Q.E.D.

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 what was specified in the enunciation—and in the setting-out—has been exactly restated as the conclusion of the demonstration. 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 ὅπερ ἔδει δεῖξαι (hoper edei deixai; abbreviated as ΟΕΔ). Translating from the Latin into English yields, "what was to be demonstrated"; however, translating the Greek phrase ὅπερ ἔδει δεῖξαι produces a slightly different meaning. Since the verb "δείκνυμι" also means to show or to prove, 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 and Archimedes.