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.

136

DESCRIPTIVE GEOMETRY

Connect the vertex of the cone and 0 by a straight line and
produce it to pierce H in d, and to pierce V in e', points in
the required traces.
Through F, the point in which B-O intersects the plane of the
base of the cone, draw a rectilinear tangent to the curve of the
base. This tangent will be vertically projected in ff-g', tangent
to the vertical projection of
fLAt ~ the base, and will be horizon_ bl tally projected in f,-g,-a,.
i 7// / b' By analysis F-G is a line
/" H of the required plane and
pierces H at k, and pierces
V at 1'. S-s, drawn through
GSo/ ~y W^ _ d, and k, is the required horiG - /! /I \ zontal trace, and S-s' drawn
/ 7 \. \| through e' and 1' is the re\ / ^ \ I The element of tangency
~/^^ ^ \ \is the straight line through G
and the vertex of the cone..FIG. 131 Since another straight
line may be drawn through
F tangent to the curve of the base, another plane answering the
conditions of the problem may be constructed.
Check. Note whether the element of tangency, which is a line
of the required plane, pierces H and V in the traces now located.
322. Problem 198. Given a cone whose axis is oblique to H and V
and whose base is a circle on V; required to assume a point without the surface and to draw through this point a plane tangent to
the cone.
323. Probem 199. Given a cone whose axis is oblique to H and V,
the plane of whose base is perpendicular to V but oblique to H, and
the horizontalprojection of whose base is a circle; required to assume
a point without the surface and to draw a plane through this point
and tangent to the cone.
324. Problem 200. Given a cone whose axis is oblique to Hand V,
and whose base is a circle in a plane parallel to If and above it;