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"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…

"Draw lines parallel to AB and CD at distant R from them. The intersection of these lines will be center of the required arc." —French, 1911

Draw Arc of Given radius R Tangent to Two Given Lines

"Draw lines parallel to AB and CD at distant R from them. The intersection of these lines will be center…

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center C and radius CB draw an arc intersecting AB at E, then AE will be equal in length be to the arc AB." —French, 1911

Approximating Length of Circle Arc using Straight Line

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center…

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces small enough as practically to coincide with the arc, and to step off the same number on the right line." —French, 1911

Rectifying Arc Using Dividers

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces…

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge of equations from analytic geometry.

Conic Section Using Circle

The cone is sliced by a circle in a plane perpendicular to the axis. This can be drawn without knowledge…

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing characteristics of each shape.

Conic Section Using Ellipse

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing…

"This (five centered arc) method is based on the principle that the radius of curvature at the end of the minor axis is the third proportional to the semi-minor and semi-major axes, and similarly at the end of the major axis is the third proportional to the semi-major and semi-minor axes. The intermediate radius found is the mean proportional between these two radii." —French, 1911

Approximate Ellipse with Five Centered Arc

"This (five centered arc) method is based on the principle that the radius of curvature at the end of…

"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 cycloid is the curve generated by the motion of a point on the circumference of a circle rolled along a straight line." —French, 1911

Cycloid

"A cycloid is the curve generated by the motion of a point on the circumference of a circle rolled along…

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle rolled inside another circle.

Epicycloid and Hypocycloid

Epicycloid is generated by a circle rolled outside of another circle, whereas a hypocycloid is circle…

"A circle may be conceived as a polygon of an infinite number of sides. Thus to draw the involute of a circle divide it into a convenient number of parts, draw tangents at these points, lay off on these tangents the rectified lengths of the arch from the point of tangency to the starting point, and connect the points by a smooth curve." —French, 1911

Involute of Circle

"A circle may be conceived as a polygon of an infinite number of sides. Thus to draw the involute of…

"Divide the circumference into a number of equal parts, drawing the radii and numbering the points. Divide the radius No. 1 into the same number of equal parts, numbering from the center. With C as center draw concentric arcs intersecting the radii of corresponding numbers, and draw a smooth curve through these intersections." —French, 1911

Draw Spiral of Archimedes

"Divide the circumference into a number of equal parts, drawing the radii and numbering the points.…

A tire is ring shaped, the earliest tires were bands of iron placed on wooden wheels which were used on carts and wagons. The tire would be heated in a forge fire, placed over the wheel and quenched.

Adjustable Tire

A tire is ring shaped, the earliest tires were bands of iron placed on wooden wheels which were used…

A wheel is a circular device that is capable of rotating on its axis, facilitating movement and transportation.

Side View of a Vehicle Wheel

A wheel is a circular device that is capable of rotating on its axis, facilitating movement and transportation.

"A circle may be shaded by shifting the center on a 45-degree line toward the lower right hand corner... by keeping the needle in the center after drawing the circle and springing the compass out and gradually pressing with the middle finger in the position as shown." —French, 1911

Shading a Circle Using Compass

"A circle may be shaded by shifting the center on a 45-degree line toward the lower right hand corner...…

A rolled out image of a cone by dividing the base in equal parts and arcs to measure the true lengths.

Development of Cone

A rolled out image of a cone by dividing the base in equal parts and arcs to measure the true lengths.

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal diameters.

Development of Sphere Gore Method

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal…

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

Development of Sphere Zone Method

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

A development or rolled out oblique cone using triangulation. The method of triangulation is done by creating series of triangles respect to the base.

Development of Oblique Cone by Triangulation

A development or rolled out oblique cone using triangulation. The method of triangulation is done by…

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is not given in the top view and must be revolved until parallel to H."—French, 1911

Oblique Cone by Triangulation Connecting to Two Parallel Pipes of Different Diameters

"An oblique cone connecting two parallel pipes of different diameters... the true size of the base is…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle are, location the elements on it and finding the true length of each from the vertex to the line of intersection." —French, 1911

Intersection of Two Cones

"The cone B would be developed by cutting a right section as S—S whose stretchout will be a circle…

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing area.

Development Exercise of Cylinder

An exercise problem in creating a development or rolled out surface of a cylinder in a 4" by 5" drawing…

The exercise problem of creating a three piece elbow development or rolled out image of the cylinder using projections or with dividers.

Development Exercise of Cylinder using Three Piece Elbow

The exercise problem of creating a three piece elbow development or rolled out image of the cylinder…

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the true shape of hip rafter by using projections or dividers.

Development Exercise of Octagonal Roof and True Shape of Rafter

Problem exercise in drawing a development or a stretchout image of the octagonal roof and finding the…

A development or rolled out image exercise problem of the dome and finding the true shape of the hip, or edge, of the dome by using projections or with dividers.

