e above.

CXXV

OF ROOFS

The pyramidal roof (Fig. 228) is so simple that it explains itself. The
chief thing to be noted is the way in which the diagonals are produced
beyond the square of the walls, to give the width of the eaves,
according to their position.

[Illustration: Fig. 228.]

Another form of the pyramidal roof is here given (Fig. 229). First draw
the cube _edcba_ at the required height, and on the side facing us,
_adcb_, draw triangle _K_, which represents the end of a gable roof.
Then draw similar triangles on the other sides of the cube (see Fig.
159, LXXXIV). Join the opposite triangles at the apex, and thus form two
gable roofs crossing each other at right angles. From _o_, centre of
base of cube, raise vertical _OP_, and then from _P_ draw sloping lines
to each corner of base _a_, _b_, &c., and by means of central lines
drawn from _P_ to half base, find the points where the gable roofs
intersect the central spire or pyramid. Any other proportions can be
obtained by adding to or altering the cube.

[Illustration: Fig. 229.]

To draw a sloping or hip-roof which falls back at each end we must first
draw its base, _CBDA_ (Fig. 230). Having found the centre _O_ and
central line _SP_, and how far the roof is to fall back at each end,
namely the distance _Pm_, draw horizontal line _RB_ through _m_. Then
from _B_ through _O_ draw diagonal _BA_, and from _A_ draw horizontal
_AD_, which gives us point _n_. From these two points _m_ and _n_ raise
perpendiculars the height required for the roof, and from these draw
sloping lines to the corners of the base. Join _ef_, that is, draw the
top line of the roof, which completes it. Fig. 231 shows a plan or
bird's-eye view of the roof and the diagonal _AB_ passing through centre
_O_. But there are so many varieties of roofs they would take almost a
book to themselves to illustrate them, especially the cottages and
farm-buildings, barns, &c., besides churches, old mansions, and others.
There is also such irregularity about some of them that perspective
rules, beyond those few here given, are of very little use. So that the
best thing for an artist to do is to sketch them from the real whenever
he has an opportunity.

[Illustration: Fig. 230.]

[Illustration: Fig. 231.]

CXXVI

OF ARCHES, ARCADES, BRIDGES, &C.

[Illustration: Fig. 232.]

For an arcade or cloister (Fig. 232) first set up the outer frame _ABCD_
according to the pr