e oblique square through which to
draw the octagon.

[Illustration: Fig. 200.]

It will be seen that this operation is very much the same as in parallel
perspective, only we make our measurements on the base line _a'B_ as we
cannot measure the vanishing line _BA_ otherwise.

CXI

HOW TO DRAW AN OCTAGONAL FIGURE IN ANGULAR PERSPECTIVE

In this figure in angular perspective we do precisely the same thing as
in the previous problem, taking our measurements on the base line _EB_
instead of on the vanishing line _BA_. If we wish to raise a figure on
this octagon the height of _EG_ we form the vanishing scale _EGO_, and
from the eight points on the ground draw horizontals to _EO_ and thus
find all the points that give us the perspective height of each angle of
the octagonal figure.

[Illustration: Fig. 201.]

CXII

HOW TO DRAW CONCENTRIC OCTAGONS, WITH ILLUSTRATION OF A WELL

The geometrical figure 202 A shows how by means of diagonals _AC_ and
_BD_ and the radii 1 2 3, &c., we can obtain smaller octagons inside the
larger ones. Note how these are carried out in the second figure
(202 B), and their application to this drawing of an octagonal well on
an octagonal base.

[Illustration: Fig. 202 A.]

[Illustration: Fig. 202 B.]

[Illustration: Fig. 203.]

CXIII

A PAVEMENT COMPOSED OF OCTAGONS AND SMALL SQUARES

To draw a pavement with octagonal tiles we will begin with an octagon
contained in a square _abcd_. Produce diagonal _ac_ to _V_. This will be
the vanishing point for the sides of the small squares directed towards
it. The other sides are directed to an inaccessible point out of the
picture, but their directions are determined by the lines drawn from
divisions on base to V2 (see back, Fig. 133).

[Illustration: Fig. 204.]

[Illustration: Fig. 205.]

I have drawn the lower figure to show how the squares which contain the
octagons are obtained by means of the diagonals, _BD_, _AC_, and the
central line OV2. Given the square _ABCD_. From _D_ draw diagonal to
_G_, then from _C_ through centre _o_ draw _CE_, and so on all the way
up the floor until sufficient are obtained. It is easy to see how other
squares on each side of these can be produced.

CXIV

THE HEXAGON

The hexagon is a six-sided figure which, if inscribed in a circle, will
have each of its sides equal to the radius of that circle (Fig. 206). If
inscribed in a rectangle _ABCD_, that rectang