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Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing the circumference of a circle according to the golden section. The ratio of the length of the larger arc to the smaller arc is equal to the ratio of the entire circumference to the larger arc. The golden angle is approximately 137.51°.

Golden Angle

Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing…

"In all the arc lamps in common use, the coil, by means of which the automatic maintenance of the arc is kept up, is placed as a shunt across the its poles."—Finley, 1917

Arc lamp

"In all the arc lamps in common use, the coil, by means of which the automatic maintenance of the arc…

"The arc lamp is essentially a device for automatically separating the carbons when the current is turned on, for 'feeding' the carbons together as they are burned away at their tips, and, in some cases, for short-circuiting the lamp in case of irregularity or accident." -Avery 1895

Arc Lamp

"The arc lamp is essentially a device for automatically separating the carbons when the current is turned…

"Diagram of inclined carbon-flame arc lamp." —Croft 1917

Carbon Flame Arc Lamp

"Diagram of inclined carbon-flame arc lamp." —Croft 1917

"Illustration showing the detail of a carbon arc lamp; S, solenoid; c, clutch; w, clutch-washer; T, electromagnet; m, short circuit point; R, resistance properly adjusted." -Avery 1895

Detailed Arc Lamp

"Illustration showing the detail of a carbon arc lamp; S, solenoid; c, clutch; w, clutch-washer; T,…

"Differential arc lamp mechanism." —Croft 1917

Differential Arc Lamp

"Differential arc lamp mechanism." —Croft 1917

"Metallic flame arc lamp." —Croft 1917

Metallic Flame Arc Lamp

"Metallic flame arc lamp." —Croft 1917

"Since arc lamps are connected in series, any particular lamp that is to be extinguished must be short-circuited. The dynamo is provided with appliances for maintaining a uniform current strength regardless of the number of lamps in use on its circiuit. When the number of lamps is increased, the voltage of the dynamo is correspondingly increased. ." -Avery 1895

Arc Lamps In Series

"Since arc lamps are connected in series, any particular lamp that is to be extinguished must be short-circuited.…

"Circuits of a series arc lamp." —Croft 1917

Circuits of Arc Lamp

"Circuits of a series arc lamp." —Croft 1917

"Arc lamp mechanism with series regulating coil." —Croft 1917

Arc Lamp Series Regulating Coil

"Arc lamp mechanism with series regulating coil." —Croft 1917

"Arc lamp mechanism with shunt regulating coil." —Croft 1917

Arc Lamp with Shunt Regulating Coil

"Arc lamp mechanism with shunt regulating coil." —Croft 1917

Arc lighting, which used two carbon rods conducting electricity to produce light. -Atkinson 1903

Carbon Arc Lighting

Arc lighting, which used two carbon rods conducting electricity to produce light. -Atkinson 1903

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration showing arcs measured in positive and negative angles.

Positive and Negative Arcs in Circles

Illustration showing arcs measured in positive and negative angles.

Method to draw the bisector of a line

Bisect A Line

Method to draw the bisector of a line

Method to bisect an angle

Bisect An Angle

Method to bisect an angle

Illustration used to show how to find the center when given an arc and its radius.

Construction Of Center

Illustration used to show how to find the center when given an arc and its radius.

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

Illustration of a circle with the arc aeb drawn and labeled.

Arc of Circle

Illustration of a circle with the arc aeb drawn and labeled.

An illustration of an arc of a circle. An arc is any part of the circumference of a circle.

Arc of Circle

An illustration of an arc of a circle. An arc is any part of the circumference of a circle.

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Circle with Arc, Chord, Inscribed Angle, Circumscribed Polygon

Illustrations of a circle with arc, chord, inscribed angle, and circumscribed about a polygon.

Illustration of circle with arc and chord.

Arc and Chord in Circle

Illustration of circle with arc and chord.

A design created by inscribing 4 congruent tangent arcs in a circle.

Arcs Inscribed In A Circle

A design created by inscribing 4 congruent tangent arcs in a circle.

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc."