Development Exercise of Dome and True Shape of Hip

A development or rolled out image exercise problem of the dome and finding the true shape of the hip,…

Development and top completion exercise problem of the cone by dividing the base into equal parts and creating an arc to revolve the sides of the plane.

Development Exercise of Cone

Development and top completion exercise problem of the cone by dividing the base into equal parts and…

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones by using series of cone development.

Development Exercise of Flange and Hood Cones

An exercise problem to complete the top and develop, stretched out, image of the flange and hood cones…

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes can be quite versatile in serving various themes. For example, a star-shaped cutter can be used for Christmas, 4th of July, and messages of congratulations. A circle can be decorated as a sun, ball, flower, spider web, or smiley face. This cutter is in the shape of a four leaf clover.

Cookie Mold Cutter

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes…

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes can be quite versatile in serving various themes. For example, a star-shaped cutter can be used for Christmas, 4th of July, and messages of congratulations. A circle can be decorated as a sun, ball, flower, spider web, or smiley face. This cutter is in the shape of a star.

Star Shaped Cookie Cutter

Many decorating techniques used today do not require elaborate cookie cutters. The simplest of shapes…

A circle in a aerodynamic chamber where the airflow hitting the object. The area at point DD is large creating a resistance.

Circle Aerodynamic

A circle in a aerodynamic chamber where the airflow hitting the object. The area at point DD is large…

Aerodynamic of the ellipse where the area at point DD is small. The small area creates less resistance for the plane while in flight.

Ellipse Aerodynamic

Aerodynamic of the ellipse where the area at point DD is small. The small area creates less resistance…

The illustration of the plane descending while spiraling down. The radius of the spiral spin is getting smaller. A nose spin drive happens when the pilot intentionally or unintentionally stalls the plane and control the plane side to side in air.

Aeroplane Nose Spin Dive Flying

The illustration of the plane descending while spiraling down. The radius of the spiral spin is getting…

An illustration of creating a hand wheel by spinning while moving threaded tool to the desired radius.

Turning Hand Wheels

An illustration of creating a hand wheel by spinning while moving threaded tool to the desired radius.

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

Wooden Sphere

A wooden hollow sphere created by using a lathe and wooden templet at a desired diameter.

A wheel is a circular device that is capable of rotating on its axis, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples are found in transport applications.

Eight Spoke Wheel

A wheel is a circular device that is capable of rotating on its axis, facilitating movement or transportation…

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is transferred to the top part of the cube by creating diagonal lines through the center and series of squares.

Isometric Drawing of Circle using Square

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is…

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular diagram is the main cylindrical body with a circle inside it for the other cylinder. The smaller development is the intersected cylinder. This is commonly used to illustrate pipes.

Development of Two Intersecting Cylinder

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular…

A drawing exercise for drawing eight concentric circles by dividing the paper in quarters as shown. When doing the exercise, the center cannot be enlarged as the circle gets smaller. The exercise is done in ink with fine lines.

Drawing Exercise Eight Concentric Circles using Ink

A drawing exercise for drawing eight concentric circles by dividing the paper in quarters as shown.…

Mechanical drawing exercise of drawing dotted lined concentric circles. The circles are first drawn by dividing the paper into quarters, then draw the circles in pencil. Ink dotted lines on the penciled circles.

Dotted Lined Eight Concentric Circles using Ink and Pencil Drawing Exercise

Mechanical drawing exercise of drawing dotted lined concentric circles. The circles are first drawn…

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal line into half inches. Using a compass, draw the large circle then the smaller circle tangent to the bigger circle using a bow instrument.

Drawing Exercise of Inscribed Circle Pattern Tangent to Left Side

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal…

A mechanical drawing exercise of a circle with curved wavy lines. The image is drawn by dividing horizontal lines into half inches, and draw smaller half circles within the large circle.

Mechanical Drawing Exercise Circle with Wavy Curved Lines Inside

A mechanical drawing exercise of a circle with curved wavy lines. The image is drawn by dividing horizontal…

Mechanical drawing exercise for circle with two tangent points on both sides of the circle. The paper is first divided into quarters, then the large circle is drawn. Smaller circles are then drawn within the circle tangent to the horizontal line.

Inscribed Circle with Smaller Circles at Tangent Points Both Sides of the Large Circle Mechanical Drawing Exercise

Mechanical drawing exercise for circle with two tangent points on both sides of the circle. The paper…

A mechanical drawing exercise of drawing a curved line with circle in the middle. The image is drawn by drawing a small circle in the middle. The curved lines around the circle is drawn by using the ticked line as the radius.

