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, the Church was born and because of its intrinsic character was soon identified as a conservative institution, determined to resist the forces of change, to identify itself with the political rulers, and to maintain a kind of splendid isolation from the masses.

Thus, a finding of conspiracy to restrain trade or attempt to monopolize was excluded from the Court's decision.

Thus, the energy transferred from the arc to the anode was partly fed back into the arc.

Thus the unstressed it of it rarely snows here gets its significance from its use with snows: nothing can snow snow but `` it ''.

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 one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.

Thus Af denotes the state of the feed to the R-stage process, and Af the state of the product from the last stage.

Thus creativity may run all the way from making a cake, building a chicken coop, or producing a book, to founding a business, creating a League of Nations or, developing a mature character.

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus, moral decision must be entirely deduced backward from the likely eventuality ; ;

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

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 a colonial bishop and colonial diocese was by nature quite a different thing from their counterparts back home.

Thus situated, the mountains make travel from north to south difficult.

Thus, from the human body, the usual form assigned to the Deity, forasmuch as it is written that God created man in his own image, issue the two supporters, Nous and Logos, symbols of the inner sense and the quickening understanding, as typified by the serpents, for the same reason that had induced the old Greeks to assign this reptile for an attribute to Pallas.

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 the possibility of re-incorporating Portugal ( up to then Southern Galicia ) into a Kingdom of Portugal and Galicia as before was eliminated and Afonso became sole ruler ( Duke of Portugal ) after demands for independence from the county's church and nobles.

Thus, Afonso continued to distinguish himself by his exploits against the Moors, from whom he wrested Santarém ( see Conquest of Santarém ) and Lisbon in 1147 ( see Siege of Lisbon ).

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

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Thus in the following days from September 20, 1945, the functions of the OSS were split between the Department of State and the Department of War.

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, without being constitutionally obligated to pay compensation, the United States may change the course of a navigable stream, South Carolina v. Georgia, 93 U. S. 4 ( 1876 ), or otherwise impair or destroy a riparian owner's access to navigable waters, Gibson v. United States, 166 U. S. 269 ( 1897 ); Scranton v. Wheeler, 179 U. S. 141 ( 1900 ); United States v. Commodore Park, Inc., 324 U. S. 386 ( 1945 ), even though the market value of the riparian owner's land is substantially diminished.

Thus the city was a part of the Prussian province of Silesia from 1815 until 1945.

'" Thus by the end of 1945 several versions of " I Will Overcome " were current as a gospel song, while on the South Carolina picket line, Lucille Simmons and other striking tobacco workers were singing a slow version of the song as, " We Will Overcome ".

Thus, despite opposition from other leaders, especially Winston Churchill, China became a permanent member of the Security Council from its creation in 1945.

Thus in 1943, it was created the National Power Company (); in 1945, the National Oil Company (); and in 1946, the Pacific Steel Company (), which opened the Huachipato steelworks next to the port of Talcahuano.

Thus, by the late autumn of 1945, the North was virtually controlled by the Tudeh and its affiliates.

Thus he was arrested by the Allies in 1945.

Thus, it was responsible, between 1942 and 1945, conducting 574 convoy operations protecting 3164 merchant ships of various nationalities.

Thus the A4-Raketen of the Operation Backfire started in October 1945 of one in the Werner forest between Arensch and Sahlenburg established starting place, from which still some shelter remainders and a soil hollow remained remaining.

Thus Bristol had readily available players when peacetime rugby union resumed in 1945.

Thus it was the British Labour government — which embraced socialism — that pushed the Truman administration in 1945 – 47 to take a strong stand against Soviet Communism.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

) Thus, for example, a 2x6 rectangle and a 3x4 rectangle are equal but not congruent, and the letter R is congruent to its mirror image.

Thus every module direct summand of R is generated by an idempotent.

Thus, Hillel called attention to seven commonly used in the interpretation of laws ( baraita at the beginning of Sifra ); R. Ishmael, thirteen ( baraita at the beginning of Sifra ; this collection is largely an amplification of that of Hillel ).

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.

Thus, on 10 February of that year, a Junker 52 of the Réseau des Liaisons Aériennes Francaises ( R. L. A. F ), later known as Air France, landed in Plaisance.

Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.

Thus, if R ≥ VC then firm should operate.

Thus the ( real < ref > The complex spinors are obtained as the representations of the tensor product H ⊗< sub > R </ sub > C = Mat < sub > 2 </ sub >( C ).

CSMA / CA can optionally be supplemented by the exchange of a Request to Send ( RTS ) packet sent by the sender S, and a Clear to Send ( CTS ) packet sent by the intended receiver R. Thus alerting all nodes within range of the sender, receiver or both, to not transmit for the duration of the main transmission.

Thus R ⊆ A < sub > 0 </ sub > and the A < sub > i </ sub > are R modules.

Thus these are precisely the class of domains for which Frac ( R )/ Prin ( R ) forms a group, the ideal class group Cl ( R ) of R. This group is trivial if and only if R is a PID, so can be viewed as quantifying the obstruction to a general Dedekind domain being a PID.