A croft is a fenced or enclosed area of land small and arable, but not always, with a crofter's dwelling thereon. A crofter is one who has tenure and use of the land as a tenant farmer in rural areas; the word croft is West Germanic in etymology and is now most familiar in Scotland, most crofts being in the Highlands and Islands area. Elsewhere the expression is archaic. In Scottish Gaelic, it is rendered croit. Similar positions have been the medieval villein and the Swedish torpare and Norwegian husmenn; the Scottish croft is a small agricultural landholding of a type, subject to special legislation applying to the Highland region of Scotland since 1886. The legislation was a response to the complaints and demands of tenant families who were victims of the Highland Clearances; the modern crofters or tenants appear little in evidence before the beginning of the 18th century. They were tenants at will underneath the tacksman and wadsetters, but their tenure was secure enough; the first evidence that can be found of small tenants holding directly of the proprietor is in a rental of the estates of Sir D. MacDonald in Skye and North Uist in 1715.
The first planned crofting townships in the Outer Hebrides were Barragloum and Kirkibost which were laid out into 32 large "lots" of between 14 and 30 acres in the uniform rectangular pattern that would become familiar in decades. This work was carried out in 1805 by James Chapman for the Earl of Seaforth; the first edition of the Ordnance Survey in 1850 highlights the division of this land and the turf and stone boundaries built by the first tenants in 1805 are still in use today as croft boundaries. Kirkibost was'cleared' of its tenants in 1823 and the 1850 mapping shows roofless ruins on each parcel of land; the township was however re-settled in 1878 following the Bernera Riot four years earlier using the same division boundaries set out in 1805. The Parliament of the United Kingdom created the Crofters' Act 1886, after the Highland Land League had gained seats in that parliament; the government was Liberal, with William Ewart Gladstone as Prime Minister. Another Crofters' Act was created in 1993.
The earlier Act established the first Crofting Commission, but its responsibilities were quite different from those of the newer Crofters Commission created in 1955. The Commission is based in Inverness. Crofts held subject to the provisions of the Crofters' Acts are in the administrative counties of Shetland, Caithness, Ross-shire, Inverness-shire and Argyll, in the north and west of Scotland. Under the 1886 legislation protected crofters are members of a crofters' township, consisting of tenants of neighbouring crofts with a shared right to use common pasture. Since 1976 it has been possible for a crofter to acquire title to his croft, thus becoming an owner-occupier; the Land Reform Act 2003 gives crofters the right to buy their land. Crofting Torp This article incorporates text from "Dwelly's Gaelic Dictionary". Scottish Crofting Federation Crofters CommissionArticles Crofters, Indigenous People of the Highlands and Islands at Scottish Crofting Foundation
In mathematics, the trigonometric functions are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications; the most familiar trigonometric functions are the sine and tangent. In the context of the standard unit circle, where a triangle is formed by a ray starting at the origin and making some angle with the x-axis, the sine of the angle gives the y-component of the triangle, the cosine gives the x-component, the tangent function gives the slope. For angles less than a right angle, trigonometric functions are defined as ratios of two sides of a right triangle containing the angle, their values can be found in the lengths of various line segments around a unit circle. Modern definitions express trigonometric functions as infinite series or as solutions of certain differential equations, allowing the extension of the arguments to the whole number line and to the complex numbers.
Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles. In this use, trigonometric functions are used, for instance, in navigation and physics. A common use in elementary physics is resolving a vector into Cartesian coordinates; the sine and cosine functions are commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, average temperature variations through the year. In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. With the last four, these relations are taken as the definitions of those functions, but one can define them well geometrically, or by other means, derive these relations; the notion that there should be some standard correspondence between the lengths of the sides of a triangle and the angles of the triangle comes as soon as one recognizes that similar triangles maintain the same ratios between their sides.
That is, for any similar triangle the ratio of the hypotenuse and another of the sides remains the same. If the hypotenuse is twice as long, so are the sides, it is these ratios. To define the trigonometric functions for the angle A, start with any right triangle that contains the angle A; the three sides of the triangle are named as follows: The hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle; the opposite side is the side opposite in this case side a. The adjacent side is the side having both the angles in this case side b. In ordinary Euclidean geometry, according to the triangle postulate, the inside angles of every triangle total 180°. Therefore, in a right-angled triangle, the two non-right angles total 90°, so each of these angles must be in the range of as expressed in interval notation; the following definitions apply to angles in this range. They can be extended to the full set of real arguments by using the unit circle, or by requiring certain symmetries and that they be periodic functions.
For example, the figure shows sin for angles θ, π − θ, π + θ, 2π − θ depicted on the unit circle and as a graph. The value of the sine repeats itself apart from sign in all four quadrants, if the range of θ is extended to additional rotations, this behavior repeats periodically with a period 2π; the trigonometric functions are summarized in the following table and described in more detail below. The angle θ is the angle between the hypotenuse and the adjacent line – the angle at A in the accompanying diagram; the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The word comes from the Latin sinus for gulf or bay, given a unit circle, it is the side of the triangle on which the angle opens. In that case: sin A = opposite hypotenuse The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse, so called because it is the sine of the complementary or co-angle, the other non-right angle; because the angle sum of a triangle is π radians, the co-angle B is equal to π/2 − A.
In that case: cos A = adjacent hypotenuse The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side, so called because it can be represented as a line segment tangent to the circle, i.e. the line that touches the circle, from Latin linea tangens or touching line. In our case: tan A = opposite adjacent Tangent may be represented in terms of sine and cosine; that is: tan A = sin A cos A = opposite
World War I
World War I known as the First World War or the Great War, was a global war originating in Europe that lasted from 28 July 1914 to 11 November 1918. Contemporaneously described as "the war to end all wars", it led to the mobilisation of more than 70 million military personnel, including 60 million Europeans, making it one of the largest wars in history, it is one of the deadliest conflicts in history, with an estimated nine million combatants and seven million civilian deaths as a direct result of the war, while resulting genocides and the 1918 influenza pandemic caused another 50 to 100 million deaths worldwide. On 28 June 1914, Gavrilo Princip, a Bosnian Serb Yugoslav nationalist, assassinated the Austro-Hungarian heir Archduke Franz Ferdinand in Sarajevo, leading to the July Crisis. In response, on 23 July Austria-Hungary issued an ultimatum to Serbia. Serbia's reply failed to satisfy the Austrians, the two moved to a war footing. A network of interlocking alliances enlarged the crisis from a bilateral issue in the Balkans to one involving most of Europe.
By July 1914, the great powers of Europe were divided into two coalitions: the Triple Entente—consisting of France and Britain—and the Triple Alliance of Germany, Austria-Hungary and Italy. Russia felt it necessary to back Serbia and, after Austria-Hungary shelled the Serbian capital of Belgrade on the 28th, partial mobilisation was approved. General Russian mobilisation was announced on the evening of 30 July; when Russia failed to comply, Germany declared war on 1 August in support of Austria-Hungary, with Austria-Hungary following suit on 6th. German strategy for a war on two fronts against France and Russia was to concentrate the bulk of its army in the West to defeat France within four weeks shift forces to the East before Russia could mobilise. On 2 August, Germany demanded free passage through Belgium, an essential element in achieving a quick victory over France; when this was refused, German forces invaded Belgium on 3 August and declared war on France the same day. On 12 August and France declared war on Austria-Hungary.
In November 1914, the Ottoman Empire entered the war on the side of the Alliance, opening fronts in the Caucasus and the Sinai Peninsula. The war was fought in and drew upon each power's colonial empire as well, spreading the conflict to Africa and across the globe; the Entente and its allies would become known as the Allied Powers, while the grouping of Austria-Hungary and their allies would become known as the Central Powers. The German advance into France was halted at the Battle of the Marne and by the end of 1914, the Western Front settled into a battle of attrition, marked by a long series of trench lines that changed little until 1917. In 1915, Italy opened a front in the Alps. Bulgaria joined the Central Powers in 1915 and Greece joined the Allies in 1917, expanding the war in the Balkans; the United States remained neutral, although by doing nothing to prevent the Allies from procuring American supplies whilst the Allied blockade prevented the Germans from doing the same the U. S. became an important supplier of war material to the Allies.
After the sinking of American merchant ships by German submarines, the revelation that the Germans were trying to incite Mexico to make war on the United States, the U. S. declared war on Germany on 6 April 1917. Trained American forces would not begin arriving at the front in large numbers until mid-1918, but the American Expeditionary Force would reach some two million troops. Though Serbia was defeated in 1915, Romania joined the Allied Powers in 1916 only to be defeated in 1917, none of the great powers were knocked out of the war until 1918; the 1917 February Revolution in Russia replaced the Tsarist autocracy with the Provisional Government, but continuing discontent at the cost of the war led to the October Revolution, the creation of the Soviet Socialist Republic, the signing of the Treaty of Brest-Litovsk by the new government in March 1918, ending Russia's involvement in the war. This allowed the transfer of large numbers of German troops from the East to the Western Front, resulting in the German March 1918 Offensive.
This offensive was successful, but the Allies rallied and drove the Germans back in their Hundred Days Offensive. Bulgaria was the first Central Power to sign an armistice—the Armistice of Salonica on 29 September 1918. On 30 October, the Ottoman Empire capitulated. On 4 November, the Austro-Hungarian empire agreed to the Armistice of Villa Giusti after being decisively defeated by Italy in the Battle of Vittorio Veneto. With its allies defeated, revolution at home, the military no longer willing to fight, Kaiser Wilhelm abdicated on 9 November and Germany signed an armistice on 11 November 1918. World War I was a significant turning point in the political, cultural and social climate of the world; the war and its immediate aftermath sparked numerous uprisings. The Big Four (Britain, the United States, It
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It is the oldest university in the German-speaking world. With its long and rich history, the University of Vienna has developed into one of the largest universities in Europe, one of the most renowned in the Humanities, it is associated with 20 Nobel prize winners and has been the academic home to a large number of scholars of historical as well as of academic importance. The University was founded on 12 March 1365 by Rudolf IV, Duke of Austria, his two brothers, Dukes Albert III and Leopold III, hence the additional name "Alma Mater Rudolphina". After the Charles University in Prague and Jagiellonian University in Kraków, the University of Vienna is the third oldest university in Central Europe and the oldest university in the contemporary German-speaking world; the University of Vienna was modelled after the University of Paris. However, Pope Urban V did not ratify the deed of foundation, sanctioned by Rudolf IV in relation to the department of theology.
This was due to pressure exerted by Charles IV, Holy Roman Emperor, who wished to avoid competition for the Charles University in Prague. Approval was received from the Pope in 1384 and the University of Vienna was granted the status of a full university, including the Faculty of Catholic Theology; the first university building opened in 1385. It grew into the biggest university of the Holy Roman Empire, during the advent of Humanism in the mid-15th century was home to more than 6,000 students. In its early years, the university had a hierarchical cooperative structure, in which the Rector was at the top, while the students had little say and were settled at the bottom; the Magister and Doctors constituted the four faculties and elected the academic officials from amidst their ranks. The students, but all other Supposita, were divided into four Academic Nations, their elected board members graduates themselves, had the right to elect the Rector. He presided over the Consistory which included procurators of each of the nations and the faculty deans, as well as over the University Assembly, in which all university teachers participated.
Complaints or appeals against decisions of faculty by the students had to be brought forward by a Magister or Doctor. Being considered a Papal Institution, the university suffered quite a setback during the Reformation. In addition, the first Siege of Vienna by Ottoman forces had devastating effects on the city, leading to a sharp decline, with only 30 students enrolled at the lowest point. For King Ferdinand I, this meant that the university should be tied to the church to an stronger degree, in 1551 he installed the Jesuit Order there. With the enacting of the Sanctio Pragmatica edict by emperor Ferdinand II in 1623, the Jesuits took over teaching at the theological and philosophical faculty, thus the university became a stronghold of Catholicism for over 150 years, it was only in the Mid-18th century that Empress Maria Theresa forced the university back under control of the monarchy. Her successor Joseph II helped in the further reform of the university, allowing both Protestants and Jews to enroll as well as introducing German as the compulsory language of instruction.
