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.

SINGCLE CUIVED SURFACES

95

It will be evident that if the dimensions or position of the
cylinder be changed, the projections of the cylinder will also be
changed. It will also be evident that a cylinder of definite dimension and position will have
definite projections fully
determining the cylinder..
It must be remembered that
in assuming the circular base
and the inclination of the axis, i a,i
both at random, we have rep- aj 'dm
resented a cylinder at random
and not one of definite dimension and position.
CASE 4. To represent the
cylinder when the plane of its
FIG. 101
base is oblique to H but perpendicular to V. In Fig. 102 the circle whose center is a, represents
the horizontal projection of the base; the straight line k'-m'
included between the two vertical
/:/ m,, lines k-k' and m-m', each drawn
/t /: /, tangent to the circle whose center
// / /// is a,, represents the vertical pro/d/ /:i/ jection of the base, and A-B repk~, a/dm< j resents the axis.
\a(n!( mThe horizontal projections of
_ t',; _ _the extreme elements D-E and
b_ ' F-G can now be determined as
d / /^// mnin the previous case. The lines
t/ / // k1-'l and m'-n' represent the verki/ / // tical projections of the highest
d7$/ 2// and lowest, and therefore the exf m'i treme, elements as seen from the
FIG. 102 observer's standpoint while projecting on V.
233. To assume a Rectilinear Element of the Cylinder. Let the
cylinder be represented with a circular base on H, as shown in
Fig. 103. Assume any point, as E, in the circumference of the