Quadrangle

“ Built on North Street in the quadrangular form so reminiscent of an Oxford or Cambridge college, the rich plum-colour which age has lent to the brick needs only the primly demure assistance of the formal flower beds to make the altogether charming enclosure which we see to-day. Entering this tranquil and ancient quadrangle one seems suddenly whisked by some [Pg 237] magic wand far from the twentieth century world outside. ”

“ Let the square be represented by a quadrangle, the sides of which are unknown to us, though they are equal among themselves, as also the angles. This is the quadrate A D, which comprises the three roots and the four of numbers mentioned in this instance. In every quadrate one of its sides, multiplied by a unit, is its root. We now cut off the quadrangle H D from the quadrate A D, and take one of its sides H C for three, which is the number of the roots. ”

“ Every quadrangle of equal sides and angles, which has one yard for every side, has also one for its area. Has such a quadrangle two yards for its side, then the area of the quadrangle is four times the area of a quadrangle, the side of which is one yard. The same takes place with three by three, and so on, ascending or descending: for instance, a half by a half, which gives a quarter, or other fractions, always following the same rule. A quadrate, every side of which is half a yard, is (51) equal to one-fourth of the figure which has one yard for its side. ”

“ An outer surrounds an inner quadrangle of buildings. The inner quadrangle, about a court which is 586 by 246 ft. and is faced by a continuous open arcade and adorned with large circular beds of tropical plants and flowers, consists of twelve one-storey buildings and a beautiful memorial church. ”

“ Study a good map—a quadrangle of the U. S. Geological Survey, for instance. Note what things are represented, and how representation is made: study the map, until it is thoroughly understood.
There are three factors with which the map-maker deals: direction, distance, and elevation. With the first, he must always reckon, and usually with the second and the third as well.
Direction is fundamental. Suppose there are three dominant points in the area to be mapped, relatively situated as here indicated. ”

“ The quarters for the men are built round a large quadrangle, with an upper story, and airy corridors for exercise in wet weather. Beyond are the married quarters for ninety couples, each with two comfortable rooms and a little garden ”

“ Much the same may be said of the dikes of cooled magma which have been injected along preëxisting fractures.
The base of the geological map.—Modern topographic maps form an important part of the library of the serious student of physiography; they are the gazetteer of this branch of science. Every civilized nation has to-day either completed a topographic atlas of its territory, or it is vigorously prosecuting a survey to furnish maps which represent the relief with some detail, and publishing the results in the form of an atlas of quadrangles. ”

“ From the pronaos a small gate admitted into a quadrangle, paved with limestone slabs, and enclosed on three sides by Corinthian colonnades. On the W. side these were divided by partitions into three sections, forming ante-rooms to the three cellæ. ”

“ In the square and in the irregular works, if there be a fosse at all, it is exterior to the embankment; except in the case of fortified hills, where the earth, for the best of reasons, is usually thrown from the interior. These facts are not without their importance in determining the character and purpose of these remains. Another fact, bearing directly upon the degree of knowledge possessed by the builders, is, that many, if not most, of the circular works are perfect circles, and that many of the rectangular works are accurate squares. ”

“ By a square in a town, one does not necessarily understand an area with four equal sides and as many right angles, but an open space that is left for air and beauty. There are air and beauty enough to satisfy any reasonable man. A square may be a parallelogram, or a triangle, or any other shape one pleases.”
“This, then, is Hanover Square!—a New York square, or a Nassau Hall square, Corny; but not a Yale College square, take my word for it. ”

“ Why, a degree of latitude or longitude is less thought of than a furlong by those at home; and, in some of the backwood settlements, neighbours are as far-away from each other as the capital cities of the continent are separated.”
“That is true,” said Mr Rawlings. “The space appears so illimitable that one’s ideas as to measurement expand in a similar way, and the agriculturists calculate by the square mile instead of the acre in all their estimates of the land. ”

“ It is an oblong square, with a tabular summit from thirty to forty yards long, and from ten to fifteen broad—attained by a broad terraced road of very gradual ascent, which, after encompassing the mound twice or thrice, comes out upon its summit at its northern extremity.
WRYNOSE.
As you creep up the mountain, you may perceive in the deep verdant glen under your left, a number of small cone-shaped tumuli, whether formed by the hand of man or by the operations of nature this deponent sayeth not. ”

“ The plan of the city is very peculiar indeed, but made with the one view of bringing the employés of the system into [286] little communities near the place of their occupation. It resembles a portion of a great checkerboard, eight squares long by six in breadth. Each square is a half-mile in length and breadth, and has an area of one-quarter of a square mile. Four of these squares is called a section, making twelve sections, or twelve square miles in the city. Each section is divided into eight triangles of equal shape and area by diagonals from its corners. ”

“ But this sun-heat, this offset to radiation, has not been received by all parts of the earth equally. The equatorial belt, or torrid zone, has always received the most per square foot, or in proportion to its area. The two intermediate or temperate zones have received the next largest amount per square foot, or in proportion to their area; while the polar or frigid zones have received the least per square foot, or in proportion to their area. ”

“ The anthropo-geography of mountain valleys depends upon the structure of the highlands themselves, whether they are fold mountains, whose ranges wall in longitudinal valleys, or dissected plateaus, whose valleys are mostly transverse river channels leading from the hydrographic center out to the rim of the highlands. Longitudinal valleys are not only long, but also broad as a rule and often show a nearly level floor.1215 They therefore form districts of considerable size, fertility, and individuality, and play distinct historical rôles in the history of their respective highlands. ”

