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Q.E.D.
Q.E.D. is an initialism of the Latin phrase ラテン語:'' 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 what was specified in the enunciation—and in the setting-out—has been exactly restated as the conclusion of the demonstration.〔Euclid's Elements translated from Greek by Thomas L. Heath. 2003 Green Lion Press pg. xxiv〕 The abbreviation thus signals the completion of the proof.
==Etymology and early use==
The phrase ''quod erat demonstrandum'' is a translation into Latin from the Greek (; abbreviated as ''ΟΕΔ''). Translating from the Latin into English yields, "what was to be demonstrated"; however, translating the Greek phrase produces a slightly different meaning. Since the verb "δείκνυμι" also means ''to show'' or ''to prove'',〔Entry (δείκνυμι ) at LSJ.〕 a better translation from the Greek would read, "The very thing it was required to have shown."〔 The phrase was used by many early Greek mathematicians, including Euclid〔(Elements 2.5 ) by Euclid (ed. J. L. Heiberg), retrieved 16 July 2005〕 and Archimedes.
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