decided upon the incline or angle, such as _CBA_, at which the
steps are to be placed, and the height _Bm_ of each step, draw _mn_ to
_CB_, which will give the width. Then measure along base _AB_ this width
equal to _DB_, which will give that for all the other steps. Obtain
length _BF_ of steps, and draw _EF_ parallel to _CB_. These lines will
aid in securing the exactness of the figure.

[Illustration: Fig. 243.]

[Illustration: Fig. 244.]

CXXXV

STEPS, FRONT VIEW

In this figure the height of each step is measured on the vertical line
_AB_ (this line is sometimes called the line of heights), and their
depth is found by diagonals drawn to the point of distance _D_. The rest
of the figure explains itself.

[Illustration: Fig. 245.]

CXXXVI

SQUARE STEPS

Draw first step _ABEF_ and its two diagonals. Raise vertical _AH_, and
measure thereon the required height of each step, and thus form scale.
Let the second step _CD_ be less all round than the first by _Ao_ or
_Bo_. Draw _oC_ till it cuts the diagonal, and proceed to draw the
second step, guided by the diagonals and taking its height from the
scale as shown. Draw the third step in the same way.

[Illustration: Fig. 246.]

CXXXVII

TO DIVIDE AN INCLINED PLANE INTO EQUAL PARTS--SUCH AS A LADDER PLACED
AGAINST A WALL

[Illustration: Fig. 247.]

Divide the vertical _EC_ into the required number of parts, and draw
lines from point of sight _S_ through these divisions 1, 2, 3, &c.,
cutting the line _AC_ at 1, 2, 3, &c. Draw parallels to _AB_, such as
_mn_, from _AC_ to _BD_, which will represent the steps of the ladder.

CXXXVIII

STEPS AND THE INCLINED PLANE

[Illustration: Fig. 248.]

In Fig. 248 we treat a flight of steps as if it were an inclined plane.
Draw the first and second steps as in Fig. 245. Then through 1, 2, draw
1V, _AV_ to _V_, the vanishing point on the vertical line _SV_. These
two lines and the corresponding ones at _BV_ will form a kind of
vanishing scale, giving the height of each step as we ascend. It is
especially useful when we pass the horizontal line and we no longer see
the upper surface of the step, the scale on the right showing us how to
proceed in that case.

In Fig. 249 we have an example of steps ascending and descending. First
set out the ground-plan, and find its vanishing point _S_ (point of
sight). Through _S_ draw vertical _BA_, and make _SA_ equal to _SB_. Set
out