Curved Line with Circle Mechanical Drawing Exercise

A mechanical drawing exercise of drawing a curved line with circle in the middle. The image is drawn…

"With a 45 degree triangle draw lines AC and BD through the center and construct three squares. Set the bow—pencil to a radius of 3∕8' and describe a circular arc in the corner of each square just touching, but not intersecting, the sides of the square. Ink the circular arcs first." —Anthony, 1904

Mechanical Drawing Exercise Three Inscribed Squares with Rounded Corners using Triangle and Bow

"With a 45 degree triangle draw lines AC and BD through the center and construct three squares. Set…

A mechanical drawing practice problem of shading the sides of the inscribed circles. The darker area shows where the light is not hitting the image making the 2D image look 3D. These shadings are done in pen.

Mechanical Drawing Exercise Shading Sides of Inscribed Circle with Ink

A mechanical drawing practice problem of shading the sides of the inscribed circles. The darker area…

An exercise to shade small circles with bow pen for mechanical drawing. The paper is first divided into 4" square. At each corners, draw a 3&fras;8" diameter. The shading is done by reducing and increasing the pressure of the bow while drawing the circle.

Mechanical Drawing Exercise Shading Sides of Small Circles with Bow Pen

An exercise to shade small circles with bow pen for mechanical drawing. The paper is first divided into…

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the right angles, then rounded off with a compass. Using a pen, the sides of the shapes are darkened to show points where no light is hitting the image.

Mechanical Drawing Exercise Shading Sides of Inscribed Squares and Circle with Ink

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the…

This is a tool used to measure circular bodies, very similar to how current calipers work. This tool features a perpendicular ruler to the circular opening.

Circular Body Measure Tool

This is a tool used to measure circular bodies, very similar to how current calipers work. This tool…

"O' is the virtual image of O formed at a spherical surface of centre C and radius CS." —Encyclopaedia Britannica, 1910

Virtual Image Formed on Spherical Surface

"O' is the virtual image of O formed at a spherical surface of centre C and radius CS." —Encyclopaedia…

A spindle governor where both balls are connected to the base. The governor is used to regulate the amount of fuel of the steam engine. As the governor spins, the diameter of the circle increases.

Governor with the Balls Connected to the Base for Steam Engine

A spindle governor where both balls are connected to the base. The governor is used to regulate the…

"As the eccentric turns in the strap, the point O moves in the dotted circle around O', and the point A also moves in a circle. When half a revolution is accomplished the point O will be at O", the Point A will be at A", and the eccentric strap and valve rod will be in the position indicated by the dotted lines." —Derr, 1911

Shaft in an Eccentric Motion from Steam Engine

"As the eccentric turns in the strap, the point O moves in the dotted circle around O', and the point…

"Hydra viridis, the freshwater polyp. The animal is attached to the stem of a plant, and is represented with the base of attachment uppermost; the mouth, not actually seen in the drawing, is at the lower extremity of the body, surrounded by the circle tentacles." — Encyclopaedia Britannica Company, 1910

Freshwater Polyp

"Hydra viridis, the freshwater polyp. The animal is attached to the stem of a plant, and is represented…

"One standing at O will only see the half of the Sky which is above the circle NESW. The whole sky will seem to be turning about the line POP'; the Stars will seem to be moving along the paths EQW, BAB', etc. Stars so near the North Pole that they are inside the dark area KPN will never set."—The Foundation Library, 1911

The Sphere of the Sky

"One standing at O will only see the half of the Sky which is above the circle NESW. The whole sky will…

"A tablet of dark brown clay, much injured, dating from the 8th or 7th century B.C. The two large concentric circles indicate the ocean, or, as it is called in the cuneiform writing between the circles, the 'Briny Flood.' Beyond the ocean are seven successive projections of land, represented by triangles. Perhaps they refer to the countries existing beyond the Black Sea and the Red Sea. The two parallel lines within the inner circle represent the Euphrates. The little rings stand for the Babylonian cities in this region."—Webster, 1913

A Babylonian Map of the World

"A tablet of dark brown clay, much injured, dating from the 8th or 7th century B.C. The two large concentric…

"The Flanch is formed of a segment of a circle placed on the side of the shield. It is always borne double or in pairs, the one on the dexter and the other on the sinister side."—Aveling, 1891

Flanch Shield

"The Flanch is formed of a segment of a circle placed on the side of the shield. It is always borne…

"The Rustre differs from the mascle in that the perforation of the device is circular and not throughout."—Aveling, 1891

Rustre Shield

"The Rustre differs from the mascle in that the perforation of the device is circular and not throughout."—Aveling,…

An example of a heraldic shield with roundels.

Shield with Roundels

An example of a heraldic shield with roundels.

"From annulus, a ring. A mark of difference of the fifth son."—Aveling, 1891

Annulet

"From annulus, a ring. A mark of difference of the fifth son."—Aveling, 1891