Eusebius has a pattern of defining the Alexandrian bishops according to texts. In Book 2 Peter's Mark is defined as THAT Mark who was the first bishop:
And they say that Peter — when he had learned, through a revelation of the Spirit, of that which had been done — was pleased with the zeal of the men, and that the work obtained the sanction of his authority for the purpose of being used in the churches. Clement in the eighth book of his Hypotyposes gives this account, and with him agrees the bishop of Hierapolis named Papias. And Peter makes mention of Mark in his first epistle which they say that he wrote in Rome itself, as is indicated by him, when he calls the city, by a figure, Babylon, as he does in the following words: The church that is at Babylon, elected together with you, salutes you; and so does Marcus my son. 1 Peter 5:13
1. And they say that this Mark was the first that was sent to Egypt, and that he proclaimed the Gospel which he had written, and first established churches in Alexandria.
2. And the multitude of believers, both men and women, that were collected there at the very outset, and lived lives of the most philosophical and excessive asceticism, was so great, that Philo thought it worth while to describe their pursuits, their meetings, their entertainments, and their whole manner of life.
In the same book Josephus's reference to Ananus seems to prompt the discussion of Mark's successor Annianus:
21. And the same writer records his death also in the twentieth book of his Antiquities in the following words: But the emperor, when he learned of the death of Festus, sent Albinus to be procurator of Judea. But the younger Ananus, who, as we have already said, had obtained the high priesthood, was of an exceedingly bold and reckless disposition. He belonged, moreover, to the sect of the Sadducees, who are the most cruel of all the Jews in the execution of judgment, as we have already shown.
22. Ananus, therefore, being of this character, and supposing that he had a favorable opportunity on account of the fact that Festus was dead, and Albinus was still on the way, called together the Sanhedrin, and brought before them the brother of Jesus, the so-called Christ, James by name, together with some others, and accused them of violating the law, and condemned them to be stoned.
23. But those in the city who seemed most moderate and skilled in the law were very angry at this, and sent secretly to the king, requesting him to order Ananus to cease such proceedings. For he had not done right even this first time. And certain of them also went to meet Albinus, who was journeying from Alexandria, and reminded him that it was not lawful for Ananus to summon the Sanhedrin without his knowledge.
24. And Albinus, being persuaded by their representations, wrote in anger to Ananus, threatening him with punishment. And the king, Agrippa, in consequence, deprived him of the high priesthood, which he had held three months, and appointed Jesus, the son of Damnæus.
25. These things are recorded in regard to James, who is said to be the author of the first of the so-called catholic epistles. But it is to be observed that it is disputed; at least, not many of the ancients have mentioned it, as is the case likewise with the epistle that bears the name of Jude, which is also one of the seven so-called catholic epistles. Nevertheless we know that these also, with the rest, have been read publicly in very many churches.
1. When Nero was in the eighth year of his reign, Annianus succeeded Mark the Evangelist in the administration of the parish of Alexandria.
In Book Three Eusebius's citation of Hegesippus's account of the Jerusalem Church prompts a list of contemporary bishops in other sees:
1. After the martyrdom of James and the conquest of Jerusalem which immediately followed, it is said that those of the apostles and disciples of the Lord that were still living came together from all directions with those that were related to the Lord according to the flesh (for the majority of them also were still alive) to take counsel as to who was worthy to succeed James.
2. They all with one consent pronounced Symeon, the son of Clopas, of whom the Gospel also makes mention; to be worthy of the episcopal throne of that parish. He was a cousin, as they say, of the Saviour. For Hegesippus records that Clopas was a brother of Joseph.
He also relates that Vespasian after the conquest of Jerusalem gave orders that all that belonged to the lineage of David should be sought out, in order that none of the royal race might be left among the Jews; and in consequence of this a most terrible persecution again hung over the Jews.
After Vespasian had reigned ten years Titus, his son, succeeded him. In the second year of his reign, Linus, who had been bishop of the church of Rome for twelve years, delivered his office to Anencletus. But Titus was succeeded by his brother Domitian after he had reigned two years and the same number of months.
In the fourth year of Domitian, Annianus, the first bishop of the parish of Alexandria, died after holding office twenty-two years, and was succeeded by Abilius, the second bishop.
In the twelfth year of the same reign Clement succeeded Anencletus after the latter had been bishop of the church of Rome for twelve years. The apostle in his Epistle to the Philippians informs us that this Clement was his fellow-worker. His words are as follows: With Clement and the rest of my fellow-laborers whose names are in the book of life.
A little later in the same book another citation of Hegesippus prompts the identification of Cerdon as the next bishop as well as the bishop of Antioch:
Chapter 20. The Relatives of our Saviour.
1. Of the family of the Lord there were still living the grandchildren of Jude, who is said to have been the Lord's brother according to the flesh.
2. Information was given that they belonged to the family of David, and they were brought to the Emperor Domitian by the Evocatus. For Domitian feared the coming of Christ as Herod also had feared it. And he asked them if they were descendants of David, and they confessed that they were. Then he asked them how much property they had, or how much money they owned. And both of them answered that they had only nine thousand denarii, half of which belonged to each of them.
4. And this property did not consist of silver, but of a piece of land which contained only thirty-nine acres, and from which they raised their taxes and supported themselves by their own labor.
