James Gregory (mathematician)
James Gregory FRS was a Scottish mathematician and astronomer. His surname is sometimes spelled as the original Scottish spelling, he described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions. In his book Geometriae Pars Universalis Gregory gave both the first published statement and proof of the fundamental theorem of the calculus, for which he was acknowledged by Isaac Barrow; the youngest of the 3 children of John Gregory, an Episcopalian Church of Scotland minister, James was born in the manse at Drumoak and was educated at home by his mother, Janet Anderson. It was his mother who endowed Gregory with his appetite for geometry, her uncle – Alexander Anderson – having been a pupil and editor of French mathematician Viète. After his father's death in 1651 his elder brother David took over responsibility for his education, he attended Aberdeen Grammar School, Marischal College from 1653–1657, graduating AM in 1657.
In 1663 he went to London, meeting John Collins and fellow Scot Robert Moray, one of the founders of the Royal Society. In 1664 he departed for the University of Padua, in the Venetian Republic, passing through Flanders and Rome on his way. At Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, he was taught by Stefano Angeli. Upon his return to London in 1668 he was elected a Fellow of the Royal Society, before travelling to St Andrews in late 1668 to take up his post as the first Regius Professor of Mathematics, a position created for him by Charles II upon the request of Robert Moray, he was successively professor at the University of Edinburgh. He had married Mary, daughter of George Jameson and widow of John Burnet of Elrick, Aberdeen, he was the grandfather of John Gregory. About a year after assuming the Chair of Mathematics at Edinburgh, James Gregory suffered a stroke while viewing the moons of Jupiter with his students, he died a few days at the age of 36.
In the Optica Promota, published in 1663, Gregory described his design for a reflecting telescope, the "Gregorian telescope". He described the method for using the transit of Venus to measure the distance of the Earth from the Sun, advocated by Edmund Halley and adopted as the basis of the first effective measurement of the Astronomical Unit. Before he left Padua, Gregory published Vera Circuli et Hyperbolae Quadratura in which he approximated the areas of the circle and hyperbola with convergent series: cannot be denied the authorship of many curious theorems on the relation of the circle to inscribed and circumscribed polygons, their relation to each other. By means of these theorems he gives with infinitely less trouble than by the usual calculations, … the measure of the circle and hyperbola to more than twenty decimal places. Following the example of Huygens, he gave constructions of straight lines equal to the arcs of the circle, whose error is still less. "The first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him."The book contains series expansions of sin, cos and arccos.
Gregory was unaware that the earliest enunciations of these expansions were made by Madhava in India in the 14th century. The book was reprinted in 1668 with an appendix, Geometriae Pars, in which Gregory explained how the volumes of solids of revolution could be determined. In his 1663 Optica Promota, James Gregory described his reflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a reflecting telescope with a parabolic mirror would correct spherical aberration as well as the chromatic aberration seen in refracting telescopes. In his design he placed a concave secondary mirror with an elliptical surface past the focal point of the parabolic primary mirror, reflecting the image back through a hole in the primary mirror where it could be conveniently viewed. According to his own confession, Gregory had no practical skill and he could find no optician capable of constructing one; the telescope design attracted the attention of several people in the scientific establishment such as Robert Hooke, the Oxford physicist who built the telescope 10 years and Sir Robert Moray and founding member of the Royal Society.
The Gregorian telescope design is used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are used in radio telescopes such as Arecibo, which features a "Gregorian dome"; the following excerpt is from the Pantologia. A new cyclopædi Mr. James Gregory was a man of a acute and penetrating genius.... The most brilliant part of his character was that of his mathematical genius as an inventor, of the first order.
Scottish Gaelic or Scots Gaelic, sometimes referred to as Gaelic, is a Celtic language native to the Gaels of Scotland. A member of the Goidelic branch of the Celtic languages, Scottish Gaelic, like Modern Irish and Manx, developed out of Middle Irish. Most of modern Scotland was once Gaelic-speaking, as evidenced by Gaelic-language placenames. In the 2011 census of Scotland, 57,375 people reported as able to speak Gaelic, 1,275 fewer than in 2001; the highest percentages of Gaelic speakers were in the Outer Hebrides. There are revival efforts, the number of speakers of the language under age 20 did not decrease between the 2001 and 2011 censuses. Outside Scotland, Canadian Gaelic is spoken in Nova Scotia and Prince Edward Island. Scottish Gaelic is not an official language of either the United Kingdom. However, it is classed as an indigenous language under the European Charter for Regional or Minority Languages, which the British government has ratified, the Gaelic Language Act 2005 established a language development body, Bòrd na Gàidhlig.
