The Catholic Church holds that both the body and the blood are present in the bread and the wine (so, bread = body + blood, etc.).
Does anyone know what the Fathers said on this teaching (if anything at all since this doctrine came straight out of the Middle Ages)? To me, it would seem redundant for Christ to have instituted the Eucharist with an unnecessary element.
This is an interesting question. I've never found an entirely satisfactory account of when, why and how the Roman Catholic Church stopped using both species. Some suggest the practice came about in the Middle Ages, since noblemen did not want to share a "common cup" with commoners.
What's even more perplexing is that many, many Roman Catholic sources call for both bread and wine. (This only makes sense, since, according to the Council of Trent -- indeed, according to any proper scholastic-influenced account of Transubstantiation! -- one MUST have both species to serve as the accident whose essence is transubstantiated).
As for the ancient Fathers, they all speak of both elements, in much the same way that most more recent Catholic sources do. It's just assumed one would consecrate and administer both bread and wine. Consider this bit from the online Catholic Encyclopedia:
In the Eucharist the Body and Blood of the God-man are truly, really, and substantially present for the nourishment of our souls, by reason of the transubstantiation of the bread and wine into the Body and Blood of Christ, and that in this change of substances the unbloody Sacrifice of the New Testament is also contained.