- a formation of people or things one beside another; "the line of soldiers advanced with their bayonets fixed"; "they were arrayed in line of battle"; "the cast stood in line for the curtain call"
- a mark that is long relative to its width; "He drew a line on the chart"
- a length (straight or curved) without breadth or thickness; the trace of a moving point
- text consisting of a row of words written across a page or computer screen; "the letter consisted of three short lines"; "there are six lines in every stanza"
- a single frequency (or very narrow band) of radiation in a spectrum
- a fortified position (especially one marking the most forward position of troops); "they attacked the enemy's line"
- argumentation: a course of reasoning aimed at demonstrating a truth or falsehood; the methodical process of logical reasoning; "I can't follow your line of reasoning"
- cable: a conductor for transmitting electrical or optical signals or electric power
- course: a connected series of events or actions or developments; "the government took a firm course"; "historians can only point out those lines for which evidence is available"
- a spatial location defined by a real or imaginary unidimensional extent
- wrinkle: a slight depression in the smoothness of a surface; "his face has many lines"; "ironing gets rid of most wrinkles"
- pipeline: a pipe used to transport liquids or gases; "a pipeline runs from the wells to the seaport"
- the road consisting of railroad track and roadbed
- telephone line: a telephone connection
- acting in conformity; "in line with"; "he got out of line"; "toe the line"
In the interval between world wars, several European countries built elaborate permanent fortifications. The largest was the French Maginot Line, a system of mammoth, self-contained forts stretching from Switzerland to the vicinity of the Belgian frontier near Montmédy. The reinforced concrete of the forts was thicker than any theretofore used, the disappearing guns bigger and more heavily armoured. Ditches, embedded steel beams, and minefields guarded against tank attack. A large part of the works were completely underground. Outposts were connected to the main forts by concrete tunnels. But, because French and British military leaders were convinced that if war came again with Germany the Allies would fight in Belgium, the French failed to extend the line to the sea, relying instead on an outmoded system of unconnected fortresses left over from before World War I. It was this weakness that the Germans subsequently exploited in executing a modified version of the Schlieffen plan, cutting in behind the permanent defenses and defeating France without having to come to grips with the Maginot Line.
The Germans confronted that portion of the Maginot Line facing the Saar River with fortifications of their own, the West Wall. Later extended northward to the Dutch frontier and southward along the Rhine to Switzerland, the West Wall was not a thin line of big forts but a deep band, up to five miles thick, of more than 3,000 small, mutually supporting pillboxes, observation posts, and troop shelters. For passive antitank defense the line depended upon natural obstacles, such as rivers and lakes, and upon “dragon's teeth,” five rows of pyramid-shaped reinforced concrete projections.
The Germans did not rely on the West Wall to halt an attack but merely to delay it until counterattacks by mobile reserves could eliminate any penetration. The value of their concept remains undetermined; the line was not attacked until late 1944, after the German armies had incurred severe defeats and lacked adequate reserves. The West Wall nevertheless forced Allied troops into costly attacks to eliminate it.
defensive barrier improvised by the German army on the Western Front in World War I. Faced with substantial numerical inferiority and a dwindling firepower advantage, the new German commanders, Field MarshalPaul von Hindenburg and Gen. Erich Ludendorff, shortened their lines and installed concrete pillboxes armed with machine guns as the start of an extended defensive system up to eight miles deep, based on a combination of firepower and counterattacks. The Hindenburg Line resisted all Allied attacks in 1917 and was not breached until late in 1918.
The human eye
The image of the external world on the retina is essentially flat or two-dimensional, and yet it is possible to appreciate its three-dimensional character with remarkable precision; to a great extent this is by virtue of the simultaneous presentation of different aspects of the world to the two eyes, but even when the subject views the world with a single eye it does not appear flat to him and he can, in fact, make reasonable estimates of the relative positions of objects in all three dimensions. Examples of monocular cues are the apparent movements of objects in relation to each other when the head is moved. Objects nearer the observer move in relation to more distant points in the opposite direction to the movement of the head. Perspective, by which is meant the changed appearance of an object when it is viewed from different angles, is another important clue to depth. Thus the projected retinal image of an object in space may be represented as a series of lines on a plane—e.g., a box—these lines, however, are not a unique representation of the box because the same lines could be used to convey the impression of a perfectly flat object with the lines drawn on it, or of a rectangular, but not cubical, box viewed at a different angle. In order that a three-dimensional object be correctly represented to the subject on a two-dimensional surface, he must know what the object is; i.e., it must be familiar to him. Thus a bicycle is a familiar object. If it is viewed at an angle from the observer the wheels seem elliptical and apparently differ in size. Because the observer knows that the wheels are circular and of the same size, he perceives depth in a two-dimensional pattern of lines. The perception of depth in a two-dimensional pattern thus depends greatly on experience—the knowledge of the true shape of things when viewed in a certain way. Other cues are light and shade, overlapping of contours, and relative sizes of familiar objects.
