Pat Madrid takes pains to argue that Augustine of Hippo was a Catholic bishop and that he believed what the Catholic church presently teaches on the Eucharist.
But Catholic teaching developed much after the time of Augustine (d. 430). Particularly important to the development of Catholic teaching were the controversies between Paschasius Radbertus (d. ca. 860) and Ratramnus (d. ca. 868), that over the teachings of Berengar of Tours (d. 1088), and the incorporation of the Aristotelian categories of substance and accidents by Thomas Aquinas (d. 1274).
Here’s another collection of Augustine quotes (it appears to be Madrid’s source). It would do well to read his sermon on John 6, too. Augustine doesn’t get into any of those points that would separate the Catholic view from, say, the Calvinist view. For Augustine, it is faith in Christ that is determinitive; to eat Christ is to have him dwell in us, and for us to dwell in him. Augustine’s teaching lacks the gritty realism of folks like Radbertus. He doesn’t speak of worshipping the Eucahrist, or of parading it around Hippo. He doesn’t speak of concomitance, or hint at withholding the cup from the laity. He doesn’t speak of having the sacrifice offered on behalf of the dead.
So be very careful. Don’t claim more for Augustine than you can get from the text itself. Don’t impute to him developments that took place centuries later.