"The degree to which the air has been exhausted from a closed vessel in which there is a partial vacuum is measured by the height to which a mercurial column in a vertical tube, whose top is connected to the vessel, will rise under the pressure of the atmosphere." —Hallock 1905

Barometer Measuring Pressure of a Partially Evacuated Vessel

"The degree to which the air has been exhausted from a closed vessel in which there is a partial vacuum…

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height of the point P above the surface; it is required to find the distance from the point P to the horizon at A.

Circle With Center o and Radius r with point P

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height…

Illustration of circle with segments labeled and arch.

Segments of Circle and Arch

Illustration of circle with segments labeled and arch.

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration could be used to find volume.

Right Circular Cone With 2 ft. Height and 1 ft. Radius

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration…

Right circular cylinder with diameter of 8 and height h.

Right Circular Cylinder

Right circular cylinder with diameter of 8 and height h.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

Right Circular Cylinder With 1 ft. Radius and 2 ft. height.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

Illustration used to show how to draw an equilateral triangle when given the altitude.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given the altitude.

An illustration of a girl measuring the heights of a boy and girl.

Girl Measuring Heights of Children

An illustration of a girl measuring the heights of a boy and girl.

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays of light from a source of light.

Illumination of a Surface When the Surface is not Perpendicular to the Source

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays…

Leveling is an operation in which the object is to determine to difference of vertical height between two given points.

Levelling

Leveling is an operation in which the object is to determine to difference of vertical height between…

A man measuring the height of a boy against a wall.

Measruing height

A man measuring the height of a boy against a wall.

Illustration of parallelogram AEFC drawn two different ways with base b and altitude/height a used to prove the area is aXb.

Area of a Parallelogram

Illustration of parallelogram AEFC drawn two different ways with base b and altitude/height a used to…

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

Parallelogram With Dimensions

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

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

Parallelogram With Dimensions

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

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

Parallelogram and Rectangle Relationship

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles and finding the sum of the areas.

Pentagon With Triangular Sections For Area

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles…

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular faces. The height of the prism and length of the side of the decagon on the smaller decagonal prism are one half that of the larger.

Similar Decagonal Prisms

Illustration of 2 similar right decagonal prisms. Both have regular decagons for bases and rectangular…

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons for bases and rectangular faces. The height of the prism and length of the side of the heptagon on the smaller heptagonal prism are one half that of the larger.

Similar Heptagonal/Septagonal Prisms

Illustration of 2 similar right heptagonal/septagonal prisms. Both have regular heptagons/septagons…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of the hexagon on the smaller hexagonal prism are one half that of the larger.

Similar Hexagonal Prisms

Illustration of 2 similar right hexagonal prisms. The height of the prism and length of the side of…

Illustration modeling the path of a projectile.

Path of Projectile

Illustration modeling the path of a projectile.

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

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.

An illustration of a right triangle inscribed in a semicircle.

Right Triangle Inscribed In A Semicircle

An illustration of a right triangle inscribed in a semicircle.

Trapezoid with angles and height labeled.

Trapezoid

Trapezoid with angles and height labeled.

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.

Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Triangle with height/altitude h and median m.

Triangle With Height and Median

Triangle with height/altitude h and median m.

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Triangle ABC With Height h

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

An illustration of a triangle comprised of a church and two lines. This illustration can be used to determine the height of the church steeple, the hypotenuse, and distance of the tower from object one and two.

Triangle with Church

An illustration of a triangle comprised of a church and two lines. This illustration can be used to…

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration used to fine the height of an object situated about the plane of observation, and its height above the plane.

Triangle with Lighthouse

An illustration of a three triangles created with boats and a lighthouse. This is an example illustration…

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine the height of the tower, the hypotenuse, and distance of the tower from the object.

Triangle with Tower

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine…

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that can be used to fine the distance of an inaccessible object without measuring elevation and whether on a horizontal plane or not.

Triangle with Tree

An illustration of a triangle comprised of a tree and two lines. This is an example of a problem that…

An illustration of an acute triangle with the height/altitude labeled h.

Acute Triangle

An illustration of an acute triangle with the height/altitude labeled h.

Illustration used to show "The altitudes of a triangle are concurrent."

Altitudes In A Triangle

Illustration used to show "The altitudes of a triangle are concurrent."

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.

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.

Triangle with sides a,b,c and height/altitude h.

Obtuse Triangle With Height Drawn

Triangle with sides a,b,c and height/altitude h.

An illustration of an obtuse triangle with the height/altitude labeled h.

Obtuse Triangle

An illustration of an obtuse triangle with the height/altitude labeled h.

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Obtuse Triangle ABC With Height h

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Illustration of similar triangles used to find height of smokestack.

Similar Triangles for Height of Smokestack

Illustration of similar triangles used to find height of smokestack.

Illustration that shows two similar triangles with altitudes drawn.

Similar Triangles With Altitudes Drawn

Illustration that shows two similar triangles with altitudes drawn.

"When any liquid is placed in one or more of several vessels communicating with each other, it will not come to rest until it stands at the same height inall of thw vessels. This principle is emobodied in the familiar expression 'Water seeks its level.' the principle is illustrated, on a large scale, in the system of pipes by which water is distributed in cities." -Avery 1895

Water Level in Multiple Connected Vessels

"When any liquid is placed in one or more of several vessels communicating with each other, it will…