The Apostolic Tradition of Hippolytus references the custom of private prayer. Firstly, the notions of prayer are also found in Clement of Alexandria, Tertullian, Cyprian, Basil etc. The text of the Didache "Do not pray as the hypocrites, but as the Lord directed in his Gospel", then it adds the words of the Our Father, with the ending "for Thine is the power and glory forever."
Didache (c 8, 2-)
The choice of these particular times is founded on Jewish prototypes: The Prophet Daniel, "Three times a day he would open his chamber window towards Jerusalem eastwards doing reverence on bended knee and praising his God. In the Acts of the Apostles, 'it was at the nineth hour, 'which is an hour of prayer that Peter and John went up to the temple and cured the lame man and it was in the afternoon at the ninth hour that Cornelius was at prayer when he had his vision.
Apparently, the act of sanctifying the day and night was not purely a Christian idea, but quite possibly appropriated from Judaism. From the 'Manual od Discipline" Qumran near the Dead Sea in 1947, writings earlier than the time of Christ, "Pray 'at the start of the dominion of light, at the height of its course and when it once again returns to its established place, at the start of the night-watch.....and at the climax of its course, and when it again recedes before the rising night."
