Two great historians of the Church,
Eusebius of Caesarea
a bishop and historian of the Council of Nicea, and
bishop and theologian, preserve for us the list of successors
of the bishop of Rome to their own time. They attest to the
sense and realization the Church had to the need for historic
succession to the Bishop of Rome.
The History of the
Book 3, 324 AD
"After the martyrdom of Paul and Peter, the
first man to be appointed Bishop of Rome was
Linus. ... Linus, who is mentioned in the
Second Epistle to Timothy as being with
Paul in Rome, as stated above was the first
after Peter to be appointed Bishop of Rome.
Clement again, who became the third Bishop
of Rome ... to Miltiades. "