Given the age of the Rig Veda being at least 1500 BC or before, this must rank as the earliest practice of beating of the war drum in the history of mankind.

Given a small ball or marbles, he would invent games and play by himself for hours.

) Given the exclusionary and ancestral conception of citizenship held by Greek city-states, a relatively large portion of the population took part in the government of Athens and of other radical democracies like it.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

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 any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

Given the opportunity, adults eat hatchlings, which may be protected by separating the two groups with a net, breeding box or separate tank.

Given that drug poisoning causes a large portion of patients in a coma, hospitals first test all comatose patients by observing pupil size and eye movement, through the vestibular-ocular reflex.

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

Given that one cannot be motivated by reason alone, requiring the input of the passions, Hume argued that reason cannot be behind morality.

Given the variety of single stranded viruses that have been described this scheme-if it is accepted by the ICTV-will need to be extended.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

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 an equilateral triangle, the counterclockwise rotation by 120 ° around the center of the triangle " acts " on the set of vertices of the triangle by mapping every vertex to another one.

Given a complex-valued function ƒ of a single complex variable, the derivative of ƒ at a point z < sub > 0 </ sub > in its domain is defined by the limit

Given these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given earlier debates by Christian authors about the existence of Jesus, e. g. in Justin Martyr's 2nd century Dialogue with Trypho, it would have been expected that the passage from Josephus would have been used as a component of the arguments.

Along with a hand-picked escort led by Given Campbell, Davis and his wife were captured on May 10, 1865, at Irwinville in Irwin County, Georgia.

Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:

Given that both A and not-A are seen to be “ true ,” Kant concludes that it ’ s not that “ God doesn ’ t exist ” but that there is something wrong with how we are asking questions about God and how we have been using our rational faculties to talk about universals ever since Plato got us started on this track!

Similarly, Hare refers to “ the crude caricature of act utilitarianism which is the only version of it that many philosophers seem to be acquainted with .” Given what Bentham says about second order evils it would be a serious misrepresentation to say that he and similar act utilitarians would be prepared to punish an innocent person for the greater good.

" As Shelly Kagan says, “ Given the parameters of the actual world, there is no question that …( maximally )… promoting the good would require a life of hardship, self-denial, and austerity … a life spent promoting the good would be a severe one indeed .”

The inscription reads: “ Belonging to Ahaz ( son of ) Yehotam, King of Judah .” Given the process that created and preserved bullae, they are virtually impossible to forge.

With regard to African Americans, Gilman wrote in the American Journal of Sociology: “ The problem, is this: Given: in the same country, Race A, progressed in social evolution, say, to Status 10 ; and Race B, progressed in social evolution, say, to Status 4..

Denis MacShane, a former Foreign Office minister, said: “ Given the appalling suffering and repression of the Bahraini people, it would be a fitting gesture for the Countess of Wessex to auction these trinkets and distribute the proceeds to the victims of the regime .”

Given the Nazi predilection for “ racial purity ”, the Roma were among their first victims.

* “ Comment on Richard Schantz, ‘ The Given Regained ’”, in Philosophy and Phenomenological Research lxii ( 2001 ), 181-5

* “ Hegel and the Myth of the Given ”, in Wolfgang Welsch und Klaus Vieweg, Herausg., Das Interesse des Denkens: Hegel aus heutiger Sicht ( München: Wilhelm Fink Verlag, 2003 ), pp. 75 – 88.

Given that Unferth shows his dislike for Beowulf early in the story, Unferth ’ s choice to award Beowulf with Hrunting, which means “ thrusting ,” can be interpreted as a sign of peace and acceptance.

* Not being automatically granted the luxury of a “ diagnostic period .” Given that they know the company, COO ’ s turned CEO ’ s are often expected to hit the ground running when in actuality they too need to enter diagnostic mode to fully understand their new role and to see the Company from a new perspective.

* Given “ Medalla de la Universidad de Alcala de Henares ” and “ Medalla de Oro de la Ciudad de Zamora ”, Spain, 2005

Given the existence of important public policy goals on both sides, a city seeking to maximize walkability should not favor cul-de-sacs over grids, but should also allow some cul-de-sacs as a legitimate residential option ’ ... ‘ In addition, there are “ middle ground ” alternatives between prohibiting cul-de-sacs and mandating them.

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 data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Apart from the very rare “ Kirill of Turov ’ ( even when this designation occurs, it tends to be just one of several variant readings ), the headings in ‘ his ’ manuscripts include “ Kirill the monk ,” “ Kirill the philosopher ,” ‘ Saint Kirill ,” “ The Blessed father Kirill ,” “ the blessed monk Kirill ,” “ Kirill the unworthy monk ,” “ the venerable Kirill .” Given this variety of labels, ‘ Kirill ’ s ’ texts invite several candidates for being their more likely authors ( writers whose existence has been substantiated with historical facts ).