Objection 1. It would seem that the Father cannot be called the principle of the Son, or of the Holy Ghost. For principle and cause are the same, according to the Philosopher (Metaph. iv). But we do not say that the Father is the cause of the Son. Therefore we must not say that He is the principle of the Son.
Objection 2. Further, a principle is so called in relation to the thing principled. So if the Father is the principle of the Son, it follows that the Son is a person principled, and is therefore created; which appears false.
Objection 3. Further, the word principle is taken from priority. But in God there is no "before" and "after," as Athanasius says. Therefore in speaking of God we ought not to used the term principle.
On the contrary, Augustine says (De Trin. iv, 20), "The Father is the Principle of the whole Deity."
I answer that, The word "principle" signifies only that whence another proceeds: since anything whence something proceeds in any way we call a principle; and conversely. As the Father then is the one whence another proceeds, it follows that the Father is a principle.
Reply to Objection 1. The Greeks use the words "cause" and "principle" indifferently, when speaking of God; whereas the Latin Doctors do not use the word "cause," but only "principle." The reason is because "principle" is a wider term than "cause"; as "cause" is more common than "element." For the first term of a thing, as also the first part, is called the principle, but not the cause. Now the wider a term is, the more suitable it is to use as regards God (13, 11), because the more special terms are, the more they determine the mode adapted to the creature. Hence this term "cause" seems to mean diversity of substance, and dependence of one from another; which is not implied in the word "principle." For in all kinds of causes there is always to be found between the cause and the effect a distance of perfection or of power: whereas we use the term "principle" even in things which have no such difference, but have only a certain order to each other; as when we say that a point is the principle of a line; or also when we say that the first part of a line is the principle of a line.
Reply to Objection 2. It is the custom with the Greeks to say that the Son and the Holy Ghost are principled. This is not, however, the custom with our Doctors; because, although we attribute to the Father something of authority by reason of His being the principle, still we do not attribute any kind of subjection or inferiority to the Son, or to the Holy Ghost, to avoid any occasion of error. In this way, Hilary says (De Trin. ix): "By authority of the Giver, the Father is the greater; nevertheless the Son is not less to Whom oneness of nature is give."
Reply to Objection 3. Although this word principle, as regards its derivation, seems to be taken from priority, still it does not signify priority, but origin. For what a term signifies, and the reason why it was imposed, are not the same thing, as stated above (Question 13, Article 8).
Source: Summa Theologica (New Advent)