I agree about the vi vs. vim part, I just suggested :N since the book itself was (as far as I could tell) strictly staying vi-compatible. :Next going backwards compared to :next is a little confusing at first, but it actually fits the same pattern as some other commands that go in two directions (f and F, t and T, gg and G), if you think about the two commands as just :n and :N. Naturally, as you observed, it's probably better to use :prev if you're in a modern vi clone or vim.

If you switch to vim as the baseline, there's a bunch of other easier ways to do things too, like using :sav (:saveas) instead of :w <filename> followed by :e <filename>.