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.
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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