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Pattern that can be cut out and folded to construct a regular icosahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Icosahedron

Pattern that can be cut out and folded to construct a regular icosahedron. Fold on the dotted lines,…

Illustration of a straight line.

Straight Line

Illustration of a straight line.

Illustration of a curved line.

Curved Line

Illustration of a curved line.

Illustration of a broken line.

Broken Line

Illustration of a broken line.

Illustration of parallel lines.

Parallel Lines

Illustration of parallel lines.

Illustration of perpendicular lines. Intersecting lines that meet at a right angle.

Perpendicular Lines

Illustration of perpendicular lines. Intersecting lines that meet at a right angle.

Illustration of perpendicular lines with the horizontal and vertical lines labeled. "A horizontal line is a line parallel to the horizon, or water level. A vertical line is a line perpendicular to a horizontal line; consequently, it has the direction of a plumb-line."

Perpendicular Lines With Horizontal and Vertical Labeled

Illustration of perpendicular lines with the horizontal and vertical lines labeled. "A horizontal line…

Illustration of intersecting lines with A being the point of intersection.

Intersecting Lines

Illustration of intersecting lines with A being the point of intersection.

Illustration that can be used to show the definition of an angle - an opening between two lines that intersect or meet.

Angle

Illustration that can be used to show the definition of an angle - an opening between two lines that…

Illustration of a line projection. If perpendiculars be drawn from the extremities of a line, as AB, to another line, as HK, as shown in the figure, that portion of HK included between the foot of each perpendicular is called the projection of AB upon HK.

Projection of a Line

Illustration of a line projection. If perpendiculars be drawn from the extremities of a line, as AB,…

Illustration of a projection of a curved line.

Projection of a Curved Line

Illustration of a projection of a curved line.

Projections of a line parallel to a plane.

Projections of a Line

Projections of a line parallel to a plane.

Projections of a line perpendicular to a plane.

Projections of a Line

Projections of a line perpendicular to a plane.

Projections of a line inclined to a plane.

Projections of a Line

Projections of a line inclined to a plane.

Projections of a lines parallel to ground line.

Projections of a Lines

Projections of a lines parallel to ground line.

Projections of a line inclined to both the horizontal and vertical planes will not show its true length, as represented in this drawing.

Projections of a Line

Projections of a line inclined to both the horizontal and vertical planes will not show its true length,…

Projections of a line's true length by revolving horizontal projection.

Projections of a Line

Projections of a line's true length by revolving horizontal projection.

Projections of a line's true length by revolving vertical projection.

Projections of a Line

Projections of a line's true length by revolving vertical projection.

Design made by drawing one large circle and then three circles that are internally tangent to the original circle and externally tangent to each other. The lines of centers of the inner circles form an equilateral triangle. Erase one side of each of the smaller circles to create the design. It resembles the yin and yang symbol.

3 Yin Yang Design Symbols In A Circle

Design made by drawing one large circle and then three circles that are internally tangent to the original…

Design made by drawing one large circle and then three circles that are internally tangent to the original circle and externally tangent to each other. The lines of centers of the inner circles form an equilateral triangle.. Erase one side of each of the smaller circles to create the design. It resembles the yin and yang symbol.

3 Yin Yang Design Symbols In A Circle

Design made by drawing one large circle and then three circles that are internally tangent to the original…