Line and interior
The scale and proportion of any interior must always relate to the architecture within which the interior exists, but the other important factor in considering the scale of man's environment is the human body. Throughout the ages, designers and architects have attempted to establish ideal proportions. The most famous of all axioms about proportion was the golden section, established by the ancient Greeks. According to this axiom, a line should be divided into two unequal parts, of which the first is to the second as the second is to the whole. Leonardo da Vinci developed a figure for the ideal man based on man's navel as the centre of a circle enclosing man with outstretched arms. The French architect Le Corbusier developed a theory of proportion called Modulor, also based on a study of humanproportions. Yet, at best, these rules are merely guidelines. They can never substitute for the eye and judgment of the designer, and it is reasonable to predict that attempts to make the all-powerful computer a substitute for the designer's sensitivity are also bound to be far from perfect.
It was stated earlier that the need for a changing scale and spatial relationship in the environment seems a natural one, almost a physiological as well as a psychological one. Perhaps the need for “personal” environment and scale can best be understood by considering some extreme examples. To a person flying at 30,000 feet in an airplane, the scale of anything seen on the ground appears so small that he loses touch with the reality of objects. People who fear heights are rarely bothered by the view out of an airplane because the distance to the objects on the ground has transcended normal perceptions of scale. In a similar manner, a person's reaction to the scale of a small house is quite different from his reaction to a large high-rise building. Details of pattern, texture, and material are accepted and expected in the small structure since they are in a meaningful scale with respect to man. By the same token, the sculptural ornaments on the tops of early skyscrapers seem absurd today.
Basic element of Euclidean geometry. Euclid defined a line as an interval between two points and claimed it could be extended indefinitely in either direction. Such an extension in both directions is now thought of as a line, while Euclid's original definition is considered a line segment. A ray is part of a line extending indefinitely from a point on the line in only one direction. In acoordinate system on a plane, a line can be represented by the linear equation ax + by + c = 0. This is often written in the slope-intercept form as y = mx + b, in which m is the slope and b is the value where the line crosses the y-axis. Because geometrical objects whose edges are line segments are completely understood, mathematicians frequently try to reduce more complex structures into simpler ones made up of connected line segments.
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line (Casey 1893), to emphasize that it has no "wiggles" anywhere along its length. While lines are intrinsically one-dimensional objects, they may be embedded in higher dimensional spaces.
Harary (1994) called an edge of a graph a "line."
A line is uniquely determined by two points, and the line passing through points 
and 
is denoted 
; AB" style="vertical-align: middle; ">. Similarly, the length of the finite line segment terminating at these points may be denoted 
. A line may also be denoted with a single lower-case letter (Jurgensen et al. 1963, p. 22).
Euclid defined a line as a "breadthless length," and a straight line as a line that "lies evenly with the points on itself" (Kline 1956, Dunham 1990).
Consider first lines in a two-dimensional plane. Two lines lying in the same plane that do not intersect one another are said to be parallel lines. Two lines lying in different planes that do not intersect one another are said to be skew lines.
Definition of the line
FREIGHT AND PIPELINES
Worldwide freight volumes, as reflected by container movements, showed modest rises in 1995, while the busiest activity continued to be in the Pacific Rim. Singapore, which began restructuring for outright privatization, and Hong Kong retained their status as the busiest ports. Both ports were above the level of 10 million TEU (20-ft equivalent units) per annum. Linked to this was growth in China of container crane and container manufacturing. Penang, Malaysia, embarked on a major capital expenditure to cope with an annual growth of 16% over the previous eight years, and Manila developed new intermodal freight services. Intermodalism, which was pioneered in Europe, continued to gather strength. A Pan-European Transport System initiative was promoted by the European Union to facilitate trade and economic development, with a focus on maintaining the balance of road, rail, and waterway traffic in Eastern Europe and avoiding domination by road transport. In the U.S., rapid growth in intermodal trade had put a great strain on service reliability. This led to plans for the development of new "mega terminals" in six U.S. West Coast ports and might prompt a decline in medium-sized container ports.
