1.
Beauvais
–
Beauvais archaic English, Beawayes, Beeway, Boway, is a city and commune in northern France. It serves as the capital of the Oise département, in the Hauts-de-France region, Beauvais is located approximately 75 kilometres from Paris. The residents of the city are called Beauvaisiens, together with its suburbs and satellite towns, the metropolitan area of Beauvais has a population of 103,885. Beauvais was known to the Romans by the Gallo-Roman name of Caesaromagus, the post-Renaissance Latin rendering is Bellovacum from the Belgic tribe the Bellovaci, whose capital it was. In the ninth century it became a countship, which about 1013 passed to the bishops of Beauvais, who became peers of France from the twelfth century. At the coronations of kings the Bishop of Beauvais wore the royal mantle and went, with the Bishop of Langres and its name is Gaulish for place where judgements are made, from *bratu-spantion. Some say that Bratuspantium is Beauvais, others theorize that it is Vendeuil-Caply or Bailleul sur Thérain. From 1004 to 1037, the Count of Beauvais was Odo II, in a charter dated 1056/1060, Eudo of Brittany granted land in pago Belvacensi to the Abbey of Angers Saint-Aubin. In 1346 the town had to defend itself against the English, the hoard, which contained a variety of rare and extremely rare Anglo-Norman pennies, English and foreign coins, was reputed to have been found in or near Paris. Beauvais was extensively damaged during World War I and again in World War II, much of the older part of the city was all but destroyed, and the cathedral badly damaged before being liberated by British forces on 30 August 1944. Beauvais lies at the foot of wooded hills on the bank of the Thérain at its confluence with the Avelon. Its ancient ramparts have been destroyed, and it is now surrounded by boulevards, in addition, there are spacious promenades in the north-east of the town. The average annual temperature is 9. 9°C, the annual average of 1669 hours. Hills Bray are provided to the precipitation of Beauvais, the precipitation is 669 mm on average per year, while it is 800 mm on average per year in Bray. However, the frequency of rainfall is high, the average number of days per year above the precipitation of a 1 mm is 116 days, or every third day. The fog is present, it is estimated at about 55 days a year. The department is affected by 41 days of average wind year, the citys cathedral, dedicated to Saint Peter, in some respects the most daring achievement of Gothic architecture, consists only of a transept and quire with apse and seven apse-chapels. The vaulting in the interior exceeds 46 m or 150 feet in height, the cathedral underwent a major repair and restoration process in 2008
2.
Paris
–
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
3.
France
–
France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established. The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural, political, and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and later dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity. In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is also a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks
4.
Roberval balance
–
The Roberval balance is a weighing scale presented to the French Academy of Sciences by the French mathematician Gilles Personne de Roberval in 1669. In this scale, two identical horizontal beams are attached, one directly above the other, to a vertical column, on each side, both horizontal beams are attached to a vertical beam. The six attachment points are pivots, two horizontal plates, suitable for placing objects to be weighed, are fixed to the top of the two vertical beams. An arrow on the horizontal beam and a mark on the vertical column may be added to aid in leveling the scale. The object to be weighed is placed on one plate, and calibrated masses are added to, the mass of the object is equal to the mass of the calibrated masses regardless of where on the plates items are placed. The vertical column supporting a plate with an offset weight must be in axial compression, the flexural force in the column is taken by a pair of equal and opposite forces in the horizontal beams. So if the weight is towards the outside of the platform, further from the centre of the scales, the top beam will be in axial tension. These tensions and compressions are carried by horizontal reactions from the central supports, certain presumptions are made in a theoretical Roberval balance. This tension will manifest as an increase in static friction and these effects must be distinguished from the feedback loops and the friction of the pivot points mentioned above, as those are undesirable effects caused by design weaknesses/ flaws. If the arms finalize in a position, this only indicates friction in the pivot points somewhere. A well-made and precise Roberval balance with a center of gravity never actually balances. The Roberval balance is less accurate and more difficult to manufacture than a beam balance with suspended plates. The beam balance, however, has the significant disadvantage of requiring suspensory strings, chains, for over three hundred years the Roberval balance has instead been popular for applications requiring convenience and only moderate accuracy, notably in retail trade. Well known manufacturers of Roberval balances include W & T Avery Ltd. and George Salter & Co. Ltd. in the United Kingdom, henry Troemner, who designed scales for the United States Department of Treasury, was the first American to use the design. J. T. Graham, Scales and Balances, Shire Publications, Aylesbury ISBN 0-85263-547-8 Bruno Kisch, Scales, a Historical Outline, Yale University Press, New Haven ISBN 0-300-00630-6 The Roberval Balance
5.
Trochoid
–
A trochoid is the curve described by a fixed point on a circle as it rolls along a straight line. The cycloid is a member of the trochoid family. The word trochoid was coined by Gilles de Roberval, parametric equations of the trochoid for which L is the x-axis are x = a θ − b sin y = a − b cos where θ is the variable angle through which the circle rolls. If P lies inside the circle, on its circumference, or outside, a curtate trochoid is traced by a pedal when a bicycle is pedaled along a straight line. A prolate trochoid is traced by the tip of a paddle when a boat is driven with constant velocity by paddle wheels, a common trochoid, also called a cycloid, has cusps at the points where P touches the L. In the case of a path, one full rotation coincides with one period of a periodic locus. The number of cusps given above also hold true for any epitrochoid and hypotrochoid, list of periodic functions Epitrochoid Hypotrochoid Cycloid Cyclogon Spirograph Trochoidal wave Online experiments with the Trochoid using JSXGraph
6.
Mathematician
–
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
7.
