I was studying Latin, and I came upon this sentence:
Magister (boys writing letters) vidit.
Translated, it means:
The teacher saw the boys writing letters.
I was wondering, what grammatical case would "letters" be in that sentence?
Letters is the direct object of writing. If it were marked for case, it would probably be accusative.
But modern English has largely lost its case system; its nouns are generally not marked for case, so more properly I would say that letters has no case. (Even in Old English, by the way, there was no accusative-nominative contrast for plural nouns like this one.)
English is quite different from Latin, and we cannot always use the same descriptions for both. Instead of marking a direct object with a case system, in English we rely on word order. As a result, we must say writing letters and not letters writing.