It’s impossible for the Apostolic churches to have apostatized into the same exact faith

Grant, then, that all have erred; that the apostle was mistaken in giving his testimony; that the Holy Ghost had no such respect to any one (church) as to lead it into truth, although sent with this view by Christ, and for this asked of the Father that He might be the teacher of truth; grant, also, that He, the Steward of God, the Vicar of Christ, neglected His office, permitting the churches for a time to understand differently, (and) to believe differently, what He Himself was preaching by the apostles,—is it likely that so many churches, and they so great, should have gone astray into one and the same faith?  No casualty distributed among many men issues in one and the same result. Error of doctrine in the churches must necessarily have produced various issues.  When, however, that which is deposited among many is found to be one and the same, it is not the result of error, but of tradition. Can any one, then, be reckless enough to say that they were in error who handed on the tradition?

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXVIII

True doctrine must be tested against the apostolic churches that are in communion with one another

If, then, these things are so, it is in the same degree manifest that all doctrine which agrees with the apostolic churches—those moulds and original sources of the faith must be reckoned for truth, as undoubtedly containing that which the (said) churches received from the apostles, the apostles from Christ, Christ from God.  Whereas all doctrine must be prejudged as false which savors of contrariety to the truth of the churches and apostles of Christ and God. It remains, then, that we demonstrate whether this doctrine of ours, of which we have now given the rule, has its origin in the tradition of the apostles, and whether all other doctrines do not ipso facto proceed from falsehood. We hold communion with the apostolic churches because our doctrine is in no respect different from theirs. This is our witness of truth.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXI

Only those churches established by the Apostles and their line of succession can be apostolic

…after first bearing witness to the faith in Jesus Christ throughout Judæa, and founding churches (there), they next went forth into the world and preached the same doctrine of the same faith to the nations. They then in like manner founded churches in every city, from which all the other churches, one after another, derived the tradition of the faith, and the seeds of doctrine, and are every day deriving them, that they may become churches. Indeed, it is on this account only that they will be able to deem themselves apostolic, as being the offspring of apostolic churches.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XX

Scripture cannot be properly interpreted outside the Apostolic churches

Our appeal, therefore, must not be made to the Scriptures; nor must controversy be admitted on points in which victory will either be impossible, or uncertain, or not certain enough. But even if a discussion from the Scriptures should not turn out in such a way as to place both sides on a par, (yet) the natural order of things would require that this point should be first proposed, which is now the only one which we must discuss: “With whom lies that very faith to which the Scriptures belong. From what and through whom, and when, and to whom, has been handed down that rule, by which men become Christians?” For wherever it shall be manifest that the true Christian rule and faith shall be, there will likewise be the true Scriptures and expositions thereof, and all the Christian traditions.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XIX

Heresies all come after the Apostolic tradition

Nor need we wonder if the speculations of philosophers have perverted the older Scriptures. Some of their brood, with their opinions, have even adulterated our new-given Christian revelation, and corrupted it into a system of philosophic doctrines, and from the one path have struck off many and inexplicable by-roads.145 And I have alluded to this, lest any one becoming acquainted with the variety of parties among us, this might seem to him to put us on a level with the philosophers, and he might condemn the truth from the different ways in which it is defended. But we at once put in a plea in bar against these tainters of our purity, asserting that this is the rule of truth which comes down from Christ by transmission through His companions, to whom we shall prove that those devisers of different doctrines are all posterior. Everything opposed to the truth has been got up from the truth itself, the spirits of error carrying on this system of opposition.

Tertullian
Apology
Chapter XLVII

Peter, James and John ordained James the Just

Now Clement, writing in the sixth book of the Hypotyposes, makes this statement. For he says that Peter and James and John, after the Savior’s ascension, though pre-eminently honored by the Lord, did not contend for glory, but made James the Just, bishop of Jerusalem.

Eusebius of Caesarea
Church History
Chapter VI.II
Quotation from lost work of Clement of Alexandria

 

Baptism of the Apostles

Yes, truly, the apostles were baptized, as Clement the Stromatist relates in the fifth book of the Hypotyposes. For, in explaining the apostolic statement, I thank God that I baptised none of you, he says, Christ is said to have baptised Peter alone, and Peter Andrew, and Andrew John, and they James and the rest.

St. John Moschus
Spiritual Meadow, Book V
Chapter 176
Quote from lost work of Clement of Alexandria

Irenaeus learned from Polycarp as a boy

For, while I was yet a boy, I saw thee in Lower Asia with Polycarp, distinguishing thyself in the royal court, and endeavouring to gain his approbation. For I have a more vivid recollection of what occurred at that time than of recent events (inasmuch as the experiences of childhood, keeping pace with the growth of the soul, become incorporated with it); so that I can even describe the place where the blessed Polycarp used to sit and discourse— his going out, too, and his coming in—his general mode of life and personal appearance, together with the discourses which he delivered to the people; also how he would speak of his familiar intercourse with John, and with the rest of those who had seen the Lord; and how he would call their words to remembrance. Whatsoever things he had heard from them respecting the Lord, both with regard to His miracles and His teaching, Polycarp having thus received [information] from the eye-witnesses of the Word of life, would recount them all in harmony with the Scriptures. These things, through, God’s mercy which was upon me, I then listened to attentively, and treasured them up not on paper, but in my heart; and I am continually, by God’s grace, revolving these things accurately in my mind.

Irenaeus of Lyons
Lost Writings
Fragment II

 

The catholicity of the Church

But the path of those belonging to the Church circumscribes the whole world, as possessing the sure tradition from the apostles, and gives unto us to see that the faith of all is one and the same, since all receive one and the same God the Father, and believe in the same dispensation regarding the incarnation of the Son of God, and are cognizant of the same gift of the Spirit, and are conversant with the same commandments, and preserve the same form of ecclesiastical constitution, and expect the same advent of the Lord, and await the same salvation of the complete man, that is, of the soul and body.

…For the Church preaches the truth everywhere, and she is the seven-branched candlestick which bears the light of Christ.

Irenaeus of Lyons
Against Heresies, Book V
Chapter XX

Biblical interpretation must be done in light of catholic tradition

But here some one perhaps will ask, Since the canon of Scripture is complete, and sufficient of itself for everything, and more than sufficient, what need is there to join with it the authority of the Church’s interpretation? For this reason—because, owing to the depth of Holy Scripture, all do not accept it in one and the same sense, but one understands its words in one way, another in another; so that it seems to be capable of as many interpretations as there are interpreters. For Novatian expounds it one way, Sabellius another, Donatus another, Arius, Eunomius, Macedonius, another, Photinus, Apollinaris, Priscillian, another,Iovinian, Pelagius, Celestius, another, lastly, Nestorius another. Therefore, it is very necessary, on account of so great intricacies of such various error, that the rule for the right understanding of the prophets and apostles should be framed in accordance with the standard of Ecclesiastical and Catholic interpretation.

Moreover, in the Catholic Church itself, all possible care must be taken, that we hold that faith which has been believed everywhere, always, by all. For that is truly and in the strictest sense Catholic, which, as the name itself and the reason of the thing declare, comprehends all universally. This rule we shall observe if we follow universality, antiquity, consent. We shall follow universality if we confess that one faith to be true, which the whole Church throughout the world confesses; antiquity, if we in no wise depart from those interpretations which it is manifest were notoriously held by our holy ancestors and fathers; consent, in like manner, if in antiquity itself we adhere to the consentient definitions and determinations of all, or at the least of almost all priests and doctors.

St. Vincent of Lerins
Commonitory
Chapter 2:5-6