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 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 coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given a situation in which water is already sitting in a tea kettle on top of a gas burner, then someone lighting the gas under the kettle may be perceived as the " cause " of the water's boiling.

Given names resonant of qualities which are perceived to be either masculine or feminine are frequently given, with males being linked with strength and firmness and females with beauty and flowers.

Given their limited vision, cave crickets will often jump towards any perceived threat in an attempt to frighten it away.

Given a finite set of n properties, a thing is good if it is perceived to have all of the properties, fair if it has more than < sup > n </ sup >/< sub > 2 </ sub > of them, average if < sup > n </ sup >/< sub > 2 </ sub > of them, and bad if it has fewer than < sup > n </ sup >/< sub > 2 </ sub >.

Given the popularity of the show and the media coverage it brought to the highlighted game, teams and fans of the West Coast teams felt that the show was only magnifying the perceived problems with excess media focus on East, South and Midwest games ; ESPN attributed its lack of West Coast games to the need for a very early start time ( 07: 00 AM PST ) and an alleged lack of high quality matchups.

Given its fundamental nature, exploratory research often concludes that a perceived problem does not actually exist.

Given the importance in Greek society of cultivating the masculinity of the adult male and the perceived feminizing effect of being the passive partner, relations between adult men of comparable social status were considered highly problematic, and usually associated with social stigma.

Given their underfocused nature, wide fields of view, and high light collecting ability, the ocelli are superbly adapted for measuring changes in the perceived brightness of the external world as an insect rolls or pitches around its body axis during flight.

Given the evidence suggesting a positive association between an outward motivation and drinking, and the potential role of perceived social influence in this association, understanding the precise nature of this relationship seems important.

*" Haven't Given Up Hope For Cyclops ", The New York Times, April 17, 1918.

* Honan, William, " Computer Admissions Test to Be Given Less Often ", New York Times, January 4, 1995.

Given the University of Georgia School of Law's low in-state tuition of $ 14, 448, the New York Times recently completed a survey comparing starting salaries and degree costs of law schools and found " Georgia Law graduates earning some of the highest salaries in the country while their educational costs were reported among the very lowest, speaking to the quality of the education as well as the excellent return on investment provided at Georgia Law.

* U. S. surveillance: the Los Angeles Times reported on 27 October 2004: " Given the size of the missing cache, it would have been difficult to relocate undetected before the invasion, when U. S. spy satellites were monitoring activity.

The band Malbec has also had their song " Given the Times " translated into Simlish.

noted, " Given that the bandwidth for conducting crawls is neither infinite nor free, it is becoming essential to crawl the Web in not only a scalable, but efficient way, if some reasonable measure of quality or freshness is to be maintained.

Given the limited spectrum a wholesale model as noted by the EU Commission reference 2 in such situation is chosen.

Given the close ties between the world of Japanese console RPGs and animation, the magazine also heavily featured information about manga and anime by noted UK based writer, Helen McCarthy.

* Given Brevet of Major and his name was noted for as qualified for Staff employment

Barron noted: Given the central position he occupied in the intelligence-gathering network for the Mid-Ulster region, this RUC officer's interview with the Inquiry was disappointing.

Given the interconnection of s and k in steady state, noted above, the question can be phrased: " How much capital per worker ( k ) is needed to achieve the maximum level of consumption per worker in the steady state?