The Problem of the Elastica by Jacob Bernoulli and the Development of this Study by Leonhard Euler

The article first recalls how Jacob Bernoulli began his study of elasticity with four problems, the solutions of which are made possible by the use of Leibniz's new differential and integral Calculus. These problems are the catenaria, the velaria, the lintearia and the elastica which gave its name to elasticity. He immediately tries to re-formulate all four problems within a single general theory. He tries to do so not only by starting with the principles of mechanics but also by starting with a variational principle or as he calls it with “isoperimetrical problems”. The article then proceeds to show how Euler will, during more than forty years, try and finally succeed in reaching Jacob's goal of generalization.