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…

Leaves - simple; alternate; edge toothed (with the points of the teeth so incurved as to appear blunt), and often finely "crinkled." Outline - usually long oval or long egg-shape. Apex - pointed. Base - rounded or slightly pointed. Leaf/Stem - usually with two to five tooth-like glands near the base of the leaf. Leaf - two to five inches long; thickish; polished, and of a deep shining green above; beneath, lighter and smooth, with the middle rib sometimes downy toward the base. In the autumn the leaves turn to orange and later to pale yellow. Bark - of old trunks, blackish and rough; of young trunks and on the larger branches, reddish or purplish brown; marked with scattered lines; on young shoots, at first green or olive brown, gradually becoming darker, and sprinkled (sic) with small orange dots. Flowers - white, with short stems, closely set in a long, cylinder-shaped cluster. May, June. Fruit - about one and a quarter inches in diameter; with short stems (one and a quarter to one and a third inches ) hanging in long, close clusters from the ends of the twigs. It is nearly black when ripe, and of a pleasant flavor though somewhat bitter; it is eagerly eaten by birds. August. Found - very widely distributed north, south, and west. It reaches its finest growth on the western slopes of the Alleghany Mountains. General Information - A tree fifty to eighty feet high. The wood is light and hard, of a brown or reddish tinge, becoming darker with exposure, and of very great value in cabinet work and interior finish. It is now becoming scarce, so that stained birch is often used as a substitute. The bitter aromatic bark is used as a valuable tonic; "cherry brandy" is made from the fruit.

Genus Prunus L. (Cherry, Plum)

Leaves - simple; alternate; edge toothed (with the points of the teeth so incurved as to appear blunt),…

Leaves - simple; alternate (often alternate in pairs); edge unequally sharp-toothed, with the base entire. Outline - triangular. Apex - taper-pointed. Base - variable, more or less squared, sometimes slightly hollowed, rounded or pointed. Leaf/Stem - long and slender, about three quarters of an inch or more in length. Leaf - one and three quarters to three inches long. Smooth and shining on both sides. Bark - The outer bark of the mature trunk is chalky-white and thin, but not, like the bark of the Paper-birch, easily separable into layers. Usually it is marked with blackish dots and lines. Often the branchlets and twigs are blackish, and in very young trees the bark may be light reddish-brown, and marked with white dots. Found - on poor soil, from Delaware and Pennsylvania northward (mostly toward the coast), and in ornamental cultivation. It springs up abundantly over burned and abandoned lands. General Information - A slender, short-lived tree, twenty to thirty feet high, with white, soft wood, not durable; used largely in making spools, shoe pegs, etc., and for fuel. A still more graceful cultivated species is the European Weeping Birch (B. pendula). Its branches are very drooping, with more slender leaves, and a spray that is exceedingly light and delicate, especially in early spring.

Genus Betula, L. (Birch)

Leaves - simple; alternate (often alternate in pairs); edge unequally sharp-toothed, with the base entire.…

Leaves - simple; alternate; edge somewhat irregularly toothed. Outline - broad egg-shape (approaching triangular-shape). Apex - long, taper-pointed. Base - squared, slightly hollowed, or slightly pointed. Leaf/Stem - long and slender and much compressed sidewise. Leaf - two to three and a half inches long (much larger on young shoots); length and width nearly the same; smooth; ribs distinct and whitish on both sides, irregular, and branching. Bark - of trunk, light "granite-gray," smooth on young trunks, becoming somewhat rough with age, and with rounded up-and-down furrows. New and vigorous shoots are green, and marked with short white or brownish lines. Seeds - covered with a white, cotton-like fibre. Found - from Western New England southward to Western Florida, westward to the Rocky Mountains. The common "cottonwood" of the West, bordering all streams flowing east from the Rocky Mountains. General Information - A tree eighty to one hundred feet high. The very light and soft wood is largely used in making paper pulp, for light boxes, and for fuel. Experiments have been made in separating and weaving the cottony fibre of the poplar seeds. It can be manufactured into cloth, but not in paying quantity and quality.

