Subject: [HM] Derived, assume local monotony, by Binet.
From: Udai Venedem (venedem@wanadoo.fr)
Date: Sun Feb 06 2000 - 09:32:34 EST
Dear (HM)ers,
I found a document from the beginning of 1809, where Jacques Binet (France,
Rennes 1786-1856) states in the simplest way the central theorem of the
differential calculus' theory. Assuming only the local monotony of a
function f, he shows that the quantity
[f(x+h) - f(x)] / h
when h goes smaller and smaller, "generally" tends to a limit, which is the
derived of f (the terms in French mean this, precisely). The document is
from the Nouveau Bulletin des sciences par la Socie/t/e Philomatique No. 16,
Paris Janvier 1809, p. 275-278.
What does one know of such a statement at such an early date, and how
(where) to trace the chronology of this and afferent questions?
Udai Venedem
venedem@wanadoo.fr
http://perso.wanadoo.fr/alta.mathematica/
the rebirth of an Internet site devoted to the endless pursuit of
collector's books in mathematics.
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