What answer did Arius and Eusebius have to Melchisedec being a representative likeness having ‘no beginning of days’ (Hebrews 7:3)?

Origen and Eternal Generation

I think it is false to say that Origen ‘taught that the relationship between the Father and the Son was one of an ‘eternal begetting’ as if this begetting is a continuous process. You refer to more than 60 pages to substantiate this claim. I would like to see more specific references. In my view, Origen described the begetting of the Son as an event in the eternal past. This must not be confused with the later-developed theory of eternal generation according to which the begetting of the Son is an eternal process in which the Son is still being generated and always will be generated.

Arius

Yes, Arius did teach that the Son had a beginning but he also taught that he was “begotten timelessly” (RPC Hanson - The Search for the Christian Doctrine of God - The Arian Controversy 318-381, page 8).

“He (Arius) and his followers insist again and again that the Son was produced before times and ages yet they hold onto the conviction that there was a time when the Son did not exist. … Perhaps they took the Platonic view that time only existed when the heavenly bodies, by which time is measured, were created, so that the Son, who was at some point brought into existence, but before the heavenly bodies, could be said in a sense to be 'before times'” (RH, 22).

“Faced with the notion that there was no 'interval’ between Father and Son, Eusebius (of Caesarea) is not necessarily being inconsistent in stressing the Father's pre-existence. From our point of view, in the world's time, Father and Son co-exist; from the Father's point of view, so to speak, they do not and cannot.” (Rowan Williams, Arius: Heresy and Tradition, page 172)

In other words, Arius taught that the Son was generated before time began. For Arius, He was begotten in the incomprehensible infinity or eternity that exists beyond the time, space, and matter of this universe. Is that so much different from what Origen taught?

In the beginning … was the Logos.

You quote this from John 1:1. I assume the beginning here is the beginning of creation – which is the beginning of time. Arius would agree that the Logos already existed at that time.

Beginning and Created

You wrote: If no ‘beginning of days’ then no possibility of calling this one ‘created’. I do not agree: In the Logos Theology of the ancient Apologists, “the Logos” was created (not begotten as a separate reality) because it is God’s Word or Thought or Wisdom, but it had no beginning because God exists timelessly and, therefore, never had a first thought. Therefore, Melchizedek, as likeness of Christ, also has no beginning of days but is created.

At the end of the question, you do mention the distinction that can be drawn between time and eternity; the eternity existing outside time. To understand the ancients, we need to understand how they applied this distinction.

• As far as Arian bible versions are concerned, Ulfilas' Gothic translation lacks Hebrews, along with half of the New Testament scriptures.

• As far as Eusebius' explicit statements on Christ's relation to Melchizedek are concerned, there are two such relevant passages in his Church History:

First Book, Third Chapter :

16. And elsewhere the same writer speaks of him as follows: The Lord said to my Lord, Sit at my right hand until I make your enemies your footstool; and, Out of the womb, before the morning star, have I begotten you. The Lord has sworn and he will not repent. You are a priest forever after the order of Melchizedek.
17. But this Melchizedek is introduced in the Holy Scriptures as a priest of the most high God, not consecrated by any anointing oil, especially prepared, and not even belonging by descent to the priesthood of the Jews. Wherefore after his order, but not after the order of the others, who received symbols and types, was our Saviour proclaimed, with an appeal to an oath, Christ and priest.
18. History, therefore, does not relate that he was anointed corporeally by the Jews, nor that he belonged to the lineage of priests, but that he came into existence from God himself before the morning star, that is before the organization of the world, and that he obtained an immortal and undecaying priesthood for eternal ages.
19. But it is a great and convincing proof of his incorporeal and divine unction that he alone of all those who have ever existed is even to the present day called Christ by all men throughout the world, and is confessed and witnessed to under this name, and is commemorated both by Greeks and Barbarians and even to this day is honored as a King by his followers throughout the world, and is admired as more than a prophet, and is glorified as the true and only high priest of God. And besides all this, as the pre-existent Word of God, called into being before all ages, he has received august honor from the Father, and is worshipped as God.

Tenth Book, Fourth Chapter :

22. Who that beholds this living temple of the living God formed of ourselves — this greatest and truly divine sanctuary, I say, whose inmost shrines are invisible to the multitude and are truly holy and a holy of holies — would venture to declare it? Who is able even to look within the sacred enclosure, except the great High Priest of all, to whom alone it is permitted to fathom the mysteries of every rational soul?
23. But perhaps it is granted to another, to one only, to be second after him in the same work, namely, to the commander of this army whom the first and great High Priest himself has honored with the second place in this sanctuary, the shepherd of your divine flock who has obtained your people by the allotment and the judgment of the Father, as if he had appointed him his own servant and interpreter, a new Aaron or Melchizedek, made like the Son of God, remaining and continually preserved by him in accordance with the united prayers of all of you.
24. To him therefore alone let it be granted, if not in the first place, at least in the second after the first and greatest High Priest, to observe and supervise the inmost state of your souls — to him who by experience and length of time has accurately proved each one, and who by his zeal and care has disposed you all in pious conduct and doctrine, and is better able than any one else to give an account, adequate to the facts, of those things which he himself has accomplished with the Divine assistance.
25. As to our first and great High Priest, it is said, 'Whatsoever he sees the Father doing those things likewise the Son also does.' John 5:19 So also this one, looking up to him as to the first teacher, with pure eyes of the mind, using as archetypes whatsoever things he sees him doing, produces images of them, making them so far as is possible in the same likeness, in nothing inferior to that Beseleel, whom God himself 'filled with the spirit of wisdom and understanding' Exodus 35:31 and with other technical and scientific knowledge, and called to be the maker of the temple constructed after heavenly types given in symbols.
26. Thus this one also bearing in his own soul the image of the whole Christ, the Word, the Wisdom, the Light, has formed this magnificent temple of the highest God, corresponding to the pattern of the greater as a visible to an invisible, it is impossible to say with what greatness of soul, with what wealth and liberality of mind, and with what emulation on the part of all of you, shown in the magnanimity of the contributors who have ambitiously striven in no way to be left behind by him in the execution of the same purpose. And this place — for this deserves to be mentioned first of all — which had been covered with all sorts of rubbish by the artifices of our enemies he did not overlook, nor did he yield to the wickedness of those who had brought about that condition of things, although he might have chosen some other place, for many other sites were available in the city, where he would have had less labor, and been free from trouble.

Despite superficial appearances to modern trinitarian Christians, there is nothing distinctly non-Arian about any of these paragraphs.