Horizontal line

“ Now, in holding up the pencil or ruler horizontally with the eye, and on a level with it, you will see what objects will appear on that horizontal line. In making a photograph of a building it is always best to have the camera a little elevated, and at a considerable distance from the object, as a better picture can be secured. All horizontal planes seem to ascend if they lie below the horizontal line, and to descend if they lie above it, vanish or merge into it, as shown in figures 5 and 6.
In making a sketch from an elevation, the distant part of the view seems higher than the foreground. ”

“ Architectural Horizontal Divisions
The architect has the surface of the ground with which to start. This gives him a horizontal line as the base of his building. He considers it of major importance in his design. We find him crossing the front of his building with horizontal moulding or long bands of colored brick, paralleling the base line and otherwise interestingly dividing the vertical face of the front and sides. His guide is the bottom line of his primary mass or the line of the ground which binds the different parts of the building into a single unit. ”

“ A perpendicular or vertical line is one perfectly upright, as a string, with a weight at the end of it, will hang from a nail, or from the hand.
In making horizontal lines, the pupil should make them parallel to the top or bottom of his slate or paper, and in making perpendiculars they should be parallel to the sides of the slate or paper. Parallel lines are lines running in the same direction equally distant from each other in every part ”

“ It will be seen that if a horizontal line is drawn from the foot of one of these figures, say G, to point O on the edge of the incline, then dropped vertically to o·, then again carried on to o·· where the other figure g is, we find it is the same height and also that the other vanishing scale is the same width at that distance, so that we can work from either one or the other. In the event of the rising ground being uneven we can make use of the scale on the level plane. ”

“ The accompanying charts comprise a series of projections formed on the following principle; A vertical line, one inch long, is divided by horizontal lines into eight parts, representing as many decades. The angle to the left of the vertical line is supposed to represent males, and that to the right, females; and the shading of either angle indicates the predomination of the sex it stands for. Figures attached to the ends of the horizontal lines indicate by thousandths the number of individuals in each decade of life. ”

“ If from any line A or B or C (Fig. 18) , &c., we drop perpendiculars from different points of those lines on to a horizontal plane, the intersections of those verticals with the plane will be on a line called the horizontal trace or projection of the original line. ”

“ For the same reason, the horizontal line, in which innumerable objects intervene between the eye and the horizon, appears so much longer than the line of altitude of the meridian, that the vault of the sky does not seem a hemisphere, but a far smaller segment of a great sphere. ”

“ In prison.—My eye, however strong and weak it may be, only encompasses a certain distance, and within this distance I move and live; this horizontal line is my immediate greater and lesser fate, from which I cannot escape. Thus round every being a concentric circle is drawn, which has a centre and which is peculiar to him. In a similar way our car encloses its in a small space, and so does our touch. ”

“ Fig. 6.
As outlines are composed of profiles, the same laws govern. That the curved line is the line of beauty stands out most evidently in the study of antique designs. Vertical lines and horizontal lines are the lines of support and strength, and must always have proper consideration; but in pure ornament the office of straight lines seems to be confined to connecting curves and to emphasizing their contrasts. ”

“ Now to give each figure its relative proportion ac- cording to its distance, draw vanishing lines to the van- ishing point from the extremities of the nearest figure, and in the angle thus formed will be found the heights of all the other figures. To find the height of a figure on any part of the road, only lead off a horizontal line, parallel to the base line, for the foot of the object, and the height is found by raising a perpendicular from the horizontal until it strikes the other converging or vanishing line. ”

“ All horizontal lines in nature that are parallel to {36} PEN DRAWING. By Jules Girardet. Showing a mantel a little below the eye. The student should practice drawing interiors with the purpose of learning the theory of perspective from every object drawn. The horizontal lines of the picture frame, for example, tip in the opposite direction to the mantel, because they are above the eye. Had the mantel been a few inches higher it would have been drawn as a perfectly horizontal line. {37} CRISPI AS CÆSAR IN HIS ROBE DE CHAMBRE. A political caricature from Don Chisciotte. ”

“ Follow with your eye any two adjacent lines, and you will see that where they are close to each other the surface has an abrupt change of level; where they are further apart the surface is nearly horizontal. Where the surface approaches the perpendicular, as on the sides, the dark line showing the separation of the strata is thin, because it has been cut through nearly at right angles. Where the surface is more horizontal the dark line is broader, because it has been cut through obliquely, the breadth varying steadily with the angle of inclination. ”

“ Given two horizontal planes cut by a vertical line, it is required to find a point on the upper part of the vertical line from which bodies may fall to the horizontal planes and there, having their motion deflected into a horizontal direction, will, during an interval equal to the time of fall, traverse distances which bear to each other any assigned ratio of a smaller quantity to a larger. ”

“ When the figure or object appears as dark upon a light ground, however, the outline should be within the silhouette, obviously, or its delicate boundary is lost.
Linear Expression of Movement
Another important attribute of line is its power of expressing or suggesting movement. By a law of inseparable association, undulating lines approaching the horizontal, or leading down to it, are connected with the sense of repose; whereas broken curves and rectangular lines always suggest action and unrest, or the resistance to force of some kind. ”

“ To sum up, the eye, owing to the laws of its mechanism, follows a line much more easily in the central than in the peripheral parts of the field, and in the central parts it follows a vertical line more easily than an oblique, and an horizontal more easily than a vertical. ”

