Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

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DESCRIPTIVE GEOMETRY

If a curve is rolled out upon a rectilinear tangent to the curve,
so that the consecutive points of the curve fall consecutively upon
the tangent, that portion of the tangent covered between the first
and last points of contact will represent the rectification of that
portion of the curve between these same points.
The work of rectification is accomplished graphically by dividing the curve into a large number of small arcs, so small that the
chords of the arcs may for practical purposes be taken as equal in
length to the arcs themselves, and by taking
the summation of these chords.
D In Fig. 85 let it be required to rectify
the portion A-B of the curve A-B-D. Set
the dividers at some sufficiently small distance
6B and apply this distance as a chord successively
5.to the curve, starting with the point A. In
this particular case the chord is applied six
times, leaving the little arc 6-B whose chord
-4, 2,3 4 5 6,B, DI is smaller than the chord assumed.
FIG. 85 Now apply the original chord distance six
times to the straight line A,-D,, starting with A,, adding to the sum
the little distance 6,-B,, which is the chord measure of the little
arc 6-B on the original curve. The distance A,-B, is the rectified
length of the arc A-B.
213. The Helix. The helix is a curve of double curvature generated by a point moving uniformly both around and in the direction
of a given straight line from which it retains a constant distance.
The straight line around and along which the generating point
moves is called the axis of the helix.
The constant distance which the generating point retains from
the axis is called the radius of the helix.
The distance over which the generating point moves in the
direction of the axis during one circuit of the axis is called the
pitch of the helix.
If, to an observer looking along the axis in that direction in
which the generating point is moving, the circuit of the generating point about the axis is clockwise, the helix is called a righthanded helix.