“ For the space of a quarter of a mile, advantage is taken of a slight natural ridge to construct between the walls a broad embankment, something higher than the parallels themselves. It is broad enough to permit fifty persons to walk abreast. A similar peculiarity is observed in the short parallel leading from the square enclosure towards the great circle E, and is exhibited by the section i l. ”

“ If the plane thus dividing the earth be that of its equator, there will be found in the northern hemisphere about 44,000,000 square miles of land, and in the southern, so far as is known, about 16,000,000 square miles. Now, the great problem in physical geography is. What is there in the southern hemisphere to counterbalance this great excess of land in the northern? ”

“ The vertical dimensions—the physical limitation—are defined by the elevation of terraces and highlands, and they exhibit the greatest diversity of phenomena.
The horizontal dimensions supply most of the material for our elementary compends for political geography, which seldom make much account of vertical dimensions, and which, by no means, penetrate to their real value. They are commonly held to be a side-matter, to be touched lightly upon, or wholly cast aside. But both must be thoroughly studied; for they are mutually dependent, and are never found divorced in nature. ”

“ That the present city of London stands upon less than 2,500 acres of ground, wherefore a city seven times as large may stand upon 10,500 acres, which is about equivalent to a circle of four miles and a half in diameter, and less than fifteen miles in circumference. 2. That a circle of ground of thirty-five miles semidiameter will bear corn, garden-stuff, fruits, hay, and timber, for the 4,690,000 inhabitants of the said city and circle, so as nothing of that kind need be brought from above thirty-five miles distance from the said city ”

“ If the cities were each to be imagined as a single point, a square could be drawn around the point so that, at nearest, each side of the square would be one thousand cubits from the city, while each side would be two thousand cubits long. ”

“ The ‘dividing ridge’ of a district is that which, while it is, as it were, the back-bone of the range of which it forms a part, heads at the same time all the transverse ravines, whether on the right or on the left hand, and thereby spares to the traveller an infinity of toilsome ascent and descent.
“I have sometimes observed that an Indian trail wound through a country in a course perfectly serpentine, and appeared to me to travel three miles when only one was necessary. ”

“ As there is scarcely a piece of level ground, even ten yards square, on the whole side of the mountain, the defect has been remedied by cutting spaces one above another at regular distances, and supporting them by low walls, the top of one being on a level with the base of that next above it. An easy flight of steps leads from one level to the other. ”

“ All our communities cover equal surface space, a square fifteen hundred by fifteen hundred terrestrial feet or 2,250,000 square feet. All the communities except those adjoining the center oval are bordered into exact squares by hedges, even though the buildings within may be laid out in different shapes, so as to make the entire plan symmetrical and harmonious. ”

“ The boundary zone in nature.
Nature abhors fixed boundary lines and sudden transitions; all her forces combine against them. Everywhere she keeps her borders melting, wavering, advancing, retreating. If by some cataclysm sharp lines of demarcation are drawn, she straightway begins to blur them by creating intermediate forms, and thus establishes the boundary zone which characterizes the inanimate and animate world. ”

“ From the edge of that hill the land seems very vague; the flat line of the horizon is the only boundary, and that horizon mixes into watery clouds. No countryside is so formless until one has seen the plan of it set down in a map, but on studying such a map one understands the scheme of the Fens. ”

“ This range is remarkable for the uniformity of outline which characterizes the different peaks, particularly of their summits, the ridges extending in the same general direction, sometimes hardly diverging from a straight line for a distance of fifty or sixty miles. Where the mountain chains are parallel, the ridges are also in parallel lines, preserving their general direction, and, to a wonderful extent, a uniformity of distance between them. When one curves round in a new direction, all curve with it. ”

“ At the foot of this elevation they mark out a square place, according to the size of the village, around which the leading men have their houses. To ascend the elevation they have a straight passage-way from bottom to top, fifteen or twenty feet wide. Here steps are made by massive beams, and others are planted firmly in the ground to serve as walls. ”

“ As the horizontal contours of any portion of the earth's surface must depend on the vertical, or, in other words, the various features which are marked on the map—the coast line, plains, rivers, vallies, lakes, hills, mountains, &c., being consequent on the different elevations of the various portions of the surface above the level of the sea ”

“ Subtract the square of the sine of the given declination from the square of the radius. The square root of the remainder will be the radius of the day-circle north or south of the Equator.
The day-circle is the diurnal circle of revolution described by a planet at any given declination from the Equator. So these day-circles are small circles parallel to the Equator. [56]
25. ”

“ Now, although I have done my utmost to draw up tables which might even convey an approximate result, I have found the number of inhabitants to a square mile to vary so much, from district to district, from season to season—and to depend upon so great a variety of local circumstances—that I am unable to give any computation which I believe would even nearly approach the truth ”

“ The streets of the city, crossing each other at right angles, are 132 feet wide; the blocks, forty rods square, and containing ten acres each, are divided into eight lots, each containing one and onefourth acres. ”

“ The simple rectangle is disguised under the fret, the circle and spiral assert their sway over the boundaries of the palmette, or circle and semicircle unite to form the oval so frequently used both as a unit in Greek ornament and as a controlling boundary. These are typical border forms: for extension and repetition in fields of pattern we find the same geometric plans at work in combination and subdivision, forming at first the ornament itself, and afterwards furnishing the plan and controlling boundaries only. ”

“ Turning to a more detailed consideration of plats, variations in the width of streets and sizes of blocks involves the proportion of public land used for communication, and of private land used for buildings. In rectangular plats streets usually range in width from forty to eighty feet, sixty feet being a fair average in the newer cities, though every city shows wide variations. There is a common impression that additional width in the street always adds to its value, since the. wider the street the greater the volume of traffic which can be accommodated. ”