Subject: Re: [HM] Hudde
From: Ed Sandifer (SANDIFER@WCSUB.CTSTATEU.EDU)
Date: Mon Mar 27 2000 - 21:44:40 EST
James Landau asks:
> Who is Hudde?
Hudde was one of the commentators on Descartes' Geometry when van Schooten
translated Descartes from French into Latin.
Hudde's commentary did not appear in the 1649 edition, but did appear in
subsequent editions, along with other commentary by van Schooten, deBeaune,
deWitt and Heuret.
The revolutionary nature of Descartes' work was not necessarily obvious to his
contemporaries, nor was it widely available, originally written in French as it
was. The commentaries both made his work widely available and also made it
useful to other scientists of the time.
Hudde's contributions to the Commentaries were two letters, titled, fittingly
"Two letters, of which the first concerns the reduction of equations and the
second concerns maxima and minima"
I personally found little interesting in the first letter, though others may
disagree. The second, however, gives an algorithmic method of finding slopes
of polynomial curves and of rational functions. In particular, it describes
what we now call the "quotient rule."
Isaac Newton (Whiteside, vol I) mentions Hudde a great many times. Newton used
Hudde's methods for finding derivatives, then a kind of GCD method to find
multiple roots of functions. Finding multiple roots was one of those steps
that Descartes thought was too obvious to explain. It was steps like this that
made the Commentaries necessary. (See the Smith/Latham translation of
Descartes' Geometry, pages 94 and 95)
There is a brief account of the work of Hudde in Boyer's History of Calculus,
page 186.
It is one of the functions of an historian to decide what to remember, and, by
exclusion, what to forget. I believe that Hudde ought to be better remembered
than he is.
*************************************************************************
* Ed Sandifer * sandifer@wcsu.ctstateu.edu *
* Professor of Mathematics * *
* Western Connecticut State University* www.wcsu.ctstateu.edu/~SANDIFER/*
* Danbury, CT 06810 * *
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