(Taken from Notes Made at the Conferences of Dom Prosper Guéranger).
With her ever wise discretion, Holy Church has limited the Saints’ names mentioned here. Let us go through the list: Petri et Pauli. The Priest has this one thought uppermost in his mind, that he is in close union with all these Saints, and that he is engaged in honouring their memory. He names St. Peter and St. Paul together, because these two Saints are really one, belonging as they both do to the Holy Roman Church which was founded by their joint labours. Then come the other Apostles: Andreae, Jacobi [James the Great], Johannis [John, the beloved disciple], Thomae, Jacobi [James the Less], Philippi, Bartholomaei, Matthaei, Simonis, et Thaddaei [Thaddeus, called also Jude].
These holy ones just named by the Church, all belong to the Gospel; but in order to show that she belongs to all ages, she deems it well to couple with these venerable names of the very Foundations of the Church, others no less dear to her. So these three Popes are mentioned in the same list: Linus, Cletus, Clement were all three ordained by St. Peter; so that at the Apostle’s death, there were these three Bishops in Rome. St. Peter had appointed Clement to be his successor, but he contrived at first to escape the burthen; nevertheless he was at last forced to accept it, but whether he succeeded St. Linus, before or after St. Cletus, on the Chair of Peter, is uncertain. Xysti, here we have another Pope; it is Sixtus II, he who had St. Laurence for his deacon. He is a very celebrated Pontiff: he was beheaded in the Cemetery Pretextatus; and the Cemetery of St. Calixtus where is the Crypt of St. Camilia, is also called by his name, i.e., of St. Sixtus. Then follows Cornelius, whose epitaph, lately discovered in the Catacombs by the Commedatore De Rossi, has been a subject of such lively interest; this epitaph was found in two separate pieces, on one was only Cor, on the other, nelius. After these Popes, we are given a Bishop’s name: it is St. Cyprian, Bishop of Carthage. He is coupled, on the diptychs, with his friend, St. Cornelius. Laurentii, the great Deacon St. Laurence ever so markedly honoured by Holy Church. These Martyrs all suffered in the persecution under Valerian; but the next, St. Chrysogonus, comes under Diocletian. As regards SS. John and Paul, they are much later, being put to death in the reign of Julian the Apostate. Finally, Cosmae et Damiani, both physicians; they were not Romans, but their bodies were brought to Rome later; they suffered under Diocletian. These two names close the list adopted by Holy Church, and no others may now be added.