cevain和cevial是什麼意思？
我在APMO的書中看到這兩個字，查字典卻查不到，請問是什麼意思？
原文：
...draw the three cevians A0A1, B0B1, C0C1,...
...repeat the process with the 'cevial' triangle A1B1C1...
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孫文先

2006-01-05 16:29
Dear Wen-Hsien,
A Cevian is a line joining a vertex of a triangle to any point on the opposite side which is not also a vertex. Examples of Cevians are medians, angle bisectors and altitudes. A Cevial triangle is the triangle determined by the feet of three concurrent Cevians. Examples of Cevial triangles are the medial triangle (from the medians) and the orthic triangle (from the altitudes). Of course, there is also one which arise from the angle bisectors, but I cannot recall off hand if it has a special name.
Best regards, Andy.

tpesamguo

2006-01-05 17:21
引用：

孫文先 寫道:
Dear Wen-Hsien,
A Cevian is a line joining a vertex of a triangle to any point on the opposite side which is not also a vertex. Examples of Cevians are medians, angle bisectors and altitudes. A Cevial triangle is the triangle determined by the feet of three concurrent Cevians. Examples of Cevial triangles are the medial triangle (from the medians) and the orthic triangle (from the altitudes). Of course, there is also one which arise from the angle bisectors, but I cannot recall off hand if it has a special name.
Best regards, Andy.


我翻譯的並不一定很好,大概是這樣:

Cevian是從三角形上任何一個頂點與對邊上的點(非頂點)的連線。Cevians的例子有三角形的中線,三角形的角平分線和三角形的高線。一個Cevial三角形是由三條共點的Cevians的足所構成的三角形。Cevial三角形例子有中線三角形 (源自中線)和垂足三角形(源自高線)。當然,還有源自角平分線的三角形,但我現在我無法馬上想起它的特殊名稱。



:-D :-D :-D :-D

孫文先

2006-01-05 20:53
cevian 一词来自数学家 G.Ceva,切瓦(约1647-1734), Ceva + ian , 常写作 Cevian . 这个词既可用作名词,又可用作形容词. 1. 当作名词用时,称"切瓦线"----指"从三角形的一个顶点到对边(或其延长线)上的一点的连线". 2. 当作型容词用时,称"切瓦的",常见的复合词有: Cevian circle (切瓦圆) ,Cevian triangle (切瓦三角形).cevial' triangle 可能是Cevian triangle 的另一写法.