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 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 their strategic location in the North Atlantic, the Faroes could have proved useful to Germany in the Battle of the Atlantic, possibly as a submarine base.

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 that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

Given the great historical link between Persian and Jewish history, modern day Persian Jews are called " Esther's Children ".

Given the distances between the stars, the great majority of stellar systems in colliding galaxies will be unaffected.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

Given the biogeography and appearance of the subgenus Olor it seems likely that these are of a more recent origin, as evidence shows by their modern ranges ( which were mostly uninhabitable during the last ice age ) and great similarity between the taxa.

On 24 July 2003, the Congregation for the Doctrine of the Faith stated, " Given the centrality of the celebration of the Eucharist in the life of a priest, one must proceed with great caution before admitting to Holy Orders those candidates unable to ingest gluten or alcohol without serious harm.

Given its great distance, the daytime " guest star " observed by the Chinese could only have been a supernova — a massive, exploding star, having exhausted its supply of energy from nuclear fusion and collapsed in on itself.

Given the great depth of Lake Tahoe, and the locations of the normal faults within the deepest portions of the lake, modeling suggests that earthquakes on these faults can trigger tsunamis.

Given the very conservative engineering of the early IBM personal computers and their higher than average prices, this was not a terribly difficult task at first, bar only the great technical challenge of crafting a BIOS that duplicated the function of the IBM BIOS exactly but did not infringe on copyrights.

Given the demands of his career in the Navy and NASA, Pete and Jane spent a great deal of time apart, and Pete saw less of his boys growing up than he would have liked.

Given that other philosophers claim that scientific accounts of our mental lives, particularly in the cognitive sciences, need this idea, this claim of McDowell's has provoked a great deal of discussion.

Given his history with the Ruthvens, and that he owed them a great deal of money, James's account of the circumstances was not universally believed.

Given the age of the institution, many of the collections have great historical as well as scientific value, such as specimens collected by Darwin.

Weekly Standard Editor William Kristol said at the time, " Given that Reagan obviously couldn't be here, I think it was important to have Mrs. Thatcher because she and Reagan are really the great heroes of conservatism in the last few decades and still today.

Given my time again, I wouldn't repeat it-but the great legend is complete, bloody rubbish.

: Given the centrality of the celebration of the Eucharist in the life of a priest, one must proceed with great caution before admitting to Holy Orders those candidates unable to ingest alcohol without serious harm.

Given the great size of the flats, there is plenty of room for these race cars to reach their full potential.

Given the ability to knock down, in essence, any gene of interest, RNAi via siRNAs has generated a great deal of interest in both basic and applied biology.

Given its extensive use in religious literature, primarily in Hinduism, and the fact that most modern Indian languages have been directly derived from or strongly influenced by Sanskrit, the language and its literature is of great importance in Indian culture akin to that of Greek and Latin in European culture.

Given a unit sphere, a " triangle " on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere.

Given the fact that, at one time, Llanrwst was one of the ten largest towns in Wales, it can be seen that the Conwy Valley had great historical significance.

Given that the Communist governments all insisted on having a total monopoly of control over educational institutions, the preservation of its independence was a great achievement.

Given the precision of Brown's calculations, it must have come as a great disappointment to have to introduce this arbitrary adjustment.

Given that winter was coming, and many lorries were overloaded with coal, a great number of lorries failed the test.