1.
Clermont-Ferrand
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Clermont-Ferrand is a city and commune of France, in the Auvergne-Rhône-Alpes region, with a population of 141,569. Its metropolitan area had 467,178 inhabitants at the 2011 census and it is the prefecture of the Puy-de-Dôme department. Olivier Bianchi is its current mayor, Clermont-Ferrand sits on the plain of Limagne in the Massif Central and is surrounded by a major industrial area. The city is famous for the chain of volcanoes, the Chaîne des Puys surrounding it, the famous dormant volcano Puy de Dôme is one of the highest of these and well known for the telecommunication antennas that sit on its top and are visible from far away. Clermont-Ferrands most famous square is Place de Jaude, on which stands a grand statue of Vercingetorix sitting imperiously on a horse. The inscription reads, Jai pris les armes pour la liberté de tous and this statue was sculpted by Frédéric Bartholdi, who also created the Statue of Liberty. Clermont-Ferrands first name was Augusta Nemetum and it was born on the central knoll where the cathedral is situated today, known then as Nemossos. It overlooked the capital of Gaulish Avernie, the fortified castle of Clarus Mons gave its name to the whole town in 848, to which the small episcopal town of Montferrand was attached in 1731, together taking the name of Clermont-Ferrand. The old part of Clermont is delimited by the route of the ramparts, the town of Clermont-Ferrand came about with the joining together of two separate towns, Clermont and Montferrand, which was decreed by Louis XIII and confirmed by Louis XV. Clermont ranks among the oldest cities of France, the first known mention was by the Greek geographer Strabo, who called it the metropolis of the Arverni. The city was at that time called Nemessos – a Gaulish word for a sacred forest and it was somewhere in the area around Nemossos that the Arverni chieftain Vercingetorix was born in around 72 BC. Also, Nemossos was situated not far from the plateau of Gergovia, after the Roman conquest, the city became known as Augustonemetum sometime in the 1st century, a name which combined its original Gallic name with that of the Emperor Augustus. Its population was estimated at 15, 000–30,000 in the 2nd century and it then became Arvernis in the 3rd century, and expanded until the mid 3rd century. The city became the seat of a bishop in the 5th century, at the time of the bishop Namatius or Saint Namace, who built a cathedral here described by Gregory of Tours. Clermont went through a period after the disappearance of the Roman Empire and during the whole High Middle Ages. Between 471 and 475, Auvergne was often the target of Visigothic expansion, a generation later, it became part of the Kingdom of the Franks. On 8 November 535 the first Council of Clermont opened at Arvernis, with fifteen bishops participating, including Caesarius of Arles, Nizier of Lyons and Saint Hilarius, bishop of Mende. Sixteen decrees were made there, notably the second canon that recalls that the granting of episcopal dignity must be according to the merits, in 570, Bishop Avitus offered the Jews of his town the alternatives of baptism or expulsion
2.
Auvergne
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Auvergne is a former administrative region of France. Since 1 January 2016, it is part of the new region Auvergne-Rhône-Alpes and it comprises four departments, Allier, Puy-de-Dôme, Cantal and Haute-Loire. The administrative region of Auvergne is larger than the province of Auvergne. The Auvergne region is composed of the old provinces, Auvergne, departments of Puy-de-Dôme, Cantal, northwest of Haute-Loire. The province of Auvergne is entirely contained inside the Auvergne region Bourbonnais, a small part of Bourbonnais is also contained inside the Centre-Val de Loire region. Velay, centre and southeast of department of Haute-Loire, velay is entirely contained inside the Auvergne region. A small part of Gévaudan, extreme southwest of Haute-Loire, Gévaudan is essentially inside the Languedoc-Roussillon region. A small part of Vivarais, extreme southeast of Haute-Loire, Vivarais is essentially inside the Rhône-Alpes region. A small part of Forez, extreme northeast of Haute-Loire, Forez is essentially inside the Rhône-Alpes region. Velay, Gévaudan, and Vivarais are often considered to be sub-provinces of the old province of Languedoc, Forez is also often considered to be a sub-province of Lyonnais. Therefore, the region of Auvergne is composed of the provinces of Auvergne, major part of Bourbonnais. The region is home to a chain of volcanoes known collectively as the chaîne des Puys, the last confirmed eruption was around 4040 BCE. The volcanoes began forming some 70,000 years ago, and most have eroded, Auvergne has a surface area of 26,013 square kilometres equivalent to 4. 8% of Frances total surface area. Auvergne is one of the smallest regions in France, Auvergne is known for its mountain ranges and dormant volcanoes. Together the Monts Dore and the Chaîne des Puys include 80 volcanoes, the Puy de Dôme is the tallest volcano in the region, with an altitude of 1,465 metres. The Sancy Massif in the Monts Dore is the highest point in Auvergne, the northern region is covered in hills while the southern portion is mountainous and dotted with pastures. The Forest of Tronçais covers nearly 11,000 hectares and is the largest oak forest in Europe, the Loire runs through the southeast and borders the northeast, and the Allier runs from north to south down the center of Auvergne, with branches going east and west. Over many years the Allier river has created what are known as the Allier gorges, Auvergne has about 50 freshwater ponds and lakes
3.
Kingdom of France
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The Kingdom of France was a medieval and early modern monarchy in Western Europe. It was one of the most powerful states in Europe and a great power since the Late Middle Ages and it was also an early colonial power, with possessions around the world. France originated as West Francia, the half of the Carolingian Empire. A branch of the Carolingian dynasty continued to rule until 987, the territory remained known as Francia and its ruler as rex Francorum well into the High Middle Ages. The first king calling himself Roi de France was Philip II, France continued to be ruled by the Capetians and their cadet lines—the Valois and Bourbon—until the monarchy was overthrown in 1792 during the French Revolution. France in the Middle Ages was a de-centralised, feudal monarchy, in Brittany and Catalonia the authority of the French king was barely felt. Lorraine and Provence were states of the Holy Roman Empire and not yet a part of France, during the Late Middle Ages, the Kings of England laid claim to the French throne, resulting in a series of conflicts known as the Hundred Years War. Subsequently, France sought to extend its influence into Italy, but was defeated by Spain in the ensuing Italian Wars, religiously France became divided between the Catholic majority and a Protestant minority, the Huguenots, which led to a series of civil wars, the Wars of Religion. France laid claim to large stretches of North America, known collectively as New France, Wars with Great Britain led to the loss of much of this territory by 1763. French intervention in the American Revolutionary War helped secure the independence of the new United States of America, the Kingdom of France adopted a written constitution in 1791, but the Kingdom was abolished a year later and replaced with the First French Republic. The monarchy was restored by the great powers in 1814. During the later years of the elderly Charlemagnes rule, the Vikings made advances along the northern and western perimeters of the Kingdom of the Franks, after Charlemagnes death in 814 his heirs were incapable of maintaining political unity and the empire began to crumble. The Treaty of Verdun of 843 divided the Carolingian Empire into three parts, with Charles the Bald ruling over West Francia, the nucleus of what would develop into the kingdom of France. Viking advances were allowed to increase, and their dreaded longboats were sailing up the Loire and Seine rivers and other waterways, wreaking havoc. During the reign of Charles the Simple, Normans under Rollo from Norway, were settled in an area on either side of the River Seine, downstream from Paris, that was to become Normandy. With its offshoots, the houses of Valois and Bourbon, it was to rule France for more than 800 years. Henry II inherited the Duchy of Normandy and the County of Anjou, and married Frances newly divorced ex-queen, Eleanor of Aquitaine, after the French victory at the Battle of Bouvines in 1214, the English monarchs maintained power only in southwestern Duchy of Guyenne. The death of Charles IV of France in 1328 without male heirs ended the main Capetian line, under Salic law the crown could not pass through a woman, so the throne passed to Philip VI, son of Charles of Valois
4.
Paris
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Paris is the capital and most populous city of France. It has an area of 105 square kilometres and a population of 2,229,621 in 2013 within its administrative limits, the agglomeration has grown well beyond the citys administrative limits. By the 17th century, Paris was one of Europes major centres of finance, commerce, fashion, science, and the arts, and it retains that position still today. The aire urbaine de Paris, a measure of area, spans most of the Île-de-France region and has a population of 12,405,426. It is therefore the second largest metropolitan area in the European Union after London, the Metropole of Grand Paris was created in 2016, combining the commune and its nearest suburbs into a single area for economic and environmental co-operation. Grand Paris covers 814 square kilometres and has a population of 7 million persons, the Paris Region had a GDP of €624 billion in 2012, accounting for 30.0 percent of the GDP of France and ranking it as one of the wealthiest regions in Europe. The city is also a rail, highway, and air-transport hub served by two international airports, Paris-Charles de Gaulle and Paris-Orly. Opened in 1900, the subway system, the Paris Métro. It is the second busiest metro system in Europe after Moscow Metro, notably, Paris Gare du Nord is the busiest railway station in the world outside of Japan, with 262 millions passengers in 2015. In 2015, Paris received 22.2 million visitors, making it one of the top tourist destinations. The association football club Paris Saint-Germain and the rugby union club Stade Français are based in Paris, the 80, 000-seat Stade de France, built for the 1998 FIFA World Cup, is located just north of Paris in the neighbouring commune of Saint-Denis. Paris hosts the annual French Open Grand Slam tennis tournament on the red clay of Roland Garros, Paris hosted the 1900 and 1924 Summer Olympics and is bidding to host the 2024 Summer Olympics. The name Paris is derived from its inhabitants, the Celtic Parisii tribe. Thus, though written the same, the name is not related to the Paris of Greek mythology. In the 1860s, the boulevards and streets of Paris were illuminated by 56,000 gas lamps, since the late 19th century, Paris has also been known as Panam in French slang. Inhabitants are known in English as Parisians and in French as Parisiens and they are also pejoratively called Parigots. The Parisii, a sub-tribe of the Celtic Senones, inhabited the Paris area from around the middle of the 3rd century BC. One of the areas major north-south trade routes crossed the Seine on the île de la Cité, this place of land and water trade routes gradually became a town
5.
French people
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The French are an ethnic group and nation who are identified with the country of France. This connection may be legal, historical, or cultural, modern French society can be considered a melting pot. To be French, according to the first article of the French Constitution, is to be a citizen of France, regardless of origin, race. The debate concerning the integration of this view with the underlying the European Community remains open. A large number of foreigners have traditionally been permitted to live in France, indeed, the country has long valued its openness, tolerance and the quality of services available. Application for French citizenship is often interpreted as a renunciation of previous state allegiance unless a dual citizenship agreement exists between the two countries, the European treaties have formally permitted movement and European citizens enjoy formal rights to employment in the state sector. Seeing itself as a nation with universal values, France has always valued. However, the success of such assimilation has recently called into question. There is increasing dissatisfaction with, and within, growing ethno-cultural enclaves, the 2005 French riots in some troubled and impoverished suburbs were an example of such tensions. However they should not be interpreted as ethnic conflicts but as social conflicts born out of socioeconomic problems endangering proper integration, the name France etymologically derives from the word Francia, the territory of the Franks. The Franks were a Germanic tribe that overran Roman Gaul at the end of the Roman Empire, in the pre-Roman era, all of Gaul was inhabited by a variety of peoples who were known collectively as the Gaulish tribes. Gaul was militarily conquered in 58-51 BCE by the Roman legions under the command of General Julius Caesar, the area then became part of the Roman Empire. Over the next five centuries the two cultures intermingled, creating a hybridized Gallo-Roman culture, the Gaulish vernacular language disappeared step by step to be replaced everywhere by Vulgar Latin, which would later develop under Frankish influence into the French language in the North of France. With the decline of the Roman Empire in Western Europe, a federation of Germanic peoples entered the picture, the Franks were Germanic pagans who began to settle in northern Gaul as laeti, already during the Roman era. They continued to filter across the Rhine River from present-day Netherlands, at the beginning, they served in the Roman army and reached high commands. Their language is spoken as a kind of Dutch in northern France. Another Germanic people immigrated massively to Alsace, the Alamans, which explains the Alemannic German spoken there and they were competitors of the Franks, thats why it became at the Renaissance time the word for German in French, Allemand. By the early 6th century the Franks, led by the Merovingian king Clovis I and his sons, had consolidated their hold on much of modern-day France, the Vikings eventually intermarried with the local people, converting to Christianity in the process
6.
17th-century philosophy
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17th-century philosophy in the Western world is generally regarded as being the start of modern philosophy, and a departure from the medieval approach, especially Scholasticism. Early 17th-century philosophy is called the Age of Reason or Age of Rationalism and is considered to succeed the Renaissance philosophy era. In the West, 17th-century philosophy is taken to start with the work of René Descartes. The three main rationalists are normally taken to have been René Descartes, Baruch Spinoza, and Gottfried Leibniz, building upon their English predecessor Francis Bacon, the two main empiricists of the 17th-century were Thomas Hobbes and John Locke. Thus the rationalists took mathematics as their model for knowledge, and this emphasis on epistemology is at the root of Kants distinction, looking at the various philosophers in terms of their metaphysical, moral, or linguistic theories, they divide up very differently. This period also saw the birth of some of the classics of political thought, especially Thomas Hobbes Leviathan, and John Lockes Two Treatises of Government
7.
Western philosophy
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Western philosophy is the philosophical thought and work of the Western world. The word philosophy itself originated from the Hellenic, philosophia, literally, the scope of philosophy in the ancient understanding, and the writings of the ancient philosophers, were all intellectual endeavors. Western Philosophy is generally said to begin in the Greek cities of western Asia Minor with Thales of Miletus and his most noted students were respectively Anaximander and Anaximenes of Miletus. Pythagoras, from the island of Samos off the coast of Ionia, pythagoreans hold that all is number, giving formal accounts in contrast to the previous material of the Ionians. They also believe in metempsychosis, the transmigration of souls, or reincarnation, Socrates The key figure in Greek philosophy is Socrates. Socrates studied under several Sophists but transformed Greek philosophy into a unified, Socrates used a critical approach called the elenchus or Socratic method to examine peoples views. He aimed to study human things, the life, justice, beauty. Although Socrates wrote nothing himself, some of his many disciples wrote down his conversations and he was tried for corrupting the youth and impiety by the Greek democracy. He was found guilty and sentenced to death, although his friends offered to help him escape from prison, he chose to remain in Athens and abide by his principles. His execution consisting in drinking the poison hemlock and he died in 399 B. C, Plato Socrates most important student was Plato. Plato founded the Academy of Athens and wrote a number of dialogues, some central ideas of Platos dialogues are the immortality of the soul, the benefits of being just, that evil is ignorance, and the Theory of Forms. Forms are universal properties that constitute reality and contrast with the changeable material things he called becoming. Aristotle Platos most outstanding student was Aristotle, Aristotle was perhaps the first truly systematic philosopher and scientist. He wrote books on physics, biology, zoology, metaphysics, aesthetics, poetry, theater, music, rhetoric, politics, Aristotelian logic was the first type of logic to attempt to categorize every valid syllogism. Aristotelian philosophy exercised considerable influence on almost all western philosophers, including Greek, Roman, Christian, Jewish, the Neoplatonic and Christian philosophers of Late Antiquity. Early medieval philosophy was influenced by the likes of Stoicism, neo-Platonism, but, above all, the prominent figure of this period was St. Augustinianism was the preferred starting point for most philosophers up until the 13th century. The foundations of many northern European universities were built in the Middle Ages by waves of Irish, Scottish & English monks from the Celtic Church begun by Columba, see Celtic Christianity. Erigena is said to have been stabbed to death by his students with their pens and his theology would today be called pantheistic, in keeping with Celtic resolutions of pagan and Christian philosophy
8.
Jansenism
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Jansenism was a Catholic heretical theological movement, primarily in France, that emphasized original sin, human depravity, the necessity of divine grace, and predestination. The movement originated from the published work of the Dutch theologian Cornelius Jansen. It was first popularized by Jansens friend Abbot Jean Duvergier de Hauranne, of Saint-Cyran-en-Brenne Abbey, through the 17th and into the 18th centuries, Jansenism was a distinct movement within the Catholic Church. The theological centre of the movement was the convent of Port-Royal Abbey, Paris, which was a haven for writers including Duvergier, Arnauld, Pierre Nicole, Blaise Pascal, Jansenism was opposed by many in the Catholic hierarchy, especially the Jesuits. Although the Jansenists identified themselves only as rigorous followers of Augustine of Hippos teachings, Jansenist leaders endeavored to accommodate the popes pronouncements while retaining their uniqueness, and enjoyed a measure of peace in the late 17th century under Pope Clement IX. However, further controversy led to the apostolic constitution Unigenitus Dei Filius, promulgated by Pope Clement XI in 1713, the origins of Jansenism lie in the friendship of Jansen and Duvergier, who met in the early 17th century when both were studying theology at the University of Leuven. Duvergier was Jansens patron for a number of years, getting Jansen a job as a tutor in Paris in 1606, two years later, he got Jansen a position teaching at the bishops college in Duvergiers hometown of Bayonne. The duo studied the Church Fathers together, with a focus on the thought of Augustine of Hippo. Duvergier became abbot of Saint Cyran Abbey in Brenne and was known as the Abbé de Saint-Cyran for the rest of his life, Jansen returned to the University of Leuven, where he completed his doctorate in 1619 and was named professor of exegesis. Jansen and Duvergier continued to correspond about Augustine, especially Augustines teachings on grace, upon the recommendation of King Philip IV of Spain, Jansen was consecrated as bishop of Ypres in 1636. Jansen died in a 1638 epidemic and this manuscript, published in 1640 as Augustinus, expounded Augustines system and formed the basis for the subsequent Jansenist Controversy. Jansen emphasized a particular reading of Augustines idea of efficacious grace which stressed that only a portion of humanity were predestined to be saved. Jansen insisted that the love of God was fundamental, and that only perfect contrition, Duvergier was not released until after Richelieus death in 1642, and he died shortly thereafter, in 1643. Jansen also insisted on justification by faith, although he did not contest the necessity of revering saints, of confession, Jansens opponents condemned his teachings for their alleged similarities to Calvinism. Pascal himself claimed that Molinists were correct concerning the state of humanity before the Fall, the heresy of Jansenism, as stated by subsequent Roman Catholic doctrine, lay in denying the role of free will in the acceptance and use of grace. Jansenism asserts that Gods role in the infusion of grace cannot be resisted, Catholic doctrine, in the Catechism of the Catholic Church, is that Gods free initiative demands mans free response—that is, humans freely assent or refuse Gods gift of grace. However, on August 1,1642, the Holy Office issued a decree condemning Augustinus, in 1602, Marie Angélique Arnauld become abbess of Port-Royal-des-Champs, a Cistercian convent in Magny-les-Hameaux. There, she reformed discipline after an experience in 1608
9.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
10.
Pascal's Wager
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Pascals Wager is an argument in apologetic philosophy devised by the seventeenth-century French philosopher, mathematician and physicist Blaise Pascal. It posits that humans bet with their lives that God either exists or does not, Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does actually exist, such a person will have only a loss, whereas they stand to receive infinite gains. Pascals Wager was based on the idea of the Christian God, the original wager was set out in section 233 of Pascals posthumously published Pensées. These previously unpublished notes were assembled to form an incomplete treatise on Christian apologetics, the Wager uses the following logic, God is, or God is not. Reason cannot decide between the two alternatives, where heads or tails will turn up. Let us weigh the gain and the loss in wagering that God is, let us estimate these two chances. If you gain, you all, if you lose. Wager, then, without hesitation that He is, there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force, when there is the finite to stake in a game there are equal risks of gain and of loss. They should then at least learn your inability to believe, and Endeavour then to convince themselves. Pascal asks the reader to analyze humankinds position, where our actions can be enormously consequential, while we can discern a great deal through reason, we are ultimately forced to gamble. On Pascals view, human finitude constrains our ability to achieve truth. Given that reason alone cannot determine whether God exists, Pascal concludes that this question functions like a coin toss, however, even if we do not know the outcome of this coin toss, we must base our actions on some expectation about the outcome. We must decide whether to live as though God exists, or whether to live as though God does not exist, in Pascals assessment, participation in this wager is not optional. Merely by existing in a state of uncertainty, we are forced to choose between the courses of action for practical purposes. The Pensées passage on Pascals Wager is as follows, If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits and we are then incapable of knowing either what He is or if He is. God is, or He is not. But to which side shall we incline, there is an infinite chaos which separated us
11.
