Today I talk about the Trinity ... and ... you know ... How not to be a heretic and stuff.

Aquinas on the Trinity

We must needs admit equality among the divine persons. For, according to the Philosopher (Metaph. x, text 15,16, 17), equality signifies the negation of greater or less. Now we cannot admit anything greater or less in the divine persons; for as Boethius says (De Trin. i): "They must needs admit a difference [namely, of Godhead] who speak of either increase or decrease, as the Arians do, who sunder the Trinity by distinguishing degrees as of numbers, thus involving a plurality." Now the reason of this is that unequal things cannot have the same quantity. But quantity, in God, is nothing else than His essence. Wherefore it follows, that if there were any inequality in the divine persons, they would not have the same essence; and thus the three persons would not be one God; which is impossible. We must therefore admit equality among the divine persons.

The Athanasian Creed

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. 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. What quality the Father has, the Son has, and the Holy Spirit has. The Father is uncreated, the Son is uncreated, the Holy Spirit is uncreated. The Father is immeasurable, the Son is immeasurable, the Holy Spirit is immeasurable. The Father is eternal, the Son is eternal, the Holy Spirit is eternal. And yet there are not three eternal beings; there is but one eternal being. So too there are not three uncreated or immeasurable beings; there is but one uncreated and immeasurable being. Similarly, the Father is almighty, the Son is almighty, the Holy Spirit is almighty. Yet there are not three almighty beings; there is but one almighty being. Thus the Father is God, the Son is God, the Holy Spirit is God. Yet there are not three gods; there is but one God. Thus the Father is Lord, the Son is Lord, the Holy Spirit is Lord. Yet there are not three lords; there is but one Lord. Just as Christian truth compels us to confess each person individually as both God and Lord, so catholic religion forbids us to say that there are three gods or lords. The Father was neither made nor created nor begotten from anyone. The Son was neither made nor created; he was begotten from the Father alone. The Holy Spirit was neither made nor created nor begotten; he proceeds from the Father and the Son. Accordingly there is one Father, not three fathers; there is one Son, not three sons; there is one Holy Spirit, not three holy spirits. Nothing in this trinity is before or after, nothing is greater or smaller; in their entirety the three persons are coeternal and coequal with each other. So in everything, as was said earlier, we must worship their trinity in their unity and their unity in their trinity. Anyone then who desires to be saved should think thus about the trinity. But it is necessary for eternal salvation that one also believe in the incarnation of our Lord Jesus Christ faithfully. Now this is the true faith: That we believe and confess that our Lord Jesus Christ, God's Son, is both God and human, equally. He is God from the essence of the Father, begotten before time; and he is human from the essence of his mother, born in time; completely God, completely human, with a rational soul and human flesh; equal to the Father as regards divinity, less than the Father as regards humanity. Although he is God and human, yet Christ is not two, but one. He is one, however, not by his divinity being turned into flesh, but by God's taking humanity to himself. He is one, certainly not by the blending of his essence, but by the unity of his person. For just as one human is both rational soul and flesh, so too the one Christ is both God and human. He suffered for our salvation; he descended to hell; he arose from the dead; he ascended to heaven; he is seated at the Father's right hand; from there he will come to judge the living and the dead. At his coming all people will arise bodily and give an accounting of their own deeds. Those who have done good will enter eternal life, and those who have done evil will enter eternal fire. This is the catholic faith: one cannot be saved without believing it firmly and faithfully.