Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique ( EGA ) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time.

Then, following the battle, the Athenian army marched the 40 ( 25 miles ) or so kilometers back to Athens at a very high pace ( considering the quantity of armour, and the fatigue after the battle ), in order to head off the Persian force sailing around Cape Sounion.

Then after-depolarization this effect leads initially to bigeminy: regular ectopic beats following each ventricular contraction.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then, for any given sequence of integers a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > k </ sub >, there exists an integer x solving the following system of simultaneous congruences.

Then the following three connected theorems hold:

Then G is a group under composition, meaning that ∀ x ∈ A ∀ g ∈ G ( = ), because G satisfies the following four conditions:

Then the following month, on May 31st 1902, in a letter to William Blackwood, Conrad remarks:

Then the generation following them received it, thus conveying it to those after them and so on.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

This melding of scientific and social speculation is clearly present in the novel Voyage from Yesteryear ( strongly influenced by Eric Frank Russell's famous story " And Then There Were None ") about a high-tech anarchist society in the Alpha Centauri system, a starship sent from Earth by a dictatorial government, and the events following their first contact.

Then the following formula is an axiom:

" Then following multiple protest from Jews in the new world and Holland and after his death they were even granted the right to pray, besides just trade.

Then the following are equivalent.

Then a subset is called a σ-algebra if it satisfies the following three properties:

Let U be a functor from D to C, and let X be an object of C. Then the following statements are equivalent:

Then in March of the same year, following the insurrection of the Paris Commune the French government under Thiers relocated to Versailles, from where the insurrection was militarily quelled.

Then the following dynamical system describes PLL behavior

Then the priest blesses kolyva ( boiled wheat with honey and raisins ) which is distributed to the faithful in commemoration of the following miracle worked by St. Theodore on the First Saturday of Great Lent: Fifty years after the death of St Theodore, the emperor Julian the Apostate ( 361-363 ), as a part of his general policy of persecution of Christians, commanded the governor of Constantinople during the first week of Great Lent to sprinkle all the food provisions in the marketplaces with the blood offered to pagan idols, knowing that the people would be hungry after the strict fasting of the first week.

Then, Cicero had the incriminating letters read before the Senate the following day, and shortly thereafter these five conspirators were condemned to death without a trial despite an eloquent protest by Julius Caesar.

Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value.

Then, each person decorates their page following the theme.

Then the following regression equation is postulated as a description of the process that generated the data:

Then write a review without using any of the following words: " Progressive rock ", " Genesis ", " Fish ", " heavy metal ", " dinosaurs ", " predictable ", " concept album ".

Then on September 22, 1862, George McClellan defeated Robert E. Lee at Antietam ; the second draft of the Emancipation Proclamation was issued to the public the following day.

Then, on July 2, there occurred another incident which set tongues to wagging at a furious clip.

Then, he receives an urgent message to investigate an incident on Venus.

The incident, like others in Matthew, is described as the fulfillment of a passage in the Old Testament read as prophecy, in this case a reading of Jeremiah: " Then was fulfilled that which was spoken through Jeremiah the prophet, saying, A voice was heard in Ramah, Weeping and great mourning, Rachel weeping for her children.

Then Shiva came to know about this incident and became furious at the non-righteous yagna.

Then came what is known as the Schnaebele incident, the arrest on the German frontier of a French official named Schnaebele, which caused immense excitement in France.

Then, after a performance where Kean went out of his way to botch the opening night of " Switzerland " by historical novelist Jane Porter in February 1819, for whom Kean had had a personal dislike, Bucke pulled the play out of contempt for Kean's conduct .. After much cajoling to still perform the play by the theatre staff, Mr. Bucke then later had it republished with a preface concerning the incident, including excerpts from correspondences between the involved parties, which was later challenged in two books, The Assailant Assailed and A Defense of Edmund Kean, Esq.

Then an incident tidal wave can be reinforced by reflections between the coast and the shelf edge, the result producing a much higher tidal range at the coast.

Then on Thursday, September 28, the Dallas Police Department reported the incident to be an " accidental overdose " and ended their investigation.

Then a bizarre combat incident occurs.

Then the officers of February 26 incident concluded that His Majesty accepted the mettle of the leaders and took the circumstances into consideration and lighter punishment.

Then ESPN commentator Bob Varsha called it as the " second major incident of the day for Ayrton Senna ", while Derek Bell, sitting in for Derek Daly during the ESPN broadcast, put the blame on Senna for having the wrong brake balance on his car.

Then occurred an incident that would set back Los Angeles organizing for years, On October 10, 1910, a bomb exploded at the Los Angeles Times newspaper plant that killed twenty-one workers.

Then on April 28, Minister of Interior Choi In-Kyu and the Chief of Security resigned taking responsibility for the Masan incident.

Then by an ordre du jour, which he did not communicate even to the president of the council, General Galliffet announced to the army that the incident was closed.

Then came this decision, which sped the process of gaining equality ( or perhaps hindered it ; ;

Then he kept Blackman awake for more than an hour while he did an imaginary dialogue between his wife and himself in which, discussing the evening, he was continually berated.

Then followed a period in which he wrote reviews for The New York Times Book Review, The Commonweal, Commentary, had a small piece in Partisan Review, and moved on to Hudson, The Village Voice, and Exodus.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then the figures which held his attention became a group of shattered trees, standing like the grotesques of a medieval damnation scene.

Then Wilson asked, `` What about this Kent House which you mention??

Then, abandoning the studies in the face of their promising outlook for all concerned, B. & O. entered on-again-off-again negotiations with C. & O. which resulted in the present situation.

Then there was the caterer's ad which read: `` are you getting married or having an affair??

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;

Then there is a matchmaker, one Mikeen Flynn, a role for which Eddie Foy was happily selected.

Then there was exercise, boating and hiking, which was not only good for you but also made you more virile: the thought of strenuous activity left him exhausted.

Then, without knowing why, she found herself running from them, fleeing wildly through the trees, dodging her own shadows until she came to a little hollow in the rocky ground with a big stone in the center behind which she knelt and hid, listening to the madness of her heart and wanting for once to cry.

Schweitzer notes that St. Paul apparently believed in the immediacy of the " Second Coming of Jesus ": " Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord " ( 1 Thessalonians 4. 17 ).

Then nodules of blue earth have to be removed and an opaque crust must be cleaned off, which can be done in revolving barrels containing sand and water.

After this, the senior priest ( or bishop ) pours pure olive oil and a small amount of wine into the shrine lamp, and says the " Prayer of the Oil ", which calls upon God to "... sanctify this Oil, that it may be effectual for those who shall be anointed therewith, unto healing, and unto relief from every passion, every malady of the flesh and of the spirit, and every ill ..." Then follow seven series of epistles, gospels, long prayers, Ektenias ( litanies ) and anointings.

Then he removed to Sura, on the Euphrates, where he established a school of his own, which soon became the intellectual center of the Babylonian Jews.

Then comes her one solo, " Liaisons ", in which her character thinks back on the art of love as a profession in a gilded age, when sex ' was but a pleasurable means to a measurable end.

Then he proves the antithesis, that time has no beginning, by showing that if time had a beginning, then there must have been " empty time " out of which time arose.

In " A Village Sketch ," author Miss Mitford wrote: " Then comes a sun-burnt gipsy of six, beginning to grow tall and thin and to find the cares of the world gathering about her ; with a pitcher in one hand, a mop in the other, an old straw bonnet of ambiguous shape, half hiding her tangled hair ; a tattered stuff petticoat once green, hanging below an equally tattered cotton frock, once purple ; her longing eyes fixed on a game of baseball at the corner of the green till she reaches the cottage door, flings down the mop and pitcher and darts off to her companions quite regardless of the storm of scolding with which the mother follows her runaway steps.

Then the Greek army counter-attacked and defeated the Bulgarians at Kilkis-Lahanas ( Kukush ), after which the mostly Bulgarian town was destroyed and its population expelled.

Then there are directives which bind members to certain goals which they must achieve, but they do this through their own laws and hence have room to manoeuvre in deciding upon them.