Is the Eucharist a sacrifice, and if so, of what kind?

a passage states it a passage rules it out

Common ground

These are affirmed by more than one position, so a passage saying only this counts for none of them.

Christ's sacrifice on the cross was once for all and complete (all positions affirm this)
The Supper remembers or proclaims Christ's death
Thanksgiving and praise are offered at the Eucharist (praise and propitiatory positions both affirm it)
Calling the Eucharist an 'offering' or 'sacrifice' with no statement of what is offered or for what purpose (decides between no-sacrifice and the others only)
Malachi 1:11 'pure offering' applied to Christian worship without further specification

Not a sacrifice

Baptist

the mass is not a sacrifice, but is a remembrance of the sacrifice and assurance of the salvation which Christ has given us.Huldrych Zwingli, Sixty-Seven Articles, Article 18 (1523)

What sets it apart: The passage says the Supper is not a sacrifice at all, only a remembrance.

Formally defined: Zwingli, Sixty-Seven Articles (1523)

No early passage in the library states it yet.

Sacrifice of praise and commemoration only

Lutheran Reformed Anglican Baptist

The other species is the eucharistic sacrifice, which does not merit the remission of sins or reconciliation, but is rendered by those who have been reconciled, in order that we may give thanksApology of the Augsburg Confession, XXIV.19 (1531)

What sets it apart: The passage limits the Eucharistic offering to praise, thanksgiving or remembrance, denying that Christ is offered or that it obtains forgiveness for anyone.

Formally defined: Augsburg Confession XXIV and Apology XXIV (1530-31); Thirty-Nine Articles XXXI (1563/71); Westminster 29.2 (1646)

No early passage in the library states it yet.

Propitiatory sacrifice

Catholic Orthodox

that same Christ is contained and immolated in an unbloody manner, who once offered Himself in a bloody manner on the altar of the crossCouncil of Trent, Session 22, ch. 2 (1562)

What sets it apart: The passage says the Eucharist is offered for sins, or for the living and the dead to obtain mercy, or that Christ (his body and blood) is the victim offered in it.

Formally defined: Council of Trent, Session 22 (1562); Synod of Jerusalem (1672)

Earliest statement: Cyril of Alexandria, c. 444

Every deciding passage, earliest first

Origen of Alexandria, c. 245
With God permitting, then, and secondly the bishops, and thirdly the presbyters and the people too, I will speak again of what is stirring me at this point. The offering is always made to God Almighty through Jesus Christ, as offering his divinity to the Father. Let the offering not be made twice, but to God through God.
- Rules out: Not a sacrifice
Translation in progress
Cyril of Alexandria, c. 444
Cyril: …and the still catechumen, and having set up-with the perfect the praise, departs from the still more mystical, and is barred from the sacrifice upon Christ. In this way well the law was pre-voicing the economy, and ordered the sacrifice of the praise to be made upon leavened breads, and in unleavened flatbreads. Each of the named, as I at least think, under-signaling a form of life; for the leavened bread will be a type of life and living not yet cleansed through the holy baptism, nor indeed altogether released from worldly uncleanness; and unleavened flatbread, of the already wiped in…
- Rules out: Not a sacrifice
Translation in progress
Cyril of Alexandria, c. 444
Cyril: So then the matter is fruit-bearing, O Palladius, and a mystical word has also been woven for it, I think, carrying the riddle up unto Emmanuel, and unto us ourselves; and I will speak again as I am able. For when the holy and true tent has been shown in this world—that is, the Church—Christ conspicuous in it many-formedly and all but from us and for us is brought forward as a sacred victim to God and Father, a ransom and exchange of the life of all, one worth-all. For when the Only-begotten has become human as one from us, he has brought himself forward to God and Father, as some first…
- Rules out: Not a sacrifice
- Rules out: Sacrifice of praise and commemoration only
- States: Propitiatory sacrifice
Translation in progress
Cyril of Alexandria, c. 444
Cyril: …for we approach the holy things, for no other grace, than so as to share the holy Christ through the unspeakable and spiritual sacrifice. And the vessels serving the sacrifices are also thoroughly cleansed, so that they may not become for some other, nor may the things having liturgized for the sacred be carried under to humans’ needs. And the law has been kept, and is saved in churches. And that being blessed is fitting for those playing-the-man, the law will clarify again saying: ‘Every male among the priests will eat them.’ (Leviticus 6:30)
- Rules out: Not a sacrifice
Translation in progress