Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus twenty `` black souls '' were to remain ignorant of their imminent journey to the land of free men.

Thus such great American documentaries as The River and The Plow That Broke The Plains were composed as visual stories rather than as illustrated lectures.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

Thus #, $ and % were placed to correspond to 3, 4, and 5 in the adjacent column.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

Thus, before the modern assembly line took shape, there were prototypical forms in various industries, as outlined below.

Thus Myspace and YouTube were not liable for a dyslexic man's inability to navigate the site regardless of how impressive the " online theater " is.

Thus we were spared the affliction of his absence and the triumph of suffering for his principles.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus while Persian-speakers were concentrated on the lower rungs of the work force, managers tended to be brought in from some distance.

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

Thus a third style, the " curved lip " style was produced, and all official and third-party cartridges during the console's lifespan were released ( or re-released ) using this style.

Thus, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

" Thus the farmers were placed in a disadvantageous economic position.

Thus, dark blue jerseys, were introduced with white shorts and the red socks of 1908.

Thus, if the score was 3 – 2 with the bases loaded in the bottom of the ninth, and the batter smacked an " over the fence home run ", the game would end at 4 – 3, with the batter only allowed a double, and the runners officially stopped on 2nd and 3rd ( since they were not needed to win the game ).

Thus in 1880 and 1882, Benedictine teaching monks were effectively exiled ; this was not completed until 1901.

Thus, in 250-1, the Bastarnae were probably involved in the Gothic and Sarmatian invasions which culminated in the Roman defeat at the Battle of Abrittus and the slaying of the emperor Decius ( 251 ).

Thus parliamentary constituencies were derived from the ancient boroughs.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

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 in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.

Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus, there is no assault if an ox gores a man.

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus, services could be moved to a different machine and, so long as they kept the same service name, there was no need for users to do anything different to continue accessing the service.

Thus, ATP was a simple request / response exchange, with no need to set up or tear down connections.

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

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

Thus, the theory asserts that the apple is no more than the collection of its properties.

Thus, according to the Bank of England's Boxall and Gallagher ( 1997 ), "... there was virtually no difference between banks and building society ' listed ' interest rates for home finance mortgage lending between 1984 and 1997.

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, no two nuclear powers have yet fought a conventional war directly, with the exception of brief skirmishes between for example, China and Russia in the 1969 Sino-Soviet conflict and between India and Pakistan in the 1999 Kargil War.

Thus, he implicitly emphasized that it is God-made (" God has joined together "), " male and female ," lifelong (" let no one separate "), and monogamous (" a man ... his wife ").

Thus no form of justification will rationally warrant our inductive inferences.

Thus, a central conclusion of Keynesian economics is that, in some situations, no strong automatic mechanism moves output and employment towards full employment levels.

Thus, the majority of communications can no longer be intercepted by earth stations ; they can only be collected by tapping cables and intercepting line-of-sight microwave signals, which is possible only to a limited extent.

Thus, there should be no need for prices.