The Eucharist as a sacrifice

We are the true adorers and the true priests, who, praying in spirit, sacrifice, in spirit, prayer,—a victim proper and acceptable to God, which assuredly He has required, which He has looked forward to for Himself! This victim, devoted from the whole heart, fed on faith, tended by truth, entire in innocence, pure in chastity, garlanded with love, we ought to escort with the pomp of good works, amid psalms and hymns, unto God’s altar, to obtain for us all things from God.

Tertullian
On Prayer
Chapter XXVIII

Traditions regarding the hours of prayer

Touching the time, however, the extrinsic observance of certain hours will not be unprofitable—those common hours, I mean, which mark the intervals of the day—the third, the sixth, the ninth—which we may find in the Scriptures to have been more solemn than the rest.

… so that—what we read to have been observed by Daniel also, in accordance (of course) with Israel’s discipline—we pray at least not less than thrice in the day, debtors as we are to Three—Father, Son, and Holy Spirit: of course, in addition to our regular prayers which are due, without any admonition, on the entrance of light and of night. But, withal, it becomes believers not to take food, and not to go to the bath, before interposing a prayer; for the refreshments and nourishments of the spirit are to be held prior to those of the flesh, and things heavenly prior to things earthly.

Tertullian
On Prayer
Chapter XXV

Traditions regarding kneeling

In the matter of kneeling also prayer is subject to diversity of observance, through the act of some few who abstain from kneeling on the Sabbath; and since this dissension is particularly on its trial before the churches, the Lord will give His grace that the dissentients may either yield, or else indulge their opinion without offense to others. We, however (just as we have received), only on the day of the Lord’s Resurrection ought to guard not only against kneeling, but every posture and office of solicitude; deferring even our businesses lest we give any place to the devil.

At fasts, moreover, and Stations, no prayer should be made without kneeling, and the remaining customary marks of humility; for (then) we are not only praying, but deprecating, and making satisfaction to God our Lord. Touching times of prayer nothing at all has been prescribed, except clearly “to pray at every time and every place.”

Tertullian
On Prayer
Chapter XXII

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

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

Christians fast and remain virgins as a longing for the greater things experienced in heaven hereafter

We even, as we may be able, excuse our mouths from food, and withdraw our sexes from union. How many voluntary eunuchs are there! How many virgins espoused to Christ! How many, both of men and women, whom nature has made sterile, with a structure which cannot procreate! Now, if even here on earth both the functions and the pleasures of our members may be suspended, with an intermission which, like the dispensation itself, can only be a temporary one, and yet man’s safety is nevertheless unimpaired, how much more, when his salvation is secure, and especially in an eternal dispensation, shall we not cease to desire those things, for which, even here below, we are not unaccustomed to check our longings!

Tertullian
On the Resurrection of the Flesh
Chapter LXI