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.

I said quietly, gaining nerve, ready to ask any question at all, no matter how intimate, ready to be rebuffed, `` Then why did she leave Israel??

Then, one must locate any relevant statutes and cases.

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 along with Archbishop Wilhelm von Brandenburg of The Archbishopric of Riga and his Coadjutor Christoph von Mecklenburg, Kettler gave to Magnus the portions of The Kingdom of Livonia, which he had taken possession of, but they refused to give him any more land.

Then to define multiplication, it suffices by the distributive law to describe the product of any two such terms, which is given by the rule

Then Fischer and Rabin ( 1974 ) proved that any decision algorithm for Presburger arithmetic has a worst-case runtime of at least, for some constant c > 0.

Then in 726, Leo issued an iconoclast edit, condemning possession of any icon of the saints.

For f a real polynomial in x, and for any a in such an algebra define f ( a ) to be the element of the algebra resulting from the obvious substitution of a into f. Then for any two such polynomials f and g, we have that ( fg ) ( a )

Then the expected number of i type organisms produced by any j type parent is,

Then, in 1964 the new Chrysler 426 Hemi engine so dominated the series in a Plymouth Belvedere " Sport Fury ", the homologation rules were changed so that 1, 000 of any engine and car had to be sold to the public to qualify as a stock part, instead of just 500.

Then, for any non-zero element x of M, the cyclic submodule xR must equal M. Fix such an x.

Then, these philosophers say, it is rational to act on those beliefs that have best withstood criticism, whether or not they meet any specific criterion of truth.

Then for any

Then the formula Cold ( r )→ High ( t ) is true for any t and therefore any t gives a correct control given r. A rigorous logical justification of fuzzy control is given in Hájek's book ( see Chapter 7 ) where fuzzy control is represented as a theory of Hájek's basic logic.

Then in 1991, President George H. W. Bush made an attempt to abolish affirmative action altogether claiming that “ any regulation, rule, enforcement practice or other aspect of these programs that mandates, encourages, or otherwise involves the use of quotas, preferences, set-asides or other devices on the basis of race, sex, religion or national origin are to be terminated as soon as is legally feasible.

Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G.

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

", Yossarian replies, " Then I'd certainly be a damned fool to feel any other way.

Then any vector in R < sup > 3 </ sup > is a linear combination of e < sub > 1 </ sub >, e < sub > 2 </ sub > and e < sub > 3 </ sub >.

Then S is not a base for any topology on R. To show this, suppose it were.

Then is an open cover of S, but any finite subcollection of has the form of C discussed previously, and thus cannot be an open subcover of S. This contradicts the compactness of S. Hence, every accumulation point of S is in S, so S is closed.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Then lay a three-inch-wide strip of cloth along the keel line from the transom to the point of the stem.

Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.

Then f = u + iv is complex-differentiable at that point if and only if the partial derivatives of u and v satisfy the Cauchy – Riemann equations ( 1a ) and ( 1b ) at that point.

Then the complex derivative of ƒ at a point z < sub > 0 </ sub > is defined by

Then each point p of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains p.

Then almost every point of A returns to A infinitely often.

Then in 1834, McCoy established Westport Landing on a bend in the Missouri River to serve as a landing point for West Port.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

Line QP can be extended beyond P to some point T, and line GP can be extended beyond P to some point R. Then and are vertical, so they are equal ( congruent ).

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

Then the sword is slashed downward to a position with the point close to the ground in front of the right foot.

Then the Zariski tangent space at a point p ∈ X is the collection of K-derivations D: O < sub > X, p </ sub >→ K, where K is the ground field and O < sub > X, p </ sub > is the stalk of O < sub > X </ sub > at p.

Then the 2-sphere shrinks again down to a single point as the 3-sphere leaves the hyperplane.

Then, after he realised his hopes of submission at that point were in vain, he began his advance on London.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then two points x and y in X are topologically distinguishable if they do not have exactly the same neighbourhoods ( or equivalently the same open neighbourhoods ); that is, at least one of them has a neighbourhood that is not a neighbourhood of the other ( or equivalently there is an open set that one point belongs to but the other point does not ).

Then he was on his way at a gallop.

Then he went on to the Cheyennes and told them that the Sioux was goin' to move up.

Then he hunkered down on the heels of his handmade boots, peered into the orderly chaos of axle, shock absorber, and spring.

Then, with a glory that almost wiped out the deep, downward sags in her careworn face, Matilda leaned over the wheel and shouted to Hez, who was stumbling along in the heat and the dust on the opposite side of the wagon `` Pa!!

Then, and only then, with the Jacksons and Dan as their true guests of honor, did the Harrows take time to catch up on the news.

Then maybe next time he won't be so quick on the trigger ''.

Then he calmly and carefully slugged the remaining five shots into the venomous head -- caught in the wicker back of the chair, the eyes dead on him as the life finally went out of the brute.

Then there was no saying how many times the marine had blown his nose on the handkerchief.

Then when Miss Langford was on the end of the line of girls, Jack, in the middle of the line, gave an extra hard pull and the young teacher sprawled backwards, sitting down hard, her dress flying over her head.

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

Then she rounded on Weston and cried, `` You always did Wright's dirty work!!

Then Miriam varied the senseless psychological warfare by suddenly withdrawing a suit for separate maintenance that had been pending, and asking for divorce on the grounds of cruelty, with the understanding that Wright would not contest it.

Then he launches into an attack on the Tory ministers, whom he calls the `` New Converts '' ; ;

Then he called on the governor to explain why.

Then I spoke at the ninetieth birthday party of W. E. Burghardt Du Bois, who embarked on a fictional trilogy at eighty-nine and who, with The Crisis, had created a Negro intelligentsia that had never existed in America before him.

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.

Then let the whole lot be hanged in a public mass execution on July 4, 1963.

Then, to conclude on an indeterminate note: `` Nevertheless, if fallout increased substantially, or remained high for a long time, it would become far more important as a potential health hazard in this country and throughout the world ''.

Then he slipped and went down on his hands and knees in the melting snow.

Then the figure moved on.

Then came their bathroom, and then a bedroom that, judging by the photographs on the walls, must belong to Mme Cestre.

Then Rector, attired in his best blue serge suit, sat in a chair out on the lawn, in the shade of a tree, smoking a cigarette and waiting.

Then she went back to the wicker chair and resolutely adjusted her eyes to the glare on the water.

Then he spread out the last list on the counter.

Then he stood back to look at Mr. Jack, who was pulling on his pigskin gloves.