Patriarch Anatolius of Constantinople
As for those things which the universal Council of Chalcedon recently ordained in favor of the church of Constantinople, let Your Holiness be sure that there was no fault in me, who from my youth have always loved peace and quiet, keeping myself in humility.  It was the most reverend clergy of the church of Constantinople who were eager about it, and they were equally supported by the most reverend priests of those parts, who agreed about it.  Even so, the whole force of confirmation of the acts was reserved for the authority of Your Blessedness.  Therefore, let Your Holiness know for certain that I did nothing to further the matter, knowing always that I held myself bound to avoid the lusts of pride and covetousness.  (To Pope Leo, Ep 132 [on the subject of canon 28 of Chalcedon], 451 A.D.)
Chalcedon Council
For if "where two or three are gathered together in His name" He has said that "there He is in the midst of them", must He not have been much more particularly present with 520 priests, who preferred the spread of knowledge concerning Him …Of whom you were Chief, as Head to the members, showing your good will.
You are set as an interpreter to all of the voice of blessed Peter, and to all you impart the blessings of that Faith.
You have often extended your Apostolic radiance even to the church of Constantinople.
Knowing that every success of the children rebounds to the parents, we therefore beg you to honor our decision by your assent, and as we have yielded agreement to the Head in noble things, so may the Head also fulfill what is fitting for the children.  (To Pope Leo, Ep. 98, 451 A.D.)
Wherefore the most holy and blessed Leo, archbishop of the great and elder Rome, through us, and through this present most holy synod together with the thrice-blessed and all-glorious Peter the Apostle, who is the Rock and foundation of the Catholic Church, and the foundation of the orthodox faith, hath stripped him (Dioscorus, Patriarch of Alexandria) of his episcopate, and hath alienated from him all hieratic worthiness…  (Acts of Chalcedon, Session 3, 451 A.D.)
Saints Cyril & Methodius
Because of his primacy, the Pontiff of Rome is not required to attend an Ecumenical Council; but without his participation, manifested by sending some subordinates, every Ecumenical Council is as non-existant, for it is he who presides over the Council.  (c. 865 A.D. in N. Brian-Chaninov, The Russian Church (1931), 46; cited by Butler, Church and Infallibility, 210 [Upon This Rock (San Francisco: Ignatius, 1999), p. 177])
Eutyches
I take refuge, therefore, with you, the defender of religion and abhorrer of such factions.  …I beseech you not to be prejudiced against me by their insidious designs about me, but to pronounce the sentence which shall seem to you right upon the Faith.  (To Pope Leo, 451 A.D.)
Bishop Flavian of Constantinople
When I began to appeal to the throne of the Apostolic See of Peter, the Prince of the Apostles, and to the whole sacred synod, which is obedient to Your Holiness, at once a crowd of soldiers surrounded me and barred my way when I wished to take refuge at the holy altar.  …Therefore, I beseech Your Holiness not to permit these things to be treated with indifference…but to rise up first on behalf of the cause of our orthodox Faith, now destroyed by unlawful acts.  …Further to issue an authoritative instruction…so that a like faith may everywhere be preached by the assembly of an united synod of fathers, both Eastern and Western.  Thus the laws of the fathers may prevail and all that has been done amiss be rendered null and void.  Bring healing to this ghastly wound.  (To Pope Leo, 449 A.D.)
Pope Julius
It behoved you to write to us that thus what is just might be decreed for all.  For they who suffered were bishops, and the churches that suffered no common ones, over which the Apostles ruled in person.  And why were we (Rome) not written to concerning the Church, especially Alexandria?  Or are they (the Arians) ignorant that this has been the custom first to write to us, and thus what is just be decreed from this place (Rome)?  If therefore, any such suspicion fell upon the bishop there (Alexandria), it was benefiting to write to this church (Rome).  (Ep. n. 6,21 - 336 A.D.)
Justinian
Yielding honor to the Apostolic See and to Your Holiness, and honoring your Holiness, as one ought to honor a father, we have hastened to subject all the priests of the whole Eastern district, and to unite them to the See of your Holiness, for we do not allow of any point, however manifest and indisputable it be, which relates to the state of the churches, not being brought to the cognizance of your Holiness, since you are the Head of all the holy churches.  (Epist. ad. Pap. Joan. ii. Cod. Justin. lib. I. tit. 1, 529 A.D.)