University of Paris
–
The University of Paris, metonymically known as the Sorbonne, was a university in Paris, France. Emerging around 1150 as an associated with the cathedral school of Notre Dame de Paris. Vast numbers of popes, royalties, scientists and intellectuals were educated at the University of Paris, following the turbulence of the French Revolution, education was suspended in 1793 whereafter its faculties were partly reorganised by Napoleon as the University of France. In 1896, it was renamed again to the University of Paris, in 1970, following the May 1968 events, the university was divided into 13 autonomous universities. Others, like Panthéon-Sorbonne University, chose to be multidisciplinary, in 1150, the future University of Paris was a student-teacher corporation operating as an annex of the Notre-Dame cathedral school. The university had four faculties, Arts, Medicine, Law, the Faculty of Arts was the lowest in rank, but also the largest, as students had to graduate there in order to be admitted to one of the higher faculties. The students were divided into four nationes according to language or regional origin, France, Normandy, Picardy, the last came to be known as the Alemannian nation. Recruitment to each nation was wider than the names might imply, the faculty and nation system of the University of Paris became the model for all later medieval universities. Under the governance of the Church, students wore robes and shaved the tops of their heads in tonsure, students followed the rules and laws of the Church and were not subject to the kings laws or courts. This presented problems for the city of Paris, as students ran wild, students were often very young, entering the school at age 13 or 14 and staying for 6 to 12 years. Three schools were especially famous in Paris, the palatine or palace school, the school of Notre-Dame, the decline of royalty brought about the decline of the first. The other two were ancient but did not have much visibility in the early centuries, the glory of the palatine school doubtless eclipsed theirs, until it completely gave way to them. These two centres were much frequented and many of their masters were esteemed for their learning, the first renowned professor at the school of Ste-Geneviève was Hubold, who lived in the tenth century. Not content with the courses at Liège, he continued his studies at Paris, entered or allied himself with the chapter of Ste-Geneviève, and attracted many pupils via his teaching. Distinguished professors from the school of Notre-Dame in the century include Lambert, disciple of Fulbert of Chartres, Drogo of Paris, Manegold of Germany. Three other men who added prestige to the schools of Notre-Dame and Ste-Geneviève were William of Champeaux, Abélard, humanistic instruction comprised grammar, rhetoric, dialectics, arithmetic, geometry, music, and astronomy. To the higher instruction belonged dogmatic and moral theology, whose source was the Scriptures and it was completed by the study of Canon law. The School of Saint-Victor arose to rival those of Notre-Dame and Ste-Geneviève and it was founded by William of Champeaux when he withdrew to the Abbey of Saint-Victor
8.
Royal College of France
–
The Collège de France, founded in 1530, is a renowned higher education and research establishment in France. It is located in Paris, in the 5th arrondissement, or Latin Quarter, the Collège does not grant degrees. Each professor is required to give lectures where attendance is free, professors, about 50 in number, are chosen by the professors themselves, from a variety of disciplines, in both science and the humanities. The Collège has research laboratories and one of the best research libraries of Europe, with focusing on history with rare books, humanities, social sciences and also chemistry. As of June 2009, over 650 audio podcasts of Collège de France lectures are available on iTunes, some are also available in English and Chinese. Similarly, the Collège de Frances website hosts several videos of classes, the classes are followed by various students, from senior researchers to PhD or master students, or even bachelor students. Moreover, the leçons inaugurales are important events in Paris intellectual and social life, the Collège was established by King Francis I of France, modeled after the Collegium Trilingue in Louvain, at the urging of Guillaume Budé. Of humanist inspiration, the school was established as an alternative to the Sorbonne to promote such disciplines as Hebrew, Ancient Greek, initially called Collège Royal, and later Collège des Trois Langues, Collège National, and Collège Impérial, it was named Collège de France in 1870. Two chairs are reserved for scholars who are invited to give lectures. Notable faculty members include Serge Haroche, awarded with Nobel Prize in Physics in 2012, notably,8 Fields medal winners have been affiliated with the College. Past faculty include, Institut de France Raymond Couvègnes Collège de France website, English home page
9.
Marin Mersenne
–
Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the father of acoustics. Mersenne, an ordained priest, had contacts in the scientific world and has been called the center of the world of science. Marin Mersenne was born of peasant parents near Oizé, Maine and he was educated at Le Mans and at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars, and, after studying theology, between 1614 and 1618, he taught theology and philosophy at Nevers, but he returned to Paris and settled at the convent of LAnnonciade in 1620. There he studied mathematics and music and met with other kindred spirits such as René Descartes, Étienne Pascal, Pierre Petit, Gilles de Roberval and he corresponded with Giovanni Doni, Constantijn Huygens, Galileo Galilei, and other scholars in Italy, England and the Dutch Republic. He was a defender of Galileo, assisting him in translations of some of his mechanical works. For four years, Mersenne devoted himself entirely to philosophic and theological writing and it is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus and he taught theology and philosophy at Nevers and Paris. He was not afraid to cause disputes among his friends in order to compare their views. In 1635 Mersenne met with Tommaso Campanella, but concluded that he could teach nothing in the sciences but still he has a good memory, Mersenne asked if René Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640,1641 and 1645, in 1643–1644 Mersenne also corresponded with the German Socinian Marcin Ruar concerning the Copernican ideas of Pierre Gassendi, finding Ruar already a supporter of Gassendis position. Among his correspondents were Descartes, Galilei, Roberval, Pascal, Beeckman and he died September 1 through complications arising from a lung abscess. Some history scientists suggest he died for having drunk a huge quantity of water, along with Descartes. It was written as a commentary on the Book of Genesis, at first sight the book appears to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a polemic against magical and divinatory arts, cabalism and he mentions Martin Del Rios Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi, a popular amongst Renaissance neo-platonists. Whilst allowing for an interpretation of the Cabala, he wholeheartedly condemned its magical application—particularly to angelology. He also criticises Pico della Mirandola, Cornelius Agrippa and Francesco Giorgio with Robert Fludd as his main target, Fludd responded with Sophia cum moria certamen, wherein Fludd admits his involvement with the Rosicrucians
10.