5. Then they showed their hands, exhibiting the hardness of their bodies and the callousness produced upon their hands by continuous toil as evidence of their own labor.
6. And when they were asked concerning Christ and his kingdom, of what sort it was and where and when it was to appear, they answered that it was not a temporal nor an earthly kingdom, but a heavenly and angelic one, which would appear at the end of the world, when he should come in glory to judge the quick and the dead, and to give unto every one according to his works.
7. Upon hearing this, Domitian did not pass judgment against them, but, despising them as of no account, he let them go, and by a decree put a stop to the persecution of the Church.
8. But when they were released they ruled the churches because they were witnesses and were also relatives of the Lord. And peace being established, they lived until the time of Trajan. These things are related by Hegesippus.
9. Tertullian also has mentioned Domitian in the following words: Domitian also, who possessed a share of Nero's cruelty, attempted once to do the same thing that the latter did. But because he had, I suppose, some intelligence, he very soon ceased, and even recalled those whom he had banished.
10. But after Domitian had reigned fifteen years, and Nerva had succeeded to the empire, the Roman Senate, according to the writers that record the history of those days, voted that Domitian's honors should be cancelled, and that those who had been unjustly banished should return to their homes and have their property restored to them.
11. It was at this time that the apostle John returned from his banishment in the island and took up his abode at Ephesus, according to an ancient Christian tradition.
1. After Nerva had reigned a little more than a year he was succeeded by Trajan. It was during the first year of his reign that Abilius, who had ruled the church of Alexandria for thirteen years, was succeeded by Cerdon.
2. He was the third that presided over that church after Annianus, who was the first. At that time Clement still ruled the church of Rome, being also the third that held the episcopate there after Paul and Peter.
3. Linus was the first, and after him came Anencletus.
At this time Ignatius was known as the second bishop of Antioch, Evodius having been the first. Symeon likewise was at that time the second ruler of the church of Jerusalem, the brother of our Saviour having been the first.
Book Four begins with a strange statement:
1. About the twelfth year of the reign of Trajan the above-mentioned bishop of the parish of Alexandria died, and Primus, the fourth in succession from the apostles, was chosen to the office.
2. At that time also Alexander, the fifth in the line of succession from Peter and Paul, received the episcopate at Rome, after Evarestus had held the office eight years.
Chapter 2. The Calamities of the Jews during Trajan's Reign.
1. The teaching and the Church of our Saviour flourished greatly and made progress from day to day; but the calamities of the Jews increased, and they underwent a constant succession of evils. In the eighteenth year of Trajan's reign there was another disturbance of the Jews, through which a great multitude of them perished.
2. For in Alexandria and in the rest of Egypt, and also in Cyrene, as if incited by some terrible and factious spirit, they rushed into seditious measures against their fellow-inhabitants, the Greeks. The insurrection increased greatly, and in the following year, while Lupus was governor of all Egypt, it developed into a war of no mean magnitude.
3. In the first attack it happened that they were victorious over the Greeks, who fled to Alexandria and imprisoned and slew the Jews that were in the city. But the Jews of Cyrene, although deprived of their aid, continued to plunder the land of Egypt and to devastate its districts, under the leadership of Lucuas. Against them the emperor sent Marcius Turbo with a foot and naval force and also with a force of cavalry.
4. He carried on the war against them for a long time and fought many battles, and slew many thousands of Jews, not only of those of Cyrene, but also of those who dwelt in Egypt and had come to the assistance of their king Lucuas.
5. But the emperor, fearing that the Jews in Mesopotamia would also make an attack upon the inhabitants of that country, commanded Lucius Quintus to clear the province of them. And he having marched against them slew a great multitude of those that dwelt there; and in consequence of his success he was made governor of Judea by the emperor. These events are recorded also in these very words by the Greek historians that have written accounts of those times.
Why not mention the name of the bishop? Eusebius seems to have forgotten. What likely prompts him to begin the fourth book with Alexandria is that Book Three ends with Papias's discussion of the gospel of Mark:
14. Papias gives also in his own work other accounts of the words of the Lord on the authority of Aristion who was mentioned above, and traditions as handed down by the presbyter John; to which we refer those who are fond of learning. But now we must add to the words of his which we have already quoted the tradition which he gives in regard to Mark, the author of the Gospel.
15. This also the presbyter said: Mark, having become the interpreter of Peter, wrote down accurately, though not in order, whatsoever he remembered of the things said or done by Christ. For he neither heard the Lord nor followed him, but afterward, as I said, he followed Peter, who adapted his teaching to the needs of his hearers, but with no intention of giving a connected account of the Lord's discourses, so that Mark committed no error while he thus wrote some things as he remembered them. For he was careful of one thing, not to omit any of the things which he had heard, and not to state any of them falsely. These things are related by Papias concerning Mark.
16. But concerning Matthew he writes as follows: So then Matthew wrote the oracles in the Hebrew language, and every one interpreted them as he was able. And the same writer uses testimonies from the first Epistle of John and from that of Peter likewise. And he relates another story of a woman, who was accused of many sins before the Lord, which is contained in the Gospel according to the Hebrews. These things we have thought it necessary to observe in addition to what has been already stated.
Notice also that immediately following the mention of 'Primus the bishop of Alexandria' is more Hegesippus. Hegesippus is the spine of the history of all the early churches.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote