After Baptism the laying on of hands and invoking the Holy Spirit is performed

In the next place the hand is laid on us, invoking and inviting the Holy Spirit through benediction.

…Then, over our cleansed and blessed bodies willingly descends from the Father that Holiest Spirit. Over the waters of baptism, recognising as it were His primeval seat…

 

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 Son is of the same substance and the Spirit proceeds from the Father through the Son

But as for me, who derive the Son from no other source but from the substance of the Father, and (represent Him) as doing nothing without the Father’s will, and as having received all power from the Father, how can I be possibly destroying the Monarchy from the faith, when I preserve it in the Son just as it was committed to Him by the Father? The same remark (I wish also to be formally) made by me with respect to the third degree in the Godhead, because I believe the Spirit to proceed from no other source than from the Father through the Son. Look to it then, that it be not you rather who are destroying the Monarchy, when you overthrow the arrangement and dispensation of it, which has been constituted in just as many names as it has pleased God to employ.

Tertullian
Against Praxeas
Chapter IV

The Son and the Holy Spirit are the same substance as the Father

Therefore, inasmuch as the Divine Monarchy also is administered by so many legions and hosts of angels, according as it is written, “Thousand thousands ministered unto Him, and ten thousand times ten thousand stood before Him;” and since it has not from this circumstance ceased to be the rule of one (so as no longer to be a monarchy), because it is administered by so many thousands of powers; how comes it to pass that God should be thought to suffer division and severance in the Son and in the Holy Ghost, who have the second and the third places assigned to them, and who are so closely joined with the Father in His substance, when He suffers no such (division and severance) in the multitude of so many angels? Do you really suppose that Those, who are naturally members of the Father’s own substance, pledges of His love, instruments of His might, nay, His power itself and the entire system of His monarchy, are the overthrow and destruction thereof? You are not right in so thinking.

Tertullian
Against Praxeas
Chapter III

God created all things out of nothing, not forming them from any existing material

If any material was necessary to God in the creation of the world, as Hermogenes supposed, God had a far nobler and more suitable one in His own wisdom—one which was not to be gauged by the writings of philosophers, but to be learnt from the words or prophets. This alone, indeed, knew the mind of the Lord. For “who knoweth the things of God, and the things in God, but the Spirit, which is in Him?” Now His wisdom is that Spirit. This was His counsellor, the very way of His wisdom and knowledge. Of this He made all things, making them through It, and making them with It.

Tertullian
Against Hermogenes
Chapter XVIII

The Holy Spirit enables man to fulfill his calling as a creature of God

The Christian Church lives by the Holy Spirit. The Spirit alone is the guarantee of God’s Kingdom on earth. He is the sole guarantee that God’s life and truth and love are with men. Only by the Holy Spirit can man and the world fulfill that for which they were created by God. All of God’s actions toward man and the world—in creation, salvation and final glorification—are from the Father through the Son (Word) in the Holy Spirit; and all of man’s capabilities of response to God are in the same Spirit, through the same Son to the same Father.

Thomas Hopko
From the Series: The Orthodox Church
Volume I – Doctrine and Scripture: The Symbol of Faith

Jesus is the source of the Holy Spirit

Now, that the very Lord Himself of all might, the Word and Spirit of the Father, was operating and preaching on earth, it was necessary that the portion of the Holy Spirit which, in the form of the prophetic gift, had been through John preparing the ways of the Lord, should now depart from John, and return back again of course to the Lord, as to its all-embracing original.

Tertullian
The Five Books Against Marcion, Book IV
Chapter XVIII

The Spirit of God is God

We must at the outset hold fast the meaning of the Greek scripture, which has afflatus, not spirit. Some interpreters of the Greek, without reflecting on the difference of the words, and careless about their exact meaning, put spirit for afflatus; they thus afford to heretics an opportunity of tarnishing the Spirit of God, that is to say, God Himself, with default.

Tertullian
The Five Books Against Marcion, Book II
Chapter IX

The Holy Spirit revealed all truth to the Apostles so that they needed no further revelation of truth

He had once said, “I have yet many things to say unto you, but ye cannot hear them now;” but even then He added, “When He, the Spirit of truth, shall come, He will lead you into all truth.” He (thus) shows that there was nothing of which they were ignorant, to whom He had promised the future attainment of all truth by help of the Spirit of truth.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXII

The Greeks had vague references to the Trinity

For I pass over Plato; he plainly, in the Epistle to Erastus and Coriscus, is seen to exhibit the Father and Son somehow or other from the Hebrew Scriptures, exhorting in these words: “In invoking by oath, with not illiterate gravity, and with culture, the sister of gravity, God the author of all, and invoking Him by oath as the Lord, the Father of the Leader, and author; whom if ye study with a truly philosophical spirit, ye shall know.” And the address in the Timœus calls the creator, Father, speaking thus: “Ye gods of gods, of whom I am Father; and the Creator of your works.” So that when he says, “Around the king of all, all things are, and because of Him are all things; and he [or that] is the cause of all good things; and around the second are the things second in order; and around the third, the third,” I understand nothing else than the Holy Trinity to be meant; for the third is the Holy Spirit, and the Son is the second, by whom all things were made according to the will of the Father.

Clement of Alexandria
The Stromata, Book V
Chapter XIV