ClipArt ETC
"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis." — Ford, 1912

Chalcocite

"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis."…

"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis. Often twinned in pseudohexagonal forms." — Ford, 1912

Chalcocite

"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis.…

The chord of a circle.

Circle Chord

The chord of a circle.

A circle and triangle situated on coordinate planes.

Circle

A circle and triangle situated on coordinate planes.

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

Illustration of a circle used to prove "All angles inscribed in the same segment are equal."

Angles Inscribed in the Same Segment Circle Proof

Illustration of a circle used to prove "All angles inscribed in the same segment are equal."

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…

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, center O lies within angle ABC.

Inscribed Angle in a Circle Proof

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

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, center O lies outside angle ABC.

Inscribed Angle in a Circle Proof

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

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an obtuse angle."

Obtuse Angles Inscribed in Circle Proof

Illustration of a circle used to prove "Any angle inscribed in a segment less than a semicircle is an…

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the given radius r to the radius R of the circle, and draw the arc cd. Draw the line ce parallel with and at a distance r from the line AB. Then the crossing c is the center of the required circle that will tangent the given line and circle."

Construction Of A Circle Tangent To A Line And A Circle

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the…

An illustration showing how to construct a circle that tangents two given lines and goes through a given point c on the line FC, which bisects the angle of the lines. "Through C draw AB at right angles to CF; bisect the angles DAB and EBA, and the crossing on CF is the center of the required circle."

Construction Of A Circle That Tangents 2 Given Lines And Goes Through A Given Point

An illustration showing how to construct a circle that tangents two given lines and goes through a given…

An illustration showing how to construct a circle that tangents two given lines inclined to one another with the one tangenting point being given. "Draw the center line GF. From E, draw EF at right angles to AB; then F is the center of the circle required.

Construction Of A Circle That Tangents 2 Given Lines

An illustration showing how to construct a circle that tangents two given lines inclined to one another…

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 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 circle with central angle AOB.

Central Angle in a Circle

Illustration of a circle with central angle AOB.

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 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 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.

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…

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…

An illustration showing how to find the center of a circle which will pass through three given points A, B, and C. "With B as a center, draw the arc DEFG; and with the same radius and A as a center, draw the cross arcs D and F; also with C as a center, draw the cross arcs E and G. Join D and F, and also E and G, and the crossing o is the required center of the circle."

Find The Center Of A Circle Through 3 Points

An illustration showing how to find the center of a circle which will pass through three given points…

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…

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

Quadrilateral Inscribed In A Circle

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

Illustration of a circle with radius QR.

Radius of a Circle

Illustration of a circle with radius QR.

An illustration showing a circle with radius r, diameter d, and chord c.

Radius, Diameter, and Chord In A Circle

An illustration showing a circle with radius r, diameter d, and chord c.

An illustration showing a triangle with sides b, c, and d inscribed in a circle with radius r.

Triangle Inscribed In A Circle

An illustration showing a triangle with sides b, c, and d inscribed in a circle with radius r.

An illustration showing a triangle with angles A, C, and D inscribed in a circle which is tangent to a line.

Triangle Inscribed In A Circle

An illustration showing a triangle with angles A, C, and D inscribed in a circle which is tangent to…

A line of interlocking circles.

Circles

A line of interlocking circles.

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 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 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 "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 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 showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

2 Intersecting Circles

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

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,…

"Orthohombic. Habit of crystals is short prismatic; often in square prisms because of prominent development of the vertical pinacoids. Terminated by basal plane, pyramids and domes; frequently complex." — Ford, 1912

Columbite

"Orthohombic. Habit of crystals is short prismatic; often in square prisms because of prominent development…

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart at the outside (bottom)." — Moss, 1914

Contours of a concave cone

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart…

The contours of a cone are circles of different sizes, one within another, and the same distance apart, because the slope is at all points the same." — Moss, 1914

Contours of a cone

The contours of a cone are circles of different sizes, one within another, and the same distance apart,…

Conic sections, cones divided by a plane.

Conic Sections

Conic sections, cones divided by a plane.

Illustration showing the correct and incorrect position of a right line pen against a T-square, triangle, or straight edge when doing geometric constructions.

Positioning Pen for Constructions

Illustration showing the correct and incorrect position of a right line pen against a T-square, triangle,…

Finding the equation of a line with polar coordinates.

Polar Coordinates

Finding the equation of a line with polar coordinates.

Changing from polar to rectangular coordinates.

Rectangular Coordinates

Changing from polar to rectangular coordinates.

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cormorant.

Cormorant

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cormorant.

Cormorant

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cormorant.

Cormorant

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cormorant.

Cormorant

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting lines also intersect."

Intersecting Lines Corollary

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting…

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular to the line."

Perpendicular to Line Corollary

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular…

Corundum.

Corundum

Corundum.

Corundum.

Corundum

Corundum.

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." — Ford, 1912

Corundum

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." —…

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." — Ford, 1912

Corundum

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." —…

A beryl crystal, an example of a basal pinacoid.

Beryl crystal

A beryl crystal, an example of a basal pinacoid.

A beryl crystal, an example of a basal pinacoid.

Beryl crystal

A beryl crystal, an example of a basal pinacoid.

A beryl crystal, an example of a basal pinacoid.

Beryl crystal

A beryl crystal, an example of a basal pinacoid.