The augmented sixth chord presented on the previous page and shown below is often called the Italian augmented sixth chord (IV degree triad in first inversion):

Adding the seventh to the chord (or a fifth to the bass) results in a German augmented sixth chord (IV degree seventh chord in first inversion). Note the parallel fifth between the German sixth chord and the dominant chord in the bass and tenor voices:

To avoid the parallel fifth, use the tonic chord in second inversion before the dominant chord:

Adding an augmented fourth to the bass note gives us the French augmented sixth chord, also known as the II degree seventh chord in second inversion: