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.

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,…

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.

Illustration of the intersection of a cylinder and a sphere.

Intersecting Cylinder and Sphere

Illustration of the intersection of a cylinder and a sphere.

Illustration of the intersection of a cylinder and a sphere.

Intersecting Cylinder and Sphere

Illustration of the intersection of a cylinder and a sphere.

"The double convex lens may be described as the part common to two spheres that intersect each other. The centers of the limiting spherical surfaces, as c and C, are the centers of curvature. The straight line, XY, passing through the centers of curvature is the principal axis of the lens." -Avery 1895

Double Convex Lens

"The double convex lens may be described as the part common to two spheres that intersect each other.…

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.

Illustration of a sphere with sectors and arcs.

Sphere With Sectors and Arcs

Illustration of a sphere with sectors and arcs.

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.

"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 showing the development of a sphere by the perspective of its resolved cones.

Development Of Sphere

Illustration showing the development of a sphere by the perspective of its resolved cones.

An illustration of a hollow sphere.

Hollow Sphere

An illustration of a hollow sphere.

Illustration of a sphere inscribed in a cube.

Sphere Inscribed in a Cube

Illustration of a sphere inscribed in a cube.

Illustration of a sphere inscribed in a cube.

Sphere Inscribed in a Cube

Illustration of a sphere inscribed in a cube.

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 sphere generated by the revolution of a semicircle ACB about its diameter AB as an axis.

Sphere Made by Revolution of Semicircle

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an…

Illustration of a material sphere that can be used to find its diameter.

Material Sphere

Illustration of a material sphere that can be used to find its diameter.

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.

An illustration of a segment of a sphere.

Segment Of Sphere

An illustration of a segment of a sphere.

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.

Zone Of Sphere

An illustration of a zone of a sphere.

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.

Illustration of two intersecting spheres. "The intersection of two spherical surfaces is the circumference of a circle whose plane is perpendicular to the line joining the centres of the surfaces and whose centre is in that line."

Intersecting Spheres

Illustration of two intersecting spheres. "The intersection of two spherical surfaces is the circumference…

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…

An illustration of a flanged spherical segment with a diameter of 10 inches. Illustration could be used to find the area.

Flanged Spherical Segment

An illustration of a flanged spherical segment with a diameter of 10 inches. Illustration could be used…

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…

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater angle, and conversely."

Side Comparison of Spherical Triangle

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater…

Diagram showing 2 superimposed symmetrical spherical triangles.

Superimposed Symmetrical Spherical Triangles

Diagram showing 2 superimposed symmetrical spherical triangles.

Diagram showing 2 symmetrical spherical triangles.

Symmetrical Spherical Triangles

Diagram showing 2 symmetrical spherical triangles.

Illustration of an isosceles spherical triangle.

Isosceles Spherical Triangle

Illustration of an isosceles spherical triangle.