Therefore, he stands third in the line of succession to the thrones of sixteen independent sovereign states known as the Commonwealth realms, and to the governorship of the Church of England, preceded by his father and elder brother, Prince William, Duke of Cambridge.

Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.

Therefore, it is in the best interest of the competitor to get as close to the foul line as possible.

Therefore the beam bounces off along the line FP: directly towards the focus.

Therefore, if the audience is not already familiar with the phrase used in the punch line, or is not aware of the multiple meanings of the words in the phrase, the surprise ending of the joke cannot be recovered by explaining the joke to the audience.

Therefore, if the equation of the line is given in the form

Therefore, the size the track will determine where the 200-meter line is ( for 250 m tracks, it is about two-thirds of the way through the first bend ; for 200-meter tracks, it is the finish line ; for 400-meter tracks, it is the start line in the back straight ).

Therefore, to establish a mathematical statement as a theorem, the existence of a line of reasoning from axioms in the system ( and other, already established theorems ) to the given statement must be demonstrated.

Therefore the frequency line width of the beam is very small compared to the frequency of the laser.

On a logarithmic scale, the function x < sup > n </ sup > translates into a straight line with slope of n. Therefore, the linearly amplified signal will exhibit a slope of 1.

Therefore specialized tools have been developed to simulate, analyze, visualize and optimize time dynamic queueing line behavior.

Therefore, the portion of the vertical shafts of those letters which lie between the base line and upper parallel can be discarded without legibility being affected.

Therefore, any surface that is not in line with the three major axis needs its own projection plane to show the features correctly.

Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate.

Therefore the only online exchange that meets the railway line is Pescara – Rome station Avezzano.

Therefore, the only rail interchange is characterized by the Adriatic railway line Bologna – Bari, Abruzzo is Martinsicuro rail-Broad-S.

Therefore, a defensive line was built here in 1800 following the Battle of Castricum in 1799.

Therefore Luxembourg still had agnatic heirs from another branch of the House of Nassau left to succeed, while in the Netherlands the male line starting with William I was depleted.

Therefore, even in a line following strict uterine succession, it is possible for different members of the line born after the development of in vitro fertilization to have different mitochrondrial DNA, if either ( a ) an heir was conceived through egg donation, or ( b ) strict application of a rule of " uterine " succession allowed a child to inherit from the surrogate who bore it, rather than from those who supplied the egg and sperm and raised the child as their own.

Therefore these switches cannot be traversed at high speed or by heavy traffic and so are not suitable for main line use.

Therefore, Jack Carson's final line was not only a very topical one, it was one of the rare times a current president was actually mentioned during a Twilight Zone episode.

Therefore, any union conducting a strike action typically seeks to include a provision of amnesty for all who honored the picket line in the agreement that settles the strike.

Therefore, we shall consider in this paper the theoretical gain and resolution capabilities of such tubes.

Therefore, they often vary since one is theoretical and the other is experimental.

Therefore, players who do not play with the maximum number of credits at a time are playing with a smaller theoretical return.

Therefore, even if the computer components responsible for simulating a brain were not significantly smaller than a biological brain, and even if the temperature of these components was not significantly lower, Eliezer Yudkowsky of the Singularity Institute for Artificial Intelligence calculates a theoretical upper bound for the speed of a future artificial neural network.

Therefore Clements developed a very large vocabulary of theoretical terms describing the various possible causes of vegetation, and various non-climax states vegetation adopts as a consequence.

Therefore, it's important to look at the theoretical basis for hyperinflation to understand why Sachs noticed shock therapy proved to be so successful in fighting it.

Therefore, at a naïve theoretical level all gauge bosons are required to be massless, and the forces that they describe are required to be long-ranged.

Therefore, recent work concentrates on finding alternative solutions, in which for example currents are summed instead of voltages, resulting in a lower theoretical limit for the operating voltage ( Banba, 1999 ).

