Illustration of pattern showing steps to make a barn. The barn is a composite figure made up of a triangular prism and a rectangular solid.

Pattern To Make A Barn

Illustration of pattern showing steps to make a barn. The barn is a composite figure made up of a triangular…

Illustration of pattern showing steps to make a box.

Pattern To Make A Box

Illustration of pattern showing steps to make a box.

Projection of a circular ring.

Projection of Circular Ring

Projection of a circular ring.

Illustration showing the combination of various regular systems.

Combination Forms

Illustration showing the combination of various regular systems.

Illustration showing the combination of various regular systems.

Combination Forms

Illustration showing the combination of various regular systems.

Illustration showing the combination of various regular systems.

Combination Forms

Illustration showing the combination of various regular systems.

Illustration showing the combination of various regular systems.

Combination Forms

Illustration showing the combination of various regular systems.

Illustration showing the combination of various regular systems.

Combination Forms

Illustration showing the combination of various regular systems.

Illustration showing tetragonal combination forms.

Tetragonal Combinations

Illustration showing tetragonal combination forms.

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into the cylinder.

Comparative Volumes Of A Cone And Cylinder

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into…

Illustration of a cone of revolution used to show that the lateral area is equal to half the product of the slant height by the circumference of the base.

Lateral Area of Cone of Revolution

Illustration of a cone of revolution used to show that the lateral area is equal to half the product…

Development and top completion exercise problem of the cone by dividing the base into equal parts and creating an arc to revolve the sides of the plane.

Development Exercise of Cone

Development and top completion exercise problem of the cone by dividing the base into equal parts and…

Illustration of the development of a cone. When the cone covered in paper (figure a) is rolled out on a flat surface, the result is shown in figure b.

Development Of Cone

Illustration of the development of a cone. When the cone covered in paper (figure a) is rolled out on…

Illustration of a double cone.

Double Cone

Illustration of a double cone.

Illustration of a frustum of a cone.

Frustum of a Cone

Illustration of a frustum of a cone.

Frustum of a cone.

Frustum of Cone

Frustum of a cone.

Frustum of a cone.

Frustum of Cone

Frustum of a cone.

"The lateral area of a frustum of a cone of revolution is equal to half the sum of the circumferences of its bases multiplied by the slant height."

Frustum of Cone to Find Lateral Area

"The lateral area of a frustum of a cone of revolution is equal to half the sum of the circumferences…

"The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum."

Frustum of Cone to Find Volume

"The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose…

Illustration showing the intersection of a plane with a cone.

Intersection Of A Plane And Cone

Illustration showing the intersection of a plane with a cone.

Illustration showing the intersection of a plane with a cone. The solid is shown in perspective and the triangles that are to be located in the projections are represented in the drawing.

Intersection Of A Plane And Cone

Illustration showing the intersection of a plane with a cone. The solid is shown in perspective and…

Illustration of an oblique cone.

Oblique Cone

Illustration of an oblique cone.

Illustration of the intersection of a cone and a plane.

Intersection of a Cone and a Plane

Illustration of the intersection of a cone and a plane.

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Plane Parallel to Base, Passing Through a Cone

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Plane Parallel to Base, Passing Through a Cone

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Plane Passing Through the Vertex of a Cone

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Plane Passing Through the Vertex of a Cone

Illustration of a plane passing through the vertex of a cone (section made is a triangle).

Illustration of the projection of a cone that is rightly inclined.

Projection Of Cone

Illustration of the projection of a cone that is rightly inclined.

Illustration of the projection of a cone that is obliquely inclined.

Projection Of Cone

Illustration of the projection of a cone that is obliquely inclined.

Illustration of a pyramid circumscribed about a cone.

Pyramid Circumscribed About a Cone

Illustration of a pyramid circumscribed about a cone.

Illustration of a pyramid and with a regular polygon inscribed in and circumscribed about a cone. "If a pyramid whose base is a regular polygon is inscribed in or circumscribed about a circular cone, and if the number of sides of the base of the pyramid is indefinitely increased, the volume of the cone is the limit of the volume of the pyramid, and the lateral area of the cone is the limit of the lateral area of the pyramid."

Cone With Regular Polygon Inscribed and Circumscribed About

Illustration of a pyramid and with a regular polygon inscribed in and circumscribed about a cone. "If…

Illustration of a pyramid inscribed in a cone.

Pyramid Inscribed in a Cone

Illustration of a pyramid inscribed in a cone.

Illustration of a cone of revolution.

Cone of Revolution

Illustration of a cone of revolution.

Illustration of a cone of revolution.

Cone of Revolution

Illustration of a cone of revolution.

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 of a plane tangent to a cone which contains one element of the cone but does not cut the surface.

Tangent Plane to a Cone

Illustration of a plane tangent to a cone which contains one element of the cone but does not cut the…

Illustration of a cone with a polygon inscribed used to show that the volume of a circular cone is equal to one third the product of its base by its altitude.

Volume of Cone

Illustration of a cone with a polygon inscribed used to show that the volume of a circular cone is equal…

Illustration of the intersection of 3 cones.

3 Intersecting Cones

Illustration of the intersection of 3 cones.

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones by using series of cone development.

Development Exercise of Flange and Hood Cones

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones…

Illustration of a right circular cone and an oblique cone.

Right and Oblique Cones

Illustration of a right circular cone and an oblique cone.

Illustration showing solid twin crystals.

Twin Crystals

Illustration showing solid twin crystals.

Illustration of 3-dimensional cube with hidden edges shown.

Cube

Illustration of 3-dimensional cube with hidden edges shown.

Cube rotated 30° with vertical plane.

Cube Rotated 30°

Cube rotated 30° with vertical plane.

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

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.

Illustration of a right circular cylinder with a smaller cylinder removed from the center and placed next to it.

Cylinder Cut From a Cylinder

Illustration of a right circular cylinder with a smaller cylinder removed from the center and placed…

Projection of a cylinder with a circular hole.

Projection of Cylinder With Circular Hole

Projection of a cylinder with a circular hole.

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing area.

Development Exercise of Cylinder

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing…

Illustration of the development of a cylinder. The cylinder is covered with paper (a) and then rolled out (b) showing the outer edges are parallel.

Development Of Cylinder

Illustration of the development of a cylinder. The cylinder is covered with paper (a) and then rolled…

Illustration of a hollow cylinder.

Hollow Cylinder

Illustration of a hollow cylinder.

Illustration of a thin hollow cylinder. It resembles a washer and is often referred to as a disc.

Hollow Cylinder

Illustration of a thin hollow cylinder. It resembles a washer and is often referred to as a disc.

Illustration of a hollow cylinder viewed at an angle.

Hollow Cylinder

Illustration of a hollow cylinder viewed at an angle.

Illustration of a hollow cylinder viewed at an angle from above.

Hollow Cylinder

Illustration of a hollow cylinder viewed at an angle from above.

Illustration of a shaded horizontal cylinder, viewed from the side.

Horizontal Cylinder

Illustration of a shaded horizontal cylinder, viewed from the side.

Illustration of a narrow right circular cylinder (with the height much smaller than the diameter) resting on its side/edge. This could also be described as a round disc.

Narrow Cylinder on Side

Illustration of a narrow right circular cylinder (with the height much smaller than the diameter) resting…

Illustration showing the intersection of a plane with a cylinder.

Plane Intersecting Cylinder

Illustration showing the intersection of a plane with a cylinder.

Illustration of a plane passing through a cylinder. Every section of a cylinder made by a plane passing through an element is a parallelogram.

Plane Passing Through A Cylinder

Illustration of a plane passing through a cylinder. Every section of a cylinder made by a plane passing…