Isaac Barrow
–
His work centered on the properties of the tangent, Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrows, and Newton went on to develop calculus in a modern form and he was the son of Thomas Barrow, a linen draper by trade. In 1624, Thomas married Ann, daughter of William Buggin of North Cray, Kent and it appears that Barrow was the only child of this union—certainly the only child to survive infancy. Ann died around 1634, and the father sent the lad to his grandfather, Isaac. Within two years, however, Thomas remarried, the new wife was Katherine Oxinden, sister of Henry Oxinden of Maydekin, Kent. From this marriage, he had at least one daughter, Elizabeth, and a son, Thomas, who apprenticed to Edward Miller, skinner and his uncle and namesake Isaac Barrow, afterwards Bishop of St Asaph, was a Fellow of Peterhouse. He took to hard study, distinguishing himself in classics and mathematics, after taking his degree in 1648 and he spent the next four years travelling across France, Italy, Smyrna and Constantinople, and after many adventures returned to England in 1659. He was known for his courageousness, particularly noted is the occasion of his having saved the ship to which he were upon by the merits of his own prowess, from capture by pirates. He is described as low in stature, lean, and of a pale complexion, slovenly in his dress, an altogether impressive personage of the time, having lived a blameless life into which he exercised conduct with due care and conscientiousness. On the Restoration in 1660, he was ordained and appointed to the Regius Professorship of Greek at Cambridge, in 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favour of Isaac Newton, about this time, Barrow composed his Expositions of the Creed, The Lords Prayer, Decalogue, and Sacraments. For the remainder of his life he devoted himself to the study of divinity and he was made a D. D. by Royal mandate in 1670, and two years later Master of Trinity College, where he founded the library, and held the post until his death. Barrows character as a man was in all respects worthy of his great talents and he died unmarried in London at the early age of 46, and was buried at Westminster Abbey. His earliest work was an edition of the Elements of Euclid, which he issued in Latin in 1655. His lectures, delivered in 1664,1665, and 1666, were published in 1683 under the title Lectiones Mathematicae and his lectures for 1667 were published in the same year, and suggest the analysis by which Archimedes was led to his chief results. In 1669 he issued his Lectiones Opticae et Geometricae and this, which is his most important work in mathematics, was republished with a few minor alterations in 1674. In 1675 he published an edition with comments of the first four books of the On Conic Sections of Apollonius of Perga
11.
Pierre de Fermat
–
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
12.
Blaise Pascal
–
Blaise Pascal was a French mathematician, physicist, inventor, writer and Christian philosopher. He was a prodigy who was educated by his father. Pascal also wrote in defence of the scientific method, in 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and 50 prototypes, he built 20 finished machines over the following 10 years, following Galileo Galilei and Torricelli, in 1647, he rebutted Aristotles followers who insisted that nature abhors a vacuum. Pascals results caused many disputes before being accepted, in 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. Following a religious experience in late 1654, he began writing works on philosophy. His two most famous works date from this period, the Lettres provinciales and the Pensées, the set in the conflict between Jansenists and Jesuits. In that year, he wrote an important treatise on the arithmetical triangle. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids, Pascal had poor health, especially after the age of 18, and he died just two months after his 39th birthday. Pascal was born in Clermont-Ferrand, which is in Frances Auvergne region and he lost his mother, Antoinette Begon, at the age of three. His father, Étienne Pascal, who also had an interest in science and mathematics, was a local judge, Pascal had two sisters, the younger Jacqueline and the elder Gilberte. In 1631, five years after the death of his wife, the newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, the young Pascal showed an amazing aptitude for mathematics and science. Particularly of interest to Pascal was a work of Desargues on conic sections and it states that if a hexagon is inscribed in a circle then the three intersection points of opposite sides lie on a line. Pascals work was so precocious that Descartes was convinced that Pascals father had written it, in France at that time offices and positions could be—and were—bought and sold. In 1631 Étienne sold his position as president of the Cour des Aides for 65,665 livres. The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, but in 1638 Richelieu, desperate for money to carry on the Thirty Years War, defaulted on the governments bonds. Suddenly Étienne Pascals worth had dropped from nearly 66,000 livres to less than 7,300 and it was only when Jacqueline performed well in a childrens play with Richelieu in attendance that Étienne was pardoned
13.
La Rochelle
–
La Rochelle is a city in southwestern France and a seaport on the Bay of Biscay, a part of the Atlantic Ocean. It is the capital of the Charente-Maritime department, the city is connected to the Île de Ré by a 2. 9-kilometre bridge completed on 19 May 1988. Its harbour opens into a protected strait, the Pertuis dAntioche, the area of La Rochelle was occupied in antiquity by the Gallic tribe of the Santones, who gave their name to the nearby region of Saintonge and the city of Saintes. The Romans subsequently occupied the area, where they developed salt production along the coast as well as wine production, roman villas have been found at Saint-Éloi and at Les Minimes, as well as salt evaporation ponds dating from the same period. La Rochelle was founded during the 10th century and became an important harbour in the 12th century, in 1137, Guillaume X to all intents and purposes made La Rochelle a free port and gave it the right to establish itself as a commune. Fifty years later Eleanor of Aquitaine upheld the communal charter promulgated by her father, and for the first time in France, Guillaume was assisted in his responsibilities by 24 municipal magistrates, and 75 notables who had jurisdiction over the inhabitants. During the Plantagenet control of the city in 1185, Henry II had the Vauclair castle built, the main activities of the city were in the areas of maritime commerce and trade, especially with England, the Netherlands and Spain. In 1196, a wealthy bourgeois named Alexandre Auffredi sent a fleet of seven ships to Africa to tap the riches of the continent. He went bankrupt and went into poverty as he waited for the return of his ships, the Knights Templar had a strong presence in La Rochelle since before the time of Eleanor of Aquitaine, who exempted them from duties and gave them mills in her 1139 Charter. La Rochelle was for the Templars their largest base on the Atlantic Ocean, from La Rochelle, they were able to act as intermediaries in trade between England and the Mediterranean. The fleet allegedly left laden with knights and treasures just before the issue of the warrant for the arrest of the Order in October 1307, during the Hundred Years War in 1360, following the Treaty of Bretigny La Rochelle again came under the rule of the English monarch. La Rochelle however expelled the English in June 1372, following the naval Battle of La Rochelle, the French and Spanish decisively defeated the English, securing French control of the Channel for the first time since the Battle of Sluys in 1340. The naval battle of La Rochelle was one of the first cases of the use of handguns on warships, having recovered freedom, La Rochelle refused entry to Du Guesclin, until Charles V recognized the privileges of the city in November 1372. In 1402, the French adventurer Jean de Béthencourt left La Rochelle, until the 15th century, La Rochelle was to be the largest French harbour on the Atlantic coast, dealing mainly in wine, salt and cheese. During the Renaissance, La Rochelle adopted Protestant ideas, calvinism started to be propagated in the region of La Rochelle, resulting in its suppression through the establishment of Cours présidiaux tribunals by Henry II. An early result of this was the burning at the stake of two heretics in La Rochelle in 1552. On the initiative of Gaspard de Coligny, the Calvinists attempted to colonize the New World to find a new home for their religion, with the likes of Pierre Richier and Jean de Léry. After the short-lived attempt of France Antarctique, they failed to establish a colony in Brazil and he has been described, by Lancelot Voisin de La Popelinière, as le père de léglise de La Rochelle
14.