Big changes were instituted in the wake of the Revolution in 1848, with the Philosophical Faculty being upgraded into equal status as Theology and Medicine. Led by the reforms of Leopold, Count von Thun und Hohenstein, the university was able to achieve a larger degree of academic freedom; the current main building on the Ringstraße was built between 1884 by Heinrich von Ferstel. The previous main building was located close to the Stuben Gate on Iganz Seipel Square, current home of the old University Church and the Austrian Academy of Sciences. Women were admitted as full students from 1897; the remaining departments followed suit, although with considerable delay: Medicine in 1900, Law in 1919, Protestant Theology in 1923 and Roman Catholic Theology in 1946. Ten years after the admission of the first female students, Elise Richter became the first woman to receive habilitation, becoming professor of Romance Languages in 1907. In the late 1920s, the university was in steady turmoil because of anti-democratic and anti-Semitic activity by parts of the student body.
Professor Moritz Schlick was killed by a former student while ascending the steps of the University for a class. His murderer was released by the Nazi Regime. Following the Anschluss, the annexation of Austria into Greater Germany by the Nazi regime, in 1938 the University of Vienna was reformed under political aspects and a huge number of teachers and students were dismissed for political and "racial" reasons. In April 1945, the 22-year-old Kurt Schubert acknowledged doyen of Judaic Studies at the University of Vienna, was permitted by the Soviet occupation forces to open the university again for teaching, why he is regarded as the unofficial first rector in the post-war period. On 25 April 1945, the constitutional lawyer Ludwig Adamovich senior was elected as official rector of the University of Vienna. A large degree of participation by students and university staff was realized in 1975, however the University Reforms of 1993 and 2002 re-established the professors as the main decision makers.
However as part of the last refo
Ljubljana is the capital and largest city of Slovenia. It has been the cultural, economic and administrative centre of independent Slovenia since 1991. During antiquity, a Roman city called. Ljubljana itself was first mentioned in the first half of the 12th century. Situated at the middle of a trade route between the northern Adriatic Sea and the Danube region, it was the historical capital of Carniola, one of the Slovene-inhabited parts of the Habsburg Monarchy, it was under Habsburg rule from the Middle Ages until the dissolution of the Austro-Hungarian Empire in 1918. After World War II, Ljubljana became the capital of the Socialist Republic of Slovenia, part of the Socialist Federal Republic of Yugoslavia, it retained this status until Slovenia became independent in 1991 and Ljubljana became the capital of the newly formed state. The origin of name of the city, Ljubljana, is unclear. In the Middle Ages, both the river and the town were known by the German name Laibach; this name was in official use as an endonym until 1918, it remains frequent as a German exonym, both in common speech and official use.
The city is alternatively named Lublana in many English language documents. The city is called Lublana in Silesian, Lubiana in Latin: Labacum and anciently Aemona. For most scholars, the problem has been in how to connect the German names; the origin from the Slavic ljub- "to love, like" was in 2007 supported as the most probable by the linguist Tijmen Pronk, a specialist in comparative Indo-European linguistics and Slovene dialectology, from the University of Leiden. He supported the thesis; the linguist Silvo Torkar, who specialises in Slovene personal and place names, argued at the same place for the thesis that the name Ljubljana derives from Ljubija, the original name of the Ljubljanica River flowing through it, itself derived from the Old Slavic male name Ljubovid, "the one of a lovely appearance". The name Laibach, he claimed, was a hybrid of German and Slovene and derived from the same personal name; the symbol of the city is the Ljubljana Dragon. It is depicted on the top of the tower of Ljubljana Castle in the Ljubljana coat of arms and on the Ljubljanica-crossing Dragon Bridge.
It symbolises power and greatness. There are several explanations on the origin of the Ljubljana Dragon. According to a Slavic myth, the slaying of a dragon releases the waters and ensures the fertility of the earth, it is thought that the myth is tied to the Ljubljana Marshes, the expansive marshy area that periodically threatens Ljubljana with flooding. According to the celebrated Greek legend, the Argonauts on their return home after having taken the Golden Fleece found a large lake surrounded by a marsh between the present-day towns of Vrhnika and Ljubljana, it was there. This monster has evolved into the dragon, it is more believable that the dragon was adopted from Saint George, the patron of the Ljubljana Castle chapel built in the 15th century. In the legend of Saint George, the dragon represents the old ancestral paganism overcome by Christianity. According to another explanation, related to the second, the dragon was at first only a decoration above the city coat of arms. In the Baroque, it became part of the coat of arms, in the 19th and the 20th century, it outstripped the tower and other elements in importance.
