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Illustration showing a line that remains parallel to a given line, and touches at one end a given circumference.

Straight Line Moving to Two circles

Illustration showing a line that remains parallel to a given line, and touches at one end a given circumference.

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular to each other. Locus of the midpoint.

Circle Made by Ends of a Line Touching Two Fixed Lines Perpendicular to Each Other

Illustration showing a line that moves so that its ends constantly touch two fixed lines which are perpendicular…

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon circumscribed about a circle.

Circle Inscribed in a Nonagon

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon…

Illustration used to show how to inscribe a regular octagon in a given circle.

Construction Of Octagon Inscribed In Circle

Illustration used to show how to inscribe a regular octagon in a given circle.

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the true shape of hip rafter by using projections or dividers.

Development Exercise of Octagonal Roof and True Shape of Rafter

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the…

Oval with dotted vertical and horizontal lines that are lines of symmetry.

Lines of Symmetry, Oval With

Oval with dotted vertical and horizontal lines that are lines of symmetry.

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

Illustration used to show how to inscribe a regular pentagon in a given circle.

Construction Of Pentagon Inscribed In Circle

Illustration used to show how to inscribe a regular pentagon in a given circle.

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

Regular pentagon inscribed in a circle, circumscribed about a circle.

Pentagon Inscribed & Circumscribed in Circles

Regular pentagon inscribed in a circle, circumscribed about a circle.

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

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…

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed about a circle.

Regular Pentagon With Circle Inscribed

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed…

Illustration of a circle with center O and diameters AB and CD perpendicular to each other.

Circle With 2 Perpendicular Diameters

Illustration of a circle with center O and diameters AB and CD perpendicular to each other.

Cross section of pipe, 2 concentric circles

Cross Section of Pipe

Cross section of pipe, 2 concentric circles

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 used to show how to inscribe any regular polygon in a given circle.

Construction Of Polygon Inscribed In Circle

Illustration used to show how to inscribe any regular polygon in a given circle.

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

Pulley

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

Two arrangements of pulley: crossed belt and uncrossed belt. The pulleys are constructed with two circles that have the radii labeled and tangent lines drawn (strings).

Pulley

Two arrangements of pulley: crossed belt and uncrossed belt. The pulleys are constructed with two circles…

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Construction of Radii of a Circle

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Illustration of a circle inside of a rectangle. The two figures have the same center.

Circle Inside Rectangle

Illustration of a circle inside of a rectangle. The two figures have the same center.

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces small enough as practically to coincide with the arc, and to step off the same number on the right line." —French, 1911

Rectifying Arc Using Dividers

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces…

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described as a circle inscribed in a regular heptagon/septagon.

Regular Heptagon/Septagon Circumscribed about a Circle

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described…

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Construction Of Regular Polygon

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Illustration of ring (small circle in larger concentric circle).

Ring Made of Concentric Circles

Illustration of ring (small circle in larger concentric circle).

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Ring With Piece Cut Out

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Illustration of ring (small circle in larger concentric circle) sprung into place.

Ring Sprung Into Place

Illustration of ring (small circle in larger concentric circle) sprung into place.

Circular rosette with 12 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 12 Petals

Circular rosette with 12 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 12 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 12 Petals

Circular rosette with 12 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 16 Petals

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 16 Petals

Circular rosette with 16 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 24 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 24 Petals

Circular rosette with 24 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 24 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 24 Petals

Circular rosette with 24 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 3 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 3 Petals

Circular rosette with 3 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 32 Petals

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 32 Petals

Circular rosette with 32 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 4 Petals

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 48 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 48 Petals

Circular rosette with 48 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 6 Petals

Circular rosette with 6 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 6 petals. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center.

Circular Rosette With 6 Petals

Circular rosette with 6 petals. It is made by rotating circles about a fixed point. The radii of the…

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. Thus, the circles meet in the center of the larger circle.

Circular Rosette With 8 Petals

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The…

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The radii of the smaller circles are less than the distance between the point of rotation and the center of the circle. Thus, there is a hole in the center.

Circular Rosette With 8 Petals

Circular rosette with 8 petals in a circle. It is made by rotating circles about a fixed point. The…

An illustration showing a circle sector with radius r, center/central angle v, and length of circle arc b.

Circle Sector

An illustration showing a circle sector with radius r, center/central angle v, and length of circle…

An illustration showing a circle sector with center/central angle v and polygon angle w.

Circle Sector

An illustration showing a circle sector with center/central angle v and polygon angle w.

An illustration showing a circle sector with height of segment h and radius r.

Circle Sector

An illustration showing a circle sector with height of segment h and radius r.

Illustration of a semicircle.

Semicircle

Illustration of a semicircle.

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Right Angles Inscribed in Semicircle Proof

Illustration of a circle used to prove "Any angle inscribed in a semicircle is a right angle."

Illustration of a semicircle with chords and radii.

Semicircle With Chords and Radii

Illustration of a semicircle with chords and radii.

A sphere with arcs and poles. "The distance of all points in the circumference of a circle of a sphere from its poles are equal."

Sphere With Arcs and Poles

A sphere with arcs and poles. "The distance of all points in the circumference of a circle of a sphere…

A sphere with arcs drawn.

Sphere With Arcs

A sphere with arcs drawn.

Illustration of a sphere with arcs drawn.

Arcs Drawn on Sphere

Illustration of a sphere with arcs drawn.

"Every section of a sphere made by a plane is a circle."

Circle Made by Plane Passing Through a Sphere

"Every section of a sphere made by a plane is a circle."

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally distant from each of its poles."

Circumference of a Circle of a Sphere

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally…

Illustration of a sphere inscribed in a tetrahedron.

Sphere Inscribed in Tetrahedron

Illustration of a sphere inscribed in a tetrahedron.

Illustration of a sphere inscribed in a tetrahedron.

Sphere Inscribed in Tetrahedron

Illustration of a sphere inscribed in a tetrahedron.

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an axis.

Sphere Made by Revolution of Semicircle

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an…

Illustration of a material sphere that can be used to find its diameter.

Material Sphere

Illustration of a material sphere that can be used to find its diameter.

Illustration of a plane passing through a sphere.

Plane Passing Through a Sphere

Illustration of a plane passing through a sphere.

Illustration of a sphere with a tangent plane. "A plane perpendicular to a radius at its extremity is tangent to the sphere."

Sphere With Tangent Plane

Illustration of a sphere with a tangent plane. "A plane perpendicular to a radius at its extremity is…