The Origin and Meaning of Q.E.D.
Date: 9/20/95 at 17:28:35 From: Anonymous Subject: math What does QED stand for?
Date: 9/21/95 at 9:57:26 From: Doctor Sarah Subject: Re: math Q.E.D. : quod erat demonstrandum The origin of this expression is to be looked for in Euclidean geometry. The pattern of Euclid's demonstrations is usually: (a) the statement of an axiom (e.g. the sum of angles in any triangle is always 180 degrees); (b) a rational demonstration to corroborate this statement, and, finally, (c) a re-statement of the proposition enunciated in (a). In order to put a seal on his demonstration, Euclid finishes with the statement, "this was to be demonstrated." (Of course in Greek.) Medieval geometers habitually translated this as "quod erat demonstrandum" as a sign that they had proved what they had set out to prove. In the 17th century the Dutch Jewish rationalist philosopher, Benedictus de Spinoza (1632-1677), set out to write a treatise on ethics (_Ethica More Geometrico Demonstrata_) in which he proved various moral propositions in a geometric manner. Like Euclid, he wrote "quod erat demonstrandum," abbreviated Q.E.D., as a seal upon his proof of each ethical proposition. Thanks to Martin Ostwald, Professor Emeritus of Classics, Swarthmore College, for this answer. -Doctor Sarah, The Geometry Forum
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