1.
1667 in science
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The year 1667 in science and technology involved some significant events. June 24 – The site of the Paris Observatory is located on the Paris Meridian, johann Joachim Becher originates what will become known as phlogiston theory in his Physical Education. Thomas Sprat publishes The History of the Royal-Society of London, for the Improving of Natural Knowledge, james Gregory demonstrates the transcendence of π. June 15 – Jean-Baptiste Denys performs the first blood transfusion from a lamb into a boy, robert Hooke demonstrates that the alteration of the blood in the lungs is essential for respiration. Thomas Willis publishes Pathologicae Cerebri, et nervosi generis specimen, nicolas Steno publishes Elementorum Myologiae Specimen, seu Musculi Descriptio Geometrica

2.
1670s in architecture
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1670 Báo Quốc Pagoda, Huế, Vietnam, is built. Saint George Palace, Rennes, France, has its foundation stones laid,1671 - Weston Park, Shropshire, England, is built for Elizabeth Wilbraham. 1672 Buildings by Christopher Wren in England, Temple Bar, London rebuilt, williamson Building at The Queens College, Oxford, completed. Construction of Castillo de San Marcos at St. Augustine, Florida, designed by Ignacio Daza,1673 April - Badshahi Masjid in Lahore, Punjab, built for Aurangzeb, is completed. Monastery of San Francisco, Lima, Peru, is consecrated,1675 June - Work on the new St Pauls Cathedral in London, designed by Christopher Wren, begins. June 11 - Theatine Church, Munich, consecrated in form as left by Agostino Barelli, august 2 - Portuguese Synagogue, designed by Elias Bouwman and begun in 1671, is completed. Bethlem Royal Hospital in London, designed by Robert Hooke, briggflatts Meeting House near Sedbergh in north-west England built. 1676 The Royal Greenwich Observatory in London, designed by Christopher Wren is completed, Wren Library, Cambridge, the library of Trinity College, England, is designed by Christopher Wren. Main courtyards of Les Invalides in Paris, designed by Libéral Bruant, are completed, St. Peter and St. Pauls Church, Vilnius is completed. 1677 The Monument to the Great Fire of London, designed by Christopher Wren, Chapel of Emmanuel College, Cambridge, designed by Christopher Wren. 1679 Chapel at Les Invalides, Paris, is completed to the design of Libéral Bruant, Černín Palace in Prague, designed by Francesco Caratti, is completed. 1671, December 30 - The Académie royale darchitecture is founded by Louis XIV of France in Paris, the worlds first school of architecture

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.
Paris Observatory
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The Paris Observatory is the foremost astronomical observatory of France, and one of the largest astronomical centers in the world. Its historic building is to be found on the Left Bank of the Seine in central Paris, administratively, it is a grand établissement of the French Ministry of National Education, with a status close to that of a public university. Its missions include, research in astronomy and astrophysics, education, diffusion of knowledge to the public and it maintains a solar observatory at Meudon and a radio astronomy observatory at Nançay. It was also the home to the International Time Bureau until its dissolution in 1987 and its foundation lies in the ambitions of Jean-Baptiste Colbert to extend Frances maritime power and international trade in the 17th century. Louis XIV promoted its construction, which was started in 1667 and it thus predates by a few years the Royal Greenwich Observatory in England, which was founded in 1675. The architect of the Paris Observatory was Claude Perrault whose brother, Charles, was secretary to Colbert, optical instruments were supplied by Giuseppe Campani. The buildings were extended in 1730,1810,1834,1850, the last extension incorporates the spectacular Meridian Room designed by Jean Prouvé. The worlds first national almanac, the Connaissance des temps, was published by the observatory in 1679, in 1863, the observatory published the first modern weather maps. In 1882, a 33 cm astrographic lens was constructed, an instrument that catalysed what proved to be the over-ambitious international Carte du Ciel project. The Meudon great refractor was a 83 cm aperture refractor, which with September 20,1909 observations by E. M. Antoniadi helped disprove the Mars canals theory and it was a double telescope completed in 1891, with secondary having 62 cm aperture lens for photography. It was one of the largest active telescopes in Europe, the title of Director of the Observatory was officially given for the first time to César-François Cassini de Thury by a Royal brevet dated November 12,1771. However, the important role played by his grandfather and father in this institution during its first century actually gives them somewhat the role of director, a coronograph was in operation there for ten years, the dome was moved there from the Perrault building of the Observatoire de Paris. Nowadays, the AstroQueyras amateur astronomy association operates the facility, using a 60 cm telescope on loan from the Observatoire de Haute Provence, numerous asteroids have been discovered there. Paris Observatory, Encyclopaedia Britannica, Deluxe CDROM edition Aubin, D, the fading star of the Paris Observatory in the nineteenth century, astronomers urban culture of circulation and observation. History of the Bureau International de lHeure, polar Motion, Historical and Scientific problems. Paris Observatory Paris Observatory History Location in Paris Publications of the Observatoire de Paris in Gallica, the digital library of the BnF

6.
James Gregory (mathematician)
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James Gregory FRS was a Scottish mathematician and astronomer. His surname is spelt as Gregorie, the original Scottish spelling. In his book Geometriae Pars Universalis Gregory gave both the first published statement and proof of the theorem of the calculus, for which he was acknowledged by Isaac Barrow. It was his mother who endowed Gregory with his appetite for geometry, her uncle – Alexander Anderson – having been a pupil, after his fathers death in 1651 his elder brother David took over responsibility for his education. He attended Aberdeen Grammar School, and then Marischal College from 1653–1657, in 1663 he went to London, meeting John Collins and fellow Scot Robert Moray, one of the founders of the Royal Society. In 1664 he departed for the University of Padua, in the Venetian Republic, passing through Flanders, Paris, at Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, and he was taught by Stefano Angeli. He was successively professor at the University of St Andrews and the University of Edinburgh and he had married Mary, daughter of George Jameson, painter, and widow of John Burnet of Elrick, Aberdeen, their son James was Professor of Physics at Kings College, Aberdeen. He was the grandfather of John Gregory, uncle of David Gregorie and brother of David Gregory, about a year after assuming the Chair of Mathematics at Edinburgh, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36, in the Optica Promota, published in 1663, Gregory described his design for a reflecting telescope, the Gregorian telescope. In 1667, Gregory issued his Vera Circuli et Hyperbolae Quadratura, in which he showed how the areas of the circle, nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed transcendental numbers. In addition the first proof of the theorem of calculus. The book also contains series expansions of sin, cos, arcsin, Gregory was probably unaware that the earliest enunciations of these expansions were made by Madhava in India in the 14th century. The book was reprinted in 1668 with an appendix, Geometriae Pars, in his 1663 Optica Promota, James Gregory described his reflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a telescope with a parabolic mirror would correct spherical aberration as well as the chromatic aberration seen in refracting telescopes. According to his own confession, Gregory had no practical skill, the Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are used in radio telescopes such as Arecibo. The following excerpt is from the Pantologia, in 1671, or perhaps earlier, he established the theorem that θ = tan θ − tan 3 θ + tan 5 θ − …, the result being true only if θ lies between −π and π. This formula was used to calculate digits of π, although more efficient formulas were later discovered

7.
Inverse trigonometric functions
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In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. There are several notations used for the trigonometric functions. The most common convention is to name inverse trigonometric functions using a prefix, e. g. arcsin, arccos, arctan. This convention is used throughout the article, when measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. Similarly, in programming languages the inverse trigonometric functions are usually called asin, acos. The notations sin−1, cos−1, tan−1, etc, the confusion is somewhat ameliorated by the fact that each of the reciprocal trigonometric functions has its own name—for example, −1 = sec. Nevertheless, certain authors advise against using it for its ambiguity, since none of the six trigonometric functions are one-to-one, they are restricted in order to have inverse functions. There are multiple numbers y such that sin = x, for example, sin =0, when only one value is desired, the function may be restricted to its principal branch. With this restriction, for x in the domain the expression arcsin will evaluate only to a single value. These properties apply to all the trigonometric functions. The principal inverses are listed in the following table, if x is allowed to be a complex number, then the range of y applies only to its real part. Trigonometric functions of trigonometric functions are tabulated below. This is derived from the tangent addition formula tan = tan + tan 1 − tan tan , like the sine and cosine functions, the inverse trigonometric functions can be calculated using power series, as follows. For arcsine, the series can be derived by expanding its derivative,11 − z 2, as a binomial series, the series for arctangent can similarly be derived by expanding its derivative 11 + z 2 in a geometric series and applying the integral definition above. Arcsin = z + z 33 + z 55 + z 77 + ⋯ = ∑ n =0 ∞, for example, arccos x = π /2 − arcsin x, arccsc x = arcsin , and so on. Alternatively, this can be expressed, arctan z = ∑ n =0 ∞22 n 2. There are two cuts, from −i to the point at infinity, going down the imaginary axis and it works best for real numbers running from −1 to 1

