Regiomontanus is an ancient lunar impact crater located in the southern highlands region to the southeast of Mare Nubium. It is joined at the chaotic northern rim by the crater Purbach, to the south-southeast is Walther; the crater is worn from impact erosion, the rim is irregular and distinctly oval in outline. The walls on the southern and western edges have been completely degraded. A prominent ridge lies off-center to the northwest, with the small crater Regiomontanus A at its summit; the crater floor is lava-flooded, has a number of small crater impacts. The summit crater; however this feature is an impact crater, is offset from the summit of the central peak. Regiomontanus is named after the 15th century German astronomer and mathematician Johannes Müller von Königsberg, known as Regiomontanus. Like many of the craters on the Moon's near side, it was given its name by Giovanni Riccioli, whose 1651 nomenclature system has become standardized. Earlier lunar cartographers had given the feature different names.
Michael van Langren's 1645 map calls it "Christinae Reg. Suec." after Christina, Queen of Sweden. And Johannes Hevelius grouped it with Walther as "Mons Libanus" after Mount Lebanon. By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint, closest to Regiomontanus
Philip Melanchthon was a German Lutheran reformer, collaborator with Martin Luther, the first systematic theologian of the Protestant Reformation, intellectual leader of the Lutheran Reformation, an influential designer of educational systems. He stands next to Luther and John Calvin as a reformer and molder of Protestantism. Melanchthon along with Luther denounced what they believed was the exaggerated cult of the saints, asserted justification by faith, denounced the coercion of the conscience in the sacrament of penance by the Catholic Church, which they believed could not offer certainty of salvation. Both rejected the doctrine of transubstantiation, but not the belief that the body and blood of Christ are present with the elements of bread and wine in the sacrament of the Lord's Supper; the Lutheran view of sacramental union contrasts with the understanding of the Roman Church that the bread and wine cease to be bread and wine at their consecration. Melanchthon made the distinction between law and gospel the central formula for Lutheran evangelical insight.
By the "law", he meant God's requirements both in New Testament. He was born Philipp Schwartzerdt on 16 February 1497, at Bretten where his father Georg Schwarzerdt was armorer to Philip, Count Palatine of the Rhine, his birthplace, along with the whole city of Bretten, was burned in 1689 by French troops during the War of the Palatinate Succession. The town's Melanchthonhaus was built on its site in 1897. In 1507 he was sent to the Latin school at Pforzheim, where the rector, Georg Simler of Wimpfen, introduced him to the Latin and Greek poets and to Aristotle, he was influenced by a Renaissance humanist. Philipp was only eleven when in 1508 both father died within eleven days, he and a brother were brought to Pforzheim to live with his maternal grandmother, Elizabeth Reuter, sister of Reuchlin. The next year he entered the University of Heidelberg, where he studied philosophy and astronomy/astrology, became known as a scholar of Greek. Denied the master's degree in 1512 on the grounds of his youth, he went to Tübingen, where he continued humanistic studies but worked on jurisprudence and medicine.
While there he was taught the technical aspects of astrology by Johannes Stöffler. After gaining a master's degree in 1516 he began to study theology. Under the influence of Reuchlin and others, he became convinced that true Christianity was something different from the scholastic theology as taught at the university, he instructed younger scholars. He lectured on oratory, on Virgil and on Livy, his first publications were a number of poems in a collection edited by Jakob Wimpfeling, the preface to Reuchlin's Epistolae clarorum virorum, an edition of Terence, a Greek grammar. Opposed as a reformer at Tübingen, he accepted a call to the University of Wittenberg from Martin Luther on the recommendation of his great-uncle, became professor of Greek there at the age of 21, he studied the Scriptures of Paul, Evangelical doctrine. Attending the disputation of Leipzig as a spectator, he nonetheless participated with his comments. After his views were attacked by Johann Eck, Melanchthon replied based on the authority of Scripture in his Defensio contra Johannem Eckium.
