short papers by Taylor were published in Phil, vols. xxvii to xxxii, including accounts of some interesting experiments in magnetism and capillary attraction. A French translation was published in 1757, in Methodus Incrementorum, Taylor gave the first satisfactory investigation of astronomical refraction. Taylor, Brook, Methodus Incrementorum Directa et Inversa, London, Taylor is an impact crater located on the Moon, named in honour of Brook Taylor. Brook Taylor’s Work on Linear Perspective, anderson, Marlow, Katz, Victor, Wilson, Robin. Sherlock Holmes in Babylon, And Other Tales of Mathematical History, Brook Taylor and the Method of Increments. Archive for History of Exact Sciences, oConnor, John J. Robertson, Edmund F. Brook Taylor, MacTutor History of Mathematics archive, University of St Andrews, beningbrough Hall has a painting by John Closterman of Taylor aged about 12 with his brothers and sisters. See also NPG5320, The Children of John Taylor of Bifrons Park Brook Taylors pedigree Taylor, a crater on the Moon named after Brook Taylor

12.
Taylor's theorem
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In calculus, Taylors theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial. For analytic functions the Taylor polynomials at a point are finite order truncations of its Taylor series. The exact content of Taylors theorem is not universally agreed upon, indeed, there are several versions of it applicable in different situations, and some of them contain explicit estimates on the approximation error of the function by its Taylor polynomial. Taylors theorem is named after the mathematician Brook Taylor, who stated a version of it in 1712, yet an explicit expression of the error was not provided until much later on by Joseph-Louis Lagrange. An earlier version of the result was already mentioned in 1671 by James Gregory, Taylors theorem is taught in introductory level calculus courses and it is one of the central elementary tools in mathematical analysis. Within pure mathematics it is the point of more advanced asymptotic analysis. Taylors theorem also generalizes to multivariate and vector valued functions f, R n → R m on any dimensions n and m and this generalization of Taylors theorem is the basis for the definition of so-called jets which appear in differential geometry and partial differential equations. If a real-valued function f is differentiable at the point a then it has an approximation at the point a. This means that there exists a function h1 such that f = f + f ′ + h 1, here P1 = f + f ′ is the linear approximation of f at the point a. The graph of y = P1 is the tangent line to the graph of f at x = a, the error in the approximation is R1 = f − P1 = h 1. Note that this goes to zero a little bit faster than x − a as x tends to a, if we wanted a better approximation to f, we might instead try a quadratic polynomial instead of a linear function. Instead of just matching one derivative of f at a, we can match two derivatives, thus producing a polynomial that has the slope and concavity as f at a. The quadratic polynomial in question is P2 = f + f ′ + f ″22, Taylors theorem ensures that the quadratic approximation is, in a sufficiently small neighborhood of the point a, a better approximation than the linear approximation. Specifically, f = P2 + h 22, lim x → a h 2 =0. Here the error in the approximation is R2 = f − P2 = h 22 which, given the behavior of h 2. Similarly, we might get better approximations to f if we use polynomials of higher degree. In general, the error in approximating a function by a polynomial of degree k will go to zero a little bit faster than k as x tends to a. Find the smallest degree k for which the polynomial Pk approximates f to within an error on a given interval

13.
Angle
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles

14.
Rhombic dodecahedron
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In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of two types and it is a Catalan solid, and the dual polyhedron of the cuboctahedron. The rhombic dodecahedron is a zonohedron and its polyhedral dual is the cuboctahedron. The long diagonal of each face is exactly √2 times the length of the diagonal, so that the acute angles on each face measure arccos. Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-transitive, meaning the symmetry group of the solid acts transitively on the set of faces. In elementary terms, this means that for any two faces A and B there is a rotation or reflection of the solid that leaves it occupying the region of space while moving face A to face B. The rhombic dodecahedron is one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron, the rhombic dodecahedron can be used to tessellate three-dimensional space. It can be stacked to fill a space much like hexagons fill a plane and this polyhedron in a space-filling tessellation can be seen as the Voronoi tessellation of the face-centered cubic lattice. It is the Brillouin zone of body centered cubic crystals, some minerals such as garnet form a rhombic dodecahedral crystal habit. Honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron, the rhombic dodecahedron also appears in the unit cells of diamond and diamondoids. In these cases, four vertices are absent, but the chemical bonds lie on the remaining edges, the graph of the rhombic dodecahedron is nonhamiltonian. The last two correspond to the B2 and A2 Coxeter planes, the rhombic dodecahedron is a parallelohedron, a space-filling polyhedron. Other symmetry constructions of the dodecahedron are also space-filling. For example, with 4 square faces, and 60-degree rhombic faces and it be seen as a cuboctahedron with square pyramids augmented on the top and bottom. In 1960 Stanko Bilinski discovered a second rhombic dodecahedron with 12 congruent rhombus faces and it has the same topology but different geometry. The rhombic faces in this form have the golden ratio, another topologically equivalent variation, sometimes called a trapezoidal dodecahedron, is isohedral with tetrahedral symmetry order 24, distorting rhombic faces into kites. It has 8 vertices adjusted in or out in sets of 4. Variations can be parametrized by, where b is determined from a for planar faces and this polyhedron is a part of a sequence of rhombic polyhedra and tilings with Coxeter group symmetry

