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"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called the frustum of the pyramid." — Hallock, 1905

Pyramid

"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Six-sided Pyramid

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Rhombohedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

An octahedron, or double four-sided pyramid. It has 8 sides.

Octahedron

An octahedron, or double four-sided pyramid. It has 8 sides.

"a shows a young tree with its second year's growth, the upright shoot of the maiden tree having been moderately headed back, being left longer if the buds near the base promise to break freely, or cut shorter if they are weak and wanting in vigour. The winter pruning, carried out with the view to shape the tree into a well-grown pyramid, would be effected at the places marked by a cross line." — Encyclopedia Britannica, 1893

Pyramid Pruning

"a shows a young tree with its second year's growth, the upright shoot of the maiden tree having been…

"Pyramidal Training." — Encyclopedia Britannica, 1893

Pyramidal Training

"Pyramidal Training." — Encyclopedia Britannica, 1893

"The section and ground plan of one of the older forms of open-mouthed furnaces used at Dowlais (Truran), consisting of a heavy mass of mascury, square at base, strongly braced together with iron tie-rods, rising in the shape of a truncated pyramid to the height of the boshes, and then surmounted with a conical top surrounded at the throat by a gallery for the introduction of the enarging materials. In the square base were four arched recesses or tuyere houses, one on each side, F, F, for the introduction of G also serving for the removal of cinder and the tapping of the furnace for the running of the pig. The lowest portion of the hearth or crucible, A, was constructed of refractory sandstone, grit, or conglomerate, or of difficulty fusible firebrick, the inner portion of the upper part of the furnace being also built of firebrick set in fireclay with an air course between the double lining thus constructed; exteriorly the furnace was built of less expensive and refractory materials, usually of stone, strongly bound round with iron hoops." — The Encyclopedia Britannica, 1893

Furnace

"The section and ground plan of one of the older forms of open-mouthed furnaces used at Dowlais (Truran),…

A pyramid

Pyramid

A pyramid

Orthogonal projection of a closed plane-faced polyhedron.

Polyhedron

Orthogonal projection of a closed plane-faced polyhedron.

Orthogonal projection of a closed plane-faced polyhedron.

Polyhedron

Orthogonal projection of a closed plane-faced polyhedron.

Top and side views of a hexagonal pyramid shaded with dimension lines.

Drawing Lines 3

Top and side views of a hexagonal pyramid shaded with dimension lines.

An orthographic projection of a pyramid from three dimensional space into two dimensional space

Orthographic Pyramid Projection

An orthographic projection of a pyramid from three dimensional space into two dimensional space

"This solid is bounded by twenty-four isosceles triangles, and may be considered as an octahedron with a low triangular pyramid on each of its faces." -The Encyclopedia Britannica 1910

Triakis-octahedron

"This solid is bounded by twenty-four isosceles triangles, and may be considered as an octahedron with…

"...a combination of the brachy-pinacoid and a prism, with the pedion, two brachy-domes and two marco-domes at the upper end, and a pyramid at the lower end." -The Encyclopedia Britannica 1910

Crystal of Hemmorphite

"...a combination of the brachy-pinacoid and a prism, with the pedion, two brachy-domes and two marco-domes…

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The Encyclopedia Britannica

Monoclinic Axes and Hemi-pyramid

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The…

"...represents a crystal of augite bounded by th clino-pinacoid, the ortho-pinacoid, a prism, and a hemi-pyramid." -The Encyclopedia Britannica 1910

Crystal of Augite

"...represents a crystal of augite bounded by th clino-pinacoid, the ortho-pinacoid, a prism, and a…

"...represents a crystal of tourmaline wit the trigonal prism, hexagonal prism, and a trigonal pyramid at each end." -The Encyclopedia Britannica 1910

Crystal of Tourmaline

"...represents a crystal of tourmaline wit the trigonal prism, hexagonal prism, and a trigonal pyramid…

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point, called the vertex." —Hallock 1905

Pryamid

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point,…

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,…

An illustration of a pyramid with a triangular base.

Pyramid With Triangular Base

An illustration of a pyramid with a triangular base.

An illustration of a pyramid with a hexagonal base.

Pyramid With Hexagonal Base

An illustration of a pyramid with a hexagonal base.