Infinitesimal calculus
–
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two branches, differential calculus, and integral calculus, these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the notions of convergence of infinite sequences. Generally, modern calculus is considered to have developed in the 17th century by Isaac Newton. Today, calculus has widespread uses in science, engineering and economics, Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, Calculus has historically been called the calculus of infinitesimals, or infinitesimal calculus. Calculus is also used for naming some methods of calculation or theories of computation, such as calculus, calculus of variations, lambda calculus. The ancient period introduced some of the ideas that led to integral calculus, the method of exhaustion was later discovered independently in China by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th century AD, Zu Gengzhi, son of Zu Chongzhi, indian mathematicians gave a non-rigorous method of a sort of differentiation of some trigonometric functions. In the Middle East, Alhazen derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, Cavalieris work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first. The formal study of calculus brought together Cavalieris infinitesimals with the calculus of finite differences developed in Europe at around the same time, pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. The combination was achieved by John Wallis, Isaac Barrow, and James Gregory, in other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the Taylor series. He did not publish all these discoveries, and at this time infinitesimal methods were considered disreputable. These ideas were arranged into a calculus of infinitesimals by Gottfried Wilhelm Leibniz. He is now regarded as an independent inventor of and contributor to calculus, unlike Newton, Leibniz paid a lot of attention to the formalism, often spending days determining appropriate symbols for concepts. Leibniz and Newton are usually credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the used in calculus today
15.
Limit (mathematics)
–
In mathematics, a limit is the value that a function or sequence approaches as the input or index approaches some value. Limits are essential to calculus and are used to define continuity, derivatives, the concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit is usually written as lim n → c f = L and is read as the limit of f of n as n approaches c equals L. Here lim indicates limit, and the fact that function f approaches the limit L as n approaches c is represented by the right arrow, suppose f is a real-valued function and c is a real number. Intuitively speaking, the lim x → c f = L means that f can be made to be as close to L as desired by making x sufficiently close to c. The first inequality means that the distance x and c is greater than 0 and that x ≠ c, while the second indicates that x is within distance δ of c. Note that the definition of a limit is true even if f ≠ L. Indeed. Now since x +1 is continuous in x at 1, we can now plug in 1 for x, in addition to limits at finite values, functions can also have limits at infinity. In this case, the limit of f as x approaches infinity is 2, in mathematical notation, lim x → ∞2 x −1 x =2. Consider the following sequence,1.79,1.799,1.7999 and it can be observed that the numbers are approaching 1.8, the limit of the sequence. Formally, suppose a1, a2. is a sequence of real numbers, intuitively, this means that eventually all elements of the sequence get arbitrarily close to the limit, since the absolute value | an − L | is the distance between an and L. Not every sequence has a limit, if it does, it is called convergent, one can show that a convergent sequence has only one limit. The limit of a sequence and the limit of a function are closely related, on one hand, the limit as n goes to infinity of a sequence a is simply the limit at infinity of a function defined on the natural numbers n. On the other hand, a limit L of a function f as x goes to infinity, if it exists, is the same as the limit of any sequence a that approaches L. Note that one such sequence would be L + 1/n, in non-standard analysis, the limit of a sequence can be expressed as the standard part of the value a H of the natural extension of the sequence at an infinite hypernatural index n=H. Thus, lim n → ∞ a n = st , here the standard part function st rounds off each finite hyperreal number to the nearest real number. This formalizes the intuition that for very large values of the index. Conversely, the part of a hyperreal a = represented in the ultrapower construction by a Cauchy sequence, is simply the limit of that sequence
16.
Quadrature (mathematics)
–
In mathematics, quadrature is a historical term which means determining area. Quadrature problems served as one of the sources of problems in the development of calculus. By Greek tradition, these constructions had to be performed using only a compass, for a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side x = a b. A similar geometrical construction solves the problems of quadrature of a parallelogram, problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge was proved in the 19th century to be impossible, nevertheless, for some figures a quadrature can be performed. The quadratures of the surface of a sphere and a parabola segment discovered by Archimedes became the highest achievement of analysis in antiquity, the area of the surface of a sphere is equal to four times the area of the circle formed by a great circle of this sphere. The area of a segment of a parabola determined by a line cutting it is 4/3 the area of a triangle inscribed in this segment. For the proof of these results, Archimedes used the method of exhaustion of Eudoxus, in medieval Europe, quadrature meant the calculation of area by any method. Most often the method of indivisibles was used, it was less rigorous than the geometric constructions of the Greeks, but it was simpler and more powerful. John Wallis algebrised this method, he wrote in his Arithmetica Infinitorum some series which are equivalent to what is now called the definite integral, isaac Barrow and James Gregory made further progress, quadratures for some algebraic curves and spirals. Christiaan Huygens successfully performed a quadrature of the area of some solids of revolution. The quadrature of the hyperbola by Saint-Vincent and de Sarasa provided a new function, with the invention of integral calculus came a universal method for area calculation. Gaussian quadrature Hyperbolic angle Numerical integration Quadrance Quadratrix Tanh-sinh quadrature Boyer, a History of Mathematics, 2nd ed. rev. by Uta C. Babin translator, William Alexander Myers editor, link from HathiTrust, christoph Scriba Gregorys Converging Double Sequence, a new look at the controversy between Huygens and Gregory over the analytical quadrature of the circle, Historia Mathematica 10, 274–85
17.
Cubature
–
This article focuses on calculation of definite integrals. The term numerical quadrature is more or less a synonym for numerical integration, Some authors refer to numerical integration over more than one dimension as cubature, others take quadrature to include higher-dimensional integration. The basic problem in numerical integration is to compute an approximate solution to a definite integral ∫ a b f d x to a degree of accuracy. If f is a smooth function integrated over a number of dimensions. The term numerical integration first appears in 1915 in the publication A Course in Interpolation, Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area and that is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates and this construction must be performed only by means of compass and straightedge. The ancient Babylonians used the trapezoidal rule to integrate the motion of Jupiter along the ecliptic, for a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side x = a b. For this purpose it is possible to use the fact, if we draw the circle with the sum of a and b as the diameter. The similar geometrical construction solves a problem of a quadrature for a parallelogram, problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge had been proved in the 19th century to be impossible, nevertheless, for some figures a quadrature can be performed. The quadratures of a surface and a parabola segment done by Archimedes became the highest achievement of the antique analysis. The area of the surface of a sphere is equal to quadruple the area of a circle of this sphere. The area of a segment of the cut from it by a straight line is 4/3 the area of the triangle inscribed in this segment. For the proof of the results Archimedes used the Method of exhaustion of Eudoxus, in medieval Europe the quadrature meant calculation of area by any method. More often the Method of indivisibles was used, it was less rigorous, john Wallis algebrised this method, he wrote in his Arithmetica Infinitorum series that we now call the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress, quadratures for some algebraic curves, christiaan Huygens successfully performed a quadrature of some Solids of revolution
18.
