2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 intersecting lines.

Intersecting Lines, 2

2 intersecting lines.

2 lines that are intersected by a third line known as a transversal.

Transversal, 2 Lines Intersected By A

2 lines that are intersected by a third line known as a transversal.

2 intersecting lines, one of which is vertical and one of which is horizontal. The intersection forms a right angle.

Intersecting Lines, 2 Perpendicular

2 intersecting lines, one of which is vertical and one of which is horizontal. The intersection forms…

3 lines which intersect at a common point.

Intersecting Lines, 3

3 lines which intersect at a common point.

4 lines which intersect at a common point.

Intersecting Lines, 4

4 lines which intersect at a common point.

4 lines which intersect at a common point.

Intersecting Lines, 4

4 lines which intersect at a common point.

4 parallel lines cut by a 5th line known as the transversal.

Transversal, 4 Parallel Lines Cut By A

4 parallel lines cut by a 5th line known as the transversal.

Star with 5 points with lines of symmetry.

Star, 5-Point

Star with 5 points with lines of symmetry.

Star with 6 points with lines of symmetry.

Star, 6-Point

Star with 6 points with lines of symmetry.

8 lines which intersect at a common point.

Intersecting Lines, 8

8 lines which intersect at a common point.

A dihedral angle is the opening between two intersecting planes.

Dihedral Angle

A dihedral angle is the opening between two intersecting planes.

"Let any irregularly shpaed body, as a stone or chair, be suspended so as to move freely. Drop a plumb line from the point of the suspendsion, and make it fast or mark its direction. The center of mass will lie in this line. From a second point, not in the line already determined, suspend the body; let it fall a plumb line as before. The center of mass will lie in this line also. But to lie in both lines, it must lie at their intersection." -Avery 1895

Finding the Center of Mass

"Let any irregularly shpaed body, as a stone or chair, be suspended so as to move freely. Drop a plumb…

Intersection of lines between a circle and its polar point.

Circle Polar Point

Intersection of lines between a circle and its polar point.

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway alignment changes. The Turn sign or the Curve sign may be combined with the Cross Road sign or the Side Road sign to create a combination Horizontal Alignment/Intersection sign that depicts the condition where an intersection occurs within a turn or curve."

Combination Horizontal Alignment/Intersection, Black and White

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway…

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway alignment changes. The Turn sign or the Curve sign may be combined with the Cross Road sign or the Side Road sign to create a combination Horizontal Alignment/Intersection sign that depicts the condition where an intersection occurs within a turn or curve."

Combination Horizontal Alignment/Intersection, Color

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway…

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway alignment changes. The Turn sign or the Curve sign may be combined with the Cross Road sign or the Side Road sign to create a combination Horizontal Alignment/Intersection sign that depicts the condition where an intersection occurs within a turn or curve."

Combination Horizontal Alignment/Intersection, Outline

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway…

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway alignment changes. The Turn sign or the Curve sign may be combined with the Cross Road sign or the Side Road sign to create a combination Horizontal Alignment/Intersection sign that depicts the condition where an intersection occurs within a turn or curve."

Combination Horizontal Alignment/Intersection, Silhouette

"The horizontal alignment Turn signs may be used in advance of situations where the horizontal roadway…

Illustration of the intersection of a cone and a plane.

Intersection of a Cone and a Plane

Illustration of the intersection of a cone and a plane.

The lines which join corresponding points in an involution on a conic all pass through a fixed point; and reciprocally, the points of intersection of conjugate lines in an involution among tangents to a conic lie on a line.

Conic Involution

The lines which join corresponding points in an involution on a conic all pass through a fixed point;…

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

Plane Intersecting A Cylinder

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant from the faces of the angle"

Plane Bisecting Dihedral Angle

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant…

Draftsman's third method for drawing an ellipse

Ellipse Third Method

Draftsman's third method for drawing an ellipse

Illustration of the intersection of a hexagonal pyramid and a plane.

Intersection of Hexagonal Pyramid and a Plane

Illustration of the intersection of a hexagonal pyramid and a plane.

Draftsman's first method to draw a parabola

Hyperbola First Method

Draftsman's first method to draw a parabola

Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.

Cone Intersected by a Plane to Form a Hyperbola

Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.

An instrument for making a reduced, enlarged, or exact copy of a plane figure

Pantograph

An instrument for making a reduced, enlarged, or exact copy of a plane figure

The segments between the point of intersection of two tangents to a conic and their points of contact are seen from a focus under equal angles. the ratio of the distances of any point on a conic from a focus and the corresponding directrix is constant.

Parabola Foci Properties

The segments between the point of intersection of two tangents to a conic and their points of contact…

Diagram of a cone intersected by plane J to form a parabola. Also pictured is a circle formed by the intersection of plane K with the cone. "Every point of a parabola is equidistant from the focus and the directrix."

Cone Intersected by a Plane to Form a Parabola

Diagram of a cone intersected by plane J to form a parabola. Also pictured is a circle formed by the…

Two planes lie perpendicular to one another. A line perpendicular to plane 1 and a line perpendicular to plane 2 will meet at a point, A, and form a perpendicular intersection.

Perpendicular Planes

Two planes lie perpendicular to one another. A line perpendicular to plane 1 and a line perpendicular…

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

2 Intersecting Planes Perpendicular To A Third Plane

"If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular…

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.

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.

"Through a given line oblique to a plane, one, and only one plane, can be passed perpendicular to the given plane."

Plane Passed Perpendicular To A Given Plane

"Through a given line oblique to a plane, one, and only one plane, can be passed perpendicular to the…

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are divided proportionally, and the section is a polygon similar to the base."

Pyramid Cut By Plane

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Sphere Cut By Plane

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane are parallel lines."

3 Intersecting Planes

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane…

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes is perpendicular to the other."

3 Intersecting Planes

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes…

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

3 Parallel Planes

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

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.

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.

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 two intersecting planes.

Intersecting Planes

Illustration of two intersecting planes.

Two parallel planes cut by a third plane.

Parallel Planes

Two parallel planes cut by a third plane.

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…

Three parallel planes cut by two lines.

Parallel Planes Cut By 2 Lines

Three parallel planes cut by two lines.

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel to the given plane."

Parallel Planes

"If two intersecting lines are each parallel to a given plane, the plane of these lines is parallel…

"If two planes are perpendicular to each other, a line in one of them perpendicular to the intersection is perpendicular to the other."

Perpendicular Planes

"If two planes are perpendicular to each other, a line in one of them perpendicular to the intersection…