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.
Fig. 231.
[ CXXVI]
Of Arches, Arcades, Bridges, &c.
For an arcade or cloister (Fig. 232) first set up the outer frame ABCD according to the proportions required. For round arches the height may be twice that of the base, varying to one and a half. In Gothic arches the height may be about three times the width, all of which proportions are chosen to suit the different purposes and effects required. Divide the base AB into the desired number of parts, 8, 10, 12, &c., each part representing 1 foot. (In this case the base is 10 feet and the horizon 5 feet.) Set out floor by means of ¼ distance. Divide it into squares of 1 foot, so that there will be 8 feet between each column or pilaster, supposing we make them to stand on a square foot. Draw the first archway EKF facing us, and its inner semicircle gh, with also its thickness or depth of 1 foot. Draw the span of the archway EF, then central line PO to point of sight. Proceed to raise as many other arches as required at the given distances. The intersections of the central line with the chords mn, &c., will give the centres from which to describe the semicircles.