 However, Chevalley did not try to reflect on the notion of style here involved. Rather he was concerned to show by means of an important example the features of the transition between two styles of doing mathematics that had characterized the passage from nineteenth century mathematics to twentieth century approaches. The first style described by Chevalley is the Weierstrassian style, ‘the style of ε’. It finds its ‘raison d’être’ in the need to rigorize the calculus moving away from the unclarities related to such notions as “infinitely small quantity” etc. The development of analysis in the nineteenth century (analytic functions, Fourier series, Gauss’ theories of surfaces, Lagrangian equations in mechanics etc.) led to a critical analysis