Parallel lines

Parallel Lines

Parallel lines

Parallel lines

Parallel Lines

Parallel lines

Parallel lines

Parallel Lines

Parallel lines

Right angle with square at perpendicular lines

Right Angle

Right angle with square at perpendicular lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Perpendicular Lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Right triangle with square

Right Triangle

Right triangle with square

A line which is divided into seven equal parts, shown by construction.

Construction of Dividing Lines

A line which is divided into seven equal parts, shown by construction.

A line which is divided into equal parts, shown by construction and square.

Construction of Dividing Lines

A line which is divided into equal parts, shown by construction and square.

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction lines shown.

Pentagon Inscribed in Circle by Construction

Illustration of pentagon inscribed in circle. Or, circle circumscribed about pentagon. Construction…

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of one base.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of two bases.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center. This illustration can be used to find the area of the zone and the volume of the segments.

Sphere With 8-inch Diameter Cut by Planes

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center.…

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Reference Angles/Triangles Formed by Angles in Quadrants

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa, ordinate, and distance labeled.

Reference Angles/Triangles Formed by Angles in Quadrants With Labels

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa,…

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Projection of a Line Segment

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

OP is a line representing a vector (directed quantity)

Vector

OP is a line representing a vector (directed quantity)

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Vector Showing Force at Angle of 20 degrees

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Angle of Elevation

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Illustration showing an angle of depression from a horizontal line to a line of sight.

Angle of Depression

Illustration showing an angle of depression from a horizontal line to a line of sight.

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking off streets at 100 foot intervals.

Triangular City Block With Angles and Lengths

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking…

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Survey of Lake Front in Chicago

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral Drawn on Piece of Paper Shown Flat

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running from A to D.

Spiral Drawn on Piece of Paper and Rolled

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running…

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal side of XOP, as B, a perpendicular can be drawn, AB, to the x-axis; and from D, any point in the terminal side o f XOQ, perpendicular CD can be drawn to the x-axis. The right triangles OAB and OCD are similar. Also, OA, AB, OB, CD, and OD are positive, while OC is negative.

Coordinate Axis With Angles, Lines, and Perpendiculars Drawn

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal…

To illustrate the structure of nerve fibers. Labels: A, nerve fiber examined fresh; n, node. B, nerve fiber with axis cylinder shaded, and medulla represented by dark lines; n.c, nucleus; p, granular cell substance near the nucleus. C, more highly magnified: m, medulla; n, node. D, nerve treated with reagents to show the axis cylinder: n.x, surrounded by medulla, m. E, nerve treated with reagents to show n.c, nucleus with fine line over it representing the neurilemma, and outside this fine connective tissue, c: n.c', nucleus lying in the fine connective tissue. F, nerve fiber deprived of its neurilemma showing medulla broken up into fragments, m, surrounding the axis cylinder, n.x.

Nerve Fibers

To illustrate the structure of nerve fibers. Labels: A, nerve fiber examined fresh; n, node. B, nerve…

Diagram of the outer surface of left cerebral hemisphere to illustrate the localization of functions. The motor area is shaded in vertical and transverse lines: Sy, fissure of Sylvius; an, angular gyrus or convolution; Ro, fissure of Rolando; Fv, frontal lobe; Pa, parietal lobe; Te, temporal lobe. Only a very few of the more important fissures are indicated.

Cerebral Hemisphere Showing Localization of Function

Diagram of the outer surface of left cerebral hemisphere to illustrate the localization of functions.…

The right retina as it would be seen if the front part of the eyeball with the lens and vitreous humor were removed. The white disk to the right marks the entry of the optic nerve (blind spot); the lines radiating from this are the retinal arteries and veins. The small central dark patch is the yellow spot, the region of most acute vision.

Retina Blind Spot

The right retina as it would be seen if the front part of the eyeball with the lens and vitreous humor…

Lines for the detection of astigmatism. "The refracting surfaces of the eye acting together are equivalent in refracting power to a single, spherical surface of fairly short curvature. Frequently, however, the result is not the same as would be given by a perfect spherical surface, owing to inequalities in the curvature of the eye. In one direction the curvature may be greater than that at right angles to it. This tendency to a cylindrical form is called astigmatism. It interferes with the formation of perfect images and sometimes leads to serious eye strain in the effort to better the vision. Astigmatism may be detected by looking at black lines radiating from a point or at fine black concentric circles. Portions of the liens or circles appear gray and others black; the gray portions are out of focus. This defect is corrected by proper cylindrical glasses which equalize the curvature of the eye" — Newell, 1900

Detection of Astigmatism

Lines for the detection of astigmatism. "The refracting surfaces of the eye acting together are equivalent…

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 cartilage; 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 aryteno-epiglottidean 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 letter point to the free vibrating 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…

Surface of normal chest; outlines of cardiac dulness to the left of the sternum. The spaces enclosed in the dotted lines represent the interspaces.

Surface of Normal Chest

Surface of normal chest; outlines of cardiac dulness to the left of the sternum. The spaces enclosed…

The origins of the three glutaei upon the dorsum of the ilium (part of the hip bone). The gluteal lines are represented by the dotted lines.

