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.

164

DESCRIPTIVE GEOMETRY

CASE 2. To draw a rectilinear tangent to the curve of intersection.
Analysis. A rectilinear tangent to the curve of intersection will
be tangent to the surface of the cylinder at the given point, and will
therefore lie in a plane tangent to the cylinder along the element
passing through this point. The rectilinear tangent will also be in
the plane of the curve which is the cutting plane. The required
line will therefore be at the intersection of these two planes.
Construction. Let it be required to draw a rectilinear tangent to
the curve of intersection at the point 0, Fig. 151.
The plane tangent to the cylinder along the element through
0 is the plane W. The intersection
u, b,/j / ~of this plane.with S is Q-O-B,
/': a q,~/1 ' rthe required tangent.! / ~ \ AA rectilinear tangent like this, T/' Kf q' S. N A L D N'
/V,.,qv
FIG. 152
It | can be drawn at any point on the
wI\ \yf ~curve before the curve itself has
FIG. 151 been drawn.
Since a rectilinear tangent to
a curve shows the direction of the curve at the point of tangency,
such tangents, when determined in sufficient number, are helpful
in drawing the curve through the points already located.
CASE 3. To find the true size of the intersection.
Analysis and Construction. See Fig. 151. Revolve the plane S,
which is the plane of the curve of intersection, about S-s' into V.
Any point, as M, will fall at mv, and other points may be found in
the same way. The curve determined by the revolved positions of
these points is the required curve of intersection.
The tangent Q-O will, when revolved, take the position qV-oV-r'
and be tangent to the revolved position of the curve of intersection.