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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".
Translation Notes a bene placito: from one well pleased: i.e., "at will" or "at one's pleasure". This phrase, and its Italian (beneplacito) and Spanish (beneplácito) derivatives, are synonymous with the more common ad libitum (at pleasure). a capite ad calcem: from head to heel: i.e., "from top to bottom", "all the way through", or "from head ...
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.
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 ...
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.
"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.
In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or " ") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "quod erat demonstrandum". It is inspired by the typographic practice of end marks, an element that marks the end of an article. [1] [2]