Thus, we have no part, and want none, in current discussions of the relative importance of science, the social studies, the humanities, the creative arts.

Thus every part and plane of the picture keeps changing place in relative depth with every other part and plane ; ;

Thus for example Heraclitus ' The Allegorist ' quoted fr. 326 and part of fr. 6, about ships in a storm, in his study on Homer's use of allegory.

“ Acts, then is a continuation of the Lucan Gospel, not in the sense that it relates what Jesus continued to do, but how his followers carried out his commission under the guidance of his Spirit .” Thus, part of the answer to the purpose of Acts is that Luke is writing to Theophilus, who is also mentioned in Luke 1: 3, in order to explain to him the occurrences that take place in the church that fulfill Jesus ’ promise to his disciples that “ you will be baptized with, the Holy Spirit not many days from now ” ( Acts 1: 5 ).

Thus, any transverse velocity of the emitting source plays no part in aberration.

Thus, only the immediate purchaser could recover for a product defect, and if a part was built up out of parts from parts manufacturers, the ultimate buyer could not recover for injury caused by a defect in the part.

Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus, southern Germany once more became part of the Frankish kingdom, as had northern Germany during the first years of the reign.

" Thus, any activity of production ( which distributism holds to be the most important part of any economy ) ought to be performed by the smallest possible unit.

Thus Bolesław the Brave might have received Kraków as his part of his father's legacy before the Dagome iudex had been written.

Thus, Egypt was by Ottoman law de jure a province of that empire, but de facto was part of the British Empire.

Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man.

Thus, in the sentence " There exists a man ", the term " man " is asserted to be part of existence.

Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.

Thus, in women with Type III FGM who have developed vesicovaginal or rectovaginal fistulae — holes that allows urine and feces to seep into the vagina — it is difficult to obtain clear urine samples as part of prenatal care making the diagnosis of certain conditions harder, such as preeclampsia.

Thus they were not gravitationally bound to the Milky Way, and were unlikely to be a part of the galaxy.

However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of data as 1024 ( 2 < sup > 10 </ sup >); this is due to the mathematical coincidence that Thus, in these fields 1 kilobyte is equal to 1 kibibyte, a new unit standardized as part of the binary prefixes to resolve the ambiguity.

Thus, the Beqaa Valley is part of the Great Rift system, which stretches from southern Turkey to Mozambique in Africa.

Thus this theory can be sometimes viewed as part of the social evolutionism theory.

Thus ingot casting, foundry techniques, blast furnace extraction, and electrolytic extraction are all part of the required knowledge of a metallurgist / engineer.

Thus C1 restores its charge and prepares for the next State 1 when it will act again as a time-setting capacitor ... and so on ... ( the next explanations are a mirror copy of the second part of Step 1 ).

Another renowned part of the coronation was the lighting of a bundle of flax at the top of a gilded pole, which would flare brightly for a moment and then promptly extinguish, with the admonition Sic transit gloria mundi (" Thus passes worldly glory ").

Thus, lack of complete information on the part of survey participants may have skewed the results.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus, what is known as the extreme value theorem in calculus generalizes to compact spaces.

Thus, using Euler's theorem we can say that the solution must be of the form:

Thus, in a sense, there is a different completeness theorem for each deductive system.

Thus the no-cloning theorem holds in full generality.

Thus if we wish to claim that no-cloning is a uniquely quantum result, some care is necessary in stating the theorem.

) Thus, the group of conformal transformations in spaces of dimension greater than 2 are much more restricted than the planar case, where the Riemann mapping theorem provides a large group of conformal transformations.

Thus no formal system ( satisfying the hypotheses of the theorem ) that aims to characterize the natural numbers can actually do so, as there will be true number-theoretical statements which that system cannot prove.

Thus, by the principal axis theorem, the second fundamental form is

Thus according to the central limit theorem, we can model jitter as a gaussian random variable.

Thus Tychonoff's theorem joins several other basic theorems ( e. g. that every nonzero vector space has a basis ) in being equivalent to AC.

Thus one can see that the Cayley – Hamilton theorem must be true.

Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole ( the no-hair theorem ).

Thus, non-real roots of real polynomials occur in complex conjugate pairs ( see Complex conjugate root theorem ).

Thus, proving the claim will prove the theorem.

Thus, according to Euler's quadrilateral theorem, the circumradius can be expressed in terms of the diagonals p and q, and the distance x between the midpoints of the diagonals as

By Taylor's theorem, this is a locally free sheaf of modules with respect to the sheaf of germs of smooth functions of M. Thus it defines a vector bundle on M: the cotangent bundle.

Thus whenever a theorem and its reciprocal are true we have a biconditional.

Thus we get the right side of Green's theorem

Thus the Picard – Lindelöf theorem guarantees the existence and uniqueness of the solution.

Thus all geodesics leaving a point will eventually reconverge after a finite time, provided the appropriate energy condition holds, a result also known as the focusing theorem.

Thus reflections generate the orthogonal group, and this result is known as the Cartan – Dieudonné theorem.

Thus h can be extended to an entire bounded function which by Liouville's theorem implies it is constant.

Thus the coimage of f is a quotient algebra of X much as the image of f is a subalgebra of Y ; and the bijection between them becomes an isomorphism in the algebraic sense as well ( this is the most general form of the first isomorphism theorem in algebra ).

Thus one obtains Stone's representation theorem for Boolean algebras.