"I'd like to see you do it in eighty days."
This is the very moment that Fogg is challenged to the wager that will drive the entire journey. It comes after they read a claim in the newspaper that the world can be traversed in eighty days. Fogg, not one to turn down a challenge to his honor, accepts the bet, and the trip round the world truly begins.
"The artistic thing is, to unmask honest countenances; it's no light task, I admit, but a real art."
This quote reveals Fix's motivation throughout the entire story. He is convinced that there is a ruthless bank robber hidden beneath Fogg's honest exterior. It also reveals a lot about Fix's character; he truly believes that what he is doing is right, and on top of that, he is exceedingly confident in his own abilities.
"You have kept London time, which is two hours behind that of Suez. You ought to regulate your watch at noon in each country."
This is the first big clue that Verne drops about time and setting watches. Multiple references to Passepartout's watch and London time will point to the novel's resolution, in which Passepartout realizes that they gained a day by traveling eastward and crossing the International Date Line. Time is even more important than they originally thought.
"Why, you are a man of heart!"
"Sometimes," replied Phileas Fogg quietly; "when I have the time."
This quote suggests that Fogg would not have decided to save Aouda if he didn't have time to spare. This mentality shows that Fogg has not yet undergone his emotional transformation, since later on he will realize that love for Aouda is the greatest thing he gained from this trip. It also reaffirms his stoic countenance for the others; he does not want them to think him too emotional, and wants to show that he is driven by logic and reason rather than by his heart.
"What nonsense! My master is the most honorable of men!"
Passepartout repeatedly denies his master's guilt as Fix insists that Fogg is a ruthless bank robber, thus affirming the deep loyalty that he has developed towards his master. Passepartout has come to align himself firmly with Fogg's goals as the journey as progressed, and is truly an honorable friend to him throughout the entire ordeal.
"It's certain," thought he, "though rascal as he is, he is a polite one!"
Throughout the journey, Fix is forced to spend quite a bit of time with the man who he believes is a criminal. As such, he starts to realize that Fogg is perhaps not as bad of a man as he originally thought. He does not let this distract him from his goal of arresting him and doing his duty, however; it simply provides him with a greater moral struggle when it comes to accomplishing this.
"It would not be right for an Englishman to permit himself to be treated in that way, without retaliating."
Fogg says this just after nearly getting into a fight with Colonel Stamp Proctor at the political rally in San Francisco. Like many other incidents, it reveals his firm commitment to maintaining his honor in all situations. Honor is what really motivates him, not greed or ego, and he will do whatever it takes to preserve this along his journey.
"But they can't prevent me from thinking that it would be more natural for us to cross the bridge on foot, and let the train come after!"
Passepartout is often dismissed because he is merely a servant, and this case is no different. However, he repeatedly shows that he is quick thinker and clever problem solver, even though very few people will actually listen to him. This incident also contrasts Verne's stereotype of Americans being rash and bold while Europeans are more refined and sensible, since the Americans want to send the train careening over the broken bridge at high speeds with all passengers aboard.
"Captain Fogg, you've got something of the Yankee about you."
This is the highest compliment that Captain Speedy, an American, can give to Fogg, and it shows that his antics have even earned him the respect of someone who he'd tied up at the beginning of the voyage across the Atlantic. Fogg certainly shows some of the typical qualities that Verne characterizes as American, but he balances these with his refined upbringing as an Englishman.
"But if I had not crossed India, I should not have saved Aouda."
This is one of the book's very last quotes, and it marks the completeness of Phileas Fogg's transformation. He sees at last that the greatest thing he gained from his journey around the world was Aouda's love, the kind of human connection that was missing from his life. He is no longer the hard-hearted man he was when he set out from London eighty days earlier.
