I find it hard to guess what the sentence should be as the literal translation is book, New York, is. I know that is just how languages are as I have that problem in other languages too. Where does the in New York come from? I am missing an obvious pointer here! Totally thick I know but please help!
"Book" is the subject: Liber. "Is" is the verb: est. We've got a sentence of the type, "The book is ... (+ location)." Imagine: The book is on the table (Liber est in mensa.). The book is in the library (Liber est in bibliotheca).
However, when the LOCATION is the name of a city (like the name, "New York"), you don't need the word "in", in Latin; and there's a special ending on the city name. (Duolingo is teaching us those names, by repetition: Philadelphia, Roma, Bostonia: use ending -ae: Philadelphiae, Romae, Bostoniae. Novum Eboracum gets the ending -i: Novi Eboraci.)
Well, I mean, it's not like they could even be bothered to use macrons for the written content in the first place, so I get the distinct impression that they actually don't want us to make any length distinctions. Not to mention that, in the audio, their own spoken length distinctions are all over the place, further compounding the confusion. It's as though the course designers have simply decided that we don't need to know which vowels are short and which vowels are long, much to my chagrin. I'm surely internalizing all vowels as short as this course is progressing, and I have no doubt that this is going to cause tremendous problems for me later on, where I'll have to unlearn what this course has neglected to teach me.
Yes, I honestly don't see how students can be expected to learn how to conjugate the 2nd conj. verbs like video, videre ( = LONG ere), which have the vowel "e" throughout the present tense (video, vides, videt, videmus, videtis, vident) as opposed to the 3rd conj. ("regular" or "plain") verbs like duco, ducere (= SHORT ere), which have no "e" in the present (duco, ducis, ducit, ducimus, ducitis, ducunt).
It's nice to learn the endings that have long vowels, such as the a and o in genitive plural -arum and -orum, accusative plural -as and -os; the long i of ablative plural -is (in 1st & 2nd declensions).
No, that would be something like Liber est Novum Eboracum.
Names of cities, towns, small islands, and a handful of other nouns like domus use the locative case (Novi Eboraci here) to specify location and this case does not use a preposition. Other nouns use prepositions like in to express location.
Though I think that, as a substantive, līber means "the free man" and not "the child," which is puer . As far as I know, the term līberī meaning "children" (I suppose it's "the free [dependent] ones in the household" as distinguished from the servī ) is plural only.
You're right that liber, librī , m., "book" has a short i (and a different stem altogether, for that matter), and is etymologically unconnected to the adjective "free" (līber, lībera, līberum). I always cringe when I see people report incorrectly that "book" is related to "freedom" in Latin...