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 the conception of Claudius as the weak fool, controlled by those he supposedly ruled, was preserved for the ages.

Thus there were in reality thirteen tribes ; but the number twelve was preserved by excluding that of Levi when Ephraim and Manasseh are mentioned separately.

Thus did Charlestown escape the more devastating aspects of “ progress .” Its heritage is preserved in the Historic District, which includes approximately 150 buildings.

Thus, for the human wave attack to succeed on the modern battlefield, it is imperative for the attackers to charge into the enemy line in the shortest time and in the greatest numbers possible, so that a sufficient mass can be preserved when the attackers reach melee range.

Thus the papyri were finally brought together in Cairo: of the 1945 find, eleven complete books and fragments of two others, ' amounting to well over 1000 written pages ' are preserved there.

" Thus, etymologically mitra / miθra means " that which causes binding ", preserved in the Avestan word for " covenant, contract, oath ".

Thus, Portugal was allied with Britain and preserved its possessions for a longer time.

Thus in Baozheng 2nd year ( 927 ), the emperor of Wuyue Kingdom, Qian Liu, installed a lake-dredging army of 1, 000 to mow grasses and deepen springs, and preserved the water body of the lake.

Thus, Jefferson ’ s admonition that an educated electorate was essential if liberty were to be preserved is transmuted into a call for universal public education.

Thus, in Frau Gauen or Gauden, German farmers have preserved the memory of a Mrs. Odin at work beside her husband in the fields long after the coming of Christianity.

Thus, the Balts ' culture is believed to have preserved primeval features of Indo-European culture for a longer time.

Thus, by the time of Littleton ( Henry VI and Edward IV ), an immense mass of material had been acquired and preserved in the rolls of the various courts.

Thus conditions in 5th century and 6th century Britain spurred the burial of hoards of which the most famous are the Hoxne Hoard, Suffolk ; the Mildenhall Treasure, the Fishpool Hoard, Nottinghamshire, the Water Newton hoard, Cambridgeshire, and the Cuerdale Hoard, Lancashire, all preserved in the British Museum.

Thus, as a hotel, the exterior of the building has been preserved, as has the central corridor of the old prison and even the old prison wall.

Thus, there is great local indignation about the excavation and removal of the Siberian Ice Maiden, an extraordinary 2, 500-year-old mummy that had been preserved in permafrost.

Thus the dates of the epitaphs of the family of Asher ben Jehiel in the first half of the fourteenth century are indicated by chronograms ( Almanzi, " Abne Zikkaron ", pp. 4, 6, 9 ); and among sixty-eight Frankfort epitaphs of that century four chronograms have been preserved ( Horowitz, " Inschriften.

Thus, while Iraq's body politic crumbled under immense political and economic pressure throughout the monarchic period, the military gained increasing power and influence ; moreover, because the officers in the new army were by necessity Sunnis who had served under the Ottomans, while the lower ranks were predominantly filled by Shia tribal elements, Sunni dominance in the military was preserved.

Thus, not only do the old songs preserved among different clans but even the folk songs being composed at present, reveal the extent of the uniformity of language that existed in the not-so-distant past.

Thus the utility function is cardinal ( it preserved the order of preference over except for an arbitrary choice of origin and scale ).

Thus, London Underground has acquired numerous former British Rail coaching stock for these special excursion trains on the Metropolitan Line, usually hauled by either steam locomotives, or the preserved electric locomotive No. 12 " Sarah Siddons ".

Thus they became in one of the oldest stringent civic republics members of the ruling class, which preserved its constitutional privileges till the German Revolution of 1918.

Thus the linguistic memory of the one-time use of the area has been preserved over more than 1, 500 years since quarrying last took place in the area.