It says "The soprano will begin on the root, third, or fifth, according to the figure over the first bass note."
So I think the number just tells you what note of the chord to begin the soprano (highest note) with.
3 for the third above the given bass, 5 for the fifth above, and 8 for the octave (all of which could be compound intervals, i.e. a tenth, twelfth or two octaves).
NB: This is a convention used in this particular book, it is not a standard part of notation (it is NOT figured bass).
Incidentally, any # or
b above a bass note will refer to the third of the chord by the way (as per the conventions of figured bass).
Check out this textbook on
Four Part Harmony.