"The flexible chain, hanging under the action of applied force, will assume a certain shape, namely the catenary if the chain is subjected only to its own weight, or a if the load is uniformly distributed horizontally. Whatever the load, there will be a corresponding shape, and the structural action in all cases is the same; purely tensile forces are transmitted along the centre line of the chain. As Hooke saw in 1675 with his ut pendet continuum flexile, sic stabit contiguum rigidum inversum, ...a hanging chain may be inverted to give a satisfactory arch to carry the same loads, but working in compression rather than tension. The compressive arch, however, if of vanishingly small thickness, would be in unstable equilibrium, and stability is conferred in practice by making the arch ring of finite depth. Now if purely compressive forces, without bending, are to be transmitted from one portion of the arch to the next (as purely tensile forces are transmitted in the chain), then the arch centre line can accept only a single type of loading. Thus a parabolic arch can carry only a uniformly distributed horizontal load (although the magnitude of the load is arbitrary). It is the depth in a real arch which enables the arch to carry wider ranges of loading; a large number of different idealized centre-line arches can be contained within a given practical profile. ...[T]his must be so, or no mediaeval bridge would have survived its decentering."