Bonaventura Cavalieri
–
Bonaventura Francesco Cavalieri was an Italian mathematician and a Jesuat. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, Cavalieris principle in geometry partially anticipated integral calculus. Born in Milan, Cavalieri studied theology in the monastery of San Gerolamo in Milan and he published eleven books, his first being published in 1632. He worked on the problems of optics and motion and his astronomical and astrological work remained marginal to these main interests, though his last book, Trattato della ruota planetaria perpetua, was dedicated to the former. He was introduced to Galileo Galilei through academic and ecclesiastical contacts, Galileo exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas, and Cavalieri would write at least 112 letters to Galileo. Galileo said of Cavalieri, few, if any, since Archimedes, have delved as far and he also benefited from the patronage of Cesare Marsili. Cavalieris first book was Lo Specchio Ustorio, overo, Trattato delle settioni coniche, in this book he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and various combinations of these mirrors. The work was purely theoretical since the needed mirrors could not be constructed with the technologies of the time, in this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. Such elements are called indivisibles respectively of area and volume and provide the building blocks of Cavalieris method, as an application, he computed the areas under the curves y = x n – an early integral – which is known as Cavalieris quadrature formula. Cavalieri is known for Cavalieris principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal, two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. Cavalieri also constructed a hydraulic pump for his monastery and published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography. According to Gilles-Gaston Granger, Cavalieri belongs with Newton, Leibniz, Pascal, Wallis, the lunar crater Cavalerius is named for Cavalieri. 31 of Amici e corrispondenti di Galileo Galilei, C, online texts by Cavalieri, Lo specchio ustorio, overo, Trattato delle settioni coniche. Short biography on bookrags. com Fabroni, Angelo, vitae Italorum doctrina excellentium qui saeculis XVII. Modern mathematical or historical research, Infinitesimal Calculus On its historical development, in Encyclopaedia of Mathematics, more information about the method of Cavalieri Cavalieri Integration
19.
Cavalieri's principle
–
If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas. 3-dimensional case, Suppose two regions in three-space are included two parallel planes. If every plane parallel to two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes. In the other direction, Cavalieris principle grew out of the ancient Greek method of exhaustion, Cavalieris principle was originally called the method of indivisibles, the name it was known by in Renaissance Europe. Archimedes was able to find the volume of a sphere given the volumes of a cone, in the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a spheres volume. The transition from Cavalieris indivisibles to Evangelista Torricellis and John Walliss infinitesimals was an advance in the history of the calculus. The indivisibles were entities of codimension 1, so that a figure was thought as made out of an infinity of 1-dimensional lines. Meanwhile, infinitesimals were entities of the dimension as the figure they make up, thus. Applying the formula for the sum of a progression, Wallis computed the area of a triangle by partitioning it into infinitesimal parallelograms of width 1/∞. If one knows that the volume of a cone is 13, then one can use Cavalieris principle to derive the fact that the volume of a sphere is 43 π r 3, where r is the radius. That is done as follows, Consider a sphere of radius r, within the cylinder is the cone whose apex is at the center of the sphere and whose base is the base of the cylinder. By the Pythagorean theorem, the plane located y units above the equator intersects the sphere in a circle of area π, the area of the planes intersection with the part of the cylinder that is outside of the cone is also π. The aforementioned volume of the cone is 13 of the volume of the cylinder, Therefore the volume of the upper half of the sphere is 23 of the volume of the cylinder. The volume of the cylinder is base × height = π r 2 ⋅ r = π r 3 Therefore the volume of the upper half-sphere is π r 3 and that of the whole sphere is π r 3. One may initially establish it in a case by partitioning the interior of a triangular prism into three pyramidal components of equal volumes. One may show the equality of three volumes by means of Cavalieris principle. The ancient Greeks used various techniques such as Archimedess mechanical arguments or method of exhaustion to compute these volumes. The cross-section of the ring is a plane annulus, whose area is the difference between the areas of two circles
20.
Tangent
–
In geometry, the tangent line to a plane curve at a given point is the straight line that just touches the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve, a similar definition applies to space curves and curves in n-dimensional Euclidean space. Similarly, the tangent plane to a surface at a point is the plane that just touches the surface at that point. The concept of a tangent is one of the most fundamental notions in geometry and has been extensively generalized. The word tangent comes from the Latin tangere, to touch, euclid makes several references to the tangent to a circle in book III of the Elements. In Apollonius work Conics he defines a tangent as being a line such that no other straight line could fall between it and the curve, archimedes found the tangent to an Archimedean spiral by considering the path of a point moving along the curve. Independently Descartes used his method of normals based on the observation that the radius of a circle is always normal to the circle itself and these methods led to the development of differential calculus in the 17th century. Many people contributed, Roberval discovered a method of drawing tangents. René-François de Sluse and Johannes Hudde found algebraic algorithms for finding tangents, further developments included those of John Wallis and Isaac Barrow, leading to the theory of Isaac Newton and Gottfried Leibniz. An 1828 definition of a tangent was a line which touches a curve. This old definition prevents inflection points from having any tangent and it has been dismissed and the modern definitions are equivalent to those of Leibniz who defined the tangent line as the line through a pair of infinitely close points on the curve. The tangent at A is the limit when point B approximates or tends to A, the existence and uniqueness of the tangent line depends on a certain type of mathematical smoothness, known as differentiability. At most points, the tangent touches the curve without crossing it, a point where the tangent crosses the curve is called an inflection point. Circles, parabolas, hyperbolas and ellipses do not have any point, but more complicated curves do have, like the graph of a cubic function. Conversely, it may happen that the curve lies entirely on one side of a line passing through a point on it. This is the case, for example, for a passing through the vertex of a triangle. In convex geometry, such lines are called supporting lines, the geometrical idea of the tangent line as the limit of secant lines serves as the motivation for analytical methods that are used to find tangent lines explicitly. The question of finding the tangent line to a graph, or the tangent line problem, was one of the central questions leading to the development of calculus in the 17th century, suppose that a curve is given as the graph of a function, y = f
21.
