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 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 steady funding throughout, the R-7 developed with some speed.

Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.

Given initial speed u, one can calculate how high the ball will travel before it begins to fall.

Given a rotating frame composed by three unitary vectors, all the three must have the same angular speed in any instant.

Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.

Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

Given von Spee ’ s superiority in speed, firepower, efficiency and numbers, why Cradock chose to engage puzzles historians.

Given the volatility of the American economy in the 1970s, with recession affecting the spending habits of most shoppers, the off-price industry gathered speed.

Given their high rotational speed of up to 4000 rpm ( 67 Hz ) and tight clearances, they are not very tolerant of solids such as sand.

Given the lack of any variable-ratio transmission between the piston engine and the wheels, the designer is forced to compromise between desired torque and desired maximum speed ; the radius of the driving wheels determines this.

Given large headways and limited average speed due to stops, the only way to increase passenger capacity is to increase the size of the vehicle.

Given Amtrak's own projected 41 hour travel time, the average speed is still in excess of 55 mph ( including stops ).

Given a curve describing the overall drag on the vehicle, it is simple to find the speed at which the total drag forces are the same as the maximum power of the engine.

Given the low limit speed of perhaps 6 knots ( or less if opposing the fierce lower Delta currents ), this " MOBILE " capability made boat assault operations in the furthest reaches of the Delta feasible.

Given the storm's faster-than-light speed, it is believed that it cannot be a natural phenomenon.

Given the small size of the organism, a great speed is achieved.

Given a single start worm, a 20 tooth worm gear will reduce the speed by the ratio of 20: 1.

Given that torques are pseudo-vectors, and hence add linearly, it follows that the rotation speed of the rocket around the aforementioned axis can only increase.

Given its mythical connection with sailing and orchids, the name Pleione is often associated with grace, speed and elegance.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given the practical weight of suitable power sources, the accelerations given by ion thrusters are frequently less than one thousandth of standard gravity.

* Given the popularity of the radio show at the time many catch phrases appear frequently in Warner Bros. cartoon shorts from the 1930s and 1940s, such as Molly's " T ' ain't funny, McGee!

Given its importance in national history, Mexican politicians and political parties refer frequently to the Revolution in their political rhetoric.

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 the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given its idiosyncratic " dark " feel and touch, Miami Vice is frequently cited as an example of made-for-TV Neo-noir.

Given crony capitalism's nature, these dishonest business practices are frequently ( yet not exclusively ) found in societies with ineffective legal systems.

Given the demand and expense of hyperpulse communication, messages are frequently bundled into batches of hundreds, sent simultaneously.

Given the tendency of political parties in India to make and break alliances frequently, the National Democratic Alliance does not have a formal governing structure in place, such as an executive board or politburo.

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 the relatively non-specific symptoms of initial hypothyroidism, Hashimoto's thyroiditis is often misdiagnosed as depression, cyclothymia, PMS, chronic fatigue syndrome, fibromyalgia and, less frequently, as ED or an anxiety disorder.

Given the repression of the times, she tried to dodge an expected arrest, and frequently changed places of residence and took only temporary jobs.

Given Australia has a population of only around 20 million people ( ranked 53rd in the world ) this fact is frequently cited as noteworthy by the mainstream Australia media due to a strong sporting culture.

Given the numerous descriptions of courses, distances, and directions in the log, this method seems more likely to pinpoint the location, and has been by far the most frequently used method of historians.

Given the scope of modern regulation, however, legislatures frequently find areas where it is impractical for lawmakers to apply the level of detail or expertise required to establish complete standards.

Given the relatively recent introduction of a law technically requiring motorists to stop at a red light, it is not surprising that drivers frequently disregard traffic lights and proceed on red.

Given that caledonite is found in oxidized copper / lead deposits, it is frequently found in association with other copper and lead minerals.