Is the Eucharist a sacrifice?

Didache c. 100 ADDidache 14.1–3

On the Lord's day of the Lord, gather together, break bread and give thanks, having first confessed your sins, so that your sacrifice may be pure. Let no one who has a quarrel with his companion join you until they are reconciled, so that your sacrifice may not be defiled. For this is what the Lord said: "In every place and time offer me a pure sacrifice; for I am a great king, says the Lord, and my name is wonderful among the nations" (Malachi 1:11, 14).

Malachi 1:11 became the standard text for the Eucharist as the pure offering of the nations.

Justin Martyr c. 100–c. 165 ADDialogue with Trypho 41.3

Of the sacrifices offered to him in every place by us Gentiles, that is, the bread of the Eucharist and likewise the cup of the Eucharist, he speaks beforehand, saying that we glorify his name and you profane it.

Justin elsewhere says the true sacrifices are prayers and thanksgivings (117).

Irenaeus of Lyons c. 130–c. 202 ADAgainst Heresies 4.17.5–4.18.1

To offer to God the firstfruits of his own creatures, not as if he stood in need of them, but so that they themselves should be neither unfruitful nor ungrateful ... and he gave thanks, saying: This is my body. And the cup likewise, which is from the creature that belongs to us, he confessed to be his blood, and he taught the new oblation of the new covenant; which the Church, receiving it from the apostles, offers in the whole world to God, who gives us our food, the firstfruits of his gifts in the new covenant ... of which Malachi, among the twelve prophets, spoke beforehand.

Christ, Irenaeus says, counselled his disciples to offer God the firstfruits of his creatures, and at the supper took the bread that is from creation and the cup and called them his body and blood. The section that follows (4.18.1) quotes Malachi 1:10-11 on the pure offering among the nations. This part of Against Heresies survives in its ancient Latin translation; in the Harvey scan the passage is broken up by the edition's footnotes, so the quote is pieced from three stretches of the same pages, each verified separately.

Cyprian of Carthage c. 200–258 ADLetter 63, to Caecilius 63.14

If Christ Jesus, our Lord and God, is himself the high priest of God the Father, and first offered himself as a sacrifice to the Father, and commanded this to be done in memory of him, then that priest truly acts in Christ's place who imitates what Christ did, and he offers a true and full sacrifice in the Church to God the Father when he begins to offer as he sees Christ himself offered.

Written against those who used only water in the cup.

Cyril of Jerusalem c. 313–386 ADMystagogic Catecheses 5.8–9

Then, after the spiritual sacrifice, the bloodless worship, is completed, over that sacrifice of propitiation we call on God for the common peace of the churches ... and we all offer this sacrifice. Then we also remember those who have fallen asleep.

"Bloodless" and "propitiation": the words Trent later used.

John Chrysostom c. 349–407 ADHomilies on Hebrews 17.6, on Hebrews 10:9

Our high priest is the one who offered the sacrifice that cleanses us. That we offer now too, the one offered then, which cannot be used up. This is done as a remembrance of what was done then: "Do this," he says, "in remembrance of me." We do not offer another sacrifice, as the high priest did then, but always the same; or rather we make a remembrance of a sacrifice.

Both Catholics (one sacrifice) and Protestants (a remembrance) cite this passage.

Council of TrentSession 22 Chapter 2

that same Christ is contained and immolated in an unbloody manner, who once offered Himself in a bloody manner on the altar of the cross

Trent called the Mass a true, propitiatory sacrifice, the same as the cross, offered in an unbloody way.