Q.E.D.
Language: English
Part of speech: phrase
Pronunciation: ipa: /ˌkjuːiːˈdiː/
ipa: /ˌkjuˌiˈdi/
Forms: form: QED
form: Q. E. D.
form: q. e. d.
form: q.e.d.
Etymology: From Late Latin QED, from Latin quod erat demonstrandum.
Senses: examples: text: [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.
ref: 1684 August 30, Mr. Ash, “A New and Easy Way of Demonstrating Some Propositions in Euclid”, in Philosophical Transactions: Giving Some Accompt of the Present Undertakings, Studies and Labours of the Ingenious in Many Considerable Parts of the World, volume XIV, number 162, London: Printed by T. R. for John Martyn, printer to the Royal Society; […] , →OCLC, page 674:
text: Now let any right line meet four harmonicals in A, C, B, D, and if those harmonicals be parallel, the thing is evident; but, if they intersect in V, draw ECF parallel to VD, the line most remote from C; then, by the first part, EC#61;CF, and AD#58;AC#58;#58;VD#58;EC or CF. Therefore AD#58;AC#58;#58;BD#58;CB. q. e. d.
ref: 1803, “The Mathematical Repository, Nº 63”, in The Gentleman’s Diary, or The Mathematical Repository; an Almanack for the Year of Our Lord 1803: […], London: Printed for the Company of Stationers by Nichols and Son, […]; [a]nd sold by George Greenhill, […], →OCLC, page 33:
text: By Cases 1 and 2, we see that any finite collection of 4k-1 primes cannot contain all such primes. Thus there are infinitely many primes of this type. ¶ Q.E.D.
ref: 1999, William Dunham, “Euler and Analytic Number Theory”, in Euler: The Master of Us All (The Dolciani Mathematical Expositions; 22), [Washington, D.C.]: Mathematical Association of America, →ISBN, page 64:
topics: mathematics
sciences
glosses: Initialism of quod erat demonstrandum (“what was to be proved; what was to be demonstrated”): placed at the end of a mathematical proof to show that the theorem under discussion is proved.
examples: text: 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.
ref: 1809, Diedrich Knickerbocker [pseudonym; Washington Irving], chapter IV, in A History of New York, from the Beginning of the World to the End of the Dutch Dynasty. […], volume I, New York, N.Y.: Inskeep & Bradford, […], →OCLC, book I, page 42:
text: 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.
ref: 1870, Benedict de Spinoza [i.e., Baruch Spinoza]; R[obert] Willis, “[The Ethics.] Part I.—Of God.”, in Benedict de Spinoza; His Life, Correspondence, and Ethics, London: Trübner & Co., […], →OCLC, page 418:
text: Of all those on the market, Eastman's is the only one with a solution tight, locking cover. ¶ Q. E. D.
ref: 1908 July, C. H. Claudy, “Tanks”, in Frank V. Chambers, editor, The Camera: An Illustrated Magazine Devoted to the Advancement of Photography, volume 12, number 7, Philadelphia, Pa.: The Camera Publishing Company, page 252:
glosses: Used to indicate that an argument or proposition is proved by the existence of some fact or scenario.
Related terms: QEF