ClipArt ETC
Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described from its vertex as a ole and included between its sides (produced if necessary)."

Measure of a Spherical Angle

Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described…

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 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…

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 used to construct a circle when given three points.

Construction of Circle Given 3 Points

Illustration used to construct a circle when given three points.

Illustration used to draw a tangent to a circle.

Construction of Tangent to a Circle

Illustration used to draw a tangent to a circle.

Illustration used to find the center of a circle.

Center of a Circle

Illustration used to find the center of a circle.

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 used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

"Azure, an annulet argent. Annulets are added to arms for a difference. ANNULET. A small circle borne as a charge in coats of arms." -Hall, 1862

Annulet

"Azure, an annulet argent. Annulets are added to arms for a difference. ANNULET. A small circle borne…

A sign may be used in advance of an intersection to indicate the presence of an intersection and the possibility of turning or entering traffic. The Circular Intersection symbol sign accompanied by an educational TRAFFIC CIRCLE plaque may be installed in advance of a circular intersection.

Circular Intersection, Black and White

A sign may be used in advance of an intersection to indicate the presence of an intersection and the…

A sign may be used in advance of an intersection to indicate the presence of an intersection and the possibility of turning or entering traffic. The Circular Intersection symbol sign accompanied by an educational TRAFFIC CIRCLE plaque may be installed in advance of a circular intersection.

Circular Intersection, Color

A sign may be used in advance of an intersection to indicate the presence of an intersection and the…

A sign may be used in advance of an intersection to indicate the presence of an intersection and the possibility of turning or entering traffic. The Circular Intersection symbol sign accompanied by an educational TRAFFIC CIRCLE plaque may be installed in advance of a circular intersection.

Circular Intersection, Outline

A sign may be used in advance of an intersection to indicate the presence of an intersection and the…

A sign may be used in advance of an intersection to indicate the presence of an intersection and the possibility of turning or entering traffic. The Circular Intersection symbol sign accompanied by an educational TRAFFIC CIRCLE plaque may be installed in advance of a circular intersection.

Circular Intersection, Silhouette

A sign may be used in advance of an intersection to indicate the presence of an intersection and the…

"DIADEM, a circle of gold with points rising from it, worn by ancient kings as the token of royalty. The diadem of most of the monarchs of Europe, as represented in ancient statuary, stained glass, and paintings, resembles the annexed engraving; the kings of England, from the Conquest to Henry VII., all wore a diadem of this shape." -Hall, 1862

Diadem

"DIADEM, a circle of gold with points rising from it, worn by ancient kings as the token of royalty.…

"EASTERN CROWN. A crown with rays proceeding from a circle, called by heralds an Eastern crown, is found in ancient achievements. The annexed cut shows its form." -Hall, 1862

Eastern Crown

"EASTERN CROWN. A crown with rays proceeding from a circle, called by heralds an Eastern crown, is found…

"The Young Variable Gordius, after escaping from the egg. b, the first circle of hooklets bordering the collar reflected, and protrusion of the second circle of hooklets and the style." -Whitney, 1911

Gordian Worm

"The Young Variable Gordius, after escaping from the egg. b, the first circle of hooklets bordering…

"Fig 27. - Bones of the right wing of a duck, Clangula islandica, A, shoulder, omos; B, elbow, ancon; C, wrist, carpus; D, end of principal finger; E, end of hand proper, metacarpus. AB, upper arm, brachium; BC, fore-arm, antibrachium; CD, whole hand or pinion, manus; composed of CE, hand proper or metacarpus, excepting d2; ED, or d2, d3, d4, fingers, digits, digiti, h, humerus; rd, radius; ul, ulna; sc, outer carpal, scapholunare or radiale; cu, inner carpal, cuneiforme or ulnare; these two composing wrist or carpus. mc, the compound hand-bone or metcarpus, composed of three metacarpal bones, bearing as many digits - the outer digit seated upon a protuberance at the head of the metacarpal, the other two situated at the end of the bone. d2, the outer or radial digit, commonly called the thumb or pollex, composed or two phalanges; d3, the middle digit, of two phalanges; d4, the inner or ulnar digit, of one phalanx d2 is the seat of the feathers of the bastard wing or alula. D to C (whole pinion), seat of the flight feathers called primaries; C to B (fore-arm), seat of the secondaries; at B and above it in direction of A, seat of tertiaries proper; below A, in direction of B, seat of scapularies (upon pteryla humeralis), often called tertiaries. The wing shown half-spread: complete extension would bring A B C D into a right line; in complete folding C goes to A, and D to B; all these motions nearly in the plane of the paper. The elbow-joint and wrist are such perfect hinges, that, in opening or closing the wing, C cannot sink below the paper, nor D fly up above the paper, as would otherwise be the effect of the pressure of the air upon the flight-feathers. Observe also rd and ul are two rods connecting B and C; the construction of their joining at B and C, and with each other, is such, that they can slide lengthwise a little upon each other. Now when the point C, revolving about B, approaches A in the arc of a circle, rd pushes on sc, while ul pulls back cu; the motion is transmitted to D, and makes this point approach B. conversely, in opening the wing, rd pulls back sc, and ul pushes on cu, making D recede from B. In other words, the angle A B C cannot be increased or diminished without similarly increasing or diminishing the angle B C D; so that no part of the wing can be opened or shut without automatically opening or shutting the rest..." Elliot Coues, 1884

The Bones of the Right Wing of a Duck

"Fig 27. - Bones of the right wing of a duck, Clangula islandica, A, shoulder, omos; B, elbow, ancon;…

Illustration of a circle with radius QR.

Radius of a Circle

Illustration of a circle with radius QR.

Illustration of a circle with diameter BC, chord DF, secant MN, and tangent HK.

Chords, Secants, Diameters, and Tangents of a Circle

Illustration of a circle with diameter BC, chord DF, secant MN, and tangent HK.

Illustration of a circle with diameter AB. Radii are RO, SO, AO, and BO. ED is a chord.

Chords, Diameters, and Radii of a Circle

Illustration of a circle with diameter AB. Radii are RO, SO, AO, and BO. ED is a chord.

Illustration of a circle with central angle AOB.

Central Angle in a Circle

Illustration of a circle with central angle AOB.

This vase is sculpted to resemble a flower. It has several shaped petals at the top, with an open center. There are also protruding petals that circle the entire base.

Floral Vase

This vase is sculpted to resemble a flower. It has several shaped petals at the top, with an open center.…

This book cover has a design of the four great seasons. It is stamped in the center with a circle that includes the twelve signs of the zodiac. In the center of the circle is a floral grouping.

Book Cover

This book cover has a design of the four great seasons. It is stamped in the center with a circle that…

This brooch has a square design in the center with a half circle on each side of the square.

Brooch

This brooch has a square design in the center with a half circle on each side of the square.

This round brooch is in the shape of a circle with a half moon shape laying on the interior bottom edge of the circle. It has a pin that goes through the center of the brooch.

Round Brooch

This round brooch is in the shape of a circle with a half moon shape laying on the interior bottom edge…

This brooch watch is designed to be pinned on a garment. It shaped in a snake that is formed into a circle, with a small watch in the center that is held by the serpents mouth.

Brooch Watch

This brooch watch is designed to be pinned on a garment. It shaped in a snake that is formed into a…

Color flag of Cape Verde. Five unequal horizontal bands; the top-most band of blue - equal to one half the width of the flag - is followed by three bands of white, red, and white, each equal to 1/12 of the width, and a bottom stripe of blue equal to one quarter of the flag width; a circle of 10, yellow, five-pointed stars, each representing one of the islands, is centered on the red stripe and positioned 3/8 of the length of the flag from the hoist side. <p>Historically, the name "Cape Verde" has been used in English for the archipelago and, since independence in 1975, for the country. In 2013, the Cape Verdean government determined that the Portuguese designation "Cabo Verde" would henceforth be used for official purposes, such as at the United Nations, even in English contexts.

Flag of Cape Verde, 2009

Color flag of Cape Verde. Five unequal horizontal bands; the top-most band of blue - equal to one half…

Black and white outline flag of Cape Verde. Five unequal horizontal bands; the top-most band of blue - equal to one half the width of the flag - is followed by three bands of white, red, and white, each equal to 1/12 of the width, and a bottom stripe of blue equal to one quarter of the flag width; a circle of 10, yellow, five-pointed stars, each representing one of the islands, is centered on the red stripe and positioned 3/8 of the length of the flag from the hoist side. <p>Historically, the name "Cape Verde" has been used in English for the archipelago and, since independence in 1975, for the country. In 2013, the Cape Verdean government determined that the Portuguese designation "Cabo Verde" would henceforth be used for official purposes, such as at the United Nations, even in English contexts.

