Alexander, Archibald (1772-1851). The Canon of the Old and New Testaments Ascertained; or, The Bible, Complete, without the Apocrypha and Unwritten Traditions. Presbyterian Board of Education, 1851. Alexander was one of the founders, and the first principal, of Princeton Theological Seminary. Alexander, B. B. Warfield, Charles Hodge, and A. A. Hodge (named after Alexander) became known as the “Princeton theologians” and left a distinctive mark on the history of American Christianity. (This information copied and pasted from Annotated Bibliography on New Testament Text and Canon.)
It is necessary, therefore, to proceed to our destined point in a more circuitous way. We must be at the pains to examine into the history of the Canon, and, as was before said, to ascertain what books were esteemed canonical by all those who had the best opportunity of judging of this matter; and when the internal evidence is found corroborating the external, the two, combined, may produce a degree of conviction which leaves no room to desire any stronger evidence.
The question to be decided is a matter of fact. It is an inquiry respecting the real authors of the books of the New Testament, whether they were written by the persons whose names they bear, or by others under their names. The inspiration of these books, though closely allied to this subject, is not now the object of inquiry. The proper method of determining a matter of fact, evidently is to have recourse to those persons who were witnesses of it, or who received their information from others who were witnesses. It is only in this way that we know that Homer, Horace, Virgil, Livy, and Tully [i.e., Cicero], wrote the books which now go under their names. [Emphasis added]
The early Christians pursued this method of determining what books were canonical. They searched into the records of the church, before their time, and from these ascertained what books should be received, as belonging to the sacred volume. They appeal to that certain and universal tradition, which attested the genuineness of these books. Irenæus, Tertullian,
Eusebius, Cyril, and Augustine, have all made use of this argument, in establishing the Canon of the New Testament. (p. 117-118; p. 69 on the pdf I am using, downloaded from the Internet Archive)
Parenthetically, while Alexander was making this point in America, Samuel P. Tregelles was making it in England. See Notes on Tregelles re: Authorship of the New Testament Books. (Tregelles wrote an entire book on the subject, and these notes recount its logic.)
For other posts on this subject, see Posts on the Means of Determining Authorship of Ancient Texts.