It has been noted that James Bernoulli (1694,1695) discussed the problem of finding the moment of resistance of a cross-section in bending. This same paper makes a fundamental contribution to the problem of the elastic flexure of a member. Bernoulli remarks that Galileo had contended (wrongly) that the deflected form of the cantilever was a parabola. Saint-Venant, in his annotated edition of Navier's Leçons, repeats this attribution to Galileo, but in fact there is no such contention to be found in the Dialogues of 1638. The first discussion of an elastic deflected form seems to be that of Pardies (1673), and he indeed asserts that the parabolic form is correct.

Pardies starts his book on Statics with clear and accurate statements of basic laws – the law of the lever, for example (in which his presentation follows exactly that of Galileo, fig. 1.2), moments of forces, the laws of pulleys, the forces in windlasses, gear trains and so on. He then moves on to discuss the question of the shape of a hanging uniform cord, and he establishes the powerful ‘Pardies’ theorem', namely that the tangents at any two points on the cord intersect at a point directly below the centre of gravity of the portion of the cord between the two points. He states that the shape of the hanging cord is not a parabola, and settles finally for the hyperbola (he had, of course no knowledge of the calculus. Leibniz (1691) published the solution of the catenary).