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, this branch spared in carpal tunnel syndrome, and there is no loss of palmar sensation.

Thus was Dong Zhuo's life spared and the three brothers went their own way.

Thus Ramón Gris is shot and Pablo's life is, at least temporarily, spared from death.

Thus Vir did not have to kill Londo and the planet was spared.

Thus, Vir was spared this decision, and it remained unclear if he had been capable of killing his long-term friend.

Thus, the more closely the crabs resemble a samurai face, the more likely they would be spared and thrown back.

Thus he made a vow to dedicate his life, should he be spared, to religious study and to seeking out the truth about the matter of life and death.

Thus, he was spared the tragic history of his motherland.

Thus the natives were spared from the incursion of the Moro invaders.

Thus from AD 451 the Armenian church became separate from the other Christian churches in Jerusalem, a fact that would have major ramifications in the ensuing struggle with fellow Christians during the Crusader and Ottoman periods.

Thus began a long and vicious quarrel which was to have unforseeable ramifications for Caravaggio decades after his death when the unforgiving Baglione became his first biographer.

Thus in the spring of 1912, consultations between the various Christian Balkan nations resulted in a network of military alliances which became known as the Balkan League.

Thus, Alexander remained in command of the 15th Army Group, and, with the support of numerous allied commanders, controversially authorised the bombing of the historic abbey at Cassino, which resulted in little advance on the German Winter Line defences.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus began a long-lasting dispute which eventually resulted in the signing of the Treaty of Tordesillas with Spain in 1494.

Thus, if a company is sued for monopolizing a market and the jury concludes the conduct resulted in consumers ' being overcharged $ 200, 000, that amount will automatically be tripled, so the injured consumers will receive $ 600, 000.

Thus, after this point in time, election to magisterial office resulted in automatic Senate membership.

Thus the Fronde finally resulted in the disempowerment of the territorial aristocracy and the emergence of absolute monarchy.

Thus the renewed contact and resurrection of common roots and goals resulted in a positive contact and exchange, producing a world-wide net of genetic and academic exchange – leading to the innovations, produce and trade of agriculture, metals and alloys that led to advanced arts, tools, craft and technology.

Thus, Green's later mathematical contributions, which exhibited knowledge of very modern developments in maths, could not have resulted from his tenure at the Robert Goodacre Academy.

Thus landscape ecology is concerned mainly with the populations and ecosystems which have resulted from traditional, regionally specific forms of land use.

Thus, these changes conflicted with the Good Neighbor Policy's fundamental principle of non-intervention and resulted in a new wave of American interference into Latin American affairs.

Thus in the spring and summer of 1912 these consultations between the various Christian Balkan nations had resulted in a network of military alliances which became known as the Balkan League.

Thus, this concept can be used to treat clients with psychological problems that resulted from maladjustments by guiding them to first change their behavior and later dealing with the ‘ problems ’.

Thus these sessions resulted in some of the most important masterpieces of early jazz, of which West End Blues is arguably the best known.

Thus a stalemate resulted, in which the Poles retained control over Lviv and a narrow strip of land around a railway linking Lviv to Poland, while the rest of eastern Galicia was under the control of the West Ukrainian National Republic.

Thus Isabella and her husband stimulated the growth of this artistic movement, which resulted in the creation of the Flemish Baroque.

Thus, the island was demoted from an administrative district to a sub-district which resulted that the island was to be stripped of its local tribunals.

Thus keying page * 7471 # actually resulted in the display of frame 7471a which could be extended by use of follow-on frames 7471b, 7471c etc.

Thus it is believed that the feature resulted from seismic energies generated by the impacts that created these maria.

Thus, this resulted in Jang holding an MC job at MBC's music show, Music Camp.

Thus, Muhammad's marriage resulted in the freedom of nearly one hundred families whom he had recently enslaved.

Thus, a rise of incidents involving local college-aged females has resulted in an increased rate of Afro-Chinese infant births to single Kenyan mothers.

Thus Eicke's men were trained by a cadre of camp personnel without outside intervention ; the first major training exercise in 1935 resulted in the clearing of the entire Dachau camp for several weeks while the Totenkopf military formation was organized.