翻訳と辞書 Words near each other ・ ADEPS ・ Adept ・ Adept (band) ・ Adept (comics) ・ Adept (disambiguation) ・ Adept 320T ・ Adept Manager ・ Adept Press ・ Adept Technology ・ Adeptia ・ Adeptol ・ Adeptus Health ・ AdeptXBBS ・ ADEQ ・ Adequacy.org ・ Adequality ・ Adequate 7 (EP) ・ Adequate and independent state ground ・ Adequate equivalence relation ・ Adequate pointclass ・ Adequate Public Facilities Ordinance ・ Adequate remedy ・ Adequate Seven ・ Adequate stimulus ・ Adequate Yearly Progress ・ Ader ・ Ader (disambiguation) ・ Ader (surname) ・ Ader Avion II ・ Ader Avion III Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Adequality ： ウィキペディア英語版 Adequality 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 $p(x)$, Fermat equated (or more precisely adequated) $p(x)$ and $p(x+e)$ and after doing algebra he could cancel out a factor of $e,$ and then discard any remaining terms involving $e.$ To illustrate the method by Fermat's own example, consider the problem of finding the maximum of $p(x)=bx-x^2$. Fermat ''adequated'' $bx-x^2$ with $b(x+e)-(x+e)^2=bx-x^2+be-2ex-e^2$. That is (using the notation $\backslash backsim$ to denote adequality, introduced by Paul Tannery): :$bx-x^2\backslash backsim\; bx-x^2+be-2ex-e^2.$ Canceling terms and dividing by $e$ Fermat arrived at :$b\backslash backsim\; 2x+e.$ Removing the terms that contained $e$ Fermat arrived at the desired result that the maximum occurred when $x=b/2$. 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.