The Ilium Bone and Origin of the Gluteal Muscles

The origins of the three glutaei upon the dorsum of the ilium (part of the hip bone). The gluteal lines…

An illustration of angles with the same vertex made up of 4 lines.

Angles With Same Vertex

An illustration of angles with the same vertex made up of 4 lines.

An illustration showing when one straight line meets another straight line and makes the adjacent angles equal, each of these angles is called a right angle.

Right Angles With Same Vertex

An illustration showing when one straight line meets another straight line and makes the adjacent angles…

An illustration of two angles that are adjacent. They have the same vertex and a common side between them. Angles BOD and AOD are adjacent

Adjacent Angles

An illustration of two angles that are adjacent. They have the same vertex and a common side between…

An illustration showing a straight angle. When the sides of an angle extend in opposite directions, so as to be in the same straight line, the angle is called a straight angle.

Straight Angle

An illustration showing a straight angle. When the sides of an angle extend in opposite directions,…

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations of the sides of the other. In this illustration, a and b are vertical angles and c and d are vertical angles.

Vertical Angles

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations…

Illustration of two lines intersecting at a point. This can be used to show vertical angles.

Intersecting Straight Lines

Illustration of two lines intersecting at a point. This can be used to show vertical angles.

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off on the given line equal segments from the foot of the perpendicular, are equal and make equal angles with the perpendicular. This illustration can be used to show the proof.

Lines Drawn to Another Line to Form Triangle

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off…

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Perpendicular Line Drawn to a Given Line from an External Point

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line from an external point.

Perpendicular Line Drawn To a Given Line From an External Point

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line…

Illustration showing two lines CA and CB drawn from the point C to the extremities of the straight line AB. OA and OB are two lines similarly drawn, but included by CA and CB. This can be used to show the theorem: The sum of two lines drawn from a point to the extremities of a straight line is greater than the sum of two other lines similarly drawn, but included by them.

Lines Drawn From the Point C to the Extremities of the Straight line AB

Illustration showing two lines CA and CB drawn from the point C to the extremities of the straight line…

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line, cutting off on the line unequal segments from the foot of the perpendicular, the more remote is the greater.

Lines Drawn From the Same Point in a Perpendicular to a Given line, Cutting Off Segments

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line,…

Illustration showing two straight lines in the same plane perpendicular to the same straight line are parallel.

Parallel Lines

Illustration showing two straight lines in the same plane perpendicular to the same straight line are…

Illustration showing if a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also.

Parallel Lines

Illustration showing if a straight line is perpendicular to one of two parallel lines, it is perpendicular…

Illustration showing that a transversal is a straight line that cuts two or more straight lines.

Lines Cut By A Transversal

Illustration showing that a transversal is a straight line that cuts two or more straight lines.

Illustration showing that if two parallel lines are cut by a transversal, then the alternate interior angles are equal.

Parallel Lines Cut By A Transversal

Illustration showing that if two parallel lines are cut by a transversal, then the alternate interior…

Illustration showing that when two straight lines in the same plane are cut by a transversal, if the alternate interior angles are equal, the two straight lines are parallel.

Parallel Lines Cut By A Transversal

Illustration showing that when two straight lines in the same plane are cut by a transversal, if the…

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles are equal.

Parallel Lines Cut By A Transversal

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles…

Illustration showing that when two parallel lines are cut by a transversal, the two interior angles on the same side of the transversal are supplementary.

Parallel Lines Cut By A Transversal

Illustration showing that when two parallel lines are cut by a transversal, the two interior angles…

Illustration showing a triangle with an interior segment drawn

Triangle With Interior Segment

Illustration showing a triangle with an interior segment drawn

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can be shown to show adjacent angles ACB and ACD as well.

Triangle With Segment Extended for Exterior Angle

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can…

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere equally distant.

Parallel Lines With Equal Segments Between

Illustration of two parallel lines with equal segments between them. Two parallel lines are everywhere…

Illustration showing that when three or more parallel lines intercept equal parts on one transversal, they intercept equal parts on every transversal.

Parallel Lines Cut By A Transversal

Illustration showing that when three or more parallel lines intercept equal parts on one transversal,…

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side, it bisects the other side also.

Triangle With Bisector Parallel to the Base

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side,…

Illustration of an axis of symmetry drawn with respect to a straight line.

Axis of Symmetry

Illustration of an axis of symmetry drawn with respect to a straight line.

Illustration of an axis of symmetry drawn with respect to a hexagon.

Axis of Symmetry Drawn on a Hexagon

Illustration of an axis of symmetry drawn with respect to a hexagon.

Illustration of an axis of symmetry drawn with respect to a hexagon.

Axis of Symmetry Drawn on a Hexagon

Illustration of an axis of symmetry drawn with respect to a hexagon.

Illustration of an axis of symmetry drawn with respect to a quadrilateral.

Axis of Symmetry Drawn on a Quadrilateral

Illustration of an axis of symmetry drawn with respect to a quadrilateral.

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It is symmetrical with respect to the diagonal joining the vertices of the angles formed by the equal sides, and the diagonals are perpendicular to each other.

Quadrilateral with Symmetry

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It…