View source for Ridders' method

'''René François Walter de Sluse''' (1622&ndash;1685) was a [[French people|French]] [[mathematician]], [[intellectual]] and [[clergyman]] who wrote many books about mathematics and contributed to the development of the subject.

He studied at a university in [[Rome]], and later moved to [[Liège]].  His position in the church prevented him from visiting other mathematicians, but he corresponded with the mathematicians and intellectuals of the day.

==Mathematical work==
Sluse contributed to the development of calculus and this work focuses upon [[spirals]], [[tangents]], turning points and points of [[inflection]]. He and [[Johannes Hudde]] found algebraic algorithms for finding [[tangent]]s, minima and maxima that were later utilized by [[Isaac Newton]]. These algorithms greatly improved upon the complicated algebraic methods of [[Pierre de Fermat]] and [[René Descartes]], who themselves had improved upon [[Gilles de Roberval|Roberval's]] kinematic, but geometric, non-algorithmic methods of determining tangents.<ref>{{cite web|last=Allen|first=G. Donald|title=Early Calculus and Probability |url=http://www.math.tamu.edu/~dallen/history/precalc/precalc.html|publisher=Texas A&M University|accessdate=9 December 2013|date=April 2, 1997}}</ref>

[[Augustus De Morgan]] has the following to say about de Sluse's contribution to Newton's [[method of Fluxions]] in his discussion of the [[Leibniz–Newton calculus controversy]].

<blockquote>
When they state that [[John Collins (mathematician)|Collins]] had been four years in circulating the letter in which the method of fluxions was sufficiently described to any intelligent person, they suppress two facts: first, that the letter itself was in consequence of Newton's learning that Sluse had a method of tangents; secondly, that it revealed no more than Sluse had done. ...this method of Sluse is never allowed to appear ...Sluse wrote an account of the method which he had previously signified to Collins, for the Royal Society, for whom it was printed. The rule is precisely that of Newton... To have given this would have shown the world that the grand communication which was asserted to have been sent to Leibniz in June 1676 might have been seen in print, and learned from Sluse, at any time in the previous years: accordingly it was buried under reference. ...Leibniz had seen Hudde at Amsterdam, and had found that Hudde was in possession of even more than Sluse.<ref>Augustus De Morgan, [http://books.google.com/books?id=SPTvAAAAIAAJ& ''Essays on the Life and Work of Newton''] (1914)</ref>
</blockquote>

There is a family of curves named after de Sluse:  the curves represented by the following equation with positive integer values of ''m'', ''n'' and ''p'':
:<math>y^n = k(a - x)^px^m </math>

==Other work==
He also wrote in the subject areas of [[life science]], [[physics]], [[history]] and [[theology]].

==See also==
*[[List of Roman Catholic scientist-clerics]]

==References==
{{reflist}}
*Hofmann, Joseph Ehrenfried (1959). ''Classical Mathematics''. Translated from the German ''Geschichte der Mathematik'' by Henrietta O. Midonick.  New York: Philosophical Library Inc., p.&nbsp;34.
*John J. O'Connor and Edmund F. Robertson, [http://www-history.mcs.st-andrews.ac.uk/Biographies/Sluze.html René François Walter de Sluze], [[MacTutor History of Mathematics archive]].
*[http://www.wallonie-en-ligne.net/1995_Wallonie_Atouts-References/1995_ch09-1_Halleux-R_Bernes-A-C_Etienne-L.htm L'évolution des sciences et des techniques en Wallonie] ('''''French''''').

{{Authority control|VIAF=57760529}}

{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Sluse, Rene Francois Walter De
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = French mathematician
| DATE OF BIRTH     = 1622
| PLACE OF BIRTH    =
| DATE OF DEATH     = 1685
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Sluse, Rene Francois Walter De}}
[[Category:1622 births]]
[[Category:1685 deaths]]
[[Category:17th-century French mathematicians]]
[[Category:Roman Catholic cleric–scientists]]

[[fr:René François Walter de Sluse]]