"The mural crown is a circle of fold embattled, and it is associated with military success in sieges."—Aveling, 1891

Mural Crown

"The mural crown is a circle of fold embattled, and it is associated with military success in sieges."—Aveling,…

"The naval crown is a golden circle surmounted with sterns and square sails of ships, placed alternately."—Aveling, 1891

Naval Crown

"The naval crown is a golden circle surmounted with sterns and square sails of ships, placed alternately."—Aveling,…

The leaves of the livistona hoogendorpii tree are a rich dark green and form a complete circle.

Livistona Hoogendorpii

The leaves of the livistona hoogendorpii tree are a rich dark green and form a complete circle.

Pictured is a double perianth as seen in the flower of abutilon insigne. A double perianth has an outer circle of green sepals and an inner circle of colored petals.

Double Perianth

Pictured is a double perianth as seen in the flower of abutilon insigne. A double perianth has an outer…

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into a triangle, parallelogram, circle, etc., based on the shape of the figure. Find the area of each part and combine the centers of gravity found for each.

Center of Gravity

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into…

Sometimes it is not necessary for an entire wheel to be used. A projection of any kind that can cause an object to move in a circle may be considered a wheel, like in the image given.

Bucket and Crank

Sometimes it is not necessary for an entire wheel to be used. A projection of any kind that can cause…

When pipes are bent at ninety degree angles, a rounded bend is best as shown along with a radius as large as possible to increase discharge.

Pipe Diameter

When pipes are bent at ninety degree angles, a rounded bend is best as shown along with a radius as…

A medal containing two circles of heads, each having seven, male and female alike. The heads of the inner circle are divided by spokes.  The upper head has on either side of it a Victory offering a crown and palm branch.

Medal with Heads

A medal containing two circles of heads, each having seven, male and female alike. The heads of the…

Young and old sitting in a circle listening to stories. A younger woman holds a distaff. there is a spinning wheel in the foreground.

Story Time

Young and old sitting in a circle listening to stories. A younger woman holds a distaff. there is a…

To find the equation of a circle whose center is the origin and whose radius is 3 units in length.

Circle Equation

To find the equation of a circle whose center is the origin and whose radius is 3 units in length.

Finding the equation of a circle with the origin as its center.

Circle Equation

Finding the equation of a circle with the origin as its center.

A circle in its common, or central form. This is used to assist students in finding the equation of any circle.

Common Form of Circle

A circle in its common, or central form. This is used to assist students in finding the equation of…

A circle with many tangent and secant lines passing through it.

Lines

A circle with many tangent and secant lines passing through it.

Finding the equation of the normal at any point on a circle.

Normal Equation

Finding the equation of the normal at any point on a circle.

Tangent lines are drawn from a given external point to a circle. The equation is found by joining their points of contact

Chord Equation

Tangent lines are drawn from a given external point to a circle. The equation is found by joining their…

The chord of a circle.

Circle Chord

The chord of a circle.

Example of an equation with a given external point.

Equation Example

Example of an equation with a given external point.

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs of tangents at the extremities of the chords will all lie on a fixed straight line.

Polar Property

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs…

Polar property example.

Example

Polar property example.

Constructing the polar of a given point P with respect to a circle.

Polar of Point

Constructing the polar of a given point P with respect to a circle.

Finding the length of a tangent from a given point to a circle.

Tangent Length

Finding the length of a tangent from a given point to a circle.

Finding the equation of a line with polar coordinates.

Polar Coordinates

Finding the equation of a line with polar coordinates.

An inscribed triangle in a circle.

Particular Cases

An inscribed triangle in a circle.

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Coordinate Plane

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

A circle and triangle situated on coordinate planes.

Circle

A circle and triangle situated on coordinate planes.

Set of standard fillet and radius gages.

Radius Gages

Set of standard fillet and radius gages.

"The constellation which is prominent in early summer in the skies of the southern United States (where the whole of the magnificent tail clears the horizon), contains the first magnitude red star Antares and several of the second magnitude. With the Chaldeans and Greeks is extended over one sixth of the planetary circle, the scorpion being represented with exaggerated claw embracing a circular space where Libra is now placed." —Whitney, 1889

The Scorpio Constellation, with Libra

"The constellation which is prominent in early summer in the skies of the southern United States (where…

"A screw cut on a solid, of such form that if any plane be taken through its longitudinal axis, the intersections of the plane by the perimeter are arcs of the pitch-circle of a wheel into which the screw is intended to work. It is so named from having been first employed by Mr. Hindley of York in England." —Whitney, 1889
<p>The hourglass shape of the screw increases the bearing area and therefore reduces wear.

Hindley's Screw

"A screw cut on a solid, of such form that if any plane be taken through its longitudinal axis, the…

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." &mdash;Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"A, acromion; C, coracoid; CA, carpus; CL, clavicle; H, humerus; M, metacarpals; O, ventral surface of the scapula; P, phalanges, proximal row; R, radius; T, head of humerus; U, ulna." —Whitney, 1889

Bones of the Shoulder and Upper Extremity - Front View

"A, acromion; C, coracoid; CA, carpus; CL, clavicle; H, humerus; M, metacarpals; O, ventral surface…

"An instrument for throwing stones or bullets, consisting of a strap and two strings attached to it. The stone or bullet is lodged to the strap, and, the ends of the strings being held in the hand, the sling is whirled rapidly round in a circle, and the missile thrown by letting go one of the strings. The velocity with which the projectile is discharged is the same as that with which it is whirled round in a circle having the string for its radius. The sling was a very general instrument of war among ancients." &mdash;Whitney, 1889

Sling

"An instrument for throwing stones or bullets, consisting of a strap and two strings attached to it.…

Also called a parabolic spiral, it is a type of Archimedean Spiral. A spiral is defined as "a plane curve which runs continuously round and round, a fixed point, called the center, with constantly increasing radius vector, so that the latter is never normal to the curve; also, a part of such a curve in the course of which the radius from the center describes 360 degrees." &mdash;Whitney, 1889

Fermat's Spiral

Also called a parabolic spiral, it is a type of Archimedean Spiral. A spiral is defined as "a plane…