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 under such a rotation, a random phase,, will be created between the eigenstates, of.

Then, as long as x is not the root of the tree and has a larger priority number than its parent z, perform a tree rotation that reverses the parent-child relation between x and z.

Then two elements of X belong to the same orbit precisely when one is simply a rotation of the other.

Then a rotation can be represented as a matrix,

Then it is well known that it possesses a unique, up-to-scale left-( or right -) rotation invariant ring ( borel regular in the case of second countable ) measure ( left and right probability measure in the case of compact ), the Haar measure.

Then the angle of the rotation is the angle between and.

Then ω should be replaced with the rotation of the axes instead of the rotation of the body.

Then for a counterclockwise rotation through angle Ωt:

Then the matrix A is similar to e < sup > iω </ sup > A, consequently the spectrum of A is invariant under multiplication by e < sup > iω </ sup > ( corresponding to the rotation of the complex plane by the angle ω ).

Then he signed a minor league contract with the Milwaukee Brewers before being called up for the 2004 season, where he earned his way onto the starting rotation.

Then the triangle ABP is a 60 ° rotation of the triangle AFQ about A so these two triangles are congruent and it follows that d ( P )

Then CQD is a 60 ° rotation of CPB about C so d ( P )

Then Barton touched Carl Dill's arm and moved off, up the river bank.

Then a monk appeared saying that the jaundice could be cured by making a medicine out of the arm and eye of one without anger.

Then the woman turns under the man's left arm on 5 & 6.

Then, trying to lay hand on sword, he could draw it out but halfway, because he had been wounded in the arm with a bamboo spear.

Then the take-up arm pulls the excess upper thread ( from the bobbin area ) back to the top, forming the lockstitch.

Then he would, as Heldman explains, " literally jump and throw his racket at the ball with all the force he could muster, wrist and arm snapping over at the hit.

Then, having explained how he wished to see peace between the families, the Earl thrust his hand and arm through the hole to shake hands with Black James.

Then the lead slips the cuddle arm out and the flyer falls again as far as the grip allows.

Then this player performs the last two moves of Opening A: taking the string which runs on the inside of the left arm onto the first finger of their right hand, then, reaching through the triangle created, the loop on the inside of the right hand is taken onto the first finger of the left hand ).

Then, having disposed of his opponent, the murderer rides into the night, a suit – case under one arm and his victim's head under the other.

Then, despite a leg injury, he tucked the ball under his arm and dove into the end zone for the winning touchdown.

Then in 1947 he moved to Madison, Wisconsin for five years, where he contracted polio at age 12 in 1949 in his back, left arm, and hand but was able to recover.

Then I saw him getting injured in his arm, the father.

Then, when the used arm when becoming tired, the swimmer turns on the other side, and the left arm works while the right arm rests.

Then Duke Benes commanded that every man should arm himself.

Then, he was stuck from behind again, amputating his other arm.

Then, he wraps his arm around the opponent's back-neck, and then from the point he catches the opponent's neck, he forces the opponent down in a Russian legsweep style and simultaneously extends a knee.

Then, in 1993, Naspers created a subsidiary company, Multichoice, which was to handle the business arm of M-Net, such as decoder sales, subscriber services and account management.

Then Hanna arrives and, when she accepts the arm of Camille, Danilo wants to hit Camille with his gloves and challenge Camille to a duel.

Then the player must locate the Security Cube itself and drop / arm the detonator.

Then grabbed by his elders the boy was placed on a bed of gum leaves and one of the senior men would make cuts on his own arm allowing the blood to cover the whole body.