Pascal's triangle
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In mathematics, Pascals triangle is a triangular array of the binomial coefficients. In the Western world, it is named after French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, the rows of Pascals triangle are conventionally enumerated starting with row n =0 at the top. The entries in each row are numbered from the beginning with k =0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the manner, In row 0. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the number in the first row is 1. The entry in the nth row and kth column of Pascals triangle is denoted, for example, the unique nonzero entry in the topmost row is =1. With this notation, the construction of the previous paragraph may be written as follows, = +, for any integer n. This recurrence for the coefficients is known as Pascals rule. Pascals triangle has higher dimensional generalizations, the three-dimensional version is called Pascals pyramid or Pascals tetrahedron, while the general versions are called Pascals simplices. The pattern of numbers that forms Pascals triangle was known well before Pascals time, centuries before, discussion of the numbers had arisen in the context of Indian studies of combinatorics and of binomial numbers and Greeks study of figurate numbers. From later commentary, it appears that the coefficients and the additive formula for generating them. Halayudha also explained obscure references to Meru-prastaara, the Staircase of Mount Meru, in approximately 850, the Jain mathematician Mahāvīra gave a different formula for the binomial coefficients, using multiplication, equivalent to the modern formula = n. r. At around the time, it was discussed in Persia by the Persian mathematician. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám, thus the triangle is referred to as the Khayyam triangle in Iran. Several theorems related to the triangle were known, including the binomial theorem, Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients. Pascals triangle was known in China in the early 11th century through the work of the Chinese mathematician Jia Xian, in the 13th century, Yang Hui presented the triangle and hence it is still called Yang Huis triangle in China. In the west, the binomial coefficients were calculated by Gersonides in the early 14th century, petrus Apianus published the full triangle on the frontispiece of his book on business calculations in 1527
12.
Pascal's law
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The law was established by French mathematician Blaise Pascal in 1647–48. The intuitive explanation of this formula is that the change in pressure between 2 elevations is due to the weight of the fluid between the elevations. A more correct interpretation, though, is that the change is caused by the change of potential energy per unit volume of the liquid due to the existence of the gravitational field. Note that the variation with height does not depend on any additional pressures, therefore, Pascals law can be interpreted as saying that any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid. If a U-tube is filled with water and pistons are placed at each end, pressure exerted against the piston will be transmitted throughout the liquid. The pressure that the left piston exerts against the water will be equal to the pressure the water exerts against the right piston. Suppose the tube on the side is made wider and a piston of a larger area is used, for example. If a 1 N load is placed on the left piston, the difference between force and pressure is important, the additional pressure is exerted against the entire area of the larger piston. Since there is 50 times the area,50 times as much force is exerted on the larger piston, thus, the larger piston will support a 50 N load - fifty times the load on the smaller piston. Forces can be multiplied using such a device, one newton input produces 50 newtons output. By further increasing the area of the piston, forces can be multiplied, in principle. Pascals principle underlies the operation of the hydraulic press, the hydraulic press does not violate energy conservation, because a decrease in distance moved compensates for the increase in force. When the small piston is moved downward 100 centimeters, the piston will be raised only one-fiftieth of this. Pascals principle applies to all fluids, whether gases or liquids, a typical application of Pascals principle for gases and liquids is the automobile lift seen in many service stations. Increased air pressure produced by an air compressor is transmitted through the air to the surface of oil in an underground reservoir, the oil, in turn, transmits the pressure to a piston, which lifts the automobile. The relatively low pressure that exerts the force against the piston is about the same as the air pressure in automobile tires. Hydraulics is employed by modern devices ranging from small to enormous. For example, there are hydraulic pistons in almost all construction machines where heavy loads are involved, Pascals barrel is the name of a hydrostatics experiment allegedly performed by Blaise Pascal in 1646
13.
Pascal's theorem
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The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel. The most natural setting for Pascals theorem is in a plane since all lines meet. However, with the interpretation of what happens when some opposite sides of the hexagon are parallel. If two pairs of sides are parallel, then all three pairs of opposite sides form pairs of parallel lines and there is no Pascal line in the Euclidean plane. This theorem is a generalization of Pappuss theorem – Pappuss theorem is the case of a degenerate conic of two lines. Pascals theorem is the reciprocal and projective dual of Brianchons theorem. It was formulated by Blaise Pascal in a written in 1639 when he was 16 years old. Par B. P. Pascals theorem is a case of the Cayley–Bacharach theorem. This can be proven independently using a property of pole-polar, six is the minimum number of points on a conic about which special statements can be made, as five points determine a conic. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a construction of the conic defined by five points. Then if 2n of those points lie on a common line, if six unordered points are given on a conic section, they can be connected into a hexagon in 60 different ways, resulting in 60 different instances of Pascals theorem and 60 different Pascal lines. This configuration of 60 lines is called the Hexagrammum Mysticum, as Thomas Kirkman proved in 1849, these 60 lines can be associated with 60 points in such a way that each point is on three lines and each line contains three points. The 60 points formed in this way are now known as the Kirkman points, the Pascal lines also pass, three at a time, through 20 Steiner points. There are 20 Cayley lines which consist of a Steiner point, the Steiner points also lie, four at a time, on 15 Plücker lines. Furthermore, the 20 Cayley lines pass four at a time through 15 points known as the Salmon points, Pascals original note has no proof, but there are various modern proofs of the theorem. It is sufficient to prove the theorem when the conic is a circle and this was realised by Pascal, whose first lemma states the theorem for a circle. His second lemma states that what is true in one plane remains true upon projection to another plane, a short elementary proof of Pascals theorem in the case of a circle was found by van Yzeren, based on the proof in. This proof proves the theorem for circle and then generalizes it to conics, a short elementary computational proof in the case of the real projective plane was found by Stefanovic We can infer the proof from existence of isogonal conjugate too
14.
Augustine of Hippo
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Augustine of Hippo was an early Christian theologian and philosopher whose writings influenced the development of Western Christianity and Western philosophy. He was the bishop of Hippo Regius, located in Numidia, Augustine is viewed as one of the most important Church Fathers in Western Christianity for his writings in the Patristic Era. Among his most important works are The City of God and Confessions, according to his contemporary, Jerome, Augustine established anew the ancient Faith. In his early years, he was influenced by Manichaeism. After his baptism and conversion to Christianity in 386, Augustine developed his own approach to philosophy and theology, accommodating a variety of methods and perspectives. Believing that the grace of Christ was indispensable to human freedom, he helped formulate the doctrine of original sin, when the Western Roman Empire began to disintegrate, Augustine developed the concept of the Church as a spiritual City of God, distinct from the material Earthly City. His thoughts profoundly influenced the medieval worldview, the segment of the Church that adhered to the concept of the Trinity as defined by the Council of Nicaea and the Council of Constantinople closely identified with Augustines On the Trinity. Augustine is recognized as a saint in the Catholic Church, the Eastern Christian Church, and he is also the patron of the Augustinians. His memorial is celebrated on 28 August, the day of his death, Augustine is the patron saint of brewers, printers, theologians, the alleviation of sore eyes, and a number of cities and dioceses. Many Protestants, especially Calvinists and Lutherans, consider him to be one of the fathers of the Protestant Reformation due to his teachings on salvation. Lutherans, and Martin Luther in particular, have held Augustine in preeminence, Luther himself was a member of the Order of the Augustinian Eremites. In the East, some of his teachings are disputed and have in the 20th century in particular come under attack by such theologians as John Romanides, but other theologians and figures of the Eastern Orthodox Church have shown significant appropriation of his writings, chiefly Georges Florovsky. The most controversial doctrine surrounding his name is the filioque, which has been rejected by the Orthodox Church, other disputed teachings include his views on original sin, the doctrine of grace, and predestination. Nevertheless, though considered to be mistaken on some points, he is considered a saint. In the Orthodox Church his feast day is celebrated on 28 August and he was an early Christian theologian and philosopher whose writings influenced the development of Western Christianity and Western philosophy. Augustine was the bishop of Hippo Regius, located in Numidia and he is viewed as one of the most important Church Fathers in Western Christianity for his writings in the Patristic Era. Among his most important works are The City of God and Confessions, Augustine was born in the year 354 AD in the municipium of Thagaste in Roman Africa. His mother, Monica or Monnica, was a devout Christian, in his writings, Augustine leaves some information as to the consciousness of his African heritage
15.
Michel de Montaigne
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Michel Eyquem de Montaigne, Lord of Montaigne was one of the most significant philosophers of the French Renaissance, known for popularizing the essay as a literary genre. His work is noted for its merging of casual anecdotes and autobiography with serious intellectual insight, in his own lifetime, Montaigne was admired more as a statesman than as an author. In time, however, Montaigne would come to be recognized as embodying, perhaps better than any other author of his time and he is most famously known for his skeptical remark, Que sçay-je. Much of modern literary non-fiction has found inspiration in Montaigne and writers of all kinds continue to read him for his balance of intellectual knowledge. Montaigne was born in the Aquitaine region of France, on the family estate Château de Montaigne, in a town now called Saint-Michel-de-Montaigne, close to Bordeaux. The family was wealthy, his great-grandfather, Ramon Felipe Eyquem, had made a fortune as a herring merchant and had bought the estate in 1477. His father, Pierre Eyquem, Seigneur of Montaigne, was a French Catholic soldier in Italy for a time and had also been the mayor of Bordeaux. Although there were several families bearing the patronym Eyquem in Guyenne and his mother, Antoinette López de Villanueva, was a convert to Protestantism. His maternal grandfather, Pedro Lopez, from Zaragoza, was from a wealthy Marrano family who had converted to Catholicism and his maternal grandmother, Honorette Dupuy, was from a Catholic family in Gascony, France. His mother lived a part of Montaignes life near him, and even survived him. Montaignes relationship with his father, however, is reflected upon. Montaignes education began in childhood and followed a pedagogical plan that his father had developed, refined by the advice of the latters humanist friends. After these first spartan years, Montaigne was brought back to the château, the objective was for Latin to become his first language. The intellectual education of Montaigne was assigned to a German tutor and his father hired only servants who could speak Latin, and they also were given strict orders always to speak to the boy in Latin. The same rule applied to his mother, father, and servants, who were obliged to use only Latin words he himself employed, Montaignes Latin education was accompanied by constant intellectual and spiritual stimulation. He was familiarized with Greek by a method that employed games, conversation. The atmosphere of the upbringing, although designed by highly refined rules taken under advisement by his father, created in the boys life the spirit of liberty. Duty by an unforced will, and of my own voluntary motion. without any severity or constraint and he then began his study of law at the University of Toulouse in 1546 and entered a career in the local legal system
16.
