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.

126

DESCRIPTIVE GEOMETRY

CASE 1. When the base of the cylinder is a circle on H.
Construction. In Fig. 122 let A-B represent the axis of the
cylinder, and let 0 represent the point assumed without the surface.
Through 0 draw 0-D parallel to the elements of the cylinder
and produce it to pierce H at d,. Through d, draw s,-d,-e,-S tangent to the circular base at e,. According to analysis this is a line
of the required plane, and since it is in H, it is the required horizontal trace. Through 0 draw O-G parallel to s,-S piercing V at g'.
S-g'-s' is the required vertical trace.
The element E-F through E is the element of tangency.
Since from the point d, another straight line may be drawn tangent to the base of the cylinder, 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 V in the vertical trace already located.
aG_____________J a~cfek \ S
FIG. 122
CASE 2. When the plane of the base of the cylinder is perpendicular to H but oblique to V.
Construction. In Fig. 123 let A-B represent the axis of the
cylinder, and let O represent the point without the surface.
Through 0 draw 0-D parallel to the elements of the cylinder
and produce it to pierce H at d, and to pierce V at e'.