The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel to the base.

Frustum Pyramid

The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel…

The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids 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 Pyramid for Volume

The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose…

The frustum of a pentagonal pyramid is the portion of a pyramid included between the base and a section parallel to the base.

Frustum of Pentagonal Pyramid

The frustum of a pentagonal pyramid is the portion of a pyramid included between the base and a section…

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a right hexagonal pyramid with hidden edges shown.  The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

An illustration of a pyramid with a hexagonal base.

Pyramid With Hexagonal Base

An illustration of a pyramid with a hexagonal base.

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Decagonal Pyramid

Illustration of a hollow right decagonal pyramid. The base is a decagon and the faces are isosceles…

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Hexagonal Pyramid

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles…

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Nonagonal Pyramid

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles…

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Octagonal Pyramid

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles…

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Inverted Pentagonal Pyramid

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Rectangular Pyramid

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top. The hidden edges are shown in this drawing.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of the isometric of an oblique pentagonal pyramid.

Isometric of Oblique Pentagonal Pyramid

Illustration of the isometric of an oblique pentagonal pyramid.

Illustration of a right nonagonal pyramid with hidden edges shown.  The base is a nonagon and the faces are isosceles triangles.

Nonagonal Pyramid

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces…

Illustration of a plan and elevation of an oblique pentagonal pyramid.

Oblique Pentagonal Pyramid

Illustration of a plan and elevation of an oblique pentagonal pyramid.

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces are isosceles triangles.

Octagonal Pyramid

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an…

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces…

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Pentagonal Pyramid For Volume

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles. The height of the pyramid is much larger then the length and width of the base.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

An illustration of a regular pyramid with a square base and labels on lateral edge, slant height, altitude, and all corners.

Regular Pyramid With Square Base

An illustration of a regular pyramid with a square base and labels on lateral edge, slant height, altitude,…

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon and the faces are isosceles triangles.

Septagonal/Heptagonal Pyramid

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon…

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Skewed Hexagonal Pyramid

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon…

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Skewed Rectangular Pyramid

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle…

Illustration of a spherical pyramid.

Spherical Pyramid

Illustration of a spherical pyramid.

Plan, front, and side views of a square pyramid.

Square Pyramid

Plan, front, and side views of a square pyramid.

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with vertical plane.

Square Pyramid Revolved 30°

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with vertical…

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with horizontal plane.

Square Pyramid Revolved 30°

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with horizontal…

An illustration of a pyramid with a triangular base.

Pyramid With Triangular Base

An illustration of a pyramid with a triangular base.

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes of a series of inscribed, or circumscribed prisms of equal altitude, if the number of prisms is indefinitely increased.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes…

Illustration of triangular pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is equal to one third of the product…

Illustration of 2 pyramids.

Pyramids

Illustration of 2 pyramids.

An illustration of the Egyptian landscape with three pyramids in the distance.

Pyramids

An illustration of the Egyptian landscape with three pyramids in the distance.

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Equivalent Triangular Pyramids

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Pyramids With Pentagonal and Triangular Bases

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Illustration showing two rhombic pyramids.

Rhombic Pyramids

Illustration showing two rhombic pyramids.

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles.

Triangular Pyramids for Volume

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and placed next to the lower section. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and placed next to the lower section. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The lower…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section is known as the frustum of the pyramid. The hidden edges are shown in this illustration.

Frustum Of A Rectangular Pyramid

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section is known as the frustum of the pyramid.

Frustum Of A Rectangular Pyramid

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section has been turned upside down. It is known as the frustum of the pyramid.

Frustum Of A Rectangular Pyramid

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base.…

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section has been turned upside down. It is known as the frustum of the pyramid. Hidden edges are shown in this drawing.

Frustum Of A Rectangular Pyramid

Illustration of a right hollow rectangular pyramid that has been cut by a plane parallel to the base.…

Illustration of a frustum of a pyramid having a rectangular base and a hole passing through the center of the frustum.

Frustum Of A Rectangular Pyramid With Hole

Illustration of a frustum of a pyramid having a rectangular base and a hole passing through the center…

Popcorn box that is in the shape of a frustum of a rectangular pyramid.

Popcorn Box Frustum Of A Rectangular Pyramid

Popcorn box that is in the shape of a frustum of a rectangular pyramid.

"In the Nile valley there had been found a few ancient inscriptions, carved upon stone in unknown characters, but no one could read them. The, about 1800 A.D., some soldiers of Napoleon in Egypt, while laying foundations for a fort, found a slab of black rock bearing three inscriptions. One of the inscriptions was in Greek, one was in the ancient hieroglyphics of the pyramids, and the third was in a later Egyptian writing, which had likewise been been forgotten." - West, 1904

Portion of Rosetta Stone

"In the Nile valley there had been found a few ancient inscriptions, carved upon stone in unknown characters,…

"Part of the Rosetta Stone inscription, on a larger scale..." - West, 1904

Part of Rosetta Stone Inscription

"Part of the Rosetta Stone inscription, on a larger scale..." - West, 1904

Illustration of a right septagonal/heptagonal pyramid, with hidden edges shown, that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Septagonal/Heptagonal Pyramid Cut By Plane

Illustration of a right septagonal/heptagonal pyramid, with hidden edges shown, that has been cut by…

Illustration of a septagonal/heptagonal pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section is known as the frustum of the pyramid. The hidden edges are shown in this illustration.

Frustum Of A Septagonal/Heptagonal Pyramid

Illustration of a septagonal/heptagonal pyramid that has been cut by a plane parallel to the base. The…

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."

Illustration of the intersection of a square pyramid and a plane.

Intersection of Square Pyramid and a Plane

Illustration of the intersection of a square pyramid and a plane.