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, with staring eyes and lips drawn thin, Miriam said to the young woman, `` You are ugly -- uglier than you used to be, and you were always very ugly.

Then people wonder why Russian pupils are more advanced than American students.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

Then, of course, there are those of us who either do not want or need or cannot afford another car.

Then, too, European drivers have reputations for being somewhat crazy on the road and some Americans are not particularly keen on getting mixed up with them.

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

Then there are the trustees and officers of the great educational foundations, who inevitably exert an influence on educational decisions by their support or refusal to support various educational programs, experiments, and demonstrations.

Then, too, misplaced or jammed-together teeth are prone to trapping food particles, increasing the likelihood of rapid decay.

Then there are a pair of old biddies played by Grace Carney and Sibly Bowan who may be right off the shelf of stock Irish characters, but they put such a combination of good will and malevolence into their parts that they're quite entertaining.

Then, after many more billions of years, when all the galaxies are whistling toward a common center, this movement will slow down and reverse itself again.

Then we have informed a large number of our crew that when they reach the United States, they will be punished but that in the meanwhile, they may run loose and are expected to perform their jobs in good order.

Then Frankie said: `` What are you gonna do ''??

In a few of her novels, including Death Comes as the End and And Then There Were None, there are multiple victims.

Seven stories are inspired by a nursery rhyme: And Then There Were None by Ten Little Indians ; One, Two, Buckle My Shoe by One, Two, Buckle My Shoe ; Five Little Pigs by This Little Piggy ; Crooked House by There Was a Crooked Man ; A Pocket Full of Rye by Sing a Song of Sixpence ; Hickory Dickory Dock by Hickory Dickory Dock, and Three Blind Mice by Three Blind Mice.

) There are also numerous instances where the killer is not brought to justice in the legal sense but instead dies ( death usually being presented as a more ' sympathetic ' outcome ), for example Death Comes as the End, And Then There Were None, Death on the Nile, Dumb Witness, The Murder of Roger Ackroyd, Crooked House, Appointment with Death, The Hollow, Nemesis, Cat Among the Pigeons, and The Secret Adversary.

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 looking at him darkly Zeus who gathers the clouds spoke to him :' Do not sit beside me and whine, you double-faced liar. To me you are the most hateful of all gods who hold Olympos. Forever quarrelling is dear to your heart, wars and battles .… And yet I will not long endure to see you in pain, sinceyou are my child, and it was to me that your mother bore you. But were you born of some other god and proved so ruinouslong since you would have been dropped beneath the gods of the bright sky.

Then we are told that P1 is not sped up, so S1 = 1, while P2 is sped up 5 ×, P3 is sped up 20 ×, and P4 is sped up 1. 6 ×.

Then he came, in his words, to " the theory of symmetry: all governments and regimes to a first approximation are bad, all peoples are oppressed, and all are threatened by common dangers.

Then the results obtained are compared with the expected results.

Then the beads are pressed in between the warp threads.

Then the runes are shaved off and the shavings are mixed with mead and sent abroad so that Æsir have some, Elves have some, Vanir have some, and Men have some, these being beech runes and birth runes, ale runes, and magic runes.