οὐκοῦν ἐστιν αὕτη γράμμη ἐκ γωνίας εἰς γωνίαν τινὰ τέμνουσα δίχα ἕκαστον τούτων τῶν χωρίων. why is the article omitted here in αὕτη γράμμη, whereas a bit further, he uses τούτων τῶν χωρίων with an article? should we understand it not as ‘this line’ but as ’ this is a line’? Next, in εἰς γωνίαν τινὰ, ‘τινὰ’ functions as an indefinite article, right? if im right in saying ’ this is a line’, then Steadman’s comment "this line’ is wrong.
Goodwin 945 says that “nouns qualified by a demonstrative pronoun regularly take the article” but note 2. says “this article may be omitted with proper names also where the demonstrative is equivalent to here or there.”
I am sure the text does not mean “this is a line”.
I think that τινὰ in there supports Philo. Something like:
οὐκοῦν ἐστιν αὕτη γράμμη ἐκ γωνίας εἰς γωνίαν τινὰ τέμνουσα δίχα ἕκαστον τούτων τῶν χωρίων
Wouldn’t this be a line from a corner to some corner that has cut each of the spaces in half?
The OCT brackets the τινὰ with “secl. Schleiermacher.”
Without the τινὰ I think it’s more naturally:
Hasn’t this line from the corner to a corner cut each of the spaces in half?
I could be wrong.
an old comment to the Meno which im reading says that τινα is due to the corruption in the manuscripts
The Loeb prints the following text omitting τινὰ:
Οὐκοῦν ἐστιν αὕτη γραμμὴ ἐκ γωνίας εἰς γωνίαν τείνουσα, τέμνουσα δίχα ἕκαστον τούτων τῶν χωρίων.
i think you are right i saying that this is more likely as: this line here
οὐκοῦν ἐστιν αὕτη γραμμὴ ἐκ γωνίας εἰς γωνίαν τινὰ τέμνουσα δίχα ἕκαστον τούτων τῶν χωρίων;
Why is the article omitted in αὕτη γραμμὴ?
Because γραμμὴ is indefinite: ‘a line”, not, “the line” (see note 1).
He uses τούτων τῶν χωρίων with an article.
Yes, because this reference is definite:
“each of these [and not any other] figures/squares/areas/spaces”.
Should we understand it (αὕτη γραμμὴ) not as “this line”, but as “this is a line”?
It does not mean “this line”(no article. See note 2). Note, however, that Guthrie and Lamb (and Steadman) disagree (see Sample translations).
“this is a line” is a possible translation: Here, αὕτη functions as a noun, and is the subject of ἐστιν (see note 2). Context should, of course, always be considered when searching for the most appropriate translation.
In εἰς γωνίαν τινὰ, ‘τινὰ’ functions as an indefinite article, right?
Yes(see note 2). Waterfield catches the sense well here: “from one corner to another” (see Sample Translations).
Note that some editors(eg, Schleiermacher) believe the text is corrupt (ie, τινὰ should be removed).
Notes
(1) Greek has a definite article (ὁ, ἡ, τό the), but no indefinite article (Engl. singular a(n)). The Greek equivalent of an indefinite article is the lack of an article. While the indefinite pronoun τις can also be used to convey indefiniteness, it is not, strictly speaking, required in any particular context.
(2) When a demonstrative pronoun is used with a noun without an accompanying (definite) article, it is being used pronominally(ie, independently, as a noun), and functions as the subject/object of the verb.
(3) The demonstrative pronoun οὗτος has a deictic (‘pointing’) function(as do ὅδε, ἐκεῖνος), so it is makes sense that it can also be used adverbially to mean ‘here’ or ‘there’ (“the man here”, “the man there”).
Sample translations (84e-85a)
“Well, is there a line here from corner to corner, cutting each of these figures in two?” (Sharples, Aris & Phillips)
“Now does this line going from corner to corner cut each of these squares in half?” (Guthrie, Penguin)
“And does this line, drawn from corner to corner, cut in two each of these spaces?” (Lamb, Loeb)
“Now is there a line like this from corner to corner, cutting in two each of these areas?” (Sedley/Long, Cambridge)
“Now, here’s a line that runs from one corner to another and cuts each of these figures in two. Right?” (Waterfield, Oxford)
Much of the above reply was written using The Cambridge Grammar of Classical Greek as a resource (in particular, Chaps 28 & 29).
could you give an example for note 2 plz? ok, i got it
This is a strange discussion. It’s the plain distinction between attributive and predicative position.
