"An inclined plane is a slope, or flat surface, making an angle with a horizontal line...the force acts parallel to the base." —Hallock 1905

Inclined Plane with the Force Acting Parallel to the Base

"An inclined plane is a slope, or flat surface, making an angle with a horizontal line...the force acts…

"An inclined plane is a slope, or a flat surface, making an angle with a horizontal line...the force acts at an angle to the plane or to the base." —Hallock 1905

Inclined Plane with Force at an Angle to Plane and Base

"An inclined plane is a slope, or a flat surface, making an angle with a horizontal line...the force…

"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…

"Angle of incidence equals angle of reflection." —Croft 1917

Reflection of Light

"Angle of incidence equals angle of reflection." —Croft 1917

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it will return in the line A F. If thrown from D however, it will glance off on the other side of the perpendicular, at the same angle, to E." —Quackenbos 1859

Reflected Motion

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it…

"When a high degree of force is required, several moveable pulleys may be combined, as represented [here]. A and B are fixed pulleys; C and D are moveable ones, from the block of which the weight W is suspended" —Quackenbos 1859

Multiple Pulleys

"When a high degree of force is required, several moveable pulleys may be combined, as represented [here].…

"One of the primary simple mechanical powers. The plane's surface is inclined to the horizon at any angle." —Quackenbos 1859

Inclined Plane

"One of the primary simple mechanical powers. The plane's surface is inclined to the horizon at any…

"As temperature elevates, the metal bar being tested expands accordingly and the dial measures the expansive power per degree of heat." —Quackenbos 1859

Pyrometer

"As temperature elevates, the metal bar being tested expands accordingly and the dial measures the expansive…

"Mirror A/B is only half of person C's height. C is able to view his entire body through such a small mirror due to the angle of incidence from D to B to F." —Quackenbos 1859

Angle of Incidence and Reflection

"Mirror A/B is only half of person C's height. C is able to view his entire body through such a small…

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and 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 diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Parallelogram with angles labeled.

Parallelogram

Parallelogram with angles labeled.

Right angle with square at perpendicular lines

Right Angle

Right angle with square at perpendicular lines

Illustration of an angle

Angle

Illustration of an angle

Right angle at perpendicular lines demonstrated by string on plumb line.

Perpendicular Lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Acute angle

Acute Angle

Acute angle

Obtuse angle

Obtuse Angle

Obtuse angle

Complementary angles

Complementary Angles

Complementary angles

Supplementary angles

Supplementary Angles

Supplementary angles

Right triangle with square

Right Triangle

Right triangle with square

Rectangle with angles labeled. Parallelogram with right angles.

Rectangle

Rectangle with angles labeled. Parallelogram with right angles.

Square with angles labeled. A rectangle with four equal sides.

Square

Square with angles labeled. A rectangle with four equal sides.

Trapezoid with angles and height labeled.

Trapezoid

Trapezoid with angles and height labeled.

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Pythagorean Theorem Triangle

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Illustration of steel square.

Steel Square

Illustration of steel square.

Illustration of steel square with hypotenuse drawn.

Steel Square

Illustration of steel square with hypotenuse drawn.

Illustration of steel square with bevel/slant.

Steel Square

Illustration of steel square with bevel/slant.

Illustration of circle with inscribed angle and central angle.

Inscribed and Central Angles

Illustration of circle with inscribed angle and central angle.

Illustration of circle with inscribed angle 30 and central angle 60.

Inscribed and Central Angles 30 60

Illustration of circle with inscribed angle 30 and central angle 60.

Illustration of circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of circle with sector and segment used to find area.

Illustration of partial circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of partial circle with sector and segment used to find area.

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Illustration of circle with quadrant and 60 degree arc.

Quadrant of Circle With 60 degree Arc

Illustration of circle with quadrant and 60 degree arc.

Illustration of construction to lay off an angle.

Construction of Angle

Illustration of construction to lay off an angle.

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Right Circular Cone 10 Feet High With 30 Degree Angle

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Positive trigonometric angle with initial and terminal sides labeled.

Positive Trigonometric Angle

Positive trigonometric angle with initial and terminal sides labeled.

Negative trigonometric angle with initial and terminal sides labeled.

Negative Trigonometric Angle

Negative trigonometric angle with initial and terminal sides labeled.

Trigonometric angle 467 degrees.

467 Degree Trigonometric Angle

Trigonometric angle 467 degrees.

Trigonometric angle -229 degrees.

-229 Degree Trigonometric Angle

Trigonometric angle -229 degrees.

Axes showing trigonometric angles, and quadrants.

Trigonometric Angles and Quadrants

Axes showing trigonometric angles, and quadrants.

Illustration showing that the radian is an angle that when placed at the center of a circle its sides intercept an arc equal to the radius.

Radians in Complete Circle

Illustration showing that the radian is an angle that when placed at the center of a circle its sides…

Illustration showing that the arc length can be found by multiplying the angle measure by the radius of the circle.

Model of Arc Length, Angle Measure, and Radius

Illustration showing that the arc length can be found by multiplying the angle measure by the radius…

Illustration of acute angle theta as part of a right triangle.

Acute Angle Theta

Illustration of acute angle theta as part of a right triangle.

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Reference Angles/Triangles Formed by Angles in Quadrants

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa, ordinate, and distance labeled.

Reference Angles/Triangles Formed by Angles in Quadrants With Labels

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa,…

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right Triangle With Sides .64 and 1 and Angle of 40 degrees

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right Triangle With Sides .7 and 1 and Angle of 35 degrees

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 45, 45, 90 degrees

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships…

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 30, 60, 90 degrees

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships…

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration could be used to find trig ratios.

Trigonometric Reference Triangles/Angles Drawn in Quadrants

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration…

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth horizontal plane.

Inclined Plane Forming Right Triangle

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth…

Illustration modeling the path of a projectile.

Path of Projectile

Illustration modeling the path of a projectile.

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…

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right Triangle ABC With Angle 67 degrees 42.8 minutes and Hypotenuse 23.47 ft.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

Right Triangle ABC With Leg 23.85 ft. and Hypotenuse 35.62 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Projection of a Line Segment

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

OP is a line representing a vector (directed quantity)

Vector

OP is a line representing a vector (directed quantity)