Objection 1. It would seem that Christ's soul should not be adored with the adoration of "latria." For on the words of Psalm 98:5, "Adore His foot-stool for it is holy," a gloss says: "The flesh assumed by the Word of God is rightly adored by us: for no one partakes spiritually of His flesh unless he first adore it; but not indeed with the adoration called 'latria,' which is due to the Creator alone." Now the flesh is part of the humanity. Therefore Christ's humanity is not to be adored with the adoration of "latria."
Objection 2. Further, the worship of "latria" is not to be given to any creature: since for this reason were the Gentiles reproved, that they "worshiped and served the creature," as it is written (Romans 1:25). But Christ's humanity is a creature. Therefore it should not be adored with the adoration of "latria."
Objection 3. Further, the adoration of "latria" is due to God in recognition of His supreme dominion, according to Deuteronomy 6:13: "Thou shalt adore [Vulgate: 'fear'; cf. Matthew 4:10] the Lord thy God, and shalt serve Him only." But Christ as man is less than the Father. Therefore His humanity is not to be adored with the adoration of "latria."
On the contrary, Damascene says (De Fide Orth. iv, 3): "On account of the incarnation of the Divine Word, we adore the flesh of Christ not for its own sake, but because the Word of God is united thereto in person." And on Psalm 98:5, "Adore His foot-stool," a gloss says: "He who adores the body of Christ, regards not the earth, but rather Him whose foot-stool it is, in Whose honor he adores the foot-stool." But the incarnate Word is adored with the adoration of "latria." Therefore also His body or His humanity.
I answer that, As stated above (Article 1) adoration is due to the subsisting hypostasis: yet the reason for honoring may be something non-subsistent, on account of which the person, in whom it is, is honored. And so the adoration of Christ's humanity may be understood in two ways. First, so that the humanity is the thing adored: and thus to adore the flesh of Christ is nothing else than to adore the incarnate Word of God: just as to adore a King's robe is nothing else than to adore a robed King. And in this sense the adoration of Christ's humanity is the adoration of "latria." Secondly, the adoration of Christ's humanity may be taken as given by reason of its being perfected with every gift of grace. And so in this sense the adoration of Christ's humanity is the adoration not of "latria" but of "dulia." So that one and the same Person of Christ is adored with "latria" on account of His Divinity, and with "dulia" on account of His perfect humanity.
Nor is this unfitting. For the honor of "latria" is due to God the Father Himself on account of His Godhead; and the honor of "dulia" on account of the dominion by which He rules over creatures. Wherefore on Psalm 7:1, "O Lord my God, in Thee have I hoped," a gloss says: "Lord of all by power, to Whom 'dulia' is due: God of all by creation, to Whom 'latria' is due."
Reply to Objection 1. That gloss is not to be understood as though the flesh of Christ were adored separately from its Godhead: for this could happen only, if there were one hypostasis of God, and another of man. But since, as Damascene says (De Fide Orth. iv, 3): "If by a subtle distinction you divide what is seen from what is understood, it cannot be adored because it is a creature"--that is, with adoration of "latria." And then thus understood as distinct from the Word of God, it should be adored with the adoration of "dulia"; not any kind of "dulia," such as is given to other creatures, but with a certain higher adoration, which is called "hyperdulia."
Hence appear the answers to the second and third objections. Because the adoration of "latria" is not given to Christ's humanity in respect of itself; but in respect of the Godhead to which it is united, by reason of which Christ is not less than the Father.
Source: Summa Theologica (New Advent)