On fasting and the Eucharist

Similarly, too, touching the days of Stations, most think that they must not be present at the sacrificial prayers, on the ground that the Station must be dissolved by reception of the Lord’s Body. Does, then, the Eucharist cancel a service devoted to God, or bind it more to God?  Will not your Station be more solemn if you have withal stood at God’s altar? When the Lord’s Body has been received and reserved each point is secured, both the participation of the sacrifice and the discharge of duty.

Tertullian
On Prayer
Chapter XIX

God alone could teach how He wants to be prayed to

God alone could teach how he wished Himself prayed to. The religious rite of prayer therefore, ordained by Himself, and animated, even at the moment when it was issuing out of the Divine mouth, by His own Spirit, ascends, by its own prerogative, into heaven, commending to the Father what the Son has taught.

Tertullian
On Prayer
Chapter IX

The Logos brings a new kind of prayer

The Spirit of God, and the Word of God, and the Reason of God—Word of Reason, and Reason and Spirit of Word—Jesus Christ our Lord, namely, who is both the one and the other,—has determined for us, the disciples of the New Testament, a new form of prayer;

Tertullian
On Prayer
Chapter I

Baptism is a new birth into the Church, our Mother

Therefore, blessed ones, whom the grace of God awaits, when you ascend from that most sacred font of your new birth, and spread your hands for the first time in the house of your mother, together with your brethren, ask from the Father, ask from the Lord, that His own specialties of grace and distributions of gifts may be supplied you. “Ask,” saith He, “and ye shall receive.” Well, you have asked, and have received; you have knocked, and it has been opened to you.  Only, I pray that, when you are asking, you be mindful likewise of Tertullian the sinner.

Tertullian
On Baptism
Chapter XX

Tertullian recommends delaying baptism even though it is permissible to baptize infants

And so, according to the circumstances and disposition, and even age, of each individual, the delay of baptism is preferable; principally, however, in the case of little children. For why is it necessary—if (baptism itself) is not so necessary—that the sponsors likewise should be thrust into danger? Who both themselves, by reason of mortality, may fail to fulfil their promises, and may be disappointed by the development of an evil disposition, in those for whom they stood? The Lord does indeed say, “Forbid them not to come unto me.” Let them “come,” then, while they are growing up; let them “come” while they are learning, while they are learning whither to come; let them become Christians when they have become able to know Christ.  Why does the innocent period of life hasten to the “remission of sins?” More caution will be exercised in worldly matters: so that one who is not trusted with earthly substance is trusted with divine! Let them know how to “ask” for salvation, that you may seem (at least) to have given “to him that asketh.”

Tertullian
On Baptism
Chapter XVIII

Anyone can perform a baptism but it’s proper for the priests and deacons to

For concluding our brief subject, it remains to put you in mind also of the due observance of giving and receiving baptism. Of giving it, the chief priest (who is the bishop) has the right: in the next place, the presbyters and deacons, yet not without the bishop’s authority, on account of the honour of the Church, which being preserved, peace is preserved. Beside these, even laymen have the right; for what is equally received can be equally given. Unless bishops, or priests, or deacons, be on the spot, other disciples are called i.e. to the work. The word of the Lord ought not to be hidden by any: in like manner, too, baptism, which is equally God’s property, can be administered by all. But how much more is the rule of reverence and modesty incumbent on laymen—seeing that these powers belong to their superiors—lest they assume to themselves the specific function of the bishop! Emulation of the episcopal office is the mother of schisms.

Tertullian
On Baptism
Chapter XVII

Baptism and Eucharist are like two united baptisms

These two baptisms He sent out from the wound in His pierced side, in order that they who believed in His blood might be bathed with the water; they who had been bathed in the water might likewise drink the blood. This is the baptism which both stands in lieu of the fontal bathing when that has not been received, and restores it when lost.

Tertullian
On Baptism
Chapter XVI

Baptism is an essential part of the New Covenant

Here, then, those miscreants provoke questions. And so they say, “Baptism is not necessary for them to whom faith is sufficient; for withal, Abraham pleased God by a sacrament of no water, but of faith.” But in all cases it is the later things which have a conclusive force, and the subsequent which prevail over the antecedent. Grant that, in days gone by, there was salvation by means of bare faith, before the passion and resurrection of the Lord. But now that faith has been enlarged, and is become a faith which believes in His nativity, passion, and resurrection, there has been an amplification added to the sacrament, viz., the sealing act of baptism; the clothing, in some sense, of the faith which before was bare, and which cannot exist now without its proper law.

Tertullian
On Baptism
Chapter XIII