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Updated: May 20, 2025
Which of the two rectangles is, according to this dictum, more beautiful, that in which the sides are in simple ratio, or that in which the angles made with the sides by a diagonal are in such ratio? that, for instance, in which the shorter side is three-fifths of the longer, or that in which the shorter side is five hundred and seventy-seven thousandths of the longer?
Also the apparent derivation of mathematical magnitudes from each other does not prove their aprioristic origin, but only their rational interconnection. Before one attained the concept that the form of a cylinder was derived from the revolution of a rectangle round one of its sides, he must have examined a number of rectangles and cylinders even if of imperfect form.
A line drawn through these points made a figure quite irregular in form, which was, however, composed of rectangles. "Which proves," he told himself, "that our friend, the lawless radio fan, drives an auto and not an airplane. An auto follows roads, which for the most part in this section form squares. He passed along two or three sides of these squares and this makes up the figure.
Then he turned back, with a sickening feeling, to the elements of art, distasteful as he found them. It was hard to pore over rectangles and curves, bones and muscles, angles and measurements, after sporting with irregular forms and fascinating colors. He tried portraiture, but he had no feeling for the business. He could not transfigure the dull and commonplace heads he was to copy.
Attached to or quite near to five of the seven are large circular inclosures, each formed by a similar though lower embankment of earth and inclosing a space somewhat larger than the squares. The respective heights of the embankments, forming four of the rectangles, are given at four, six, ten, and twelve feet; and of three of the circular embankments, at five and six feet, respectively.
"And now, Walter, for the better understanding of what follows and and " he hesitated. "Should you decide later to return with me or, if I am taken, to to follow us listen carefully to my description of this place: Nan-Tauach is literally three rectangles. The first rectangle is the sea-wall, built up of monoliths hewn and squared, twenty feet wide at the top.
When you come to consider it, the traditionary method of erecting the buildings in the center of a rectangular ten acres compels him to plow around the center in broken rectangles." Gulhuss nodded enthusiastically. "Sure. And there's always the roadway from the center out to the county road or right of way. That breaks the efficiency of his plowing.
One must be very far gone if some note of it does not for a moment bring back the tenderest recollections of the days of joyous innocence. Even the city, with its mass of stone and brick, rectangles, straight lines, dust, noise, and fever of activity, is penetrated by this divine suggestion of the renewal of life.
"Monsieur le Préfet," said Weber, producing the third sheet, "would you mind looking at these lines drawn in pencil and enclosed in a large square containing some other smaller squares and rectangles of all sizes? Wouldn't you say that it was the plan of a house?" "Yes, I should." "It is the plan of the house in which we are," declared Weber solemnly.
The turbid water which seemed to meet the horizon edge before us flowed at right angles in sluggish rivers through the streets. Nature had revenged herself on the local taste by disarraying the regular rectangles by huddling houses on street corners, where they presented abrupt gables to the current, or by capsizing them in compact ruin.
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