As has been seen, Galileo's problem was the determination of the ultimate moment of resistance of a member (wooden, stone, metal, glass) in bending. The problem was posed by reference to a cantilever beam, acted upon by a tip load, or its self-weight, or both; the value of the breaking load(s) was sought. Static equilibrium requires that the moment of the applied load(s) at the root of the cantilever must equal the moment of resistance of the cross-section; since the problem is statically determinate, a problem in the theory of structures is transformed into a problem of strength of materials. Galileo, and later scientists, did not of course think in this way; in particular, the notion of hyperstatic structures, for example the beam on three supports or, later, the propped cantilever or the fixed-ended beam, is not made explicit. These last two more complex structures were in fact discussed in 1798 by Girard, and ‘correct’ solutions were found (see Chapter 6); the solutions were, however, specific for the problems, and Girard does not make general statements about statical indeterminacy. Such ideas became formalized a quarter of a century later; the date of 1826, when Navier published his Leçons, is a convenient marker, and indeed it was not until over a century after that date that the straitjacket imposed by Navier on structural design was finally loosened.

Girard starts the introduction to his book (on the strength of materials and on solids of equal resistance) by stating that his subject consists of something more than rigid-body statics.