Genus Populus, L. (Aspen, Poplar)

Leaves - simple; alternate; edge somewhat irregularly toothed. Outline - broad egg-shape (approaching…

Leaves - compound (odd-feathered; leaflets, seven to nine); opposite; edge of leaflets slightly toothed or entire; entire at base. Outline - of leaflet, long oval or long egg-shape. Apex - taper-pointed. Base - somewhat pointed. Leaf/Stem - smooth. Leaflet/Stem - about one fourth of an inch long, or more; smooth. Leaf/Bud - rusty-colored and smooth. Leaflet - two to six inches long; pale beneath; downy when young, but becoming nearly smooth, except on the ribs. Bark - of the trunk, light gray. In very young trees it is nearly smooth, but it soon becomes deeply furrowed - the furrows crossing each other, and so breaking the bark into irregular, somewhat square or lozenge-shaped plates. Then in very old trees it becomes smooth again, from the scaling off of the plates. The branches are smooth and grayish-green. The young shoots have a polished, deep-green bark, marked with white lines or dots. Winged seeds - one and a half to two inches long, with the "wing" about one fourth of an inch wide, hanging in loose clusters from slender stems. The base of the seed it pointed and not winged. Found - in rich woods, from Southern Canada to Northern Florida and westward. It is most common in the Northern States. The finest specimens are seen in the bottom lands of the lower Ohio River basin. General Information - a tree forty to eighty feet high. Often the trunk rises forty feet without branching. Its tough and elastic timer is of very great value, being widely used in the manufacture of agricultural implements, for oars, and the shafts of carriages, and in cabinet-work. Fraxinus from a Greek word meaning "separation," because of the ease with which the wood of the Ash can be split. I find in the notes of an old copy of White's "Natural History of Selborne" this comment: "The Ash, I think, has been termed by Gilpin the Venus of British trees." Gerardes' "Herbal" comments: "The leaves of the Ash are of so great a vertue against serpents, as that the serpents dare not be so bolde as to touch the morning and evening shadowes of the tree, but shunneth them afarre off, as Pliny reporteth in his 16 book, 13 chap. He also affirmeth that the serpent being penned in with boughes laide rounde about, will sooner run into the fire, if any be there, than come neere to the boughes of the Ash." In Scandinavian mythology the great and sacred tree, Yggdrasil, the greatest and most sacred of all trees, which binds together heaven and earth and hell, is an Ash. Its roots spread over the whole earth. Its branches reach above the heavens. Underneath lies a serpent; above is an eagle; a squirrel runs up and down the trunk, trying to breed strife between them.

Genus Fraxinus, L. (Ash)

Leaves - compound (odd-feathered; leaflets, seven to nine); opposite; edge of leaflets slightly toothed…

The larynx viewed from its pharyngeal opening. The back wall of the pharynx has been divided and its edges (11) turned aside. Labels 1, body of hyoid; 2, its small, and 3, its great, horns; 4, upper and lower horns of thyroid cartilages; 5, mucous membrane of front of pharynx, covering the back of the cricoid cartilage; 6, upper end of gullet; 7, windpipe, lying in front of the gullet; 8, eminence caused by cartilage of Santorini; 9, eminence caused by cartilage of Wrisberg; both lie in, 10, the artytenoepiglottic fold of mucous membrane, surrounding the opening (aditus laryngis) from pharynx to larynx; a, projecting tip of epiglottis; c, the glottis, the lines leading from the latter point to the free vibratory edges of the vocal cords; b', the ventricles of the larynx; their upper edges, marking them off from the eminences b, are the false vocal cords.

Larynx

The larynx viewed from its pharyngeal opening. The back wall of the pharynx has been divided and its…

A T-square is used to aid drawing straight and parallel lines. It consist of a thin straightedge, the blade, and a head fastened at right angles.

T-square

A T-square is used to aid drawing straight and parallel lines. It consist of a thin straightedge, the…

T-squares can be used in conjunction with a drawing board to draw parallel lines.

Drawing Parallel Lines

T-squares can be used in conjunction with a drawing board to draw parallel lines.

Triangles are used in drawing lines at right angles to the T-square.

Drawing Vertical Parallel Lines

Triangles are used in drawing lines at right angles to the T-square.

It is possible to draw lines forming angles of 15 and 75 degrees by arranging two triangles.