Therefore, he likely did not even rule Egypt in his theoretical first year and could only properly administer the country sometime during his second year.

Therefore, the theoretical Great Sioux Nation occupies only parts of the United States where Sioux tribes have some legal claim with regard to treaties with the Federal government.

Therefore, the system will always recover from an injection attack, and the time it takes to do so is at most a constant factor greater than the theoretical time it could take if we were able to identify which sources of entropy were corrupt and which not.

Therefore, in theoretical physics, a non-perturbative solution or theory is one that does not require perturbation theory to explicate, or does not simply describe the dynamics of perturbations around some fixed background.

Therefore, GPS is mostly a theoretical tool for benchmarking practical scheduling algorithms that approximate the GPS ideal.

Therefore, we can hold the realist view that our theoretical terms refer to something in the world and our theories are approximately true.

Therefore, their understanding is closely linked to the practice of neuropsychology and cognitive neuroscience, two disciplines that broadly seek to understand how the structure and function of the brain relates to perception defragmentation of concepts, memory embed, association and recall both in the thought process and behaviour.

Therefore, the third principle of the plan must be that it does not depend for effectiveness on engagement by the same types, unless at an assured favorable exchange rate.

Therefore, a base on balls does not increase nor decrease a player's batting average, but it does increase his on-base percentage, unless a player's on-base percentage is 1. 000, in which case it remains the same.

Therefore, as clock rate increases, so does heat dissipation, causing the CPU to require more effective cooling solutions.

Therefore, when continuum mechanics refers to a point or particle in a continuous body it does not describe a point in the interatomic space or an atomic particle, rather an idealized part of the body occupying that point.

Therefore, the diagonal of a 4 x 9 lattice does not intersect any other square lattice | lattice points

Therefore, just as Christianity does not accept that Mosaic Law has any authority over Christians, Judaism does not accept that the New Testament has any religious authority over Jews.

Therefore, as long as the lower pot does not become pressurized or boiled dry, the maximum temperature contacted by the upper vessel will be the boiling point of water, and scalding or uneven heat is avoided.

Therefore an ordination ceremony that concerns only the individual himself does not, they say, correspond to the definition of an ordination and is without effect.

" Therefore, federal copyright law does not pre-empt the players ' claimed right of publicity.

Therefore he does not believe in equal rights, but the person's life that should be favored that is most conducive to the general good.

Therefore, who does this is not forbidden to the priesthood because of harlotry, and a woman is not prohibited to her husband by this, since it is not harlotry.

Therefore, HMAC-MD5 does not suffer from the same weaknesses that have been found in MD5.

Therefore, the outcome assessment in terms of failure or success of the new EITI regulation does not only " rest on the government's shoulders " but also on civil society and companies .< ref name =" Owona, S. O.

Therefore, after a rhetorical analyst discovers a use of language that is particularly important in achieving persuasion, she typically moves onto the question of " How does it work?

Therefore, carbon will not replace the glaze as it does the melted wax.

Therefore, it does not contract when it freezes like most substances, but expands, similar to how ice is less dense than water and has less mass per unit of volume than liquid water.

# Therefore, an all-powerful and perfectly good god does not exist.

# ( Therefore ) There does not exist an omnipotent, omniscient, wholly good being.

" power we allow infinite: Whatever he wills is executed: But neither man nor any other animal are happy: Therefore he does not will their happiness.

With a declination of + 38. 78 °, Vega can only be viewed at latitudes north of 51 ° S. Therefore, it does not rise at all anywhere in Antarctica or in the southernmost part of South America, including Punta Arenas, Chile ( 53 ° S ).

Therefore, the " T " must always fill two corners, and there is only one orientation ( discounting rotations ) in which it does that.

Therefore, any Internet connected network must by definition either pay another network for transit, or peer with every other network who also does not purchase transit.

Therefore, the pressure wave produced by a high explosive is not significantly increased by confinement as detonation occurs so quickly that the resulting plasma does not expand much before all the explosive material has reacted.