A circle divided into twelfths with five twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with five twelfths shaded.

A circle divided into sevenths with six sevenths shaded.

Fraction Pie Divided into Sevenths

A circle divided into sevenths with six sevenths shaded.

A circle divided into eighths with six eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with six eighths shaded.

A circle divided into ninths with six ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with six ninths shaded.

A circle divided into tenths with six tenths shaded.

Fraction Pie Divided into Tenths

A circle divided into tenths with six tenths shaded.

A circle divided into elevenths with six elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with six elevenths shaded.

A circle divided into twelfths with six twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with six twelfths shaded.

A circle divided into twelfths with six twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with six twelfths shaded.

A circle divided into twelfths with six twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with six twelfths shaded.

A circle divided into eighths with seven eighths shaded.

Fraction Pie Divided into Eighths

A circle divided into eighths with seven eighths shaded.

A circle divided into ninths with seven ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with seven ninths shaded.

A circle divided into tenths with seven tenths shaded.

Fraction Pie Divided into Tenths

A circle divided into tenths with seven tenths shaded.

A circle divided into elevenths with seven elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with seven elevenths shaded.

A circle divided into twelfths with seven twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with seven twelfths shaded.

A circle divided into ninths with eight ninths shaded.

Fraction Pie Divided into Ninths

A circle divided into ninths with eight ninths shaded.

A circle divided into tenths with eight tenths shaded.

Fraction Pie Divided into Tenths

A circle divided into tenths with eight tenths shaded.

A circle divided into elevenths with eight elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with eight elevenths shaded.

A circle divided into twelfths with eight twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with eight twelfths shaded.

A circle divided into tenths with nine tenths shaded.

Fraction Pie Divided into Tenths

A circle divided into tenths with nine tenths shaded.

A circle divided into elevenths with nine elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with nine elevenths shaded.

A circle divided into twelfths with nine twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with nine twelfths shaded.

A circle divided into elevenths with ten elevenths shaded.

Fraction Pie Divided into Elevenths

A circle divided into elevenths with ten elevenths shaded.

A circle divided into twelfths with ten twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with ten twelfths shaded.

A circle divided into twelfths with eleven twelfths shaded.

Fraction Pie Divided into Twelfths

A circle divided into twelfths with eleven twelfths shaded.

Oval with dotted vertical and horizontal lines that are lines of symmetry.

Lines of Symmetry, Oval With

Oval with dotted vertical and horizontal lines that are lines of symmetry.

Compass beam is used for large circles a compass or a lengthening bar cannot draw.

Beam Compass

Compass beam is used for large circles a compass or a lengthening bar cannot draw.

Drop pen, or rivet pen, can make small circles faster than the bow pen. The pen is useful in bridge work, constructional work, and topographical drawing.

Drop Pen

Drop pen, or rivet pen, can make small circles faster than the bow pen. The pen is useful in bridge…

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise motion.

Drawing a Circle Using Compass

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise…

"Circles up to perhaps three inches in diameter may be drawn with the legs straight but for larger sizes both the needle-point and the pencil leg should be at the knuckle joints so as to be perpendicular to the paper." — French, 1911

Drawing Large Circles with Compass

"Circles up to perhaps three inches in diameter may be drawn with the legs straight but for larger sizes…

Lengthening bar is used to draw circles bigger than 10 inches.

Use of Lengthening Bar

Lengthening bar is used to draw circles bigger than 10 inches.

Bow instruments can be used for drawing small circles. Hold the the left hand and spin the nut in or out with the finger to avoid wear and stripping the thread. "Small adjustments should be made with one hand, with needle point in position on the paper." — French, 1911

Drawing Small Circles with Bow Instrument

Bow instruments can be used for drawing small circles. Hold the the left hand and spin the nut in or…

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4" apart. In drawing concentric circles always draw the smallest first. The dotted circles are drawn in in pencil with long dashes, and inked as shown." —French, 1911

Drawing Concentric Circles with Compass

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4"…

"Draw a circle three inches in diameter. Divide the circumference into five equal parts by trial with dividers. From these points draw radial lines and divide each into four equal parts with spacers. With these points as centers draw the semicircles as shown The radial lines are not to be inked." —French, 1911

Drawing Tangent Arcs with Compass and Dividers

"Draw a circle three inches in diameter. Divide the circumference into five equal parts by trial with…

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the angles with the 30-degree angle, extending the bisectors to the opposite sides. With these middle points of the sides as centers and radius equal to 1/2 the side, draw arcs cutting the bisectors. These intersection will be centers for the inscribed circles. With centers on the intersection of these circles and the bisectors, round off the points of the triangle as shown." —French, 1911

Drawing Tangent Circles and Lines with Compass and Triangles

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the…

"Draw one and one-half inch square about center of space. Divide AE into four 3/16" spaces, with scale. With bow pencil and centers A, B, C, D draw four semicircles with 3/8" radius and so on. Complete the figure by drawing the horizontal and vertical tangents as shown." —French, 1911

Drawing Tangent to Circle Arcs with Bow Compass

"Draw one and one-half inch square about center of space. Divide AE into four 3/16" spaces, with scale.…

"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…

"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…

"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…

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 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…