As was mentioned in Chapter 2, Coulomb's memoir of 1773 made contributions to each of the four major problems of civil engineering in the eighteenth century – the strength of beams, the strength of columns, the thrust of soil and the thrust of arches. In all four of these topics Coulomb made advances by considering closely the basic equations of equilibrium, both for the structure overall and at imaginary internal cuts. The work on the fracture of beams has been summarized in Chapter 2.

For the next two problems, columns and soil, Coulomb studies failure planes along which slip is occurring, resisted by the cohesion and friction of the material. That is, just as for the beam problem, solutions are obtained from equilibrium equations combined with a knowledge of material properties. These solutions, and their relation to previous work, are described further in Heyman (1972). By contrast, Coulomb's solutions for arches make only marginal reference to the strength of the material (masonry), and his exploration of the stability of the arch is based solely on considerations of equilibrium, coupled (as is made explicit in the title of his memoir) by principles of maximum and minimum. Indeed the arch seems to have been regarded as a problem separate from other studies in the development of structural mechanics, at least until the end of the nineteenth century.