quod erat demonstrandum


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quod erat demonstrandum

(ˈkwɒd ˈɛræt ˌdɛmənˈstrændʊm)
1. (Logic) (at the conclusion of a proof, esp of a theorem in Euclidean geometry) which was to be proved. Abbreviation: QED
2. (Mathematics) (at the conclusion of a proof, esp of a theorem in Euclidean geometry) which was to be proved. Abbreviation: QED
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

quod erat demonstrandum

A Latin phrase meaning which was to be demonstrated, the full form of the abbreviation Q.E.D., used to show that something has been proved.
Dictionary of Unfamiliar Words by Diagram Group Copyright © 2008 by Diagram Visual Information Limited
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They were being shared with an air of quod erat demonstrandum, proving that not only was the man not unhappy about his wife's demise, but was also somehow complicit in the same.
or quod erat demonstrandum means 'which was to be shown.' It is used at the end of a mathematical or logical proof.