Clearly any 3 lines perpendicular to the red ones in Fig 1, in particular those joining the centres of the circles, must also cut at angles of 60 ° and thereby form an equilateral triangle.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

Clearly there is always at least one such string for any n, as otherwise all possible strings ( infinitely many ) could be generated by the ( finitely many ) programs with lower complexity, so GenerateComplexString must always return.

MSP Alex Johnstone wrote " Clearly, the Declaration of Arbroath is a literary work of outstanding universal significance by any stretch of the imagination " In 2008, the Campaign Group Chairman, Councillor Jim Millar launched a public petition to reinforce the bid explaining " We're simply asking people to, local people especially, to sign up to the campaign to have the Declaration of Arbroath and Arbroath Abbey recognised by the United Nations.

Clearly, then, any two Englishmen must have at least this one ancestor in common, and thus any individual could claim kinship with the king.

Clearly, lethality, level of activity, and hippocampal plasticity are rescued, but are the animals free of any other RTT signs such as social behavior deficits, anxiety, and cognitive impairments?

Clearly, Tolkien knew when firearms were invented, but he deliberately set out to write a lighthearted fantasy tale disregarding any consideration of historical accuracy.

Clearly, Elpenor is embarrassed to have died young without any honor, and seeks to hide his true fate from everyone else.

Clearly if all states can be reached from the origin then any state can be reached from another state ( merely a shift in coordinates ).

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

Clearly this procedure is reversible – given any point on the surface of the sphere that is not the north pole, we can draw a straight line connecting that point to the north pole and intersecting the flat plane in exactly one point.

Clearly if one does not have enough money to pay the price then they cannot buy any of that item.

Clearly, the British were penetrated by Philby, but it has never been determined, in any public forum, if there were other serious penetrations.

Similar definitions apply to a Lie group G, a maximal commutative Lie subgroup H and any representation V of G. Clearly, if λ is a weight of the representation V of G, it is also a weight of V as a representation of the Lie algebra g of G.

Clearly the empty set cannot belong to any collection with the f. i. p.

Clearly, the two statements contradict, but nevertheless, the " genius " has an urge to try to figure out which of the two statements ( if any ) is true.

Clearly he would have little hope of reelection to the U. S. Senate or any future in Delaware politics.

Clearly, any of the general approaches for planar point location may be used.

Clearly the largest application for any human memory studies of learning effects is for education and finding better ways to relate information to students at every grade level.

The court wrote, " It is well settled that the landlord of a private apartment or dwelling house may, without violating any provision of the Federal or State Constitutions, select tenants of its own choice because of race, color, creed or religion ... Clearly, housing accommodation is not a recognized civil right.

Clearly we can assign meaning to any such power series of quotients ( orbits ) with respect to permutation groups, where we restrict the groups of degree n to the conjugacy classes of the symmetric group, which form a unique factorization domain.

Clearly, any non-zero real number can be normalized.

Clearly, these studies and the dozens of others like them serve to demonstrate that labeling can have a very real and very large effect on the mentally ill. None of these studies, however, proved that labeling is the sole cause of any symptoms of mental illness.

Clearly, for simulators with side-by side crew, a system that gave correct cross-cockpit viewing was required.

Clearly, an entire segment of the population ( males ) cannot become pregnant in the first place, thus it is moot to argue or take a side regarding the right of abortion ( or right to give birth ) for men.

On the more positive side, he wrote, " Clearly, WB's goal here is to find an acceptable time-period companion for 7th Heaven, and it's entirely possible the network has.

Clearly, God was on Charles ’ s side, and to let France escape a fight would be to tempt fate — he would not have the chance, as resources would not be mobilized so easily next time.

Clearly the box must have a volume of 60 units.

Clearly, a # P problem must be at least as hard as the corresponding NP problem.

" Clearly, Vinson suggested, clear and present danger did not intimate " that before the Government may act, it must wait until the putsch is about to be executed, the plans have been laid and the signal is awaited.

Clearly, the limits of these fields must also be different as the sources shrink to zero size.

Clearly radio sources must start small and grow larger.

Clearly America must continue to lead the world we did so much to make.

Clearly this creates a circular dependency, so the address of at least one root server must be known by a host in order to bootstrap access to the DNS.

Clearly, the limits of these fields must also be different as the sources shrink to zero size.

Clearly, Sinan must have appreciated this form, since he repeated it later in mosques such as the Sokollu Mehmed Pasha Mosque at Kadırga and the Atik Valide Mosque at Üsküdar.

Clearly there are limits to what talk can achieve ; ultimately, talk must be backed up by action, in the form of successful policies.

Clearly, world peace must be our number one priority.

It must be emphasized that these studies were small — only tens of patients-and the results were therefore stated tentatively ; in the words of one of the cited sources: " Clearly more studies are needed before GH replacement for the elderly becomes established.

Clearly, the club must somehow decide ahead of time what that title will be.

Clearly these residuals cannot be independent of each other, but they must be constrained by some kind of relationship.

) Clearly it must be preceded by another cognitive action, which must in turn be preceded by another and so on, in an infinite regress ( always a sign that something has gone wrong with a theory ).

Clearly Bob will not go on his own: he would not set off alone, but if he did then Alice would follow, and Alice's personal liberty means the joint preference must have both to go > Bob to go.

By policy, the uniform worn by Auxiliary Troopers must be " Clearly Distinguishable " from that of regular Troopers.

David Starkey writes: " The Groom of the Stool had ( to our eyes ) the most menial tasks ; his standing, though, was the highest ... Clearly then, the royal body service must have been seen as entirely honorable, without a trace of the demeaning or the humiliating.

Clearly the phenomenon cannot be a property of the exact solution, since this is the same for both problems, and must be a property of the differential system itself.