The conceptualization and codification of infinitesimal calculus during the 17th century were not able to elucidate their fundamental notions. The criticisms and controversies surrounding the foundation of calculus finally led to important scientific activity which gave rise to the rigorous foundation of analysis. Nevertheless, before the final period of its arithmetization in the 19th century, there was a turning point in the 18th century when algebrization transformed the metaphysical face of analysis.