“ By placing all the persons in a line according to their height, and drawing a line at the top of their heads we shall always get a curve differing little from the one below (the greater the number of persons, the lower the point A, the higher the point D, and the more nearly horizontal the line BC) . ”

“ What is a Scalene triangle ?
25.
When a perpendicular is raised on a right line, must the right line be a horizontal ? Ans. No. A perpendicular may be raised on any right line whether horizontal or oblique. ”

“ There must be horizontal divisions of colour which attract the attention and make one oblivious of what is above them.
Every one knows the effect of a paper with perpendicular stripes in apparently heightening a ceiling which is too low, but not every one is equally aware of the contrary effect of horizontal lines of varied surface. ”

“ The downward force is embodied in the horizontal lines of the lintel, architrave, cornice, and in the hanging mutules and gutta. The two forces come to rest in the abaci, which, as the crowning members of the columns, directly carry the weight of the entire entablature. The equilibrium between the horizontal and the vertical tendencies is, however, not a static but a moving one; for the two opposing forces are present in every part of the building from the stylobate to the ridge of the triangular pediment. ”

“ Fig. 293, is now constructed by drawing short horizontal lines equal in length to the several base lines of Fig. 292 and with numbers and letters that correspond to the order adopted. Perpendicular lines are erected at each end of these lines. Upon these perpendiculars are set off the lengths of the correspondingly numbered extension lines in the half-profiles. Attention is called to the fact that points 1 and 5 have no altitudes, since they fall on the horizontal plane upon which the entire figure
Figs. ”

“ But there is nothing to prevent us from assuming that between the verticals and horizontals we have mentioned there lie an indefinite number of other similar lines, to which intermediary fractional numbers will be assigned. Henceforth every point of the plane can be regarded as defined by the intersection of some particular horizontal and some particular vertical. ”

“ And in this he first explained the distinction between two styles, which have been called the “ horizontal and vertical systems, ” the “ horizontal system ” being that by which the older contrapuntists regulated the onward motion of their several' parts, and the “ vertical system ” that which constructs an entire passage out of a single harmony. ”

“ The complete intersection of the surface by the tangent plane is made up of the line counting once and of a residual curve of the order n-I. A quadric surface is a regulus in a twofold manner, for there are on the surface two systems of lines each of which is a regulus. ”

“ No one, I presume, will doubt the truth of this proposition, who reflects, that it is much easier to move any spherical body on an horizontal plane, than to raise the same body up against a perpendicular wall. ”

“ If a straight line, falling on two other straight lines, make the exterior angle equal to the interior and opposite angle on the same side of the line, or make the interior angles on the same side together equal to two right angles, the two straight lines shall be parallel to one another. ”

“ If a point lies in the horizontal plane, its elevation lies in the axis and the plan coincides with the point itself. If a point lies in the vertical plane, its plan lies in the axis and the elevation coincides with the point itself. ”

“ If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also he at right angles to the plane which passes through them, that is, to the plane in which they are. ”

“ But when a straight line, standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle, and the straight line which stands on the other is called a perpendicular to it. ”

“ For working sections the horizontal scale adopted is usually three or four chains to the inch, and the vertical scale 30 or 40 feet to the inch. A working section should show the level of the ground, the level of the proposed work, and the height of embankment or depth of cutting at every point of the ground where the level has been taken, these quantities being found by calculation, not by measurement on the paper. ”

“ Thus a plane is the simplest and most symmetrical boundary by which a solid can be divided; and a straight line is the simplest and most symmetrical boundary by which a plane can be separated. These conceptions are obtained by considering the boundaries of an interminable space, capable of imaginary division in every direction. And as a limited space may be separated into two parts by a plane, and a plane again separated into two parts by a straight line, so a line is divided into two portions by a point, which is the common boundary of the two portions ”

“ Having the horizontal sections given, we may obtain a complete knowledge of the direction in which the ground slopes by drawing perpendicular to them any number of lines of greatest descent; the degree of declivity is expressed by purely conventional means. The means adopted for this purpose are of two kinds. One depends upon the principle of vertical illumination, in which the maximum quantity of light is reflected upwards to the eye by a horizontal surface, and a minimum by a surface inclined 45° to the horizon. ”

“ Three straight lines not in the same plane meet at a point, and a plane cuts these straight lines at equal distances from the point of intersection: shew that the perpendicular from that point on the plane will meet it at the centre of the circle described about the triangle formed by the portion of the plane intercepted by the planes passing through the straight lines.
424. Give a geometrical construction for drawing a straight line which shall be equally inclined to three straight lines meeting at a point. ”

“ The apical pole of the vertical main axis (principal or longitudinal axis) is different from the basal pole. The ventral pole of the horizontal sagittal axis (or dorso-ventral axis) is different from the dorsal pole. The right pole of the horizontal transverse axis (lateral or frontal axis) is equal to the left pole. ”

“ The tendency of the primary strata to remain straight in the horizontal direction, and to be bent in the vertical, is a phenomenon which points very directly to the causes from whence it has arisen. A surface of simple curvature, or a surface straight in one direction, is - 231 - what the application of forces to different points of a plane, which is flexible, though with a certain degree of rigidity, will naturally produce. ”

“ Accordingly, a body hanging by a line, which over a level surface would be drawn by the earth's attraction into a direction with reference to its point of suspension, the prolongation of the line of which would pass through the center of the earth—that is, would be perpendicular, or plumb—would be attracted and turned away from the perpendicular by a mass like a mountain in the neighborhood. ”