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单词 Quod Erat Demonstrandum
释义

Quod Erat Demonstrandum

中文百科

证明完毕 Q.E.D.

(重定向自Quod Erat Demonstrandum)

证明完毕/证讫,又写作Q.E.D.。这是拉丁词组「quod erat demonstrandum」(这就是所要证明的)的缩写,译自希腊语「ὅπερ ἔδει δεῖξαι」(hoper edei deixai),很多早期数学家用过,包括欧几里得和阿基米德。「Q.E.D.」可以在证明的尾段写出,以显示证明所需的结论已经完整了。

现在的证明完毕符号,通常是(实心黑色正方形),称之为「墓碑」或「哈尔莫斯(Halmos symbol)」(因保罗·哈尔莫斯最先采用此做法)。墓碑有时是空心的。另一个简单方法是写「proven」、「shown」或「证毕」之类的文本,或写上两个斜划(//),或三角形内画三点。

英语百科

Q.E.D. 证明完毕

(重定向自Quod Erat Demonstrandum)
Philippe van Lansberge's 1604 Triangulorum Geometriæ used quod erat demonstrandum to conclude some proofs; others ended with phrases such as sigillatim deinceps demonstrabitur, magnitudo demonstranda est, and other variants.[4]
Spinoza's original text of Ethics, Part 1.  Q.E.D. is used at the end of DEMONSTRATIO of PROPOSITIO III. in the right page.
Une des plus anciennes versions connues d'un des traités d'Euclide

Q.E.D. is an initialism of the Latin phrase quod erat demonstrandum, meaning "which is what had to be proven". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been exactly restated as the conclusion of the demonstration. The abbreviation thus signals the completion of the proof.

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更新时间:2025/6/18 20:17:41