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The phrase quod erat demonstrandum is a translation into Latin from the Greek ὅπερ ἔδει δεῖξαι (hoper edei deixai; abbreviated as ΟΕΔ). The meaning of the Latin phrase is "that [thing] which was to be demonstrated" (with demonstrandum in the gerundive).
Q.E.D. or QED is an initialism of the Latin phrase Latin: '''quod erat demonstrandum''', meaning "that which was to be demonstrated". Literally it states "what was to be shown".
Definition. The term 'q.e.d.' stands for 'quod erat demonstrandum,' which is a Latin phrase meaning 'which was to be demonstrated.' It is traditionally used at the end of mathematical proofs to signify that the proof is complete and that what was proposed has been successfully established.
In the Elements Euclid concluded his proofs with ὅπερ ἔδει δεῖξαι "that which was to be shown": see e.g. the end of the proof of Proposition 4 on p. 11 of Fitzpatrick's Greek-English Euclid. Medieval geometers translated the expression as quod erat demonstrandum ("that which was to be proven").
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The initials of Quod Erat Demonstrandum, which is Latin for which was to be demonstrated. These initials were traditionally added to the end of a proof, after the last line which is supposed to contain the statementthat was to be proved. The usage is considered hopelessly old-fashioned nowadays, and is rarely seen outside nerd sitcoms. The Halmos s...
In order to render ■◼, use the template {{qed}}. In order to render □◻, use the template {{qed|lemma}}. When {{qed}} is used, it automatically adds the page on which it is implemented to Category:Proven Results.
1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): QED1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): quod erat demonstrandum1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): QED2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): QEDOct 5, 2024 · (mathematics, dated) 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. (by extension) Used to indicate that an argument or proposition is proved by the existence of some fact or scenario. Usage notes. [edit]
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The meaning of QUOD ERAT DEMONSTRANDUM is which (is what) was to be shown (originally) —abbreviation QED—used at the end of a logical or mathematical proof.
