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 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 the wide disparity of concepts and methods across domains, 4GL limitations lead to recognition of the need for the 5GL.

Given the diversity of functions performed by neurons in different parts of the nervous system, there is, as expected, a wide variety in the shape, size, and electrochemical properties of neurons.

Given that SAD impacts a wide variety of occupational performance areas in a person ’ s life as described in the aforementioned section, occupational therapists ( OTs ) play a key role in helping individuals cope with SAD.

Given wide praise for his efforts, the Flyers gave Holmgren a two-year contract and removed the interim label from his title.

Given the wide variety of clientele at the club, which includes Willie the Giant and Elliott the Dragon, the amount of seating at the club could vary wildly at times.

Given its sharp-edged beak, huge bill and wide gape, the Shoebill can hunt quite large prey, often targeting larger prey than other large wading birds.

Given the wide variety of symptoms that are associated with whiplash injuries, the Quebec Task Force on Whiplash-Associated Disorders coined the phrase ' Whiplash-Associated Disorders '.

Given a stimulus such as embarrassment, the person's sympathetic nervous system will cause blood vessels to open wide, flooding the skin with blood and resulting in reddening of the face.

Given the wide expectation that the war was going to be a short one, the majority however supported the war effort and the call to restore the " freedom of small nations " on the European continent.

Given this wide availabity of icon tools and icon sets, a problem can arise with custom icons which are mismatched in style to the other icons included on the system.

Given the wide breadth of its mission there was plenty of room for the CCLRC staff to promote different activities of the Council.

Given the origins of the cardinal tetra, namely blackwater rivers whose chemistry is characterised by an acidic pH, low mineral content and the presence of humic acids, the species is adaptable to a wide range of conditions in captivity, though deviation from the soft, acidic water chemistry of their native range will impact severely upon breeding and fecundity.

Given its wide range of shop mix and entertainment facilities, including theaters / cinemas, the centre became a very important destination for visitors in Denizli and neighbouring cities.

Given their wide range of habitats and diets, the skulls of enantiornithines varied considerably between species.

Given the wide diversity of skull shape among enantiornithines, many different dietary specializations must have been present among the group.

Given the wide range of services, such as policing, health care and education, that fall under provincial jurisdiction, these divergences have considerable importance.

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 this fact, though, some meters are more common or popular ; but there is a wide variation of less frequent combinations, as well.

Given this wide range of mostly non-downward entailing environments, the Fauconnier-Ladusaw Hypothesis has gradually been replaced in favor of theories based on the notion of nonveridicality ( proposed by Zwarts and Giannakidou ).

Given the wide range of nectar species used by Karner blue butterfly ( see section " Food habits "), planting several often used or preferred nectar species is favored over selecting 1 or 2 specific species.

Given Larry ’ s well-established reputation and strengths as a DJ, the release of the album was followed by a deluge of bookings for an album world tour that continued for the rest 2005 ; two U. S. tours, two Australian tours, and countless European dates ensured that the Calyx sound spread far and wide.

Given his unusual voice, he is able to perform a wide melodramatic and chamber repertoire going far beyond the Baroque repertoire and including compositions specially written for his vocality.

Given his wide range of appropriate skills and experience, Hetherington was invited to work with a group of undergraduate students ( ranging from second to fourth year ) from the ( then ) Department of Indonesian and Malayan Studies at the University of Sydney, over the entire three-term year of 1980, in the task of preparing them for a performance of " Irawan Rabi ", or " Irwan ’ s Wedding ", as it had been adapted for a western audience by James R. Brandon, in the manner of the traditional Javanese shadow puppet theatre ( or wayang kulit ) ( Day, 1981 ).