Latin (adj.) Look up Latin at Dictionary.com
Old English latin, from Latin Latinus "belonging to Latium," the region of Italy around Rome, possibly from PIE root *stela- "to spread, extend," with a sense of "flat country" (as opposed to the mountainous district of the Sabines), or from a prehistoric non-IE language. The Latin adjective also was used of the Roman language and people.
Centurion: What's this, then? "People called Romanes they go the house?"
Brian: It ... it says, "Romans, go home."
Centurion [thrashing him like a schoolboy]: No, it doesn't. 'Go home?' This is motion towards. Isn't it, boy?
Brian: Ah ... ah, dative, sir! Ahh! No, not dative! Not the dative, sir! No! Ah! Oh, the ... accusative! Domum, sir! Ah! Oooh! Ah!
Centurion [pulling him by the ear]: Except that domum takes the ...?
Brian: The locative, sir!
[Monty Python, "Life of Brian"]
Used as a designation for "people whose languages descend from Latin" (1856), hence Latin America (1862). The Latin Quarter (French Quartier latin) of Paris, on the south (left) bank of the Seine, was the site of university buildings in the Middle Ages, hence the place where Latin was spoken. The surname Latimer, Lattimore, etc. is from Vulgar Latin latimarus, from Latin latinarius "interpreter," literally "a speaker of Latin." "What Latin was to the learned, that their tongue was to laymen; hence latino was used for any dialect, even Arabic and the language of birds ...." [Donkin, "Etymological Dictionary of the Romance Languages," 1864].
Latin (n.) Look up Latin at Dictionary.com
"the language of the (ancient) Romans," Old English latin, from Latin latinium (see Latin (adj.)). The more common form in Old English was læden, from Vulgar Latin *ladinum, probably influenced by Old English leoden "language."