It would be "linguam latīnam" (accusative). as in "linguam latīnam discimus (we learn the latin language). But "studēre" doesn't really have the same meaning as "to study".
you should understand it as "we dedicate ourselves TO the latin language". with the dative (linguae latīnae) having the function of the word "to".
Thank you very much for this. I was stuck on a similar phrase in the "School" section and I couldn't understand why it wasn't in the accusative. "Discipuli in ludo linguae Latinae student". It's the dative case! I've had the idea to use the word studious to help me remember eg. we are studious to the Latin language. Ok it might not be great English but it puts the word 'to' in there so I'll remember it's the dative case!
For me, this evokes the English expression, "I am a student of X" where X could be any inanimate object, concept, or phenomenon, and it means essentially "I am dedicated to the study of X."
Of course, "of X" is the English equivalent of genitive case, so it's clearly not a perfect parallel...
Studēre • Present Infinitive • To Devote, Dedicate oneself to, To Direct one's efforts or attention to, To Strive after, Attached or Favorable to, To be diligent (in) + Verb Object ( usually ) in Dative Case
Because this is the accusative case.
The subject in the sentence is "we" (in Latin, the pronoun is dropped, but the form of the verb tells us that it is first person plural).
So the other noun of the sentence must be something else than the subject; in this case it is an accusative object.
Because of the dative declension.
Normally verb+object = takes the accusative.
But here, with "studere", it's an exception.
Nominative -> lingua (sing)
Genitive -> linguae (sing)
Dative -> linguae (sing)
Accusative -> linguam (sing)
Ablative -> linguā (sing)
Vocative -> lingua (sing)