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are commensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured by its intercepted arc." Angle AOB and angle COE are incommensurable.

Central Angles and Arcs in a Circle

Illustration of a circle that can be used to show that an "angle at the center of a circle is measured…

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its subtended arc."

Diameter Perpendicular to a Chord in a Circle

Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its…

Circle with diameter, radius, arc, chord, and arc.

Circle With Parts

Circle with diameter, radius, arc, chord, and arc.

Illustration of circle with arc, chord, diameter and radius.

Parts of Circle

Illustration of circle with arc, chord, diameter and radius.

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.

An illustration showing a circle with radius r, diameter d, and chord c.

Radius, Diameter, and Chord In A Circle

An illustration showing a circle with radius r, diameter d, and chord c.

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. The arcs are inverted.

Reflected Arcs Of A Circle

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of Circle

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the…

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of A Hollow Circle

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn…

Illustration of a circle with two intersecting chords within the circumference. The angle formed is measured by half the sum of the intercepted arcs.

Circle With Two Intersecting Chords

Illustration of a circle with two intersecting chords within the circumference. The angle formed is…

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they subtend equal arcs; conversely, if two arcs are equal, the chords that subtend them are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they are equally distant from the center; conversely, if two chords are equally distant from the center, they are equal."

Equal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord subtends the greater minor arc; conversely, if two minor arcs are unequal, the chord that subtends the greater arc is the greater."

Unequal Chords in Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal, the greater chord is at the less distance from the center."

Unequal Chords in Equal Circles Theorem

Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…

Illustration of equal circles to show that two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted between its sides.

Circles With Inscribed Angles

Illustration of equal circles to show that an inscribed angle is measured by half the arc intercepted…

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.

Illustration of a circle with parallels intercepting equal arcs on a circumference.

Circles With Parallels Intercepting Equal Arcs

Illustration of a circle with parallels intercepting equal arcs on a circumference.

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 2 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° and the overlapping curves are removed to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 8 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration.

Reflected Arcs Of 8 Circles

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required circle." —French, 1911

Draw Circular Arc Through Three Given Points

"Join AB and BC, bisect AB and BC by perpendiculars. Their intersection will be the center of the required…

"Condensing Apparatus for Steamer's Side Lights.—By means of this application of the condensing principle all the light can be distributed with strict equality over 112 degrees, which is the arc prescribed for steamers by the Board of Trade. Several of the Transatlantic and other steamers have adopted this kind of apparatus, which is hung on gimbals and placed in iron towers, having an entry from below the deck, which can be made use of in bad weather." —The Encyclopedia Britannica, 1910

Condensing Apparatus

"Condensing Apparatus for Steamer's Side Lights.—By means of this application of the condensing…

"Condensing Apparatus for Steamer's Side Lights.—By means of this application of the condensing principle all the light can be distributed with strict equality over 112 degrees, which is the arc prescribed for steamers by the Board of Trade. Several of the Transatlantic and other steamers have adopted this kind of apparatus, which is hung on gimbals and placed in iron towers, having an entry from below the deck, which can be made use of in bad weather." —The Encyclopedia Britannica, 1910

Condensing Apparatus

"Condensing Apparatus for Steamer's Side Lights.—By means of this application of the condensing principle…

"When all of the positive plates are connected on one side, and all of the negative plates are connected on the other side, as shown, the cells are said to be joined in parallel, or in multiple arc." -Avery 1895

Parallel Connection

"When all of the positive plates are connected on one side, and all of the negative plates are connected…

Method to construct an equilateral triangle

Construct Equilateral Triangle

Method to construct an equilateral triangle

Method to construct an isosceles triangle

Construct Isosceles Triangle

Method to construct an isosceles triangle

Illustration of of construction of an arc when the chord and height of the segment are given.

Construction of Arc When Given the Chord and Height of the Segment

Illustration of of construction of an arc when the chord and height of the segment are given.

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.

"Cycloidal Arch. Elliptical Arch."-Whitney, 1902

Cycloidal Arch

"Cycloidal Arch. Elliptical Arch."-Whitney, 1902