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

Given a 5 % male excess birth rate, there appears to be 3. 15 male SIDS cases per 2 female, for a male fraction of 0. 61.

Given an adequate supply of food, larvae should pupate and weave a silken cocoon within 1 – 2 weeks after 3 larval stages.

Given the elevations of those three places, at least a 3 % grade would have been required.

Given a unit vector n in R < sup > 3 </ sup > and an angle φ, let R ( φ, n ) represent a counterclockwise rotation about the axis through n ( with orientation determined by n ).

Given the option in the final of wearing their first strip, they chose the away strip for luck ; but Everton managed to claw back a 2 – 0 deficit after 54 minutes and eventually won the game 3 – 2.

* Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3 × 3 × 3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 cubes whose sum of values is 42.

#" Given to Fly " ( McCready, Vedder ) – 3: 53

Given this grammar, we can now say that the number of NPs expected while deriving VPs is 0. 7 x 1 + 0. 3 x 2 = 1. 3.

Given the empty string, 00 ( or 11 ), 01 and 10 are distinguished extensions resulting in the three classes ( corresponding to numbers that give remainders 0, 1 and 2 when divided by 3 ), but after this step there is no distinguished extension anymore.

Given a fundamental domain for the group action ( for the full, orientation-reversing symmetry group, a ( 2, 3, 7 ) triangle ), the reflection domains ( images of this domain under the group ) give a tiling of the quartic such that the automorphism group of the tiling equals the automorphism group of the surface – reflections in the lines of the tiling correspond to the reflections in the group ( reflections in the lines of a given fundamental triangle give a set of 3 generating reflections ).

Given the outlandish idea that a blind man could be a detective, in the introduction to the second Carrados book The Eyes of Max Carrados Bramah compared his hero ’ s achievements to those of real life blind people such as Nicholas Saunderson, Lucasian Professor of Mathematics at Cambridge, Blind Jack of Knaresborough the road builder, John Fielding the Bow Street Magistrate of whom it was said he could identify 3, 000 thieves by their voices, and Helen Keller.

Given 20 minutes a game, Szczerbiak averaged 7 points, 3. 2 rebounds, and 1. 1 assists while shooting. 450 % from the field and. 411 % from 3.

Given Encke's low orbital inclination near the ecliptic and brief orbital period of 3 years, the orbit of Encke is frequently perturbed by the inner planets.

Given projected growth, and the limited ability to expand Terminal 2, the Egyptian Ministry of Civil Aviation began construction of Terminal 3 in 2004.

On 18 July 2011, Given joined Aston Villa for a fee believed to be around £ 3. 5 million.

Given returned for the final group match against Feyenoord in the Netherlands, and Newcastle's 3 – 2 win meant that they qualified for the second round.

Having finished third in the league in May 2003, Given and Newcastle lost 4 – 3 on penalties to Partizan Belgrade early in the 2003 – 04 season, meaning that Newcastle failed to reach the group stages of the Champions League.

Given the distance that these troops had to march in order to make contact with the enemy, it was clear to the two Corps commanders that they would be unable to attack at 4: 00 as ordered.

#" Given to Fly " ( McCready, Vedder ) – 4: 00

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 the variety of card values, single cards have a price range of $. 05 to $ 15. 00.