Curve
–
In mathematics, a curve is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero, various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows, a curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, a simple example of a curve is the parabola, shown to the right. A large number of curves have been studied in multiple mathematical fields. A closed curve is a curve that forms a path whose starting point is also its ending point—that is, closely related meanings include the graph of a function and a two-dimensional graph. Interest in curves began long before they were the subject of mathematical study and this can be seen in numerous examples of their decorative use in art and on everyday objects dating back to prehistoric times. Curves, or at least their graphical representations, are simple to create, historically, the term line was used in place of the more modern term curve. Hence the phrases straight line and right line were used to distinguish what are called lines from curved lines. For example, in Book I of Euclids Elements, a line is defined as a breadthless length, Euclids idea of a line is perhaps clarified by the statement The extremities of a line are points. Later commentators further classified according to various schemes. For example, Composite lines Incomposite lines Determinate Indeterminate The Greek geometers had studied many kinds of curves. One reason was their interest in solving problems that could not be solved using standard compass. These curves include, The conic sections, deeply studied by Apollonius of Perga The cissoid of Diocles, studied by Diocles, the conchoid of Nicomedes, studied by Nicomedes as a method to both double the cube and to trisect an angle. The Archimedean spiral, studied by Archimedes as a method to trisect an angle, the spiric sections, sections of tori studied by Perseus as sections of cones had been studied by Apollonius. A fundamental advance in the theory of curves was the advent of analytic geometry in the seventeenth century and this enabled a curve to be described using an equation rather than an elaborate geometrical construction. Previously, curves had been described as geometrical or mechanical according to how they were, or supposedly could be, conic sections were applied in astronomy by Kepler. Newton also worked on an example in the calculus of variations
22.
Asymptote
–
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, in some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος which means not falling together, + σύν together + πτωτ-ός fallen. The term was introduced by Apollonius of Perga in his work on conic sections, there are potentially three kinds of asymptotes, horizontal, vertical and oblique asymptotes. For curves given by the graph of a function y = ƒ, vertical asymptotes are vertical lines near which the function grows without bound. Asymptotes convey information about the behavior of curves in the large, the study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis. The idea that a curve may come close to a line without actually becoming the same may seem to counter everyday experience. The representations of a line and a curve as marks on a piece of paper or as pixels on a screen have a positive width. So if they were to be extended far enough they would seem to merge, but these are physical representations of the corresponding mathematical entities, the line and the curve are idealized concepts whose width is 0. Therefore, the understanding of the idea of an asymptote requires an effort of reason rather than experience, consider the graph of the function f =1 x shown to the right. The coordinates of the points on the curve are of the form where x is an other than 0. But no matter how large x becomes, its reciprocal 1 x is never 0, so the curve extends farther and farther upward as it comes closer and closer to the y-axis. Thus, both the x and y-axes are asymptotes of the curve and these ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below. The asymptotes most commonly encountered in the study of calculus are of curves of the form y = ƒ and these can be computed using limits and classified into horizontal, vertical and oblique asymptotes depending on its orientation. Horizontal asymptotes are lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicate they are parallel to the x-axis, vertical asymptotes are vertical lines near which the function grows without bound. Oblique asymptotes are diagonal lines so that the difference between the curve and the line approaches 0 as x tends to +∞ or −∞, more general type of asymptotes can be defined in this case. Only open curves that have some infinite branch, can have an asymptote, no closed curve can have an asymptote
23.
Evangelista Torricelli
–
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
24.
Heliocentrism
–
Heliocentrism is the astronomical model in which the Earth and planets revolve around the Sun at the center of the Solar System. Historically, Heliocentrism was opposed to geocentrism, which placed the Earth at the center, in the following century, Johannes Kepler elaborated upon and expanded this model to include elliptical orbits, and Galileo Galilei presented supporting observations made using a telescope. With the observations of William Herschel, Friedrich Bessel, and others, astronomers realized that the sun, the Ptolemaic system was a sophisticated astronomical system that managed to calculate the positions for the planets to a fair degree of accuracy. However, he rejected the idea of a spinning earth as absurd as he believed it would create huge winds and his planetary hypotheses were sufficiently real that the distances of moon, sun, planets and stars could be determined by treating orbits celestial spheres as contiguous realities. This system postulated the existence of a counter-earth collinear with the Earth and central fire, the Sun revolved around the central fire once a year, and the stars were stationary. The Earth maintained the same face towards the central fire. Kepler gave an explanation of the Pythagoreans central fire as the Sun. Heraclides of Pontus said that the rotation of the Earth explained the apparent daily motion of the celestial sphere and it used to be thought that he believed Mercury and Venus to revolve around the Sun, which in turn revolves around the Earth. Macrobius Ambrosius Theodosius later described this as the Egyptian System, stating that it did not escape the skill of the Egyptians, the first person known to have proposed a heliocentric system, however, was Aristarchus of Samos. Like Eratosthenes, Aristarchus calculated the size of the Earth, and measured the size and distance of the Moon and Sun, from his estimates, he concluded that the Sun was six to seven times wider than the Earth and thus hundreds of times more voluminous. His writings on the system are lost, but some information is known from surviving descriptions and critical commentary by his contemporaries. This is the account as you have heard from astronomers. The stars are in fact much farther away than the distance that was assumed in ancient times. Archimedes says that Aristarchus made the stars distance larger, suggesting that he was answering the natural objection that Heliocentrism requires stellar parallactic oscillations and he apparently agreed to the point but placed the stars so distant as to make the parallactic motion invisibly minuscule. Thus Heliocentrism opened the way for realization that the universe was larger than the geocentrists taught, according to one of Plutarchs characters in the dialogue, the philosopher Cleanthes had held that Aristarchus should be charged with impiety for moving the hearth of the world. Since Plutarch mentions the followers of Aristarchus in passing, it is likely there were other astronomers in the Classical period who also espoused Heliocentrism. Seleucus adopted the system of Aristarchus and is said to have proved the heliocentric theory. He may have used trigonometric methods that were available in his time
25.
