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

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

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 Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given more time to prepare for trial, Kidd likely would have been able to find the deposition Palmer gave when he was captured in Rhode Island two years earlier.

Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given two groups G and H and a group homomorphism f: G → H, let K be a normal subgroup in G and φ the natural surjective homomorphism G → G / K ( where G / K is a quotient group ).

Given two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.

: Given two points, determine the azimuth and length of the line ( straight line, arc or geodesic ) that connects them.

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 two Lie algebras and, their direct sum is the Lie algebra consisting of the vector space

Given this understanding, the Board withdrew the allegation of unsportsmanlike behaviour two days before the fourth Test, thus saving the tour.

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given the above commonalities there appear to be only two string theories: the heterotic string theory ( which is also the type I string theory ) and the type II theory.

Given the notion of a lexeme, it is possible to distinguish two kinds of morphological rules.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

Given barely two months to assemble a large sea-going invasion fleet, the Kriegsmarine opted to convert inland river barges into makeshift landing craft.

In the account books of Johanna, Duchess of Brabant and Wenceslaus I, Duke of Luxemburg, an entry dated May 14, 1379 reads: " Given to Monsieur and Madame four peters, two forms, value eight and a half moutons, wherewith to buy a pack of cards ".

# Given any two distinct points, there is exactly one line incident with both of them.

# Given any two distinct lines, there is exactly one point incident with both of them.

Given four points in general linear position ( no three collinear ; in particular, no two coincident ), there are exactly three pairs of lines ( degenerate conics ) passing through them, which will in general be intersecting, unless the points form a trapezoid ( one pair is parallel ) or a parallelogram ( two pairs are parallel ).

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.

It is described as " the ancient grayhound .. that had been with Lugh of the Mantles, / Given him by the sons of Tuireann Bicreann ;.."

Given that premise, the notion of absolute knowledge ( as described by Plato and the rationalists ) is seen as mere illusion, and this is what he set out to demonstrate in the first part of his magnum opus " The Critique of Pure Reason " ( 1781 ).

Given the opportunity, for example during an illness that suppresses the immune system, the virus is reactivated and travels to the end of the nerve cell, where it causes the symptoms described above.

Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix.

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 that it is surrounded on three sides by watery regions, it is not implausible that the entire region can be flooded, as described in the second book Gormenghast.

Given an SVD of M, as described above, the following two relations hold:

Given that his death in 1040 is described as being " at an immature age " in the Annals of Tigernach, he must have been a young man in 1034.

Given the lack of standardized road signs at the time, it was decided to place distinctive bells along the route, hung on supports in the form of an high shepherd's crook, also described as " a Franciscan walking stick.

Given this fact, and the results of the animal studies described, it is likely that oxcarbazepine is a human teratogen.

Given the rarity of continuously flowing rivers in any part of Saudi Arabia, the existence of a river such as that described in the Book of Mormon has long been questioned by its critics.

" However, the City of Corsicana was extremely critical of Beyler's report, and produced a 21-page response pointing out that his report lacked objectivity, stating " Given some of Dr. Beyler ’ s distortions of the trial record, as described below, it may be that he has assumed the role of an advocate.

Given a faster than light technology and weapons scaled similar to those of the Age of Sail, some of the battles described in the Honor Harrington series resemble real-life sea battles in our historical record.

Newcastle manager Joe Kinnear had already stated that the club was " not interested at all in selling him ", and described the amount on offer for Given as " insulting ".

While team captain Kolo Touré was on international duty, Given was given the captain's armband by manager Roberto Mancini, who described the Donegal-born player as " one of the five best goalkeepers in the world ".

Given how critical transportation is to every human culture, it is unsurprising that in an interstellar culture, which must deal with distances orders of magnitude greater than terrestrial cultures, the unique ways in which interstellar travel is described in various fictional universes tends to create major plot elements in that universe.

Given the sensitive nature of his death, for many years the cause of death continued to be described as heart disease.

* Given three distinct points on a projective line, any other point can be described by its cross-ratio with these three points.

Given the inherent technical limitations of the visible and palpable signs from these sacroiliac joint mobility maneuvers another broad category of clinical signs have been described called provocative maneuvers.

" Given the collaborative nature of reggae, Goldman described how " That song may very well have been a conversation that they had sitting around one night.