Idealised assumptions are made about masonry: it has zero tensile strength, unlimited compressive strength and zero sliding. These assumptions allow calculations about masonry structures that equilibrate and accommodate small changes in boundary conditions. Such small changes produce cracks that in an arch form ‘hinges’ through which the line of thrust passes. With four or more hinges, large loads make the arch collapse as the line of thrust strays outside it; a ‘flat arch’, whose abutments can be joined by an internal straight line, does not collapse. To keep the line of thrust within it, an arch must have at least a minimum thickness. The ratio of the actual thickness to this minimum is the ‘geometrical factor of safety’. Often it exceeds 2, but by the so-called ‘safe’ theorem, if it exceeds 1 then the arch is safe. New cathedral buildings have collapsed within two decades, a typical period for soil settlement. Later collapses may be due to changes in the soil or the masonry. Without evidence of recent shifts, cracks are just responding to previous change, and should merely be filled with mortar to keep them dry.