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A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points down and toward the right.

Ray Pointing Down and Right

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points up and toward the left.

Ray Pointing Up and Right

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points toward the left.

Ray Pointing Left

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points toward the right.

Ray Pointing Right

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points down.

Ray Pointing Down

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration points up.

Ray Pointing Up

A ray has one endpoint and extends indefinitely in the other direction. The ray in this illustration…

Illustrations of a segment, a ray, and a line that can be used when providing definitions.

Definitions, Segment, Ray, Line

Illustrations of a segment, a ray, and a line that can be used when providing definitions.

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.

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.

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…

4 lines which intersect at a common point.

Intersecting Lines, 4

4 lines which intersect at a common point.

8 lines which intersect at a common point.

Intersecting Lines, 8

8 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.

3 lines which intersect at a common point.

Intersecting Lines, 3

3 lines which intersect at a common point.

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints.

Segment, Horizontal Line

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints.

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints.

Segment, Horizontal Line

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints.

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints. The endpoints are marked A and B.

Segment, Horizontal Line

Illustration of a horizontal line segment. A line segment is a section of a line with definite endpoints.…

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints. The endpoints are marked A and B.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.…

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints. The endpoints are A and B.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.…

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints. The endpoints are marked A and B.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.…

Illustration of line segment AB, which is made up of line segments AC and CB. C is considered the midpoint of segment AB.

Segment, 3 Points on a Line

Illustration of line segment AB, which is made up of line segments AC and CB. C is considered the midpoint…

2 line segments, AB and CD. AB is half the length of CD.

Segments, 2 Line

2 line segments, AB and CD. AB is half the length of CD.

6 parallel horizontal line segments.

Segments, 6 Parallel Line

6 parallel horizontal line segments.

5 parallel horizontal line segments.

Segments, 5 Parallel Line

5 parallel horizontal line segments.

4 parallel horizontal line segments.

Segments, 4 Parallel Line

4 parallel horizontal line segments.

3 parallel horizontal line segments.

Segments, 3 Parallel Line

3 parallel horizontal line segments.

2 parallel horizontal line segments.

Segments, 2 Parallel Line

2 parallel horizontal line segments.

6 slanted parallel line segments.

Segments, 6 Parallel Line

6 slanted parallel line segments.

6 slanted parallel line segments.

Segments, 6 Parallel Line

6 slanted parallel line segments.

2 slanted parallel line segments.

Segments, 2 Parallel Line

2 slanted parallel line segments.

2 slanted parallel line segments.

Segments, 2 Parallel Line

2 slanted parallel line segments.

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.

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge of equations from analytic geometry.

Conic Section Using Circle

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge…

The object can revolve around an axis (H) to create a projection on the other plane without changing the size, shape, and dimensions.

Revolution About Axis Perpendicular to H

The object can revolve around an axis (H) to create a projection on the other plane without changing…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Perpendicular to V

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Forward or Back

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

"A block revolved from its first position about an axis perpendicular to H through 45 degrees, then about an axis perpendicular to P through 45 degrees until the cut face MNO is parallel to the vertical plane. To avoid confusion it is well to letter or number the corresponding points as the views are carried along." —French, 1911

Successive Revolutions of Geometric Shapes

"A block revolved from its first position about an axis perpendicular to H through 45 degrees, then…

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars from AB to the plane. These perpendiculars form what is known as the projecting plane. If this projecting plane to be revolved about its H trace, which is the H projection of the line, until it coincides with H, the line will be seen in its true length." —French, 1911

Revolutions into the Plane of Geometric Shapes

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars…

"The distance of A and B below H is indicated on the V projection. Thus if to A∧h B∧h the perpendiculars A∧h A;and;r and B∧h B∧r be drawn, A∧r B∧r will be the true length of A B." —French, 1911

Construction of Geometric Revolution

"The distance of A and B below H is indicated on the V projection. Thus if to A∧h B∧h the perpendiculars…

"The intersection of two cylinders might represent a dome on a boiler. If the top view of cylinder A is divided into a number of equal parts the points will represent the top views of elements."—French, 1911

Intersection of Two Cylinders

"The intersection of two cylinders might represent a dome on a boiler. If the top view of cylinder A…

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose stretchout would be a straight line. If the cutting planes were taken at uniform distances apart, or at random, the elements would not be spaced uniformly on the stretchout but would be found as they project on the turned section of S—S." —French, 1911

Two Cylinders with Axes Not Intersecting

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle are, location the elements on it and finding the true length of each from the vertex to the line of intersection." —French, 1911

Intersection of Two Cones

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle…

"A series of planes as S—S are passed perpendicular to the axis of revolution, cutting out the circles shown on the end view. The points at which these circles cut the 'flat' are projected back as points on the curve." —French, 1911

Intersection of Surface of Revolution and Plane

"A series of planes as S—S are passed perpendicular to the axis of revolution, cutting out the…

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

Wooden Sphere

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn by the series of perpendicular lines parallel to the axis.

Drawing Irregular Isometric Curves of Solid

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn…

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom of each triangles to guide the straight lines. The triangle ABC is the base of the pyramid. When folded, the pyramid will form from the image.

Development of Triangle Pyramid

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom…

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at point E for reference, and the shape of the sides are by using the reference point.

Development of Rectangle Pyramid

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at…