Trent and Eucharistic Sacrifice
Though primarily a sacramentological text the Tridentine definition of Eucharistic sacrifice has a number of arresting soteriological implications. Session 22, chapter 2 of the council’s declarations outlines the propitiatory character of the Eucharist:
In this divine sacrifice which is performed in the mass, the very same Christ is contained and offered in bloodless manner who made a bloody sacrifice of himself once for all on the cross. Hence the council teaches that this is a truly propitiatory sacrifice, and bring it about that if we approach God with sincere hearts and upright faith, and with awe and reverence, we receive mercy and find grace to help in time of need. [sic] For the Lord is appeased by this offering, he gives the gracious gift of repentance, he absolves even enormous offences and sins. For it is one and the same victim here offering himself by the ministry of his priests, who then offered himself on the cross: it is only the manner of offering that is different. For the benefits of that sacrifice (name the sacrifice of blood) are received in the fullest measure through the bloodless offering, so far is this latter in any way from impairing the value of the former. Therefore it is quite properly offered according to apostolic tradition not only for the sins, penalties, satisfactions and other needs of the faithful who are living, but also for those who have died in Christ but are not yet fully cleansed. 
The most pressing question is the following: in what sense is the sacrifice taking place at the the same as that on the cross? What is the precise nature of the ontological reality being asserted? This question has great soteriological implications, especially in light of the tradition Protestant/Anglican critique of the Tridentine definition: that the uniqueness of Christ’s sacrifice on the cross is impugned. The nub of the Protestant critique is that the Eucharist itself is made out by Catholic teaching to be salvific. This critique stems from the understanding that by the theology that “[i]n this divine sacrifice which is performed in the mass, the very same Christ is contained and offered in bloodless manner who made a bloody sacrifice of himself once for all on the cross” the Roman church was asserting that the sacrifice of Christ on the cross is repeated. Through the repetition of Christ’s salvific sacrifice the Eucharistic celebration becomes a source of mercy and grace. This soteriological understanding of the Eucharist, which was rightly understood to be, at least partly, an event of human initiative, was thus suggestive of the Protestant catch-all sin of ‘works righteousness.’
Protestant reformers often took the view that the Catholic teaching was that Christ’s sacrifice on the cross was repeated. The Church of England’s Articles of Religion address this question specifically in Article 31:
The offering of Christ once made is that perfect redemption, propitiation, and satisfaction, for all the sins of the whole world, both original and actual; and there is no1 other satisfaction for sin, but that alone. Wherefore the sacrifices of the Masses, in which it was commonly said, that the priest did offer Christ for the quick and the dead, to have remission of sin and guilt, were blasphemous fables, and dangerous deceits. 
This assessment is repeated almost verbatim in the later Methodist Articles of Religion, themselves based largely upon the earlier Anglican model. The Catholic understanding of Eucharistic sacrifice was similarly rejected by the earlier Lutheran Augsburg Confession, which asserted instead the power of the Eucharist to strengthen and inform faith:
…the holy sacrament was not instituted to provide a sacrifice for sin – for the sacrifice has already occurred – but to awaken our faith and comfort our consciences. The sacrament makes them aware that they are promised grace and forgiveness of sin by Christ. That is why this sacrament requires faith and without faith is used in vain. 
The Augsburg Confession also makes faith the ultimate prerequisite for the fruitfulness of the Eucharist. a prerequisite without which those who receive communion cannot receive what the confession deems the true benefit of the Eucharist.
None of these Eucharistic theologies necessarily excludes ‘Eucharistic sacrifice’ in the broadest sense. What is strictly excluded is their own understanding of the Roman Catholic theology of Eucharistic sacrifice: that the sacrifice of the Eucharistic celebration constitutes a repetition of the sacrifice of the cross. What is rejected along with this understanding of the Eucharist is the implied soteriological character of the Eucharistic celebration. The classical Protestant emphasis on the uniqueness of Christ extended not simply to a rejection of the cult of the saints but to an emphasis on the total uniqueness of the acts of Christ, especially his crucifixion and resurrection. To assign a soteriological character to the human-initiated Eucharistic celebration, which the Protestant reading of the Catholic theology did, makes of the Eucharist a human work which impugns the unique power of Christ’s acts and generates grace through human activity.
