Chapter 3.
The statement of the Apostle, that all things are of the Father by the Son, does not separate the Spirit from Their company, since what is referred to one Person is also attributed to each. So those baptized in the Name of Christ are held to be baptized in the Name of the Father and of the Holy Spirit, if, that is, there is belief in the Three Persons, otherwise the baptism will be null. This also applies to baptism in the Name of the Holy Spirit. If because of one passage the Holy Spirit is separated from the Father and the Son, it will necessarily follow from other passages that the Father will be subordinated to the Son. The Son is worshipped by angels, not by the Spirit, for the latter is His witness, not His servant. Where the Son is spoken of as being before all, it is to be understood of creatures. The great dignity of the Holy Spirit is proved by the absence of forgiveness for the sin against Him. How it is that such sin cannot be forgiven, and how the Spirit is one.
32. But perhaps some one may say that there was a reason why the writer said that all things were of the Father, and all things through the Son, 1 Corinthians 8:6 but made no mention of the Holy Spirit, and would obtain the foundation of an argument from this. But if he persists in his perverse interpretation, in how many passages will he find the power of the Holy Spirit asserted, in which Scripture has stated nothing concerning either the Father or the Son, but has left it to be understood?
40. Where, then, the grace of the Spirit is asserted, is that of God the Father or of the Only-begotten Son denied? By no means; for as the Father is in the Son, and the Son in the Father, so, too, the love of God is shed abroad in our hearts by the Holy Spirit, Who has been given us. Romans 5:5 And as he who is blessed in Christ is blessed in the Name of the Father, and of the Son, and of the Holy Spirit, because the Name is one and the Power one; so, too, when any divine operation, whether of the Father, or of the Son, or of the Holy Spirit, is treated of, it is not referred only to the Holy Spirit, but also to the Father and the Son, and not only to the Father, but also to the Son and the Spirit.
41. Then, too, the Ethiopian eunuch of Queen Candace, when baptized in Christ, obtained the fullness of the sacrament. And they who said that they knew not of any Holy Spirit, although they said that they had been baptized with John's baptism, were baptized afterwards, because John baptized for the remission of sins in the Name of the coming Jesus, not in his own. And so they knew not the Spirit, because in the form in which John baptized they had not received baptism in the Name of Christ. For John, though he did not baptize in the Spirit, nevertheless preached Christ and the Spirit. And then, when he was questioned whether he were perchance himself the Christ, he answered: I baptize you with water, but a stronger than I shall come, Whose shoes I am not worthy to bear, He shall baptize you with the Holy Spirit and with fire. They therefore, because they had been baptized neither in the Name of Christ nor with faith in the Holy Spirit, could not receive the sacrament of baptism.
42. So they were baptized in the Name of Jesus Christ, and baptism was not repeated in their case, but administered differently, for there is but one baptism. But where there is not the complete sacrament of baptism, there is not considered to be a commencement nor any kind of baptism. But baptism is complete if one confess the Father, the Son, and the Holy Spirit. If you deny One you overthrow the whole. And just as if you mention in words One only, either the Father, or the Son, or the Holy Spirit, and in your belief do not deny either the Father, the Son, or the Holy Spirit, the mystery of the faith is complete, so, too, although you name the Father, Son, and Holy Spirit, and lessen the power of either the Father, the Son, or the Holy Spirit, the whole mystery is made empty. And, lastly, they who had said: We have not heard if there be any Holy Spirit, were baptized afterwards in the Name of the Lord Jesus Christ. And this was an additional abundance of grace, for now through Paul's preaching they knew the Holy Spirit.
43. Nor ought it to seem opposed to this, that although subsequently mention is not made of the Spirit, He is yet believed in, and what had not been mentioned in words is expressed in belief. For when it is said, In the Name of our Lord Jesus Christ, the mystery is complete through the oneness of the Name, and the Spirit is not separated from the baptism of Christ, since John baptized unto repentance, Christ in the Spirit.
