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Bernoulli Family
The Bernoulli family () of Basel was a patrician family, notable for having produced eight mathematically gifted academics who, among them, contributed substantially to the development of mathematics and physics during the early modern period. History Originally from Antwerp, a branch of the family relocated to Basel in 1620. While their origin in Antwerp is certain, proposed earlier connections with the Dutch family ''Bornouilla'' (''Bernoullie''), or with the Castilian family ''de Bernuy'' (''Bernoille'', ''Bernouille''), are uncertain. The first known member of the family was Leon Bernoulli (d. 1561), a doctor in Antwerp, at that time part of the Spanish Netherlands. His son, Jacob, emigrated to Frankfurt am Main in 1570 to escape from the Spanish persecution of the Protestants. Jacob's grandson, a spice trader, also named Jacob, moved to Basel, Switzerland in 1620, and was granted citizenship in 1622. His son, (Nicolaus, 1623–1708), Leon's great-great-grandson, marr ...
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Basel
, french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS), Saint-Louis (FR-68), Weil am Rhein (DE-BW) , twintowns = Shanghai, Miami Beach , website = www.bs.ch Basel ( , ), also known as Basle ( ),french: Bâle ; it, Basilea ; rm, label= Sutsilvan, Basileia; other rm, Basilea . is a city in northwestern Switzerland on the river Rhine. Basel is Switzerland's third-most-populous city (after Zürich and Geneva) with about 175,000 inhabitants. The official language of Basel is (the Swiss variety of Standard) German, but the main spoken language is the local Basel German dialect. Basel is commonly considered to be the cultural capital of Switzerland and the city is famous for its many museums, including the Kunstmuseum, which is the first collection of art accessible ...
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Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of phys ...
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Differential Equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ...
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Infinitesimal Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing. Today, calculus has widespread uses i ...
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Alderman
An alderman is a member of a municipal assembly or council in many jurisdictions founded upon English law. The term may be titular, denoting a high-ranking member of a borough or county council, a council member chosen by the elected members themselves rather than by popular vote, or a council member elected by voters. Etymology The title is derived from the Old English title of '' ealdorman'', literally meaning "elder man", and was used by the chief nobles presiding over shires. Similar titles exist in some Germanic countries, such as the Swedish language ', the Danish, Low German language ', and West Frisian language ', the Dutch language ', the (non-Germanic) Finnish language ' (a borrowing from the Germanic Swedes next door), and the High German ', which all mean "elder man" or "wise man". Usage by country Australia Many local government bodies used the term "alderman" in Australia. As in the way local councils have been modernised in the United Kingdom and Ireland ...
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Ars Conjectandi
(Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre. Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Bla ...
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Bernoulli Numbers
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of ''m''-th powers of the first ''n'' positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function. The values of the first 20 Bernoulli numbers are given in the adjacent table. Two conventions are used in the literature, denoted here by B^_n and B^_n; they differ only for , where B^_1=-1/2 and B^_1=+1/2. For every odd , . For every even , is negative if is divisible by 4 and positive otherwise. The Bernoulli numbers are special values of the Bernoulli polynomials B_n(x), with B^_n=B_n(0) and B^+_n=B_n(1). The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and inde ...
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Protestant
Protestantism is a Christian denomination, branch of Christianity that follows the theological tenets of the Reformation, Protestant Reformation, a movement that began seeking to reform the Catholic Church from within in the 16th century against what its followers perceived to be growing Criticism of the Catholic Church, errors, abuses, and discrepancies within it. Protestantism emphasizes the Christian believer's justification by God in faith alone (') rather than by a combination of faith with good works as in Catholicism; the teaching that Salvation in Christianity, salvation comes by Grace in Christianity, divine grace or "unmerited favor" only ('); the Universal priesthood, priesthood of all faithful believers in the Church; and the ''sola scriptura'' ("scripture alone") that posits the Bible as the sole infallible source of authority for Christian faith and practice. Most Protestants, with the exception of Anglo-Papalism, reject the Catholic doctrine of papal supremacy, ...
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Frankfurt Am Main
Frankfurt, officially Frankfurt am Main (; Hessian: , " Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its namesake Main River, it forms a continuous conurbation with the neighboring city of Offenbach am Main and its urban area has a population of over 2.3 million. The city is the heart of the larger Rhine-Main metropolitan region, which has a population of more than 5.6 million and is Germany's second-largest metropolitan region after the Rhine-Ruhr region. Frankfurt's central business district, the Bankenviertel, lies about northwest of the geographic center of the EU at Gadheim, Lower Franconia. Like France and Franconia, the city is named after the Franks. Frankfurt is the largest city in the Rhine Franconian dialect area. Frankfurt was a city state, the Free City of Frankfurt, for nearly five centuries, and was one of the ...
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Spanish Netherlands
Spanish Netherlands ( Spanish: Países Bajos Españoles; Dutch: Spaanse Nederlanden; French: Pays-Bas espagnols; German: Spanische Niederlande.) (historically in Spanish: ''Flandes'', the name "Flanders" was used as a '' pars pro toto'') was the Habsburg Netherlands ruled by the Spanish branch of the Habsburgs from 1556 to 1714. They were a collection of States of the Holy Roman Empire in the Low Countries held in personal union by the Spanish Crown (also called Habsburg Spain). This region comprised most of the modern states of Belgium and Luxembourg, as well as parts of northern France, the southern Netherlands, and western Germany with the capital being Brussels. The Army of Flanders was given the task of defending the territory. The Imperial fiefs of the former Burgundian Netherlands had been inherited by the Austrian House of Habsburg from the extinct House of Valois-Burgundy upon the death of Mary of Burgundy in 1482. The Seventeen Provinces formed the core of the ...
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Early Modern Switzerland
The early modern history of the Old Swiss Confederacy ('' Eidgenossenschaft'', also known as the "Swiss Republic" or ''Republica Helvetiorum'') and its constituent Thirteen Cantons encompasses the time of the Thirty Years' War (1618–1648) until the French invasion of 1798. The early modern period was characterized by an increasingly aristocratic and oligarchic ruling class as well as frequent economic or religious revolts. This period came to be referred to as the ''Ancien Régime'' retrospectively, in post-Napoleonic Switzerland. The loosely organized Confederation remained generally disorganized and crippled by the religious divisions created by the Swiss Reformation. During this period the Confederation gained formal independence from the Holy Roman Empire with support from France, and had very close relations with France. The early modern period also saw the growth of French-Swiss literature, and notable authors of the Age of Enlightenment such as the mathemat ...
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Patrician (post-Roman Europe)
Patricianship, the quality of belonging to a patriciate, began in the ancient world, where cities such as Ancient Rome had a social class of patrician families, whose members were initially the only people allowed to exercise many political functions. In the rise of European towns in the 12th and 13th century, the patriciate, a limited group of families with a special constitutional position, in Henri Pirenne's view, was the motive force. In 19th century Central Europe, the term had become synonymous with the upper Bourgeoisie and cannot be interchanged with the medieval patriciate in Central Europe. In German-speaking parts of Europe as well as in the maritime republics of the Italian Peninsula, the patricians were as a matter of fact the ruling body of the medieval town. Particularly in Italy, they were part of the nobility. With the establishment of the medieval towns, Italian city-states and maritime republics, the patriciate was a formally-defined social class of go ...
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