ipal points of the
plan to the station-point _P_, such as _bP_, _cP_, _dP_, &c., and where
these lines intersect the picture plane (_VV'_ here represents it as
well as the horizon), drop perpendiculars _b'B_, _aA_, _d'D_, &c., to
meet the vanishing lines _AV_, _AV'_, which will determine the points
_A_, _B_, _C_, _D_, 1, 2, 3, &c., and also the perspective lengths of
the sides of the figure _AB_, _AD_, and the divisions _B_, 1, 2, &c.
Taking the height of the figure _AE_ from the elevation, we measure it
on _Aa_; as in this instance _A_ touches the ground line, it may be used
as a line of heights.

I have here placed the perspective drawing under the ground plan to show
the relation between the two, and how the perspective is worked out, but
the general practice is to find the required measurements as here shown,
to mark them on a straight edge of card or paper, and transfer them to
the paper on which the drawing is to be made.

This of course is the simplest form of a plan and elevation. It is easy
to see, however, that we could set out an elaborate building in the same
way as this figure, but in that case we should not place the drawing
underneath the ground-plan, but transfer the measurements to another
sheet of paper as mentioned above.

CIX

THE OCTAGON

To draw the geometrical figure of an octagon contained in a square, take
half of the diagonal of that square as radius, and from each corner
describe a quarter circle. At the eight points where they touch the
sides of the square, draw the eight sides of the octagon.

[Illustration: Fig. 198.]

[Illustration: Fig. 199.]

To put this into perspective take the base of the square _AB_ and
thereon form the perspective square _ABCD_. From either extremity of
that base (say _B_) drop perpendicular _BF_, draw diagonal _AF_, and
then from _B_ with radius _BO_, half that diagonal, describe arc _EOE_.
This will give us the measurement _AE_. Make _GB_ equal to _AE_. Then
draw lines from _G_ and _E_ towards _S_, and by means of the diagonals
find the transverse lines _KK_, _hh_, which will give us the eight
points through which to draw the octagon.

CX

HOW TO DRAW THE OCTAGON IN ANGULAR PERSPECTIVE

Form square _ABCD_ (new method), produce sides _BC_ and _AD_ to the
horizon at _V_, and produce _VA_ to _a'_ on base. Drop perpendicular
from _B_ to _F_ the same length as _a'B_, and proceed as in the previous
figure to find the eight points on th