idth of that oblong. Another thing to note is that we have made use of
the half distance, which enables us to make our pavement look flat
without spreading our lines outside the picture.

[Illustration: Fig. 209.]

CXVI

A PAVEMENT OF HEXAGONAL TILES IN ANGULAR PERSPECTIVE

This is more difficult than the previous figure, as we only make use of
one vanishing point; but it shows how much can be done by diagonals, as
nearly all this pavement is drawn by their aid. First make a geometrical
plan _A_ at the angle required. Then draw its perspective _K_. Divide
line 4b into four equal parts, and continue these measurements all
along the base: from each division draw lines to _V_, and draw the
hexagon _K_. Having this one to start with we produce its sides right
and left, but first to the left to find point _G_, the vanishing point
of the diagonals. Those to the right, if produced far enough, would meet
at a distant vanishing point not in the picture. But the student should
study this figure for himself, and refer back to Figs. 204 and 205.

[Illustration: Fig. 210.]

CXVII

FURTHER ILLUSTRATION OF THE HEXAGON

[Illustration: Fig. 211 A.]

[Illustration: Fig. 211 B.]

To draw the hexagon in perspective we must first find the rectangle in
which it is inscribed, according to the view we take of it. That at _A_
we have already drawn. We will now work out that at _B_. Divide the base
_AD_ into four equal parts and transfer those measurements to the
perspective figure _C_, as at _AD_, measuring other equal spaces along
the base. To find the depth _An_ of the rectangle, make _DK_ equal to
base of square. Draw _KO_ to distance-point, cutting _DO_ at _O_, and
thus find line _LO_. Draw diagonal _Dn_, and through its intersections
with the lines 1, 2, 3, 4 draw lines parallel to the base, and we shall
thus have the framework, as it were, by which to draw the pavement.

[Illustration: Fig. 212.]

CXVIII

ANOTHER VIEW OF THE HEXAGON IN ANGULAR PERSPECTIVE

[Illustration: Fig. 213.]

Given the rectangle _ABCD_ in angular perspective, produce side _DA_ to
_E_ on base line. Divide _EB_ into four equal parts, and from each
division draw lines to vanishing point, then by means of diagonals, &c.,
draw the hexagon.

In Fig. 214 we have first drawn a geometrical plan, _G_, for the sake of
clearness, but the one above shows that this is not necessary.

[Illustration: Fig. 214.]

To rais