Gilles de Roberval
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Gilles Personne de Roberval, French mathematician, was born at Roberval near Beauvais, France. His name was originally Gilles Personne or Gilles Personier, with Roberval the place of his birth, like René Descartes, he was present at the siege of La Rochelle in 1627. In the same year he went to Paris, and in 1631 he was appointed the chair at Gervais College. Two years after that, in 1633, he was made the chair of mathematics at the Royal College of France. Notwithstanding this, Roberval was able to keep the chair till his death, another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, to these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name Robervallian lines. Traité de Mécanique des Poids Soutenus par des Puissances sur des Plans Inclinés à l’Horizontale, le Système du Monde d’après Aristarque de Samos. Divers Ouvrages de M. de Roberval, a Study of the Traité des Indivisibles of Gilles Persone de Roberval. New York, Teachers College, Columbia University, un Savant Méconnu, Gilles Personne de Roberval. Roberval Philosophe, Journal des Savants, pp. 129–149, carroll, Maureen T. Dougherty, Steven T. Perkins, David. Indivisibles, Infinitesimals and a Tale of Seventeenth-Century Mathematics, La Lettre de Torricelli à Roberval dOctobre 1643. Les Étendues Géométriques et la Ligne Droite de Roberval, eléments de Géométrie de G. P. de Roberval. New York, Charles Scribner’s Sons, Vol.11, p. 486–491, works by or about Gilles de Roberval at Internet Archive OConnor, John J. Robertson, Edmund F. Gilles de Roberval, MacTutor History of Mathematics archive, University of St Andrews. Gilles de Roberval at the Mathematics Genealogy Project Roberval in Galileo Project Roberval in the Notable Names Database
17.
Cornelius Jansen
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Corneille Janssens, commonly known by the Latinized name Cornelius Jansen or Jansenius, was the Dutch Catholic bishop of Ypres in Flanders and the father of a theological movement known as Jansenism. He was born of humble Catholic parentage at Acquoy then in the province of Holland, now in Gelderland, the Netherlands. In 1602 he entered the University of Leuven, then in the throes of a conflict between the Jesuit — or scholastic — party and the followers of Michael Baius, who swore by St. Augustine. After taking his degree he went to Paris, partly to improve his health by a change of scene, eventually he joined Du Vergier at his country home near Bayonne, and spent some years teaching at the bishops college. All his spare time was spent in studying the early Fathers with Du Vergier, in 1616 he returned to Leuven, to take charge of the college of St Pulcheria, a hostel for Dutch students of theology. Pupils found him a somewhat choleric and exacting master and a recluse from academic society. In the hope of suppressing their encroachments, Jansen was sent twice to Madrid, in 1624 and 1626 and he also crossed more than once the Dutch Calvinist–Presbyterian champion, Gisbertus Voetius, still remembered for his attacks on René Descartes. This became the object of his lectures, when he was appointed regius professor of scriptural interpretation at Leuven in 1630. Still more was it the object of his Augustinus, a treatise on the theology of St. Augustine. Its preparation was his chief occupation since his return to Leuven and he had introduced in this treaty a long development favourable to contrition. But Jansen, as he said, did not mean to be a school-pedant all his life, within two years he was however cut down by a sudden illness, the Augustinus, the book of his life, was published posthumously in 1640. They accused Jansenius of having misinterpreted St. Augustine, conflating Jansenists with Lutherans and this led Pope Innocent X to condemn in 1643 these 5 propositions in the Cum Occasione papal bull, and again ten years later, without attributing them to Jansenius in particular. The formulary controversy led Pascal to write the famous Lettres provinciales in which he attacked the Jesuits and their moral. Following this anonymous publication, the King sent spies everywhere, condemned the librarians, the Jansenists of Port-Royal, Antoine Arnauld, Pierre Nicole, la Mère Angélique, Soeur Agnès, etc. were forced to sign the formulary. The Jansenists reasoning was that the Pope had of course the power to condemn heretical propositions and this strategy would impose decades of theological disputes and debate. The controversy did not involve only Papal authority, but rather his authority concerning Biblical exegesis, further controversy led to the bull Unigenitus, issued by Clement XI in 1713, which marked the end of Catholic toleration of Jansenist doctrine. Up until the French Revolution, Jansenism would live on as a force in France. Anonymous Jansenists published a magazine called Nouvelles ecclésiastiques, which frequently featured anti-Jesuit propaganda, eventually, Jansenists would collaborate with independent-minded Gallicanists in promoting the Jesuits expulsion from France in 1764
18.
Epictetus
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Epictetus was a Greek-speaking Stoic philosopher. He was born a slave at Hierapolis, Phrygia and lived in Rome until his banishment and his teachings were written down and published by his pupil Arrian in his Discourses and Enchiridion. Epictetus taught that philosophy is a way of life and not just a theoretical discipline, to Epictetus, all external events are beyond our control, we should accept calmly and dispassionately whatever happens. However, individuals are responsible for their own actions, which they can examine, Epictetus was born c.50 A. D. presumably at Hierapolis, Phrygia. He spent his youth as a slave in Rome to Epaphroditos, origen stated that his leg was deliberately broken by his master. Simplicius stated that he had been lame from childhood, Epictetus obtained his freedom sometime after the death of Nero in 68 A. D. and he began to teach philosophy in Rome. Emperor Domitian banished all philosophers from the city, and Epictetus went to Nicopolis in Epirus, Greece, Arrian describes Epictetus as being a powerful speaker who could induce his listener to feel just what Epictetus wanted him to feel. Many eminent figures sought conversations with him, Emperor Hadrian was friendly with him, and may have listened to him speak at his school in Nicopolis. He lived a life of simplicity, with few possessions. He lived alone for a time, but in his old age he adopted a friends child who otherwise, would have been left to die. It is unclear whether Epictetus and she were married and he died sometime around 135 A. D. After his death, according to Lucian, his oil lamp was purchased by an admirer for 3,000 drachmae, no writings by Epictetus are known. His discourses were transcribed and compiled by his pupil Arrian, the main work is The Discourses, four books of which have been preserved. Arrian also compiled a popular digest, entitled the Enchiridion, or Handbook, Epictetus maintains that the foundation of all philosophy is self-knowledge, that is, the conviction of our ignorance and gullibility ought to be the first subject of our study. Logic provides valid reasoning and certainty in judgment, but it is subordinate to practical needs, the first and most necessary part of philosophy concerns the application of doctrine, for example, that people should not lie. The second concerns reasons, e. g. why people should not lie, while the third, lastly, examines and establishes the reasons. This is the part, which finds reasons, shows what is a reason. This last part is necessary, but only on account of the second, both the Discourses and the Enchiridion begin by distinguishing between those things in our power and those things not in our power
19.
Gerolamo Cardano
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He wrote more than 200 works on science. He made significant contributions to hypocycloids, published in De proportionibus, the generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses. Today, he is known for his achievements in algebra. He was born in Pavia, Lombardy, the child of Fazio Cardano, a mathematically gifted jurist, lawyer. In his autobiography, Cardano wrote that his mother, Chiara Micheri, had taken various abortive medicines to terminate the pregnancy, he was taken by violent means from my mother and she was in labour for three days. Shortly before his birth, his mother had to move from Milan to Pavia to escape the Plague and his eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan and he suffered from impotence throughout the early part of his life, but recovered and married Lucia Banderini in 1531. Before her death in 1546, she bore him three children, Giovanni Battista, Chiara and Aldo, Cardano was the first mathematician to make systematic use of numbers less than zero. He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna. The solution to one case of the cubic equation a x 3 + b x + c =0, had been communicated to him by Niccolò Fontana Tartaglia in the form of a poem. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem, Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. He used the game of throwing dice to understand the concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes and he was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied. Cardano made several contributions to hydrodynamics and held that perpetual motion is impossible and he published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a tool, in 1550. Someone also assigned to Cardano the credit for the invention of the so-called Cardanos Rings, also called Chinese Rings and he was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write. Two of Cardanos children—Giovanni and Aldo Battista—came to ignoble ends, Giovanni Battista, Cardanos eldest and favorite son, was tried and beheaded in 1560 for poisoning his wife, after he discovered that their three children were not his. Aldo Battista was a gambler, who stole money from his father and was disinherited by him in 1569, Cardano was arrested by the Inquisition in 1570 for unknown reasons, and forced to spend several months in prison and abjure his professorship
20.
William Lane Craig
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William Lane Craig is an American analytic philosopher, Christian theologian, Christian apologist and historian. He holds faculty positions at Talbot School of Theology, Biola University, Craig is best known for his development and defense of the Kalam cosmological argument, for the existence of God. He also focused in his work on a historical argument for the Resurrection of Jesus. His research on divine aseity and Platonism culminated with his book God Over All and he is currently researching the Doctrine of the Atonement. He is known to a lay audience for his debates on the existence of God with public figures such as Christopher Hitchens, Craig established and runs the online apologetics ministry ReasonableFaith. org. He is also an author of books, including Reasonable Faith. Craig is the second of three born to Mallory and Doris Craig in Peoria, Illinois. His fathers work with the T. P. & W. railroad took the family to Keokuk, Iowa, until his transfer to the home office in East Peoria in 1960. In September 1965, his year, he converted to Christianity, and after graduating from high school, attended Wheaton College. Craig graduated in 1971 and the year married his wife Jan. In 2014, he was named alumnus of the year by Wheaton, in 1973 Craig entered the program in philosophy of religion at Trinity Evangelical Divinity School north of Chicago, where he studied under Norman Geisler. In 1975 Craig commenced doctoral studies in philosophy at the University of Birmingham in England, out of this study came his first book, The Kalam Cosmological Argument, a defense of the argument he first encountered in Hacketts work. Craig joined the faculty of Trinity Evangelical Divinity School in 1980, in 1982 Craig received an invitation to debate Kai Nielsen at the University of Calgary, Canada, on the question of Gods existence. Craig has participated in debates on philosophical and theological questions with philosophers, scientists, and biblical scholars, including Antony Flew, E. M. Bradley, Sam Harris, and Sean Carroll. He has also engaged in debates on Islam, having engaged academic and Islamic scholar Shabir Ally, Jamal Badawi and South African Muslim apologist, out of that period of research issued seven books, among them God, Time, and Eternity. In 1994 Craig joined the Department of Philosophy and Ethics at Talbot School of Theology in suburban Los Angeles as Research Professor of Philosophy, Craig established an online apologetic ministry, ReasonableFaith. org. Craig is best known for his work on a version of the cosmological argument. In The Kalām Cosmological Argument, he formulates the argument in the following manner, therefore, the universe has a cause of its existence
21.
