Thus it follows that the secants of **zg are all invariant.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus, the above conditions could be re-written as follows:

Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows.

Thus the dactylic line most normally looks as follows:

Thus, if is the total number of trials and is the number of trials where the event occurred, the probability of the event occurring will be approximated by the relative frequency as follows:

Thus the loop f ∗ g first follows the loop f with " twice the speed " and then follows g with twice the speed.

Thus, it follows that all power laws with a particular scaling exponent are equivalent up to constant factors, since each is simply a scaled version of the others.

Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows.

Thus, by definition, one mole of pure < sup > 12 </ sup > C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance.

Thus, the term " MVC " in the context of Squeak refers to both one of the available user interface frameworks and the pattern the framework follows.

Thus " luen " can mean " I am reading " or " I will read " depending on the case form of the word that follows.

Thus can be estimated as the function of ( flux to voltage converter ) as follows:

Thus postmenopause is all of the time in a woman's life that take place after her last period, or more accurately, all of the time that follows the point when her ovaries become inactive.

Thus, the actus reus and mens rea of homicide in a modern criminal statute can be considered as follows:

Thus if G is any finitely generated group of exponent n, then G a homomorphic image of B ( m, n ), where m is the number of generators of G. Burnside's problem can now be restated as follows:

Thus, in classical ( Newtonian ) mechanics a cause may be represented by a force acting on a body, and an effect by the acceleration which follows as quantitatively explained by Newton's second law.

Thus, for example, the description " T1SR20E S13 MDM " reads as follows: Township 1 South, Range 20 East, Section 13, Mount Diablo Meridian.

Thus, the lyric of Ghana ’ s National Anthem is as follows:

Thus bent the ski follows the turn without sliding.

Thus it follows, according to Zeno, that motion ( travelling a non-zero distance in finite time ) is a supertask.

Thus the Law of Mass Action was first stated as follows:

Thus, it follows that some economists, socialists and anarchists contend that the existing indicators of economic freedom are too narrowly defined and should take into account a broader conception of economic freedoms.

Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 < sup >− 27 </ sup > kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.

Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.

Thus, a short path between the hot surface and the cold surface is necessary, typically by suspending a hot plate covered with a film of feed next to a cold plate with a line of sight in between.

Thus, man then directs his path to that One, and the love for, and of, Christ guides man's very nature to become centered on the One, and on his neighbor as well.

Thus, the eight items of the path are not to be understood as stages, in which each stage is completed before moving on to the next.

Thus the Augustinian theodicist would argue that the problem of evil and suffering is void because God did not create evil ; it was man who chose to deviate from the path of perfect goodness.

Thus, if a wave is traveling through several different media, then the optical path length of each medium can be added to find the total optical path length.

Thus augmented, and swollen into a stream wide, the Elbe carves a path through the basaltic mass of the České Středohoří, churning its way through a deep, narrow rocky gorge.

Thus human beings have free will and can choose the path in life that they will take.

Thus, the perforant path establishes the EC as the main " interface " between the hippocampus and other parts of the cerebral cortex.

Thus, intuitively we could interpret the fraction of as representing the ratio of the labor one has to perform when going from a randomly chosen configuration to another randomly chosen configuration, relative to the difficulty of having to cross the " most difficult " path of length which involves moving all the disks from one peg to another.

Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition ( the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit ).

Thus, for a fixed path length, UV / Vis spectroscopy can be used to determine the concentration of the absorber in a solution.

Porro prism designs have the added benefit of folding the optical path so that the physical length of the binoculars is less than the focal length of the objective and wider spacing of the objectives gives a better sensation of depth. Thus, the size of binoculars are reduced.

In one direction, the Hamiltonian path problem for graph G is equivalent to the Hamiltonian cycle problem in a graph H obtained from G by adding a new vertex and connecting it to all vertices of G. Thus, finding a Hamiltonian path cannot be significantly slower ( in the worst case, as a function of the number of vertices ) than finding a Hamiltonian cycle.

Thus in general usage, a world line is the sequential path of personal human events ( with time and place as dimensions ) that marks the history of a person — perhaps starting at the time and place of one's birth until one's death.

Thus, the 0-homology group measures the number of path connected components of the space.

Thus, doubling the propagation path distance from the transmitter reduces each of their received field strengths over a free-space path by one-half.

Thus linked, the user was able to choose an arbitrary path through the city ; the only restrictions being the necessity to stay in the center of the street ; move ten feet between steps ; and view the street from one of the four orthogonal views.

Thus prepared for life, Virginia falls for the first handsome young man who crosses her path — Oliver Treadwell, the black sheep of a family of capitalist entrepreneurs who, during the time of Reconstruction, brought industry and the railroad to the South.