These words of Christian worship state that the Lord's Supper is to be repeated
and in his holy gospel command us to continue,
a perpetual memory of that his precious death,
until his coming again.
The tradition claims that Judas betrayed Jesus just after the Last Supper, when Judas kissed Jesus and they arrested him. So this is why the liturgy says
Who, in the same night
that he [Jesus] was betrayed, took bread;
and when he had given thanks to thee,
he broke it,
and gave it to his disciples, saying,
this is my body which is given for you:
do this in remembrance of me.
Note that the bread is in the meal, early, and the cup follows the meal, each of which includes a giving of thanks
Likewise after supper he took the cup;
and when he had given thanks to thee,
he gave it to them saying,
Drink ye all of this;
for this is my blood of the new covenant,
which is shed for you and for many
for the remission of sins:
do this, as oft as ye shall drink it,
in remembrance of me.
Jesus is introducing a New Covenant, which means a new agreement between God and the people for the future. The words link the drinking of wine to the shedding of blood, which Jesus was then likely to do but also to other Christian beliefs. It is important to remember that these words are as likely to come from the early Churches and what writers thought he said, rather than what he did say, and link it to the developing theology, starting with Paul.
Wherefore, O Lord and heavenly Father,
with this bread and this cup
we make the memorial of his saving passion,
his resurrection from the dead,
and his glorious ascension into heaven,
and we look for the coming of his kingdom.
When the actual drinking of the wine and the eating of the bread come close, the worship links Jesus dying to everyone else living everlasting life
Receive the body of our Lord Jesus Christ
which he gave for you,
and his blood which he shed for you.
Eat and drink
in remembrance that he died for you,
and feed on him in your hearts
by faith with thanksgiving.
Around Easter the service says:
Alleluia. Christ our Passover is sacrificed for us.
Therefore let us keep the feast. Alleluia.
So Christ becomes himself the passover meal, that same Jewish festival as when Jesus presided over the Last Supper. When the people take the wine and bread the priest says
The body of our Lord Jesus Christ,
which was given for you, preserve your body and soul unto everlasting life.
Take and eat this in remembrance that Christ died for you,
and feed on him in your hearts by faith with thanksgiving.
The blood of our Lord Jesus Christ,
which was shed for you,
preserve your body and soul unto everlasting life.
Drink this in remembrance that Christ's blood was shed for you,
and be thankful.
Afterwards the people in a church congregation say
Through him [Christ] we offer thee [God]
our souls and bodies
to be a living sacrifice
In the Roman Catholic Mass the breaking of the body of Christ is not a repeat of the crucifixion, but that Christ's body is being broken as part of the one crucifixion. For Protestants the death of Christ took place once and sufficiently, so these actions are symbolic, being a communion or Lord's Supper. In that these actions are a celebration, eucharist itself means thanksgiving and an optimistic meal. Nevertheless the meal can be understood as an exchange, people giving their faith and loyalty in exchange for the power of Christ, as in those words above.
So just like Christ gave himself on the cross for others so faithful Christians must give themselves to others in what they do.
The multiple layers of this ritual and even its name and understanding link to many different beliefs of Christians. For a fuller survey, see The Eucharist in Postmodernity. This discusses key words such as transubstantiation, consubstantiation, transignification, virtualism, memorialism, real presence, real absence and introduces simulacration.
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