Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

A pilot's cockpit from a propeller aeroplane, or airplane. The diagram illustrates the different parts of the cockpit used to control the plane. The cockpit contains gauges; watch; joystick controlling ailerons and elevators; and wires to adjust wings.

Aeroplane Cockpit

A pilot's cockpit from a propeller aeroplane, or airplane. The diagram illustrates the different parts…

An instrument consisting essentially of a dipping needle, a verticle graduated circle whose center coincides with the axis of the needle, and a graduated horizontal circle, the whole being supported by a tripod. Also called an inclinometer.

Dipping Compass

An instrument consisting essentially of a dipping needle, a verticle graduated circle whose center coincides…

Illustration of a right circular cone resting on an element such that the vertex is on the bottom and a vertical and horizontal element meet at a right angle.

Right Circular Cone on Side

Illustration of a right circular cone resting on an element such that the vertex is on the bottom and…

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of the triangles. The intersections of the bisectors of the exterior angles of a triangle are the centers of three circles, each of which will touch one side of the triangle, and the two other circles.

Construction of Escribed Circles With Ex-centres

Illustration of the construction used to escribe circles with centres (centers) called ex-centres of…

Illustration of the construction used upon a given straight line, to describe a segment of a circle in which a given angle may be inscribed.

Construction to Describe a Segment of a Circle in Which an Angle Can Be Inscribed

Illustration of the construction used upon a given straight line, to describe a segment of a circle…

Illustration of the construction used to make a triangle when given a side and two angles.

Construction of a Triangle When Given a Side and Two Angles

Illustration of the construction used to make a triangle when given a side and two angles.

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate in either the second or fourth quadrant.

Negative Cotangent Angles

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate…

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve of a road.

Curve in Pavement of Road

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve…

Illustration showing an angle of depression from a horizontal line to a line of sight.

Angle of Depression

Illustration showing an angle of depression from a horizontal line to a line of sight.

A design of the propeller airplane, or aeroplane, in flight with a higher tail to create an angle of incidence when landing.

Aeroplane High Tail Normal Attitude Design

A design of the propeller airplane, or aeroplane, in flight with a higher tail to create an angle of…

A propeller airplane, or aeroplane, design with a high tail. This design creates a larger angle of incidence for a effective air brake to stop the plane in a shorter distance.

Aeroplane High Tail Slow Landing Design

A propeller airplane, or aeroplane, design with a high tail. This design creates a larger angle of incidence…

Illustration of a propeller aeroplane, or airplane, with lower tail in flight.

Aeroplane Low Tail Design

Illustration of a propeller aeroplane, or airplane, with lower tail in flight.

The propeller airplane, or aeroplane, design in fast landing. This design requires a large landing area to stop the plane.

Aeroplane Low Tail Fast Landing Design

The propeller airplane, or aeroplane, design in fast landing. This design requires a large landing area…

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant from the faces of the angle"

Plane Bisecting Dihedral Angle

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant…

The 45-degree triangle can be used to make a line at a multiple of 15 degrees.

Drawing Lines using Triangle at Angles in Multiples of 15 degrees

The 45-degree triangle can be used to make a line at a multiple of 15 degrees.

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Angle of Elevation

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Draftsman's first method for creating an ellipse

Ellipse First Method

Draftsman's first method for creating an ellipse

Draftsman's fourth method for drawing an ellipse, case 3

Ellipse Fourth Method Case 3

Draftsman's fourth method for drawing an ellipse, case 3

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

A flashcard featuring an illustration of a Right Triangle

Flashcard of a Right Triangle

A flashcard featuring an illustration of a Right Triangle

A flashcard featuring an illustration of a Scalene Triangle

Flashcard of a Scalene Triangle

A flashcard featuring an illustration of a Scalene Triangle

A flashcard featuring an illustration of an Acute angle

Flashcard of an Acute angle

A flashcard featuring an illustration of an Acute angle

A flashcard featuring an illustration of an Acute Triangle

Flashcard of an Acute Triangle

A flashcard featuring an illustration of an Acute Triangle

A flashcard featuring an illustration of an angle

Flashcard of an angle

A flashcard featuring an illustration of an angle

A flashcard featuring an illustration of an Isosceles Triangle

Flashcard of an Isosceles Triangle

A flashcard featuring an illustration of an Isosceles Triangle

A flashcard featuring an illustration of an Obtuse angle

Flashcard of an Obtuse angle

A flashcard featuring an illustration of an Obtuse angle

A flashcard featuring an illustration of an Obtuse Triangle

Flashcard of an Obtuse Triangle

A flashcard featuring an illustration of an Obtuse Triangle

A plane flying above land illustrating the use of ailerons to adjust the angle of incidence to adjust the lift. Ailerons are located at the wing tips and controlled by the pilot.

Airplane Flying Above Land

A plane flying above land illustrating the use of ailerons to adjust the angle of incidence to adjust…

An airplane flying above the show illustrating the aerodynamics of the plane with the tail wing at the same angle as the main body. This reduces the lift of the plane by decreasing the angle of incidence.

