IV. ACTIVITY AND DEATH IN ROME; BURIAL PLACE
It is an indisputably established historical fact that St. Peter laboured in Rome during the last portion of his life, and there ended his earthly course by martyrdom. As to the duration of his Apostolic activity in the Roman capital, the continuity or otherwise of his residence there, the details and success of his labours, and the chronology of his arrival and death, all these questions are uncertain, and can be solved only on hypotheses more or less well-founded. The essential fact is that Peter died at Rome: this constitutes the historical foundation of the claim of the Bishops of Rome to the Apostolic Primacy of Peter.
St. Peter's residence and death in Rome are established beyond contention as historical facts by a series of distinct testimonies extending from the end of the first to the end of the second centuries, and issuing from several lands.
That the manner, and therefore the place of his death, must have been known in widely extended Christian circles at the end of the first century is clear from the remark introduced into the Gospel of St. John concerning Christ's prophecy that Peter was bound to Him and would be led whither he would not -- "And this he said, signifying by what death he should glorify God" (John 21:18-19, see above). Such a remark presupposes in the readers of the Fourth Gospel a knowledge of the death of Peter. St. Peter's First Epistle was written almost undoubtedly from Rome, since the salutation at the end reads: "The church that is in Babylon, elected together with you, saluteth you: and so doth my son Mark" (v, 13). Babylon must here be identified with the Roman capital; since Babylon on the Euphrates, which lay in ruins, or New Babylon (Seleucia) on the Tigris, or the Egyptian Babylon near Memphis, or Jerusalem cannot be meant, the reference must be to Rome, the only city which is called Babylon elsewhere in ancient Christian literature (Revelation 17:5; 18:10; "Oracula Sibyl.", V, verses 143 and 159, ed. Geffcken, Leipzig, 1902, 111).
From Bishop Papias of Hierapolis and Clement of Alexandria, who both appeal to the testimony of the old presbyters (i.e., the disciples of the Apostles), we learn that Mark wrote his Gospel in Rome at the request of the Roman Christians, who desired a written memorial of the doctrine preached to them by St. Peter and his disciples (Eusebius, "Hist. Eccl.", II, xv; III, xl; VI, xiv); this is confirmed by Irenaeus (Adv. haer., III, i). In connection with this information concerning the Gospel of St. Mark, Eusebius, relying perhaps on an earlier source, says that Peter described Rome figuratively as Babylon in his First Epistle.
And the source you cite IS CONTEMPORARY to Peter ?