The usage of Q.E.D.
Adviolin
which was meant to proven" I think or something like that, but in what
language and what are the exact words. I know I saw it before, and one of the
d I think is for demonstratus.
I also read somewhere that it is thought to be arrogant today to use the
letteger qed at the end of a proof, and there are better ways to do it. What
are these ways, and why the big deal?
Thanks
Adam
Virgil
advi...@aol.com (Adviolin) wrote:
The letters stand for the Latin phrase "Quod erat demonstrandum", which
translates as "That which was to be proven".
In geometry, there is also q.e.f. for "quod erat faciendum", meaning
"that which was to be constructed".
Nat Silver
> I know that the letters qed...
It's Q.E.D. (more)
>traditionally followed a proof, and they mean...
>"that which was meant to proven"
has been demonstrated. (more)
>I think or something like that,
sloppy (more)
>but in what language...
Latin, the richest language in Europe for centuries. (more)
>and what are the exact words.
>I know I saw it before, and one
>of the d I think is for demonstratus.
close but no cigar (more)
> I also read somewhere that it is thought to be arrogant today...
You have little credibility without a reference. (more)
>to use the letteger...
letters (more)
>qed at the end of a proof, and there are better ways to do it.
>What are these ways,...
In the modern style, at the end, one can put a box
like the one at the right angle of a right triangle. (more)
>and why the big deal?
You're making a big deal.
Doug Magnoli
with your demonstratus.
Demonstratus is the past passive participle of the verb demonstrare, so that
demonstratus (or demonstratum in the neuter) means 'proven'--the way to use that
in qed would be 'quod est denomstratum'--'which has been proven.' (Est, of
course, is 'is.' 'Quod erat demonstratum' would mean 'which had been proven.')
Demonstrandus is the future passive participle (if I remember right), and has the
flavor of '... was to be proven,' so 'quod erat demonstrandum' means 'which was to
be proven.' (Erat is one of the past tense forms of est, so it means 'was.')
Your Latin lesson for today.
-Doug Magnoli
Doug Magnoli
Nat Silver wrote:
> Adviolin wrote:.
> > I know that the letters qed...
>
> It's Q.E.D. (more)
>
> >traditionally followed a proof, and they mean...
> >"that which was meant to proven"
>
> has been demonstrated. (more)
Nope--in your own words on this same topic (vide infra), 'close but no
cigar,' 'Has been demonstrated' would be 'quod est demonstratum,' the
same word the OP thought the D stood for. QED means 'quod erat
demonstrandum,' -- 'which was to be demonstrated.'
-Doug Magnoli
Nat Silver
> Nat Silver wrote:
> > Adviolin wrote:.
> > > I know that the letters qed...
> > It's Q.E.D. (more)
> > >traditionally followed a proof, and they mean...
> > >"that which was meant to proven"
> > has been demonstrated. (more)
> Nope--in your own words on this same topic (vide infra), 'close but no
> cigar,' 'Has been demonstrated' would be 'quod est demonstratum,'
"Quod est demonstrandum" would mean "What is demonstrated." (more)
>the same word the OP thought the D stood for. QED means 'quod erat
> demonstrandum,' -- 'which was to be demonstrated.'
Quod erat demonstrandum literally translates to: what was shown.
"Erat" is the 3rd person singular past tense of the verb to be.
One may take liberties with translation,which does not
have to be literal; however, not to the extent you and Adviolin
have done. QED
Doug Magnoli
Nat Silver wrote:
> Doug Magnoli <dmag...@home.com> wrote:
> > Nat Silver wrote:
> > > Adviolin wrote:.
> > > > I know that the letters qed...
> > > It's Q.E.D. (more)
> > > >traditionally followed a proof, and they mean...
> > > >"that which was meant to proven"
> > > has been demonstrated. (more)
> > Nope--in your own words on this same topic (vide infra), 'close but no
> > cigar,' 'Has been demonstrated' would be 'quod est demonstratum,'
>
> "Quod est demonstrandum" would mean "What is demonstrated." (more)
Nope. 'Quod est demonstrandum' would mean 'what is to be demonstrated,' in
the sense of 'what is supposed to be demonstrated.'
'What is demonstrated' would be present tense passive--quod demonstratur.
Recall the Latin,unlike English, has separate forms for the present
passive. The present *perfect* passive is made of the present tense of the
verb 'to be' and the perfect passive participle, demonstratum. So 'quod
est demonstratum' means 'what has been demonstrated.'
'demonstrandum' is not the perfect passive participle, it's the future
passive participle, which we don't have in English. The sense of the
future passive participle is 'about to be ...' or '...[was/is] to be...,'
in the sense of '...was supposed to be...' or '...was intended to be....'
Therefore 'quod erat demonstrandum' means 'what was [intended, supposed to]
be proven' or 'what was about to be proven.'
To go a little further, Latin verbs have 4 participles, unlike English's
two (going, gone / demonstrating, demonstrated):
present active participle: demonstrans -- means 'demonstrating'
future active participle: demonstraturus -- means 'about to demonstrate'
perfect participle: demonstratus -- means 'demonstrated'
future passive part: demonstrandus -- means 'about to be demonstrated' or
'intended to be demonstrated'
Enough?
-Doug Magnoli
Stan Brown
in executive summary: Q.E.D. means "quod erat demonstrandum", which
in literal non-idiomatic English is "which was to be demonstrated"
(or pointed out or shown or proved -- my Latin dictionary gives
about eight translations of "demonstrare").
