Theorema Egregium

[Anonymous]

Hello all,

This is my first visit to this forum and I appreciate any help.
Gauss, the famous mathematician, published a "Theorema Egregium",
which is translated in every source I have seen as
"most excellent theorem". This was published around 1827.

My questions: how valid is this translation? Are there other possibilities?
Since the phrasing is a little awkward, it makes me wonder. (I
want to quote the theorem in a book I'm working on.)

Thanks for any advice,
Alan

 

[Andy]

Egregium is an Latin adjective, here in the neuter nominative. I don't know how that fits with Theorema, which to me, sounds feminine, but I don't know the general rules of Greek gender declensions.

Anyway, the work does exist. The word 'egregius' translates as singular, distinguished, exceptional, extraordinary, eminent, excellent, remarkable - take your pick.

Apparently the adjective comes from e-grege, or ex + grege: out of the flock. Something particularly impressive that stands out.

This is from where we get our word 'egregious'. In the archaic sense it means distinguished, now it just means conspicuously bad.

 

[QMF]

It does match Andy, the -ma ending is a Greek third declension neuter ending, cf. stigma.

 

[Anonymous]

Thank you both, esp. Andy -- that was very helpful.

 

[Andy]

By the way, QMF, what's this double declension in Greek you told us about, how does it work? Does it make a singular a plural or what?

 

[QMF]

Double declension? Oh the dual. It's just like the singular and plural, except it's...a dual. It has its own set of endings. I'd have to check but I believe it also only exists in a few cases.
It isn't an actual declension like 1st 2nd 3rd.
Yay I'm triumvirate now.

 

[Marius Magnus]

The dual is a number, not a case or declension. Proto-Indo-European had three grammatical numbers: singular, dual, and plural. The dual, as you might guess, was used for things that naturally came in twos (such as eyes, hands, etc.).

The dual survived into Sanskrit and Old Norse; it is lost in modern Scandinavian languages (except Icelandic), and I don't know if it exists in Hindi. I wasn't aware Greek had any duals, but I don't know much about Greek.

There are remnants of the dual in modern English:

both vs. all
either vs. any
etc.

And it is perceived as a grammatical error to say, e.g. "I used all of my hands!", unless you mean to imply you have at least three.

 

[QMF]

Greek's dual died out before Koine (so it didn't even exist into the A.D. years I believe), so it's not very well known.

 

[Aviator Maximus]

The Greek dual number more or less exists in all cases (depending on the dialect and time), just not always in a form different from the plural.

δύο, δυοῖν, δυοῖν, δύο (pls forgive the tilde in lieu of a real circumflex) is really a dual itself.

Other examples, according to Smyth, are as follows:

From ἡ φυγή:
φυγά (with a long alpha--again excuse my ghetto font resources) in the Nom., Acc., and Voc.
φυγαῖν in the Gen. and Dat.

From ὁ ἵππος: (same case pattern as above)
ἵππω
ἵπποιν

Finally, from ὁ πατήρ:
πατέρε
πατέροιν


Here's a transliterated reproduction of the above Greek text, in case it doesn't go through well:

duo, duoin, duoin, duo

hē phugē:
phugā
phugain

ho hippos:
hippō
hippoin

ho patēr:
patere
pateroin



At any rate, the patterns you see above (long alpha in the first declension, omega in the second, epsilon third) are pretty standard.

 

[Iacobulus]

Yes, the dual is so seldom seen that it's rarely taught in Greek grammar.

Typically you see it employed with things that are naturally paired, such as hands, eyes, etc.

And it did survive in post-Classical times believe or not, but not in Koine. Late Greek authors such as Plutarch and Lucian still used dual forms, but only for naturally paired things as I said.