Montag has picked up Gulliver's Travels, written by Jonathan Swift, which remains one of literature's most-revered political satires. In this novel, Swift criticizes mankind's pride and its propensity to follow theories which have not been proven.

While Swift's audience could have more easily drawn the parallels between the fictional worlds of the Brobdingnagians, Laputans, Houyhnhnms, and Lilliputians and their own political structures in Britain in the early 1700s, much of that history is not evident to a modern American reader—let alone one in the futuristic dystopia that Bradbury creates. Therefore, when Montag reads this one sentence aloud, completely out of context, Mildred feels vindicated. It seems to make no sense, and she is certain that books therefore can't "mean anything."

Montag is instead determined to find the relevancy in the books which Beatty has condemned. He tells Mildred that they must determine why they are in "such a mess" and whether the books contain anything worth knowing. He recognizes that men like Beatty are afraid of people like Clarisse, and he is desperate to understand why.

This sentence speaks to the power of the human spirit. Rather than follow edicts which they do not agree with, regardless of how insignificant those decrees might seem to outsiders, people throughout history have proven themselves capable of facing death rather than submitting to an unjust governing body. In this sentence, people have chosen death rather than being forced to break their eggs at a particular end. If people are willing to die over eggs, then they are certainly willing to die over matters which hold more significance, such has the censorship of ideas and literature. Montag proves capable of this determination himself, following in the spirit of Clarisse and the lady who burned herself in the fire when the firemen came.

Toward the end of Part 1, Captain Beatty finally leaves Montag's apartment after giving him a lecture regarding the history and necessity of the fireman institution, and Montag begins to remove the books he has hidden inside his ventilator. After explaining to Mildred that the books might contain valuable information that is worth learning, Montag opens a random book and reads a sentence describing how eleven thousand people have suffered death rather than break eggs at the smaller end.

The book Montag is reading is Gulliver's Travels, which was written by Jonathan Swift and published in 1726. Gulliver's Travels is one of the most revered and recognized works of political satire in the history of literature. The sentence Montag reads regarding the deaths of thousands of individuals who refuse to break the smaller ends of eggs is written in Part One of Gulliver's Travels while Gulliver is visiting the fantasy island of Lilliput. In the miniature civilization of Lilliput, there is a long-standing war between Blefuscu over what is the proper way to break an egg, which satirizes the long-standing religious conflict between Catholic France and Protestant England.

It is significant that Montag would initially read a political satire because he is also challenging the government similar to the way Jonathan Swift challenged Great Britain by publishing his satirical work. It is also significant that Montag would read Gulliver's Travels because Ray Bradbury is essentially satirizing western culture and its ideals throughout the novel similar to how Jonathan Swift satirized Great Britain and other European nations.

This quote appears in the closing lines of Part One of Fahrenheit 451 when Montag picks up a book at random and starts to read aloud to Mildred. The quote comes from the book Gulliver's Travels by Jonathan Swift, and tells the story of how the two great empires Lilliput and Blefescu came to be at war. The conflict arose over the question of which end to break one's eggs: those in Blefescu break their eggs at the big end, as tradition dictates, but those in Lilliput are forced to break their eggs at the smaller end as a result of royal edict. There are, however, rebels in Lilliput who refuse to break their eggs this way, which eventually causes a war, as Montag learns when he reads this section:

"It is computed that eleven thousand persons have at several times suffered death rather than submit to break their eggs at the smaller end."

This quote is significant because it encourages Montag's growing sense of rebellion. It is like a call to action because it suggests that if people are prepared to sacrifice their lives over something as trivial as the breaking of an egg then Montag ought to stand up against the serious problem of censorship. While Montag does not understand the quote at the time of reading (he asks Mildred what it means), it clearly has an impact on his subconscious because he continues reading the books and later seeks the help of the retired professor, Faber.

Please take a look at the second reference link for more information on the war between Lilliput and Blefescu.

This occurs at the end of the first section, "The Hearth and the Salamander" of Fahrenheit 451. The quote is from Gulliver's Travels by Jonathan Swift. Gulliver's Travels is a fantasy but it is also a political satire of England during Swift's time. It is fitting that the first book Montag reads from is one that criticizes government and society. The quote about the eggs is: 

It is computed that eleven thousand persons have at several times suffered death rather than submit to break eggs at the smaller end. 

The Lilliputians have an ongoing threat from a neighboring island. The cause of the dispute is a disagreement over the way an egg should be broken. Swift is mocking the trivial disagreements in politics and religion (particularly the arguments between Catholics and Protestants). Those persons who have submitted to death have chosen to challenge the idea that an egg must be broken a certain way. Thus, they have challenged authority, albeit in a seemingly silly way (this is part of the satire). 

Montag reads this quote from a book that mocks, via satire, the governing institutions of his time. Montag is also beginning to question his own work as a fireman and questions the burning of books. Like Swift, Montag is challenging the authority of his society.