(This only covers the beginning of the third day.)
Two New Sciences is an interesting book, possibly more interesting for its history than for its contents. Galileo wrote it very carefully to avoid offending a school of thought within the Catholic Church that regarded the Aristotelian model of the universe to be perfect and complete. From my understanding, he tried very hard to simply present things without making attacks on the former reasoning. A large part of this is showing how mathematical formulas show how things work, rather than just observing and presenting a theory to explain it.
The book takes the form of a conversation between three men, Simplicio, Sagredo, and Salviati. These men discuss various theories and the three are sometimes thought to represent Galileo's thought process from young man to more experienced and older man. This allows Galileo to present an idea and then attack and defend it. It works pretty well. To my (modern) eyes, it's very readable.
The section that comes up from the Great Books reading list is about whether objects accelerate or slow down(!) as they fall. Galileo argues that they fall faster and has a spiffy geometric chart to show that the rate of acceleration is, well, geometric. The whole thing makes sense to me and I was left with a sense of 'wait, did they really think things slowed down as they fell?'. Apparently so.
There are two things that make this type of reading especially striking now. First, this is all well established science now. There is broad (unanimous?) agreement on gravity and acceleration. This wasn't true then and in fact had still to be argued out.
The other thing is that with our modern equipment, we can easily show how things behave as they fall. I kept thinking about Mythbusters and their use of slow motion cameras and replay. How different things would have been if Galileo could have marched people into a theater and shown them proof! (And yes, that gets several horses and carts confused. The thought still occurred to me.)
I liked reading Galileo. We return to his writings in year seven and I look forward to it.