8.
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

9.
China
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China, officially the Peoples Republic of China, is a unitary sovereign state in East Asia and the worlds most populous country, with a population of over 1.381 billion. The state is governed by the Communist Party of China and its capital is Beijing, the countrys major urban areas include Shanghai, Guangzhou, Beijing, Chongqing, Shenzhen, Tianjin and Hong Kong. China is a power and a major regional power within Asia. Chinas landscape is vast and diverse, ranging from forest steppes, the Himalaya, Karakoram, Pamir and Tian Shan mountain ranges separate China from much of South and Central Asia. The Yangtze and Yellow Rivers, the third and sixth longest in the world, respectively, Chinas coastline along the Pacific Ocean is 14,500 kilometers long and is bounded by the Bohai, Yellow, East China and South China seas. China emerged as one of the worlds earliest civilizations in the basin of the Yellow River in the North China Plain. For millennia, Chinas political system was based on hereditary monarchies known as dynasties, in 1912, the Republic of China replaced the last dynasty and ruled the Chinese mainland until 1949, when it was defeated by the communist Peoples Liberation Army in the Chinese Civil War. The Communist Party established the Peoples Republic of China in Beijing on 1 October 1949, both the ROC and PRC continue to claim to be the legitimate government of all China, though the latter has more recognition in the world and controls more territory. China had the largest economy in the world for much of the last two years, during which it has seen cycles of prosperity and decline. Since the introduction of reforms in 1978, China has become one of the worlds fastest-growing major economies. As of 2016, it is the worlds second-largest economy by nominal GDP, China is also the worlds largest exporter and second-largest importer of goods. China is a nuclear weapons state and has the worlds largest standing army. The PRC is a member of the United Nations, as it replaced the ROC as a permanent member of the U. N. Security Council in 1971. China is also a member of numerous formal and informal multilateral organizations, including the WTO, APEC, BRICS, the Shanghai Cooperation Organization, the BCIM, the English name China is first attested in Richard Edens 1555 translation of the 1516 journal of the Portuguese explorer Duarte Barbosa. The demonym, that is, the name for the people, Portuguese China is thought to derive from Persian Chīn, and perhaps ultimately from Sanskrit Cīna. Cīna was first used in early Hindu scripture, including the Mahābhārata, there are, however, other suggestions for the derivation of China. The official name of the state is the Peoples Republic of China. The shorter form is China Zhōngguó, from zhōng and guó and it was then applied to the area around Luoyi during the Eastern Zhou and then to Chinas Central Plain before being used as an occasional synonym for the state under the Qing

10.
Algebra
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Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols, as such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine, abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are unknown or allowed to take on many values. For example, in x +2 =5 the letter x is unknown, in E = mc2, the letters E and m are variables, and the letter c is a constant, the speed of light in a vacuum. Algebra gives methods for solving equations and expressing formulas that are easier than the older method of writing everything out in words. The word algebra is used in certain specialized ways. A special kind of object in abstract algebra is called an algebra. A mathematician who does research in algebra is called an algebraist, the word algebra comes from the Arabic الجبر from the title of the book Ilm al-jabr wal-muḳābala by Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the century, from either Spanish, Italian. It originally referred to the procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century, the word algebra has several related meanings in mathematics, as a single word or with qualifiers. As a single word without an article, algebra names a broad part of mathematics, as a single word with an article or in plural, an algebra or algebras denotes a specific mathematical structure, whose precise definition depends on the author. Usually the structure has an addition, multiplication, and a scalar multiplication, when some authors use the term algebra, they make a subset of the following additional assumptions, associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word refers to a generalization of the above concept. With a qualifier, there is the distinction, Without an article, it means a part of algebra, such as linear algebra, elementary algebra. With an article, it means an instance of some abstract structure, like a Lie algebra, sometimes both meanings exist for the same qualifier, as in the sentence, Commutative algebra is the study of commutative rings, which are commutative algebras over the integers

11.
Japan
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Japan is a sovereign island nation in Eastern Asia. Located in the Pacific Ocean, it lies off the eastern coast of the Asia Mainland and stretches from the Sea of Okhotsk in the north to the East China Sea, the kanji that make up Japans name mean sun origin. 日 can be read as ni and means sun while 本 can be read as hon, or pon, Japan is often referred to by the famous epithet Land of the Rising Sun in reference to its Japanese name. Japan is an archipelago consisting of about 6,852 islands. The four largest are Honshu, Hokkaido, Kyushu and Shikoku, the country is divided into 47 prefectures in eight regions. Hokkaido being the northernmost prefecture and Okinawa being the southernmost one, the population of 127 million is the worlds tenth largest. Japanese people make up 98. 5% of Japans total population, approximately 9.1 million people live in the city of Tokyo, the capital of Japan. Archaeological research indicates that Japan was inhabited as early as the Upper Paleolithic period, the first written mention of Japan is in Chinese history texts from the 1st century AD. Influence from other regions, mainly China, followed by periods of isolation, from the 12th century until 1868, Japan was ruled by successive feudal military shoguns who ruled in the name of the Emperor. Japan entered into a period of isolation in the early 17th century. The Second Sino-Japanese War of 1937 expanded into part of World War II in 1941, which came to an end in 1945 following the bombings of Hiroshima and Nagasaki. Japan is a member of the UN, the OECD, the G7, the G8, the country has the worlds third-largest economy by nominal GDP and the worlds fourth-largest economy by purchasing power parity. It is also the worlds fourth-largest exporter and fourth-largest importer, although Japan has officially renounced its right to declare war, it maintains a modern military with the worlds eighth-largest military budget, used for self-defense and peacekeeping roles. Japan is a country with a very high standard of living. Its population enjoys the highest life expectancy and the third lowest infant mortality rate in the world, in ancient China, Japan was called Wo 倭. It was mentioned in the third century Chinese historical text Records of the Three Kingdoms in the section for the Wei kingdom, Wa became disliked because it has the connotation of the character 矮, meaning dwarf. The 倭 kanji has been replaced with the homophone Wa, meaning harmony, the Japanese word for Japan is 日本, which is pronounced Nippon or Nihon and literally means the origin of the sun. The earliest record of the name Nihon appears in the Chinese historical records of the Tang dynasty, at the start of the seventh century, a delegation from Japan introduced their country as Nihon

