| Quote #4
[B]eing on some Occasion made asham'd of my Ignorance in Figures, which I had twice fail'd in learning when at School, I took Cocker's Book of Arithmetic, and went thro' the whole by myself with great Ease. I also read Seller's and Sturmy's Books of Navigation, and became acquainted with the little Geometry they contain, but never proceeded far in that Science. (1.21)
Education for Franklin isn't just about reading, although that's what he likes best. He wants to know everything. Even though he was only in school for a little while, he managed to flunk out of math twice. So he's compelled by both his desire just to be better educated and his embarrassment at not knowing better math, to seek out subjects he finds difficult and master them.
| Quote #5
The two works I allude to, Sir, will in particular give a noble rule and example of self-education. School and other education constantly proceed upon false principles, and show a clumsy apparatus pointed at a false mark; but your apparatus is simple, and the mark a true one (2.12)
Vaughan makes an argument for why Franklin should keep writing in a way that suggests he knows very well how to influence his old friend. Since Franklin's been so invested in educating himself throughout his life, Vaughan encourages him to keep writing by telling him his life story (and the Art of Virtue, which Franklin doesn't finish) will help other people engage in that same kind of "self-education." This may appeal to Franklin even more than flattery or compliments: seeing his work as an instrument that will help other people to do something he believes in so much.
| Quote #6
Reading was the only Amusement I allow'd myself. I spent no time in Taverns, Games, or Frolics of any kind. (2.36)
Franklin's such a crazy, wild man. Right. What we really mean is, he comes off here as constantly virtuous and industrious, not as someone who likes to party. Whether that's true is another story. According to what he says here, though, in order to motivate himself to keep getting better educated and continue learning, he considers reading a pleasure as well as a practical or important activity. He equates it to more traditional "Amusements" like gambling and drinking, and uses it as a replacement for fun social time.