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Updated: May 20, 2025
During the last eighteen hours, a mournful change had taken place in her heart, where womanly tenderness was rapidly retreating before unwomanly hate, bitterness, and blasphemous defiance; and she laughed scornfully at the "idiocy" that led her to weary heaven with prayers for the preservation of a life that must ever run as an asymptote to her own.
"The eccentricity is less than unity!" screamed M'Nicholl. "Talking of eccentricity " put in Ardan. "Therefore it's a parabola, and must be!" cried Barbican, triumphantly. "Therefore it's hyperbola and nothing shorter!" was the Captain's quite as confident reply. "For gracious sake! " resumed Ardan. "Then produce your asymptote!" exclaimed Barbican, with an angry sneer.
Attempts have been made to attain the desired aim by artificial constitutions and systematic codes of law; but they are not in complete touch with the facts they remain an asymptote, for the simple reason that hard and fast conceptions never embrace all possible cases, and cannot be made to meet individual instances.
The divine perfection is the asymptote of human life to which it is always striving, and always approaching, though it can only be reached in infinity. The Christian religion seems to exclude the possibility life only when men mistake the pointing to an ideal as the laying down of a rule. It is only then that the principles presented in Christ's teaching appear to be destructive of life.
For Fabre was born a poet, and mathematics borders upon poetry; he saw in algebra "the most magnificent flights," and the figures of analytical geometry unrolled themselves in his imagination "in superb strophes"; the Ellipse, "the trajectory of the planets, with its two related foci, sending from one to the other a constant sum of vector radii"; the Hyperbole, "with repulsive foci, the desperate curve which plunges into space in infinite tentacles, approaching closer and closer to a straight line, the asymptote, without ever finally attaining it"; the Parabola, "which seeks fruitlessly in the infinite for its second, lost centre: it is the trajectory of the bomb: it is the path of certain comets which come one day to visit our sun, then flee into the depths whence they never return."
Martin, to whose earthly course death stood rather as the asymptote than as the end. She was perceptibly smaller in form than when he had left her, and she could see less distinctly. A rather affecting greeting followed, in which his grandmother murmured the words of Israel: "Now let me die, since I have seen thy face, because thou art yet alive."
All that is left of the universe henceforward is a whirl of atoms in which nothing counts but certain fixed quantities translated by our systems of equations; the rest has vanished "in algebraical smoke." There is therefore nothing more or less in the effect than in the group of causes; and the causal relation moves towards identity as towards its asymptote.
Beginning at A', the instantaneous axis moves downward and to the right, as the crank travels from A in the direction of the arrow, until it becomes vertical, when the axis will be found upon C'R, at an infinite distance below AB', the locus for this quarter of the revolution being a curve A'G, to which C'R is an asymptote.
If the text implied that, the abatement would, as regards its duration, go on to infinity; and yet that abatement would, as regards its extent, have a non plus ultra. Even so there are asymptote figures in geometry where an infinite length makes only a finite progress in breadth.
To-day is but the asymptote of to-morrow, that curve perpetually drawing near, but never reaching the straight line flying into infinity. To-morrow, the great future, belongs to the heaven where it tends. Were it otherwise, seeing the indestructible elements, and the two great central forces forever at their work, we might fancy ourselves, in one form or another, continual here on the round world.
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