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It is important to remember that all of the angles made by the four axes are right angles a thing possible only in a space of four dimensions. Because the 16-hedroid is a symmetrical hyper-solid all of its eight apexes will be equidistant from the centre of a containing hyper-sphere, whose "surface" these will intersect at symmetrically disposed points.
"Big stuff," replied Bunker, "but I want you to listen to me they's no use running off at the head." "Who's running off at the head? Go on and shoot your wad. Is it something about my mine?" "Yes and mine," answered Bunker. "I don't know whether you know it, but your property apexes the Lost Burro. And another thing, silver has gone up. But Pinal is just as dead as it was a year ago.
There was no discordant note, not one harsh contrast; even the hay-ricks seemed to have been modelled rather than pitched into shape; their sloping sides and finely pointed apexes giving them the dignity of structural intent. Why should not a peasant, in blouse and sabots, with a grinning idiot face, have put the picture out? But he did not.
Sanatoria, memoranda, gymnasia are now replacing sanatorium, memorandums, and gymnasiums; automata, formulae, and lacunae are taking the place of automatons, formulas, and lacunas; indices and apices of indexes and apexes, miasmata of miasmas or miasms; and even forms like lexica, rhododendra, and chimeræ have been recently noted in the writings of authors of repute.
He arrived at a goal for the sun's way shifted eastward to the constellation Cygnus a result congruous with the marked tendency of recently determined apexes to collect in or near Lyra; and the most probable corresponding velocity seemed to be about nineteen miles a second, or just that of the earth in its orbit.
These apexes are established in our representation by describing a circle the plane projection of the hyper-sphere about the central point of intersection of the axes. From each apex it is now necessary to draw straight lines to every other, each line representing one edge of the sixteen tetrahedral cells.
Must they not be sacrificed to those powers of the present who, day after day, call out to them from the never-ending columns of the press 'We are culture! We are education! We are at the zenith! We are the apexes of the pyramids!
Then he went before a judge that was as crooked as he was and the rest you can see for yourself." He thrust his thumb scornfully through a hole in his shirt and waved a hand in the direction of the office. "No, he cleaned me out, using a friend of mine; and now I'm down to nothing. What do you think of a law that will take away a man's mine because it apexes on another man's claim?
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