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.

140

DESCRIPTIVE GEOMETRY

The element R-Q- U is the element of tangency.
Check. Through 0, or through any point on the element of tangency, draw a straight line parallel to S-s, and note whether it
intersects V in the vertical trace already located.
330. Problem 206. To draw a plane tangent to a helical convolute
and through a point assumed without the surface.
Analysis. A plane through the given point and intersecting the
surface will cut from the surface a line, usually curved, and from
the required plane a straight line running through the given point
and tangent to the curve. Therefore, through the given point pass
a plane cutting from the surface a curved line. Through the given
/ / d
I'
by
FIG. 135
point and tangent to this curved line draw a straight line. This
straight line is a line of the required plane and will pierce H and V
in points of the required traces.
The element of the surface through the point of tangency just
determined on the curve of the surface is the element of tangency
and is a line of the required plane.
A straight line tangent to the surface at any point on the
element of tangency is another line of the required plane.
Construction. Let the helical convolute be represented as in
Fig. 135. A-B represents the axis and O represents the given point.