Antoine Arnauld
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Not to be confused with his father Antoine Arnauld or his nephew Antoine Arnauld. Antoine Arnauld — le Grand, as contemporaries called him, to him from his father — was a French Roman Catholic theologian, philosopher. He was one of the intellectuals of the Jansenist group of Port-Royal and had a very thorough knowledge of patristics. Antoine Arnauld was born in Paris to the Arnauld family, the twentieth and youngest child of the original Antoine Arnauld, he was originally intended for the bar, but decided instead to study theology at the Sorbonne. His book, De la fréquente Communion, was an important step in making the aims and it attracted controversy by being against frequent communion. Pascal was assisted in this task by Arnaulds nephew Antoine Le Maistre, during the formulary controversy which opposed Jesuits to Jansenists concerning the orthodoxy of Jansenius propositions, Arnauld was forced to go into hiding. In 1655 two very outspoken Lettres à un duc et pair on Jesuit methods in the confessional brought a motion of censorship voted against him in the Sorbonne and this motion prompted Pascal to anonymously write the Provincial Letters. For more than twenty years Arnauld dared not appear publicly in Paris, Pascal, however, failed to save his friend, and in February 1656 Arnauld was ceremonially degraded. Twelve years later the so-called peace of Pope Clement IX put an end to his troubles, he was received by Louis XIV. He now set to work with Pierre Nicole on a work against the Calvinist Protestants. Ten years later, however, persecution resumed, Arnauld was compelled to leave France for the Netherlands, finally settling down at Brussels. Here the last sixteen years of his life were spent in incessant controversy with Jesuits, Calvinists and his inexhaustible energy is best expressed by his famous reply to Nicole, who complained of feeling tired. Echoed Arnauld, when you have all eternity to rest in and his energy was not exhausted by purely theological questions. On the whole, public opinion leant to Arnaulds side, when Malebranche complained that his adversary had misunderstood him, Boileau silenced him with the question, My dear sir, whom do you expect to understand you, if M. Arnauld does not. Next Arnauld was engaged in a correspondence with Gottfried Wilhelm Leibniz. Arnauld died, aged 82, in Brussels, Arnauld came to be regarded as important among the mathematicians of his time, one critic described him as the Euclid of the 17th century. After his death, his reputation began to wane, contemporaries admired him as a master of intricate reasoning, on this, Jacques-Bénigne Bossuet, the greatest theologian of the age, agreed with Henri François dAguesseau, the greatest lawyer. However, his eagerness to win every argument endeared him to no one, in spite of myself, Arnauld once said regretfully, my books are seldom very short
22.
Pierre Duhem
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Pierre Maurice Marie Duhem was a French physicist, mathematician, historian and philosopher of science. As a scientist, Duhem also contributed to hydrodynamics and to the theory of elasticity, Duhems views on the philosophy of science are explicated in his 1906 work The Aim and Structure of Physical Theory. In this work, he opposed Newtons statement that the Principias law of universal gravitation was deduced from phenomena, including Keplers second. Since no proposition can be logically deduced from any it contradicts, according to Duhem. Duhems name is given to the under-determination or Duhem–Quine thesis, which holds that for any set of observations there is an innumerably large number of explanations. It is, in essence, the same as Humes critique of induction, possible alternatives to induction are Duhems instrumentalism and Poppers thesis that we learn from falsification. As popular as the Duhem–Quine thesis may be in the philosophy of science, in reality Pierre Duhem, Pierre Duhem believed that experimental theory in physics is fundamentally different from fields like physiology and certain branches of chemistry. Also Duhems conception of theoretical group has its limits, since not all concepts are connected to each other logically and he did not include at all a priori disciplines such as logic and mathematics within these theoretical groups in physics which can be tested experimentally. Quine, on the hand, conceived this theoretical group as a unit of a whole human knowledge. To Quine, even mathematics and logic must be revised in light of recalcitrant experience, a quote of Duhem on physics, A theory of physics is not an explanation. Duhem argues that physics is subject to certain limitations that do not affect other sciences. In his The Aim and Structure of Physical Theory, Duhem provided a critique of Baconian crucial experiments. According to this critique, an experiment in physics is not simply an observation, furthermore, no matter how well one constructs ones experiment, it is impossible to subject an isolated single hypothesis to an experimental test. Instead, it is an interlocking group of hypotheses, background assumptions. This thesis has come to be known as confirmation holism and this inevitable holism, according to Duhem, renders crucial experiments impossible. More generally, Duhem was critical of Newtons description of the method of physics as a deduction from facts. Since they do not have any common term, these two sorts of judgments can neither contradict nor agree with each other. Nonetheless, Duhem argues that it is important for the theologian or metaphysician to have detailed knowledge of theory in order not to make illegitimate use of it in speculations
23.
William James
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William James was an American philosopher and psychologist who was also trained as a physician. A Review of General Psychology survey, published in 2002, ranked James as the 14th most cited psychologist of the 20th century and he also developed the philosophical perspective known as radical empiricism. James work has influenced intellectuals such as Émile Durkheim, W. E. B, du Bois, Edmund Husserl, Bertrand Russell, Ludwig Wittgenstein, Hilary Putnam, and Richard Rorty, and has even influenced Presidents, such as Jimmy Carter. Born into a family, James was the son of the Swedenborgian theologian Henry James Sr. James wrote widely on topics, including epistemology, education, metaphysics, psychology, religion. William James was born at the Astor House in New York City and he was the son of Henry James Sr. a noted and independently wealthy Swedenborgian theologian well acquainted with the literary and intellectual elites of his day. William James received an eclectic trans-Atlantic education, developing fluency in both German and French, education in the James household encouraged cosmopolitanism. The family made two trips to Europe while William James was still a child, setting a pattern that resulted in thirteen more European journeys during his life. In his early adulthood, James suffered from a variety of ailments, including those of the eyes, back, stomach. Two younger brothers, Garth Wilkinson and Robertson, fought in the Civil War, the other three siblings all suffered from periods of invalidism. He took up studies at Harvard Medical School in 1864. His studies were interrupted once again due to illness in April 1867 and he traveled to Germany in search of a cure and remained there until November 1868, at that time he was 26 years old. During this period, he began to publish, reviews of his works appeared in periodicals such as the North American Review. James finally earned his M. D. degree in June 1869, what he called his soul-sickness would only be resolved in 1872, after an extended period of philosophical searching. He married Alice Gibbens in 1878, in 1882 he joined the Theosophical Society. Jamess time in Germany proved intellectually fertile, helping him find that his interests lay not in medicine but in philosophy. Later, in 1902 he would write, I originally studied medicine in order to be a physiologist, I never had any philosophic instruction, the first lecture on psychology I ever heard being the first I ever gave. In 1875–1876, James, Henry Pickering Bowditch, Charles Pickering Putnam, G. Stanley Hall, Henri Bergson and Sigmund Freud
24.
Gottfried Wilhelm Leibniz
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Leibnizs notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and he became one of the most prolific inventors in the field of mechanical calculators. He also refined the number system, which is the foundation of virtually all digital computers. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism and he wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibnizs contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and he wrote in several languages, but primarily in Latin, French, and German. There is no complete gathering of the writings of Leibniz in English, Gottfried Leibniz was born on July 1,1646, toward the end of the Thirty Years War, in Leipzig, Saxony, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his journal,21. Juny am Sontag 1646 Ist mein Sohn Gottfried Wilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, in English, On Sunday 21 June 1646, my son Gottfried Wilhelm is born into the world a quarter after six in the evening, in Aquarius. Leibniz was baptized on July 3 of that year at St. Nicholas Church, Leipzig and his father died when he was six and a half years old, and from that point on he was raised by his mother. Her teachings influenced Leibnizs philosophical thoughts in his later life, Leibnizs father had been a Professor of Moral Philosophy at the University of Leipzig, and the boy later inherited his fathers personal library. He was given access to it from the age of seven. Access to his fathers library, largely written in Latin, also led to his proficiency in the Latin language and he also composed 300 hexameters of Latin verse, in a single morning, for a special event at school at the age of 13. In April 1661 he enrolled in his fathers former university at age 15 and he defended his Disputatio Metaphysica de Principio Individui, which addressed the principle of individuation, on June 9,1663. Leibniz earned his masters degree in Philosophy on February 7,1664, after one year of legal studies, he was awarded his bachelors degree in Law on September 28,1665. His dissertation was titled De conditionibus, in early 1666, at age 19, Leibniz wrote his first book, De Arte Combinatoria, the first part of which was also his habilitation thesis in Philosophy, which he defended in March 1666. His next goal was to earn his license and Doctorate in Law, in 1666, the University of Leipzig turned down Leibnizs doctoral application and refused to grant him a Doctorate in Law, most likely due to his relative youth. Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, the title of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure. Leibniz earned his license to practice law and his Doctorate in Law in November 1666 and he next declined the offer of an academic appointment at Altdorf, saying that my thoughts were turned in an entirely different direction
25.
Alexis de Tocqueville
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Alexis Charles Henri Clérel, Viscount de Tocqueville was a French diplomat, political scientist, and historian. He was best known for his works Democracy in America and The Old Regime, in both he analyzed the improved living standards and social conditions of individuals, as well as their relationship to the market and state in Western societies. Democracy in America was published after Tocquevilles travels in the United States and is considered an early work of sociology. Tocqueville was active in French politics, first under the July Monarchy and he retired from political life after Louis Napoléon Bonapartes 2 December 1851 coup, and thereafter began work on The Old Regime and the Revolution. He argued the importance of the French Revolution was to continue the process of modernizing and centralizing the French state which had begun under King Louis XIV, the failure of the Revolution came from the inexperience of the deputies who were too wedded to abstract Enlightenment ideals. Tocqueville was a liberal who advocated parliamentary government, but he was skeptical of the extremes of democracy. Alexis de Tocqueville came from an old Norman aristocratic family with ancestors who participated in the Battle of Hastings in 1066, after an exile in England, they returned to France during the reign of Napoleon. Under the Bourbon Restoration, his became an noble peer. Tocqueville attended the Lycée Fabert in Metz, Tocqueville, who despised the July Monarchy, began his political career in 1839. From 1839 to 1851, he served as deputy of the Manche department, in parliament, he defended abolitionist views and upheld free trade, while supporting the colonisation of Algeria carried on by Louis-Philippes regime. Tocqueville was also elected general counsellor of the Manche in 1842, in 1831, he obtained from the July Monarchy a mission to examine prisons and penitentiaries in America, and proceeded there with his lifelong friend Gustave de Beaumont. While Tocqueville did visit some prisons, he traveled widely in America and he returned within nine months, and published a report, but the real result of his tour was De la démocratie en Amerique, which appeared in 1835. Beaumont also wrote an account of their travels in Jacksonian America, apart from America, Tocqueville also made an observational tour of England, producing Memoir on Pauperism. In 1841 and 1846, he traveled to Algeria and he went as far as openly advocating racial segregation between the European colonists and the Arabs through the implementation of two different legislative systems. In 1835, Tocqueville made a journey through Ireland and his observations provide one of the best pictures of how Ireland stood before the Great Famine. The observations chronicle the growing Catholic middle-class and the conditions in which most Catholic tenant farmers lived. Tocqueville made clear both his libertarian sympathies and his affinity for his Irish co-religionists and he defended bicameralism and the election of the President of the Republic by universal suffrage. As the countryside was thought to be more conservative than the population of Paris
26.
