Objection 1. It would seem that Christ "paid tithes" in Abraham's loins. For the Apostle says (Hebrews 7:6-9) that Levi, the great-grandson of Abraham, "paid tithes in Abraham," because, when the latter paid tithes to Melchisedech, "he was yet in his loins." In like manner Christ was in Abraham's loins when the latter paid tithes. Therefore Christ Himself also paid tithes in Abraham.
Objection 2. Further, Christ is of the seed of Abraham according to the flesh which He received from His Mother. But His Mother paid tithes in Abraham. Therefore for a like reason did Christ.
Objection 3. Further, "in Abraham tithe was levied on that which needed healing," as Augustine says (Gen. ad lit. x). But all flesh subject to sin needed healing. Since therefore Christ's flesh was the subject of sin, as stated above (Article 7), it seems that Christ's flesh paid tithes in Abraham.
Objection 4. Further, this does not seem to be at all derogatory to Christ's dignity. For the fact that the father of a bishop pays tithes to a priest does not hinder his son, the bishop, from being of higher rank than an ordinary priest. Consequently, although we may say that Christ paid tithes when Abraham paid them to Melchisedech, it does not follow that Christ was not greater than Melchisedech.
On the contrary, Augustine says (Gen. ad lit. x) that "Christ did not pay tithes there," i.e. in Abraham, "for His flesh derived from him, not the heat of the wound, but the matter of the antidote."
I answer that, It behooves us to say that the sense of the passage quoted from the Apostle is that Christ did not pay tithes in Abraham. For the Apostle proves that the priesthood according to the order of Melchisedech is greater than the Levitical priesthood, from the fact that Abraham paid tithes to Melchisedech, while Levi, from whom the legal priesthood was derived, was yet in his loins. Now, if Christ had also paid tithes in Abraham, His priesthood would not have been according to the order of Melchisedech, but of a lower order. Consequently we must say that Christ did not pay tithes in Abraham's loins, as Levi did.
For since he who pays a tithe keeps nine parts to himself, and surrenders the tenth to another, inasmuch as the number ten is the sign of perfection, as being, in a sort, the terminus of all numbers which mount from one to ten, it follows that he who pays a tithe bears witness to his own imperfection and to the perfection of another. Now, to sin is due the imperfection of the human race, which needs to be perfected by Him who cleanses from sin. But to heal from sin belongs to Christ alone, for He is the "Lamb that taketh away the sin of the world" (John 1:29), whose figure was Melchisedech, as the Apostle proves (Hebrews 7). Therefore by giving tithes to Melchisedech, Abraham foreshadowed that he, as being conceived in sin, and all who were to be his descendants in contracting original sin, needed that healing which is through Christ. And Isaac, Jacob, and Levi, and all the others were in Abraham in such a way so as to be descended from him, not only as to bodily substance, but also as to seminal virtue, by which original sin is transmitted. Consequently, they all paid tithes in Abraham, i.e. foreshadowed as needing to be healed by Christ. And Christ alone was in Abraham in such a manner as to descend from him, not by seminal virtue, but according to bodily substance. Therefore He was not in Abraham so as to need to be healed, but rather "as the balm with which the wound was to be healed." Therefore He did not pay tithes in Abraham's loins.
Thus the answer to the first objection is made manifest.
Reply to Objection 2. Because the Blessed Virgin was conceived in original sin, she was in Abraham as needing to be healed. Therefore she paid tithes in him, as descending from him according to seminal virtue. But this is not true of Christ's body, as stated above.
Reply to Objection 3. Christ's flesh is said to have been subject to sin, according as it was in the patriarchs, by reason of the condition in which it was in His forefathers, who paid the tithes: but not by reason of its condition as actually in Christ, who did not pay the tithes.
Reply to Objection 4. The levitical priesthood was handed down through carnal origin: wherefore it was not less in Abraham than in Levi. Consequently, since Abraham paid tithes to Melchisedech as to one greater than he, it follows that the priesthood of Melchisedech, inasmuch as he was a figure of Christ, was greater than that of Levi. But the priesthood of Christ does not result from carnal origin, but from spiritual grace. Therefore it is possible that a father pay tithes to a priest, as the less to the greater, and yet his son, if he be a bishop, is greater than that priest, not through carnal origin, but through the spiritual grace which he has received from Christ.
Source: Summa Theologica (New Advent)