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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,

-Doctor Sarah,  The Geometry Forum
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