44. Let us now consider whether as we read that the sacrament of baptism in the Name of Christ was complete, so, too, when the Holy Spirit alone is named, anything is wanting to the completeness of the mystery. Let us follow out the argument that he who has named One has signified the Trinity. If you name Christ, you imply both God the Father by Whom the Son was anointed, and the Son Himself Who was anointed, and the Holy Spirit with Whom He was anointed. For it is written: This Jesus of Nazareth, Whom God anointed with the Holy Spirit. Acts 10:38 And if you name the Father, you denote equally His Son and the Spirit of His mouth, if, that is, you apprehend it in your heart. And if you speak of the Spirit, you name also God the Father, from Whom the Spirit proceeds, and the Son, inasmuch as He is also the Spirit of the Son.
45. Wherefore that authority may also be joined to reason Scripture indicates that we can also be rightly baptized in the Spirit, when the Lord says: But you shall be baptized in the Holy Spirit. Acts 1:5 And in another place the Apostle says: For we were all baptized in the body itself into one Spirit. 1 Corinthians 12:13 The work is one, for the mystery is one; the baptism one, for there was one death on behalf of the world; there is, then, a oneness of working, a oneness of setting forth, which cannot be separated.
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Chapter 4.
The Holy Spirit is one and the same Who spoke in the prophets and apostles, Who is the Spirit of God and of Christ; Whom, further, Scripture designates the Paraclete, and the Spirit of life and truth.
55. But no one will doubt that the Spirit is one, although very many have doubted whether God be one. For many heretics have said that the God of the Old Testament is one, and the God of the New Testament is another. But as the Father is one Who both spoke of old, as we read, to the fathers by the prophets, and to us in the last days by His Son; Hebrews 1:1-2 and as the Son is one, Who according to the tenour of the Old Testament was offended by Adam, Genesis 3:17 seen by Abraham, Genesis 18:22-23 worshipped by Jacob; Genesis 28:17 so, too, the Holy Spirit is one, who energized in the prophets, 2 Peter 1:21 was breathed upon the apostles, John 20:22 and was joined to the Father and the Son in the sacrament of baptism. Matthew 28:19 For David says of Him: And take not Your Holy Spirit from me. And in another place he said of Him: Whither shall I go from Your Spirit?
56. That you may know that the Spirit of God is the same as the Holy Spirit, as we read also in the Apostle: No one speaking in the Spirit of God says Anathema to Jesus and no one can say, Lord Jesus, but in the Holy Spirit, 1 Corinthians 12:3 the Apostle calls Him the Spirit of God. He called Him also the Spirit of Christ, as you read: But you are not in the flesh but in the Spirit, if so be that the Spirit of God dwells in you. Romans 8:9 And farther on: But if the Spirit of Him Who raised Jesus from the dead dwells in you. Romans 8:11 The same is, then, the Spirit of God, Who is the Spirit of Christ.
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73. And with good cause did the Son of God say: Go and baptize all nations in the Name of the Father, and of the Son, and of the Holy Spirit, Matthew 28:19 not disdaining association with the Holy Spirit. Why, then, do some take it ill that He Whom the Lord disdained not in the sacrament of baptism, should be joined in our devotion with the Father and the Son?
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132. Who, then, would dare to deny the oneness of Name, when he sees the oneness of the working. But why should I maintain the unity of the Name by arguments, when there is the plain testimony of the Divine Voice that the Name of the Father, the Son, and the Holy Spirit is one? For it is written: Go, baptize all nations in the Name of the Father, and of the Son, and of the Holy Spirit. Matthew 28:19 He said, in the Name, not in the Names. So, then, the Name of the Father is not one, that of the Son another, and that of the Holy Spirit another, for God is one; the Names are not more than one, for there are not two Gods, or three Gods.
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http://www.newadvent.org/fathers/34021.htm