From Pope Pius XII's encyclical Mediator Dei.
67. Christ the Lord, "Eternal Priest according to the order of Melchisedech," "loving His own who were of the world," "at the last supper, on the night He was betrayed, wishing to leave His beloved Spouse, the Church, a visible sacrifice such as the nature of men requires, that would re-present the bloody sacrifice offered once on the cross, and perpetuate its memory to the end of time, and whose salutary virtue might be applied in remitting those sins which we daily commit, . . . offered His body and blood under the species of bread and wine to God the Father, and under the same species allowed the apostles, whom he at that time constituted the priests of the New Testament, to partake thereof; commanding them and their successors in the priesthood to make the same offering."
68. The august sacrifice of the altar, then, is no mere empty commemoration of the passion and death of Jesus Christ, but a true and proper act of sacrifice, whereby the High Priest by an unbloody immolation offers Himself a most acceptable victim to the Eternal Father, as He did upon the cross. "It is one and the same victim; the same person now offers it by the ministry of His priests, who then offered Himself on the cross, the manner of offering alone being different."
69. The priest is the same, Jesus Christ, whose sacred Person His minister represents. Now the minister, by reason of the sacerdotal consecration which he has received, is made like to the High Priest and possesses the power of performing actions in virtue of Christ's very person. Wherefore in his priestly activity he in a certain manner "lends his tongue, and gives his hand" to Christ.
70. Likewise the victim is the same, namely, our divine Redeemer in His human nature with His true body and blood. The manner, however, in which Christ is offered is different. On the cross He completely offered Himself and all His sufferings to God, and the immolation of the victim was brought about by the bloody death, which He underwent of His free will. But on the altar, by reason of the glorified state of His human nature, "death shall have no more dominion over Him," and so the shedding of His blood is impossible; still, according to the plan of divine wisdom, the sacrifice of our Redeemer is shown forth in an admirable manner by external signs which are the symbols of His death. For by the "transubstantiation" of bread into the body of Christ and of wine into His blood, His body and blood are both really present: now the eucharistic species under which He is present symbolize the actual separation of His body and blood. Thus the commemorative representation of His death, which actually took place on Calvary, is repeated in every sacrifice of the altar, seeing that Jesus Christ is symbolically shown by separate symbols to be in a state of victimhood.
71. Moreover, the appointed ends are the same. The first of these is to give glory to the Heavenly Father. From His birth to His death Jesus Christ burned with zeal for the divine glory; and the offering of His blood upon the cross rose to heaven in an odor of sweetness. To perpetuate this praise, the members of the Mystical Body are united with their divine Head in the eucharistic sacrifice, and with Him, together with the Angels and Archangels, they sing immortal praise to God and give all honor and glory to the Father Almighty.
72. The second end is duly to give thanks to God. Only the divine Redeemer, as the eternal Father's most beloved Son whose immense love He knew, could offer Him a worthy return of gratitude. This was His intention and desire at the Last Supper when He "gave thanks." He did not cease to do so when hanging upon the cross, nor does He fail to do so in the august sacrifice of the altar, which is an act of thanksgiving or a "eucharistic" act; since this "is truly meet and just, right and availing unto salvation."
73. The third end proposed is that of expiation, propitiation and reconciliation. Certainly, no one was better fitted to make satisfaction to Almighty God for all the sins of men than was Christ. Therefore, He desired to be immolated upon the cross "as a propitiation for our sins, not for ours only but also for those of the whole world" and likewise He daily offers Himself upon our altars for our redemption, that we may be rescued from eternal damnation and admitted into the company of the elect. This He does, not for us only who are in this mortal life, but also "for all who rest in Christ, who have gone before us with the sign of faith and repose in the sleep of peace;" for whether we live, or whether we die "still we are not separated from the one and only Christ."
74. The fourth end, finally, is that of impetration. Man, being the prodigal son, has made bad use of and dissipated the goods which he received from his heavenly Father. Accordingly, he has been reduced to the utmost poverty and to extreme degradation. However, Christ on the cross "offering prayers and supplications with a loud cry and tears, has been heard for His reverence." Likewise upon the altar He is our mediator with God in the same efficacious manner, so that we may be filled with every blessing and grace.
75. It is easy, therefore, to understand why the holy Council of Trent lays down that by means of the eucharistic sacrifice the saving virtue of the cross is imparted to us for the remission of the sins we daily commit.
57. John, 13:1.
58. Council of Trent, Sess. 22, c. 1.
59. Ibid., c. 2.
60. Cf. Saint Thomas, Summa Theologica, Illa, q. 22, art. 4.
61. Saint John Chrysostom, In Joann. Hom., 86:4.
62. Rom. 6:9.
63. Cf. Roman Missal, Preface.
64. Cf. Ibid., Canon.
65. Mark, 14:23.
66. Roman Missal, Preface.
67. I John, 2:2.
68. Roman Missal, Canon of the Mass.
69. Saint Augustine, De Trinit., Book Xlll, c. 19.
70. Heb. 5:7.
71. Cf. Sess. 22, c. 1.