From: Brian E. Wilson (brian@twonh.demon.co.uk)
Date: Thu Jan 22 1998 - 17:16:18 EST
In a message dated 98-01-22 10:03:00 EST, anku@celsiustech.com.au
writes:
>>At the end of solutions to problems or theorem proofs, the letters QED
>>are often used to state that enough information has been presented to
>> justify the conclusion. I believe the letters are a Latin acronym.
>>What do they actually mean?
>Andrew,
>They mean "quod erat demonstrandum," that which was to be demonstrated
>(by the argument thus ending). It's a mark of high Scholasticism.
At the age of eleven years, I started Euclidean Geometry. Our revered
maths teacher instructed us always to put QED at the end of every
theorem we proved. We were told with unquestionable authority that the
letters QED stood for -
.
. Quite Easily Done
.
Which was not always the case. Some proofs were very difficult.
Amazingly, as I discovered decades later, some of Euclid's theorems were
not provable from Euclid's axioms. For instance the theorem that the sum
of the angles of a triangle is two right angles cannot be demonstrated
from Euclid's axioms. In traditional Euclidian Geometry, QED would not
be true, in its Latin meaning, at the end of this theorem. Euclid was
wrong at this point.
Is not the moral of the story that in any sphere of study, even in New
Testament studies, we should not accept something simply because we have
been taught it? Whenever you find QED written at the end of any work,
Andrew, view it with suspicion, not satisfaction! Where you find QED is
not true, you really begin to learn.
Brian E. Wilson
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