Weighing scale
–
Weighing scales are devices to measure weight or calculate mass. Scales and balances are used in commerce, as many products are sold. Very accurate balances, called analytical balances, are used in fields such as chemistry. Although records dating to the 1700s refer to spring scales for measuring weight, the earliest design for such a device dates to 1770 and credits Richard Salter, an early scale-maker. Postal workers could work quickly with spring scales than balance scales because they could be read instantaneously. By the 1940s various electronic devices were being attached to these designs to make more accurate. A spring scale measures weight by reporting the distance that a spring deflects under a load and this contrasts to a balance, which compares the torque on the arm due to a sample weight to the torque on the arm due to a standard reference weight using a horizontal lever. Spring scales measure force, which is the force of constraint acting on an object. They are usually calibrated so that measured force translates to mass at earths gravity, the object to be weighed can be simply hung from the spring or set on a pivot and bearing platform. In a spring scale, the spring either stretches or compresses, by Hookes law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Rack and pinion mechanisms are used to convert the linear spring motion to a dial reading. With proper manufacturing and setup, however, spring scales can be rated as legal for commerce, to remove the temperature error, a commerce-legal spring scale must either have temperature-compensated springs or be used at a fairly constant temperature. To eliminate the effect of gravity variations, a spring scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use force to sense weight. The test force is applied to a piston or diaphragm and transmitted through hydraulic lines to an indicator based on a Bourdon tube or electronic sensor. A digital bathroom scale is a type of electronic weighing machine, the digital bathroom scale is a smart scale which has many functions like smartphone integration, cloud storage, fitness tracking, etc. In electronic versions of spring scales, the deflection of a beam supporting the weight is measured using a strain gauge. The capacity of such devices is only limited by the resistance of the beam to deflection and these scales are used in the modern bakery, grocery, delicatessen, seafood, meat, produce and other perishable goods departments
26.
Victor Cousin
–
Victor Cousin was a French philosopher. He was the founder of eclecticism, an influential school of French philosophy that combined elements of German idealism. As the administrator of public instruction for over a decade, Cousin also had an important influence on French educational policy, the son of a watchmaker, he was born in Paris, in the Quartier Saint-Antoine. At the age of ten he was sent to the grammar school, the Lycée Charlemagne. The classical training of the lycée strongly disposed him to literature and he was already known among his fellow students for his knowledge of Greek. From the lycée he graduated to the most prestigious of higher schools, École Normale Supérieure. That day decided my whole life and that school has remained ever since the living heart of French philosophy — Henri Bergson, Jean-Paul Sartre and Jacques Derrida are among its past students. Cousin wanted to lecture on philosophy and quickly obtained the position of master of conferences in the school, the second great philosophical impulse of his life was the teaching of Pierre Paul Royer-Collard. The Scottish Philosophy being the Common Sense Philosophy of Thomas Reid, in 1815–1816 Cousin attained the position of suppliant to Royer-Collard in the history of modern philosophy chair of the faculty of letters. Another thinker who influenced him at this period was Maine de Biran. These men strongly influenced Cousins philosophical thought, to Laromiguière he attributes the lesson of decomposing thought, even though the reduction of it to sensation was inadequate. Royer-Collard taught him that even sensation is subject to certain laws and principles which it does not itself explain, which are superior to analysis. De Biran made a study of the phenomena of the will. He taught him to distinguish in all cognitions, and especially in the simplest facts of consciousness, the influence of Schelling may be observed very markedly in the earlier form of his philosophy. He sympathized with the principle of faith of Jacobi, but regarded it as arbitrary so long as it was not recognized as grounded in reason, in 1817 he went to Germany, and met Hegel at Heidelberg. Hegels Encyclopädie der philosophischen Wissenschaften appeared the year, and Cousin had one of the earliest copies. He thought Hegel not particularly amiable, but the two became friends, the following year Cousin went to Munich, where he met Schelling for the first time, and spent a month with him and Jacobi, obtaining a deeper insight into the Philosophy of Nature. Frances political troubles interfered for a time with his career, in the events of 1814–1815 he took the royalist side
27.
Internet Archive
–
The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of universal access to all knowledge. As of October 2016, its collection topped 15 petabytes, in addition to its archiving function, the Archive is an activist organization, advocating for a free and open Internet. Its web archive, the Wayback Machine, contains over 150 billion web captures, the Archive also oversees one of the worlds largest book digitization projects. Founded by Brewster Kahle in May 1996, the Archive is a 501 nonprofit operating in the United States. It has a budget of $10 million, derived from a variety of sources, revenue from its Web crawling services, various partnerships, grants, donations. Its headquarters are in San Francisco, California, where about 30 of its 200 employees work, Most of its staff work in its book-scanning centers. The Archive has data centers in three Californian cities, San Francisco, Redwood City, and Richmond, the Archive is a member of the International Internet Preservation Consortium and was officially designated as a library by the State of California in 2007. Brewster Kahle founded the Archive in 1996 at around the time that he began the for-profit web crawling company Alexa Internet. In October 1996, the Internet Archive had begun to archive and preserve the World Wide Web in large quantities, the archived content wasnt available to the general public until 2001, when it developed the Wayback Machine. In late 1999, the Archive expanded its collections beyond the Web archive, Now the Internet Archive includes texts, audio, moving images, and software. It hosts a number of projects, the NASA Images Archive, the contract crawling service Archive-It. According to its web site, Most societies place importance on preserving artifacts of their culture, without such artifacts, civilization has no memory and no mechanism to learn from its successes and failures. Our culture now produces more and more artifacts in digital form, the Archives mission is to help preserve those artifacts and create an Internet library for researchers, historians, and scholars. In August 2012, the Archive announced that it has added BitTorrent to its file download options for over 1.3 million existing files, on November 6,2013, the Internet Archives headquarters in San Franciscos Richmond District caught fire, destroying equipment and damaging some nearby apartments. The nonprofit Archive sought donations to cover the estimated $600,000 in damage, in November 2016, Kahle announced that the Internet Archive was building the Internet Archive of Canada, a copy of the archive to be based somewhere in the country of Canada. The announcement received widespread coverage due to the implication that the decision to build an archive in a foreign country was because of the upcoming presidency of Donald Trump. Kahle was quoted as saying that on November 9th in America and it was a firm reminder that institutions like ours, built for the long-term, need to design for change. For us, it means keeping our cultural materials safe, private and it means preparing for a Web that may face greater restrictions
28.