Henri Bergson
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Henri-Louis Bergson was a French philosopher, influential especially in the first half of the 20th century and after WWII in continental philosophy. Bergson is known for his arguments that processes of immediate experience and intuition are more significant than abstract rationalism. He was awarded the 1927 Nobel Prize in Literature in recognition of his rich and vitalizing ideas, in 1930 France awarded him its highest honour, the Grand-Croix de la Legion dhonneur. Bergson was born in the Rue Lamartine in Paris, not far from the Palais Garnier in 1859 and his father, the pianist Michał Bergson, was of a Polish Jewish background. His great-grandmother, Temerl Bergson, was a well-known patroness and benefactor of Polish Jewry and his mother, Katherine Levison, daughter of a Yorkshire doctor, was from an English and Irish Jewish background. The Bereksohns were a famous Jewish entrepreneurial family of Polish descent, Henri Bergsons great-great-grandfather, Szmul Jakubowicz Sonnenberg, called Zbytkower, was a prominent banker and a protégé of Stanisław August Poniatowski, King of Poland from 1764 to 1795. Henri Bergsons family lived in London for a few years after his birth, before he was nine, his parents settled in France, Henri becoming a naturalized French citizen. Henri Bergson married Louise Neuberger, a cousin of Marcel Proust, Henri and Louise Bergson had a daughter, Jeanne, born deaf in 1896. Bergsons sister, Mina Bergson, married the English occult author Samuel Liddell MacGregor Mathers, a founder of the Hermetic Order of the Golden Dawn, and he then replaced Gabriel Tarde in the Chair of Modern Philosophy, which he held until 1920. The public attended his open courses in large numbers, Bergson attended the Lycée Fontanes in Paris from 1868 to 1878. He had previously received a Jewish religious education, between 14 and 16, however, he lost his faith. While at the lycée Bergson won a prize for his work and another, in 1877 when he was eighteen. His solution was published the year in Annales de Mathématiques. It was his first published work, after some hesitation as to whether his career should lie in the sphere of the sciences or that of the humanities, he decided in favour of the latter, to the dismay of his teachers. When he was nineteen, he entered the École Normale Supérieure, during this period, he read Herbert Spencer. He obtained there the degree of licence ès lettres, and this was followed by that of agrégation de philosophie in 1881 from the University of Paris, the same year he received a teaching appointment at the lycée in Angers, the ancient capital of Anjou. Two years later he settled at the Lycée Blaise-Pascal in Clermont-Ferrand, while teaching and lecturing in this part of his country, Bergson found time for private study and original work. He crafted his dissertation Time and Free Will, which was submitted, along with a short Latin thesis on Aristotle, the work was published in the same year by Félix Alcan
27.
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
28.
Physicist
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A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe. A physicist is a scientist who specializes or works in the field of physics, physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists can also apply their knowledge towards solving real-world problems or developing new technologies, some physicists specialize in sectors outside the science of physics itself, such as engineering. The study and practice of physics is based on a ladder of discoveries. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture and Asian culture, the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo and Kepler in the early 1600s. New knowledge in the early 21st century includes an increase in understanding physical cosmology. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences, many physicist positions require an undergraduate degree in applied physics or a related science or a Masters degree like MSc, MPhil, MPhys or MSci. In a research oriented level, students tend to specialize in a particular field, Physics students also need training in mathematics, and also in computer science and programming. For being employed as a physicist a doctoral background may be required for certain positions, undergraduate students like BSc Mechanical Engineering, BSc Electrical and Computer Engineering, BSc Applied Physics. etc. With physics orientation are chosen as research assistants with faculty members, the highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. The three major employers of career physicists are academic institutions, laboratories, and private industries, with the largest employer being the last, physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr. /Jr. As per the American Institute for Physics, some 20% of new physics Ph. D. s holds jobs in engineering development programs, while 14% turn to computer software, a majority of physicists employed apply their skills and training to interdisciplinary sectors. For industry or self-employment. and also in science and programming. Hence a majority of Physics bachelors degree holders are employed in the private sector, other fields are academia, government and military service, nonprofit entities, labs and teaching
29.
Child prodigy
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In psychology research literature, the term child prodigy is defined as a person under the age of ten who produces meaningful output in some domain to the level of an adult expert performer. Child prodigies are rare, and, in domains, there are no child prodigies at all. Prodigiousness in childhood does not always predict adult eminence, the term Wunderkind is sometimes used as a synonym for prodigy, particularly in media accounts. Wunderkind also is used to recognize those who achieve success and acclaim early in their adult careers, PET scans performed on several mathematics prodigies have suggested that they think in terms of long-term working memory. This memory, specific to a field of expertise, is capable of holding relevant information for extended periods, the PET scans also answer questions about which specific areas of the brain associate themselves with manipulating numbers. One subject never excelled as a child in mathematics, but he taught himself algorithms and tricks for calculatory speed and his brain, compared to six other controls, was studied using the PET scan, revealing separate areas of his brain that he manipulated to solve the complex problems. Some of the areas that he and presumably prodigies use are brain sectors dealing in visual and spatial memory, as well as visual mental imagery. Other areas of the brain showed use by the subject, including a sector of the brain related to childlike finger counting. Citing extensive imaging evidence, Vandervert first proposed this approach in two publications appeared in 2003. In addition to imaging evidence, Vanderverts approach is supported by the award winning studies of the cerebellum by Masao Ito. Some researchers believe that prodigious talent tends to arise as a result of the talent of the child. Others believe that the environment plays the dominant role, many times in obvious ways, but on the other hand George Frideric Handel was an example of the natural talent. He had discovered such a strong propensity to music, that his father who intended him for the study of the Civil Law, had reason to be alarmed. He strictly forbade him to meddle with any musical instrument but Handel found means to get a little clavichord privately conveyd to a room at the top of the house, to this room he constantly stole when the family was asleep. Despite his fathers opposition, Handel became a performer on the harpsichord. Chess prodigy List of child prodigies List of music prodigies Gifted education Giftedness Late bloomer Malleable intelligence Polymath Savant syndrome Ellenberg, the Wrong Way to Treat Child Geniuses. How working memory and the cerebellum collaborate to produce creativity and innovation, the Gradual Path to Creative Breakthroughs. Notebook, Child Prodigies, CBS News Online, YouTube, February 26,2010
30.
Rouen
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Rouen is a city on the River Seine in the north of France. It is the capital of the region of Normandy, formerly one of the largest and most prosperous cities of medieval Europe, Rouen was the seat of the Exchequer of Normandy during the Middle Ages. It was one of the capitals of the Anglo-Norman dynasties, which ruled both England and large parts of modern France from the 11th to the 15th centuries. The population of the area at the 2007 census was 532,559. People from Rouen are known as Rouennais, Rouen and its metropolitan area of 70 suburban communes form the Agglomeration community of Rouen-Elbeuf-Austreberthe, with 494,382 inhabitants at the 2010 census. Rouen was founded by the Gaulish tribe of Veliocasses, who controlled an area in the lower Seine valley. The Gauls named the settlement Ratumacos and the Romans called it Rotomagus, Roman Rotomagus was the second city of Gallia Lugdunensis, after Lugdunum. In the 5th century, it became the seat of a bishopric, in the 10th century Rouen became the capital of the Duchy of Normandy and the residence of the dukes, until William the Conqueror established his castle at Caen. During the early 12th century the population reached 30,000. In 1150, Rouen received its charter, which permitted self-government. During the 12th century, Rouen was probably the site of a Jewish yeshiva, at that time, about 6,000 Jews lived in the town, comprising about 20% of the total population. The well-preserved remains of a medieval Jewish building, that could be a yeshiva, were discovered in the 1970s under the Rouen Law Courts. In 1200, a destroyed part of Rouens Romanesque cathedral, leaving just St Romains tower, the side porches of its front. New work on the present Gothic cathedral of Rouen began, in the nave, transept, choir, on 24 June 1204, Philip Augustus entered Rouen and annexed Normandy to the French Kingdom. The fall of Rouen meant the end of Normandys sovereign status and he demolished the Norman castle and replaced it with his own, the Château Bouvreuil, built on the site of the Gallo-Roman amphitheatre. A textile industry developed based on wool imported from England, competing with the northern County of Flanders, the city found its market niche in the Champagne fairs. Rouen also depended on the traffic of the Seine for its prosperity. Wine and wheat were exported to England, with tin and wool received in return, in the late 13th century urban strife threatened the city, in 1291, the mayor was assassinated and noble residences in the city were pillaged
31.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
32.
Vacuum
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Vacuum is space void of matter. The word stems from the Latin adjective vacuus for vacant or void, an approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. In engineering and applied physics on the hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum, the quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum, for example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth of atmospheric pressure, outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average. In the electromagnetism in the 19th century, vacuum was thought to be filled with a medium called aether, in modern particle physics, the vacuum state is considered the ground state of matter. Vacuum has been a frequent topic of debate since ancient Greek times. Evangelista Torricelli produced the first laboratory vacuum in 1643, and other techniques were developed as a result of his theories of atmospheric pressure. A torricellian vacuum is created by filling a glass container closed at one end with mercury. Vacuum became an industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes. The recent development of human spaceflight has raised interest in the impact of vacuum on human health, the word vacuum comes from Latin an empty space, void, noun use of neuter of vacuus, meaning empty, related to vacare, meaning be empty. Vacuum is one of the few words in the English language that contains two consecutive letters u. Historically, there has been dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, Aristotle believed that no void could occur naturally, because the denser surrounding material continuum would immediately fill any incipient rarity that might give rise to a void. Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void, by the ancient definition however, directional information and magnitude were conceptually distinct. The explanation of a clepsydra or water clock was a topic in the Middle Ages. Although a simple wine skin sufficed to demonstrate a partial vacuum, in principle and he concluded that airs volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent. However, according to Nader El-Bizri, the physicist Ibn al-Haytham and the Mutazili theologians disagreed with Aristotle and Al-Farabi, using geometry, Ibn al-Haytham mathematically demonstrated that place is the imagined three-dimensional void between the inner surfaces of a containing body
33.