15.
Newcomen atmospheric engine
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The atmospheric engine was invented by Thomas Newcomen in 1712, often referred to simply as a Newcomen engine. The engine operated by condensing steam drawn into the cylinder, thereby creating a partial vacuum and it was the first practical device to harness steam to produce mechanical work. Newcomen engines were used throughout Britain and Europe, principally to pump out of mines. Hundreds were constructed through the 18th century, James Watts later engine design was an improved version of the Newcomen engine that roughly doubled fuel efficiency. Many atmospheric engines were converted to the Watt design, for a price based on a fraction of the savings in fuel, as a result, Watt is today better known than Newcomen in relation to the origin of the steam engine. Prior to Newcomen a number of small devices of various sorts had been made. Around 1600 a number of experimenters used steam to power small fountains working like a coffee percolator, first a container was filled with water via a pipe, which extended through the top of the container to nearly the bottom. The bottom of the pipe would be submerged in the water, the container was then heated to make the water boil. These devices had limited effectiveness but illustrated the principles viability, in 1662 Edward Somerset, second Marquess of Worcester, published a book containing several ideas he had been working on. One was for a pump to supply water to fountains. A fresh charge of steam under pressure then drove the water from the container up another pipe to a header before that steam condensed. By working the two containers alternately, the rate to the header tank could be increased. In 1698 Thomas Savery patented a steam-powered pump he called the Miners Friend, essentially identical to Somersets design, the process of cooling and creating the vacuum was fairly slow, so Savery later added an external cold water spray to quickly cool the steam. Saverys invention cannot be regarded as the first steam engine since it had no moving parts. There were evidently high hopes for the Miners Friend, which led Parliament to extend the life of the patent by 21 years, unfortunately, Saverys device proved much less successful than had been hoped. This was insufficient to pump out of a mine. In Saverys pamphlet, he suggests setting the boiler and containers on a ledge in the mineshaft, obviously these were inconvenient solutions and some sort of mechanical pump working at surface level – one that lifted the water directly instead of sucking it up – was desirable. Such pumps were common already, powered by horses, but required a vertical reciprocating drive that Saverys system did not provide, the more practical problem concerned having a boiler operating under pressure, as demonstrated when the boiler of an engine at Wednesbury exploded, perhaps in 1705

16.
Black Country
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The Black Country is an area of the West Midlands in England, West of Birmingham, including Dudley, Walsall and Sandwell. In the Industrial Revolution, it one of the most industrialised parts of Britain with coal mines, coking, iron foundries. The 14-mile road between Wolverhampton and Birmingham was described as one town in 1785. The first trace of The Black Country as an expression dates from the 1840s, the name is believed to come from the soot from the heavy industries that covered the area, although the 30-foot-thick coal seam close to the surface is another possible origin. The borders of the Black Country can be defined by using the cultural and industrial characteristics of the area. Areas around the canals which had mines extracting mineral resources and heavy industry refining these are included in this definition, cultural parameters include unique foods and dialect. The Black Country Society defines the Black Countrys borders as the area on the thirty foot coal seam and this definition includes West Bromwich and Oldbury, which had many deep pits, and Smethwick. The thick coal that underlies Smethwick wasnt mined until the 1870s, Sandwell Park Collierys pit was located in Smethwick and had thick coal as shown in written accounts from 1878 and coal was also heavily mined in Hamstead further east. Smethwick and Dudley Port were described as a thousand swarming hives of metallurgical industries by Samuel Griffiths in 1872, warley is also included, despite lacking industry and canals, as housing for industrial workers in Smethwick and Oldbury was built there. Another geological definition, the seam outcrop definition, only areas where the coal seam is shallow. Some coal mining areas to the east and west of the geologically defined Black Country are therefore excluded by this definition because the coal here is too deep down, the seam outcrop definition excludes areas in North Worcestershire and South Staffordshire. This is the basis for much of the controversy over definitions and he describes going into the black country of Staffordshire - Wolverhampton, Bilston and Tipton. He introduces the area as that region of mines and forges, commonly called the Black Country. The phrase was used again, though as a rather than a proper noun. An alternative theory for the meaning of the name is proposed as having been caused by the darkening of the soil due to the outcropping coal. In 1642 at the start of the Civil War, Charles I failed to capture the two arsenals of Portsmouth and Hull, which although in cities loyal to Parliament were located in counties loyal to him. As he had failed to capture the arsenals, Charles did not possess any supply of swords, pikes, guns, or shot, all these the Black Country could, from Stourbridge came shot, from Dudley cannon. Numerous small forges which then existed on every brook in the north of Worcestershire turned out successive supplies of sword blades and his method was employed on the Kings behalf