But is this assessment of Catholic theology backed up or disproved by the Tridentine formulation? The phrase “[f]or the Lord is appeased by this offering,” “[h]uius quippe oblatione placatus Dominus” in the original Latin, is perhaps the portion of the text which seems most strongly to justify the classical protestant reading. ‘Placatus,’ here translated as ‘is appeased,’ but which could also have been rendered as ‘is pacified’ or ‘is placated,’  is fairly unambiguous and can, indeed, likely should, be read as suggesting that the sacrifice in the Eucharistic celebration itself affects God’s disposition (though the object of that disposition is only implied) and the offering (or ‘oblation’) referred to is clearly that of the Eucharistic celebration rather than that of the cross.
The final two sentences (of the English translation) could also lend weight to the Protestant objection. The first portrays the Eucharist as a means or vehicle equal to the cross itself. The key question there is whether it is means or vehicle. If the former and the Eucharist is being defined as itself a source of grace then the classical critique appears entirely justified. If the latter, that the Eucharist is a vehicle through which the grace of the cross flows, then the definition is certainly less offensive to Protestant sensibilities, though not in line with Protestant thinking on the Eucharist. The final sentence is perhaps the most problematic. To assert that the Eucharistic celebration, which is inescapably, if only partially, a work of human effort, can be employed to achieve the satisfaction of sins can certainly be read as ‘works righteousness’ by Protestant eyes. That the Eucharist is described as being “offered” is particularly problematic, if in relation more to the problem of works righteousness than to any soteriological character of the Eucharistic celebration, since this seems to make the human act inviolable: when the Eucharist is offered it achieves the desired effect on the disposition of God. This power of the Eucharist is certainly derived from the identification of the Eucharistic offering with Christ on the cross rather than the practice of making the offering but this identification is itself an issue for the classical Protestant reader.
If, as many Protestant traditions have long held, Trent posited that the sacrifice of Christ on the cross is repeated, then was the uniqueness of Christ’s sacrifice on the cross impugned? The text of the definition does not reasonably allow for the reading that the sacrifice of Christ on the cross is repeated in the Eucharist. This position was long disavowed by major Catholic theologians, including Thomas Aquinas,  before there were Protestants to take issue with it and there is no reason to assert that it was intended by the Council Fathers. Assuming, therefore, that the Tridentine definition does not entail a repetition of the sacrifice on the cross then the question remains of by what means the benefits of the once-for-all sacrifice of Christ are to be attained by the Eucharistic celebration. The definition itself answers this question: “[i]n this divine sacrifice which is performed in the mass, the very same Christ is contained and offered in bloodless manner who made a bloody sacrifice of himself once for all on the cross.”
The identification of presence of Christ in the Eucharist and the Eucharistic celebration with the cross itself does mean that the Eucharistic celebration repeats the event of the cross or otherwise impugns the uniqueness of Christ’s sacrifice, rather it asserts a belief in something at once more extraordinary and more inchoate. The sacrifice on the cross is not understood to be happening again in the Eucharistic celebration, in the Eucharistic celebration the unique act on the cross is understood to be present. What precisely this means is difficult to describe is a manner unsurprisingly reminiscent of the real presence of Christ in the Eucharistic elements themselves, a parallel reality to which this one is intimately connected. Though it may well not be how the Council Fathers themselves thought of the matter such an analogy may a helpful way to conceptualise this difficult theology: Christ’s sacrifice on the cross is present in the Eucharistic celebration similarly to how Christ himself is present in the Eucharistic bread and wine. The soteriological character which the Council Fathers assigned to the Eucharistic celebration was understood to derive from the shared reality of the celebrations and the unique, salvific act of Christ on the cross.
Notes and Bibliography
 Norman P Tasser, s.j., Decrees of the Ecumenical Councils: Volume Two: Trent to Vatican II (Washington D.C.: Sheed and Ward Limited and Georgetown University Press, 1990), 733-734.
 Anglican Church of Canada, The Book of Common Prayer (Toronto: Anglican Book Center, 1962), 711.
 The Augsburg Confession, XXIV, 30 [Robert Kolb, Timothy Wengert, eds., The Book of Concord: The Confessions of the Evangelical Lutheran Churches (Minneapolis: Fortress Press, 2000), 70.]
 The Latin root, ‘placare,’ can also be taken to mean ‘to make atonement’ but there would be two issues with such a translation: (1) constructing a passive would be awkward and wordy and (2) such a translation would be more loaded theologically since ‘atonement’ is a native English constructed word meant to render the Hebrew ‘kippur’ and thus has no true cognate in non-West Semitic languages.
 ST III.83.1 Thomas held that the sacrament of the Eucharist was an image of the sacrifice on the cross.