12.
Grenoble
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Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Auvergne-Rhône-Alpes region, Grenoble is the capital of the department of Isère, the city advertises itself as the Capital of the Alps, due to its size and its proximity to the mountains. Grenobles history goes back more than 2,000 years, to a time when it was a small Gallic village, industrial development increased the prominence of Grenoble, through several periods of economic expansion over the last three centuries. The city has grown to be one of Europes most important research, technology, the population of the city of Grenoble was 160,215 at the 2013 census, while the population of the Grenoble metropolitan area was 664,832. The residents of the city are called Grenoblois, the many communes that make up the metropolitan area include three suburbs with populations exceeding 20,000, Saint-Martin-dHères, Échirolles, and Fontaine. For the ecclesiastical history, see Bishopric of Grenoble, the first references to Grenoble date back to 43 BC. Cularo was at time a little Gallic village founded by the Allobroges tribe near a bridge across the Isère River. Three centuries later and with insecurity rising in the late Roman empire, the Emperor Gratian visited Cularo and, touched by the peoples welcome, made the village a Roman city. In honour of this, Cularo was renamed Gratianopolis in 381, Christianity spread to the region during the 4th century, and the diocese of Grenoble was founded in 377 AD. From that time on, the bishops exercised significant political power over the city, until the French Revolution, they styled themselves the bishops and princes of Grenoble. Arletian rule was interrupted between 942 and 970 due to Arabic rule based in Fraxinet, Grenoble grew significantly in the 11th century when the Counts of Albon chose the city as the capital of their territories. At the time, their possessions were a patchwork of several territories sprawled across the region, the central position of Grenoble allowed the Counts to strengthen their authority. When they later took the title of Dauphins, Grenoble became the capital of the State of Dauphiné, despite their status, the Counts had to share authority over the city with the Bishop of Grenoble. One of the most famous of those was Saint Hugh, under his rule, the citys bridge was rebuilt, and both a regular hospital and a leper one were built. The inhabitants of Grenoble took advantage of the conflicts between the Counts and the bishops and obtained the recognition of a Charter of Customs that guaranteed their rights and that charter was confirmed by Kings Louis XI in 1447 and Francis I in 1541. In 1336 the last Dauphin Humbert II founded a court of justice, the Conseil delphinal and he also established the University of Grenoble in 1339. Aging and heirless, Humbert sold his state to France in 1349, the first one, the future Charles V, spent nine months in Grenoble. The city remained the capital of the Dauphiné, henceforth a province of France, the only Dauphin who really governed his province was Louis XI, whose reign lasted from 1447 to 1456

13.
Jacques Rohault
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Jacques Rohault was a French philosopher, physicist and mathematician, and a follower of Cartesianism. Rohault was born in Amiens, the son of a wine merchant. Having grown up with the scholastic philosophy of his day. His Wednesday lectures in Paris became celebrated, they began in the 1650s, Rohault died on December 27,1672 in Paris. Rohault held to the philosophy, and gave qualified support to its corpuscular or atomic form of explanation. His Traité de physique became a textbook for half a century. It followed the precedent set by Henricus Regius in separating physics from metaphysics and it also included the theory of gravitation of Christiaan Huygens, given in terms of an experiment. The translation of Samuel Clarke gained an independent status, and numerous editions, rohaults experimental orientation remained popular, despite the criticisms of his theories. The Traité referred to a model of the eye that Rohault had worked on

14.
Mechanical explanations of gravitation
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These theories were developed from the 16th until the 19th century in connection with the aether. Modern quantum gravity hypotheses also attempt to describe gravity by more fundamental processes such as particle fields, the theory posits that the force of gravity is the result of tiny particles or waves moving at high speed in all directions, throughout the universe. Likewise, B will be struck by particles from the direction of A than from the opposite direction. One can say that A and B are shadowing each other, the result is, that the shadow of each body is proportional to the surface of every single element of matter. Also drag, i. e. the resistance of the streams in the direction of motion, is a great problem too. This problem can be solved by assuming superluminal speeds, but this largely increases the thermal problems. Because of his beliefs, René Descartes proposed in 1644 that no empty space can exist. Descartes also distinguishes between different forms and sizes of matter in which rough matter resists the movement more strongly than fine matter. Due to centrifugal force, matter tends towards the edges of the vortex. The rough matter cannot follow this movement due to its greater inertia—so due to the pressure of the outer matter those parts will be pushed into the center of the vortex. According to Descartes, this pressure is nothing else than gravity. He compared this mechanism with the fact if a rotating, liquid filled vessel is stopped. Now, if one drops small pieces of matter into the vessel. Following the basic premises of Descartes, Christiaan Huygens between 1669 and 1690 designed a more exact vortex model. This model was the first theory of gravitation which was worked out mathematically, so also in his model the fine matter presses the rough matter into the center of the vortex. Huygens also found out that the force is equal to the force. He also posited that bodies must consist mostly of empty space so that the aether can penetrate the bodies easily and he further concluded that the aether moves much faster than the falling bodies. Newtons discovery that gravity obeys the inverse square law surprised Huygens, criticism, Newton objected to the theory because drag must lead to noticeable deviations of the orbits which were not observed