Aside from "Scottish Gaelic", the language may be referred to as "Gaelic", pronounced or in English. "Gaelic" may refer to the Irish language. Scottish Gaelic is distinct from Scots, the Middle English-derived language varieties which had come to be spoken in most of the Lowlands of Scotland by the early modern era. Prior to the 15th century, these dialects were known as Inglis by its own speakers, with Gaelic being called Scottis. From the late 15th century, however, it became common for such speakers to refer to Scottish Gaelic as Erse and the Lowland vernacular as Scottis. Today, Scottish Gaelic is recognised as a separate language from Irish, so the word Erse in reference to Scottish Gaelic is no longer used. Gaelic was believed to have been brought to Scotland, in the 4th–5th centuries CE, by settlers from Ireland who founded the Gaelic kingdom of Dál Riata on Scotland's west coast in present-day Argyll.:551:66 However, archaeologist Dr Ewan Campbell has argued that there is no archaeological or placename evidence of a migration or takeover.
This view of the medieval accounts is shared by other historians. Regardless of how it came to be spoken in the region, Gaelic in Scotland was confined to Dál Riata until the eighth century, when it began expanding into Pictish areas north of the Firth of Forth and the Firth of Clyde. By 900, Pictish appears to have become extinct replaced by Gaelic.:238–244 An exception might be made for the Northern Isles, where Pictish was more supplanted by Norse rather than by Gaelic. During the reign of Caustantín mac Áeda, outsiders began to refer to the region as the kingdom of Alba rather than as the kingdom of the Picts. However, though the Pictish language did not disappear a process of Gaelicisation was under way during the reigns of Caustantín and his successors. By a certain point during the 11th century, all the inhabitants of Alba had become Gaelicised Scots, Pictish identity was forgotten. In 1018, after the conquest of the Lothians by the Kingdom of Scotland, Gaelic reached its social, cultural and geographic zenith.:16–18 Colloquial speech in Scotland had been developing independently of that in Ireland since the eighth century.
For the first time, the entire region of modern-day Scotland was called Scotia in Latin, Gaelic was the lingua Scotica.:276:554 In southern Scotland, Gaelic was strong in Galloway, adjoining areas to the north and west, West Lothian, parts of western Midlothian. It was spoken to a lesser degree in north Ayrshire, the Clyde Valley and eastern Dumfriesshire. In south-eastern Scotland, there is no evidence that Gaelic was widely spoken. Many historians mark the reign of King Malcom Canmore as the beginning of Gaelic's eclipse in Scotland, his wife Margaret of Wessex spoke no Gaelic, gave her children Anglo-Saxon rather than Gaelic names, brought many English bishops and monastics to Scotland.:19 When Malcolm and Margaret died in 1093, the Gaelic aristocracy rejected their anglicised sons and instead backed Malcolm's brother Donald Bàn. Donald had spent 17 years in Gaelic Ireland and his power base was in the Gaelic west of Scotland, he was the last Scottish monarch to be buried on Iona, the traditional burial place of the Gaelic Kings of Dàl Riada and the Kingdom of Alba.
However, during the reigns of Malcolm Canmore's sons, Alexander I and David I, Anglo-Norman names and practices spread throughout Scotland south of the Forth–Clyde line and along the northeastern coastal plain as far north as Moray. Norman French displaced Gaelic at court; the establishment of royal burghs throughout the same area under David I, attracted large numbers of foreigners speaking Old English. This was the beginning of Gaelic's status as a predominantly rural language in Scotland.:19-23 Clan chiefs in the northern and western parts of Scotland continued to support Gaelic bards who remained a central feature of court life there. The semi-independent Lordship of the Isles in the Hebrides and western coastal mainland remained Gaelic since the language's recovery there in the 12th century, providing a political foundation for cultural prestige down to the end of the 15th century.:553-6By the mid-14th century what came to be called Scots emerged as the official language of government and law.:139 Scotland's emergent nat
Robert Adam was a Scottish neoclassical architect, interior designer and furniture designer. He was the son of William Adam, Scotland's foremost architect of the time, trained under him. With his older brother John, Robert took on the family business, which included lucrative work for the Board of Ordnance, after William's death. In 1754, he left for Rome, spending nearly five years on the continent studying architecture under Charles-Louis Clérisseau and Giovanni Battista Piranesi. On his return to Britain he established a practice in London, where he was joined by his younger brother James. Here he developed the "Adam Style", his theory of "movement" in architecture, based on his studies of antiquity and became one of the most successful and fashionable architects in the country. Adam held the post of Architect of the King's Works from 1761 to 1769. Robert Adam was a leader of the first phase of the classical revival in England and Scotland from around 1760 until his death, he influenced the development of Western architecture, both in North America.
