If by "rendered" you mean "sacrificed," this is not what the Mass is and this is not what the Church teaches. Christ's sacrifice happened ONCE at Calvary, ca. 33 AD. Christ is not re-sacrificed.
If you want to understand Catholic Doctrine, I strongly recommend your first reference should be the Catholic Catechism.
1367 The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: "The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different." "And since in this divine sacrifice which is celebrated in the Mass, the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and is offered in an unbloody manner. . . this sacrifice is truly propitiatory."
This was very easy to locate in the Catechism, which is in searchable form online. I urge you to check it out. These are the results from using the keywords one sacrifice (LINK)
There are a number of very interesting parallel passages there.
That would be your first step.
the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and is offered in an unbloody manner.
As has been pointed out before...where there is no shedding of blood there is no sacrifice.
Are you saying what O'Brien, an ordained Roman Catholic priest, wrote is wrong?
Again, from the Faith of Millions....[breaks and emphasis mine]
When the priest pronounces the tremendous words of consecration, he reaches up into the heavens,
brings Christ down from His throne,
and places Him upon our altar
to be offered up again as the Victim for the sins of man.
It is a power greater than that of monarchs and emperors: it is greater than that of saints and angels, greater than that of Seraphim and Cherubim. Indeed it is greater even than the power of the Virgin Mary. While the Blessed Virgin was the human agency by which Christ became incarnate a single time,
the priest brings Christ down from heaven,
and renders Him present on our altar
as the eternal Victim for the sins of man—
not once but a thousand times!
The priest speaks and lo! Christ, the eternal and omnipotent God, bows His head in humble obedience to the priest’s command.
And as stated before and will continue to do so...this is in complete contradiction of the New Testament.
The term rendered is used by O'Brien as noted below:
the priest brings Christ down from heaven, and renders Him present on our altar as the eternal Victim for the sins of man—not once but a thousand times!
Again, an ordained Roman Catholic priest, says Christ is brought down from Heaven [in contradiction of Hebrews] and is rendered present on the altar.
Are you suggesting that O'Brien doesn't understand what is happening at the Mass?? Isn't this what Roman Catholic priests are trained to do??