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 its long stability and isolation, New Caledonia serves as a unique island refugium — a sort of biological ' ark ' — hosting a unique ecosystem and preserving Gondwanan plant and animal lineages no longer found elsewhere.

Given the difficulty of this position, it is not uncommon for the best player on the team to play Number Two so long as another strong player is available to play Three.

Given that the cities of Los Angeles and San Francisco have long been competitors in economic, cultural, and political arenas, the new venue in California became fertile ground for rivalry transplantation.

Given his jazz and salsa conga playing experience and knowledge ( working as a sideman with such bands as salsa's Frankie Dante's Orquesta Flamboyan and jazz saxophonist Archie Shepp ), Dawson also created the long running " Salsa Meets Jazz " weekly concert series at the Village Gate jazz club where jazz musicians would sit in with an established salsa band, for example Dexter Gordon jamming with the Machito band.

Given that many of the talented young artists had been raised in housing projects and were short on social and dress skills, this Motown department was not only necessary, it created an elegant style of presentation long associated with the label.

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 IBM's resources, the 750 core will be produced with new features as long as there is a willing buyer.

Given the small likelihood of his older brothers producing heirs, and William's relative youth and good health, it had long been considered extremely likely that he would become King in due course.

Given a long enough barrel, there would eventually be a point at which friction between the bullet and the barrel, and air resistance, would equal the force of the gas pressure behind it, and from that point, the velocity of the bullet would decrease.

Given the technical limitations of daguerreotype photography which required long exposure times, this was one situation where the portrait subject remained quite still.

Given the name Pithecanthropus erectus (" erect ape-man "), it became the first in what is now a long list of human evolution fossils.

Given two strings, equally taut and heavy, one twice as long as the other, the longer would vibrate with a pitch one octave lower than the shorter.

Given the abnormalities of the microvasculature and other side effects of diabetes, these wounds take a long time to heal and require a specialized treatment approach for proper healing.

Given this dismal track record there is no evidence that had Taichang reign lasted any longer than it did, he could have turned around the fortunes of the beleaguered Ming Dynasty after the long steady decline of the latter years of Wanli's reign.

Given the mission to both bring Rosicrucian ideas back to America ( an early group had a settlement in Pennsylvania during the 17th century, but it had long been dissolved ), and to promote them in a modern way, Lewis established AMORC, becoming its first Imperator and writing what became the order's first canon of lessons in mysticism, and spending the rest of his life working on AMORC's behalf.

Given the chaotic situation in China, the corruption Doihara methodically spread didn't take long to reach the very top.

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

Given the rarity of continuously flowing rivers in any part of Saudi Arabia, the existence of a river such as that described in the Book of Mormon has long been questioned by its critics.

Given their long history, references to Consols can be found in many places, including literature such as David Copperfield by Charles Dickens, Howards End by E. M. Forster, Vanity Fair by William Makepeace Thackeray, Of Human Bondage by William Somerset Maugham and The Forsyte Saga by John Galsworthy and in economics.

Given the scale civil engineering problems are rare but it is notable that long established companies have a significantly better track record than more recent start-ups.

In November 1997, Given conceded a strange goal against Coventry City when, after collecting a cross, he rolled the ball out in preparation to make a long clearance.

Given the long surveillance hours, Morrison feels the odds are against him to smoke on the sly.

Given the controversy that has long surrounded the use of feedback, some extend their distaste for negative feedback amplifier designs ( and so a high damping factor ) as a mark of poor quality.