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In "Suite des Lecons d'Analyse" de Prony says that Lans and Haros have had much success with the problem of Mouton.

What is the problem of Mouton?

Thanks for any insight.

Cheers, Scott

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Do you have full names and years of birth/death for some of these people? –  Will Jagy Aug 17 '10 at 0:45
    
Found this, mentions three out of four people but not Haros. realroleplaying.com/rmsmf/… –  Will Jagy Aug 17 '10 at 1:03
    
aleph0.clarku.edu/~djoyce/mathhist/chronology.html $$ $$ Gabriel Mouton (1618-1694) *SB *W Gaspard Clair François Marie Rich de Prony (1755-1839) MacTutor $$ $$ *SB: Mathematicians noted *SB have entries in the Dictionary of Scientific Biography. 15 volumes. Edited by Charles Coulston Gillispie. Scribner, New York, 1970-1978, with later additions. $$ $$ *W: Mathematicians noted *W have biographies compiled by Richard S. Westfall, Professor Emeritus in the department of History and Philosophy of Science at Indiana University, and appear in theCatalogue of the Scientific Community, –  Will Jagy Aug 17 '10 at 1:16
    
I note the number-theory tag - do you have some reason to think this is a problem in Number Theory? There is a brief biography of Mouton at www-history.mcs.st-and.ac.uk/history/Biographies/Mouton.html which mentions interpolation, measurement, and tables, but I see no Number Theory. –  Gerry Myerson Aug 17 '10 at 3:59
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I have the suspicion that this is not about the problem of Mouton, but rather the "probleme de mouton". google and a French dictionary will help -) –  Franz Lemmermeyer Aug 17 '10 at 9:19
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1 Answer

The problem studied by the seventeenth century astronomer Gabriel Mouton was to construct logarithmic and trigonometric tables using only addition and subtraction, avoiding multiplication and division (so that the calculations could be performed by unskilled workers). Mouton derived an interpolation formula using successive numerical differences, that would later be used by Gaspard de Prony and others.

See: "The history of mathematical tables", by Martin Campbell-Kelly (Oxford UP, 2003). or see http://youryuboku2.web.fc2.com/eBooks/Hairdressers.pdf

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