It was clear to Galileo that a beam resting on three supports (which, in modern terminology, would be hyperstatic) could be subjected to forces not envisaged by the engineer. That is, an accidental imperfection (and Galileo used the word accidente), such as decay of one of the end supports, could lead to a set of forces that would break the beam. He was equally clear that no such accident could happen to a beam on two supports; if the supports sink then the beam follows – the statics of a statically determinate beam are unique.

However, it does not seem that Galileo was concerned with any concepts that might stem from the consideration of what is now known as the hyperstatic structure. His objective was, as has been described, to calculate the breaking strength of beams, and for this purpose he determined the greatest value of bending moment in a beam, whether that beam were simply supported or a simple cantilever. The value of bending moment having been found, the problem then became one of the strength of materials, and the historical notes given in Chapter 2 are concerned with the correct way of calculating the moment of resistance of a cross-section.

Girard 1798

It was noted in passing in Chapter 2 that Mariotte made tests on fixed-ended beams, and that he concluded from his experiments that their strengths were twice those of corresponding simply supported beams. Mariotte gave no theoretical explanation for this result, and the problem of the strength of the hyperstatic beam seems to have remained unexplored throughout the eighteenth century.