17.
England
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England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west, the Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east, the country covers five-eighths of the island of Great Britain in its centre and south, and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight. England became a state in the 10th century, and since the Age of Discovery. The Industrial Revolution began in 18th-century England, transforming its society into the worlds first industrialised nation, Englands terrain mostly comprises low hills and plains, especially in central and southern England. However, there are uplands in the north and in the southwest, the capital is London, which is the largest metropolitan area in both the United Kingdom and the European Union. In 1801, Great Britain was united with the Kingdom of Ireland through another Act of Union to become the United Kingdom of Great Britain and Ireland. In 1922 the Irish Free State seceded from the United Kingdom, leading to the latter being renamed the United Kingdom of Great Britain, the name England is derived from the Old English name Englaland, which means land of the Angles. The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages, the Angles came from the Angeln peninsula in the Bay of Kiel area of the Baltic Sea. The earliest recorded use of the term, as Engla londe, is in the ninth century translation into Old English of Bedes Ecclesiastical History of the English People. According to the Oxford English Dictionary, its spelling was first used in 1538. The earliest attested reference to the Angles occurs in the 1st-century work by Tacitus, Germania, the etymology of the tribal name itself is disputed by scholars, it has been suggested that it derives from the shape of the Angeln peninsula, an angular shape. An alternative name for England is Albion, the name Albion originally referred to the entire island of Great Britain. The nominally earliest record of the name appears in the Aristotelian Corpus, specifically the 4th century BC De Mundo, in it are two very large islands called Britannia, these are Albion and Ierne. But modern scholarly consensus ascribes De Mundo not to Aristotle but to Pseudo-Aristotle, the word Albion or insula Albionum has two possible origins. Albion is now applied to England in a poetic capacity. Another romantic name for England is Loegria, related to the Welsh word for England, Lloegr, the earliest known evidence of human presence in the area now known as England was that of Homo antecessor, dating to approximately 780,000 years ago. The oldest proto-human bones discovered in England date from 500,000 years ago, Modern humans are known to have inhabited the area during the Upper Paleolithic period, though permanent settlements were only established within the last 6,000 years

