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.

128

DESCRIPTIVE GEOMETRY

Construction. In Fig. 124 let A-B represent the axis of the
cylinder, and let 0 represent the point without the surface.
A straight line through 0 parallel to the axis A-B will be a line
of the required plane, and since this line is parallel to G-L, we
know that both traces of
the required plane will be
- d, \- s, parallel to G-L.
Through 0 pass a profile
plane cutting the cylinder
~~~\ ~ in the circle whose center
_- _ — _ — ~is C. Revolve this profile
a,_ / _ plane about its horizontal
C \i \y^ tb trace into H. O will fall
at o11 and the circle C will
oG t i h,\*en L take the position of the
/,~? circle whose center is cH.
ar c~ ""-~,, /7 b-r Through OH draw o_-d, tan-__ - //' -— gent to the circle c, According to analysis this is
S e...::. s' the revolved position of a
line of the required plane.
In true position this line
pierces H at d,, a point in the required horizontal trace; and
pierces V at e', a point in the required vertical trace. The two
traces S-s, and S-s' are now located.
The element of tangency is that one determined by the point K.
Since through o, another straight line may be drawn tangent
to the circle cu, another plane answering the conditions of the
problem may be constructed.
Check. Through some point of the element of tangency draw a
profile plane cutting from the cylinder a circle. A rectilinear tangent to this circle at the point assumed is a line of the required
plane and should pierce H and V in the traces already located.
308. Problem 184. Given a cylinder in the third quadrant 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 cylinder.