How we cite our quotes: (Chapter.Paragraph)
Quote #7
"We do not know if, out on the moons of Saturn, you will meet with good or with evil—or only with ruins a thousand times older than Troy." (30.23)
Heywood Floyd compares the possible alien ruins to the ruined city of ancient Greece. It's hard to imagine that anyone would actually say something like this; it sounds like something you'd read from a script. But it's thrown in there for the same reason the novel is called "A Space Odyssey"—to reference other old, important, impressive stories and make the events here seem important and impressive.
Quote #8
"It's just like the thing you found on the Moon! This is TMA-1's big brother!" (36.6)
Size is used as a way to provoke awe and amazement. The novel first has the little slab that teaches the man-apes; then the bigger slab on the moon, then the biggest slab, each more amazing than the last.
Quote #9
"The thing's hollow—it goes on forever—and—oh my God!—it's full of stars!" (39.20)
Bowman is wowed by the Star Gate. We would be too, understandably. This could be read as a description of the way Clarke sees sci-fi itself. It is vast, it is full of stars, and isn't that just shockingly nifty?