Doc has just finished insulting Ringo by saying that he reminds him of himself. Trying to avoid trouble, Wyatt Earp (Kurt Russell), his hand on a sawed-off swivel shotgun under the faro table, says to Ringo, "He’s drunk."
Doc smirks, gulps a slug of whiskey, and says "In vino veritas," or, "In wine there is truth," an aphorism which supposedly reflected the Romans' belief that what a man said while drunk was what he truly felt but would not say under usual circumstances.
Ringo surprises Doc with an aphorism of his own "Age quod agis," or, "Do what you do." Ringo’s precise meaning is unclear, presumably he is challenging Doc to "Cut the talk and do what you do best."
Doc smiles and says, "Credat Judaeus Apella, non ego." This line is from the Roman poet Horace, specifically from his Satires, Book One, Satire Five. Horace and his Greek friend Heliodorus, are visiting a town where the locals try to convince them miracles occur at their sacred shrines. In the Modern Library translation by classical scholar Casper J.Kraemer, Jr., the line reads "Apella the Jew may believe this. I don’t." In other words, "Tell someone else, I ain’t buying it."
Ringo pats his gun and fires back, "Enventus stultorum magister," or "Youth is the master of fools." Again, his meaning is unclear, but he is essentialy saying, "You may think you know what you are getting involvedwith, but your experience hasn’t prepared you for what I have got here(patting his holster)."
Doc smiles again and replies, "In pace requiescat," literally, "May he rest in piece." As this was a popular inscription on tombstones, Ringo cannot fail to catch Doc’s drift, and ends the verbal duel by displaying his gun-handling skills.
But, screenwriter Kevin Jarre may have intended a second meaning as well. Doc’s last line is also the last line of Edgar Allen Poe’s "The Cask of Amontillado." This is one of Poe’s "doppelganger" stories— "William Wilson" is another— in which two men are presented in a way which suggests that they are seperate parts of the same dark soul. In "The Cask of Amontillado" an Italian nobleman murders a friend who has insulted him, and in doing so, Poe suggests, kills a part of himself as well.
One of the ingenious undercurrents of Jarre’s script is that Doc and Ringo are joined together by some mystical bond of torment. (In reality, Ringo suffered from Post Traumatic Stress Syndrome, alcoholism and possible depression; Doc suffered from tuberculosis and his own struggle with the bottle.) Recall that Doc set off the Latin duel by saying that Ringo "Reminds me of…me! No, I’m sure of it, I hate him." Ringo foresees Doc’s coming early in the film when he tells the Cow-boys of the doomed priest’s last words, a quote from Revelation "Behold a pale horse, and the ones that sat upon him was death…"
The suggestion is that they are the only ones who can put each out of their misery. "All right you lunger, I’ll put you out of your misery," says Ringo in the street. When Doc delivers the fatal bullet to Ringo he urges John ("C’mon, Johnny, c’mon.") to get off one last round himself to return the favor and grant Doc a quick death. In any event, Doc cannot long survive Ringo’s death; in killing him he was symbolically slain himself.