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Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth the altitude into the sum of the two bases and four times the mid-section."

Volume of Prismatoid

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth…

"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,…

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 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…

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

Rectangle With Dimensions

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

"The two roundlets are arranged in pale, but they may appear in chief or base. When there are many figures of the same species borne in coats of arms, their number must be observed as they stand, and properly expressed." -Hall, 1862

Two Roundlets

"The two roundlets are arranged in pale, but they may appear in chief or base. When there are many figures…

A curvy bouche heraldic shield with a base division.

Bouche Shield

A curvy bouche heraldic shield with a base division.

A heraldic bouche-shaped shield with a base division.

Bouche Shield

A heraldic bouche-shaped shield with a base division.

A couche heraldic shield with a base division.

Couche Shield

A couche heraldic shield with a base division.

A pointed heraldic shield with a base division.

Pointed Shield

A pointed heraldic shield with a base division.

"A, Palate process of upper jawbone; B, zygoma, forming zygomatic arch; C, condyle, for forming articulation with atlas; D, foramen magnum; E, occipital bone" — Blaisedell, 1904

Base of skull

"A, Palate process of upper jawbone; B, zygoma, forming zygomatic arch; C, condyle, for forming articulation…

The Half-figure Socle of Altar is the base platform design of the altar. It is a design of two half-figure human bodies with the bottom part is a scroll foliage design. This socle is found in the cathedral of Orvieto, Italy, designed during the Italian Renaissance.

Half-Figure Socle of Altar

The Half-figure Socle of Altar is the base platform design of the altar. It is a design of two half-figure…

The Renaissance spanrail panel is a plinth (base) of a column. It is found in the St. Anthony cathedral in Padua, Italy.

Renaissance Spanrail Panel

The Renaissance spanrail panel is a plinth (base) of a column. It is found in the St. Anthony cathedral…

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.…

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…

A stand is a standing support or foundation which in this case is strictly to hold a camera in place.

Stand for Supporting Cameras

A stand is a standing support or foundation which in this case is strictly to hold a camera in place.

This ornamental stand is designed with small figures in the center that are holding the frame of the stand, and the base is designed with horned serpents. The stand is used as a decorative piece of artwork to be displayed.

Ornamental Stand

This ornamental stand is designed with small figures in the center that are holding the frame of the…

This table is carved with a base made of animal feet.

Table

This table is carved with a base made of animal feet.

The Parthenon is a temple of the Greek Goddess Athena, who was considered as the protector of the city of Athens. The Temple was built in the 5th B.C. on Athenian Acropolis. The Parthenon is designed in a Doric Order style which consists of vertical columns that stand flat without a base, and a smooth capital.

The Parthenon

The Parthenon is a temple of the Greek Goddess Athena, who was considered as the protector of the city…

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…

Trapezoid with dimensions labeled. Trapezoid can be used to calculate area.

Trapezoid With Dimensions

Trapezoid with dimensions labeled. Trapezoid can be used to calculate area.

Illustration of a trapezoid, with the median drawn. The median of a trapezoid is parallel to the bases, and is equal to half the sum of the bases.

Trapezoid With Median

Illustration of a trapezoid, with the median drawn. The median of a trapezoid is parallel to the bases,…

Illustration to show altitudes drawn from base angles of an isosceles triangle.

Altitudes Drawn from Base Angles of Isosceles Triangles

Illustration to show altitudes drawn from base angles of an isosceles triangle.

Parallelogram illustration to show where the area of a triangle formula comes from.

Area of Triangle

Parallelogram illustration to show where the area of a triangle formula comes from.

Illustration of triangle ABC with altitude a and base b to be used to demonstrate that the area is 1/2ba.

Area of a Triangle

Illustration of triangle ABC with altitude a and base b to be used to demonstrate that the area is 1/2ba.

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing one of the legs through the vertex, is parallel o the base.

Bisector of an Exterior Angle of an Isosceles Triangle

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing…

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side, it bisects the other side also.

Triangle With Bisector Parallel to the Base

Illustration of a triangle showing that when a line parallel to the base of a triangle bisects one side,…

Illustration to show if the bisector of the base angles of a triangle are drawn, and through their point of intersection a line is drawn parallel to the base, the length of this parallel between the sides is equal to the sum of the segments of the sides between the parallel and the base.

Triangle With Bisectors of Base Angles

Illustration to show if the bisector of the base angles of a triangle are drawn, and through their point…

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex by its own length, the line joining he end of the leg produced to the nearer end of the base is perpendicular to the base.

Leg Produced through the Vertex of an Isosceles Triangle

Illustration to show that if one of the legs of an isosceles triangle is produced through the vertex…

Illustration to show the medians drawn to the legs of an isosceles triangle.

Medians Drawn Drawn to Legs of Isosceles Triangles

Illustration to show the medians drawn to the legs of an isosceles triangle.

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the triangle into four equal triangles.

Midpoints of Triangle Divide Triangle into Four Equal Triangles

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the…

Illustration of a triangle with a segment parallel to the base.

Triangle With Parallel Segment Drawn

Illustration of a triangle with a segment parallel to the base.

Illustration to show that the perpendicular bisector of the base of an isosceles triangle passes through the vertex and bisects the angle at the vertex.

Perpendicular Bisector of the Base of an Isosceles Triangle

Illustration to show that the perpendicular bisector of the base of an isosceles triangle passes through…

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles triangle are equal.

Perpendiculars Dropped From Midpoint of Base to Legs of Isosceles Triangles

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles…

Illustration to show that the difference of the distances from any point in the base produced of an isosceles triangle to the equal sides of the triangle is constant.

Point in Base of Isosceles Triangle

Illustration to show that the difference of the distances from any point in the base produced of an…

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…

Diagram used to prove the theorem: "The volume of a triangular prism is equal to the product of its base and its altitude."

Volume of Triangular Prism

Diagram used to prove the theorem: "The volume of a triangular prism is equal to the product of its…

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular prism of the same base and altitude."

Volume of Triangular Pyramid

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular…

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes are equivalent."

Equivalent Triangular Pyramids

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes…

This tureen is footed with two horse figures at the base. The tureen lid has a small infant figure at the top and the handles are in a fish design.

Tureen

This tureen is footed with two horse figures at the base. The tureen lid has a small infant figure at…

This flower vase has a unique design of animal heads at the base and serpents as the handles.

Flower Vase

This flower vase has a unique design of animal heads at the base and serpents as the handles.

The Ford Mansion is part of the Morristown National Historical Park, and is located on a hilltop in Morristown, New Jersey. The Ford Mansion was the "hard winter" (from December 1779 - May 1780) quarters of George Washington and the Continental Army. That winter remains the coldest on record for New Jersey.

Washington's Headquarters at Morristown

The Ford Mansion is part of the Morristown National Historical Park, and is located on a hilltop in…

The Morris-Jumel Mansion (also known as the Roger and Mary Philipse Morris House), located in historic Washington Heights, is the oldest house in Manhattan. It served as a headquarters for both sides in the American Revolution. Between September 14 and October 20, 1776, General George Washington used the mansion as his temporary headquarters after he and his army were forced to evacuate Brooklyn Heights following their loss to the British Army under the command of General William Howe in the Battle of Long Island.

Washington's Headquarters at New York

The Morris-Jumel Mansion (also known as the Roger and Mary Philipse Morris House), located in historic…

"The next simple mechanical power is the wedge. This instrument may be considered as two inclined planes, placed base to base." -Comstock 1850

Wedge

"The next simple mechanical power is the wedge. This instrument may be considered as two inclined planes,…