View source for Q.E.D.

{{also|QED}}
==English==
{{was wotd|2020|January|24}}

===Etymology===
From {{der|en|LL.|QED}}, from {{der|en|la|quod erat demonstrandum}}.<ref>{{R:OED Online|entry=Q.E.D.|pos=''int.'' and ''n.{{sup|1}}''|noformat=yes|id=240240|date=December 2007|nodot=yes}}; {{R:Lexico|pos=abbrev}}</ref>

===Pronunciation===
* {{IPA|en|/ˌkjuːiːˈdiː/|a=RP}}
* {{audio|en|En-uk-QED.oga|a=RP}}
* {{IPA|en|/ˌkjuˌiˈdi/|a=GA}}

===Phrase===
{{head|en|phrase}}

# {{senseid|en|mathematics}} {{lb|en|mathematics|dated}} {{initialism of|en|quod erat demonstrandum|t=what was to be proved; what was to be demonstrated|nodot=1}}: {{non-gloss|placed at the end of a [[mathematical]] [[proof]] to [[show#Verb|show]] that the [[theorem]] under [[discussion]] is [[prove]]d.}}
#* {{quote-journal|en|author=Mr. Ash|title=A New and Easy Way of Demonstrating Some Propositions in {{w|Euclid}} |journal=[[w:Philosophical Transactions of the Royal Society|Philosophical Transactions: Giving Some Accompt of the Present Undertakings, Studies and Labours of the Ingenious in Many Considerable Parts of the World]]|location=London|publisher=Printed by T. R. for John Martyn, printer to the {{w|Royal Society}}; {{...|at the Bell in St. Pauls Church-Yard.}}|date={{J2G|20 August 1684}}|volume=XIV|issue=162|page=674|pageurl=https://books.google.com/books?id=wvwSuBLY6GgC&pg=RA1-PA674|oclc=630046584|passage=[A]fter the same manner S and U are proved to be equal, therefore the square of CB is equal to the square of the 2 other sides '''Q E D'''.}}
#* {{quote-book|en|chapter=The Mathematical Repository, Nº 63|title=The Gentleman’s Diary, or The Mathematical Repository; an Almanack for the Year of Our Lord 1803:{{nb...|Being the Seventh after Bissextile. Containing Many Useful and Entertaining Particulars, peculiarly Adapted to the Ingenious Gentlemen Engaged in the Study and Practice of the Mathematicks. The Sixty-third Almanack Published of this Kind; and the Fifty-first of the New Style in England.}}|location=London|publisher=Printed for the [[w:Worshipful Company of Stationers and Newspaper Makers|Company of Stationers]] by [[w:John Nichols (printer)|Nichols and Son]],{{nb...|Red Lion Passage, Fleet-street.}}; [a]nd sold by George Greenhill,{{nb...|Treasurer to the Company, at their Hall, Ludgate-Street.}}|year=1803|page=33|pageurl=https://books.google.com/books?id=pyMsAAAAMAAJ&pg=PA33|oclc=225667331|passage=Now let any right line meet four harmonicals in <math>A</math>, <math>C</math>, <math>B</math>, <math>D</math>, and if those harmonicals be parallel, the thing is evident; but, if they intersect in <math>V</math>, draw <math>ECF</math> parallel to <math>VD</math>, the line most remote from <math>C</math>; then, by the first part, <math>EC = CF</math>, and <math>AD:AC::VD:EC</math> or <math>CF</math>. Therefore <math>AD:AC::BD:CB</math>. '''q. e. d.'''}}
#* {{quote-book|en|author=[[w:William Dunham (mathematician)|William Dunham]]|chapter=Euler and Analytic Number Theory|title=[[w:Leonhard Euler|Euler]]: The Master of Us All|series=The Dolciani Mathematical Expositions|seriesvolume=22|location=[Washington, D.C.]|publisher=w:Mathematical Association of America|year=1999|page=64|pageurl=https://books.google.com/books?id=x7p4tCPPuXoC&pg=PA64|isbn=978-0-88385-328-3|passage=By Cases 1 and 2, we see that any finite collection of <math>4k - 1</math> primes cannot contain all such primes. Thus there are infinitely many primes of this type. ¶ '''Q.E.D.'''}}
# {{senseid|en|extended use outside mathematics}} {{lb|en|by extension}} {{non-gloss|Used to [[indicate]] that an [[argument]] or [[proposition]] is proved by the [[existence]] of some [[fact]] or [[scenario]].}}
#* {{RQ:Irving History of New York|volume=I|chapter=IV|page=42|passage=That this part of the world has actually ''been peopled'' ('''Q. E. D.''') to support which, we have living proofs in the numerous tribes of Indians that inhabit it.}}
#* {{quote-book|en|author=Benedict de Spinoza [''i.e.'', {{w|Baruch Spinoza}}]; R[obert] Willis|chapter=[The [[w:Ethics (Spinoza)|Ethics]].] Part I.—Of God.|title=Benedict de Spinoza; His Life, Correspondence, and Ethics|location=London|publisher=[[w:Nicholas Trübner|Trübner & Co.]],{{nb...|60, Paternoster Row.}}|year=1870|page=418|pageurl=https://books.google.com/books?id=isIwAAAAYAAJ&pg=PA418|oclc=1021877894|passage=PROP[OSITION] VI. One substance cannot be produced by another substance. ¶ ''Demonst''[''ration'']. In the preceding proposition we have seen that there cannot in the nature of things be two Substances of the same attribute, or that they have anything in common (by Prop. II.); and so (by Prop. III.) one cannot be the cause of, or be produced by, another: '''q. e. d.'''}}
#* {{quote-journal|en|author=C. H. Claudy|title=Tanks|editor=Frank V. Chambers|magazine=The Camera: An Illustrated Magazine Devoted to the Advancement of Photography|location=Philadelphia, Pa.|publisher=The Camera Publishing Company|month=July|year=1908|volume=12|issue=7|page=252|pageurl=https://books.google.com/books?id=KDQyAQAAMAAJ&pg=PA252|oclc=|passage=Of all those on the market, Eastman's is the only one with a solution tight, locking cover. ¶ '''Q. E. D.'''}}

