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The Trinity is the term employed to signify the central doctrine of the Christian religion — the truth that in the unity of the Godhead there are Three Persons, the Father, the Son, and the Holy Spirit, these Three Persons being truly distinct one from another.

This is, I believe more of mormonism attempting to force Christian belief into a form to fit the mormonism box. by careful editing.

The ACTUAL comment from the link you posted to The Advent, Catholic Encylopedia is THIS:

"Thus, in the words of the Athanasian Creed: "the Father is God, the Son is God, and the Holy Spirit is God, and yet there are not three Gods but one God." In this Trinity of Persons the Son is begotten of the Father by an eternal generation, and the Holy Spirit proceeds by an eternal procession from the Father and the Son. Yet, notwithstanding this difference as to origin, the Persons are co-eternal and co-equal: all alike are uncreated and omnipotent. This, the Church teaches, is the revelation regarding God's nature which Jesus Christ, the Son of God, came upon earth to deliver to the world: and which she proposes to man as the foundation of her whole dogmatic system."