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.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given the dangers, the maximum sentence was three months.

Given a deadline of seven months to coincide with the North American launch of the Dreamcast, the transition was difficult for the team, due to the differences in hardware.

Given the concentration of most of this rainfall in the 4 months of Monsoon period, excess rain can lead to floods and shortage to droughts.

Given the abundance of snow for several months in winter, it is a popular area for snowmobiling and four-wheel drive vehicles as well as for downhill and cross-country skiing.

Given this lengthy support it was reasonable for Tyrconnell and Tyrone to try to solicit help from Philip III, but Spanish policy was to maintain its recent ( 1604 ) peace with England, and its European fleet had anyway been destroyed by the Dutch over four months earlier.

Given command of the 44th ( Home Counties ) Infantry Division, he spent 9 months organising the

Given special funding by the Provincial Government, the school hired George Curtis from Dalhousie's Faculty of Law to serve as their first Dean and within two months the Faculty was educating its first incoming class.

“ Given that I was born a few months after Auschwitz was liberated, it is hardly surprising that I have a strong sense of the evil that humans – individually and collectively – do.

Given the assignment by then-Seton Hall University president Monsignor James Kelly to create a radio station, Monsignor Gillhooly got WSOU up and running in just three months and provided a steady hand during the station ’ s early days.

Whilst playing, he tripped on the Villa Park pitch and suffered a ruptured achilles injury in a game that saw him, Shay Given and Javier Hernandez all leave on stretchers ; the injury kept him out for six months.

Given the nature of the transaction, booked and paid for many months in advance the culprit can disappear without trace leaving the client out of pocket

Given this apparent gap in international law, several months later US President Bush announced the initiative with his counterpart, Polish President Aleksander Kwaśniewski at Wawel Castle in Kraków on May 31, 2003.

Given the quality of his performance, and the uncertainty over Brady's recovery, NFL analysts and reporters raised the question of whether the Patriots should, or would, franchise Cassel, less than three months after some of those same reporters predicted Cassel would be cut from the team.

Given the bias of the Victorian age, female students were denied direct study in anatomy and could not attend drawing classes with live models ( who were often prostitutes ) until a decade later.

Given that in biology many phyla, families and genera have some species that live in the sea and others that live on land, marine biology classifies species based on the environment rather than on taxonomy.

Given proper nutrition, exercise, and veterinary care, most whippets live for 12 to 15 years.

Given this Scriptural principle, the UPCI teaches that one should live a life that demonstrates Christ's attributes.

Given the option to once again suppress her memory of killing, she chose to live with it instead (" The Seventh ").

Given that there are around 700, 000 live births in Britain each year, Meadow argued that a double cot death would be expected to occur once every hundred years.

Given the high death rate, many servants did not live to the end of their terms.

Given The Holy Land lies around the Great Rift, which causes occasional volcanic activity due to continental drift, the most logical explanation for fire and brimstone is the fire and sulfur emitted by live volcanoes and the lake of fire being the caldera.

Also Given the fact that the neighbourhood is well maintained, it can be assumed that the residents are very proud of where they live and thus major changes in the future are very unlikely.

Given half a year to live, Kon chose to spend the remainder of his life in his home.

Given the importance of reason, Clement stresses apatheia as a reasonable ordering of our passions in order to live within God's love, which is seen as a form of truth.

Given the fact that many working poor people do not own a car or cannot afford to drive their car, where they live can significantly limit where they are able to work, and vice versa.

Given that his father had wished him to be a medical doctor, he creates the faux Sri Hari Prasad Sharma Charitable Hospital ( named after his father ) and pretends to live in accordance with this wish whenever his father ( Sunil Dutt ) and mother ( Rohini Hattangadi ) visit him in Mumbai.

Given the choice, most elders would prefer to continue to live in their own homes ( aging in place ).

Given the migratory routes of French-Canadians, their descendents thus live mainly in Canada ( especially Quebec and Manitoba ), but also in communities in New England, upstate New York, and the midwest ( especially Michigan, Missouri, Illinois, Minnesota )....

Given the timing of Led Zeppelin's first live performances of " Since I've Been Loving You " ( early 1970 ), it has been suggested that " Never " is the original source for this composition.

* The Wound That Was Given Birth To Must Be Bigger Than The Wound That Gave Birth known as Purple Trap-2-CD ( Purple Trap, 1996 ) live in London

Given his parents ' busy jobs as studio chiefs, Tian was raised primarily by his grandmother, though his parents ' positions also allowed him to live a relatively comfortable childhood.

Given the software limitations at the time, to make the sound work correctly required a full live orchestra, the first that Soule had ever worked with ; the orchestral tracks in Evermore had been performed by Soule and his brother by themselves, two instruments at a time.

Given these two things and a supply of insects for food, American toads can live almost everywhere, ranging from forests to flat grassland.

Given that the programmes were pre-shot on film as opposed to being shown live, unlike most of the BBC's output from the late 1940s, examples of Television Newsreel do survive in the archives, some of the oldest extant pieces of BBC-produced television programming.