Drawing Lines at an Angle 15 and 75

It is possible to draw lines forming angles of 15 and 75 degrees by arranging two triangles.

For drawing straight lines and curves that are not arcs of circles, the ruling pen is used. The distance between the pen points, which regulates the width of line to be drawn, is adjusted by the thumb screw, and the blades are given a slight curvature so that there will be a cavity for ink when the points are close together.

Ruling Pen

For drawing straight lines and curves that are not arcs of circles, the ruling pen is used. The distance…

Diamond pattern exercise: Divide A D and A B into 4 equal parts, then draw horizontal lines through E, F, and G and vertical lines through L, M, and N. Draw lines from A and B to the intersection O of lines E and M, and from A and D to the intersection P of lines F and L. Similarly, draw D J, J C, C I, and I B. Also connect the points O, P, J, and I, thus forming a square. The four diamond-shaped areas are formed by drawing lines from the middle points of A D, A B, B C, and D C to the middle points of lines A P, A O, O B, I B, etc.

Diamond Exercise

Diamond pattern exercise: Divide A D and A B into 4 equal parts, then draw horizontal lines through…

Square pattern exercise: Divide A D and A B into 4 equal parts and draw horizontal and vertical lines. Now divide these dimensions, A L, M N, etc., and E F, G B, etc., into 4 equal parts- each 1/4 inch- and draw light pencil lines with the T-square and triangle.

Square Exercise

Square pattern exercise: Divide A D and A B into 4 equal parts and draw horizontal and vertical lines.…

Weave pattern exercise: Divide A D and A B into 8 equal parts, and through the points O, P, Q, H, I, J, etc., draw horizontal and vertical lines. Now draw lines connecting O and H, P and I, Q and J, etc. As these lines form an angle of 45 degrees with the horizontal, a 45-degree triangle may be used. Similarly from each one of the given points on A B and A D, draw lines at an angle of 45 degrees to B C and D C respectively.

Weave Exercise

Weave pattern exercise: Divide A D and A B into 8 equal parts, and through the points O, P, Q, H, I,…

Surface of the breast in a normal condition; contours or cardial torpor to the left of the breast bone. The spaces included in the dotted lines represent the intermediate spaces.

Breast Surface

Surface of the breast in a normal condition; contours or cardial torpor to the left of the breast bone.…

A body is shown as projecting from its surface projection lines, and these lines are cut by a plane. By connecting the points on the plane made by the projection lines the projection of the body is formed, and it corresponds in shape with the body itself.

Projected Geometric View

A body is shown as projecting from its surface projection lines, and these lines are cut by a plane.…

All lines in a mechanical drawing are made with the aid of an instrument. Horizontal lines are drawn with the upper edge of the T-square blade as a guide.

Drawing a Horizontal Line

All lines in a mechanical drawing are made with the aid of an instrument. Horizontal lines are drawn…

Vertical lines are drawn by using a triangle held against the T-square.

Drawing a Vertical Line

Vertical lines are drawn by using a triangle held against the T-square.

15 degrees with the horizontal or 75 degrees with the vertical.

Triangle Set Up for 15 Degrees

15 degrees with the horizontal or 75 degrees with the vertical.

30 degrees with the horizontal or 60 degrees with the vertical.

Triangle Set Up for 30 Degrees

30 degrees with the horizontal or 60 degrees with the vertical.

45 degrees with the horizontal or 45 degrees with the vertical.

Triangle Set Up for 45 Degrees

45 degrees with the horizontal or 45 degrees with the vertical.

60 degrees with the horizontal or 30 degrees with the vertical.

Triangle Set Up for 60 Degrees

60 degrees with the horizontal or 30 degrees with the vertical.

75 degrees with the horizontal or 15 degrees with the vertical.

Triangle Set Up for 75 Degrees

75 degrees with the horizontal or 15 degrees with the vertical.

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel to the one given, place a triangle against the T-square and move them together until the hypotenuse of the triangle matches the line. Hold the T-square firmly and slide the triangle in the direction of the arrow until the desired position of the parallel line is reached.

