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"When, therefore," says the Archbishop, "matter, motion and free-will are constituted, the Deity must necessarily permit corruption of things and the abuse of liberty, or something worse, for these cannot be separated without a contradiction, and God is no more important, because he cannot separate equality of radii from a circle." Chap. v. s. 5, subs. 7.
The thorough investigations of Gegenbaur have shown that the fish's fins, of which very erroneous opinions were formerly held, are many-toed feet. The various cartilaginous or bony radii that are found in large numbers in each fin correspond to the fingers or toes of the higher Vertebrates. The several joints of each fin-radius correspond to the various parts of the toe.
To this polygonal line, a work destined to disappear as the real toils are woven, I will give the name of the 'auxiliary spiral. Its object is to supply cross-bars, supporting rungs, especially in the outer zone, where the radii are too distant from one another to afford a suitable groundwork.
Two globes in contact will have a distance between their centres which is equal to the sum of their radii. Take the earth as having a radius of four thousand miles, and the moon a radius of one thousand miles, the two centres must at their shortest distance be five thousand miles apart, that is, the moon must then be at the forty-eighth part of its present distance from the earth.
How vigilant we are! determined not to live by faith if we can avoid it; all the day long on the alert, at night we unwillingly say our prayers and commit ourselves to uncertainties. So thoroughly and sincerely are we compelled to live, reverencing our life, and denying the possibility of change. This is the only way, we say; but there are as many ways as there can be drawn radii from one centre.
As an old, quaint divine said of fate and free-will, they are two converging lines which of necessity must somewhere unite, though our human vision does not see the point; so all mysteries are radii, and could we follow one implicitly, then we have found the centre of all.
Afterward, when I want to compare the radii of a semi-circle, Émile will laugh at me and tell me that the same cord, held with the same tension, cannot describe unequal distances. When I want to measure an angle of sixty degrees, I will describe from the apex of the angle not an arc only, but an entire circle; for with children nothing must be taken for granted.
His wife attempted to be a centre, too, but never in the middle of the circle, for that was exclusively occupied by him, and therefore the radii fell now on the top of one another, now far apart, and their life lacked harmony. In the tenth year of their marriage he obtained the post of secretary to the Board of Prisons, and in that capacity he was obliged to travel about the country.
These first loops, like the radii, are of white, dry, and inelastic silk, and may be recognized by the little notches at their junction with the radii.
Lucien, who was altogether a man of peace principles, and but little of a shot compared with either of his brothers, handled the oar not to propel the canoe, but merely to guide it. In this way the party floated on in silence. Norman soon kindled his torch, which now cast its red glare over the surface of the river, extending its fiery radii even to the banks on both sides of the stream.
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