Adam designed fittings as well as houses. He served as the member of Parliament for Kinross-shire from 1768 to 1774. Adam was born on 3 July 1728 at Gladney House in Kirkcaldy, the second son Mary Robertson, the daughter of William Robertson of Gladney, architect William Adam; as a child he was noted as having a "feeble constitution". From 1734 at the age of six Adam attended the Royal High School, Edinburgh where he learned Latin until he was 15, he was taught to read works by Virgil, Horace and parts of Cicero and in his final year Livy. In autumn 1743 he matriculated at the University of Edinburgh, compulsory classes for all students were: the Greek language, logic and natural philosophy. Students could choose three elective subjects, Adam attended classes in mathematics, taught by Colin Maclaurin, anatomy, taught by Alexander Monro primus, his studies were interrupted by the arrival of Bonnie Prince Charlie and his Highlanders, who occupied Edinburgh during the 1745 Jacobite rising. At the end of the year, Robert fell ill for some months, it seems unlikely that he returned to university, having completed only two years of study.
On his recovery from illness in 1746, he joined his elder brother John as apprentice to his father. He assisted William Adam on projects such as the building of Inveraray Castle and the continuing extensions of Hopetoun House. William's position as Master Mason to the Board of Ordnance began to generate much work, as the Highlands were fortified following the failed Jacobite revolt. Robert's early ambition was to be an artist rather than architect, the style of his early sketches in the manner of Salvator Rosa are reflected in his earliest surviving architectural drawings, which show picturesque gothic follies. William Adam died in June 1748, left Dowhill, a part of the Blair Adam estate which included a tower house, to Robert. On William Adam's death, John Adam inherited both the family business and the position of Master Mason to the Board of Ordnance, he took Robert into partnership to be joined by James Adam. The Adam Brothers' first major commission was the decoration of the grand state apartments on the first floor at Hopetoun House, followed by their first "new build" at Dumfries House.
For the Board of Ordnance, the brothers were the main contractor at Fort George, a large modern fort near Inverness designed by military engineer Colonel Skinner. Visits to this project, begun in 1750, would occupy the brothers every summer for the next 10 years, along with works at many other barracks and forts, provided Robert with a solid foundation in practical building. In the winter of 1749 -- 1750, Adam travelled to London with the poet John Home, he took the opportunity for architectural study, visiting Wilton, designed by Inigo Jones, the Queens Hermitage in Richmond by Roger Morris. His sketchbook of the trip shows a continuing interest in gothic architecture. Among his friends at Edinburgh were the philosophers Adam Ferguson and David Hume and the artist Paul Sandby whom he met in the Highlands. Other Edinburgh acquaintances included Gilbert Elliot, William Wilkie, John Home and Alexander Wedderburn. On 3 October 1754, Robert Adam in the company of his brother James set off from Edinburgh for his Grand Tour, stopping for a few days in London, where they visited the Mansion House, London, St Stephen Walbrook, St Paul's Cathedral, Berkshire, in the company of Thomas Sandby who showed them his landscaping at Windsor Great Park and Virginia Water Lake.
They sailed from Dover arriving in Calais on 28 October 1754. He joined Charles Hope-Weir, brother of the Earl of Hopetoun in Brussels and together they travelled to Rome. Hope agreed to take Adam on the tour at the suggestion of his uncle, the Marquess of Annandale, who had undertaken the Grand Tour himself. While in Brussels the pair attended a Play and Masquerade, as well as visiting churches and palaces in the city. Travelling on to Tournai Lille, where they visited the Citadal designed by Sébastien Le Prestre de Vauban. By 12 November 1754 Adam and Hope were in Paris. Adam and Hope travelled on to Italy together, before falling out in Rome over travelling expenses and accommodation. Robert Adam stayed on in Rome until 1757, studying classical architecture and honing his drawing skills, his tutors included the French architect and artist Charles-Louis Clérisseau, the Italian artist Giovanni Battista Piranesi. Here, he became acquainted with the work of the pioneering classical archaeologist and art historian, theorist Johan
The Scottish people or Scots, are a nation and Celtic ethnic group native to Scotland. They emerged from an amalgamation of two Celtic-speaking peoples, the Picts and Gaels, who founded the Kingdom of Scotland in the 9th century; the neighbouring Celtic-speaking Cumbrians, as well as Germanic-speaking Anglo-Saxons and Norse, were incorporated into the Scottish nation. In modern usage, "Scottish people" or "Scots" is used to refer to anyone whose linguistic, family ancestral or genetic origins are from Scotland; the Latin word Scoti referred to the Gaels, but came to describe all inhabitants of Scotland. Considered archaic or pejorative, the term Scotch has been used for Scottish people outside Scotland. John Kenneth Galbraith in his book The Scotch documents the descendants of 19th-century Scottish pioneers who settled in Southwestern Ontario and affectionately referred to themselves as'Scotch', he states the book was meant to give a true picture of life in the community in the early decades of the 20th century.