It seems Nat Silver <mat...@worldnet.att.net> wrote in
alt.algebra.help:
>"Quod est demonstrandum" would mean "What is demonstrated." (more)
More than what? In any event, it doesn't mean that, though you've
got the general idea. The short and literal translation is "which
was to be demonstrated", though that doesn't convey a lot to modern
speakers of English.
>Quod erat demonstrandum literally translates to: what was shown.
I fear that is literally incorrect.
"Demonstrandum" is a gerundive, which is a future passive
participle. (What a mouthful!) The usual English translation is "to
be proved" or "shown" or something similar.(*)
So when we write the conclusion of a proof, and then write "Q.E.D.",
we are saying literally "which (quod) was (erat) to be proved
(demonstrandum)", meaning that at the time we started the proof it
was to be shown, but now it has been shown. We're reminding that
reader that we have done what we were asked to do or set out to do.
More loosely and in more modern language, "and that's the thing I
was supposed to prove."
(The on-line dictionaries are always a useful starting point. M-W
<http://www.m-w.com/mw/netdict.htm> translates "QED" as "quod erat
demonstrandum" and defines the latter as "which was to be proved".
Macquarie <http://www.dict.mq.edu.au/> also says "which was to be
proved", and <http://www.dictionary.com> says "which was to be
demonstrated".)
>"Erat" is the 3rd person singular past tense of the verb to be.
>One may take liberties with translation,which does not
>have to be literal; however, not to the extent you and Adviolin
>have done. QED
I agree that one may take liberties with translation; in fact a good
translation will usually not be word for word because languages
express themselves differently. Latin is (was) highly inflected;
English depends much more on word order and auxiliary and modal
verbs.
But when you say you are giving a literal translation, then of
course it should be an accurate literal translation.
(*) Latin had a lot more kinds of participles than English does.
Here's one explanation of the gerundive. Humez & Humez write on page
83 of "Latina pro Populo" (1976, but Latin hasn't changed that much
in the past quarter of a century :-):
"The gerundive, sometimes known as the future passive participle, is
formed by. ... Thus /salutandus, salutanda, salutandum/, worthy to
be greeted, as in /Ursus comissime salutandus est/ (The bear is to
be greeted as politely as possible, It is necessary that the bear be
greeted as politely as possible, The bear has yet to be greeted as
politely as possible, and so on).
--
Stan Brown, Oak Road Systems, Cortland County, New York, USA
http://oakroadsystems.com
My reply address is correct as is. The courtesy of providing a correct
reply address is more important to me than time spent deleting spam.
anonymous
Some ppl put a little square (usually solid colored) at the end of a
proof.
I don't see how qed is arrogant though, except when you use it like
Nat =P
For humor, I suggest putting IAG at the end for "It's all good"
Ex:
Proof by induction that everyone is mad.
base case: in a set containing 1 person either everybody is mad or
everybody is not mad
IH: assume in a set containing n ppl, either everybody is mad or
everybody is not mad.
for a set S containing n+1 ppl, take a subset T containing n ppl.
everybody in T is either mad or not mad. pick a person p in T. Q=S\{p}
(the ppl in S excluding person p) is a set with n ppl, and hence
either everybody is Q is mad or everybody is not. The person p is in
the same state as the ppl in both T and Q who are in the same state as
the person in Q but not in T. Therefore everybody in the set is in the
same state. By induction, everybody must be mad or everybody must be
sane. John Rocker (or your favorite mentally disturbed person) is mad,
so clearly everyone cannot be sane. Hence everyone is mad.
IAG
you say my proof is wrong? what?! clearly my proof is good. as you can
see, it's all good. =P
Ken Pledger
> are these ways, and why the big deal? ...
This thread has elicited plenty of Latin grammar, but not yet any
history. (I'm in favour of both. :-)
Euclid's "Elements" (c. 300 B.C.) used a definite format for proofs.
I'll use Book I, Proposition 30 as an example.
Each proposition begins by stating what is to be proved or
constructed. (I'll concentrate on theorems rather than constructions.)
Euclid I.30 begins "Straight lines parallel to the same straight line are
also parallel to one another."
Next Euclid sets up some notation, and restates the theorem in that
notation. I.30 says "Let each of the straight lines AB, CD be parallel to
EF. I say that AB is also parallel to CD."
Then he continues "For ..." and sets out the actual proof. The proof
ends the way he claimed it would, and then he adds the words which this
thread is discussing. I.30 ends with "Therefore AB is parallel to CD,
which was to be proved."
Of course all of that was originally in Greek. In mediaeval and
renaissance Europe the international language of learning was Latin, so
Latin translations of Euclid came into use. Euclid's standard ending
"which was to be proved" became "quod erat demonstrandum"; and to save
repeatedly writing that, people abbreviated it to "Q.E.D." (They were
just as lazy as we are when we write "IMHO" or "ROTFL".)
Euclid's _constructions_ ended with the Greek words for "which was to
be done," whose Latin translation "quod erat faciendum" became abbreviated
to "Q.E.F."
You say that someone thinks it arrogant to use these letters now. If
so, it seems to me no more or less arrogant than using any other
conventional Latin expression such as "sub judice". But there is the
problem that "which was to be proved" really makes sense only at the end
of a sentence re-stating the theorem as Euclid did. If it's not
convenient to do that, you may do better to use the little rectangle which
some people have already mentioned. What about the origin of _that_?
Paul Halmos invented it, as he also invented the abbreviation "iff" for
"if and only if".
Ken Pledger.
Don Stewart
There is a website somewhere that translates.
Don
"Adviolin" <advi...@aol.com> wrote in message
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