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"Armillary Sphere, an instrument used in astronomy. In its simplest form, consisting of a ring fixed in the plane of the equator, the armilla is one of the most ancient of astronomical instruments. Slightly developed, it was crossed by another ring fixed in the plane of the meridian." — The Encyclopedia Britannica, 1910

Armilla

"Armillary Sphere, an instrument used in astronomy. In its simplest form, consisting of a ring fixed…

"Some of the Egyptian female sports were rather of a hoydenish character, as the game of ball, in one picture of which we are instructed that the loser was obliged to suffer another to ride on her back. Some of these identical balls have been found in the tombs at Thebes." — Goodrich, 1844

Egyptian Ball

"Some of the Egyptian female sports were rather of a hoydenish character, as the game of ball, in one…

A small bell inside of a glass sphere.

Bell in globe

A small bell inside of a glass sphere.

An illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16 inches.

Vertical Cross Section of Spherical Zones of a Casting

An illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16…

Possible forms of the invariable cone by means of the intersections with a concentric spherical surface.

Invariable Cone

Possible forms of the invariable cone by means of the intersections with a concentric spherical surface.

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Comparative Volumes Of A Cone, Sphere, And Cylinder

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Illustration used to compare the surfaces of a cylinder and a sphere.

Comparative Surfaces Of A Cylinder And Sphere

Illustration used to compare the surfaces of a cylinder and a sphere.

"Distrbution of electrification on a charged hollow sphere. If an insulated conductor d be inserted through the opening in the sphere and brought in contact with the interior surface and afterwards carefully removed, it will be found, by testing with the gold leaf electroscope, tat it has recieved no charge. If touched to the outside, however, the conductor will recieve part of the charge." -Hawkins, 1917

Distribution of Charge

"Distrbution of electrification on a charged hollow sphere. If an insulated conductor d be inserted…

"The Earth, whose diameter is 7,912 miles, is represented by the globe, or sphere. The straight line passing through its center, and about which it turns, is called its axis, and the two extremities of the axis are the poles of the Earth, A being the north pole, and B the south pole. The line C D, crossing the axis, passes quite round the Earth, and divides it into two equal parts. This is called the equinoctial line, or the equator. That part of the Earth situated north of this line, is caled the northern hemisphere, and that part south of it, the southern hemisphere. The small circles E F and G H, surrounding or including the poles, are called the polar circles." —Comstock, 1850

Earth Divisions

"The Earth, whose diameter is 7,912 miles, is represented by the globe, or sphere. The straight line…

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments, are externally tangent to the circle. The illustration could be used as a 3-dimensional drawing of a sphere.

2 Ellipses Inscribed In A Circle

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

A flashcard featuring an illustration of a Sphere

Flashcard of a Sphere

A flashcard featuring an illustration of a Sphere

"An artificial sphere on whose surface is drawn a map or representation of the earth." -Whitney, 1911

Terrestrial Globe

"An artificial sphere on whose surface is drawn a map or representation of the earth." -Whitney, 1911

Three suspended concentric circles free to move independently of each other at right angles.

Gyroscope

Three suspended concentric circles free to move independently of each other at right angles.

"The contours of a half sphere are a series of circles, far apart near the center (top) and near together at the outside (bottom), showing that the slope of a hemisphere varies at all points, being nearly flat on top and increasing in steepness near bottom." — Moss, 1914

Contours of a half sphere

"The contours of a half sphere are a series of circles, far apart near the center (top) and near together…

"Helios the Sun-God." —Bulfinch, 1897

Helios

"Helios the Sun-God." —Bulfinch, 1897

"Bring a metallic sphere postively charged near an insulated cylindrical conductor with hemispherical ends and provided with pith-ball and lined thread electroscopes as shown. The divergence of the pith-balls shown electrification at the ends but not at the middle of the conductor." -Avery 1895

Electrostatic Induction

"Bring a metallic sphere postively charged near an insulated cylindrical conductor with hemispherical…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

"A convex mirror is a part of a sphere, or globe, reflecting from the outside." -Comstock 1850

Convex Mirror

"A convex mirror is a part of a sphere, or globe, reflecting from the outside." -Comstock 1850

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."

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to the sphere."

Sphere Tangent to Plane

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to…

Illustration of a spherical polygon.

Spherical Polygon

Illustration of a spherical polygon.

Illustration of a spherical polygon.

Spherical Polygon

Illustration of a spherical polygon.

Illustration of a spherical pyramid.

Spherical Pyramid

Illustration of a spherical pyramid.

Illustration of a spherical sector.

Spherical Sector

Illustration of a spherical sector.

Diagram of a sphere with sectors and arcs drawn.

Sphere With Sectors and Arcs

Diagram of a sphere with sectors and arcs drawn.

Illustration of a spherical segments.

Spherical Segments

Illustration of a spherical segments.

A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant from a point within, called the center.

Sphere

A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant from…

"A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant from a point within, called the center." —Hallock 1905

Sphere

"A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant…

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal diameters.

Development of Sphere Gore Method

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal…

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

Development of Sphere Zone Method

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center. This illustration can be used to find the area of the zone and the volume of the segments.

Sphere With 8-inch Diameter Cut by Planes

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center.…

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.

"A number of rings arranged round a centre, so as to represent a sphere; used to illustrate the relative positions of the ecliptic, equator, etc., of the celestial sphere." — Williams, 1889

Armillary sphere

"A number of rings arranged round a centre, so as to represent a sphere; used to illustrate the relative…

"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…

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

Sphere Cut Into Pyramids.

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing how volume is found.

Sphere Inside of Cylinder.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing…

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.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center.

Sphere with arcs and circles labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center. This shows the zones of a sphere.

Sphere With Arcs, Circles, and Zones Labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

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…

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…

Illustration of a sphere with a polyhedral angle whose vertex is at the center of the sphere and whose face angles are measured by the sides of the polygon, whose dihedral angles have the same numerical measure as the angles of the polygon.

Polyhedral Angle in a Sphere

Illustration of a sphere with a polyhedral angle whose vertex is at the center of the sphere and whose…

Illustration of a sphere with a polyhedral angle.

Polyhedral Angle in a Sphere

Illustration of a sphere with a polyhedral angle.

Illustration showing that "the solids formed by the dissected part of the sphere are pyramids."

Sphere Formed By Pyramids

Illustration showing that "the solids formed by the dissected part of the sphere are pyramids."

A sphere with quadrants and poles. "A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through theses points."

Sphere With Quadrants and Poles

A sphere with quadrants and poles. "A point on the surface of a sphere, which is at the distance of…

A sphere with quadrants drawn on it.

Sphere With Quadrants

A sphere with quadrants drawn on it.

An illustration of a sphere showing a radius of 1 foot. Illustration could be used for calculating volume.

Sphere With a Radius of 1 foot

An illustration of a sphere showing a radius of 1 foot. Illustration could be used for calculating volume.

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

Wooden Sphere

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of one base.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of two bases.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

Illustration of equal spheres with equal triangles.

Equal Spheres With Triangles

Illustration of equal spheres with equal triangles.

Illustration of equal spheres with equilateral and equiangular triangles.

Equal Spheres With Triangles

Illustration of equal spheres with equilateral and equiangular triangles.