Stresses in ancient and medieval structures are low. The stone in a Greek temple, in a Gothic cathedral, or in the arch ring of a masonry bridge, is working at a level one or two orders of magnitude below its crushing strength. This is a necessary condition for survival through the centuries; it is not sufficient. It is necessary also that the shape of the structure should be correct, so that structural forces may somehow be accommodated satisfactorily; this is a question of correct geometry. Thus for such structures the calculation of stress is of secondary interest; it is the shape of the structure that governs its stability. All surviving ancient and medieval writings on buildings are concerned precisely with geometrical rules. The architects had, no doubt, an intuitive understanding of forces and resulting stresses, but this understanding was not articulated in a form that would be of use in design; there is no trace in the records, over the two or three millennia for which they exist, of any ideas of this sort.

Instead, the design process would have proceeded by trial and error, by recording past experience, by venturing, more or less timidly, into the unknown, and by the use of models. A large-scale model served several functions – to demonstrate the design to the commissioner, for example, and to solve constructional problems; above all, if the model were stable, so would be the full-scale building, since the model proved that the geometry was correct. All of this experience was recorded, and refined into rules of construction.