...This refers to the following theorem discovered by the Italian G. Ceva (1647-1734). Suppose that there are points D, E, and F on the sides BC, CA, and AB of triangle ABC, or on their extensions, respectively, which are not vertices of triangle ABC. In this case, the necessary and sufficient condition for the lines AD, BE, and CF to intersect at a point or be parallel to each other is that the following holds. Here, each fraction on the left side of the above equation should be considered with a + or - sign depending on whether D, E, and F are internal or external division points of the line segments BC, CA, and AB. ... *Some of the terminology that mentions "Ceva, G." is listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
…イタリアのチェバG.Ceva(1647‐1734)が発見した次の定理をいう。三角形ABCの辺BC,CA,AB,またはそれらの延長上にそれぞれ点D,E,Fがあり,これらは三角形ABCの頂点でないとする。このとき直線AD,BE,CFが1点で交わるか,または互いに平行になるための必要かつ十分条件は,が成り立つことである。ここに上式の左辺の各分数はD,E,Fが線分BC,CA,ABの内分点であるか外分点であるかに応じて,+,または-の符号をつけて考えるものとする。… ※「Ceva,G.」について言及している用語解説の一部を掲載しています。 出典|株式会社平凡社世界大百科事典 第2版について | 情報 |
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