In chapter 4 of his work On the Trinity (De Trinitate), Augustine explains “What the Doctrine of the Catholic Faith is Concerning the Trinity.” The “Catholic faith” is the faith believed by all true Christians.
All those Catholic expounders of the divine Scriptures, both Old and New, whom I have been able to read, who have written before me concerning the Trinity, Who is God, have purposed to teach, according to the Scriptures, this doctrine, that the Father, and the Son, and the Holy Spirit intimate a divine unity of one and the same substance in an indivisible equality; and therefore that they are not three Gods, but one God: although the Father hath begotten the Son, and so He who is the Father is not the Son; and the Son is begotten by the Father, and so He who is the Son is not the Father; and the Holy Spirit is neither the Father nor the Son, but only the Spirit of the Father and of the Son, Himself also co-equal with the Father and the Son, and pertaining to the unity of the Trinity.
He goes on:
Yet not that this Trinity was born of the Virgin Mary, and crucified under Pontius Pilate, and buried, and rose again the third day, and ascended into heaven, but only the Son. Nor, again, that this Trinity descended in the form of a dove upon Jesus when He was baptized; nor that, on the day of Pentecost, after the ascension of the Lord, when “there came a sound from heaven, as of a rushing mighty wind,” the same Trinity “sat upon each of them with cloven tongues like as of fire,” but only the Holy Spirit. Nor yet that this Trinity said from heaven, “Thou art my Son,” whether when He was baptized by John, or when the three disciples were with Him in the mount, or when the voice sounded, saying, “I have both glorified it, and will glorify it again;” but that it was a word of the Father only, spoken to the Son; although the Father, and the Son, and the Holy Spirit, as they are indivisible, so work indivisibly. This is also my faith, since it is the Catholic faith.
In chapter 5, Augustine summarizes that “the Father is God, and the Son God, and the Holy Spirit God, and yet that this Trinity is not three Gods, but one God.”
The Athanasian Creed upholds Augustine’s conclusion:
Now this is the catholic faith: That we worship one God in trinity and the trinity in unity, neither blending their persons nor dividing their essence. For the person of the Father is a distinct person, the person of the Son is another, and that of the Holy Spirit still another. But the divinity of the Father, Son, and Holy Spirit is one, their glory equal, their majesty coeternal.
The Creed warns, “Whoever desires to be saved should above all hold to the catholic faith. Anyone who does not keep it whole and unbroken will doubtless perish eternally.”