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 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 the rapidity with which its last population was eliminated, it is likely that aboriginal hunting caused its extinction over the rest of its original range ( aboriginal peoples apparently never inhabited the Commander Islands ).

Given that she was not trained or welcome in the hunting parties among Broud's clan, she must invent, for each new case, new techniques.

Given State and Local laws, types of weapon can also vary depending on type, size, sex of game and also the geographical layout of that specific hunting area.

Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

Given that the bulk of family chores fell to women, and that they were five times more likely than men to head a single-parent family, the shortcomings of Finland's child day-care system affected women more than it did men.

Given Pauling's recent success in discovering the Alpha helix, they feared that Pauling might also be the first to determine the structure of DNA.

Given that Gable and Cukor had worked together before, in Manhattan Melodrama and Gable had no objection to working with him then, and given Selznick's desperation to get Gable for Rhett Butler, if Gable had any objections to Cukor, certainly they would have been expressed before he signed his contract for the film.

Given that starters knew only the target recipient's name and address, they had a seemingly impossible task.

Given a color name to match the name of amber mutants, ochre mutant viruses had a similar property in that they recovered infectious ability within certain suppressor strains of bacteria.

Given the versatility of both vegetables, they were usually boiled or steamed, and eaten by itself or as ingredients in soups and strews.

Given the recent lynching of Roy Belton, a white man, they believed that Rowland was greatly at risk of meeting a similar fate.

Given that the right to be politically active has granted them the opportunity to expand their knowledge and influence in current affairs, they are now considered one of the main components in the country's decision-making in both politics and economy.

Given that companies are collections of projects and markets, individual areas can be judged on how successful they are at adding to the corporate net profit.

Given this they would have qualified as Corbett summits had they been under 3, 000 feet.

Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant.

Given the choice, who wouldn't rather believe their children are special and chosen for some high mission rather than that they have a brain disorder?

Given the reputed humorous character of Valencians, it was natural that they began to burn figurines depicting people and events of the past year.

BONUS: " Given a pair of resistors, give their equivalent resistance if they were connected in parallel with each other.

Given the short distances of super special stages compared to the regular special stages and consequent near-identical times for the frontrunning cars, it is very rare for these spectator-oriented stages to decide rally results, though it is a well-known axiom that a team can't win the rally at the super special, but they can certainly lose it.

: Given any set A and any set B, if A is a nonempty set ( that is, if there exists a member C of A ), then if A and B have precisely the same members, then they are equal.

Given the inexperience of the locals with living elephants, they were unlikely to recognize the skull for what it actually was.

# Given u and v in W, then they can be expressed as u = ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, 0 ) and v = ( v < sub > 1 </ sub >, v < sub > 2 </ sub >, 0 ).

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given a pre-modern understanding of reason, rationalism is identical to philosophy, the Socratic life of inquiry, or the zetetic ( skeptical ) clear interpretation of authority ( open to the underlying or essential cause of things as they appear to our sense of certainty ).