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Different compasses used in mechanical drawing.

Compasses

Different compasses used in mechanical drawing.

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

Composite Figure

Illustration of a composite figure made up of rings, rectangles, triangles, etc..

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

Cross section of concrete conduit. The diagram can be used to find volume.

Cross Section of Concrete Conduit

Cross section of concrete conduit. The diagram can be used to find volume.

"A cone is a solid whose base is a circle and whose convex surface tapers uniformly to a point." —Hallock 1905

Cone

"A cone is a solid whose base is a circle and whose convex surface tapers uniformly to a point." —Hallock…

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…

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.

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Plane Parallel to Base, Passing Through a Cone

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

Plane Parallel to Base, Passing Through a Cone

Illustration of a plane parallel to the base passing through a cone (section made is a circle).

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…

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the curve vertices of the conic.

Conic Axes

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the…

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…

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Cone depicting Conic Sections

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle, ellipse.

Cone depicting Conic Sections

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

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 used to construct a circle when given two points that it passes through and a radius.

Construction of a Circle When Given Two Points and a Radius

Illustration used to construct a circle when given two points that it passes through and a radius.

Illustration of a triangle with its incircle and three excircles constructed.

Triangle With Circle Constructions

Illustration of a triangle with its incircle and three excircles constructed.

Illustration used to construct a common tangent when given two circles.

Construction of a Common Tangent When Given Two Circles

Illustration used to construct a common tangent when given two circles.

Illustration used to construct a circle that shall pass through a given point and cut chords of a given length from two parallels.

Construction of a Circle Through a Given Point that Cuts Chords of Given Lengths From Parallels

Illustration used to construct a circle that shall pass through a given point and cut chords of a given…

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

Illustration of of construction of a radius when given only a part of the circumference.

Construction of Radius When Given Only a Part of the Circumference

Illustration of of construction of a radius when given only a part of the circumference.

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…

Finding the equation of a line with polar coordinates.

Polar Coordinates

Finding the equation of a line with polar coordinates.

Isometric of a cube with circles inscribed on its faces.

Isometric of a Cube With Circles Inscribed

Isometric of a cube with circles inscribed on its faces.

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…

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…

"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…

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…

Projection of a cylinder with a circular hole.

Projection of Cylinder With Circular Hole

Projection of a cylinder with a circular hole.

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…

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a cylinder.

Cylinder Inscribed in Pentagonal Prism

Right circular cylinder inscribed in a pentagonal prism. Or, Pentagonal prism circumscribed about a…

Isometric of a cylinder.

Isometric of a Cylinder

Isometric of a cylinder.

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

Plane Intersecting A Cylinder

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

Illustration of planes passing through a cylinder.

Planes Passing Through A Cylinder

Illustration of planes passing through a cylinder.

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder greatly inclined to a plane.

Projection of Cylinder

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder…

Projections of a cylinder inclined to horizontal plane.

Projections of Cylinder

Projections of a cylinder inclined to horizontal plane.

a solid which may be concieved as generated by the revolution of a rectangle about one of its sides.

Right Cylinder

a solid which may be concieved as generated by the revolution of a rectangle about one of its sides.

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

2 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

3 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

4 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

7 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent…

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and two parallel lines at given points A and B. "Join A and B; divide AB into four equal parts and erect perpendiculars. Draw Am at right angles from A, and Bn at right angles from B; then m and n are the centers of the circle arcs of the required cyma."

Construction Of A Cyma

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and…

Design made by drawing one large circle and then two circles that are vertically placed and internally tangent to the original circle. Erase the left side of the top circle and the right side of the bottom circle to create the design. It resembles the yin and yang symbol.

Design Similar to Yin Yang Symbol

Design made by drawing one large circle and then two circles that are vertically placed and internally…

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

A solid belonging to the isometric system, with 24 trapezoidal planes. It is the parallel hemihedral form of the hexoctahedron.

Diploid

A solid belonging to the isometric system, with 24 trapezoidal planes. It is the parallel hemihedral…

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,…

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 should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

Drawing Lines 4

Circles should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

"Were the Earth's orbit a perfect circle, and her axis perpendicular to the plane of this orbit, the days would be of a uniform length, and there would be no difference between the clock and the Sun." -Comstock 1850

Suns in the Equator and Ecliptic

"Were the Earth's orbit a perfect circle, and her axis perpendicular to the plane of this orbit, the…

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate end, B, of the transverse axis, called the eccentric angle of the point H." -Whitney, 1911

Eccentric Angle

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate…

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal to the length of the major axis of the ellipse. The ellipse is externally tangent to the circle.

Ellipse Inscribed In A Circle

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal…

Illustration showing an ellipse (and circle) as a section from a cylinder.

Section of a Cylinder Showing an Ellipse

Illustration showing an ellipse (and circle) as a section from a cylinder.

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

16 Rotated Concentric Ellipses

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals…