Notes from the reading:
Figured bass is the way we label function within a piece of music. It is most often used as shorthand for keyboardists.
These pianists became great improvisors because they had a bass line and figured bass. Everything else had to be improvised. They would read a bass line and see small numbers or accidentals and assume the other implied notes for the harmony.
It is important not to mix Lead Sheet Notation, Figured Bass, and Roman Numeral Analysis. Firgured bass does not exist without a bass line. Roman numerals tell you the bass line and give us context. Lead sheet notation gives you absolutes and tell you the exact pitches to use.