The Son and the Spirit are also God

Jesus Christ Himself, who came (into the world), was born of the Father before all creatures; that, after He had been the servant of the Father in the creation of all things—“For by Him were all things made”—He in the last times, divesting Himself (of His glory), became a man, and was incarnate although God, and while made a man remained the God which He was; that He assumed a body like to our own, differing in this respect only, that it was born of a virgin and of the Holy Spirit:  that this Jesus Christ was truly born, and did truly suffer, and did not endure this death common (to man) in appearance only, but did truly die; that He did truly rise from the dead; and that after His resurrection He conversed with His disciples, and was taken up (into heaven).

Then, Thirdly, the apostles related that the Holy Spirit was associated in honour and dignity with the Father and the Son.  But in His case it is not clearly distinguished whether He is to be regarded as born or innate, or also as a Son of God or not:  for these are points which have to be inquired into out of sacred Scripture according to the best of our ability, and which demand careful investigation.  And that this Spirit inspired each one of the saints, whether prophets or apostles; and that there was not one Spirit in the men of the old dispensation, and another in those who were inspired at the advent of Christ, is most clearly taught throughout the Churches.

Origen
On First Principles, Book I
Preface

We are cleansed through Baptism to receive the Holy Spirit which connects us to the Church

Not that in the waters we obtain the Holy Spirit; but in the water, under (the witness of) the angel, we are cleansed, and prepared for the Holy Spirit. In this case also a type has preceded; for thus was John beforehand the Lord’s forerunner, “preparing His ways.” Thus, too, does the angel, the witness of baptism, “make the paths straight” for the Holy Spirit, who is about to come upon us, by the washing away of sins, which faith, sealed in (the name of) the Father, and the Son, and the Holy Spirit, obtains.

Moreover, after the pledging both of the attestation of faith and the promise of salvation under “three witnesses,” there is added, of necessity, mention of the Church; inasmuch as, wherever there are three, (that is, the Father, the Son, and the Holy Spirit, ) there is the Church, which is a body of three.

Tertullian
On Baptism
Chapter VI

The revelation of the Trinity makes the New Covenant possible

What need would there be of the gospel, which is the substance of the New Covenant, laying down (as it does) that the Law and the Prophets lasted until John the Baptist, if thenceforward the Father, the Son, and the Spirit are not both believed in as Three, and as making One Only God? God was pleased to renew His covenant with man in such a way as that His Unity might be believed in, after a new manner, through the Son and the Spirit, in order that God might now be known openly, in His proper Names and Persons, who in ancient times was not plainly understood, though declared through the Son and the Spirit.

Tertullian
Against Praxeas
Chapter XXXI

The Holy Spirit is the third person of the Godhead

He will come again on the clouds of heaven, just as He appeared when He ascended into heaven. Meanwhile He has received from the Father the promised gift, and has shed it forth, even the Holy Spirit—the Third Name in the Godhead, and the Third Degree of the Divine Majesty; the Declarer of the One Monarchy of God…

Tertullian
Against Praxeas
Chapter XXX

The Father did not suffer

Then, again, the Father is as incapable of fellow-suffering as the Son even is of suffering under the conditions of His existence as God. Well, but how could the Son suffer, if the Father did not suffer with Him? My answer is, The Father is separate from the Son, though not from Him as God.

Tertullian
Against Praxeas
Chapter XXIX

Christians are baptised by immersion into three persons

After His resurrection He promises in a pledge to His disciples that He will send them the promise of His Father; and lastly, He commands them to baptize into the Father and the Son and the Holy Ghost, not into a unipersonal God. And indeed it is not once only, but three times, that we are immersed into the Three Persons, at each several mention of Their names.

Tertullian
Against Praxeas
Chapter XXVI

The Son and Spirit belong to the Father and so are not the same as the Father, but are both God

For both the Spirit is the substance of the Word, and the Word is the operation of the Spirit, and the Two are One (and the same). Now John must mean One when he speaks of Him as “having been made flesh,” and the angel Another when he announces Him as “about to be born,” if the Spirit is not the Word, and the Word the Spirit. For just as the Word of God is not actually He whose Word He is, so also the Spirit (although He is called God) is not actually He whose Spirit He is said to be. Nothing which belongs to something else is actually the very same thing as that to which it belongs.

…And thus the Spirit is God, and the Word is God, because proceeding from God, but yet is not actually the very same as He from whom He proceeds. Now that which is God of God, although He is an actually existing thing, yet He cannot be God Himself (exclusively), but so far God as He is of the same substance as God Himself, and as being an actually existing thing

Tertullian
Against Praxeas
Chapter XXVI

Father, Son and Spirit are three persons but one essence

Thus the connection of the Father in the Son, and of the Son in the Paraclete, produces three coherent Persons, who are yet distinct One from Another. These Three are one essence, not one Person, as it is said, “I and my Father are One,” in respect of unity of substance not singularity of number.

Tertullian
Against Praxeas
Chapter XXV

John 1:1 can only be interpreted to mean one thing — Christ is God but distinct from the Father

…first of all there comes at once to hand the preamble of John to his Gospel, which shows us what He previously was who had to become flesh.  “In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God: all things were made by Him, and without Him was nothing made.” Now, since these words may not be taken otherwise than as they are written, there is without doubt shown to be One who was from the beginning, and also One with whom He always was: one the Word of God, the other God (although the Word is also God, but God regarded as the Son of God, not as the Father); One through whom were all things, Another by whom were all things.  But in what sense we call Him Another we have already often described. In that we called Him Another, we must needs imply that He is not identical—not identical indeed, yet not as if separate; Other by dispensation, not by division.

Tertullian
Against Praxeas
Chapter XXI

Praxeas’ heresy mistakenly uses a few passages against a great many

For, inasmuch as only a few testimonies are to be found (making for them) in the general mass, they pertinaciously set off the few against the many, and assume the later against the earlier. The rule, however, which has been from the beginning established for every case, gives its prescription against the later assumptions, as indeed it also does against the fewer.

Tertullian
Against Praxeas
Chapter XX