A flashcard featuring an illustration of a Parallel Lines

Flashcard of a Parallel Lines

A flashcard featuring an illustration of a Parallel Lines

A flashcard featuring an illustration of Perpendicular Lines

Flashcard of Perpendicular Lines

A flashcard featuring an illustration of Perpendicular Lines

A flashcard featuring an illustration of a Ray

Flashcard of a Ray

A flashcard featuring an illustration of a Ray

A flashcard featuring an illustration of a Straight angle

Flashcard of a Straight angle

A flashcard featuring an illustration of a Straight angle

Illustration of a plane rotated about a straight line.

Plane Rotated About a Straight Line

Illustration of a plane rotated about a straight line.

Illustration of a plane determined by 2 intersecting lines

Plane Determined by 2 Intersecting Lines

Illustration of a plane determined by 2 intersecting lines

Illustration of a plane determined by 2 parallel lines

Plane Determined by 2 Parallel Lines

Illustration of a plane determined by 2 parallel lines

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

If a straight line is perpendicular to each of two other straight lines in a plane at their point of intersection, it is perpendicular to the plane of the two lines.

Line Perpendicular to Plane

If a straight line is perpendicular to each of two other straight lines in a plane at their point of…

Straight line AB is perpendicular to the lines in plane MN at point B.

Line Perpendicular to Plane

Straight line AB is perpendicular to the lines in plane MN at point B.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

Oblique lines drawn from a point to a plane.

Oblique Lines Drawn to a Plane

Oblique lines drawn from a point to a plane.

"The locus of a point in space equidistant from the extremities of a straight line is the plane perpendicular to this line at its middle point."

Locus Point to a Plane

"The locus of a point in space equidistant from the extremities of a straight line is the plane perpendicular…

Straight line AB is perpendicular to the lines in plane MN at point B. "If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane."

Line Perpendicular to Plane

Straight line AB is perpendicular to the lines in plane MN at point B. "If from the foot of a perpendicular…

Two straight lines, AB and CD, perpendicular to the same plane (MN) are parallel.

Lines Perpendicular to Plane

Two straight lines, AB and CD, perpendicular to the same plane (MN) are parallel.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

Illustration of two parallel planes. "Two planes perpendicular to the same straight line are parallel."

Parallel Planes

Illustration of two parallel planes. "Two planes perpendicular to the same straight line are parallel."

Two parallel planes perpendicular to a line (AB).  "A straight line perpendicular to one of two parallel planes is perpendicular to the other also."

Parallel Planes

Two parallel planes perpendicular to a line (AB). "A straight line perpendicular to one of two parallel…

Two intersecting planes on a third plane. "If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular to that plane."

Intersecting Planes

Two intersecting planes on a third plane. "If two intersecting planes are each perpendicular to a third…

Illustration of a straight line projected upon a plane.

Line Projected Upon Plane

Illustration of a straight line projected upon a plane.

Illustration of two intersecting spheres. "The intersection of two spherical surfaces is the circumference of a circle whose plane is perpendicular to the line joining the centres of the surfaces and whose centre is in that line."

Intersecting Spheres

Illustration of two intersecting spheres. "The intersection of two spherical surfaces is the circumference…

Illustration of a spherical segments.

Spherical Segments

Illustration of a spherical segments.

Illustration of a parabola - a curve which is the locus of a point that moves in a plane so that its distance from a fixed point in the plane is always equal to its distance from a fixed line in the plane.

Parabola With Focus and Directrix

Illustration of a parabola - a curve which is the locus of a point that moves in a plane so that its…

Illustration of a parabola - a curve which is the locus of a point that moves in a plane so that its distance from a fixed point (focus) in the plane is always equal to its distance from a fixed line (directrix) in the plane.

Parabola With Focus and Directrix

Illustration of a parabola - a curve which is the locus of a point that moves in a plane so that its…

Illustration of a parabola. "If a line PT is drawn from any point P of the curve, bisecting the angle between PF and the perpendicular from P to the directrix, every point of the line PT, except P, is without the curve."

