  Cauchy's contribution to the foundations of analysis is often viewed through
the lens of developments that occurred some decades later, namely the
formalisation of analysis on the basis of the epsilon-delta doctrine in the
context of an Archimedean continuum. What does one see if one refrains from
viewing Cauchy as if he had read Weierstrass already? One sees, with Felix
Klein, a parallel thread for the development of analysis, in the context of an
infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the
theory of rates of growth of functions as developed by Paul du Bois-Reymond.
One sees, with E. G. Bjorling, an infinitesimal definition of the criterion of
uniform convergence. Cauchy's foundational stance is hereby reconsidered.
