E145 -- Recherches sur les plus grands et plus petits qui se trouvent dans les actions des forces

(Research into the largest and the smallest which are found in the action of forces)

(based on C. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances)
Euler shows that any discrete system obeys the Maupertuis principle; from this result, he derives the general equation for the balance of moments in a plane elastica, which includes the general catenary as a special case. He also proves that Daniel Bernoulli's principle for the elastica that is free of distributed loads is also a special case of this general equation.

According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on December 19, 1748.

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