Following lectures on the Gospel of Matthew and the Epistle to the Romans, together with his investigations into Pauline doctrine, he was granted the degree of bachelor of theology, transferred to the theological faculty. He married Katharina Krapp, daughter of Wittenberg's mayor, on 25 November 1520, they had four children: Anna, Philipp and Magdalen. In the beginning of 1521 in his Didymi Faventini versus Thomam Placentinum pro M. Luthero oratio, he defended Luther, he argued that Luther rejected only papal and ecclesiastical practises which were at variance with Scripture. But while Luther was absent at Wartburg Castle, during the disturbances caused by the Zwickau prophets, Melanchthon wavered; the appearance of Melanchthon's Loci communes rerum theologicarum seu hypotyposes theologicae was of subsequent importance for Reformation. Melanchthon presented the new doctrine of Christianity under the form of a discussion of the "leading thoughts" of the Epistle to the Romans. Loci communes began the gradual rise of the Lutheran scholastic tradition, the theologians Martin Chemnitz, Mathias Haffenreffer, Leonhard Hutter expanded upon it.
Melanchthon continued to lecture on the classics. On a journey in 1524 to his native town, he encountered the papal legate, Cardinal Lorenzo Campeggio, who tried to draw him from Luther's cause. In his Unterricht der Visitatorn an die Pfarherrn im Kurfürstentum zu Sachssen Melanchthon presented the evangelical doctrine of salvation as well as regulations for churches and schools. In 1529 he accompanied the elector to the Diet of Speyer, his hopes of inducing the Imperial party to a recognition of the Reformation were not fulfilled. A friendly attitude towards the Swiss at the Diet was something he changed, calling Huldrych Zwingli's doctrine of the Lord's Supper "an i
Electorate of Saxony
The Electorate of Saxony was a state of the Holy Roman Empire established when Emperor Charles IV raised the Ascanian duchy of Saxe-Wittenberg to the status of an Electorate by the Golden Bull of 1356. Upon the extinction of the House of Ascania, it was feoffed to the Margraves of Meissen from the Wettin dynasty in 1423, who moved the ducal residence up the river Elbe to Dresden. After the Empire's dissolution in 1806, the Wettin Electors raised Saxony to a territorially reduced kingdom. After the dissolution of the medieval Duchy of Saxony, the name Saxony was first applied to a small territory midway along the river Elbe, around the city of Wittenberg, which had belonged to the March of Lusatia. Around 1157 it was held by the first Margrave of Brandenburg; when Emperor Frederick Barbarossa deposed the Saxon duke, Henry the Lion in 1180, the Wittenberg lands belonged to Albert's youngest son, Count Bernhard of Anhalt, who assumed the Saxon ducal title. Bernard's eldest son, Albert I, ceded the territory known as, Anhalt to his younger brother, retaining the ducal title and attched to this territory the lordship of Lauenburg.
His sons divided the territory into the duchies of Saxe-Lauenburg. Both lines claimed the Saxon electoral dignity or privilege, which led to confusion during the 1314 election of the Wittelsbach duke, Louis of Bavaria as King of the Romans against his Habsburg rival, Duke Frederick the Fair of Austria, as both candidates received one vote each from each of the two rival Ascanian branches. Louis was succeeded by Charles of Bohemia. After his coronation as Holy Roman Emperor in 1355, Charles issued the Golden Bull of 1356, the fundamental law of the Empire settling the method of electing the German King by seven Prince-electors; the rival Wittelsbach and Habsburg dynasties got nothing, instead the Duke of Saxe-Wittenberg, Archmarshal of the Empire, received the right to elect the King of the Romans and the prospective Emperor, together with six other elector Princes of the Empire. Thus, the country, though small in area, gained influence far beyond its extent; the electoral privilege contained the obligation of male primogeniture.
