The arch and its construction
A stone arch on two piers, drawn with its centres and radii; choose any of eighteen arch families and show the line of thrust.
The rules it illustrates
Wedges that lock by their own weight. Build an arch of wedge-shaped stones (voussoirs) whose joints all point towards the centre of the curve: each stone can then fall only by forcing its neighbours apart, and so the ring holds itself up once the last stone, the keystone, is in place.
The flatter the arch, the harder it pushes. An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
As hangs the chain, so stands the arch. A chain hanging freely takes the one shape in which it is in pure tension; turn that shape upside down and it is the shape of an arch in pure compression for the same loads.
An arch stands if its thrust line fits inside it. Trace the path of the resultant force through the stones from crown to foundations. If a line can be found that stays everywhere within the masonry, the arch will stand; where it touches an edge, a hinge will open, and four hinges make it collapse.
How the pointed arches are drawn. Draw a pointed arch from two centres on the springing line. With the centres at the springings, the arch is equilateral; with centres beyond them, a lancet; with centres between them, a drop arch. Late Gothic added arches of four centres and the reversed curve of the ogee.
Relieve a lintel with an arch. Over a doorway or window spanned by a lintel, turn an arch in the wall above so that the weight of the masonry is carried round the opening onto the jambs, leaving the lintel to carry only the small triangle of wall beneath the arch.
Where it appears in the book
In the chapters What Is Architecture?, The Arch.
The terms it shows
Impost · Keystone · Pointed arch · Semicircular arch · Thrust · Voussoir