Document Type
Article
Publication Date
12-15-2011
Abstract
We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline.
Recommended Citation
Ferraro, G., Panza, M. Lagrange’s theory of analytical functions and his ideal of purity of method. Arch. Hist. Exact Sci. 66, 95–197 (2012). https://doi.org/10.1007/s00407-011-0091-4
Peer Reviewed
1
Copyright
Springer
Included in
Algebra Commons, Analysis Commons, Logic and Foundations Commons, Logic and Foundations of Mathematics Commons, Other Mathematics Commons
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Archive for History of Exact Sciences, volume 66, in 2012 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s00407-011-0091-4.
A free-to-read copy of the final published article is available here.