Pipeline construction was down by 5% in 1995. Decline in the U.S. was linked to the cost of meeting environmental, safety, and regulatory mandates, while Russian recession and political upheaval reduced activity. Nonetheless, in Europe and especially the Far East, new long-distance natural gas networks spurred ambitious new programs. In the U.S. natural gas schemes prevailed. Of significance were expansions in California, with 1,489 km (1 km=0.62 mi) of pipeline laid, and a 604-km line from Malin, Ore., to Reno, Nev. In Europe the focus of gas-line construction was in the North Sea and Spain. Plans were made to lay dual 122-cm (48-in) pipes across the Baydarata Bay as part of the development of the Yamal Peninsula in Siberia. Oman planned a 1,135-km crossing of the Arabian Sea, while Australia went ahead with a 1,400-km 20.3-cm (8-in) ethane line from Moomba to Botany. Other major developments included a start on phase three of the 645-km line extension to Bukit Ketei, Malaysia, and major gas lines in South Korea, the Philippines, Taiwan, and China. In South America there were plans to link Bolivia with Brazil and to construct a 1,200-km main line from Argentina to Chile.
Stephane Mallarme
A THROW OF THE DICE NEVER, EVEN WHEN TRULY CAST IN THE ETERNAL CIRCUMSTANCE OF A SHIPWRECK’S DEPTH, Can be only the Abyss raging, whitened, stalled beneath the desperately sloping incline of its own wing, through an advance falling back from ill to take flight, and veiling the gushers, restraining the surges, gathered far within the shadow buried deep by that alternative sail, almost matching its yawning depth to the wingspan, like a hull of a vessel rocked from side to side
THE MASTER, beyond former calculations, where the lost manoeuvre with the age rose implying that formerly he grasped the helm of this conflagration of the concerted horizon at his feet, that readies itself; moves; and merges with the blow that grips it, as one threatens fate and the winds, the unique Number, which cannot be another Spirit, to hurl it into the storm, relinquish the cleaving there, and pass proudly; hesitates, a corpse pushed back by the arm from the secret, rather than taking sides, a hoary madman, on behalf of the waves: one overwhelms the head, flows through the submissive beard, straight shipwreck that, of the man without a vessel, empty no matter where
ancestrally never to open the fist clenched beyond the helpless head, a legacy, in vanishing, to someone ambiguous, the immemorial ulterior demon having, from non-existent regions, led the old man towards this ultimate meeting with probability, this his childlike shade caressed and smoothed and rendered supple by the wave, and shielded from hard bone lost between the planks born of a frolic, the sea through the old man or the old man against the sea, making a vain attempt, an Engagement whose dread the veil of illusion rejected, as the phantom of a gesture will tremble, collapse, madness, WILL NEVER ABOLISH
AS IF A simple insinuation into silence, entwined with irony, or the mystery hurled, howled, in some close swirl of mirth and terror, whirls round the abyss without scattering or dispersing and cradles the virgin index there AS IF
a solitary plume overwhelmed, untouched, that a cap of midnight grazes, or encounters, and fixes, in crumpled velvet with a sombre burst of laughter, that rigid whiteness, derisory, in opposition to the heavens, too much so not to signal closely any bitter prince of the reef, heroically adorned with it, indomitable, but contained by his petty reason, virile in lightning
anxious expiatory and pubescent dumb laughter that IF the lucid and lordly crest of vertigo on the invisible brow sparkles, then shades, a slim dark tallness, upright in its siren coiling, at the moment of striking, through impatient ultimate scales, bifurcated, a rock a deceptive manor suddenly evaporating in fog that imposed limits on the infinite
IT WAS THE NUMBER, stellar outcome, WERE IT TO HAVE EXISTED other than as a fragmented, agonised hallucination; WERE IT TO HAVE BEGUN AND ENDED, a surging that denied, and closed, when visible at last, by some profusion spreading in sparseness; WERE IT TO HAVE AMOUNTED to the fact of the total, though as little as one; WERE IT TO HAVE LIGHTED, IT WOULD BE, worse no more nor less indifferently but as much, CHANCE Falls the plume, rhythmic suspense of the disaster, to bury itself in the original foam, from which its delirium formerly leapt to the summit faded by the same neutrality of abyss
NOTHING of the memorable crisis where the event matured, accomplished in sight of all non-existent human outcomes, WILL HAVE TAKEN PLACE a commonplace elevation pours out absence BUT THE PLACE some lapping below, as if to scatter the empty act abruptly, that otherwise by its falsity would have plumbed perdition, in this region of waves, in which all reality dissolves
EXCEPT at the altitude PERHAPS, as far as a place fuses with, beyond, outside the interest signalled regarding it, in general, in accord with such obliquity, through such declination of fire, towards what must be the Wain also North A CONSTELLATION cold with neglect and desuetude, not so much though that it fails to enumerate, on some vacant and superior surface, the consecutive clash, sidereally, of a final account in formation, attending, doubting, rolling, shining and meditating before stopping at some last point that crowns it All Thought expresses a Throw of the Dice
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