In the 18th century period, several mathematicians contributed to the
development of Infinitesimal Calculus (IC). Among the exponents of this context,
Joseph-Louis Lagrange (1736 – 1813) and Lazare Nicolas Marguerite Carnot
(1753 – 1823) stood out. Thus, as a research question, the present work raised
the following problem: what points of closeness and distance do the works
Réflexions sur la Métaphysique du Calcul Infinitésimal (RMCI), of 1813, by
Lazare Carnot, and Théorie des Fonctions Analytiques (TFA), of 1813, by
Lagrange, present, concerning the concepts of the Infinitesimal Calculus? To
answer it, we used the methodological contributions of content analysis as well
as the steps established in Bardin (2016), adapted for this research. Therefore,
this thesis aimed to compare, based on content analysis, the approximations and
detachments between the works RMCI and TFA. With this, we realized, as
approximations, that both perform descriptions about their concepts and
definitions and involve the same problems with the infinitesimals about the
infinitely large and infinitely small quantities. As detachments, we observe that
the central elements in Lagrange's work are functions and series and only the
algebraic method is under discussion, while in Carnot's work infinitely small
quantities and the theory of error compensation are present, and it conceives the
use of infinitesimals without disregarding the other methods.
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