the first step _CD_. Draw _EA_, _CA_, _DA_, and _GA_, for the
ascending guiding lines. Complete the steps facing us, at central line
_OO_. Then draw guiding line _FB_ for the descending steps (see Rule 8).

[Illustration: Fig. 249.]

CXXXIX

STEPS IN ANGULAR PERSPECTIVE

First draw the base _ABCD_ (Fig. 251) at the required angle by the new
method (Fig. 250). Produce _BC_ to the horizon, and thus find vanishing
point _V_. At this point raise vertical _VV'_. Construct first step
_AB_, refer its height at _B_ to line of heights hI on left, and thus
obtain height of step at _A_. Draw lines from _A_ and _F_ to _V'_. From
_n_ draw diagonal through _O_ to _G_. Raise vertical at _O_ to represent
the height of the next step, its height being determined by the scale of
heights at the side. From _A_ and _F_ draw lines to _V'_, and also
similar lines from _B_, which will serve as guiding lines to determine
the height of the steps at either end as we raise them to the required
number.

[Illustration: Fig. 250.]

[Illustration: Fig. 251.]

CXL

A STEP LADDER AT AN ANGLE

[Illustration: Fig. 252.]

First draw the ground-plan _G_ at the required angle, using vanishing
and measuring points. Find the height _hH_, and width at top _HH'_, and
draw the sides _HA_ and _H'E_. Note that _AE_ is wider than _HH'_, and
also that the back legs are not at the same angle as the front ones, and
that they overlap them. From _E_ raise vertical _EF_, and divide into as
many parts as you require rounds to the ladder. From these divisions
draw lines 1 1, 2 2, &c., towards the other vanishing point (not in the
picture), but having obtained their direction from the ground-plan in
perspective at line _Ee_, you may set up a second vertical _ef_ at any
point on _Ee_ and divide it into the same number of parts, which will be
in proportion to those on _EF_, and you will obtain the same result by
drawing lines from the divisions on _EF_ to those on _ef_ as in drawing
them to the vanishing point.

CXLI

SQUARE STEPS PLACED OVER EACH OTHER

[Illustration: Fig. 253.]

This figure shows the other method of drawing steps, which is simple
enough if we have sufficient room for our vanishing points.

The manner of working it is shown at Fig. 124.

CXLII

STEPS AND A DOUBLE CROSS DRAWN BY MEANS OF DIAGONALS
AND ONE VANISHING POINT

Although in this figure we have taken a longer distance-point than in
th