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Circular Cone Frustum

An illustration of a circular cone with the top cut off by a plane parallel to the base. The remaining…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Pyramid Frustum

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

Cube for Illustrating Volume

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has hexagonal bases, one with 10 inch side and the other with a 6 inch side. Height is 18 inches.

Pyramid Frustum With Hexagonal Bases and 6 inch and 10 inch Sides

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has right triangular bases, one with 20 inch side and the other with a 30 inch side. Height is 27 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has triangular bases with 14 inch sides. The other sides are 16 and 22 inches. The altitude is 24 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

Section through the right kidney from its outer to inner border. Labels: 1, cortex; 2, medulla; 2', pyramid of Malpighi; 2'', pyramid of Ferrein; 5, small branches of the renal artery entering between the pyramids; A, a branch of the renal artery; C, the pelvis of the kidney; U, ureter; C, a calyx.

Kidney Section

Section through the right kidney from its outer to inner border. Labels: 1, cortex; 2, medulla; 2',…

The base of brain. Labels: 1. Olfactory Bulb; 2. Second, or Optic Nerves; 3. Anterior Perforated Space; 4. Optic Tract; 5. Crus Cerebri; 6. 3rd Nerve; 7. 4th Nerve.; 8. 5th Nerve; 9. 6th Nerve; 10. Pyramid; 11. Olivary Body; 12. Vertebral Artery; 13. Anterior Spinal Artery; 14. Anterior Cerebral Artery; 15. Lamina Cinerea; 16. Middle Cerebral Artery; 17. Tuber Cinereum; 18. Corpora Albicantia; 19. Posterior Perforated Space; 20. Posterior Cerebral Artery; 21. Superior Cerebral Artery; 22. Pons Varolii; 23. Inferior Cerebellar Artery; 24. 7th and 8th Nerves; 25. 9th, 10th, and 11th Nerves; 26. 12th Nerve; 27. Cerebellum.

Base of the Brain

The base of brain. Labels: 1. Olfactory Bulb; 2. Second, or Optic Nerves; 3. Anterior Perforated Space;…

A flashcard featuring an illustration of a Pyramid with a Hexagonal Base

Flashcard of a Pyramid with a Hexagonal Base

A flashcard featuring an illustration of a Pyramid with a Hexagonal Base

A flashcard featuring an illustration of a Pyramid with a Pentagonal Base

Flashcard of a Pyramid with a Pentagonal Base

A flashcard featuring an illustration of a Pyramid with a Pentagonal Base

A flashcard featuring an illustration of a Pyramid with a Rectangular Base

Flashcard of a Pyramid with a Rectangular Base

A flashcard featuring an illustration of a Pyramid with a Rectangular Base

A flashcard featuring an illustration of a Pyramid with a Square Base

Flashcard of a Pyramid with a Square Base

A flashcard featuring an illustration of a Pyramid with a Square Base

A flashcard featuring an illustration of a Pyramid with a Triangular Base

Flashcard of a Pyramid with a Triangular Base

A flashcard featuring an illustration of a Pyramid with a Triangular Base

Illustration of 2 pyramids.

Pyramids

Illustration of 2 pyramids.

Illustration of 2 regular pyramids.

Regular Pyramids

Illustration of 2 regular pyramids.

Illustration of a regular pyramid with a pentagon for a base.

Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

Illustration of a regular pyramid with a square for a base.

Regular Pyramid With Square Base

Illustration of a regular pyramid with a square for a base.

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

Pyramid Frustum

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

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 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 regular pyramid with a pentagon for a base.

Frustum of a Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

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 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…

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 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 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…

The frustum of a triangular pyramid is equivalent to the sum 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 two bases of the frustum.

Triangular Pyramid Frustum

The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude…

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…

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…

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.

Truncated Triangular Prism for Volume

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base…

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.

Truncated Triangular Prism for Volume

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base…

A volume of a truncated right triangular prism is equal to the product of its base by one third the sum of its lateral edges.

Truncated Right Triangular Prism for Volume

A volume of a truncated right triangular prism is equal to the product of its base by one third the…

A volume of a truncated right triangular prism is equal to the product of its base by one third the sum of its lateral edges.

Truncated Right Triangular Prism for Volume

A volume of a truncated right triangular prism is equal to the product of its base by one third the…

Illustration of a pyramid inscribed in a cone.

Pyramid Inscribed in a Cone

Illustration of a pyramid inscribed in a cone.

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 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.