After Erasmus put together the Greek text, he translated the text into Latin. Bainton writes about the translation task in part as follows:
At this point Erasmus noted that Greek was not the mother tongue of the evangelists and their use of it was affected by their native idioms. They did not write the Greek of Demosthenes. “Do you mean to say,” demanded John Eck in Germany [later one of Luther’s adversaries], “that the best Greek was not written by the apostles on whom the Holy Spirit conferred the gift of tongues?” “My dear fellow,” answered Erasmus, “if you will look at the list of languages of which the Holy Spirit gave command to the apostles on the day of Pentecost you will discover that Greek was not one of them. Besides the gift lasted for only one day.” Ibid., p. 139.
When Walter was a freshman at Davidson College, he decided to major in Classics so that he could study Greek. He wanted to be able to read the New Testament in the original text. First Davidson required him to take Classical Greek, and only then “New Testament Greek," known as Koine. Finally, he got to the New Testament. He told me that he was surprised to see the variation in the quality of the Greek, especially among the four Gospels (I recall that he said that the Gospel of Mark was the roughest and John the most elegant).
(Bainton, in his notes to his chapter on Erasmus' "publication, translation, and elucidation" of the NT cites Bruce Metzger, The Text of the New Testament (Oxford, 1964). That title is also in Bainton's bibliography. As I have mentioned several times, I had the pleasure of meeting Dr. Metzger during the 1970s when he visited our church to give a series of lectures on the Sermon on the Mount. They were splendid lectures.)