Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum of three pyramids (cones) whose common altitude is the altitude of the frustum and whose bases are respectively the upper base, the lower base, and a mean proportional between them."

Volume of Frustum of a Pyramid

Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

Illustration of a regular octahedron. A polyhedron with eight equal faces.

Regular Octahedron

Illustration of a regular octahedron. A polyhedron with eight equal faces.

Illustration of a the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal faces.

Bottom Half of a Regular Dodecahedron

Illustration of a the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron…

Illustration of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal faces.

Regular Dodecahedron

Illustration of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal…

Diagram used to prove the theorem: "The area of the surface generated by a straight line revolving about an axis in its plane is equal to the product of the projection of the line on the axis by the circumference whose radius is perpendicular erected at the middle point of the line and terminated by the axis."

Area of Surface Generated by a Straight Line

Diagram used to prove the theorem: "The area of the surface generated by a straight line revolving about…

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees, is equal to its spherical excess expressed in angular degrees."

Area of Spherical Triangle

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees,…

Diagram used to prove the theorem: "The volume of a spherical segment is equal to the sum of two cylinders and a sphere, the altitudes of the cylinders being one half the altitude of the segment, and their bases the upper and lower bases of the segment, respectively, and the diameter of the sphere being the altitude of the segment."

Volume of Spherical Segment

Diagram used to prove the theorem: "The volume of a spherical segment is equal to the sum of two cylinders…

The Many-flowered Darnel (Lolium multiflorum) is the most showy species of rye grass cultvated. Three to several flowered, compressed spikelets with the flat side toward the rachis. Glumes nearly equal and opposite, nerved. The lower palea like the glumes, convex on the back, awned from the tip, upper flattened. Three stamens. Mostly annuals but some are perennials.

Many-flowered Darnel

The Many-flowered Darnel (Lolium multiflorum) is the most showy species of rye grass cultvated. Three…

The Many-flowered Darnel (Lolium multiflorum) is the most showy species of rye grass cultvated. Three to several flowered, compressed spikelets with the flat side toward the rachis. Glumes nearly equal and opposite, nerved. The lower palea like the glumes, convex on the back, awned from the tip, upper flattened. Three stamens. Mostly annuals but some are perennials. A magnified spikelet is shown here.

Many-flowered Darnel

The Many-flowered Darnel (Lolium multiflorum) is the most showy species of rye grass cultvated. Three…

Illustration used to show how to divide a line into any number of equal parts by construction.

Construction Used to Divide a Line Into Equal Parts

Illustration used to show how to divide a line into any number of equal parts by construction.

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…

Civil Service Reform is equal justice for both the briber and the bribed.

Justice for Briber and Bribed

Civil Service Reform is equal justice for both the briber and the bribed.

"Argent, a lozenge, vert. The lozenge is formed by four equal and parallel lines but not rectangular, two of its opposite angles being acute, and two obtuse." -Hall, 1862

Lozenge Ordinary

"Argent, a lozenge, vert. The lozenge is formed by four equal and parallel lines but not rectangular,…

"Barry of eight pieces, azure and argent. BARRY. A field divided transversely into several equal parts, and consisting of two different tinctures interchangeably disposed." -Hall, 1862

Barry Ordinary

"Barry of eight pieces, azure and argent. BARRY. A field divided transversely into several equal parts,…

Pecopteris, frond of an ancient tree fern, was a form genus of leaves from several unrelated plant groups that flourished the early Carboniferous period and on to c. 250 Ma. Pecopteris first appeared in the Devonian period, but flourished in the Carboniferous, especially the Pennsylvanian. Plants bearing these leaves went extinct around the beginning of the Permian period.

Pecopteris Tree Fern

Pecopteris, frond of an ancient tree fern, was a form genus of leaves from several unrelated plant groups…

Strata (plural of stratum), is the geological formation of an area of land. A sequence of discrete rock layers used for age dating and identification of concurrent regional or worldwide events in the geologic record. Section from East to West across the peninsula of Michigan. The Several groups of strata from the Coal measures to the Lower Silurian.

Michigan Peninsula

Strata (plural of stratum), is the geological formation of an area of land. A sequence of discrete rock…

"Paly of four, argent and gules. PALY. A field divided by perpendicular lines into several equal parts of metal and tincture interchangeably disposed." -Hall, 1862

Paly

"Paly of four, argent and gules. PALY. A field divided by perpendicular lines into several equal parts…

"QUARTERED. A shield divided into four equal parts by a cross is said to be quartered. The quarter occupying the dexter chief is marked 1, or the first quarter; that occupying the sinister chief, 2; the dexter base, 3; the sinister base, 4; as in the annexed example." -Hall, 1862

Quartered

"QUARTERED. A shield divided into four equal parts by a cross is said to be quartered. The quarter occupying…

Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or supplementary."

Angles With Perpendicular Sides Are Equal or Supplementary Proof

Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or…

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior angles."

Exterior Angle Proof

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior…

Illustration used to prove the theorem "Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other."

