Q.E.D.From Wikipedia, the free encyclopedia(Redirected from Quod erat demonstrandum)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 hper dei dexai ( ), 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 enunciationand in the setting-outhas been exactly restated as the conclusion of the demonstration.[1] The abbreviation thus signals the completion of the proof.Contents 1 Etymology and early use 2 Modern philosophy 3 QEF 4 Equivalents in other languages 5 Electronic forms 6 Modern humorous usage 7 See also 8 References 9 External linksEtymology and early useThe phrase quod erat demonstrandum is a translation into Latin from the Greek (hoper edei deixai; abbreviated as ). 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 "" also means to show or to prove,[2] a better translation from the Greek would read, "The very thing it was required to have shown."[1] The phrase was used by many early Greek mathematicians, including Euclid[3] and Archimedes.Modern philosophy

Philippe van Lansberge's 1604 Triangulorum Geometri used quod erat demonstrandum to conclude some proofs; others ended with phrases such as sigillatim deinceps demonstrabitur, magnitudo demonstranda est, and other variants.[4]In the European Renaissance, scholars often wrote in Latin, and phrases such as Q.E.D. were often used to conclude proofs.

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.Perhaps the most famous use of Q.E.D. in a philosophical argument is found in the Ethics of Baruch Spinoza, published posthumously in 1677. Written in Latin, it is considered by many to be Spinoza's magnum opus. The style and system of the book is, as Spinoza says, "demonstrated in geometrical order", with axioms and definitions followed by propositions. For Spinoza, this is a considerable improvement over Ren Descartes's writing style in the Meditations, which follows the form of a diary.[5]QEFThere is another Latin phrase with a slightly different meaning, and less common in usage. Quod erat faciendum, originating from the Greek geometers' closing (hoper edei poisai), 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 shows how to construct an equilateral triangle given one side. It is usually shortened to QEF.Equivalents in other languagesQ.E.D. has acquired many translations in various languages, including:LanguageAbbreviationsStands for...

Arabic..

Armenian...(rarely used as an abbreviation)

Bengali. .

Bosnian.T.D.to je trebalo dokazati

Bulgarian /

Chinese//// (/ are already the full form themselves)

Croatian.T.D.to je trebalo dokazati

CzechC.B.D.co bylo dokzati/co se mlo dokzat

Dutchw.m.b.w.w.t.b.wwat moest bewezen wordenwat te bewijzen was

EstonianM.O.T.T.mida oligi tarvis testada

FinnishM.O.T.mik oli todistettava

FrenchC.Q.F.D.ce qu'il fallait dmontrer

CatalanC.V.D.com volem demostrar

Georgian..

GermanQ.E.D.was zu beweisen war

Greek...

Hebrew...

HungarianE.K.B. (rarely used as an abbreviation)Ezt kellett bizonytani

Icelandic.S.S..a sem sanna tti

ItalianC.V.D.come volevasi dimostrare

JapaneseQ.E.D.

NorwegianQ.E.D.hvilket skulle demonstrereshvilket skulle bevises

PersianQ.E.D

Polishc.b.d.u.co byo do udowodnienia

PortugueseC.Q.D.como queramos demonstrar

Romanianc.c.t.d.ceea ce trebuia demonstrat

Russian...

Sanskrit..

Serbian...

Slovak.b.t.d.o bolo treba dokza

Sloveniank.e.d.konec enega dokaza

SpanishQ.E.D.lo que se quera demostrar

SwedishV.S.B.V.S.Vvilket skulle bevisasvilket skulle visas

Tamil..

Thai...

Ukrainian.......

Vietnamesepcm.iu phi chng 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 formsMain article: Tombstone (typography)When typesetting was done by a compositor with letterpress printing, complex typography such as mathematics and foreign languages were called "penalty copy" (the author paid a "penalty" to have them typeset, as it was harder than plain text).[6] With the advent of systems such as LaTeX, mathematicians found their options more open, so there are several symbolic alternatives in use, either in the input, the output, or both. When creating TeX, Knuth provided the symbol (solid black square), also called by mathematicians tombstone or Halmos symbol (after Paul Halmos, who pioneered its use as an equivalent of Q.E.D.). The tombstone is sometimes open: (hollow black square). Unicode explicitly provides the "End of proof" character U+220E (), but also offers (U+25AE, black vertical rectangle) and (U+2023, triangular bullet) as alternatives. Some authors have adopted variants of this notation with other symbols, such as two forward slashes (//), or simply some vertical white space, implying no further statements need to be made in the proof.[citation needed]Modern humorous usageLists of miscellaneous information should be avoided. Please relocate any relevant information into other sections or articles. (December 2014)

Q.E.D. is sometimes jokingly claimed to abbreviate "quite easily done", or "Quit. Enough done."In Joseph Heller's book Catch-22, the Chaplain, having been told to examine a forged letter allegedly signed by him (which he knew he didn't sign), verified that his name was in fact there. His investigator replied, "Then you wrote it. Q.E.D." The chaplain said he didn't write it and that it wasn't his handwriting, but the investigator's faulty logic caused him to point out, "Then you signed your name in somebody else's handwriting again."[7]Thomas Dolby, in his 1988 song "Airhead", imagines a conversation with the titular young woman and says "quod erat demonstrandum, baby", to which she squeals the eager reply "ohhh, you speak French!"Another potential English transliteration is in the movie Ice Princess. Michelle Trachtenberg's lead character Casey is a physics nerd who writes a paper on the physics of figure skating concluding she has shown passion for the topic, "QED," to which her best friend replies, "What has been Quite Easily Demonstrated?"In the mid eighties, BBC ran a series called Q.E.D. which showed how certain things were made or put together.Dannay and Lee, authors of the famous Ellery Queen mystery novels, often had their protagonist refer to his solving of the murder case as "Queen's Elementary Deduction".In Justice League: Crisis on Two Earths, the supervillain Owlman names the bomb that he intends to use to destroy the multiverse the "Quantum Eigenstate Device," which he abbreviates as "Q.E.D."In the 1987 movie No Way Out, Will Patton's character Scott Pritchard, proved that Kevin Costner's character, Lt. Cmdr. Tom Farrell, was a double agent named 'Yuri', afterwards he said "quod erat demonstrandum".In Call of Duty: Black Ops, a weapon is introduced in the final Zombies map Moon called a "Quantum Entanglement Device," also abbreviated as "Q.E.D.". This weapon has the potential to either help or harm the user in many different ways.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 A priori and a posteriori List of Latin abbreviationsReferences1. Euclid's Elements translated from Greek by Thomas L. Heath. 2003 Green Lion Press pg. xxiv Entry at LSJ. Elements 2.5 by Euclid (ed. J. L. Heiberg), retrieved 16 July 2005 Philippe van Lansberge (1604). Triangulorum Geometri. Apud Zachariam Roman. pp.15. The Chief Works of Benedict De Spinoza, translated by R. H. M. Elwes, 1951. ISBN 0-486-20250-X. Donald E. Knuth, "Mathematical Typography", lecture to the ACM, 1975 Heller, Joseph (1971). Catch-22. ISBN9780573606854. Retrieved 15 July 2011. 0. 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.6264. ISBN0-330-43798-4.External linksLook up quod erat demonstrandum in Wiktionary, the free dictionary.

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