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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).
quod erat demonstrandum : what was to be demonstrated: The abbreviation is often written at the bottom of a mathematical proof. Sometimes translated loosely into English as "The Five Ws", W.W.W.W.W., which stands for "Which Was What We Wanted". quod erat faciendum (Q.E.F.) which was to be done: Or "which was to be constructed".
quod erat demonstrandum "that which was to be demonstrated" [1] Cited in many texts at the end of a mathematical proof. Example: "At the end of the long proof, the professor exclaimed ' QED! '" q.v. qq.v. quod vide quae vide "which see" Imperative, [1] used after a term or phrase that should be looked up elsewhere in the current document or book.
"quod erat demonstrandum" "what was required to be proved" Used by early mathematicians including Euclid (Elements, 1.4), Aristotle (APo.90b34), and Archimedes, written at the end of a mathematical proof or philosophical argument, to signify the proof as complete. Later it was latinized as "QED" or the Halmos tombstone box symbol.
quod erat demonstrandum (Q.E.D.) is a calque of ὅπερ ἔδει δεῖξαι. quintessence is post-classical quinta essentia, from Greek πέμπτη οὐσία. Sometimes the Latin is in turn calqued in English: English commonplace is a calque of locus communis, itself a calque of Greek κοινός τόπος.
Q.E.D. (quod erat demonstrandum), used at the end of a mathematical proof; Quantum electrodynamics, a field in particle physics; QED manifesto and project, a database of mathematical knowledge; QED: The Strange Theory of Light and Matter, a 1985 physics book by Richard Feynman
quod erat demonstrandum 'which was to be demonstrated' is a calque of ὅπερ ἔδει δεῖξαι (hoper edei deixai) 'what needed to be [shown] has been shown'. [64] similaris 'similar' calques ὁμοιομερής. [65] Many grammatical terms: participium 'participle' from μετοχή, declinationem 'declension' from κλίσις, etc.
A gerundive appears in the phrase quod erat demonstrandum ("which was to be demonstrated"), whose abbreviated form Q.E.D. is often used after the final conclusion of a proof. The motto Nil desperandum 'Nothing is to be despaired at' i.e. 'Never despair'. Based on this the cod Latin Nil illegitimis carborundum 'Don't let the bastards grind you ...