Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Given the large number of U. S. military personnel and their dependents residing in Europe, it was expected that over 7 % of donors would be deferred due to the policy.

Given their great antiquity, where and when they first existed is not known and perhaps unknowable.

Given that the ColecoVision could produce near arcade-quality ports, industry magazines like Electronic Games were unanimous in their enthusiasm over the console.

Given their speed and maneuverability, clippers frequently mounted cannon or carronades and were used for piracy, privateering, smuggling, or interdiction service.

Given limited defense budgets, air forces tended to be conservative in their aircraft purchases, and biplanes remained popular with pilots because of their agility, and remained in service long after they had ceased to be competitive.

Given f ∈ G ( x * x < sup >- 1 </ sup >, y * y < sup >-1 </ sup >) and g ∈ G ( y * y < sup >-1 </ sup >, z * z < sup >-1 </ sup >), their composite is defined as g * f ∈ G ( x * x < sup >-1 </ sup >, z * z < sup >-1 </ sup >).

Given that the Qur ' an is vague regarding the punishment of homosexual sodomy, Islamic jurists turned to the collections of the hadith and seerah ( accounts of Muhammad's life ) to support their argument for Hudud punishment ; these are perfectly clear but particularly harsh.

Given two Lie algebras and, their direct sum is the Lie algebra consisting of the vector space

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

Given their wide historical distribution, red wolves probably utilized a large suite of habitat types at one time.

Given that by this time it was common for castles to be built in stone, and that many barons had expanded or refortified their castles, this was not an easy task.

Given that the decree was issued at Memphis, the ancient capital of Egypt, rather than Alexandria, the centre of government of the ruling Ptolemies, it is evident that the young king was anxious to gain their active support.

Given its exposed spot on the top of Stow Hill, the town is often referred to with the couplet " Stow on the Wold, where the winds blow cold and the cooks can't roast their dinners ", but there is no source for this.

Given their hunting instincts, they are prone to chasing moving objects.

Given a list of cities and their pairwise distances, the task is to find the shortest possible route that visits each city exactly once and returns to the origin city.

Given this new danger, the United States participated in an arms race with the Soviet Union that included development of the hydrogen bomb, as well as intercontinental strategic bombers and intercontinental ballistic missiles ( ICBMs ) capable of delivering nuclear weapons.

Given its strategic value, Winston Churchill would later quote a telegram he sent to the Chief of the Imperial General Staff on 4 June 1940: " To lose Crete because we had not sufficient bulk of forces there would be a crime.

Given its harbors and fortifications, Saint Thomas still retained a strategic importance, and thus, in the 1860s, during the American Civil War and its aftermath, the United States government considered buying the island and its neighbors from Denmark for $ 7. 5 million, but at the time failed to find domestic legislative support for the bid.

Given the strategic requirements of winning the war, British Prime Minister Winston Churchill and U. S. President Franklin D. Roosevelt had no option but to accept the demands of their erstwhile ally, Soviet Premier Joseph Stalin, at Tehran, Yalta and Potsdam, argues retired diplomat Charles G. Stefan.

Given Newfoundland's strategic location in the Battle of the Atlantic, the Allies ( especially the United States of America ) built many military bases there.

Given that National Education is France's largest employer, and employs more than half of the French state civil servants, the position is traditionally a fairly strategic one.

Given the strategic and ( usually ) tactical importance of control of the center, the pawn is important enough that the player must consistently defend it, but with no pawns available for its defense, the player must " tie down " a minor or major piece ( in the opening, usually the king's knight or the queen ) with that task.

Given the misery visited upon the local population by the Japanese, criticism has arisen as to whether Operation Jaywick was justified, especially with its relatively limited strategic results.

Given that broad strategic decisions, such as the decision to declare a war, start an invasion, or end a conflict, have a major impact on the citizens of the country, they are seen by civilian control advocates as best guided by the will of the people ( as expressed by their political representatives ), rather than left solely to an elite group of tactical experts.

Given its small domestic market but favourable location and a superb transport and communications base, Namibia is a leading advocate of regional economic integration.

* Named entity recognition ( NER ): Given a stream of text, determine which items in the text map to proper names, such as people or places, and what the type of each such name is ( e. g. person, location, organization ).

Given good viewing conditions, Thuban is relatively easy to spot in the night sky, due to its location in relation to the Big Dipper asterism of Ursa Major.

Given a sample of wood, the variation of the tree ring growths provides not only a match by year, it can also match location because the climate across a continent is not consistent.

Given its location, Perth was perfectly placed to become a key transport centre with the coming of the railways, and its first station was built in 1848.

Given City Hall's attractive location and park atmosphere, weddings are regularly performed on the lawn.

Given the extent and central location of his original holding from the Mill Seat Tract, and the fact that most of the town's pre-1944 building lots are to, Bare's ability to shape the size and extent of development in Roaring Spring was substantial.

Given its location at the base of the Black Hills and its proximity to the High Plains, the climate in Spearfish is highly variable at any time of the year.

Given the dynamic nature of the seafloor, changes in the location of shoals and bars may cause the locus of beach or cliff erosion to change position along the shore.

Given its location toward the south end of campus, this building was temporarily " South Hall " but was later changed as a dedication to Rev.

* Point location: Given a partitioning of the space into cells, produce a data structure that efficiently tells in which cell a query point is located.

Given the variety of approaches, Economic Geography has taken to many different subject matters, including: the location of industries, economies of agglomeration ( also known as " linkages "), transportation, international trade, economic development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy ( tying into a long history of geographers studying culture-environment interaction ), and globalization.

Given its central location, Athlone is a natural hub for transport, with frequent bus and rail schedules.

Given its limited attendance and location, this kurultai was of questionable validity.

Given the finite supply of natural resources at any specific cost and location, agriculture that is inefficient or damaging to needed resources may eventually exhaust the available resources or the ability to afford and acquire them.

Given the university's location in Nashville, many of its alumni become involved in the music industry.

: Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance.

Given the coastal location, the town is also served by an RNLI lifeboat station and a HM Coastguard post.

Given its island location, the risk of severe frost is negated by the surrounding waters.

Given its location, Saint-Nazaire has a long tradition of fishing and shipbuilding.

Given its location, timber and Brazil-nuts make up important trades, as do petroleum refining, soap manufacturing, and chemical industries.

Given its privileged location, lately it has been considered as the Pacific Door of Colombia.

Given its rural location, much of the focus of the school has been on undergraduate studies in education and agriculture, although many other courses of study are offered, particularly in the liberal arts, and in recent years there has been an increasing emphasis on business, engineering, and music.

Given the village's rich history, coastal location and close proximity to eastern U. S. cities, Cabot Cove was transformed from a small, sleepy fishing village to a tourist destination for the people coming from New York.