Thus, over time, the expression " a cappella " ( Italian for " in the manner of the chapel ") came to mean exclusively vocal music in contradistinction to the spreading use of the organ in cathedrals.

Thus, this early revolt against colonial rule ( one of the first in Spanish America ) was, paradoxically, an expression of loyalty to the Spanish king.

Thus our expression simplifies to:

Thus, by iteratively substituting the into the expression,

Thus an example of the expression would look like this:

Thus, we should amend the expression given above into: Metallic bonding is an extremely delocalized communal form of electron deficient covalent bonding.

Thus one can create and use infinite streams as in Haskell, but their expression is comparatively indirect.

Thus the reverse procedure, though originally uncommon, enabled northern analysis to evolve into gene expression profiling, in which many ( possibly all ) of the genes in an organism may have their expression monitored.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

Thus, in the 1930s and 1940s, Egyptian nationalism – and not pan-Arabism – was the dominant mode of expression of Egyptian political activists.

Thus, the derogatory meaning of the word " myth " is the traditional Christian meaning, and the expression " Christian mythology ", as used in academic discourse, may offend Christians for this reason.

Thus, short story writers may define their works as part of the artistic and personal expression of the form.

Thus for finite n, the expression " n-th element " of a well-ordered set requires context to know whether this counts from zero or one.

Thus, the most famous and iconic expression of the Brazilian Carnival takes place in the Rio Carnival, with samba schools parading in the Sambadrome (" sambódromo " in Portuguese ).

Thus, the law, inasmuch as it is created by the people acting as a body, is not a limitation of individual freedom, but its expression.

Thus the nouns " cutlery " and " water " have cumulative reference, while the expression " a chair " does not.

Thus, there is no such thing as a sentence, term, expression or word symbolically representing a single true meaning ; it is underspecified ( which cat sat on which mat?

Thus suicide was deemed as the ultimate, albeit tragic, expression of hatred directed inwardly, a final rejection of God's gifts.

Thus, the meaning of expressions depends on the conditions in which they emerge and exist within a field of discourse ; the discursive meaning of an expression is reliant on the succession of statements that precede and follow it.

The preceding two paragraphs are an expression in English which unambiguously defines a real number r. Thus r must be one of the numbers r < sub > n </ sub >.

Thus kiai is the expression or projection of our own, internal energy while aiki is coordination with an attacker's energy.

Thus the diagnosis " often says more about the clinician's negative reaction to the patient than it does about the patient ... as an expression of counter transference hate, borderline explains away the breakdown in empathy between the therapist and the patient and becomes an institutional epithet in the guise of pseudoscientific jargon ".

Thus, the expression " I am parked out back " conveys the meaning of " parked " from " car " to the property of " I possess a car ".

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.

Thus this class of molecules belong to the D < sub > 2d </ sub > point group.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Thus, the boiling point is dependent on the pressure.

Thus, the Big Bang theory cannot and does not provide any explanation for such an initial condition ; rather, it describes and explains the general evolution of the universe going forward from that point on.

Thus, the use of a psalm creates an important theological point.

Thus the P5 was integer superscalar but not floating point superscalar.

Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.

Thus at any point in time most of their content resides in nonvolatile storage.

Thus a line has a dimension of one because only one coordinate is needed to specify a point on it ( for example, the point at 5 on a number line ).

Thus at any point in time most of their content resides in nonvolatile storage.

Thus, the change in slope between each successive point is small, reducing the apparent " jaggedness " of the approximation.

Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.

Thus, many typical household applications already in existence like word processing and email were designed specifically to avoid using floating point operations.

Thus, Muhammad, by saying this, clearly made it a point to the Arabs to not make any distinction between the great apostles of God.

Thus at any point there should be one special coordinate system, " at rest relative to the aether ".

Thus for map projections we must introduce the concept of point scale, which is a function of position, and strive to keep its variation within narrow bounds.

Thus, the maximum theoretical extent of a given mass transfer is typically determined by the point at which the chemical potential is uniform.

Thus a point y in V is a cluster point of the net if and only if every neighborhood Y of y contains infinitely many elements of the sequence.

Thus the first derivative at that point is undefined and leads to a jump discontinuity in the marginal revenue curve.

Thus Osiris was identified explicitly with Apis, really an aspect of Ptah, who had already been identified as Osiris by this point, and a syncretism of the two was created, known as Serapis, and depicted as a standard Greek god.

Thus, a player who bids three and takes either two or four tricks will lose one point.

Thus, the vertex is at point