Book 1 starts with tunes on open strings D, G and B. Fretted notes on those strings are added gradually. By the end of the book, the note range is DE, GA, BCD. By the end of Book 2, the pupil knows the notes all six strings, up to fret 3, including the sharps. Here is a fingerboard graphic which is frequently used in Book 2 as a neat way of reminding the pupil of the notes learned.
The first version, from the start of the book, shows the notes which have already been learned in Book 1:
and by the end of Book 2 the blanks have been filled in and the range extended: