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A suction so powerful, felt along radii so vast, and a consciousness, at the same time, that upon other radii still more vast, both by land and by sea, the same suction is operating, night and day, summer and winter, and hurrying forever into one centre the infinite means needed for her infinite purposes, and the endless tributes to the skill or to the luxury of her endless population, crowds the imagination with a pomp to which there is nothing corresponding upon this planet, either amongst the things that have been or the things that are.
It is self-evident that the hypocycloid must return into itself at the point of beginning, without crossing: each branch, then, must subtend an aliquot part of the circumference, and can be traced also by another and a smaller describing circle, whose diameter therefore must be an aliquot part of the diameter of the outer pitch-circle; and since this last must be equal to the sum of the diameters of the two describing circles, it follows that the radii of the pitch circles must be to each other in the ratio of two successive integers; and this is also the ratio of the number of pins to that of the epicycloidal branches.
Referring to the diagram, let the inner circle represent the earth's surface, the outer circle the limits of the atmosphere, C being the earth's centre, and RR radii of the earth.
The correctness of those generalizations, as generalizations, is without a flaw: the equality of all the radii of a circle is true of all circles, so far as it is true of any one: but it is not exactly true of any circle; it is only nearly true; so nearly that no error of any importance in practice will be incurred by feigning it to be exactly true.
The body is immediately wrapped up in the skin or clothing worn during life, and in the course of a day or two, it is placed upon the wirkatti or bier, which is made of branches crossed so as to form the radii of a circle, an examination is then entered upon as to the cause of death, in the following manner.
But between the gable and circle, in all the three figures, there are an infinite number of pointed arches, describable with different radii; and the three round arches, be it remembered, are themselves representatives of an infinite number, passing from the flattest conceivable curve, through the semicircle and horseshoe, up to the full circle.
No; in this more, perhaps, than in anything else is Mr. Coleridge's discourse distinguished: that it springs from an inner centre, and illustrates by light from the soul. His thoughts are, if we may so say, as the radii of a circle, the centre of which may be in the petals of a rose, and the circumference as wide as the boundary of things visible and invisible.
The direction lines bisected the outer concentric circles like the radii of an orb spider's web. In the center of the web was the smallest circle. Within the circle was the focal point of all flying object observations. Rick said the name aloud. "Swamp Creek!" Calvert's Favor
By this characteristic we recognize the 'logarithmic spiral. Geometricians give this name to the curve which intersects obliquely, at angles of unvarying value, all the straight lines or 'radii vectores' radiating from a centre called the 'Pole. The Epeira's construction, therefore, is a series of chords joining the intersections of a logarithmic spiral with a series of radii.
It is assumed that there is such a thing as a circle, and that all its radii are equal; such things as ellipses, and that the sums of the focal distances are equal for every point in an ellipse; such things as parallel lines, and that those lines are everywhere equally distant.
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