That is, only the eldest son could succeed as ruler. It therefore forbade the division of the territory among several heirs, in order to prevent the disintegration of the country; the importance of this stipulation is shown by the history of most of the fragmented German principalities which were not constituted as electorates. The Ascanian line of Saxe-Wittenberg became extinct with the death of Elector Albert III in 1422, after which Emperor Sigismund granted the country and electoral privilege upon Margrave Frederick IV of Meissen, a loyal supporter in the Hussite Wars; the late Albert's Ascanian relative, Duke Eric V of Saxe-Lauenburg protested in vain. Frederick, one of the seven Prince-electors, was a member of the House of Wettin, which since 1089 had ruled over the adjacent Margravate of Meissen up the Elbe river - established under Emperor Otto I in 965 - and over the Landgravate of Thuringia since 1242. Thus, in 1423, Saxe-Wittenberg, the Margravate of Meissen and Thuringia were united under one ruler, as a unified territory became known as, Upper Saxony.
When Elector Frederick II died in 1464, his two surviving sons overrode the primogeniture principle and divided his territories by the Treaty of Leipzig on 26 August 1485. This resulted in the separated Wettin dynasty becoming the Ernestine and Albertine branches; the elder Ernest, founder of the Ernestine line, received large parts of the former Duchy of Saxe-Wittenberg with the electoral privilege attached to it, the southern Landgravate of Thuringia. While the younger Albert, founder of the Albertine line, received northern Thuringia and the lands of the former Margravate of Meissen. Thus, although the Ernestine line had had greater authority until the Battle of Mühlberg in 1547, the electoral privilege and territory fell to the Albertine line, which also became a royal house when Saxony was proclaimed a kingdom in the 19th century; this partition was to decisively enfeeble the Wettin dynasty in relation to the rising House of Hohenzollern. It had achieved its own electoral privilege as Margraves of Brandenburg since 1415.
The Protestant movement of the 16th century spread under the protection of the Saxon rulers. Ernest's son, Elector Frederick the Wise established in 1502 the University at Wittenberg, where the Augustinian monk, Martin Luther, was appointed professor of philosophy in 1508. At the same time he became one of the preachers at the castle church in Wittenberg. On 31 October 1517, he enclosed in a protest letter to Albert of Brandenburg the Archbishop of Mainz, The Ninety-Five Theses against the sale of indulgences and other Catholic practices, an action that marked the start of what came to be called the Reformation. Although the Elector did not at first share the new attitude, he granted his protection to Luther anyway. Owing to this intervention, Pope Leo X decided against summoning Luther to Rome in 1518, the Elector secured for Luther Imperial safe-conduct to the Diet of Worms in 1521; when Luther was declared banned in the entire empire by Emperor Charles V, the Elector had him brought to live in Wartburg Castle on his Thuringian estate.
Lutheran doctrines spread first in Ernestine Saxony. In 1525, Frederick died never having left the Catholic Church, unless on his deathbed in 1525, but he was sympathetic towards Lutheranism by the time of his death, he was succeeded by John the Constant. John was a zealous Lutheran, he exercised full authority over the new chu
Vienna is the federal capital and largest city of Austria, one of the nine states of Austria. Vienna is Austria's primate city, with a population of about 1.9 million, its cultural and political centre. It is the 7th-largest city by population within city limits in the European Union; until the beginning of the 20th century, it was the largest German-speaking city in the world, before the splitting of the Austro-Hungarian Empire in World War I, the city had 2 million inhabitants. Today, it has the second largest number of German speakers after Berlin. Vienna is host to many major international organizations, including the United Nations and OPEC; the city is located in the eastern part of Austria and is close to the borders of the Czech Republic and Hungary. These regions work together in a European Centrope border region. Along with nearby Bratislava, Vienna forms a metropolitan region with 3 million inhabitants. In 2001, the city centre was designated a UNESCO World Heritage Site. In July 2017 it was moved to the list of World Heritage in Danger.
Apart from being regarded as the City of Music because of its musical legacy, Vienna is said to be "The City of Dreams" because it was home to the world's first psychoanalyst – Sigmund Freud. The city's roots lie in early Celtic and Roman settlements that transformed into a Medieval and Baroque city, the capital of the Austro-Hungarian Empire, it is well known for having played an essential role as a leading European music centre, from the great age of Viennese Classicism through the early part of the 20th century. The historic centre of Vienna is rich in architectural ensembles, including Baroque castles and gardens, the late-19th-century Ringstraße lined with grand buildings and parks. Vienna is known for its high quality of life. In a 2005 study of 127 world cities, the Economist Intelligence Unit ranked the city first for the world's most liveable cities. Between 2011 and 2015, Vienna was ranked second, behind Melbourne. In 2018, it replaced Melbourne as the number one spot. For ten consecutive years, the human-resource-consulting firm Mercer ranked Vienna first in its annual "Quality of Living" survey of hundreds of cities around the world.
Monocle's 2015 "Quality of Life Survey" ranked Vienna second on a list of the top 25 cities in the world "to make a base within."The UN-Habitat classified Vienna as the most prosperous city in the world in 2012/2013. The city was ranked 1st globally for its culture of innovation in 2007 and 2008, sixth globally in the 2014 Innovation Cities Index, which analyzed 162 indicators in covering three areas: culture and markets. Vienna hosts urban planning conferences and is used as a case study by urban planners. Between 2005 and 2010, Vienna was the world's number-one destination for international congresses and conventions, it attracts over 6.8 million tourists a year. The English name Vienna is borrowed from the homonymous Italian version of the city's name or the French Vienne; the etymology of the city's name is still subject to scholarly dispute. Some claim that the name comes from Vedunia, meaning "forest stream", which subsequently produced the Old High German Uuenia, the New High German Wien and its dialectal variant Wean.
Others believe that the name comes from the Roman settlement name of Celtic extraction Vindobona meaning "fair village, white settlement" from Celtic roots, vindo-, meaning "bright" or "fair" – as in the Irish fionn and the Welsh gwyn –, -bona "village, settlement". The Celtic word Vindos may reflect a widespread prehistorical cult of a Celtic God. A variant of this Celtic name could be preserved in the Czech and Polish names of the city and in that of the city's district Wieden; the name of the city in Hungarian, Serbo-Croatian and Ottoman Turkish has a different Slavonic origin, referred to an Avar fort in the area. Slovene-speakers call the city Dunaj, which in other Central European Slavic languages means the Danube River, on which the city stands. Evidence has been found of continuous habitation in the Vienna area since 500 BC, when Celts settled the site on the Danube River. In 15 BC the Romans fortified the frontier city they called Vindobona to guard the empire against Germanic tribes to the north.
Close ties with other Celtic peoples continued through the ages. The Irish monk Saint Colman is buried in Melk Abbey and Saint Fergil served as Bishop of Salzburg for forty years. Irish Benedictines founded twelfth-century monastic settlements. Evidence of these ties persists in the form of Vienna's great Schottenstift monastery, once home to many Irish monks. In 976 Leopold I of Babenberg became count of the Eastern March, a 60-mile district centering on the Danube on the eastern frontier of Bavaria; this initial district grew into the duchy of Austria. Each succeeding Babenberg ruler expanded the march east along the Danube encompassing Vienna and the lands east. In 1145 Duke Henry II Jasomirgott moved the Babenberg family residence from Klosterneuburg in Lower Austria to Vienna. From that time, Vienna remained the center of the Babenberg dynasty. In 1440 Vienna became the resident city of the Habsburg dynasty, it grew to become the de facto capital of the Holy Roman Empire in 1437 and a cultural centre for arts and science and fine cuisine.
Hungary occupied the city between 1485 and 1490. In the 16th and 1
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. 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", 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 many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; 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 scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 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; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, 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 a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
Esztergom is a city in northern Hungary, 46 kilometres northwest of the capital Budapest. It lies in Komárom-Esztergom county, on the right bank of the river Danube, which forms the border with Slovakia there. Esztergom was the capital of Hungary from the 10th till the mid-13th century when King Béla IV of Hungary moved the royal seat to Buda. Esztergom is the seat of the prímás of the Roman Catholic Church in Hungary, the former seat of the Constitutional Court of Hungary; the city has the largest ecclesiastical collection in Hungary. Its cathedral, Esztergom Basilica is the largest church in Hungary; the Roman town was called Solva. The medieval Latin name was Strigonium; the first early medieval mention is "ſtrigonensis comes". The first interpretation of the name was suggested by Antonio Bonfini, he tried to explain it from Istrogranum, "city at the confluence of Ister and Gran". This interpretation is still popular. Viktor Récsey attempted to derive the name from Germanic languages. After the conquest of the country by Charlemagne, the Franks should give the name Osterringun to their easternmost castle.
Pavel Jozef Šafárik tried to explain the name from Slavic ostřehu. Gyula Pauler suggested a Slavic personal name Stigran without a deeper analysis of its origin. In 1927, Konrad Schünemann summarized these older views and proposed the origin in a Slavic stem strěg; this theory was extended by Ján Stanislav who explained the origin of the initial vowel missing in Latin and Czech sources. The introduction of a vowel before the initial consonant group is a regular change in the Hungarian language, but the initial "O" in Slavic forms can be explained by an independent change–an incorrect decomposition of the Slavic prepositional form. Both authors noticed the high number of Slavic placenames in the region and similar Slavic names in other countries. Both authors believed that the stem strěg was a part of the Slavic personal name, but Šimon Ondruš suggests a straightforward etymology; the Proto-Slavic stregti – to watch, to guard, present participle stregom, strägom – a guard post. The Slavic form was created by an incorrect decomposition as follows: vъ Strägome → vo Strägome → v Osträgome like Slovak Bdokovce → Obdokovce, Psolovce → Obsolovce.
Lajos Kiss considered the name to be of uncertain origin derived from Slavic strgun or Proto-Bulgaric estrogin käpe, estrigim küpe - a leather armor However, the last theory is criticized by Šimon Ondruš as obsolete and unreliable, because of its dependency on sources, the high number of Slavic names in the region and missing adoption of the word in the Hungarian language. Other names of the town are Croatian Ostrogon, Polish Ostrzyhom, Serbian Ostrogon and Estergon, Slovak Ostrihom and Czech Ostřihom; the German name is Gran, like the German name of river Garam. Esztergom is one of the oldest towns in Hungary. Esztergom, as it existed in the Middle Ages, now rests under today's town; the results of the most recent archeological excavations reveal that the Várhegy and its vicinity have been inhabited since the end of the Ice Age 20,000 years ago. The first people known by name were the Celts from Western Europe, who settled in the region in about 350 BC. A flourishing Celtic settlement existed on the Varhegy.
Thereafter it became an important frontier town of Pannonia, known by the name of Salvio Mansio, Salvio, or Solva. By the seventh century the town was called Stregom and Gran, but soon reverted to the former, which evolved into Esztergom by the thirteenth century; the German and Avar archaeological finds found in the area reveal that these people settled there following the period of the migrations that were caused by the fall of the Roman Empire. At about 500 AD, Slavic peoples immigrated into the Pannonian Basin. In the 9th century, the territory was under Frankish control, it might have been part of Great Moravia too. In Old Slavonic language, it was called Strěgom, as it was strategic point of control for the Danube valley; the Magyars entered the Pannonian Basin in 896 AD and conquered it systematically, succeeding in 901. In 960, the ruling prince of the Hungarians, Géza, chose Esztergom as his residence, his son, called Saint Stephen of Hungary, was born in his palace built on the Roman castrum on the Várhegy around 969-975.
In 973, Esztergom served as the starting point of an important historical event: during Easter of that year, Géza sent a committee to the international peace conference of Emperor Otto I in Quedlinburg. He asked for missionaries; the prince's residence stood on the northern side of the hill. The center of the hill was occupied by a basilica dedicated to St. Adalbert, according to legend, baptised St. Stephen; the Church of St. Adalbert was the seat of the archbishop of Esztergom, the head of the Roman Catholic Church in Hungary. By that time, significant numbers of craftsmen and merchants had settled in the city. Stephen's coronation took place in Esztergom on either Christmas Day 1000 or January 1, 1001. From the time of his rule up to the beginning of the 13th century, the only mint for the country operated here. During t