What is the connection between the allusion to Master Ridley and what is taking place in Bradbury's story Fahrenheit 451?
In Bradbury's Fahrenheit 451, the old woman at 11 N. Elm Street alludes to a famous quote by Hugh Latimer. As the firemen prepare to burn her home and books (and perhaps even then she knows she also will face a similar fate), she quotes the following:
Play the man, Master Ridley; we shall this day light such a candle, by God's grace in England, as I trust shall never be put out.
In England in October of 1555, Latimer and Ridley were facing execution—being burned at the stake because of their religious beliefs. Latimer encourages his companion, Nicholas Ridley, to remain strong in the face of death. He believes that their deaths are not as important as is the message of their dedication to their beliefs: a dedication that will speak more loudly than anything they could say. The inference is that their sacrifice would not be in vain, but might spark deeper dedication in others, perhaps even a revival of faith for all Protestants—even the clergy—who were being persecuted and killed by Mary Tudor ("Bloody Mary").
This quote is especially relevant in Bradbury's novel. In this futuristic dystopian society, the government has banned books—and people discovered in possession of them are arrested, and their books and homes burned by firemen such as Montag and Beatty.
When Montag and the rest of the firemen arrive at 11 N. Elm Street, Montag is deeply distressed to discover the owner still in the house. At this point in the story, Montag has had no understanding or concern over the ramifications of how his job hurts others:
How inconvenient! Always before it had been like snuffing a candle. The police went first and adhesive-taped the victim's mouth and bandaged him off into their glittering beetle cars, so when you arrived you found an empty house. You weren't hurting anyone, you were hurting only things!
It is only as he witnesses the deep dedication of the woman for her books that he realizes something is taking place that he does not understand. He cannot conceive why books are so important that someone would give up her life (which she does) rather than live without the scores of printed works hidden in her home.
When the old woman quotes Hugh Latimer, Bradbury uses her character to present the idea that her life is not what is important, but that books be saved and knowledge be preserved. Whether she is aware of it or not (the author does not reveal this), Montag becomes changed by this event in a way he could never have imagined. From that moment, he does all he can to resist going to work. He hides books in his home. He seeks out the company and counsel of Faber, a retired English professor, to learn the truth. He stops living a superficial life centered on the government's control of people's thoughts.
It is when Montag finally breaks free of this desensitization visited upon this society that he kills Beatty to stop him from arresting Montag and hunting down Faber. Montag escapes the Mechanical Hound and the authorities, making his way to the river and then the railway track that leads him to others like himself—people dedicated to saving the knowledge and ideas held in books, and to eventually rebuilding society, even as it is bombed and rests burning in the distance.
Hugh Latimer's quote speaks of the promise that what he and Ridley sacrifice that day will live on to impact others in the struggle with their devotion to their faith. In Fahrenheit 451, the old woman quotes Latimer with (we can infer) the sense that her sacrifice will be for the greater good, inspiring others to give their all to save books and thereby, save society. Her hope is realized in Montag, a man who becomes dedicated to the same vision, to bring about change in the world.