"Following a suggestion by Daniel Bernoulli, Euler gave the first treatment of elastic lines by means of the in the Additamentum I to his Methodus inveniendi (1744...) which carries the title De curvis elasticus. Euler characterized the equilibrium position of an elastic line by the following variational principle: Among all curves of equal length, joining two points where they have prescribed tangents, to determine that which minimizes the value of the expression \int ds/\rho^2 [where \rho is the radius of curvature]. In other words, Euler interpreted an elastic line as an inextensible curve \boldsymbol\zeta with a "" of \int \kappa^2 ds, \kappa [i.e., 1/\rho] being the function of \boldsymbol\zeta, whose positions of (stable) equilibrium are characterized by the minima of the potential energy, i.e., by 's principle of . Thus the problem of the elastic line leads to the isoperimetric problem\int_{\boldsymbol \zeta} \kappa^2 ds \to min \qquad with \int_{\boldsymbol\zeta} ds = L..."