University of St Andrews
–
The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland, St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy. St Andrews is made up from a variety of institutions, including three constituent colleges and 18 academic schools organised into four faculties, the university occupies historic and modern buildings located throughout the town. The academic year is divided into two terms, Martinmas and Candlemas, in term time, over one-third of the towns population is either a staff member or student of the university. It is ranked as the third best university in the United Kingdom in national league tables, the Times Higher Education World Universities Ranking names St Andrews among the worlds Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom, St Andrews has many notable alumni and affiliated faculty, including eminent mathematicians, scientists, theologians, philosophers, and politicians. Six Nobel Laureates are among St Andrews alumni and former staff, a charter of privilege was bestowed upon the society of masters and scholars by the Bishop of St Andrews, Henry Wardlaw, on 28 February 1411. Wardlaw then successfully petitioned the Avignon Pope Benedict XIII to grant the university status by issuing a series of papal bulls. King James I of Scotland confirmed the charter of the university in 1432, subsequent kings supported the university with King James V confirming privileges of the university in 1532. A college of theology and arts called St Johns College was founded in 1418 by Robert of Montrose, St Salvators College was established in 1450, by Bishop James Kennedy. St Leonards College was founded in 1511 by Archbishop Alexander Stewart, St Johns College was refounded by Cardinal James Beaton under the name St Marys College in 1538 for the study of divinity and law. Some university buildings that date from this period are still in use today, such as St Salvators Chapel, St Leonards College Chapel, at this time, the majority of the teaching was of a religious nature and was conducted by clerics associated with the cathedral. During the 17th and 18th centuries, the university had mixed fortunes and was beset by civil. He described it as pining in decay and struggling for life, in the second half of the 19th century, pressure was building upon universities to open up higher education to women. In 1876, the University Senate decided to allow women to receive an education at St Andrews at a roughly equal to the Master of Arts degree that men were able to take at the time. The scheme came to be known as the L. L. A and it required women to pass five subjects at an ordinary level and one at honours level and entitled them to hold a degree from the university. In 1889 the Universities Act made it possible to admit women to St Andrews. Agnes Forbes Blackadder became the first woman to graduate from St Andrews on the level as men in October 1894
29.
NNDB
–
The Notable Names Database is an online database of biographical details of over 40,000 people of note. NNDB describes itself as an aggregator of those it determines to be noteworthy. Each person has an executive summary giving a description of NNDBs opinion of his/her notability. Some entries have a brief biography, or contain facts or citations of note. Entries may contain summaries of the organizations they belong to, illnesses, phobias, addictions, drug use, criminal records, in the case of authors, actors, film directors, and architects, the entry lists the persons artistic works in chronological order. Businesspeople and government officials have chronologies of their posts and positions. NNDB also has articles on films with user-submitted reviews, discographies of selected music groups, readers may suggest corrections through a form on the website, these are later vetted by an NNDB staff member. A former feature was the Level of Fame assigned by NNDB from Niche to Icon, the NNDB Mapper, a visual tool for exploring connections between people, was made available in May 2008. The interface allows the user to map how various individuals and institutions are connected, and save and share these maps
30.
Virtual International Authority File
–
The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to a service of the OCLC on April 4,2012, the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together, a VIAF record receives a standard data number, contains the primary see and see also records from the original records, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs clustering algorithm is run every month, as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records
31.
Integrated Authority File
–
The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format
32.
Bibsys
–
BIBSYS is an administrative agency set up and organized by the Ministry of Education and Research in Norway. They are a provider, focusing on the exchange, storage and retrieval of data pertaining to research. BIBSYS are collaborating with all Norwegian universities and university colleges as well as research institutions, Bibsys is formally organized as a unit at the Norwegian University of Science and Technology, located in Trondheim, Norway. The board of directors is appointed by Norwegian Ministry of Education, BIBSYS offer researchers, students and others an easy access to library resources by providing the unified search service Oria. no and other library services. They also deliver integrated products for the operation for research. As a DataCite member BIBSYS act as a national DataCite representative in Norway and thereby allow all of Norways higher education, all their products and services are developed in cooperation with their member institutions. The purpose of the project was to automate internal library routines, since 1972 Bibsys has evolved from a library system supplier for two libraries in Trondheim, to developing and operating a national library system for Norwegian research and special libraries. The target group has expanded to include the customers of research and special libraries. BIBSYS is an administrative agency answerable to the Ministry of Education and Research. In addition to BIBSYS Library System, the product consists of BISBYS Ask, BIBSYS Brage, BIBSYS Galleri. All operation of applications and databases is performed centrally by BIBSYS, BIBSYS also offer a range of services, both in connection with their products and separate services independent of the products they supply
33.
JSTOR
–
JSTOR is a digital library founded in 1995. Originally containing digitized back issues of journals, it now also includes books and primary sources. It provides full-text searches of almost 2,000 journals, more than 8,000 institutions in more than 160 countries have access to JSTOR, most access is by subscription, but some older public domain content is freely available to anyone. William G. Bowen, president of Princeton University from 1972 to 1988, JSTOR originally was conceived as a solution to one of the problems faced by libraries, especially research and university libraries, due to the increasing number of academic journals in existence. Most libraries found it prohibitively expensive in terms of cost and space to maintain a collection of journals. By digitizing many journal titles, JSTOR allowed libraries to outsource the storage of journals with the confidence that they would remain available long-term, online access and full-text search ability improved access dramatically. Bowen initially considered using CD-ROMs for distribution, JSTOR was initiated in 1995 at seven different library sites, and originally encompassed ten economics and history journals. JSTOR access improved based on feedback from its sites. Special software was put in place to make pictures and graphs clear, with the success of this limited project, Bowen and Kevin Guthrie, then-president of JSTOR, wanted to expand the number of participating journals. They met with representatives of the Royal Society of London and an agreement was made to digitize the Philosophical Transactions of the Royal Society dating from its beginning in 1665, the work of adding these volumes to JSTOR was completed by December 2000. The Andrew W. Mellon Foundation funded JSTOR initially, until January 2009 JSTOR operated as an independent, self-sustaining nonprofit organization with offices in New York City and in Ann Arbor, Michigan. JSTOR content is provided by more than 900 publishers, the database contains more than 1,900 journal titles, in more than 50 disciplines. Each object is identified by an integer value, starting at 1. In addition to the site, the JSTOR labs group operates an open service that allows access to the contents of the archives for the purposes of corpus analysis at its Data for Research service. This site offers a facility with graphical indication of the article coverage. Users may create focused sets of articles and then request a dataset containing word and n-gram frequencies and they are notified when the dataset is ready and may download it in either XML or CSV formats. The service does not offer full-text, although academics may request that from JSTOR, JSTOR Plant Science is available in addition to the main site. The materials on JSTOR Plant Science are contributed through the Global Plants Initiative and are only to JSTOR