Objection 1. It would seem that adoration is not an act of latria or religion. The worship of religion is due to God alone. But adoration is not due to God alone: since we read (Genesis 18:2) that Abraham adored the angels; and (1 Kings 1:23) that the prophet Nathan, when he was come in to king David, "worshiped him bowing down to the ground." Therefore adoration is not an act of religion.
Objection 2. Further, the worship of religion is due to God as the object of beatitude, according to Augustine (De Civ. Dei x, 3): whereas adoration is due to Him by reason of His majesty, since a gloss on Psalm 28:2, "Adore ye the Lord in His holy court," says: "We pass from these courts into the court where we adore His majesty." Therefore adoration is not an act of latria.
Objection 3. Further, the worship of one same religion is due to the three Persons. But we do not adore the three Persons with one adoration, for we genuflect at each separate invocation of Them [At the adoration of the Cross, on Good Friday]. Therefore adoration is not an act of latria.
On the contrary, are the words quoted Matthew 4:10: "The Lord thy God shalt thou adore and Him only shalt thou serve."
I answer that, Adoration is directed to the reverence of the person adored. Now it is evident from what we have said (81, 2,4) that it is proper to religion to show reverence to God. Hence the adoration whereby we adore God is an act of religion.
Reply to Objection 1. Reverence is due to God on account of His excellence, which is communicated to certain creatures not in equal measure, but according to a measure of proportion; and so the reverence which we pay to God, and which belongs to latria, differs from the reverence which we pay to certain excellent creatures; this belongs to dulia, and we shall speak of it further on (103). And since external actions are signs of internal reverence, certain external tokens significative of reverence are offered to creatures of excellence, and among these tokens the chief is adoration: yet there is one thing which is offered to God alone, and that is sacrifice. Hence Augustine says (De Civ. Dei x, 4): "Many tokens of Divine worship are employed in doing honor to men, either through excessive humility, or through pernicious flattery; yet so that those to whom these honors are given are recognized as being men to whom we owe esteem and reverence and even adoration if they be far above us. But who ever thought it his duty to sacrifice to any other than one whom he either knew or deemed or pretended to be a God?" Accordingly it was with the reverence due to an excellent creature that Nathan adored David; while it was the reverence due to God with which Mardochai refused to adore Aman fearing "lest he should transfer the honor of his God to a man" (Esther 13:14).
Again with the reverence due to an excellent creature Abraham adored the angels, as did also Josue (Joshua 5:15): though we may understand them to have adored, with the adoration of latria, God Who appeared and spoke to them in the guise of an angel. It was with the reverence due to God that John was forbidden to adore the angel (Apocalypse 22:9), both to indicate the dignity which he had acquired through Christ, whereby man is made equal to an angel: wherefore the same text goes on: "I am thy fellow-servant and of thy brethren"; as also to exclude any occasion of idolatry, wherefore the text continues: "Adore God."
Reply to Objection 2. Every Divine excellency is included in His majesty: to which it pertains that we should be made happy in Him as in the sovereign good.
Reply to Objection 3. Since there is one excellence of the three Divine Persons, one honor and reverence is due to them and consequently one adoration. It is to represent this that where it is related (Genesis 18:2) that three men appeared to Abraham, we are told that he addressed one, saying: "Lord, if I have found favor in thy sight," etc. The triple genuflection represents the Trinity of Persons, not a difference of adoration.
Source: Summa Theologica (New Advent)