Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given any of the above definitions of " myth ", the myths of many religions, both ancient and modern, share common elements.

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 multiple people often consume food from the same source, it is common for more than a single person to be affected simultaneously.

Given that noise-equivalent power can be expressed as a function of the responsivity ( in units of or ) and the noise spectral density ( in units of or ) as, it's common to see the specific detectivity expressed as.

Given the closeness shared by the countries bordering the Mediterranean basin, and very topical interest to the consolidation of the European Union's enlargement policy, he also intended to establish trade relations with the Republic of Malta aimed at encouraging mutual knowledge and awareness in a profitable way their local communities on European issues of common interest and current.

* Given two circles, to draw any of their common tangents.

Given a triangle ABC, let the lines AO, BO and CO be drawn from the vertices to a common point O to meet opposite sides at D, E and F respectively.

Given that human languages share many common traits, the idea is that humans share a universal grammar which is built into our brain structure.

Given the weather conditions close to the summit, cold weather injuries are very common.

Given that some common statistical packages ( e. g., SAS, SPSS ) do not provide likelihood ratio test statistics, it can be more difficult to assess the contribution of individual predictors in the multiple logistic regression case.

Given two sequences X and Y, a sequence G is said to be a common subsequence of X and Y, if G is a subsequence of both X and Y.

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

Given the often complex badge-engineering that BMC undertook, it is common amongst enthusiasts to use the ADO number when referring to vehicles as a single design ( for example, saying ' The ADO15 entered production in 1959 '- this encompasses the fact that when launched, the ADO15 was marketed as both the Morris Mini Minor and the Austin Seven ).

* Given a positive integer n, the set of all positive divisors of n forms a distributive lattice, again with the greatest common divisor as meet and the least common multiple as join.

Given the lack of surviving objects, we cannot know how common the techniques employed were, but the quality of the execution suggests that the binder was experienced in them.

); others were given more abstract, " spiritual " names, not common in Russia: " Uspeniye " (' Dormition '), " Terpeniye " (' Patience '), " Bogomdannoye " (' Given by God '), " Osvobozhdeniye " (' Liberation ').

Given enough time, natural change in isolated language can obliterate any meaningful linguistic evidence of a known common genetic source for the languages.

Another partition of the given interval, Q, is defined as a refinement of the partition, P, when it contains all the points of P and possibly some other points as well ; the partition Q is said to be “ finer ” than P. Given two partitions, P and Q, one can always form their common refinement, denoted P ∨ Q, which consists of all the points of P and Q, re-numbered in order.

Given a set of sequence fragments the object is to find the Shortest common supersequence.

Given the country's vast production of beef, red meat is an especially common part of the Argentine diet.

Given a graph G = ( V, E ), a matching M in G is a set of pairwise non-adjacent edges ; that is, no two edges share a common vertex.

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given the repeated failures and frustrations of workers ' revolutions and movements, Marx also sought to understand capitalism, and spent a great deal of time in the reading room of the British Museum studying and reflecting on the works of political economists and on economic data.

Given our political differences, people are sometimes surprised how close Ronnie and I have been to the Kennedy family.

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 Pinckney's lack of political experience, he would have been expected to be open to Hamilton's influence.

Given the creation of the Moscow IFF and the political decision to organize only one " A " festival for all socialist countries, Karlovy Vary was forced to alternate with Moscow between 1959 and 1993.

Given such possibilities, we can expect TC to be used to suppress everything from pornography to writings that criticize political leaders.

Given these harsh constitutional requirements, neither the pan-greens nor pan-blues can unilaterally change Taiwan ’ s political and legal status with respect to the ROC ’ s constitution.

Song Jiaoren (; Given name at birth: Liàn 鍊 ; Courtesy name: Dùnchū 鈍初 ) ( 5 April 1882 – 22 March 1913 ) was a Chinese republican revolutionary, political leader and a founder of the Kuomintang ( KMT ).

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

Given the social state that was emerging, Tocqueville believed that a " new political science " would be needed.

Given Klein's aggressive spending cuts, which shaped the political climate of Alberta for much of the 1990s, Getty's legacy with respect to public finances has been criticized.

Given the shifting political climate of Macau, some Macanese are coming to recognize and identify closer with a Chinese heritage.

Given the political intrigue present at court, Cabral may have been part of a faction that furthered his appointment.

Given the controversy over the struggle over territory, a vocal minority of Cherokee and a generation of political leaders in Washington considered Ross to be dictatorial, greedy, and an " aristocratic leader sought to defraud " the Cherokee Nation.

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 the ecological crisis is a " historic compromise " between these two political directions was necessary.

Given the goals of the first Five Year Plan, the state sought increased political control of agriculture, hoping to feed the rapidly growing urban areas and to export grain, a source of foreign currency needed to import technologies necessary for heavy industrialization.

Given that his reign lasted for, at best, only a few weeks after his acclamation and he does not seem to have secured significant military or political support Domitianus is more properly categorized as a Roman Usurper rather than an Emperor.

Given its proximity to these buildings and the fact that it has served as a home and meeting place for many notable political figures over the years, the hotel has often been referred to as " the third chamber of Parliament ".

Given the increasing role of the European Union in the political arena, the National Academies acknowledge that the scope of their advisory tasks must exceed the national borders and that it's important not to lose sight of the European level.

Given the new religious and political climate, and perhaps also to escape a serious outbreak of plague in England, Baltimore moved to Ireland.

Given the unstable political climate during these years, Bolívar and other patriot leaders, such as Santiago Mariño, Manuel Piar, José Francisco Bermúdez and Francisco de Paula Santander often had to go into exile in the Caribbean or nearby areas of Spanish America that at the moment were controlled by those favoring independence, and from there, carry on the struggle.