Thus armed, they fought in a phalanx formation.

Thus, in the Spartan phalanx at Leuctra, Cleombrotus and the elite ' Spartiates ' were on the right, while the less experienced Peloponnesian allies were on the left.

Thus a phalanx does not have a standard combat strength or composition but includes the total number of infantry, which is or will be deployed in action in a single phalanx formation.

Thus in 941, when the Byzantines were facing the vastly more numerous Rus ' fleet, siphons were placed also amidships and even astern.

Thus, criminals tend to repeat their crimes, and eventually end up facing execution or exile.

Thus for n cascaded sections all having matching impedances facing each other, the overall propagation constant is given by,

Thus, there was a global rise of religious nationalism in the wake of the end of the cold war, but also as postcolonial politics ( facing considerable developmental challenges, but also dealing with the reality of colonially-defined – and therefore somewhat artificial borders ) become challenged.

Thus PIE ( traditional ) * anti " in front of and facing " > Greek antí " against "; Latin ante " in front of, before "; ( Sanskrit ánti " near ; in the presence of ").

Thus, it has two flat blades, facing away from each other, and one rotated 90 ° relative to the other.

Thus, while smaller in terms of total number of planes, the FAE of January 1995 felt qualitatively capable of facing the FAP on more or less equal terms, in striking contrast to the situation during the crisis of 1981, where except for a small number of missions, the FAE had been kept on the ground armed and ready for immediate action, to be committed only in case of a full-fledged war, their positions in the Cordillera del Cóndor was well defended due to tactically placed SAMs by the FAE, and units armed with British-made Blowpipe and Russian-made SA-16 MANPADs, nevertheless, such defences didn ´ t stop the continuous raids of the Peruvian Air Force, which lost several aircraft in the effort.

Thus, the culmination of the invention of the photograph was a break in art's history towards the challenge facing the artist-since the earliest known cave drawings-trying to replicate the scenes they viewed.

Thus, China being still legally one single country including the Mainland and Taiwan, the question facing the General Assembly was that of deciding which is the legitimate Government of China: the Government controlling the whole of the Mainland, or the Government deposed from the Mainland and in control of an archipelago only.

Thus, in addition to facing the problem of escalating hostilities, their food shortage was magnified by the arrival of more men.

Thus, with the HCP evenly split and facing a bid at the three level by the opposition, bidding to a level above the number of trumps held can be a useful sacrifice at favourable vulnerability.

Thus, the Southern Tang began as an empire, however under Li Jing it was no longer diplomatically possible to claim the title of emperor in facing other states, thus he assumed the title of king instead, thus technically lowering the political status of the realm.

Thus, for companies facing uncertainty of this type, the stock price may ( should ) be seen as the sum of the value of existing businesses ( i. e. the discounted cash flow value ) plus any real option value.

Thus, the team could not afford to play any games with foreign opponents and limited itself to facing Polish sides.

Thus Scipio was facing two concentrated enemy forces, one of which would no doubt fall upon his rear if he tried to attack the other.

Thus Hasdrubal was left alone in facing Scipio ’ s concentrated force, but the Carthaginian general was able to avoid battle by splitting his troops among fortified cities.

Thus two bears are facing each other in perfect symmetry (" confronted "), forming the shape of a heart.

Thus arose the company name, Thames & Hudson, the rivers represented by two dolphins symbolizing friendship and intelligence, one facing east, one west, suggesting a connection between the Old World and the New.

Thus the supporting formations will themselves be part of this supporting structure.

Thus, Ukrainians also actively fought the Polish invasion in Ukrainian formations of the Red Army.

Thus a number of operations of the order of Af are required.

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, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus his calculations should have required an additional year, ending in 1967.

Thus it has been alleged that many credentes would eventually receive the consolamentum as death drew near — performing the ritual of liberation at a moment when the heavy obligations of purity required of Perfecti would be temporally short.

Thus miniatures were no longer required for game play, although some players continued to use them as a visual reference.

Thus, they required that the Estates be arranged as in 1614.

Thus, numerical mathematical methods are required, even to solve the system of one nucleus and two electrons.

Thus the tonewheel assembly generates 91 frequencies, which are all that are required for the entire organ.

Thus, the state required service from both the old and the new nobility, primarily in the military.

Thus, the Holy Alliance needed Russia to supply the required armies.

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, reflection in a resonant cavity is usually required for a laser, but is not absolutely necessary.

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

Thus, while dialectical methods are necessary to find truth in theoretical matters, rhetorical methods are required in practical matters such as adjudicating somebody's guilt or innocence when charged in a court of law, or adjudicating a prudent course of action to be taken in a deliberative assembly.

Thus to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction.

Thus, many modern pumps have a molecular drag stage such as a Holweck or Gaede mechanism near the exhaust to reduce the size of backing pump required.

Thus, it is easy to convert from a vector file to a range of bitmap / raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required.

Thus no special modifications are required to be made to operating systems which would otherwise not know about them.

Thus such studies undermine the broad consensus required for good science by excluding certain people, and so proving themselves in the end to be unscientific.

Thus, according to Coule, an Alcubierre Drive is required in order to build an Alcubierre Drive.

Thus, Electronic Support provides a source of information required for decisions involving Electronic Protection ( EP ), Electronic Attack ( EA ), avoidance, targeting, and other tactical employment of forces.

Thus, a proactive and comprehensive approach to HD is required for US's response.

Thus the amount of the test substance required to produce the same biological effect as a given quantity the unit of a standard preparation is compared and the potency of the unknown is expressed as a % of that of the standard by employing a simple formula.