Updated: Jan 12, 2022
5. The Epistle was written, not in Hebrew, as Clement of Alexandria, and others, and recently Salmasius, have insisted; but in Greek.
There has been some doubt in what language this Epistle was written. That it was written in Hebrew, not a few of the Ancients, Clement of Alexandria, Theodoret, Jerome, supposed, thinking that it was translated into Greek by Luke or Clement; to which opinion the Most Illustrious Salmasius adds his second, de Hellensitica, page 255. But not one of the ancients claims to have seen a Hebrew text firsthand. And this tradition came down from Clement of Alexandria alone, not led by any other reason or conjecture than that it was written to the Hebrews. Although it was written, not to Palestinian Hebrews alone, but also to those of the dispersion, little skilled in Hebrew idiom. Also to the Hebrews wrote James, Peter, and John, yet not in Hebrew. Paul wrote to the Romans, but not in Latin. Therefore, we do not doubt that this Epistle was written in Greek. For this language was the most well known, as in the whole world, so also among the Hebrews, even the Palestinian ones, Josephus and the Talmudists, who can be seen in the Most Learned Lightfoot. Also, the Greek exemplar was received by the Churches, circulated, translated into other languages, and preserved by Divine Providence; not another. Neither does the Greek edition have any marks of translation; but a great many marks of pure Grecanity. Nor does the elegance of that writing savor of a translation. In addition, the passages of the Old Testatment are cited from the Greek translation, but rather to be cited and brought from the Hebrew, if indeed it was first written in Hebrew. I pass over in silence the unlearned Greeks that here appear, as if διαθήκη and διατίθεσθαι have here the notion of a testament and making a testament, when בְּרִית of the Hebrews expresses any pact whatsoever. Paronomasiæ also, in which the Greeks delight more than others, occur frequently here, as in Hebrews 5:8; 11:37. Finally, the Author translated the Hebrew name מַלְכִּי־צֶדֶק/Melchizedek in Greek, Μελχισεδέκ/ Melchisedec.
 That is, word-play.  Hebrews 5:8: “Though he were a Son, yet learned he (ἔμαθεν/emathen) obedience by the things which he suffered (ἔπαθεν/epathen)…”  Hebrews 11:37: “They were stoned (ἐλιθάσθησαν/elithasthesan), they were sawn asunder (ἐπρίσθησαν/epristhesan), were tempted (ἐπειράσθησαν/epeirasthesan), were slain with the sword: they wandered about in sheepskins and goatskins; being destitute, afflicted, tormented…”
Dr. Dilday's Lecture: "A Pauline Miscellany, Part 6"