Use one side of AB as a radius and A as the center. Draw

an arc from B to the extension of side AC, as shown in

view B. Next, measure a radius the length of AC plus

its extension. With C as the center, draw an arc to the

extension of side BC. With BC plus its extension as the

radius and B as the center, draw an arc to the extension

of side AB, as shown in view C. Continue in this

manner until the figure is the desired size.

Consider the circle as a polygon with many sides.

Divide the circumference of the circle into several equal

segments (fig. 14-32, view A). Then, draw tangents

from each segment (view B). With the cord of a

segment as a radius, draw an arc from one segment to

intersect the tangent of the next segment, as shown in

view B. With the intersection point on this tangent to

the point of tangency as a radius, draw an arc to intersect

the next tangent (view C). Continue until the figure is

the required size.

as a center, draw an arc from each of the numbered

segments that intersect the corresponding numbered

The spiral is generated by a point moving around a

divisions on the radius (view B). These intersections

fixed point, its distance increasing uniformly with the

are the points of the curve (view C).

angle. To draw a spiral that makes one turn in a given

circle, divide the circle into several equal segments (fig.

14-33, view A). Then, divide the radius of a circle into

the same number of parts, and number them from the

Consider the helix (fig. 14-34), a curve that is

center outward (view A). Using the center of the circle

generated by a point moving uniformly along a straight

line that revolves around an axis. If the line moves

parallel to the axis, it will generate a cylindrical helix.

If it moves at an angle to the. axis, it will generate a

conical helix. The lead of a helix is the distance along

the axis to which the point advances in one revolution.

To draw a helix, draw two views of the cylinder, as

shown in view A. Divide the lead into an equal number

of parts. Divide the circle into the same number of parts

(view B). The intersection of the lines from these points

(view C) are the points of a cylindrical helix.

You must be able to calculate the amount of

material needed to manufacture or repair many different

items used throughout the Navy. You must also be able

to determine the weight of the finished product to

calculate the approximate weight of an object. To do

this, you must have a knowledge of geometry and be

able to determine areas and volumes of geometric

shapes and figures.

14-18

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