People of Scottish descent live in many countries. Emigration, influenced by factors such as the Highland and Lowland Clearances, Scottish participation in the British Empire, latterly industrial decline and unemployment, have resulted in Scottish people being found throughout the world. Scottish emigrants took with them their Scottish languages and culture. Large populations of Scottish people settled the new-world lands of North and South America and New Zealand. Canada has the highest level of Scottish descendants per capita in the world and the second-largest population of Scottish descendants, after the United States. Scotland has seen settlement of many peoples at different periods in its history; the Gaels, the Picts and the Britons have their respective origin myths, like most medieval European peoples. Germanic peoples, such as the Anglo-Saxons, arrived beginning in the 7th century, while the Norse settled parts of Scotland from the 8th century onwards. In the High Middle Ages, from the reign of David I of Scotland, there was some emigration from France and the Low Countries to Scotland.
Some famous Scottish family names, including those bearing the names which became Bruce, Balliol and Stewart came to Scotland at this time. Today Scotland is one of the countries of the United Kingdom, the majority of people living there are British citizens; the highest concentrations of people of Scottish descent in the world outside of Scotland are located in Nova Scotia and Prince Edward Island in Canada and Southland in New Zealand, the Falklands Islands, Northern Ireland in the United Kingdom. In the Early Middle Ages, Scotland saw several ethnic or cultural groups mentioned in contemporary sources, namely the Picts, the Gaels, the Britons, the Angles, with the latter settling in the southeast of the country. Culturally, these peoples are grouped according to language. Most of Scotland until the 13th century spoke Celtic languages and these included, at least the Britons, as well as the Gaels and the Picts. Germanic peoples included the Angles of Northumbria, who settled in south-eastern Scotland in the region between the Firth of Forth to the north and the River Tweed to the south.
They occupied the south-west of Scotland up to and including the Plain of Kyle and their language, Old English, was the earliest form of the language which became known as Scots. Use of the Gaelic language spread throughout nearly the whole of Scotland by the 9th century, reaching a peak in the 11th to 13th centuries, but was never the language of the south-east of the country. King Edgar divided the Kingdom of Northumbria between England. South-east of the Firth of Forth in Lothian and the Borders, a northern variety of Old English known as Early Scots, was spoken; as a result of David I, King of Scots' return from exile in England in 1113 to assume the throne in 1124 with the help of Norman military force, David invited Norman families from France and England to settle in lands he granted them to spread a ruling class loyal to him. This Davidian Revolution, as many historians call it, brought a European style of feudalism to Scotland along with an influx of people of Norman descent - by invitation, unlike England where it was by conquest.
To this day, many of the common family names of Scotland can trace ancestry to Normans from this period, such as the Stewarts, the Bruces, the Hamiltons, the Wallaces, the Melvilles, some Browns and many others. The Northern Isles and some parts of Caithness were Norn-speaking. From 1200 to 1500 the Early Scots language spread across the lowland parts of Scotland between Galloway and the Highland line, being used by Barbour in his historical epic The Brus in the late 14th century in Aberdeen. From 1500 on, Scotland was divided by language into two groups of people, Gaelic-speaking "Highlanders" and the Inglis-speaking "Lowlanders". Today, immigrants have brought other languages, but every adult throughout Scotland is fluent in the English language. Today, Scotland has a population of just over five million people, the majority of whom co
Duchy of Lorraine
The Duchy of Lorraine Upper Lorraine, was a duchy now included in the larger present-day region of Lorraine in northeastern France. Its capital was Nancy, it was founded in 959 following the division of Lotharingia into two separate duchies: Upper and Lower Lorraine, the westernmost parts of the Holy Roman Empire. The Lower duchy was dismantled, while Upper Lorraine came to be known as the Duchy of Lorraine; the Duchy of Lorraine was coveted and occupied by the Dukes of Burgundy and the Kings of France. In 1737, the Duchy was given to Stanisław Leszczyński, the former king of Poland, who had lost his throne as a result of the War of the Polish Succession, with the understanding that it would fall to the French crown on his death; when Stanisław died on 23 February 1766, Lorraine was annexed by France and reorganized as a province. Lorraine's predecessor, was an independent Carolingian kingdom under the rule of King Lothair II, its territory had been a part of Middle Francia, created in 843 by the Treaty of Verdun, when the Carolingian empire was divided between the three sons of Louis the Pious.
Middle Francia was allotted to Emperor Lothair I, therefore called Lotharii Regnum. On his death in 855, it was further divided into three parts, of which his son Lothair II took the northern one, his realm comprised a larger territory stretching from the County of Burgundy in the south to the North Sea. In French, this area became known as Lorraine, while in German, it was known as Lothringen. In the Alemannic language once spoken in Lorraine, the -ingen suffix signified a property; as Lothair II had died without heirs, his territory was divided by the 870 Treaty of Meerssen between East and West Francia and came under East Frankish rule as a whole by the 880 Treaty of Ribemont. After the East Frankish Carolingians became extinct with the death of Louis the Child in 911, Lotharingia once again attached itself to West Francia, but was conquered by the German king Henry the Fowler in 925. Stuck in the conflict with his rival Hugh the Great, in 942 King Louis IV of France renounced all claims to Lotharingia.
In 953, the German king Otto. In 959, Bruno divided the duchy into Lower Lorraine; the Upper Duchy was further "up" the river system. Upper Lorraine was first denominated as the Duchy of the Moselle, both in charters and narrative sources, its duke was the dux Mosellanorum; the usage of Lotharingia Superioris and Lorraine in official documents begins around the fifteenth century. The first duke and deputy of Bruno was Frederick I of Bar, son-in-law of Bruno's sister Hedwig of Saxony. Lower Lorraine disintegrated into several smaller territories and only the title of a "Duke of Lothier" remained, held by Brabant. After the duchy of the Moselle came into the possession of René of Anjou, the name "Duchy of Lorraine" was adopted again, only retrospectively called "Upper Lorraine". At that time, several territories had split off, such as the County of Luxembourg, the Electorate of Trier, the County of Bar and the "Three Bishoprics" of Verdun and Toul; the border between the Empire and the Kingdom of France remained stable throughout the Middle Ages.
In 1301, Count Henry III of Bar had to receive the western part of his lands as a fief by King Philip IV of France. In 1475, the Burgundian duke Charles the Bold campaigned for the Duchy of Lorraine, but was defeated and killed at the 1477 Battle of Nancy. In the 1552 Treaty of Chambord, a number of insurgent Protestant Imperial princes around Elector Maurice of Saxony ceded the Three Bishoprics to King Henry II of France in turn for his support. Due to the weakening of Imperial authority during the 1618-1648 Thirty Years' War, France was able to occupy the duchy in 1634 and retained it until 1661 when Charles IV was restored. In 1670, the French invaded again. France returned the Duchy in the 1697 Treaty of Ryswick ending the Nine Years' War and Charles' son Leopold, became duke and was known as'Leopold the Good. In 1737, after the War of the Polish Succession, an agreement between France, the Habsburgs and the Lorraine House of Vaudémont assigned the Duchy to Stanisław Leszczyński, former king of Poland.
He was father-in-law to King Louis XV of France, who lost out to a candidate backed by Russia and Austria in the War of the Polish Succession. The Lorraine duke Francis Stephen, betrothed to the Emperor's daughter Archduchess Maria Theresa, was compensated with the Grand Duchy of Tuscany, where the last Medici ruler had died without issue. France promised to support Maria Theresa as heir to the Habsburg possessions under the Pragmatic Sanction of 1713. Leszczyński received Lorraine with the understanding that it would fall to the French crown on his death; the title of Duke of Lorraine was of course given to Stanisław, but retained by Francis Stephen, it figures prominently in the titles of his successors, the House of Habsburg-Lorraine. When Stanisław died on 23 February 1766, Lorraine was annexed by France and reorganized as a province by the French government. Two regional languages survive in the re
Alexander Hume-Campbell, 2nd Earl of Marchmont
Alexander Hume-Campbell, 2nd Earl of Marchmont, was a Scottish nobleman and judge. The third but eldest surviving son of Patrick Hume, 1st Earl of Marchmont, by his spouse Grisel, daughter of Sir Thomas Ker of Cavers, he assumed the additional surname of Campbell upon his marriage in 1697 with Margaret and heiress of Sir George Campbell of Cessnock, Ayrshire, he studied law at Utrecht University and became an advocate in 1696. He was appointed to the Court of Session in 1704 with the judicial title Lord Cessnock, served there until 1714, he was a Commissioner to the Parliament of Scotland for Berwickshire in 1706, was a supporter of the Union with England. He was Lord Clerk Register from 1716 to 1733, he was ambassador to Denmark from 1715 to 1721, to the Congress at Cambray in 1722. He succeeded his father to the earldom in 1724, was a Scottish representative peer from 1727 to 1734. Alexander served as one of the founding governors of Britain's first childcare charity, the Foundling Hospital, which received its royal charter in 1739.
The Peerage of Scotland, published by Peter Brown, Edinburgh, 1834, p. 146. "Campbell, Alexander". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900
Leonhard Euler was a Swiss mathematician, astronomer and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while making pioneering contributions to several branches such as topology and analytic number theory. He introduced much of the modern mathematical terminology and notation for mathematical analysis, such as the notion of a mathematical function, he is known for his work in mechanics, fluid dynamics, optics and music theory. Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history, he is widely considered to be the most prolific mathematician of all time. His collected works fill more than anybody in the field, he spent most of his adult life in Saint Petersburg, in Berlin the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Leonhard Euler was born on 15 April 1707, in Basel, Switzerland to Paul III Euler, a pastor of the Reformed Church, Marguerite née Brucker, a pastor's daughter.
He had two younger sisters: Anna Maria and Maria Magdalena, a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, where Euler spent most of his childhood. Paul Euler was a friend of the Bernoulli family. Euler's formal education started in Basel. In 1720, aged thirteen, he enrolled at the University of Basel, in 1723, he received a Master of Philosophy with a dissertation that compared the philosophies of Descartes and Newton. During that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who discovered his new pupil's incredible talent for mathematics. At that time Euler's main studies included theology and Hebrew at his father's urging in order to become a pastor, but Bernoulli convinced his father that Leonhard was destined to become a great mathematician. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono. At that time, he was unsuccessfully attempting to obtain a position at the University of Basel.
In 1727, he first entered the Paris Academy Prize Problem competition. Pierre Bouguer, who became known as "the father of naval architecture", won and Euler took second place. Euler won this annual prize twelve times. Around this time Johann Bernoulli's two sons and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. On 31 July 1726, Nicolaus died of appendicitis after spending less than a year in Russia, when Daniel assumed his brother's position in the mathematics/physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel. Euler arrived in Saint Petersburg on 17 May 1727, he was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration.
Euler settled into life in Saint Petersburg. He took on an additional job as a medic in the Russian Navy; the Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia and to close the scientific gap with Western Europe. As a result, it was made attractive to foreign scholars like Euler; the academy possessed ample financial resources and a comprehensive library drawn from the private libraries of Peter himself and of the nobility. Few students were enrolled in the academy in order to lessen the faculty's teaching burden, the academy emphasized research and offered to its faculty both the time and the freedom to pursue scientific questions; the Academy's benefactress, Catherine I, who had continued the progressive policies of her late husband, died on the day of Euler's arrival. The Russian nobility gained power upon the ascension of the twelve-year-old Peter II; the nobility was suspicious of the academy's foreign scientists, thus cut funding and caused other difficulties for Euler and his colleagues.
Conditions improved after the death of Peter II, Euler swiftly rose through the ranks in the academy and was made a professor of physics in 1731. Two years Daniel Bernoulli, fed up with the censorship and hostility he faced at Saint Petersburg, left for Basel. Euler succeeded him as the head of the mathematics department. On 7 January 1734, he married Katharina Gsell, a daughter of Georg Gsell, a painter from the Academy Gymnasium; the young couple bought a house by the Neva River. Of their thirteen children, only five survived childhood. Concerned about the continuing turmoil in Russia, Euler left St. Petersburg on 19 June 1741 to take up a post at the Berlin Academy, which he had been offered by Frederick the Great of Prussia, he lived for 25 years in Berlin. In Berlin, he published the two works for which he would become most renowned: the Introductio in analysin infinitorum, a text on functions published in 1748, the Institutiones calculi differentialis, published in 1755 on differential calculus.