“οὐκοῦν ἐστιν αὕτη γραμμὴ …” means “isn’t this a line …”
while
“οὐκοῦν ἐστιν αὕτη ἡ γραμμὴ …” means “isn’t this line …”
the last wouldn’t make much sense in the sentence.
you are probably right and that was my first impression as well, however Steadman’s comment confused me…he is wrong then…
Well, yes…more or less, but there are some differences when using demonstrative pronouns instead of, say, adjectives, that are worth pointing out.
Note the following:
ἀγαθὸς ὁ ἀνήρ———the man is good———Predicative position/predicative function.
οὗτος ὁ ἀνήρ———-this man…———Predicative position/attributive function.
ὁ ἀγαθὸς ἀνήρ———the good man————Attributive position/attributive function.
ὁ οὗτος ἀνήρ——— [not applicable]———Attributive position/not allowed(nominative case).
Also, the position of the definite article is an important clue to how the above noun phrases work, such that its absence from the sentence quoted from Meno might make one pause to think(the indefinite article being ‘invisible’ here).
As previously mentioned, context is, of course, always important in searching for the best translation, and you can see that there is a fair amount of variety in the Example Sentences(some important, others more a matter of expression).
It’s necessary to distinguish between οὐκοῦν(above) and οὔκουν.
οὐκοῦν has no negative force, and means just the same as οὖν. It should be translated as well, then/so, then/ accordingly:
Well, then, is this a line…
The example with the supplied definite article becomes:
Well, then, is this line…
I agree this doesn’t make sense, but a little rephrasing, à la Guthrie(see Example Sentences), makes it perfectly acceptable.
You may wish to double-check οὐκοῦν A.I in the LSJ.
I followed your advice(did I not?) and yes, there indeed it is, right at the top of the entry in the big LSJ just as you said! Let me see if I can come up with some excuses for my oversight. 
I have to confess that, when it comes to lexica, I rely mainly on Brill, with some use of Middle Liddell and its younger, smaller sibling. Although I own the parent LSJ, I only ever refer to it(when I do) by means of the Perseus digital version.
As you will have gathered, Brill does not allow for a negative sense of οὐκοῦν at all, but, also, somewhat more bizarrely, neither do the smaller LSJs, each of which states categorically that the adverb has no negative sense(!).
Middle Liddell
οὐκοῦν, Adv. orig. identical with οὔκουν, but losing all negat. force…
Little Liddell
οὐκοῦν…When the word has this accent[ie, the circumflex], the negat. sense vanishes, and the force of οὖν only remains.
Out of curiosity, I decided to read(or re-read) the full entries in both LSJ and Brill, and to check the sources of the citations in each, along with the Perseus English translations.
I was particularly interested in the citations shared by both lexica, and found the results interesting(see below).
LSJ: οὐκοῦν with negative force
Of the 5 shared citations, Brill interprets all 5 as having positive force(as you might expect!).
Of the Perseus English translations, 2 are negative(as LSJ), 3 are positive(as Brill).
Brill: οὐκοῦν with positive force
Of the 6 shared citations, LSJ interprets 3 as positive, 3 as negative.
Of the Perseus English translations, 6 are positive(as Brill), 0 are negative(pace LSJ).
Although quoting from some(admittedly authoritative) dictionaries and a handful of translations doesn’t necessarily prove a case, I think the exercise does at least suggest that there is some disagreement here as to how οὐκοῦν should be translated in affirmations and in questions. This makes sense, I think, as it requires that the translator diagnose the level of confidence being expressed by the speaker that his/her question will receive a reply in the affirmative.
“You think then, do you not, that…” suggests that a positive answer is very much expected.
“Do you think, then, that…” is (more) open to either a positive or negative response(although tone of voice may also play a part).
Whatever the above shows, there is, however, no doubt, as far as LSJ père is concerned, that οὐκοῦν may be interpreted as having a negative force.
Thanks for pointing this out, and, of course, apologies to polemistes!
“Isn’t it?” is interrogative, not negative, I think. You may also wish to see Denniston’s section on οὐκοῦν.
It’s both, I think.
However, if you are saying that the negative force is greatly diminished(or even absent?) in this formulation, then I believe I agree with you. The construction is only formally negative, and can be construed as a polite way of inviting assent to the claim being made in the rest of the query. If this is agreed, then it would help explain why some translators prefer a positively phrased translation rather than a negatively phrased one.
Compare these examples in English:
“Didn’t you receive a letter yesterday?” - inviting assent to a belief held by the questioner.
“Wouldn’t you like a cup of tea?” - a polite formulation of the more direct question, “Would you like a cup of tea?”.
The reference to Denniston is pertinent. I have only glanced through it, as yet, but I hope to read it in some detail when I have time(it is quite long).