====Usage notes====
* When used to end a mathematical proof, ''QED'' is somewhat dated or traditional; modern textbooks often use the graphical symbol [[∎]] (the [[halmos]] or [[tombstone]]) instead. Other languages generally use a vernacular abbreviation, such as {{noncog|fr|CQFD|t=ce qu'il fallait démontrer}} or {{noncog|pt|C.Q.D.|t=como queríamos demonstrar}}.

====Alternative forms====
* {{alt|en|QED|Q. E. D.|q. e. d.|q.e.d.}}

====Related terms====
* {{l|en|QEF}}

====Translations====
<!--please only add initialisms; full phrases belong at quod erat demonstrandum-->
{{trans-top-see|''initialism placed at the end of a mathematical proof to show that the theorem under discussion is proved''|quod erat demonstrandum}}
* Aramaic: {{t|arc|קמ׳׳ל|tr=qa mashma' lan}}
* Chinese:
*: Mandarin: {{t|cmn|證畢|tr=zhèngbì}}, {{t|cmn|證訖|tr=zhèngqì}}, {{t+|cmn|得證|tr=dézhèng}}
* Czech: {{t|cs|c.b.d.}}
* Esperanto: {{t|eo|KEP}}
* Estonian: {{t|et|m.o.t.t|alt=MOTT}}
* Finnish: {{t+|fi|MOT}}
* French: {{t+|fr|CQFD}}
* Georgian: {{t|ka|რ.დ.გ}}
* German: {{t|de|w. z. b. w.}}
*: Alemannic German: {{t|gsw|h.x.}} {{qualifier|humorous, informal, uncommon}}
* Greek: {{t|el|Ό.Έ.Δ.}}
* Hebrew: {{t+|he|מָשָׁ"ל|tr=masha"l}}, {{t|he|מ.ש.ל.|m-p|tr=m.sh.l.}}
* Hindi: {{t|hi|इ. सि.}}
* Icelandic: {{t|is|þ.s.s.á.}}
* Italian: {{t+|it|CVD}}
* Polish: {{t+|pl|c.b.d.o.}}, {{t|pl|c.b.d.u.}}, {{t+|pl|cnd.}}, {{t|pl|ckd.}}
* Portuguese: {{t+|pt|CQD}}, {{t|pt|QED}}
* Russian: {{t+|ru|ч. т. д.}}
* Slovak: {{t|sk|Č.B.T.D.}}
* Spanish: {{t|es|C.Q.D.}}
* Swedish: {{t+|sv|VSV}}, {{t+|sv|VSB}}
* Vietnamese: {{t+|vi|đpcm}}
{{trans-bottom}}

===Noun===
{{en-noun}}

# A certain [[fact]] or [[scenario]] that [[prove]]s an [[argument]] or [[proposition]]; a [[justification]].
#* {{quote-book|en|author={{w|Ouida}} [pseudonym; Maria Louise Ramé]|chapter=The General’s Match-making; or, Coaches and Cousinship|title=Cecil Castlemaine’s Gage, and Other Novelettes|location=London|publisher=[[w:Chapman & Hall|Chapman and Hall]],{{nb...|193, Piccadilly}}|year=1867|page=233|pageurl=https://books.google.com/books?id=50RWAAAAcAAJ&pg=PA233|oclc=35980974|passage=We all go in for the dolce here except you, and you're such a patent machine for turning out '''Q.E.D.s''' by the dozen, that you can no more help working than the bedmaker can help taking my tea and saying the cat did it,{{nb...}}}}
#* {{quote-journal|en|author=Nina Melville|title=The Theatre|editor=[[w:V. F. Calverton|V[ictor] F[rancis] Calverton]] [pseudonym; George Goetz]|magazine=[[w:Modern Quarterly (American magazine)|The Modern Monthly: An Independent Journal of Radical Opinion]]|month=April|year=1936|volume=IX|issue=9|page=27|pageurl=https://books.google.com/books?id=RoweAQAAMAAJ&pg=PA27|column=1|oclc=4756578|passage=The same thing, I believe, that was lacking in ''Let Freedom Ring''—lack of dramatic integration, lack of dramatic intensity, lack of all those elements, call them what you will, which make a play a play and not a tract, and certainly not a '''Q.E.D.''' thesis.}}

====Alternative forms====
* {{l|en|QED}}

====Translations====
{{trans-see|fact or scenario that proves an argument or proposition|justification}}

===References===
<references />

===Further reading===
* {{pedia}}

===Anagrams===
* {{anagrams|en|a=deq|DEQ}}