Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Af if and only if Af.

Thus F satisfies Af if and only if F has the form Af.

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, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

Thus, if one accelerometer is properly aligned, the other is also.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus, red wine must, if possible, never be disturbed or shaken ; ;

Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.

Thus most Affidavits now require to be Apostilled if used for cross border issues.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.

Thus, a court officer taking possession of goods under a court order may use force if reasonably necessary.

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

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

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, by the end of 1992, Azerbaijan received arms and military hardware sufficient for approximately four motor rifle divisions with prescribed army units.

Thus in 565 or 566 Justinian's successor Justin II sent his son-in-law Baduarius as magister militum ( field commander ) to lead a Byzantine army against Alboin in support of Cunimund, ending in the Lombards ' complete defeat.

Thus, in the mid-1990s the army sought to reduce the number of active-duty generals.

Thus, " the image of the German ' Blitzkrieg ' army is a figment of propaganda imagination ".

Thus, only those who could afford such weaponry fought as hoplites ; as with the Roman Republican army it was the middle classes who formed the bulk of the infantry.

Thus the scutage was introduced, whereby most Englishmen paid to escape their service and this money was used to create a permanent army.

Thus, in August 480 BC, when the Persian army was approaching Thessaly, the Allied fleet sailed to Artemisium, and the Allied army marched to Thermopylae.

Thus the Scots won a significant victory which boosted the confidence of their army.

Thus, ' Abd-al-Raḥmân recalled all his troops, which did give him an even larger army — but it also gave Charles time for more of his veteran infantry to arrive from outposts of the Kingdom.

Thus, rather than being formed from a trained, armed, and organised army, the Republican armed forces began to grow in September from usually younger, less trained groups built around charismatic leaders.

Thus the history of English military law up to 1879 may be divided into three periods, each having a distinct constitutional aspect: ( I ) prior to 1689, the army, being regarded as so many personal retainers of the sovereign rather than servants of the state, was mainly governed by the will of the sovereign ; ( 2 ) between 1689 and 1803, the army, being recognized as a permanent force, was governed within the realm by statute and without it by the prerogative of the crown and ( 3 ) from 1803 to 1879, it was governed either directly by statute or by the sovereign under an authority derived from and defined and limited by statute.

Thus in 1879 the government and discipline of the army became for the first time completely subject either to the direct action or the close supervision of parliament.

Thus, PMC contractors are civilians ( in governmental, international, and civil organizations ) authorized to accompany an army to the field ; hence, the term civilian contractor.

Thus, the strategic position of Antony and Octavian became quite serious, since the already depleted regions of Macedonia and Thessaly were unable to supply their army for long, while Brutus could easily receive supplies from the sea.

Thus, Brutus ’ s army could not reform, which made the triumvirs ’ victory complete.

Thus began the Battle of Crécy ; and when it was done, the French army had been well-nigh annihilated, and a wounded Philip barely escaped capture.

Thus, he induced Ivan Mazepa, the Cossack hetman, to desert Peter the Great at the most critical period of the Great Northern War between Russia and Sweden, and Stanisław placed a small army corps at the disposal of the Swedes.

Thus Pym lost the unity of the House of Commons, which had allowed him to oppose the King from a firm platform ; previously the King had had to agree to demands because he could not raise an army alone to fight the Irish rebels.

Thus, both the police and army of Puntland were already established in the region based on the desires of the local population for their security and the territorial integrity of Somalia.

Thus the army will have food enough for its needs.

Thus, Khatami had no legal authority over key state institutions: the armed forces, the police, the army, the revolutionary guards, the state radio and television, the prisons, etc.

Thus at Numbers 24: 7 it replaces Agag, a mysterious but clearly powerful figure, with Gog, and at Amos 7: 1 the Greek has Gog as the leader of a threatening locust-like army.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

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

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

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

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.