Evangelista Torricelli
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Evangelista Torricelli was born on 15 October 1608 in Rome, he invented the barometer in Florence, Italy. The firstborn child of Gaspare Ruberti and Giacoma Torricelli and his family was from Faenza in the Province of Ravenna, then part of the Papal States. His father was a worker and the family was very poor. Seeing his talents, his parents sent him to be educated in Faenza, under the care of his uncle, Jacobo, a Camaldolese monk, who first ensured that his nephew was given a sound basic education. He then entered young Torricelli into a Jesuit College in 1624, possibly the one in Faenza itself, to mathematics and philosophy until 1626, by which time his father. The uncle then sent Torricelli to Rome to study science under the Benedictine monk Benedetto Castelli, Castelli was a student of Galileo Galilei. Benedetto Castelli made experiments on running water, and he was entrusted by Pope Urban VIII with hydraulic undertakings, there is no actual evidence that Torricelli was enrolled at the university. It is almost certain that Torricelli was taught by Castelli, in exchange he worked for him as his secretary from 1626 to 1632 as a private arrangement. Because of this, Torricelli was exposed to experiments funded by Pope Urban VIII, while living in Rome, Torricelli became also the student of the brilliant mathematician, Bonaventura Cavalieri, with whom he became great friends. It was in Rome that Torricelli also became friends with two students of Castelli, Raffaello Magiotti and Antonio Nardi. Galileo referred to Torricelli, Magiotti, and Nardi affectionately as his triumvirate in Rome, although Galileo promptly invited Torricelli to visit, he did not accept until just three months before Galileos death. The reason for this was that Torricellis mother, Caterina Angetti died, after Galileos death on 8 January 1642, Grand Duke Ferdinando II de Medici asked him to succeed Galileo as the grand-ducal mathematician and chair of mathematics at the University of Pisa. Right before the appointment, Torricelli was considering returning to Rome because of there being nothing left for him in Florence, in this role he solved some of the great mathematical problems of the day, such as finding a cycloids area and center of gravity. As a result of study, he wrote the book the Opera Geometrica in which he described his observations. The book was published in 1644 and he was interested in Optics, and invented a method whereby microscopic lenses might be made of glass which could be easily melted in a lamp. As a result, he designed and built a number of telescopes and simple microscopes, several large lenses, on 11 June 1644, he famously wrote in a letter to Michelangelo Ricci, Noi viviamo sommersi nel fondo dun pelago daria. Torricelli died in Florence on 25 October 1647,10 days after his 39th birthday and he left all his belongings to his adopted son Alessandro. This early work owes much to the study of the classics, in Faenza, a statue of Torricelli was created in 1868 as a thank you for all that Torricelli had done in advancing science during his short lifetime
34.
Scientific method
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The scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry is commonly based on empirical or measurable evidence subject to specific principles of reasoning, experiments need to be designed to test hypotheses. The most important part of the method is the experiment. The scientific method is a process, which usually begins with observations about the natural world. Human beings are naturally inquisitive, so often come up with questions about things they see or hear. The best hypotheses lead to predictions that can be tested in various ways, in general, the strongest tests of hypotheses come from carefully controlled and replicated experiments that gather empirical data. Depending on how well the tests match the predictions, the hypothesis may require refinement. If a particular hypothesis becomes very well supported a theory may be developed. Although procedures vary from one field of inquiry to another, identifiable features are shared in common between them. The overall process of the method involves making conjectures, deriving predictions from them as logical consequences. A hypothesis is a conjecture, based on knowledge obtained while formulating the question, the hypothesis might be very specific or it might be broad. Scientists then test hypotheses by conducting experiments, the purpose of an experiment is to determine whether observations agree with or conflict with the predictions derived from a hypothesis. Experiments can take anywhere from a college lab to CERNs Large Hadron Collider. There are difficulties in a statement of method, however. Though the scientific method is presented as a fixed sequence of steps. Not all steps take place in scientific inquiry, and are not always in the same order. Some philosophers and scientists have argued there is no scientific method, such as Lee Smolin. Nola and Sankey remark that For some, the idea of a theory of scientific method is yester-years debate
35.
Pascal's calculator
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Pascals calculator is a mechanical calculator invented by Blaise Pascal in the early 17th century. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his fathers work as supervisor of taxes in Rouen and he designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction. Pascals calculator was successful in the design of its carry mechanism, which adds 1 to 9 on one dial. His innovation made each digit independent of the state of the others, Pascal designed the machine in 1642, and after 50 prototypes, he presented it to the public in 1645, dedicating it to Pierre Séguier, then chancellor of France. Pascal built around twenty more machines during the decade, many of which improved on his original design. In 1649, King Louis XIV of France gave Pascal a royal privilege, gottfried Leibniz invented his Leibniz wheels after 1671 after trying to add an automatic multiplication feature to the Pascaline. In 1820, Thomas de Colmar designed his arithmometer and it is not at all clear whether he ever saw Leibnizs device, but he either re-invented it or utilised Leibnizs invention of the step drum. The arithmometer was the first mechanical calculator strong enough and reliable enough to be used daily in an office environment, Pascal was also influential in seeking to commercialise his machine. Nine Pascal calculators have been made, including the first surviving mechanical calculator from the 17th century, most of them are on display in European museums. Pascal has been called and celebrated as the inventor of the mechanical calculator, Pascal began to work on his calculator in 1642, when he was 19 years old. He had been assisting his father, who worked as a tax commissioner, Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating machines in France. By 1654 he had sold about twenty machines, but the cost and complexity of the Pascaline was a barrier to further sales, by that time Pascal had moved on to the study of religion and philosophy, which gave us both the Lettres provinciales and the Pensées. The tercentenary celebration of Pascals invention of the mechanical calculator occurred during WWII when France was occupied by Germany and therefore the main celebration was held in London, the calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. This displayed the number in the windows at the top of the calculator, then, one simply redialed the second number to be added, causing the sum of both numbers to appear in the accumulator. Each dial is associated with a display window located directly above it. The complement of this digit, in the base of the wheel, is displayed just above this digit. A horizontal bar hides either all the complement numbers when it is slid to the top and it thereby displays either the content of the accumulator or the complement of its value. Since the gears of the calculator rotated in one direction
36.
Mechanical calculator
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A mechanical calculator, or calculating machine, was a mechanical device used to perform automatically the basic operations of arithmetic. Most mechanical calculators were comparable in size to small computers and have been rendered obsolete by the advent of the electronic calculator. Surviving notes from Wilhelm Schickard in 1623 reveal that he designed and had built the earliest of the attempts at mechanizing calculation. A study of the surviving notes shows a machine that would have jammed after a few entries on the dial. Schickard abandoned his project in 1624 and never mentioned it again until his death years later in 1635. Two decades after Schickards supposedly failed attempt, in 1642, Blaise Pascal decisively solved these problems with his invention of the mechanical calculator. Co-opted into his fathers labour as tax collector in Rouen, Pascal designed the calculator to help in the amount of tedious arithmetic required. It was called Pascals Calculator or Pascaline, for forty years the arithmometer was the only type of mechanical calculator available for sale. The comptometer, introduced in 1887, was the first machine to use a keyboard which consisted of columns of nine keys for each digit, the Dalton adding machine, manufactured from 1902, was the first to have a 10 key keyboard. Electric motors were used on some mechanical calculators from 1901, the production of mechanical calculators came to a stop in the middle of the 1970s closing an industry that had lasted for 120 years. The first one was a mechanical calculator, his difference engine. In 1855, Georg Scheutz became the first of a handful of designers to succeed at building a smaller and simpler model of his difference engine, a crucial step was the adoption of a punched card system derived from the Jacquard loom making it infinitely programmable. The desire to economize time and mental effort in arithmetical computations and this instrument was probably invented by the Semitic races and later adopted in India, whence it spread westward throughout Europe and eastward to China and Japan. After the development of the abacus, no further advances were made until John Napier devised his numbering rods, or Napiers Bones, in 1617. The 17th century marked the beginning of the history of mechanical calculators, as it saw the invention of its first machines, including Pascals calculator, Blaise Pascal invented a mechanical calculator with a sophisticated carry mechanism in 1642. After three years of effort and 50 prototypes he introduced his calculator to the public and he built twenty of these machines in the following ten years. This machine could add and subtract two numbers directly and multiply and divide by repetition and this suggests that the carry mechanism would have proved itself in practice many times over. Pascals invention of the machine, just three hundred years ago, was made while he was a youth of nineteen
37.
Projective geometry
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Projective geometry is a topic of mathematics. It is the study of properties that are invariant with respect to projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translations. The first issue for geometers is what kind of geometry is adequate for a novel situation, one source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing. See projective plane for the basics of geometry in two dimensions. While the ideas were available earlier, projective geometry was mainly a development of the 19th century and this included the theory of complex projective space, the coordinates used being complex numbers. Several major types of more abstract mathematics were based on projective geometry and it was also a subject with a large number of practitioners for its own sake, as synthetic geometry. Another topic that developed from axiomatic studies of projective geometry is finite geometry, the topic of projective geometry is itself now divided into many research subtopics, two examples of which are projective algebraic geometry and projective differential geometry. Projective geometry is an elementary form of geometry, meaning that it is not based on a concept of distance. In two dimensions it begins with the study of configurations of points and lines and that there is indeed some geometric interest in this sparse setting was first established by Desargues and others in their exploration of the principles of perspective art. In higher dimensional spaces there are considered hyperplanes, and other linear subspaces, Projective geometry can also be seen as a geometry of constructions with a straight-edge alone. Since projective geometry excludes compass constructions, there are no circles, no angles, no measurements, no parallels and it was realised that the theorems that do apply to projective geometry are simpler statements. For example, the different conic sections are all equivalent in projective geometry, during the early 19th century the work of Jean-Victor Poncelet, Lazare Carnot and others established projective geometry as an independent field of mathematics. Its rigorous foundations were addressed by Karl von Staudt and perfected by Italians Giuseppe Peano, Mario Pieri, Alessandro Padoa, after much work on the very large number of theorems in the subject, therefore, the basics of projective geometry became understood. The incidence structure and the cross-ratio are fundamental invariants under projective transformations, Projective geometry can be modeled by the affine plane plus a line at infinity and then treating that line as ordinary. An algebraic model for doing projective geometry in the style of geometry is given by homogeneous coordinates. In a foundational sense, projective geometry and ordered geometry are elementary since they involve a minimum of axioms and either can be used as the foundation for affine, Projective geometry is not ordered and so it is a distinct foundation for geometry
38.