Flag of Cape Verde, 2009

Black and white outline flag of Cape Verde. Five unequal horizontal bands; the top-most band of blue…

Color flag of Cook Islands. Blue, with the flag of the UK in the upper hoist-side quadrant and a large circle of 15 white five-pointed stars (one for every island) centered in the outer half of the flag.

Flag of Cook Islands, 2009

Color flag of Cook Islands. Blue, with the flag of the UK in the upper hoist-side quadrant and a large…

Black and white outline flag of Cook Islands. Blue, with the flag of the UK in the upper hoist-side quadrant and a large circle of 15 white five-pointed stars (one for every island) centered in the outer half of the flag

Flag of Cook Islands, 2009

Black and white outline flag of Cook Islands. Blue, with the flag of the UK in the upper hoist-side…

Color flag of European Union Blue field with 12 five-pointed gold stars arranged in a circle in the center, representing the union of the peoples of Europe; the number of stars is fixed

Flag of the European Union, 2009

Color flag of European Union Blue field with 12 five-pointed gold stars arranged in a circle in the…

Black and white outline flag of European Union Blue field with 12 five-pointed gold stars arranged in a circle in the center, representing the union of the peoples of Europe; the number of stars is fixed

Flag of the European Union, 2009

Black and white outline flag of European Union Blue field with 12 five-pointed gold stars arranged in…

Color flag of Singapore. Two equal horizontal bands of red (top) and white; near the hoist side of the red band, there is a vertical, white crescent (closed portion is toward the hoist side) partially enclosing five white five-pointed stars arranged in a circle.

Flag of Singapore, 2009

Color flag of Singapore. Two equal horizontal bands of red (top) and white; near the hoist side of the…

Black and white outline flag of Singapore. Two equal horizontal bands of red (top) and white; near the hoist side of the red band, there is a vertical, white crescent (closed portion is toward the hoist side) partially enclosing five white five-pointed stars arranged in a circle

Flag of Singapore, 2009

Black and white outline flag of Singapore. Two equal horizontal bands of red (top) and white; near the…

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.

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they subtend equal arcs; conversely, if two arcs are equal, the chords that subtend them are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord subtends the greater minor arc; conversely, if two minor arcs are unequal, the chord that subtends the greater arc is the greater."

Unequal Chords in Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its subtended arc."

Diameter Perpendicular to a Chord in a Circle

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its…

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they are equally distant from the center; conversely, if two chords are equally distant from the center, they are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "A tangent to a circle is perpendicular to the radius drawn to the point of tangency."

Tangent to Perpendicular Radius Circle Theorem

Illustration used to show that "A tangent to a circle is perpendicular to the radius drawn to the point…

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

Quadrilateral Circumscribed About a Circle

Illustration of a quadrilateral circumscribed about a circle. This could also be described as a circle…

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents are equal."

Equal Tangents to Circle Theorem

Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents…

Illustration used to inscribe a circle in a given triangle.

Construction Used to Inscribe a Circle in a Triangle

Illustration used to inscribe a circle in a given triangle.

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of a triangle and to the the other two sides prolonged is said to be escribed to the triangle."

Construction Used to Escribe a Circle to a Triangle

Illustration used to escribe a circle to a given triangle. "A circle which is tangent to one side of…

Illustration used to circumscribe a circle about a given triangle.

Construction Used to Circumscribe a Circle About a Triangle

Illustration used to circumscribe a circle about a given triangle.

Illustration used to prove "If two circumferences meet at a point which is not on their line of centers, they also meet in one other point."

Circumferences of 2 Circles

Illustration used to prove "If two circumferences meet at a point which is not on their line of centers,…

Illustration of two circles that are externally tangent to each other.

2 Externally Tangent Circles

Illustration of two circles that are externally tangent to each other.

Illustration of two circles that are internally tangent to each other.

2 Internally Tangent Circles

Illustration of two circles that are internally tangent to each other.

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc."

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are commensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are incommensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle is measured by one half of its intercepted arc." In this case, one side of angle ABC passes through the center of the circle.

Inscribed Angle in a Circle Proof

Illustration of a circle with an inscribed angle that can be used to prove that "An inscribed angle…