QED: Quod erat demonstrandum

[Chagen]

How would your conlang translate this favorite phrase of snarky internet logicians everywhere?

which was to be demonstrated

quod erat dēmonstrandum
who-NEU.NOM.SING be.IMPER-3SG demonstrate-FUT.PASS-PCPL-NEU.ACC

Pazmat:
Icj na seqxesibus yazj
who.which REL out-played-PCPL.PASS be.INFIN-PST
(Lit. "which that is to be out-played")

[kiwikami]

Cástían

con ansenítnó
which.is GER-demonstrate<ADJ><FUT><PASS>
which is to be demonstrated

Though con may become wen if the thing being demonstrated is not mentioned directly before this phrase. A different construction entirely would be used if one wanted to put this in past tense, because the statementive con could no longer be used:

mtúl zón ansenítnó
exist<3S.inanimate><PST> which.is GER-demonstrate<ADJ><FUT><PASS>
which was to be demonstrated

[Creyeditor]

German
was zu beweisen war
was zu beweis-en war
what to prove-INF be.PST.IND.3.SG
which was to be demonstrated

[Aseca]

Utnagasvrimahi:
Ham savrTham āstrati.
What.rel.N.sbj show.ppp.acc be.(strong.v)-IMP.3sg
That-which must-be (made) a-demonstration.

[Visinoid]

(ce) qui était à démontrer
(that) who be-3.IMPF to demonstrate
/(sə) ki e.tɛ a de.mɔ̃.tʁe/
[(s)kje.tɛ a de.mɔ̃ʊ̯̃.tχe] :qbc:

[Sangfroidish]

Ylle des, dás leņola chí their fin
[ɨɫːə d̪ɛs d̪aːs ˈlɛɲ.ˌɔɫ.ɐ xiː θɛ̯ir fin]
DEM.AB thing that show-PST NEC null_argument 3.AB.SNG
That which had to be shown

[Click]

Proto-Northern

uy tʼaki wo
UTIL show PRF
which was to be demonstrated

[Ean]

Κη νήραι α ση λημοστάρο.
[ci 'ni.ɾe a si li.mos.'ta.ɾo]
what be.there.3S.PAST to be.INF demonstrate-PART
That which was to be shown.

(ΚΗΔ/QED)

[clawgrip]

Japanese
Japanese has no good word for 'demonstrate' so I have used 'show'

見せるつもりのあったX
show intention REL.SBJ exist-PST X
X that (someone) intended to show

見せるはずのあったX
show expectation REL.SBJ exist-PST X
X that should have been shown

(REL.SBJ is a subject marker that only appears in relative clauses)

[prettydragoon]

Rireinutire

kaki toteriye yakiva:
kaki toteri-ye ya-ki-va
which.NOM demonstrate-PAS.PRESP be-PST-SENS
which was to be demonstrated

[Khemehekis]

Kankonian borrows a phrase from Ciladian, just as English borrowed it from Latin:

pilet dakyaph
therefore PP-prove
therefore proven

[Chagen]

Azenti:

çol os muta dyrafibharsya
who/which be.MID CAUS-see-PASS-SUP
(Lit. "Who/Which is to be caused to be seen")

[zyx3166]

Llipetadharceek.
see-PASS-CAUS-NEC-noun.clause-3SG

[Lambuzhao]

Çetara

Qu suesa gesmœtrandũ.
[qʊ swe.sɒ ʤez.mʊɛ.t̪rãn.dũ]
REL.INAN.NOM.SG be-IMPFT.3SG show-OBLIG.PTCP.N.SG

---

Older Sadrås

Ün ves ütschuanðe.[ỹn ves yt.ʃu.ãn.ðə]
REL.INAN.NOM.SG be-IMPFT show-OBLIG.PTCP.SG

More colloquial Sadrås

Ün bêd ütschuanðe.
[ỹn bɛ:d yt.ʃu.ãn.ðə]
REL.INAN.NOM.SG be-PST show-OBLIG.PTCP.SG

---

Rozwi

Wo fuetos kēzbieye.
[wɔ fwɛ.tɔs kɛ:z.bʲɛ.je]
REL.INAN.NOM.SG show-PST.PTCP CVRB<FUT>=be3SG

[Lambuzhao]

Ancient Greek

ὅπερ ἔδει δεῖξαι
REL.INAN.NOM.SG=EMPHATIC ought-IMPFT.3SG show<PST>ACT.INF

Which was to have demonstrated

NOT

Which was to have been demonstrated

That would be more literally

ὅπερ ἔδει δειχθῆναι
REL.INAN.NOM.SG=EPHATIC ought-IMPFT.3SG show<PST>PASS.INF

[Click]

Ardelian

• Votšatkə.
  votša·t·kə̆·Ø
  prove·PAT·PHST·3SG
  Proven.

[Znex]

A bit off-topic, but what does QED actually mean? It's quoted all over as being "which was to be demonstrated", but that means nothing to me, and we never use it in the literal way.

We never say things like "This, QED, is why etc., etc., etc.", we just say things like "QED, the plural of octopus is octopodes", and so QED is much more used like "therefore" or "thusly" or "soothly".

Is this a fair summation to make?

[eldin raigmore]

A bit off-topic, but what does QED actually mean? It's quoted all over as being "which was to be demonstrated", but that means nothing to me, and we never use it in the literal way.
We never say things like "This, QED, is why etc., etc., etc.", we just say things like "QED, the plural of octopus is octopodes", and so QED is much more used like "therefore" or "thusly" or "soothly".
Is this a fair summation to make?

This is not my experience at all.
QED (or some synonym) is always used right after the last statement of a proof, which, not at all coincidentally, is the statement it's a proof of.
So the last statement of the proof is the statement which one was required to prove.

In written proofs the end of the proof is often signalled by "and that's what we were trying to prove" or "which is what was to be shown" or some such thing.
In speech it's often something less formal like "and that's what we're after".

"Demonstrandum" is a gerundive; it means "requiring to be demonstrated".

I have never heard or read QED used in any of the ways you mention.
I have always heard and read it used in the way you say it's never used.
Since the differences in our ages is a mere fraction of a century, rather than a century plus a fraction, I can't imagine this is just due to ordinary language-change.
If it were "rarely" instead of "never" and "usually" instead of "always", maybe it could be language-change.
But if I interpret your "never" and "always" literally, then I have to believe you are in a small speech-community of people who use QED only in ways that the larger English speakership would not recognize as correct or would not understand.
Lexical items do gain new meanings; but usually retain the old meanings for a while, first as the more common meaning, later perhaps as the less common meaning.
(For instance, consider "gay", "turn on", "trip", etc.)
I thought it was unusual for one to completely shift to a new meaning and completely lose its old meaning in less than a few centuries.

If I've been wrong about this, I wonder how long, and where, and among how large a subset of English-speakers?

Edit: I am feeling and trying to express . I am not feeling , neither am I trying to express it. I don't know whether my typing made that clear.

[Bagliun Edar]

Obulamga

imzlōrzu bejeniaoron
[ˈimzlɔːɾzu ˈbɛʒɛniaˌɔɾɔn]
im-zlo-or-zu b<ej>eniaoron
cause-INTV-PASS-REL <INF>is_proven
which is to be demonstrated

INTV: "intentive" mood

[Znex]

A bit off-topic, but what does QED actually mean? It's quoted all over as being "which was to be demonstrated", but that means nothing to me, and we never use it in the literal way.
We never say things like "This, QED, is why etc., etc., etc.", we just say things like "QED, the plural of octopus is octopodes", and so QED is much more used like "therefore" or "thusly" or "soothly".
Is this a fair summation to make?

This is not my experience at all.
QED (or some synonym) is always used right after the last statement of a proof, which, not at all coincidentally, is the statement it's a proof of.
So the last statement of the proof is the statement which one was required to prove.

In written proofs the end of the proof is often signalled by "and that's what we were trying to prove" or "which is what was to be shown" or some such thing.
In speech it's often something less formal like "and that's what we're after".

"Demonstrandum" is a gerundive; it means "requiring to be demonstrated".

I have never heard or read QED used in any of the ways you mention.
I have always heard and read it used in the way you say it's never used.
Since the differences in our ages is a mere fraction of a century, rather than a century plus a fraction, I can't imagine this is just due to ordinary language-change.
If it were "rarely" instead of "never" and "usually" instead of "always", maybe it could be language-change.
But if I interpret your "never" and "always" literally, then I have to believe you are in a small speech-community of people who use QED only in ways that the larger English speakership would not recognize as correct or would not understand.
Lexical items do gain new meanings; but usually retain the old meanings for a while, first as the more common meaning, later perhaps as the less common meaning.
(For instance, consider "gay", "turn on", "trip", etc.)
I thought it was unusual for one to completely shift to a new meaning and completely lose its old meaning in less than a few centuries.

If I've been wrong about this, I wonder how long, and where, and among how large a subset of English-speakers?

Edit: I am feeling and trying to express . I am not feeling , neither am I trying to express it. I don't know whether my typing made that clear.

Oh okay. I was most likely generalising anyway - I haven't been in much contact with proofs. Although I was sure QED was used in statements like "QED, the plural of octopus is octopodes"...