2 Equal Parallelograms

Illustration used to prove the theorem "Two parallelograms are equal if two sides and the included angle…

Illustration used to prove the theorem "If three or more parallel lines intercept equal segments on one transversal, they intercept equal segments on any other transversal."

4 Parallel Lines Cut By 2 Transversals

Illustration used to prove the theorem "If three or more parallel lines intercept equal segments on…

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to one half the third side."

Line Joining Midpoints on a Triangle

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…

Illustration used to show how to divide a given straight line into any number of equal parts.

Line Divided Into Equal Parts

Illustration used to show how to divide a given straight line into any number of equal parts.

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector are equal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector…

"Grapnel. A boat's anchor having from three to six flukes placed at equal distances about the end of the shank. Also grapline." -Whitney, 1911

Grapnel

"Grapnel. A boat's anchor having from three to six flukes placed at equal distances about the end of…

"Bill shorter than head, comparatively stout at base, very acute at tip, the culmen quite convex, the gonys just appreciably concave, Tarsus a little longer that the middle tow an claw. 3d and 4th primaries about equal and longest, 5th and 6th successively slightly shorter, 2 d equal to 7th, 1st equal to penultimae secondary in the closed wing. Entire upper parts, including surfaces of wings and tail, uniform dull pale grayish-brown, with narrow, faintly-rusty edge of the wing-coverts and inner quills, and equally obscure whitish tipping of the tail-feathers. No maxillary nor auricular streaks; no markings about the head except slight speckling on the cheeks. Under parts brownish-white, palest (nearly white) on the belly and throat, more numerous small arrow-head spots on the color of the back. Bill light-colored at base below." Elliot Coues, 1884

Arizona Thrasher

"Bill shorter than head, comparatively stout at base, very acute at tip, the culmen quite convex, the…

"Bill shorter than head, slender, straight, depressed at base, compressed at end, notched. Wings long, pointed, the tip formed by the 2d-4th quills, the 1st spurious, scarcely or not one-fourth as long as the 2d. Tail much shorter than wing, square. Tarsi booted, but with 4 scutella below in front; long and slender, much exceeding the middle toe and claw; lateral toes of about equal lengths, very short, the tips of their claws not reaching the base of the middle claw; claws little curved; feet thus adapted to terrestrial habits." Elliot Coues, 1884

Stone Chats

"Bill shorter than head, slender, straight, depressed at base, compressed at end, notched. Wings long,…

This silk fabric shows a design of groups of flowers, fern leaves and trails of ivy.

Silk Fabric

This silk fabric shows a design of groups of flowers, fern leaves and trails of ivy.

The frieze is a long stretch of a sculpted decoration that is typically found under crown moldings or cornices. This frieze in ornamented with flowers, leaves and groups of fruit.

Frieze

The frieze is a long stretch of a sculpted decoration that is typically found under crown moldings or…

This inkstand is designed in a Cinquecento (Italian 16th century) style. It is made of part gold, part silver, gilt and enamel. There is a bird in the front that is attacking a dragon. The groups of figures in the back signify moral Christian Virtues and domestic scenes.

Inkstand

This inkstand is designed in a Cinquecento (Italian 16th century) style. It is made of part gold, part…

Color flag of Algeria. Two equal vertical bands of green (hoist side) and white; a red, five-pointed star within a red crescent centered over the two-color boundary.

Flag of Algeria, 2009

Color flag of Algeria. Two equal vertical bands of green (hoist side) and white; a red, five-pointed…

Black and white outline flag of Algeria. Two equal vertical bands of green (hoist side) and white; a red, five-pointed star within a red crescent centered over the two-color boundary

Flag of Algeria, 2009

Black and white outline flag of Algeria. Two equal vertical bands of green (hoist side) and white; a…

Color flag of Angola. Two equal horizontal bands of red (top) and black with a centered yellow emblem consisting of a five-pointed star within half a cogwheel crossed by a machete (in the style of a hammer and sickle).

Flag of Angola, 2009

Color flag of Angola. Two equal horizontal bands of red (top) and black with a centered yellow emblem…

Black and white outline flag of Angola. Two equal horizontal bands of red (top) and black with a centered yellow emblem consisting of a five-pointed star within half a cogwheel crossed by a machete (in the style of a hammer and sickle)

Flag of Angola, 2009

Black and white outline flag of Angola. Two equal horizontal bands of red (top) and black with a centered…

Color flag of Armenia. Three equal horizontal bands of red (top), blue, and orange.

Flag of Armenia, 2009

Color flag of Armenia. Three equal horizontal bands of red (top), blue, and orange.

Black and white outline flag of Armenia. Three equal horizontal bands of red (top), blue, and orange

Flag of Armenia, 2009

Black and white outline flag of Armenia. Three equal horizontal bands of red (top), blue, and orange

Color flag of Austria. Three equal horizontal bands of red (top), white, and red.

Flag of Austria, 2009

Color flag of Austria. Three equal horizontal bands of red (top), white, and red.

Black and white outline flag of Austria. Three equal horizontal bands of red (top), white, and red

Flag of Austria, 2009

Black and white outline flag of Austria. Three equal horizontal bands of red (top), white, and red

Color flag of Azerbaijan. Three equal horizontal bands of blue (top), red, and green; a crescent and eight-pointed star in white are centered in red band.

Flag of Azerbaijan, 2009

Color flag of Azerbaijan. Three equal horizontal bands of blue (top), red, and green; a crescent and…

Black and white outline flag of Azerbaijan. Three equal horizontal bands of blue (top), red, and green; a crescent and eight-pointed star in white are centered in red band

Flag of Azerbaijan, 2009

Black and white outline flag of Azerbaijan. Three equal horizontal bands of blue (top), red, and green;…

Color flag of the Bahamas, Three equal horizontal bands of aquamarine (top), gold, and aquamarine, with a black equilateral triangle based on the hoist side.

Flag of the Bahamas, 2009

Color flag of the Bahamas, Three equal horizontal bands of aquamarine (top), gold, and aquamarine, with…

Black and white outline flag of the Bahamas. Three equal horizontal bands of aquamarine (top), gold, and aquamarine, with a black equilateral triangle based on the hoist side

Flag of Bahamas, The, 2009

Black and white outline flag of the Bahamas. Three equal horizontal bands of aquamarine (top), gold,…

Color flag of Barbados. Three equal vertical bands of blue (hoist side), gold, and blue with the head of a black trident centered on the gold band; the trident head represents independence and a break with the past (the colonial coat of arms contained a complete trident).

Flag of Barbados, 2009

Color flag of Barbados. Three equal vertical bands of blue (hoist side), gold, and blue with the head…

Black and white outline flag of Barbados. Three equal vertical bands of blue (hoist side), gold, and blue with the head of a black trident centered on the gold band; the trident head represents independence and a break with the past (the colonial coat of arms contained a complete trident)

Flag of Barbados, 2009

Black and white outline flag of Barbados. Three equal vertical bands of blue (hoist side), gold, and…

Color flag of Belgium. Three equal vertical bands of black (hoist side), yellow, and red.

Flag of Belgium, 2009

Color flag of Belgium. Three equal vertical bands of black (hoist side), yellow, and red.

Black and white outline flag of Belgium. Three equal vertical bands of black (hoist side), yellow, and red

Flag of Belgium, 2009

Black and white outline flag of Belgium. Three equal vertical bands of black (hoist side), yellow, and…

Color flag of Benin. Two equal horizontal bands of yellow (top) and red (bottom) with a vertical green band on the hoist side.

Flag of Benin, 2009

Color flag of Benin. Two equal horizontal bands of yellow (top) and red (bottom) with a vertical green…

Black and white outline flag of Benin. Two equal horizontal bands of yellow (top) and red (bottom) with a vertical green band on the hoist side

Flag of Benin, 2009

Black and white outline flag of Benin. Two equal horizontal bands of yellow (top) and red (bottom) with…

Color flag of Bulgaria. Three equal horizontal bands of white (top), green, and red.

Flag of Bulgaria, 2009

Color flag of Bulgaria. Three equal horizontal bands of white (top), green, and red.

Black and white outline flag of Bulgaria. Three equal horizontal bands of white (top), green, and red

Flag of Bulgaria, 2009

Black and white outline flag of Bulgaria. Three equal horizontal bands of white (top), green, and red

Color flag of Burkina Faso. Two equal horizontal bands of red (top) and green with a yellow five-pointed star in the center.

Flag of Burkina Faso, 2009

Color flag of Burkina Faso. Two equal horizontal bands of red (top) and green with a yellow five-pointed…

Black and white outline flag of Burkina Faso. Two equal horizontal bands of red (top) and green with a yellow five-pointed star in the center

Flag of Burkina Faso, 2009

Black and white outline flag of Burkina Faso. Two equal horizontal bands of red (top) and green with…

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 Central African Republic. Four equal horizontal bands of blue (top), white, green, and yellow with a vertical red band in center; a yellow five-pointed star to the hoist side of the blue band.

Flag of Central African Republic, 2009

Color flag of Central African Republic. Four equal horizontal bands of blue (top), white, green, and…

Black and white outline flag of Central African Republic. Four equal horizontal bands of blue (top), white, green, and yellow with a vertical red band in center; a yellow five-pointed star to the hoist side of the blue band

Flag of Central African Republic, 2009

Black and white outline flag of Central African Republic. Four equal horizontal bands of blue (top),…

Color flag of Chad. Three equal vertical bands of blue (hoist side), yellow, and red.

Flag of Chad, 2009

Color flag of Chad. Three equal vertical bands of blue (hoist side), yellow, and red.

Black and white outline flag of Chad. Three equal vertical bands of blue (hoist side), yellow, and red

Flag of Chad, 2009

Black and white outline flag of Chad. Three equal vertical bands of blue (hoist side), yellow, and red