Galileo does not attempt any theory to account for the flexure of the beam. This theory, supplied by Hooke's law, was applied by Mariotte, Leibnitz, De Lahire, and Varignon, but they neglect compression of the fibres, and so place the neutral in the lower face of Galileo's beam. The true position of the neutral plane was assigned by James Bernoulli 1695, who in his investigation of the simplest case of bent beam, was led to the consideration of the curve called the "elastica." This "elastica" curve speedily attracted the attention of the great Euler (1744), and must be considered to have directed his attention to the elliptic integrals. Probably the extraordinary divination which led Euler to the formula connecting the sum of two elliptic integrals, thus giving the fundamental theorem of the addition equation of elliptic functions, was due to mechanical considerations concerning the "elastica" curve; a good illustration of the general principle that the pure mathematician will find the best materials for his work in the problems presented to him by natural and physical questions.

What It Means

This is a placeholder explanation generated by the low-overhead model. It interprets "Galileo does not attempt any theory to account for the flexure of the beam. This theory, supplied by Hooke's law, was applied by Mariotte, Leibnitz, De Lahire, and Varignon, but they neglect compression of the fibres, and so place the neutral in the lower face of Galileo's beam. The true position of the neutral plane was assigned by James Bernoulli 1695, who in his investigation of the simplest case of bent beam, was led to the consideration of the curve called the "elastica." This "elastica" curve speedily attracted the attention of the great Euler (1744), and must be considered to have directed his attention to the elliptic integrals. Probably the extraordinary divination which led Euler to the formula connecting the sum of two elliptic integrals, thus giving the fundamental theorem of the addition equation of elliptic functions, was due to mechanical considerations concerning the "elastica" curve; a good illustration of the general principle that the pure mathematician will find the best materials for his work in the problems presented to him by natural and physical questions." in the context of "A. G. Greenhill, Nature (Feb. 3, 1887) Review of A History of the Theory of Elasticity, Volume 35, pp. 313-314." to mean that wisdom is timeless.