e/Routh's theorem

Information
has gloss	eng: In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the intersection of three cevians. The theorem states that if in triangle ABC points D, E, and F lie on segments BC, CA, and AB, then writing \tfracCD}BD} = x, \tfracAE}CE} = y, and \tfracBF}AF} = z, the signed area of the triangle formed by the cevians AD, BE, and CF is the area of triangle ABC times
lexicalization	eng: Routh's theorem
instance of	e/Area

Meaning
German
has gloss	deu: Der Satz von Routh, benannt nach Edward Routh, ist ein mathematischer Satz zur Geometrie des Dreiecks. Er macht folgende Aussage über den Flächeninhalt von Dreiecken (siehe Grafik):
lexicalization	deu: Satz von Routh
Central Khmer
has gloss	khm: ក្នុងធរណីមាត្រ ទ្រឹស្តីបទរូទ (Routh's theorem) ពោលដូចខាងក្រោមៈ
lexicalization	khm: ទ្រឹស្តីបទ រូទ
Chinese
has gloss	zho: 在几何学中，罗斯定理是关于三角形面积的一个定理。给定一个三角形，在它的三边上各取一点，并和对面的顶点相连。三条连线将会在三角形中央围出一个新的小三角形。罗斯定理给出了这个新三角形的面积与三角形边上三个点的位置的关系。罗斯定理可以看成是塞瓦定理的一种推广。
lexicalization	zho: 罗斯定理

Media
media:img	Routh theorem.svg
media:img	Rouths theorem.png