Confession is on the knees before other Christians who stand in Christ’s stead

In a company of two is the church; but the church is Christ. When, then, you cast yourself at the brethren’s knees, you are handling Christ, you are entreating Christ. In like manner, when they shed tears over you, it is Christ who suffers, Christ who prays the Father for mercy.

Tertullian
On Repentance
Chapter X

By confession repentance is born

The narrower, then, the sphere of action of this second and only (remaining) repentance, the more laborious is its probation; in order that it may not be exhibited in the conscience alone, but may likewise be carried out in some (external) act. This act, which is more usually expressed and commonly spoken of under a Greek name, is ἐξομολόγησις , whereby we confess our sins to the Lord, not indeed as if He were ignorant of them, but inasmuch as by confession satisfaction is settled, of confession repentance is born; by repentance God is appeased.

…All this exomologesis (does), that it may enhance repentance; may honour God by its fear of the (incurred) danger; may, by itself pronouncing against the sinner, stand in the stead of God’s indignation, and by temporal mortification (I will not say frustrate, but) expunge eternal punishments.

Tertullian
On Repentance
Chapter IX

The heresies of Blastus, Theodotus and Praxeas

…there is likewise Blastus, who would latently introduce Judaism. For he says the passover is not to be kept otherwise than according to the law of Moses, on the fourteenth of the month. But who would fail to see that evangelical grace is escheated if he recalls Christ to the Law?

Add to these Theodotus the Byzantine, who, after being apprehended for Christ’s Name, and apostatizing, ceased not to blaspheme against Christ.  For he introduced a doctrine by which to affirm that Christ was merely a human being, but deny His deity; teaching that He was born of the Holy Spirit indeed of a virgin, but was a solitary and bare human being, with no pre-eminence above the rest (of mankind), but only that of righteousness.

…After him brake out a second heretical Theodotus, who again himself introduced a sister-sect, and says that the human being Christ Himself was merely conceived alike, and born, of the Holy Spirit and the Virgin Mary, but that He was inferior to Melchizedek;

…But after all these, again, one Praxeas introduced a heresy which Victorinus was careful to corroborate. He asserts that Jesus Christ is God the Father Almighty.  Him he contends to have been crucified, and suffered, and died;

Tertullian
Against All Heresies
Chapter VIII

Peter and Paul were martyred in Rome

We read the lives of the Cæsars: At Rome Nero was the first who stained with blood the rising faith. Then is Peter girt by another, when he is made fast to the cross. Then does Paul obtain a birth suited to Roman citizenship, when in Rome he springs to life again ennobled by martyrdom.  Wherever I read of these occurrences, so soon as I do so, I learn to suffer; nor does it signify to me which I follow as teachers of martyrdom, whether the declarations or the deaths of the apostles, save that in their deaths I recall their declarations also.

Tertullian
Scorpiace
Chapter XV

The Lord gave the keys to heaven to Peter, then to the Church, then to every believer

For though you think heaven still shut, remember that the Lord left here to Peter and through him to the Church, the keys of it, which every one who has been here put to the question, and also made confession, will carry with him.

Tertullian
Scorpiace
Chapter X

The revelation of the Trinity makes the New Covenant possible

What need would there be of the gospel, which is the substance of the New Covenant, laying down (as it does) that the Law and the Prophets lasted until John the Baptist, if thenceforward the Father, the Son, and the Spirit are not both believed in as Three, and as making One Only God? God was pleased to renew His covenant with man in such a way as that His Unity might be believed in, after a new manner, through the Son and the Spirit, in order that God might now be known openly, in His proper Names and Persons, who in ancient times was not plainly understood, though declared through the Son and the Spirit.

Tertullian
Against Praxeas
Chapter XXXI

The Holy Spirit is the third person of the Godhead

He will come again on the clouds of heaven, just as He appeared when He ascended into heaven. Meanwhile He has received from the Father the promised gift, and has shed it forth, even the Holy Spirit—the Third Name in the Godhead, and the Third Degree of the Divine Majesty; the Declarer of the One Monarchy of God…

Tertullian
Against Praxeas
Chapter XXX

The Father did not suffer

Then, again, the Father is as incapable of fellow-suffering as the Son even is of suffering under the conditions of His existence as God. Well, but how could the Son suffer, if the Father did not suffer with Him? My answer is, The Father is separate from the Son, though not from Him as God.

Tertullian
Against Praxeas
Chapter XXIX

Jesus is the Word of God and man

But the truth is, we find that He is expressly set forth as both God and Man; the very psalm which we have quoted intimating (of the flesh), that “God became Man in the midst of it, He therefore established it by the will of the Father,”—certainly in all respects as the Son of God and the Son of Man, being God and Man, differing no doubt according to each substance in its own especial property, inasmuch as the Word is nothing else but God, and the flesh nothing else but Man. Thus does the apostle also teach respecting His two substances, saying, “who was made of the seed of David;” in which words He will be Man and Son of Man.  “Who was declared to be the Son of God, according to the Spirit;” in which words He will be God, and the Word—the Son of God. We see plainly the twofold state, which is not confounded, but conjoined in One Person—Jesus, God and Man.

…In like manner, again, the apostle calls Him “the Mediator between God and Men,” and so affirmed His participation of both substances.

Tertullian
Against Praxeas
Chapter XXVII

Christians are baptised by immersion into three persons

After His resurrection He promises in a pledge to His disciples that He will send them the promise of His Father; and lastly, He commands them to baptize into the Father and the Son and the Holy Ghost, not into a unipersonal God. And indeed it is not once only, but three times, that we are immersed into the Three Persons, at each several mention of Their names.

Tertullian
Against Praxeas
Chapter XXVI