Hi Frank,
With regards to your BHO entry into the archives, which is a very nice book for beginners and intermediate players, the only correction I would make is that the "1st. inversion" as you call it would not be c, e, g. That is called the "root position" of a chord or triad. The 1st. inversion would be: e, g, c and the 2nd inversion would be: g, c, e. Only when you have a 4 note chord is the 3rd inversion then used.
Just my observation and how I teach theory at NYU and privately...Very nice book though and I apologize if I've mis-interpreted what you wrote...Jack Baker