Résumé : It is standard to present Gaussian quadrature in connection with orthogonal polynomials. However Gauss himself arrived at his quadrature rules by following a very different path. The talk will be a guided tour through Gauss's original memoir, a fascinating mathematical work that uses, in a masterly way, rational approximation, continued fractions, integral transforms, and many other resources. As any numerical analyst would do today, Gauss wraps up by presenting an experiment that shows the superiority of his approach when compared with other available techniques.

Keywords : Gaussian quadrature; rational approximation; continued fractions