ellipse will be drawn away
from the cylinder B, and the ellipse, after being found, would have to
be transferred to the end of B. But since centre line G G is obviously
at the same angle to A A that A A is to G G, we may start from the
centre line of the body whose elliptical appearance is to be drawn, and
draw a centre line A A at the same angle to G G as the end of B is
supposed to be viewed from. This is done in Figure 231 _a_, in which the
end face of B is to be drawn viewed from a point on the line G G, but at
an angle of 45 degrees; hence line A A is drawn at an angle of 45
degrees to centre line G G, and centre line E is drawn from the centre
of the end of B at a right angle to G G, and from where it cuts A A, as
at F, a side view of B is drawn, or a single line of a length equal to
the diameter of B may be drawn at a right angle to A A and equidistant
on each side of F. A line, D D, at a right angle to A A, and at any
convenient distance above F, is then drawn, and from its intersection
with A A as a centre, a circle C equal to the diameter of B is drawn;
one-half of the circumference of C is divided off into any number of
equal divisions as by arcs _a_, _b_, _c_, _d_, _e_, _f_. From these
points of division, lines _g_, _h_, _i_, _j_, _k_, _l_ are drawn, and
also lines _m_, _n_, _o_, _p_, _q_, _r_. From the intersection of these
last lines with the face in the side view, lines _s_, _t_, _u_, _t_,
_w_, _x_, _y_, _z_ are drawn, and from point F line E is drawn. Now it
is clear that the width of the end face of the cylinder will appear the
same from any point of view it may be looked at, hence the sides H H are
made to equal the diameter of the cylinder B and marked up to centre
line E.

[Illustration: Fig. 231 _a_.]

[Illustration: Fig. 232.]

It is obvious also that the lines _s_, _z_, drawn from the extremes of
the face to be projected will define the width of the ellipse, hence we
have four of the points (marked respectively 1, 2, 3, 4) in the ellipse.
To obtain the remaining points, lines _t_, _u_, _v_, _w_, _x_, _y_
(which start from the point on the face F where the lines _m_, _n_, _o_,
_p_, _q_, _r_, respectively meet it) are drawn across the face of B as
shown. The compasses are then set to the radius _g_; that is, from
centre line D to division _a_ on the circle, and this radius is
transferred to the face to be projected the compass-point being rested
at the intersection of centre line G and line _t_,