18.
John Fothergill (physician)
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John Fothergill FRS was an English physician, plant collector, philanthropist and Quaker. His medical writings were influential, and he built up a botanic garden in what is now West Ham Park in London. Fothergill was born at Carr End, near Bainbridge in Yorkshire, the son of John Fothergill, a Quaker preacher and farmer, after studying at Sedbergh School, Fothergill was apprenticed to an apothecary. He later took the degree of M. D. at Edinburgh, in 1736, followed by studies at St Thomass Hospital. After visiting continental Europe in 1740, he settled in London, for example, during the epidemics of influenza in 1775 and 1776 he is said to have treated sixty patients a day. He is credited with first identifying and naming trigeminal neuralgia in his work Of a Painful Affection of the Face in 1765. Fothergills pamphlet, Account of the Sore Throat attended with Ulcers, contains one of the first descriptions of streptococcal sore throat in English and his rejection of ineffective traditional therapies for this disease saved many lives. He also supported the publication of Benjamin Franklins papers on electricity, in his leisure, John Fothergill made a study of conchology and botany. In 1762 he bought Upton House near Stratford, London and in its grounds he built up a botanical garden. In the garden, with its glasshouses, John Coakley Lettsom, a Quaker physician and a protégé of his, exclaimed that the sphere seemed transposed, as the Arctic Circle joined with the equator. Lettsom published a catalogue of the plants of Fothergills garden Hortus Uptonensis, or a catalogue of the plants in the Dr. Fothergill’s garden at Upton, fothergilla is named in his honour. Fothergill was elected a Fellow of the Royal Society in 1763 and he was the patron of Sydney Parkinson, the South Sea voyager, and also of William Bartram, the American botanist in his Southern travels 1773–76. A translation of the Bible, known as the Quaker Bible by Anthony Purver and he founded Ackworth School, Pontefract, Yorkshire in 1779. John Fothergill died in London on 26 December 1780, aged 68, fanny Burney, having earlier described him as an upright, stern old man. An old prig, later recorded when she was his patient, He really has been… amazingly civil and his niece Betty Fothergill described him in her journal as surely the first of men. With the becoming dignity of age he unites the cheerfulness and liberality of youth and he possesses the most virtues and the fewest failings of any man I know. Memoires of John Fothergill, M. D. John Fothergill, attribution This article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. Fothergill, John. A Complete Collection of the Medical and Philosophical Works of John Fothergill, memoirs of the Life and Gospel Labours of Samuel Fothergill, with Selections from his Correspondence

19.
English people
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The English are a nation and an ethnic group native to England, who speak the English language. The English identity is of medieval origin, when they were known in Old English as the Angelcynn. Their ethnonym is derived from the Angles, one of the Germanic peoples who migrated to Great Britain around the 5th century AD, England is one of the countries of the United Kingdom. Collectively known as the Anglo-Saxons, they founded what was to become England along with the later Danes, Normans, in the Acts of Union 1707, the Kingdom of England was succeeded by the Kingdom of Great Britain. Over the years, English customs and identity have become closely aligned with British customs. The English people are the source of the English language, the Westminster system and these and other English cultural characteristics have spread worldwide, in part as a result of the former British Empire. The concept of an English nation is far older than that of the British nation, many recent immigrants to England have assumed a solely British identity, while others have developed dual or mixed identities. Use of the word English to describe Britons from ethnic minorities in England is complicated by most non-white people in England identifying as British rather than English. In their 2004 Annual Population Survey, the Office for National Statistics compared the ethnic identities of British people with their national identity. They found that while 58% of white people in England described their nationality as English and it is unclear how many British people consider themselves English. Following complaints about this, the 2011 census was changed to allow respondents to record their English, Welsh, Scottish, another complication in defining the English is a common tendency for the words English and British to be used interchangeably, especially overseas. In his study of English identity, Krishan Kumar describes a common slip of the tongue in which people say English, I mean British. He notes that this slip is made only by the English themselves and by foreigners. Kumar suggests that although this blurring is a sign of Englands dominant position with the UK and it tells of the difficulty that most English people have of distinguishing themselves, in a collective way, from the other inhabitants of the British Isles. In 1965, the historian A. J. P. Taylor wrote, When the Oxford History of England was launched a generation ago and it meant indiscriminately England and Wales, Great Britain, the United Kingdom, and even the British Empire. Foreigners used it as the name of a Great Power and indeed continue to do so, bonar Law, by origin a Scotch Canadian, was not ashamed to describe himself as Prime Minister of England Now terms have become more rigorous. The use of England except for a geographic area brings protests and this version of history is now regarded by many historians as incorrect, on the basis of more recent genetic and archaeological research. The 2016 study authored by Stephan Schiffels et al, the remaining portion of English DNA is primarily French, introduced in a migration after the end of the Ice Age

20.
Physician
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Both the role of the physician and the meaning of the word itself vary around the world. Degrees and other qualifications vary widely, but there are common elements, such as medical ethics requiring that physicians show consideration, compassion. Around the world the term refers to a specialist in internal medicine or one of its many sub-specialties. This meaning of physician conveys a sense of expertise in treatment by drugs or medications and this term is at least nine hundred years old in English, physicians and surgeons were once members of separate professions, and traditionally were rivals. Henry VIII granted a charter to the London Royal College of Physicians in 1518 and it was not until 1540 that he granted the Company of Barber/Surgeons its separate charter. In the same year, the English monarch established the Regius Professorship of Physic at the University of Cambridge, newer universities would probably describe such an academic as a professor of internal medicine. Hence, in the 16th century, physic meant roughly what internal medicine does now, currently, a specialist physician in the United States may be described as an internist. Another term, hospitalist, was introduced in 1996, to describe US specialists in internal medicine who work largely or exclusively in hospitals, such hospitalists now make up about 19% of all US general internists, who are often called general physicians in Commonwealth countries. In such places, the more general English terms doctor or medical practitioner are prevalent, in Commonwealth countries, specialist pediatricians and geriatricians are also described as specialist physicians who have sub-specialized by age of patient rather than by organ system. Around the world, the term physician and surgeon is used to describe either a general practitioner or any medical practitioner irrespective of specialty. This usage still shows the meaning of physician and preserves the old difference between a physician, as a practitioner of physic, and a surgeon. The term may be used by state medical boards in the United States of America, in modern English, the term physician is used in two main ways, with relatively broad and narrow meanings respectively. This is the result of history and is often confusing and these meanings and variations are explained below. In the United States and Canada, the term physician describes all medical practitioners holding a professional medical degree, the American Medical Association, established in 1847, as well as the American Osteopathic Association, founded in 1897, both currently use the term physician to describe members. However, the American College of Physicians, established in 1915, does not, its title uses physician in its original sense. A physician trained in the United States has either a Doctor of Medicine degree, all boards of certification now require that physicians demonstrate, by examination, continuing mastery of the core knowledge and skills for a chosen specialty. Recertification varies by particular specialty between every seven and every ten years, graduates of osteopathic medical schools in the United States should not be confused with osteopaths, who are trained in the European and Commonwealth nations. Their training is similar to physical therapy and they are not licensed to prescribe medications or perform surgeries, also in the United States, the American Podiatric Medical Association defines podiatrists as physicians and surgeons that fall under the department of surgery in hospitals

21.
Claude Bourgelat
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Claude Bourgelat was a French veterinary surgeon. He was the founder of veterinary colleges at Lyon in 1761, as well as an authority on horse management, other dates claimed for the establishment of the Lyon College, the first veterinary school in the world, are 1761 and 1764. The plague to which Lupton referred was cattle plague, also known by its German name. He was a member of the French Academy of Sciences and the Prussian Academy of Sciences, Bourgelat also contributed to Diderot and dAlamberts Encyclopédie. A Lyon, Chez Henri Declaustre, libraire-imprimeur ruë Neuve, les freres Duplain, matiere médicale raisonnée, ou, Précis des médicamens considérés dans leurs effets, a l’usage des éleves de l’Ecole royale vétérinaire, avec les formules médicinales. Lehrbegriff der medicinischen Materie, oder, Beschreibung der einfachen Arzeneyen nach ihren Wirkungen, zum Gebrauche der Lehrlinge in der königl. Leipzig, M. G. Wiedmanns Erben und Reich,1766, &c, le tout à l’usage des elèves des ecoles royales vétérinaires. A Paris, Chez Vallat-La-Chapelle, libraire, au Palais, sur le Perron de la Sainte-Chapelle, elémens de l’art vétérinaire, précis anatomique du corps du cheval, à l’usage des éleves des écoles royales vétérinaires. A Paris, Chez Vallat-la-Chapelle, libraire, au Palais, sur le Perron de la Sainte-Chapelle, essai sur les appareils et sur les bandages propres aux quadrupèdes. A l’usage des élèves des écoles royales vétérinaires, matiere médicale raisonnée, ou, Précis des médicamens considérés dans leurs effets, a l’usage des éleves de l’École royale vétérinaire, avec les formules médicinales de la même École. Précis anatomique du corps du cheval, à l’usage des éleves des écoles vétérinaires, matiere médicale raisonnée, ou précis des médicamens considérés dans leurs effets, à l’usage des eleves des ecoles vétérinaires, avec les formules médicinales & officinales. 125-158. on line Hugues Plaideux, « La descendance de Claude Bourgelat », in Bulletin de la Société française dhistoire de la médecine et des sciences vétérinaires,12,2012, p. 161-176. On line Bourgelat, Claude, in, Frank Arthur Kafker, The encyclopedists as individuals, richard Tagand, Claude Bourgelat, écuyer lyonnais, 1712–1779, in, Revue de médecine vétérinaire 1959, p. 888–897. Alcide Railliet, Léon Moulé, Histoire de l’École d’Alfort, Paris 1908, online Louis Furcy Grognier, london and New York, Frederick Warne