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It was then that the chiens de faience, which the smug Paris suburbanite of to-day so loves, were born. By the seventeenth century the equalized carreaux of the early geometrically disposed gardens were often replaced with the oblongs, circles and, somewhat timidly introduced, more bizarre forms, the idea being to give variety to the ensemble.
The other arm of the lever describes also a triangle; and the corresponding sides of those two triangles, calculated scientifically, or measured geometrically, and also the sines, tangents, and secants generated from the angles, and geometrically measured, have the same proportions to each other as the different weights have that will balance each other on the lever, leaving the weight of the lever out of the case.
The rectangle formed by the length and breadth of this figure, in the simplest form, has several extraordinary properties; it may be cut into three equal parts by straight lines parallel to the shorter side, and these parts will all be precisely and geometrically similar to each other and to the whole figure, strangely applicable to the symbolism attached at that time to the Trinity in Unity, and the subdivision may be proceeded with indefinitely without making any change in form.
The great mass of sheep in the fair consisted of South Downs and the old Wessex horned breeds, to the latter class Bathsheba's and Farmer Boldwood's mainly belonged. These filed in about nine o'clock, their vermiculated horns lopping gracefully on each side of their cheeks in geometrically perfect spirals, a small pink and white ear nestling under each horn.
Later she refused to go out with them. She stayed in her room a good deal, fussing about, arranging bureau drawers already geometrically precise, winding endless old ribbons, ripping the trimming off hats long passé and re-trimming them with odds and ends and scraps of feathers and flowers.
Geometrically speaking, the shortest distance between two points is a straight line. Teachers should make every possible effort to find the straight line of technic which will carry the pupil from his first steps to technical proficiency without wandering about through endless lanes and avenues which lead to no particular end.
It is limited by geography; by the means of transportation and communication; by overhead costs that increase geometrically as the civilization expands arithmetically; by the means of delegating responsibility; by accounting devices, available raw materials and labor power; by power struggles inside the ruling oligarchies; by the failure to maintain a balance between centerism and localism; by growing local demands for self-determination; by the invasion of nomads seeking to plunder the tempting honey pot at the nucleus of the civilization.
"One of our errors," said he, "is that of judging things by abstract calculations, which though geometrically true, are practically false."
Patchwork infers a rather more mosaic-like design than inlaid work, to which it is in some respects similar. The geometrically planned mosaic and inlay pavements that are to be seen so commonly in Italy and the East suggest great variety of patterns that could be applied to patchwork. The illustration at fig. 97 is a simple example taken from this source.
Here I have placed the wonderful old fireplace which I bought for you in France, and above it the Reynolds for which you paid forty thousand dollars; here in the centre is the carved table which I got for you in Florence, and geometrically arranged about its corners are books of travel; with its back to it, a great divan covered with most expensive leather, so that you can lounge in its depths and watch the fire.
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