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

A balance with three apples on the left and 15 blocks on the right.

Balance with Apples and Blocks

A balance with three apples on the left and 15 blocks on the right.

A balance with two blocks and a slice of cake on the left and three one-unit blocks and one 25-unit block on the right.

Balance with Cake and Blocks

A balance with two blocks and a slice of cake on the left and three one-unit blocks and one 25-unit…

Illustration of a trapezoid with altitude a and bases b and b' used to demonstrate that the area is 1/2 the sum of the bases multiplied by the altitude.

Area of a Trapezoid

Illustration of a trapezoid with altitude a and bases b and b' used to demonstrate that the area is…

Illustration of a right triangle used to show the Pythagorean Theorem (the square of the hypotenuse is equal to the sum of the squares of the legs).

Right Triangle

Illustration of a right triangle used to show the Pythagorean Theorem (the square of the hypotenuse…

Illustration of a triangular prism - a prism whose base is a triangle.

Triangular Prism

Illustration of a triangular prism - a prism whose base is a triangle.

Illustration of a truncated prism - the part of a prism included between the base and a section made by a plane oblique to the base.

Truncated Prism

Illustration of a truncated prism - the part of a prism included between the base and a section made…

Illustration of a parallelopiped - a prism with a parallelogram as its base

Parallelopiped

Illustration of a parallelopiped - a prism with a parallelogram as its base

Illustration of a parallelopiped - a prism with a parallelogram as its base

Parallelopiped

Illustration of a parallelopiped - a prism with a parallelogram as its base

Illustration of a parallelopiped with a plane passing through two diagonally opposite edges. The plane divides the parallelopiped into two equivalent triangular prisms.

Parallelopiped with Plane Passing Through

Illustration of a parallelopiped with a plane passing through two diagonally opposite edges. The plane…

Illustration of a parallelopiped with a plane passing through two diagonally opposite edges. The plane divides the parallelopiped into two equivalent triangular prisms.

Parallelopiped with Plane Passing Through

Illustration of a parallelopiped with a plane passing through two diagonally opposite edges. The plane…

Illustration of 2 parallelopipeds/rectangular prisms.

Rectangular prisms

Illustration of 2 parallelopipeds/rectangular prisms.

Illustration of 3 parallelopipeds/rectangular prisms.

Rectangular prisms

Illustration of 3 parallelopipeds/rectangular prisms.

Illustration of a parallelopiped (a prism with a parallelogram as its base) used to demonstrate that the volume of any parallelopiped is equal to the product of its base by its altitude.

Parallelopiped Showing Volume

Illustration of a parallelopiped (a prism with a parallelogram as its base) used to demonstrate that…

Illustration of a prism used to demonstrate that the volume of any prism is equal to the product of its base by its altitude.

Prism Showing Volume

Illustration of a prism used to demonstrate that the volume of any prism is equal to the product of…

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 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 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 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…

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…

"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…

Trade Dollar ($1.00) United States coin from 1873. Obverse has a seated, left-facing Liberty holding a label in her left hand which reads LIBERTY. At the base of her seat is inscribed IN GOD WE TRUST just above the date. She is surrounded by 13 stars - 6 facing. Reverse shows an eagle with a right-facing head with a label on which the motto is inscribed. Inscription - TRADE DOLLAR.

Silver Trade Dollar Coin, 1873

Trade Dollar ($1.00) United States coin from 1873. Obverse has a seated, left-facing Liberty holding…

Projection of a round bar.

Projection of Round Bar

Projection of a round bar.

Projection of a cylinder with a circular hole.

Projection of Cylinder With Circular Hole

Projection of a cylinder with a circular hole.

Projection of a frustum of a square pyramid.

Projection of Frustum of Square Pyramid

Projection of a frustum of a square pyramid.

Projection of a turned block.

Projection of Turned Block

Projection of a turned block.

Projections of a rectangular prism or block.

Projections of Rectangular Prism

Projections of a rectangular prism or block.

Projections of a triangular prism or block.

Projections of Triangular Prism

Projections of a triangular prism or block.

Projections of a triangular prism or block with a square hole.

Projections of Triangular Prism With Hole

Projections of a triangular prism or block with a square hole.

Projections of a cylinder inclined to horizontal plane.

Projections of Cylinder

Projections of a cylinder inclined to horizontal plane.

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder greatly inclined to a plane.

Projection of Cylinder

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder…

Illustration of a right circular cone with the diameter of the base equal to the height of the cone.

Right Circular Cone

Illustration of a right circular cone with the diameter of the base equal to the height of the cone.

Illustration of a right circular cone with the diameter of the base greater than the height of the cone.

Right Circular Cone

Illustration of a right circular cone with the diameter of the base greater than the height of the cone.

Illustration of 4 congruent tangent right circular cylinders. The height of all the cylinders is greater than the diameter of the base.

4 Congruent Tangent Right Circular Cylinders

Illustration of 4 congruent tangent right circular cylinders. The height of all the cylinders is greater…

Illustration of 3 right congruent tangent circular cylinders.  The height of all the cylinders is greater than the diameter of the base.

3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

Illustration of 3 right congruent tangent circular cylinders.  The height of all the cylinders is greater than the diameter of the base.

3 Congruent Tangent Right Circular Cylinders

Illustration of 3 right congruent tangent circular cylinders. The height of all the cylinders is greater…

Illustration of a frustum of a right circular cone with hidden edges shown. When a cone is cut by a plane parallel to the base, the lower part is known as the frustum.

Frustum of A Cone

Illustration of a frustum of a right circular cone with hidden edges shown. When a cone is cut by a…

Illustration of a frustum of a right circular cone. When a cone is cut by a plane parallel to the base, the lower part is known as the frustum.

Frustum of A Cone

Illustration of a frustum of a right circular cone. When a cone is cut by a plane parallel to the base,…

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

Cone Cut By Plane

Illustration of a right circular cone that has been cut by a plane parallel to the base. The lower part…

Illustration of a right circular cone that has been cut by a plane parallel to the base. The top section has been removed and placed in front of the lower section. The lower part is known as the frustum.

Cone Cut By Plane

Illustration of a right circular cone that has been cut by a plane parallel to the base. The top section…

Illustration of a decagonal 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 Decagonal Pyramid

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

Illustration of a hollow decagonal 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 Decagonal Pyramid

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