Pierre de Fermat
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He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermats principle for light propagation and his Fermats Last Theorem in number theory, Fermat was born in the first decade of the 17th century in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Dominique Fermat, was a leather merchant. Pierre had one brother and two sisters and was almost certainly brought up in the town of his birth, there is little evidence concerning his school education, but it was probably at the Collège de Navarre in Montauban. He attended the University of Orléans from 1623 and received a bachelor in law in 1626. In Bordeaux he began his first serious mathematical researches, and in 1629 he gave a copy of his restoration of Apolloniuss De Locis Planis to one of the mathematicians there, there he became much influenced by the work of François Viète. In 1630, he bought the office of a councillor at the Parlement de Toulouse, one of the High Courts of Judicature in France and he held this office for the rest of his life. Fermat thereby became entitled to change his name from Pierre Fermat to Pierre de Fermat, fluent in six languages, Fermat was praised for his written verse in several languages and his advice was eagerly sought regarding the emendation of Greek texts. He communicated most of his work in letters to friends, often little or no proof of his theorems. In some of these letters to his friends he explored many of the ideas of calculus before Newton or Leibniz. Fermat was a trained lawyer making mathematics more of a hobby than a profession, nevertheless, he made important contributions to analytical geometry, probability, number theory and calculus. Secrecy was common in European mathematical circles at the time and this naturally led to priority disputes with contemporaries such as Descartes and Wallis. Anders Hald writes that, The basis of Fermats mathematics was the classical Greek treatises combined with Vietas new algebraic methods, Fermats pioneering work in analytic geometry was circulated in manuscript form in 1636, predating the publication of Descartes famous La géométrie. This manuscript was published posthumously in 1679 in Varia opera mathematica, in these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature. Fermat was the first person known to have evaluated the integral of power functions. With his method, he was able to reduce this evaluation to the sum of geometric series, the resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus. In number theory, Fermat studied Pells equation, perfect numbers, amicable numbers and it was while researching perfect numbers that he discovered Fermats little theorem. Fermat developed the two-square theorem, and the polygonal number theorem, although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived
39.
Probability theory
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Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. It is not possible to predict precisely results of random events, two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, a great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics. Christiaan Huygens published a book on the subject in 1657 and in the 19th century, initially, probability theory mainly considered discrete events, and its methods were mainly combinatorial. Eventually, analytical considerations compelled the incorporation of continuous variables into the theory and this culminated in modern probability theory, on foundations laid by Andrey Nikolaevich Kolmogorov. Kolmogorov combined the notion of space, introduced by Richard von Mises. This became the mostly undisputed axiomatic basis for modern probability theory, most introductions to probability theory treat discrete probability distributions and continuous probability distributions separately. The more mathematically advanced measure theory-based treatment of probability covers the discrete, continuous, consider an experiment that can produce a number of outcomes. The set of all outcomes is called the space of the experiment. The power set of the space is formed by considering all different collections of possible results. For example, rolling an honest die produces one of six possible results, one collection of possible results corresponds to getting an odd number. Thus, the subset is an element of the set of the sample space of die rolls. In this case, is the event that the die falls on some odd number, If the results that actually occur fall in a given event, that event is said to have occurred. Probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results be assigned a value of one, the probability that any one of the events, or will occur is 5/6. This is the same as saying that the probability of event is 5/6 and this event encompasses the possibility of any number except five being rolled. The mutually exclusive event has a probability of 1/6, and the event has a probability of 1, discrete probability theory deals with events that occur in countable sample spaces. Modern definition, The modern definition starts with a finite or countable set called the sample space, which relates to the set of all possible outcomes in classical sense, denoted by Ω
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Social science
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Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society. It in turn has many branches, each of which is considered a social science, the social sciences include economics, political science, human geography, demography, psychology, sociology, anthropology, archaeology, jurisprudence, history, and linguistics. The term is sometimes used to refer specifically to the field of sociology. A more detailed list of sub-disciplines within the sciences can be found at Outline of social science. Positivist social scientists use methods resembling those of the sciences as tools for understanding society. In modern academic practice, researchers are often eclectic, using multiple methodologies, the term social research has also acquired a degree of autonomy as practitioners from various disciplines share in its aims and methods. Social sciences came forth from the philosophy of the time and were influenced by the Age of Revolutions, such as the Industrial Revolution. The social sciences developed from the sciences, or the systematic knowledge-bases or prescriptive practices, the beginnings of the social sciences in the 18th century are reflected in the grand encyclopedia of Diderot, with articles from Jean-Jacques Rousseau and other pioneers. The growth of the sciences is also reflected in other specialized encyclopedias. The modern period saw social science first used as a distinct conceptual field, Social science was influenced by positivism, focusing on knowledge based on actual positive sense experience and avoiding the negative, metaphysical speculation was avoided. Auguste Comte used the term science sociale to describe the field, taken from the ideas of Charles Fourier, following this period, there were five paths of development that sprang forth in the social sciences, influenced by Comte on other fields. One route that was taken was the rise of social research, large statistical surveys were undertaken in various parts of the United States and Europe. Another route undertaken was initiated by Émile Durkheim, studying social facts, a third means developed, arising from the methodological dichotomy present, in which social phenomena were identified with and understood, this was championed by figures such as Max Weber. The fourth route taken, based in economics, was developed and furthered economic knowledge as a hard science, the last path was the correlation of knowledge and social values, the antipositivism and verstehen sociology of Max Weber firmly demanded this distinction. In this route, theory and prescription were non-overlapping formal discussions of a subject, around the start of the 20th century, Enlightenment philosophy was challenged in various quarters. The development of social science subfields became very quantitative in methodology, examples of boundary blurring include emerging disciplines like social research of medicine, sociobiology, neuropsychology, bioeconomics and the history and sociology of science. Increasingly, quantitative research and qualitative methods are being integrated in the study of action and its implications. In the first half of the 20th century, statistics became a discipline of applied mathematics
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Galileo Galilei
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Galileo Galilei was an Italian polymath, astronomer, physicist, engineer, philosopher, and mathematician. He played a role in the scientific revolution of the seventeenth century. Galileo also worked in applied science and technology, inventing an improved military compass, Galileos championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of a stellar parallax. He was tried by the Inquisition, found vehemently suspect of heresy and he spent the rest of his life under house arrest. He has been called the father of observational astronomy, the father of modern physics, the father of scientific method, and the father of science. Galileo was born in Pisa, Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia, three of Galileos five siblings survived infancy. The youngest, Michelangelo, also became a noted lutenist and composer although he contributed to financial burdens during Galileos young adulthood, Michelangelo was unable to contribute his fair share of their fathers promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo to support his musical endeavours and these financial burdens may have contributed to Galileos early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence and he then was educated in the Vallombrosa Abbey, about 30 km southeast of Florence. Galileo Bonaiuti was buried in the church, the Basilica of Santa Croce in Florence. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents surname, hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name Galileo derives from the Latin Galilaeus, meaning of Galilee, the biblical roots of Galileos name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair, one of Galileos opponents, in it he made a point of quoting Acts 1,11, Ye men of Galilee, why stand ye gazing up into heaven. Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba and they had two daughters, Virginia and Livia, and a son, Vincenzo. Their only worthy alternative was the religious life, both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent and she died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life, Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri
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Aristotle
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Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, at seventeen or eighteen years of age, he joined Platos Academy in Athens and remained there until the age of thirty-seven. Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books and he believed all peoples concepts and all of their knowledge was ultimately based on perception. Aristotles views on natural sciences represent the groundwork underlying many of his works, Aristotles views on physical science profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, some of Aristotles zoological observations, such as on the hectocotyl arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known study of logic, which was incorporated in the late 19th century into modern formal logic. Aristotle was well known among medieval Muslim intellectuals and revered as The First Teacher and his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotles philosophy continue to be the object of academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his style as a river of gold – it is thought that only around a third of his original output has survived. Aristotle, whose means the best purpose, was born in 384 BC in Stagira, Chalcidice. His father Nicomachus was the physician to King Amyntas of Macedon. Aristotle was orphaned at a young age, although there is little information on Aristotles childhood, he probably spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy. At the age of seventeen or eighteen, Aristotle moved to Athens to continue his education at Platos Academy and he remained there for nearly twenty years before leaving Athens in 348/47 BC. Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor, there, he traveled with Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island. Aristotle married Pythias, either Hermiass adoptive daughter or niece and she bore him a daughter, whom they also named Pythias. Soon after Hermias death, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander in 343 BC, Aristotle was appointed as the head of the royal academy of Macedon. During that time he gave not only to Alexander
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Catholicism
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The use of terms catholicism and catholicity is closely related to the use of term Catholic Church. The earliest evidence of the use of term is the Letter to the Smyrnaeans that Ignatius of Antioch wrote in about 108 to Christians in Smyrna. In 380, Emperor Theodosius I limited use of the term Catholic Christian exclusively to those who followed the faith as Pope Damasus I of Rome. Numerous other early writers including Cyril of Jerusalem, Augustine of Hippo further developed the use of the term catholic in relation to Christianity. In Christian theology, and specially in ecclesiology, terms Catholicism, when used with small c, terms catholicism and catholicity generally designate theological doctrine of the catholicity of the Church without denominational connotations. A common belief in Catholicism is institutional continuity with the early Christian church founded by Jesus Christ, many churches or communions of churches identify singularly or collectively as the authentic church. The Bishop of Rome was also considered to have the right to convene ecumenical councils, when the Imperial capital moved to Constantinople, Romes influence was sometimes challenged. The first great rupture in the Church followed this Council and they are often called Ancient Oriental Churches. The next major break was after the Council of Chalcedon and this Council repudiated Eutychian Monophysitism which stated that the divine nature completely subsumed the human nature in Christ. This Council declared that Christ, though one person, exhibited two natures without confusion, without change, without division, without separation and thus is both fully God and fully human, the next great rift within Christianity was in the 11th century. This division between the Western Church and the Eastern Church is called the East–West Schism, several eastern churches reunited, constituting some of the Eastern Catholic Churches. Liturgical and canonical practices vary between all these particular Churches constituting the Roman and Eastern Catholic Churches, in all these cases the beliefs and practices of Catholicism would be identical with the beliefs and practices of the Church in question. However, in Roman Catholicism, the term catholic is understood as to cover those who recognize and are in standing with the Magisterium. The sense given to the word by those who use it to distinguish their position from a Calvinistic or Puritan form of Protestantism. It is then meaningful to attempt to draw up a list of common characteristic beliefs, the Roman Catholic Church includes the 23 rites who recognize the Magisterium. Belief in the Real Presence of Christ in the Eucharist, the belief that Christ is made manifest in the elements of Holy Communion, possession of the threefold ordained ministry of Bishops, Priests and Deacons. Belief that the Church is the vessel and deposit of the fullness of the teachings of Jesus and this teaching is preserved in both written scripture and in unwritten tradition, neither being independent of the other. A belief in the necessity and efficacy of sacraments, liturgical and personal use of the Sign of the Cross The use of sacred images, candles, vestments and music, and often incense and water, in worship
. doi:10.4169/amer.math.monthly.118.06.549.
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"Blaise Pascal". Catholic Encyclopedia. 1913.
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