Airplane Flying Above Shore

An airplane flying above the show illustrating the aerodynamics of the plane with the tail wing at the…

An illustration of the plane flying over land from point A to B by flying the plane with the direction of the plane. Then, flying to point D by creating a diagonal line at 100 mph onto destination point B.

Aeroplane Flying Over Plane

An illustration of the plane flying over land from point A to B by flying the plane with the direction…

"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…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: "x = aR/(R - r), a = √(t&sup2 + (R - r)&sup2), t = √(a&sup2 - (R - r)&sup2, sin.v = t/a."

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: " t = √(a&sup2 - (R + r)&sup2, a = √(t&sup2 - (R + r)&sup2 "

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant that illustrates the following geometric relationship: a:t = t:b, t&sup2 = ab

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant…

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates the following geometric relationship: t&sup2 = (a + b)(a - b).

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates…

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…

Illustration that can be used to show that when given an angle, expressed as an inverse function of u, it can be used to find the value of any function of the angle in terms of u.

Angle Expressed As An Inverse Function

Illustration that can be used to show that when given an angle, expressed as an inverse function of…

To find the angle between two given lines a, b of which the projections a1, b1 and a2, b2 are given.

Angle of Two Lines

To find the angle between two given lines a, b of which the projections a1, b1 and a2, b2 are given.

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line from an external point.

Perpendicular Line Drawn To a Given Line From an External Point

Illustration showing that the perpendicular is the shortest line that can be drawn to a straight line…

Illustration of two lines intersecting at a point. This can be used to show vertical angles.

Intersecting Straight Lines

Illustration of two lines intersecting at a point. This can be used to show vertical angles.

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line, cutting off on the line unequal segments from the foot of the perpendicular, the more remote is the greater.

Lines Drawn From the Same Point in a Perpendicular to a Given line, Cutting Off Segments

Illustration showing two straight lines drawn from the same point in a perpendicular to a given line,…

Illustration showing two lines CA and CB drawn from the point C to the extremities of the straight line AB. OA and OB are two lines similarly drawn, but included by CA and CB. This can be used to show the theorem: The sum of two lines drawn from a point to the extremities of a straight line is greater than the sum of two other lines similarly drawn, but included by them.

Lines Drawn From the Point C to the Extremities of the Straight line AB

Illustration showing two lines CA and CB drawn from the point C to the extremities of the straight line…

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off on the given line equal segments from the foot of the perpendicular, are equal and make equal angles with the perpendicular. This illustration can be used to show the proof.

Lines Drawn to Another Line to Form Triangle

Illustration of two straight lines drawn from a point in a perpendicular to a given line, cutting off…

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Perpendicular Line Drawn to a Given Line from an External Point

Illustration showing only one perpendicular can be drawn to a given line from a given external point.

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles are equal.

Parallel Lines Cut By A Transversal

Illustration showing that when two parallel lines are cut by a transversal, the exterior-interior angles…

Illustration showing that when two parallel lines are cut by a transversal, the two interior angles on the same side of the transversal are supplementary.

Parallel Lines Cut By A Transversal

Illustration showing that when two parallel lines are cut by a transversal, the two interior angles…

"The circles for position angle and declination are read by micrometer microscopes illuminated by the lamp L; the scales are illuminated by the lamp l. T is part of the tube proper and turns with the head. The tube V, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles a p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination." —The Encyclopedia Britannica, 1903

Micrometer

"The circles for position angle and declination are read by micrometer microscopes illuminated by the…

An instrument for making a reduced, enlarged, or exact copy of a plane figure

Pantograph

An instrument for making a reduced, enlarged, or exact copy of a plane figure

Draftsman's first method for drawing a parabola

Parabola First Method

Draftsman's first method for drawing a parabola

Parallelogram with angles labeled.

Parallelogram

Parallelogram with angles labeled.

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed about a circle.

Regular Pentagon With Circle Inscribed

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed…

To determine the angle between two planes.

Angle of Two Planes

To determine the angle between two planes.

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

Illustration of a polygon with exterior angles drawn.

Exterior Angles of Polygons

Illustration of a polygon with exterior angles drawn.

Illustration of a polygon with interior angles drawn.

Interior Angles of Polygons

Illustration of a polygon with interior angles drawn.

"A prism is a transparent body with two refraction surfaces that lie in intersecting planes. The angle formed by these planes is called the refracting angle." -Avery 1895

Prism

"A prism is a transparent body with two refraction surfaces that lie in intersecting planes. The angle…

"Cathetal prisms readily yield the phenomena of total reflection as shown, and are often used when light is to be turned through a right angle." -Avery 1895

Cathetal Prism

"Cathetal prisms readily yield the phenomena of total reflection as shown, and are often used when light…

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one are equal respectively to the three faces about a trihedral of the other, and similarly arranged."

Two Equal Prisms

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one…

Illustration modeling the path of a projectile.

Path of Projectile

Illustration modeling the path of a projectile.