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Mr Malthus, and those who agree with him, have generally referred to the United States, as a country in which the human race increases in a geometrical ratio, and have fixed on thirty-five years as the term in which the population of that country doubles itself.
The child then takes a wooden geometrical form and places it, as quickly as possible, on the corresponding cards which he has recognized at a glance among all the rest.
Whether the admissibility of these postulates rests on intuition, or on proof, may be a matter of dispute; but in either case they are the premisses on which the theorems depend; and while these are retained it would make no difference in the certainty of geometrical truths, though every definition in Euclid, and every technical term therein defined, were laid aside.
But at that moment my attention was drawn to an unexpected sight. At a distance of five hundred paces, at the turn of a high promontory, appeared a high, tufted, dense forest. It was composed of trees of moderate height, formed like umbrellas, with exact geometrical outlines.
The front of each contains three large windows; the highest, Perpendicular in style, containing three lights; the middle, curvilinear Decorated, containing four; and the lowest, the west windows of the aisle, being geometrical Decorated, and containing three lights. The middle windows to the north and south are of very curious half geometrical, half curvilinear tracery.
But for a few square abaci which are used, and for the appearance of early tracery in the side windows, it might pass as a purely Lancet building. The choir is fully developed geometrical work, of excellent character, with a beautifully designed triforium and clerestory. Altogether we think Dol may make good its claim to a high place among churches of the second order.
The carved pulpit, from a mosque in Cairo, which is in the South Kensington Museum, was made for Sultan Kaitbeg, 1468-96. The side panels, of geometrical pattern, though much injured by time and wear, shew signs of ebony inlaid with ivory, and of painting and gilding; they are good specimens of the kind of work.
For all his boorish ways, he was an excellent man at heart. I owe him for a piece of advice which greatly influenced my future studies. That day, he suddenly appeared, alone, in the schoolroom, where I was taking a class in geometrical drawing.
A few rise somewhat above the ordinary level, having handles of some elegance, and being painted with designs and patterns, generally of a geometrical character. A vase about six inches high, found at Jerusalem, has, between horizontal bands, a series of geometric patterns, squares, octagons, lozenges, triangles, pleasingly arranged, and painted in brown upon a ground which is of a dull grey.
From the darkened surface of the Earth, at the time when the Earth approached Mars most nearly, would blaze out to the Martians the four great geometrical figures. The test was made at last. All that had been hoped for in the way of an effort was attained. All along the lines of those great figures, night in the Argentine Republic was turned into glorious day.
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