Maximus
How much more in the case of the clergy and church of the Romans, which from old until now presides over all the churches which are under the sun?  Having surely received this canonically, as well as from councils and the apostles, as from the princes of the latter (Peter & Paul), and being numbered in their company, she is subject to no writings or issues in synodical documents, on account of the eminence of her pontificate…even as in all these things all are equally subject to her (the Church of Rome) according to sacerodotal law.  And so when, without fear, but with all holy and becoming confidence, those ministers (the popes) are of the truly firm and immovable rock, that is of the most great and Apostolic Church of Rome.  (J.B. Mansi, ed. Amplissima Collectio Conciliorum, vol. 10, 650 A.D.)
Methodius
It is not true, as this canon (Canon 28 of Chalcedon) states, that the holy fathers gave the primacy to old Rome because it was the capital of the Empire; it is from on high, from Divine grace, that this primacy drew its origin.  Because of the intensity of his faith, Peter, the first of the Apostles, was addressed in these words by our Lord Jesus Christ Himself: "Peter, lovest thou me?  Feed my sheep."  That is why in hierarchical order Rome holds the pre-eminent place and is the first See.  That is why the leges of old Rome are eternally immovable, and that is the view of all the Churches.  (N. Brian-Chaninov, The Russian Church (1931), 46; cited by Butler, Church and Infallibility, 210 (Upon This Rock (San Francisco: Ignatius, 1999), p. 177), 451 A.D.)
Nicephorus, Patriarch of Constantinople
Without whom (the Romans presiding in the seventh Council) a doctrine brought forward in the Church could not, even though confirmed by canonical decrees and by ecclesiastical usage, ever obtain full approval or currency.  For it is they (the Popes of Rome) who have had assigned to them the rule in sacred things, and who have received into their hands the dignity of headship among the Apostles.  (Niceph. Cpl. pro. s. imag. c 25 [Mai N. Bibl. pp. ii. 30], 815 A.D.)
Theodoret
If Paul, the herald of the truth, the trumpet of the Holy Spirit, hastened to the great Peter, to convey from him the solution to those in Antioch, who were at issue about living under the law, how much more do we, poor and humble, run to the Apostolic Throne (Rome) to receive from you (Pope Leo) healing for wounds of the churches.  For it pertains to you to have primacy in all things; for your throne is adorned with many prerogatives.  (Epistle Leoni, 449 A.D.)
Listen to your Apostolic See in order to receive from you a cure for the wounds of the Church.  For every reason it is fitting for you to hold the first place, inasmuch as your see is adorned with many priviledges.  I havebeen condemned without trial.  But I await the sentence of your Apostolic See.  I beseech and implore Your Holiness to succor me in my appeal to your fair and righteous tribunal.  Bid me hasten to you and prove to you that my teaching follows in the footsteps of the Apostles.  (To Pope Leo, Ep. 113, 449 A.D.)
St. John Cassian
But if you prefer the authority of a greater person…let us interrogate no beginner or untaught schoolboy, nor a woman whose faith might perhaps appear to be but rudimentary; but that greatest of disciples among disciples, and of teachers among teachers, who presided and ruled over the Roman Church, and held the chief place in the priesthood as he did in the faith.  Tell us then, tell us, we pray, O Peter, thou chief of Apostles, tell us how the Churches ought to believe in God.  For it is right that you should teach us, as you were taught by the Lord, and that you should open to us the gate, of which you received the key.  Shut out all those who try to overthrow the heavenly house: and those who are endeavouring to enter by secret holes and unlawful approaches: as it is clear that none can enter the gate of the kingdom save one to whom the key bestowed on the Churches is revealed by you.  (Against the Nestorians on the Incarnation, III, 12, 360 A.D.)
Council of Sardica
If any bishop looses the judgment in some case [decided by his fellow bishops] and still believes that he has not a bad but a good case, in order that the case may be judged anew…let us honor the memory of the Apostle Peter by having those who have given the judgment write to Julius, Bishop of Rome, so that if it seem proper he may himself send arbiters and the judgment may be made again by the bishops of a neighboring province.  (Council of Sardica, 342-343 A.D.)