Translation:Talking in the library is not right.
(responding because you said you would like the opinion of a philologist of the [ancient] Greek language about this; I am a Greek and Latin philologist)
There is a gerund in ancient Greek. The articular infinitive is the gerund.
This is true of languages in general, i.e., that the infinitive supplies the nominative or subjective case of the gerund, other forms being used for the oblique cases.
In Ancient Greek, the article is declined, and so there is no need for inflection of the verb, but there are forms of the gerund.
Nom. τὸ λέγειν
Gen. τοῦ λέγειν
Dat. τῷ λέγειν
Acc. τὸ λέγειν
Subjects of gerunds are always accusative, and subjects, direct objects, and any adverbial modifiers of the gerund, or of the other parts of the phrase, are conventionally placed within the article noun group (demonstrating further that the ancients saw it as a syntax item).
e.g., Our speaking in the library is apparently bad at all times.
τὸ ἡμᾶς ?ἐν τῇ βιβλιοθήκῃ λέγειν κακὸν πάντοτε φαίνεται.
• He has a great love of speaking at the library.
αὐτῷ ἐστι μεγάλη τοῦ ἐν τῇ βιβλιοθήκῃ λέγειν φιλία.
• There is a plot afoot against our speaking in the library.
ἐπὶ τῷ ἡμᾶς ἐν τῇ βιβλιοθήκῃ λέγειν ἐπιβουλεύεται.
Thanks for this scientific treatise about the Ancient (newly introduced) Greek Gerund. It is obvious that it was used as a noun in the above examples. But the Modern Greek use the form - οντας or -ωντας not as an articular infinite as in the above examples but with more likely adverbial use. If it's a matter of terminology it makes confusion with the gerunds in other languages, including English. I am not a philologist of course, so I had to search about. Here is a doc: http://el.science.wikia.com/wiki/Γερούνδιο in Greek. It would be a scholastic discussion all this if this hadn't some importance in translation of English to Greek, when it is used the English Gerund to translate it as an articulated subjunctive verbal phrases: ο/η/το να... This is not good Greek sentences. Generally speaking a literal translation does not make good translations. Duolingo is made to favors this kind of translations, the unit that it is translated is the word. It is a word by word translation and not an integrated free one. But it is a machine actually, we cannot ask more from a machine, unless it is very intelligent. We have not arrived at this stage yet.
Yes, it is. In English. In Greek, it is the participle in -οντας or -ώντας. But is not the same. It was a controversial part of speech till 1999. It was proposed in relation and influenced by the Latin Gerundium. Never used in the Ancient Greek Grammar and in Modern Greek the term was Ενεργητική Μετοχή=Active Participle, which is not exactly the same. The first who proposed it was the book: Holton , David, and Peter Mackridge and Ειρήνη Φιλιππάκη - Warburton . 1999. Γραμματική της Ελληνικής Γλώσσας , Αθήνα : Πατάκης. There are some philology papers that analyze it more. In Greek unfortunately most of them. See more in http://booksandjournals.brillonline.com/docserver/15665844/v1n1_s6.pdf?expires=1473626449=id=guest=02B19A08AEC53BA34E4AA597006955FD, a paper that supports it and http://www.icgl.gr/files/greek/96-990-999.pdf, page 3, in Greek, that rejects it, as it makes confusion with Active Participle. And the latter proposes to reject it as soon as possible specially for the foreigners, who try to learn Greek. I put the discussion in FB, in the special DL group for Greek, with many different opinions about. I would like the opinion of a philologist of the Greek language about.
I see that both adjectives have been included in the list of accepted translations, all of which use the preposition "in", but not "at". However, is it necessarily wrong to talk at the library? What I have in mind is this this sentence: "We're at the library, outside, talking".