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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
    
Associated Topics:
High School History/Biography

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