From Wikipedia, the free encyclopedia
  (Redirected from Q.E.D)
Jump to: navigation, search
This article is about the Latin phrase. For the physical theory, see quantum electrodynamics. For other uses, see QED (disambiguation).

Q.E.D. is an initialism of the Latin phrase quod erat demonstrandum, originating from the Ancient Greek analogous hóper édei deîxai (ὅπερ ἔδει δεῖξαι), meaning "which 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.[1] The abbreviation thus signals the completion of the proof.

Etymology and early use[edit]


Modern philosophy[edit]



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.



There is another Latin phrase with a slightly different meaning, and less common in usage. Quod erat faciendum, originating from the Greek geometers' closing ὅπερ ἔδει ποιῆσαι (hoper edei poiēsai), meaning "which had to be done". Euclid used this phrase to close propositions which were not proofs of theorems, but constructions. For example, Euclid's first proposition showing how to construct an equilateral triangle given one side is usually shortened to QEF.

Equivalents in other languages[edit]

Q.E.D. has acquired many translations in various languages, including:

Language Abbreviations Stands for...
Arabic هـ.ط.ث وهو المطلوب إثباته
Armenian Ի.Պ.Ա.(rarely used as an abbreviation) ինչը և պահանջվում էր ապացուցել
Bengali অ. সি. অতঃ সিদ্ধ
Bosnian Š.T.D. što je trebalo dokazati
Bulgarian КТДД Което трябваше да докажем/Което трябваше да се докаже
Chinese 证毕/證畢/证讫/證訖 证明完毕/證明完畢 (证讫/證訖 are already the full form themselves)
Croatian Š.T.D. što je trebalo dokazati
Czech C.B.D. což bylo dokázati/což se mělo dokázat
Dutch w.m.b.w.
wat moest bewezen worden
wat te bewijzen was
Estonian M.O.T.T. mida oligi tarvis tõestada
Finnish M.O.T. mikä oli todistettava
French C.Q.F.D. ce qu'il fallait démontrer
Catalan C.V.D. com volíem demostrar
Georgian რ.დ.გ რისი დამტკიცებაც გვსურდა
German w.z.b.w. was zu beweisen war
Greek Ο.Ε.Δ. όπερ έδει δείξαι
Hebrew .מ.ש.ל מה שנדרש להוכיח
Hungarian E.K.B. (rarely used as an abbreviation) Ezt kellett bizonyítani
Icelandic Þ.S.S.Á. Það sem sanna átti
Italian C.V.D. come volevasi dimostrare
Latvian k.b.j. kas bija jāpierāda
Polish c.b.d.u. co było do udowodnienia
Portuguese C.Q.D. como queríamos demonstrar
Romanian c.c.t.d. ceea ce trebuia demonstrat
Russian ч.т.д. что и требовалось доказать
Sanskrit इ.सि. इति सिद्धम्
Serbian ш.т.д. што је и требало да се докаже
Slovak č.b.t.d. čo bolo treba dokázať
Slovenian k.e.d. konec enega dokaza
Spanish C.Q.D. lo que se quería demostrar
como queda demostrado
Swedish V.S.B.
vilket skulle bevisas
vilket skulle visas
Tamil நி.வே. நிரூபிக்கப்படவேண்டியது
Turkish G.İ.B. Gösterilmek istenen şey de buydu.
Bu da gosterimimizi bitirir.
Ukrainian щ.с.б.д.
що й слід було довести
що і треба було довести
Vietnamese đpcm. Điều phải chứng minh

There is no common formal English equivalent, though the end of a proof may be announced with a simple statement such as "this completes the proof", "as required", "hence proved", "ergo", or a similar locution. WWWWW or W5 - an abbreviation of "Which Was What Was Wanted" - has also been used. This is often considered to be more tongue-in-cheek than the usual Halmos symbol (see below) or Q.E.D.

Electronic forms[edit]


Modern humorous usage[edit]


In the mid eighties, BBC ran a series called Q.E.D. which showed how certain things were made or put together.

In the 1978 sci-fi radio comedy, and later in the TV and novel adaptations of The Hitchhiker's Guide to the Galaxy, "Q.E.D." is referred to in the Guide's entry for the babel fish, when it is claimed that the babel fish is used as evidence for the non-existence of God.[8]

See also[edit]


  1. ^ a b Euclid's Elements translated from Greek by Thomas L. Heath. 2003 Green Lion Press pg. xxiv
  2. ^ Entry δείκνυμι at LSJ.
  7. ^ Heller, Joseph (1971). Catch-22. ISBN 9780573606854. Retrieved 15 July 2011. 
  8. ^ Adams, Douglas (2005). The Hitchhiker's Guide to the Galaxy. The Hitchhiker's Guide to the Galaxy (Film tie-in edition ed.). Basingstoke and Oxford: Pan Macmillan. pp. 62–64. ISBN 0-330-43798-4. 

External links[edit]