The alphabet of mouldings

Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.

To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.

pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet

Divide the inside of a dome into coffers that shrink in step with the meridians as they rise, so that their perspective deepens the dome and draws the eye to the light of the lantern.

To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.

sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2

If the sphere that forms the pendentives is simply continued above the ring, the bay is covered by a single shallow dome, the sail vault or pendentive dome, which springs directly from the four corners.

crown = h₀ + S⁄√2 (lower than a hemisphere on the ring, h₀ + S)

Edge the beds before the portico with box, clip box into figures of animals set facing one another, and in the garden beyond cut it into many shapes, even into the letters of the owner’s name.