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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stewart's theorem ： ウィキペディア英語版 Stewart's theorem In geometry, Stewart's theorem yields a relation between a lengths of the sides of the triangle and the length of a cevian of the triangle. Its name is in honor of the Scottish mathematician Matthew Stewart who published the theorem in 1746.〔 "Proposition II"〕 == Theorem == Let $a$, $b$, and $c$ be the lengths of the sides of a triangle. Let $d$ be the length of a cevian to the side of length $a$. If the cevian divides $a$ into two segments of length $m$ and $n$, with $m$ adjacent to $c$ and $n$ adjacent to $b$, then Stewart's theorem states that :$b^2m\; +\; c^2n\; =\; a(d^2\; +\; mn).\backslash ,$ : (This can also be written $dad\; +\; man\; =\; bmb\; +\; cnc.\backslash ,$, a form which invites mnemonic memorization, e.g. "A man and his dad put a bomb in the sink.") Apollonius' theorem is the special case where $d$ is the length of the median. The theorem may be written more symmetrically using signed lengths of segments, in other words the length ''AB'' is taken to be positive or negative according to whether ''A'' is to the left or right of ''B'' in some fixed orientation of the line. In this formulation, the theorem states that if ''A'', ''B'', and ''C'' are collinear points, and ''P'' is any point, then :$PA^2\backslash cdot\; BC+PB^2\backslash cdot\; CA+PC^2\backslash cdot\; AB\; +\; BC\backslash cdot\; CA\backslash cdot\; AB\; =0.\backslash ,$ 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「Stewart's theorem」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.