15.
Luigi Guido Grandi
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Cam. was an Italian monk, priest, philosopher, theologian, mathematician, and engineer. Grandi was born on Oct.1,1671 in Cremona, Italy, when he was of age, he was educated at the Jesuit college there. After he completed his studies there in 1687, he entered the novitiate of the Camaldolese monks at Ferrara and took the name of Guido. In 1693 he was sent to the Monastery of St. Gregory the Great, a year later, Grandi was assigned as professor of both fields at the Camaldolese Monastery of St. Mary of the Angels in Florence. It appears that it was during this period of his life that he took an interest in mathematics. He did his research privately, however, as he was appointed professor of philosophy at St. Gregory Monastery in 1700, subsequently holding a post in the same field in Pisa. By 1707, however, Dom Grandi had developed such a reputation in the field of mathematics that he was named court mathematician to the Grand Duke of Tuscany, the University of Pisa named him Professor of Mathematics in 1714. It was there that he died on 4 July 1742, in 1701 Grandi published a study of the conical loxodrome, followed by a study in 1703 of the curve which he named versiera, from the Latin, vertere. This curve was studied by one of the few women scientists to achieve a degree. Through a mistranslation by the translator of her work into English who mistook the term witch for Grandis term and it was through his studies on this curve that Grandi helped introduce Leibniz ideas on calculus to Italy. In mathematics Grandi is best known for his work Flores geometrici, studying the rose curve, a curve which has the shape of a petalled flower and he named the rose curve rhodonea. He also contributed to the Note on the Treatise of Galileo Concerning Natural Motion in the first Florentine edition of Galileo Galileis works, oConnor, John J. Robertson, Edmund F. Luigi Guido Grandi, MacTutor History of Mathematics archive, University of St Andrews

16.
Italians
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Italians are a nation and ethnic group native to Italy who share a common culture, ancestry and speak the Italian language as a native tongue. The majority of Italian nationals are speakers of Standard Italian. Italians have greatly influenced and contributed to the arts and music, science, technology, cuisine, sports, fashion, jurisprudence, banking, Italian people are generally known for their localism and their attention to clothing and family values. The term Italian is at least 3,000 years old and has a history that goes back to pre-Roman Italy. According to one of the common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú. The bull was a symbol of the southern Italic tribes and was often depicted goring the Roman wolf as a defiant symbol of free Italy during the Social War. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. The Etruscan civilization reached its peak about the 7th century BC, but by 509 BC, when the Romans overthrew their Etruscan monarchs, its control in Italy was on the wane. By 350 BC, after a series of wars between Greeks and Etruscans, the Latins, with Rome as their capital, gained the ascendancy by 272 BC, and they managed to unite the entire Italian peninsula. This period of unification was followed by one of conquest in the Mediterranean, in the course of the century-long struggle against Carthage, the Romans conquered Sicily, Sardinia and Corsica. Finally, in 146 BC, at the conclusion of the Third Punic War, with Carthage completely destroyed and its inhabitants enslaved, octavian, the final victor, was accorded the title of Augustus by the Senate and thereby became the first Roman emperor. After two centuries of rule, in the 3rd century AD, Rome was threatened by internal discord and menaced by Germanic and Asian invaders. Emperor Diocletians administrative division of the empire into two parts in 285 provided only temporary relief, it became permanent in 395, in 313, Emperor Constantine accepted Christianity, and churches thereafter rose throughout the empire. However, he moved his capital from Rome to Constantinople. The last Western emperor, Romulus Augustulus, was deposed in 476 by a Germanic foederati general in Italy and his defeat marked the end of the western part of the Roman Empire. During most of the period from the fall of Rome until the Kingdom of Italy was established in 1861, Odoacer ruled well for 13 years after gaining control of Italy in 476. Then he was attacked and defeated by Theodoric, the king of another Germanic tribe, Theodoric and Odoacer ruled jointly until 493, when Theodoric murdered Odoacer. Theodoric continued to rule Italy with an army of Ostrogoths and a government that was mostly Italian, after the death of Theodoric in 526, the kingdom began to grow weak

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Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems

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Giovanni Battista Riccioli
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Giovanni Battista Riccioli was an Italian astronomer and a Catholic priest in the Jesuit order. Riccioli was born in Ferrara, Italy and he entered the Society of Jesus on 6 October 1614. After completing his novitiate, he study of the humanities in 1616, pursuing those studies first at Ferrara. From 1620 to 1628 he studied philosophy and theology at the College of Parma, Parma Jesuits had developed a strong program of experimentation, such as with falling bodies. One of the most famous Italian Jesuits of the time, Giuseppe Biancani, was teaching at Parma when Riccioli arrived there, Riccioli mentions him with gratitude and admiration. By 1628 Ricciolis studies were complete and he requested missionary work, but that request was turned down. Instead he was assigned to teach at Parma, there he taught logic, physics, and metaphysics from 1629 to 1632, and engaged in some experiments with falling bodies and pendulums. In 1632 he became a member of a group charged with the formation of younger Jesuits and he spent the 1633-1634 academic year in Mantua, where he collaborated with Niccolo Cabeo in further pendulum studies. In 1635 he was back at Parma, where he taught theology, in 1636 he was sent to Bologna to serve as Professor of theology. Riccioli described himself as a theologian, but one with a strong and ongoing interest in astronomy since his student days and he said that many Jesuits were theologians, but few were astronomers. He said that once the enthusiasm for astronomy arose within him he could never extinguish it, eventually his superiors in the Jesuit order officially assigned him to the task of astronomical research. However, he continued to write on theology. Riccioli dealt not only with astronomy in his research, but also with physics, arithmetic, geometry, optics, gnomonics, geography and he was awarded a prize by Louis XIV in recognition of his activities and their relevance to contemporary culture. Riccioli continued to publish on both astronomy and theology up to his death and he died in Bologna at 73 years of age. One of Ricciolis most significant works was his 1651 Almagestum Novum, a work consisting of over 1500 folio pages densely packed with text, tables. Riccioli envisioned that the New Almagest would have three volumes, but only the first was completed, Riccioli is credited with being the first person to precisely measure the acceleration due to gravity of falling bodies. Books 2 and 9 of the New Almagest Riccioli included a significant discussion of and extensive experimental reports on the motions of falling bodies and he was interested in the pendulum as a device for precisely measuring time. He also reported that a pendulums period increases if the amplitude of its swing is increased to 40 degrees and he sought to develop a pendulum whose period was precisely one second – such a pendulum would complete 86,400 swings in a 24-hour period

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Astronomer
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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as other celestial objects — either in observational astronomy. Examples of topics or fields astronomers work on include, planetary science, solar astronomy, there are also related but distinct subjects like physical cosmology which studies the Universe as a whole. Astronomers usually fit into two types, Observational astronomers make direct observations of planets, stars and galaxies, and analyze the data, theoretical astronomers create and investigate models of things that cannot be observed. They use this data to create models or simulations to theorize how different celestial bodies work, there are further subcategories inside these two main branches of astronomy such as planetary astronomy, galactic astronomy or physical cosmology. Today, that distinction has disappeared and the terms astronomer. Professional astronomers are highly educated individuals who typically have a Ph. D. in physics or astronomy and are employed by research institutions or universities. They spend the majority of their time working on research, although quite often have other duties such as teaching, building instruments. The number of astronomers in the United States is actually quite small. The American Astronomical Society, which is the organization of professional astronomers in North America, has approximately 7,000 members. This number includes scientists from other such as physics, geology. The International Astronomical Union comprises almost 10,145 members from 70 different countries who are involved in research at the Ph. D. level. Before CCDs, photographic plates were a method of observation. Modern astronomers spend relatively little time at telescopes usually just a few weeks per year, analysis of observed phenomena, along with making predictions as to the causes of what they observe, takes the majority of observational astronomers time. Astronomers who serve as faculty spend much of their time teaching undergraduate and graduate classes, most universities also have outreach programs including public telescope time and sometimes planetariums as a public service to encourage interest in the field. Those who become astronomers usually have a background in maths, sciences. Taking courses that teach how to research, write and present papers are also invaluable, in college/university most astronomers get a Ph. D. in astronomy or physics. Keeping in mind how few there are it is understood that graduate schools in this field are very competitive