The Bernoullis and the Elastica: From Leibniz’s Nova Methodus to Euler’s Methodus Inveniendi

This chapter is dedicated to the birth of the theory of elasticity. When proposing the problem of the rupture of an embedded beam, Galileo certainly did not realize that he was opening one of the largest and most difficult part of the science of constructions, a part containing all different problems of ruptures, of flexions and deformations. The next important step after Galileo will be the study of the deformation of that beam. The curve that will be studied on that occasion is called the elastica, but we shall meet many other curves, many of which play an important role in architecture. Other curves will also appear because they play a role in the mathematical development that itself becomes fundamental for architecture after 1850.