Illustration of concentric circles.

Concentric Circles

Illustration of concentric circles.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

Illustration of three circles enclosed in an equilateral triangle.

Circles Enclosed in Equilateral Triangle

Illustration of three circles enclosed in an equilateral triangle.

Illustration of equal circles to show that two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii

Illustrations of 2 equal circles with radii drawn.

Illustrations of 2 equal circles with radii drawn.

Equal Circles With Radii and Chords

Illustrations of 2 equal circles with radii drawn.

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero. This is often called a Hawaiian earring.

Infinite Tangent Circles

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero.…

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted between its sides.

Circles With Inscribed Angles

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted…

Illustration of a circle with a polygon (octagon) and square inscribed.

Circle With Polygon and Square Inscribed

Illustration of a circle with a polygon (octagon) and square inscribed.

Illustration of large circle and square with 4 smaller circles inside.

Circles Inside of a Square

Illustration of large circle and square with 4 smaller circles inside.

Intersecting circles with chords and radii.

Intersecting Circles

Intersecting circles with chords and radii.

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

Illustration of intersecting circles with a common chord.

Intersecting Circles With a Common Chord

Illustration of intersecting circles with a common chord.

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated by the circumferences. The chords joining the ends of theses lines are parallel.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated…

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Circles With Parallels Intercepting Equal Arcs

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Illustration of box filled with pipes.

Circular Pipes in Box

Illustration of box filled with pipes.

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 2 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° and the overlapping curves are removed to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 8 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration.

Reflected Arcs Of 8 Circles

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact terminated by the circumference. The chords joining the ends of theses lines are parallel.

Tangent Circles With Chords

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact…

Projection of a circular ring.

Projection of Circular Ring

Projection of a circular ring.

Illustration used to show how to pass a circumference through any three points not in the same straight line.

Construction Of Circumference

Illustration used to show how to pass a circumference through any three points not in the same straight…

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the handle between the thumb and finger.

Inking a Circle

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the…

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

Composite Figure

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

Illustration of a circle inside of 2 concentric rectangles whose vertices are connected by line segments.

Circle Inside Concentric Rectangles

Illustration of a circle inside of 2 concentric rectangles whose vertices are connected by line segments.

Cross section of concrete conduit. The diagram can be used to find volume.

Cross Section of Concrete Conduit

Cross section of concrete conduit. The diagram can be used to find volume.

Development and top completion exercise problem of the cone by dividing the base into equal parts and creating an arc to revolve the sides of the plane.

Development Exercise of Cone

Development and top completion exercise problem of the cone by dividing the base into equal parts and…

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones by using series of cone development.

Development Exercise of Flange and Hood Cones

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones…

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…

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Cone depicting Conic Sections

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle, ellipse.

Cone depicting Conic Sections

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Illustration of of construction of an arc when the chord and height of the segment are given.

Construction of Arc When Given the Chord and Height of the Segment

Illustration of of construction of an arc when the chord and height of the segment are given.

Illustration used to construct a circle when given two points that it passes through and a radius.

Construction of a Circle When Given Two Points and a Radius

Illustration used to construct a circle when given two points that it passes through and a radius.

Illustration of a triangle with its incircle and three excircles constructed.

Triangle With Circle Constructions

Illustration of a triangle with its incircle and three excircles constructed.

Illustration of the construction used to circumscribe a circle about a given triangle.

Construction to Circumscribe a Circle About a Triangle

Illustration of the construction used to circumscribe a circle about a given triangle.

Illustration used to construct a common tangent when given two circles.

Construction of a Common Tangent When Given Two Circles

Illustration used to construct a common tangent when given two circles.

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of the triangles. The intersections of the bisectors of the exterior angles of a triangle are the centers of three circles, each of which will touch one side of the triangle, and the two other circles.

Construction of Escribed Circles With Ex-centres

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of…

Illustration of the construction used to inscribe a circle in a given triangle.

Construction to Inscribe a Circle in a Triangle

Illustration of the construction used to inscribe a circle in a given triangle.

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

Illustration of the construction used upon a given straight line, to describe a segment of a circle in which a given angle may be inscribed.

Construction to Describe a Segment of a Circle in Which an Angle Can Be Inscribed

Illustration of the construction used upon a given straight line, to describe a segment of a circle…

Illustration of the construction used to draw a tangent to a given circle through a given point.

Construction of Tangent Line Through a Given Point to a Given Circle

Illustration of the construction used to draw a tangent to a given circle through a given point.

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…

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing area.

Development Exercise of Cylinder

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing…

The illustration shows the cylinder rolled out in a tangent plane of the base to create a development of the solid.

Development of Cylinder

The illustration shows the cylinder rolled out in a tangent plane of the base to create a development…

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a cylinder.

Cylinder Inscribed in Pentagonal Prism

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a…

Isometric of a cylinder.

Isometric of a Cylinder

Isometric of a cylinder.

Illustration of planes passing through a cylinder.

Planes Passing Through A Cylinder

Illustration of planes passing through a cylinder.

Right circular cylinder.

Right Circular Cylinder

Right circular cylinder.