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Updated: May 18, 2025
Its pole will become displaced while still keeping on one straight line. The endless scroll leads to rectilinear progression; the perpetually varied begets uniformity. Now is this logarithmic spiral, with its curious properties, merely a conception of the geometers, combining number and extent, at will, so as to imagine a tenebrous abyss wherein to practise their analytical methods afterwards?
He succumbed, but he met his fate bravely and with the colors of his wit flying. The circumstances are these: There is a certain railway thoroughfare which justly prides itself upon the beauty of its scenery. This road passes through a hill-country, and what it gains in the picturesque it loses in that rectilinear directness most grateful to the traveler with a sensitive stomach.
Assuming that our forecasts of rectilinear motion are correct, these rects occupy the straight lines in timeless space which are traversed. Thus the rects are symbols in immediate sense-awareness of a future which can only be expressed in terms of timeless space. We are now in a position to explore the fundamental character of perpendicularity.
In the rectilinear beds the stocks glinted like bright, wavy silk, and the scent of the box-hedges was warm and bitter. A servant stationed himself on the steps of the garden porch and rang a large bell as signal that it was time to dress for dinner. The host, old Count Hamilcar of Wandl-Dux, was already completely dressed and came out into the garden with his guest, Professor von Pinitz.
But a fresh field is opened if for the one-direction suspension of pendulum B we substitute a gimbal, or universal joint, permitting movement in all directions, so that the pendulum is able to describe a more or less circular path. The figures obtained by this simple modification are the results of compounded rectilinear and circular movements.
The polished surfaces stretch continuously over hundreds and hundreds of miles; the rectilinear scratches, grooves, and furrows are unbroken for great distances; the drift spreads in one vast sheet over the whole land, consisting of an indiscriminate medley of clays, sands, gravels, pebbles, boulders of all dimensions, and so uniformly mixed together that it presents hardly any difference in its composition, whether we examine it in New England, New York, Pennsylvania, Ohio, Michigan, Indiana, Illinois, Wisconsin, in Iowa beyond the Mississippi, in the more northern Territories, or in Canada.
Drafted in accordance with the "Contrat-Social," filled with Greek and Latin reminiscences, it is a summary "in pithy style" of the manual of current aphorisms then in vogue, Rousseau's mathematical formulas and prescriptions, "the axioms of truth and the consequences flowing from these axioms," in short, a rectilinear constitution which any school-boy may spout on leaving college.
The direction of this second part of the motion must be referred entirely to necessity, which directly interferes with the purpose of him who designed the rectilinear direction. We are not, in this case, to go back to find design in the creation of the powers or laws of inertia and elasticity, after the order of which the deflection, at the instant of collision, necessarily takes place.
Fit resting-place for what remains to earth of such a poet's clay! It is as though archangels, flying, had carried the marble chest and set it down here on the hillside, to be a sign and sanctuary for after-men. A simple rectilinear coffin, of smooth Verona mandorlato, raised on four thick columns, and closed by a heavy cippus-cover.
From whence we may conclude, without subjecting ourselves to the reproach of being hasty, that error will not stand the test of investigation; that it will not pass the ordeal of comparison; that it is in its hues a perfect chamelion; that consequently it can never do more than lead to the most absurd deductions: that the most ingenious systems, when they have their foundations in hallucination, crumble like dust under the rude band of the assayer; that the most sublimated doctrines, when they lack the substantive quality of rectitude, evaporate under the scrutiny of the sturdy examiner, who tries them in the crucible; that it is not by levelling abusive language against those who investigate sophisticated theories, they will either be purged of their absurdities, acquire solidity, or find an establishment to give them perpetuity; that moral obliquities, can never be made rectilinear by the mere application of unintelligible terms, or by the inconsiderate jumble of discrepant properties, however gaudy the assemblage: in short, that the only criterion of truth is, that it is ever consistent with itself.
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