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Pierre de Fermat developed the technique of adequality (''adaequalitas'' in Latin) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in mathematical analysis. According to André Weil, Fermat "introduces the technical term adaequalitas, adaequare, etc., which he says he has borrowed from Diophantus. As Diophantus V.11 shows, it means an approximate equality, and this is indeed how Fermat explains the word in one of his later writings." (Weil 1973).〔See also 〕 Diophantus coined the word παρισὀτης (''parisotēs'') to refer to an approximate equality. Claude Gaspard Bachet de Méziriac translated Diophantus's Greek word into Latin as ''adaequalitas''. Paul Tannery's French translation of Fermat’s Latin treatises on maxima and minima used the words ''adéquation'' and ''adégaler''. == Fermat's method == Fermat used ''adequality'' first to find maxima of functions, and then adapted it to find tangent lines to curves. To find the maximum of a term , Fermat equated (or more precisely adequated) and and after doing algebra he could cancel out a factor of and then discard any remaining terms involving To illustrate the method by Fermat's own example, consider the problem of finding the maximum of . Fermat ''adequated'' with . That is (using the notation to denote adequality, introduced by Paul Tannery): : Canceling terms and dividing by Fermat arrived at : Removing the terms that contained Fermat arrived at the desired result that the maximum occurred when . Fermat also used his principle to give a mathematical derivation of Snell's laws of refraction directly from the principle that light takes the quickest path. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「adequality」の詳細全文を読む スポンサード リンク
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