The Beginnings of Christianity: The Acts of the Apostles Volume 1, Prolegomena 1:
The Jewish Gentile, and Christian Backgrounds by F. J. Foakes Jackson and Kirsopp Lake 1979 version pages 335-337. "There is little doubt as to the sacramental nature of baptism by the middle of the first century in the circles represented by the Pauline Epistles, and it is indisputable in the second century. The problem is whether it can in this (Trinitarian) form be traced back to Jesus, and if not what light is thrown upon its history by the analysis of the synoptic Gospels and Acts.
According to Catholic teaching, (traditional Trinitarian) baptism was instituted by Jesus. It is easy to see how necessary this was for the belief in sacramental regeneration. Mysteries, or sacraments, were always the institution of the Lord of the cult; by them, and by them only, were its supernatural benefits obtained by the faithful. Nevertheless, if evidence counts for anything, few points in the problem of the Gospels are so clear as the improbability of this teaching.
The reason for this assertion is the absence of any mention of Christian baptism in Mark, Q, or the third Gospel, and the suspicious nature of the account of its institution in Matthew 28:19: "Go ye into all the world, and make disciples of all Gentiles (nations), baptizing them in the name of the Father, the Son, and the Holy Spirit." It is not even certain whether this verse ought to be regarded as part of the genuine text of Matthew. No other text, indeed, is found in any extant manuscripts, in any language, but it is arguable that Justin Martyr, though he used the trine formula, did not find it in his text of the Gospels; Hermas seems to be unacquainted with it; the evidence of the Didache is ambiguous, and Eusebius habitually, though not invariably, quotes it in another form, "Go ye into all the world and make diciples of all the Gentiles in My Name."
No one acquainted with the facts of textual history and patristic evidence can doubt the tendency would have been to replace the Eusebian text (In My Name) by the ecclesiastical (Catholic Trinitarian) formula of baptism, so that transcriptional evedence" is certainly on the side of the text omitting baptism.
But it is unnecessary to discuss this point at length, because even if the ordinary (modern Trinity) text of Matthew 28:19 be sound it can not represent historical fact.
Would they have baptized, as Acts says that they did, and Paul seem to confirm the statement, in the name of the Lord Jesus if the Lord himself had commanded them to use the (Catholic Trinitarian) formula of the Church? On every point the evidence of Acts is convincing proof that the (Catholic) tradition embodied in Matthew 28:19 is a late (non-Scriptural Creed) and unhistorical.
Neither in the third gospel nor in Acts is there any reference to the (Catholic Trinitarian) Matthaean tradition, nor any mention of the institution of (Catholic Trinitarian) Christian baptism. Nevertheless, a little later in the narrative we find several references to baptism in water in the name of the Lord Jesus as part of recognized (Early) Christian practice. Thus we are faced by the problem of a Christian rite, not directly ascribed to Jesus, but assumed to be a universal (and original) practice. That it was so is confirmed by the Epistles, but the facts of importance are all contained in Acts."
Also in the same book on page 336 in the footnote number one, Professor Lake makes an astonishing discovery in the so-called Teaching or Didache. The Didache has an astonishing contradiction that is found in it. One passage refers to the necessity of baptism in the name of the Lord, which is Jesus the other famous passage teaches a Trinitarian Baptism. Lake raises the probability that the apocryphal Didache or the early Catholic Church Manual may have also been edited or changed to promote the later Trinitarian doctrine. It is a historical fact that the Catholic Church at one time baptized its converts in the name of Jesus but later changed to Trinity baptism.
"1. In the actual description of baptism in the Didache the trine (Trinity) formula is used; in the instructions for the Eucharist (communion) the condition for admission is baptism in the name of the Lord. It is obvious that in the case of an eleventh-century manuscript *the trine formula was almost certain to be inserted in the description of baptism, while the less usual formula had a chance of escaping notice when it was only used incidentally."
The Catholic University of America in Washington, D. C. 1923, New Testament Studies Number 5:
The Lord's Command To Baptize An Historical Critical Investigation. By Bernard Henry Cuneo page 27. "The passages in Acts and the Letters of St. Paul. These passages seem to point to the earliest form as baptism in the name of the Lord." Also we find. "Is it possible to reconcile these facts with the belief that Christ commanded his disciples to baptize in the trine form? Had Christ given such a command, it is urged, the Apostolic Church would have followed him, and we should have some trace of this obedience in the New Testament. No such trace can be found. The only explanation of this silence, according to the anti-traditional view, is this the short christological (Jesus Name) formula was (the) original, and the longer trine formula was a later development."