  In 1797, Pfaff gave a simple proof of a ${}_3F_2$ hypergeometric series
summation formula which was much later reproved by Andrews in 1996. In the same
paper, Andrews also proved other well-known hypergeometric identities using
Pfaff's method. In this paper, we prove a number of terminating
$q$-hypergeometric series-product identities using Pfaff's method thereby
providing a detailed account of its wide applicability.
