Page Plate 7

Plate 7 Fig. A shews how to find the length and backing of any hip square
or bevel, a, b the pitch or height of the roof is 1/3 a, d, a Square pitch
the height equal to half the width a, c, amean between b, and d, the length
of the hips are given to the pitch a, c, and backing of ditto the length
of the hip e, h, is equal to f, c, and the length of the hip I, k is equal
to c, g, to find the backing of the hips, draw the lines l, p, m, and then
n, p, o at right angles with a, I, and a, e, then set the compasses at ,p,
and draw a circle touching the hip line at r, then from point s draw  the
lines s, m, s, l, and s, n, s, o which gives the backing of the hip.  Fig.
B gives the miter for the angle stiles of a pitch sky-light and likewise
the bevel of the level bar or pnrline to the hip in roofs, scc.