TO DRAW A TRUNCATED CIRCULAR CONE, GIVEN IN POSITION AND MAGNITUDE,
THE TRUNCATIONS BEING IN HORIZONTAL PLANES, AND THE AXIS OF THE CONE
VERTICAL.
Let _ABCD_, Fig. 37., be the portion of the cone required.
[Illustration: Fig. 37.]
As it is given in magnitude, its diameters must be given at the base
and summit, _AB_ and _CD_; and its vertical height, _CE_.[24]
And as it is given in position, the center of its base must be given.
[Illustration: Fig. 38.]
Draw in position, about this center,[25] the square pillar _afd_,
Fig. 38., making its height, _bg_, equal to _CE_; and its side, _ab_,
equal to _AB_.
In the square of its base, _abcd_, inscribe a circle, which therefore
is of the diameter of the base of the cone, _AB_.
In the square of its top, _efgh_, inscribe concentrically a circle
whose diameter shall equal _CD_. (Coroll. Prob. XIII.)
Join the extremities of the circles by the right lines _kl_, _nm_.
Then _klnm_ is the portion of cone required.