Drawing Parallel Lines Exercise

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel…

Lines perpendicular to each other may be drawn by using a triangle in combination with the T-square. To draw a line perpendicular to a given line place a triangle against the T-square and move them together until the hypotenuse of the triangle matches the line. Turn the triangle on its right angled corner until the perpendicular line can be drawn on the hypotenuse of the triangle.

Drawing Perpendicular Lines Exercise

Lines perpendicular to each other may be drawn by using a triangle in combination with the T-square.…

Russia Stamp (3 ruble 50 kopec) from 1884

Russia 3 Ruble 50 Kopec Stamp, 1884

Russia Stamp (3 ruble 50 kopec) from 1884

"Profile of a dune, from back to front, showing its relation to the wind. The flow-lines of air are drawn above, with the eddy in front of the dune." -Gilbert, 1910

Dune and Wind

"Profile of a dune, from back to front, showing its relation to the wind. The flow-lines of air are…

"The map measurer is an instrument specially designed for quickly measuring distances or lines on a map. It consists of a dial case, handle, and a small wheel or roller." -U.S. Chief of Engineers

Map Measurer

"The map measurer is an instrument specially designed for quickly measuring distances or lines on a…

Showing relief on a map using hachures: short parallel lines. Close together is a steeper incline, farther apart represents a more gradual incline.

Hachures

Showing relief on a map using hachures: short parallel lines. Close together is a steeper incline, farther…

"To illustrate the revolution of the earth around the sun. The shaded portion represents night. The end of the axis around which the earth rotates is the point where the lines come together." -Tarr, 1910

Seasons

"To illustrate the revolution of the earth around the sun. The shaded portion represents night. The…

This figure "shows the cotidal lines and the lines of equal rise and fall for a diurnal component in latitude 30 degrees north." -Coast and Geodetic Survey, 1901

Cotidal Lines

This figure "shows the cotidal lines and the lines of equal rise and fall for a diurnal component in…

The diagram shows cotidal lines projected for a larger body of water.

Diurnal Cotidal Lines

The diagram shows cotidal lines projected for a larger body of water.

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea of 20 degrees radius, the latitude of the center being 30 degrees north." -Coast and Geodetic Survey, 1901

Diurnal Cotidal Lines

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea…

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea of 20 degrees radius, the latitude of the center being 30 degrees north." -Coast and Geodetic Survey, 1901

Diurnal Cotidal Lines

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea…

The figure "shows the effect of a circular island upon the cotidal lines." -Coast and Geodetic Survey, 1901

Island Tides

The figure "shows the effect of a circular island upon the cotidal lines." -Coast and Geodetic Survey,…

"Diagram suggestive of the distribution of intercellular spaces throughout a plant. The heavy horizontal lines in stem and root indicate intercellular spaces in medullary rays. The arrows indicate the entrance of gasses through the stomata of the leaves and stomata and lenticels of the roots and everywhere over the younger roots where waterproofing is slight." -Stevens, 1916

Intercellular Spaces of a Plant

"Diagram suggestive of the distribution of intercellular spaces throughout a plant. The heavy horizontal…

"A, cross section of stem of Juncus...the black lines traversing the section are really chains of cells and thin-walled cells with relatively large intercellular spaces between them fill up i." -Stevens, 1916

Juncus Stem

"A, cross section of stem of Juncus...the black lines traversing the section are really chains of cells…

"The sun is so far away that it would appear at the same angle from Philadelphia, St. Louis, and Denver, and if it were noon at one of these places, it would be noon at the others. Vertical lines at the three places would be parallel. But when it is noon at St. Louis, it is 1 P.M. at Philadelphia and 11 A.M. at Denver." -Dryer, 1901

Earth Curvature

"The sun is so far away that it would appear at the same angle from Philadelphia, St. Louis, and Denver,…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…