Whether the priesthood of Christ was according to the order of Melchisedech?

Objections

Objection 1 : It would seem that Christ's priesthood was not according to the order of Melchisedech. For Christ is the fountain-head of the entire priesthood, as being the principal priest. Now that which is principal is not . secondary in regard to others, but others are secondary in its regard. Therefore Christ should not be called a priest according to the order of Melchisedech.
Objection 2 : Further, the priesthood of the Old Law was more akin to Christ's priesthood than was the priesthood that existed before the Law. But the nearer the sacraments were to Christ, the more clearly they signified Him; as is clear from what we have said in the SS, Question [2], Article [7]. Therefore the priesthood of Christ should be denominated after the priesthood of the Law, rather than after the order of Melchisedech, which was before the Law.
Objection 3 : Further, it is written (Heb. 7:2,3): "That is 'king of peace,' without father, without mother, without genealogy; having neither beginning of days nor ending of life": which can be referred only to the Son of God. Therefore Christ should not be called a priest according to the order of Melchisedech, as of some one else, but according to His own order.