Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its bisector are unequal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its…

Illustration of polyhedral angle. "The opening of three or more planes which meet at a common point is called a polyhedral angle."

Polyhedral Angle

Illustration of polyhedral angle. "The opening of three or more planes which meet at a common point…

An illustration showing a straight angle. When the sides of an angle extend in opposite directions, so as to be in the same straight line, the angle is called a straight angle.

Straight Angle

An illustration showing a straight angle. When the sides of an angle extend in opposite directions,…

Trihedral angle. "The sum of any two face angles of a trihedral angle is greater than the third face angle."

Trihedral Angle

Trihedral angle. "The sum of any two face angles of a trihedral angle is greater than the third face…

An illustration of two angles that are adjacent. They have the same vertex and a common side between them. Angles BOD and AOD are adjacent

Adjacent Angles

An illustration of two angles that are adjacent. They have the same vertex and a common side between…

Illustration of adjacent dihedral angles M-AB-N and P-AM-N made by planes.

Adjacent Dihedral Angle

Illustration of adjacent dihedral angles M-AB-N and P-AM-N made by planes.

Illustration of 2 equal dihedral angles.

Two Equal Dihedral Angles

Illustration of 2 equal dihedral angles.

Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

Equal Dihedral Angles

Illustration of 3 equal dihedral angles. "Two dihedral angles have the same ratio as their plane angles."

Illustration of two polyhedral angles that are equal.

Equal Polyhedral Angles

Illustration of two polyhedral angles that are equal.

Illustration used to show that two trihedral angles are equal or symmetrical when the three face angles of the one are respectively equal to the three face angles of the other.

Equal trihedral angles

Illustration used to show that two trihedral angles are equal or symmetrical when the three face angles…

An illustration showing when one straight line meets another straight line and makes the adjacent angles equal, each of these angles is called a right angle.

Right Angles With Same Vertex

An illustration showing when one straight line meets another straight line and makes the adjacent angles…

An illustration of angles with the same vertex made up of 4 lines.

Angles With Same Vertex

An illustration of angles with the same vertex made up of 4 lines.

Illustration of two symmetrical polyhedral angles.

Symmetrical Polyhedral Angles

Illustration of two symmetrical polyhedral angles.

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations of the sides of the other. In this illustration, a and b are vertical angles and c and d are vertical angles.

Vertical Angles

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations…

Illustration of two vertical dihedral angles.

Vertical Dihedral Angles

Illustration of two vertical dihedral angles.

"When the minor axis is at least two-thirds the major, the following method ma be used:Make CF and CG equal to AB-DE.Make CH and CI equal to 3/4 CFF, G, H, I will be centers for arcs E, D, B, and A." —French 1911

Approximate Ellipse using Lines

"When the minor axis is at least two-thirds the major, the following method ma be used: Make CF and…

"Distribution of magnetic lines through a ring armature. Since the lines follow the metal of the ring instead of penetrating the interior no electromotive force is induced in that portion of the winking lying on the interior surface of the ring. There is, therefore, a large amount of dead wire or wire that is ineffective in inducing electromotive force; that is the chief objective to the ring type of armature." -Hawkins, 1917

Distribution of Magnetic Lines, Ring Armature

"Distribution of magnetic lines through a ring armature. Since the lines follow the metal of the ring…

"Formed by lines drawn horizontally, crossed by others drawn diagonally."—Aveling, 1891

Barry Bendy

"Formed by lines drawn horizontally, crossed by others drawn diagonally."—Aveling, 1891

"Produced by lines drawn vertically, by others drawn diagonally, or by a compound of Paly and Bendy."—Aveling, 1891

Paly Bendy

"Produced by lines drawn vertically, by others drawn diagonally, or by a compound of Paly and Bendy."—Aveling,…

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Circle With Diameter, Radius, Segment, Line

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference between the sum of the legs and the hypotenuse.

Circle Inscribed in a Right Triangle

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference…

Illustration showing a circle with an inscribed triangle and radii.

Circle With Inscribed Triangle and Radii

Illustration showing a circle with an inscribed triangle and radii.

Illustration showing a circle with various chords drawn.

Circle With Various Chords

Illustration showing a circle with various chords drawn.

Illustration showing a circle with various chords drawn.

Circle With Various Chords

Illustration showing a circle with various chords drawn.

Illustration showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point where the circumference cuts the hypotenuse bisects the other leg.

Circle With a Right Triangle

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point…

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated by the circumferences. The chords joining the ends of theses lines are parallel.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated…

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact terminated by the circumference. The chords joining the ends of theses lines are parallel.

Tangent Circles With Chords

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact…

"If a sector revolves about its bounding radius as an axis, it generates what may be called a spherical cone."

Spherical Cone

"If a sector revolves about its bounding radius as an axis, it generates what may be called a spherical…

Illustration of the construction used to bisect a given angle.

Construction of Bisecting a Given Angle

Illustration of the construction used to bisect a given angle.

Illustration of the construction used to bisect a given arc.

Construction of Bisecting a Given Arc

Illustration of the construction used to bisect a given arc.

Illustration of the construction used to bisect a given line.

Construction of Bisecting a Given Line

Illustration of the construction used to bisect a given line.

Illustration of the construction used to create an equal angle given a point in a given straight line and a given angle.

Construction of an Equal Angle Given a Point and a Straight Line

Illustration of the construction used to create an equal angle given a point in a given straight line…

Illustration to let fall a perpendicular upon a given line from a given external point.

Construction of Perpendicular Upon a Given Line From an External Point

Illustration to let fall a perpendicular upon a given line from a given external point.

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Illustration of the construction used to divide a straight line into a given number of equal parts.

Construction of a Straight Line Divided Into Equal Parts

Illustration of the construction used to divide a straight line into a given number of equal parts.

Illustration of the construction used to create straight line parallel to a given straight line through a given external point.

Construction of a Straight Line Parallel to a Given Straight Line

Illustration of the construction used to create straight line parallel to a given straight line through…

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing as much of an arc as will practically coincide with the curve, then changing the center and radius for the next portion, remembering always that if arcs are to be tangent, their centers must lie on the common normal at the point of tangency." —French 1911

Curve Inked with Circle Arcs

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing…

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints. This illustration resembles a parabola.

Line, Curved

A curved line with endpoints. This illustration resembles a parabola.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved line with endpoints.

Line, Curved

A curved line with endpoints.

A curved s-shaped line.

Line, Curved

A curved s-shaped line.

Illustration of a projection of a curved line.

Projection of a Curved Line

Illustration of a projection of a curved line.

A curved wavy line.

Line, Curved Wavy

A curved wavy line.

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn by the series of perpendicular lines parallel to the axis.

Drawing Irregular Isometric Curves of Solid

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn…

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.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.