Around 2000 BC, the Ljubljana Marshes in the immediate vicinity of Ljubljana were settled by people living in pile dwellings. Prehistoric pile dwellings and the oldest wooden wheel in the world are among the most notable archeological findings from the marshland; these lake-dwelling people lived through hunting and primitive agriculture. To get around the marshes, they used dugout canoes made by cutting out the inside of tree trunks, their archaeological remains, nowadays in the Municipality of Ig, have been designated a UNESCO World Heritage Site since June 2011, in the common nomination of six Alpine states. The area remained a transit point for numerous tribes and peoples, among them the Illyrians, followed by a mixed nation of the Celts and the Illyrians called the Iapydes, in the 3rd century BC a Celtic tribe, the Taurisci. Around 50 BC, the Romans built a military encampment that became a permanent settlement called Iulia Aemona; this entrenched fort was occupied by the Legio XV Apollinaris.
In 452, it was destroyed by the Huns under Attila's orders, by the Ostrogoths and the Lombards. Emona housed 5,000 -- 6,000 played an important role during numerous battles, its plastered brick houses, painted in different colours, were connected to a drainage system. In the 6th century, the ancestors of the Slovenes moved in. In the 9th century, they fell while experiencing frequent Magyar raids. Not much is known about the area during the settlement of Slavs in the period between the downfall of Emona and the Early Middle Ages; the parchment sheet Nomina defunctorum, most written in the second half of 1161, mentions the nobleman Rudolf of Tarcento, a lawyer of the Patriarchate of Aquileia, who had bestowed a canon with 20 farmsteads beside the castle of Ljubljana to the Patriarchate. According to the historian Peter Štih's deduction, this happened between 1112 and 1125, thus representing the earliest mention of Ljubljana. Owned by a number of possessors, until the first half of the 12th century, the territory south of the Sava where the town of
Arithmetic is a branch of mathematics that consists of the study of numbers the properties of the traditional operations on them—addition, subtraction and division. Arithmetic is an elementary part of number theory, number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra and analysis; the terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory. The prehistory of arithmetic is limited to a small number of artifacts which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed; the earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system influence the complexity of the methods.
The hieroglyphic system for Egyptian numerals, like the Roman numerals, descended from tally marks used for counting. In both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a counting board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the sexagesimal system for Babylonian numerals and the vigesimal system that defined Maya numerals; because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much than the Babylonian and Egyptian examples. Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, their relationships to each other, in his Introduction to Arithmetic. Greek numerals were used by Archimedes and others in a positional notation not different from ours; the ancient Greeks lacked a symbol for zero until the Hellenistic period, they used three separate sets of symbols as digits: one set for the units place, one for the tens place, one for the hundreds. For the thousands place they would reuse the symbols for the units place, so on, their addition algorithm was identical to ours, their multiplication algorithm was only slightly different. Their long division algorithm was the same, the digit-by-digit square root algorithm, popularly used as as the 20th century, was known to Archimedes, who may have invented it, he preferred it to Hero's method of successive approximation because, once computed, a digit doesn't change, the square roots of perfect squares, such as 7485696, terminate as 2736.
For numbers with a fractional part, such as 546.934, they used negative powers of 60 instead of negative powers of 10 for the fractional part 0.934. The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra; the ancient Chinese used a positional notation similar to that of the Greeks. Since they lacked a symbol for zero, they had one set of symbols for the unit's place, a second set for the ten's place. For the hundred's place they reused the symbols for the unit's place, so on, their symbols were based on the ancient counting rods. It is a complicated question to determine when the Chinese started calculating with positional representation, but it was before 400 BC; the ancient Chinese were the first to meaningfully discover and apply negative numbers as explained in the Nine Chapters on the Mathematical Art, written by Liu Hui. The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing 0.
This allowed the system to represent both large and small integers. This approach replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number and determined the results for multiplication, division and subtraction of zero and all other numbers, except for the result of division by 0, his contemporary, the Syriac bishop Severus Sebokht said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols." The Arabs learned this new method and called it hesab. Although the Codex Vigilanus described an early form of Arabic numerals by 976 AD, Leonardo of Pisa was responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202, he wrote, "The method of the Indians surpasses any known method to compute.
It's a marvelous method. They do their computations using nine figures and symbol zero". In the Middle Ages, arithmetic was one of the seven