Point on Parabola

Illustration of a parabola. "If a line PT is drawn from any point P of the curve, bisecting the angle…

"Two motors are usually employed on each [electric railway] car, and the connection between them and the rails is made through the car-wheels and axles, and between them and the line wire, by a wire connected with a wheel called the <em>trolley.,/i> which is carried at the end of a pole supported on the car roof...." -Atkinson 1903

Electric Railway

"Two motors are usually employed on each [electric railway] car, and the connection between them and…

"When a person speaks into the transmitter, the pulsations of the air, produced by the voice, produce the slight vibrations of the diaphragm...and these vary the pressure of the platinum point on the carbon disk, and these vary the strength of the electric current, and reproduce precisely similar vibrations in the diaphragm of the receiver, at the opposite end of the line, which reproduce the spoken words." -Atkinson 1903

Electric Telephone

"When a person speaks into the transmitter, the pulsations of the air, produced by the voice, produce…

Illustration of a tangent line drawn from an external point to a parabola.

Tangent to a Parabola

Illustration of a tangent line drawn from an external point to a parabola.

Illustration showing that if two tangents RP and RQ are drawn from a point R to a parabola, the line drawn through R parallel to the axis bisects the chord of contact.

Tangents to a Parabola

Illustration showing that if two tangents RP and RQ are drawn from a point R to a parabola, the line…

Illustration showing that the area of a parabolic segment made by a chord is two thirds the area of the triangle formed by the chord and the tangents drawn through the ends of the chord.

Tangents and Chords of a Parabola

Illustration showing that the area of a parabolic segment made by a chord is two thirds the area of…

Illustration showing the definition of a parabola as a conic section. "The section of a right circular cone made by a plane parallel to one, and only one, element of the surface is a parabola."

Conic Section Showing Parabola

Illustration showing the definition of a parabola as a conic section. "The section of a right circular…

Illustration showing the definition of a parabola as a conic section. "The section of a right circular cone made by a plane parallel to one, and only one, element of the surface is a parabola."

Conic Section Showing Parabola

Illustration showing the definition of a parabola as a conic section. "The section of a right circular…

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the angle between one of the focal radii and the other produced, every point in this line except P is without the curve."

Line Bisecting Angle Between Focal Radii on Ellipse

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the…

Illustration of how to draw a tangent to an ellipse from an external point.

Tangent From External Point to an Ellipse

Illustration of how to draw a tangent to an ellipse from an external point.

Illustration showing the tangents drawn at two corresponding points of an ellipse and its auxiliary circle cut the major axis produced at the same point.

Tangents to an Ellipse

Illustration showing the tangents drawn at two corresponding points of an ellipse and its auxiliary…

Illustration showing that tangents drawn at the ends of any diameter are parallel to each other.

Parallel Tangents to an Ellipse

Illustration showing that tangents drawn at the ends of any diameter are parallel to each other.

Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola a line is drawn bisecting the angle between the focal radii, every point in this line except P is on the convex side of the curve.

Line Bisecting Angle Between Focal Radii in Hyperbola

Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola…

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 that can be used to show supplementary angles. The angles form a straight line.

Supplementary Angles

Illustration that can be used to show supplementary angles. The angles form a straight line.

Illustration of a triangle divided by a parallel line to form two similar triangles.

Similar Triangles

Illustration of a triangle divided by a parallel line to form two similar triangles.

Illustration of intersecting circles. "If two circles intersect each other, the line joining their centers bisects at right angles the line joining the two points of intersection."

Intersecting Circles

Illustration of intersecting circles. "If two circles intersect each other, the line joining their centers…

Illustration of an ellipse with major and minor axes, foci, and points on the ellipse. "An ellipse is a plane figure bounded by a curved line, to any point of which the sum of the distances from two fixed points within, called the foci, is equal to the sum of the distances from the foci to any other point on the curve."

Ellipse

Illustration of an ellipse with major and minor axes, foci, and points on the ellipse. "An ellipse is…

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.

The line ab is projected in the coordinate plane.

Length of a Line in Coordinate Plane

The line ab is projected in the coordinate plane.

The line ab is projected in the coordinate plane.

Length of a Line in Coordinate Plane

The line ab is projected in the coordinate plane.

The line revolved into V and projection H in coordinate plane.

Profile Line

The line revolved into V and projection H in coordinate plane.

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,…