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.

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.

Peer Reviewed

1

Copyright

Springer

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