the Divine Nature
Below are some relevant quotes from a book which I recommend as a good resource for Catholics:
The Teachings of the Church Fathers
by John R. Willis S.J.
50. The essence of God is His very existence.
St. Hilary: "It is known that there is nothing more characteristic of God than to be....what is divine is not liable to destruction nor does it have a beginning...."
St. Gregory Nazianzen: "But we are enquiring into a Nature Whose Being is absolute and not into Being bound up with something else." "He is Eternal Being."
St. John of Damascus: "For He keeps all being in His own embrace, like a sea of essence infinite and unseen."
51. God is per se independent existence
St. Athanasius: "God has being, and men are said to be, having received from God this gift also. Yet does God create as men do? or is His being as man's being? Perish the thought.... God, being without parts, is Father of the Son without partition or passion."
St. Hilary: "It is the Father from whom everything that exists has been formed.... His being is in Himself and He does not derive what He is from anywhere else, but possesses what He is from Himself and in Himself. He is infinite.... He is always outside of space because He is not restricted; He is always before time because time comes from Him."
52. The divine attributes are really the same as the divine substance
St. Augustine: "God's substance is eternity itself, which has nothing changeable. There, nothing is past as if it were no longer; nothing is future, as if it existed not as yet. There is nothing there but, Is."
St. Augustine: "But in God to be is the same as to be strong, or to be just, or to be wise, or whatever is said of that simple multiplicity, or multifold simplicity, whereby to signify His substance."
53. God is utter simplicity, and admits of no composition whatever
St. Clement of Alexandria: "Nor are any parts to be predicated of Him. For the One is indivisible; wherefore also it is infinite…. there is nothing antecedent to the Unbegotten."
Origen: "God, therefore, is not to be thought of as being either a body or as existing in a body, but as an uncompounded intellectual nature, admitting within Himself no addition of any kind; so that He cannot be believed to have within Him a greater and a less…."
St. Athanasius: "If then any man conceives God to be compound, as accident is in essence, or to have any external envelopment and to be encompassed, or as if there is anything about Him which completes the essence, so that when we say 'God,' or name 'Father,' we do not signify the invisible and incomprehensible essence, but something about it, then let them complain of the Council's stating that the Son was from the essence of God; but let them reflect, that in thus considering they utter two blasphemies; for they make God corporeal, and they falsely say that the Lord is not Son of the very Father, but of what is about Him…."
St. Basil: "God is universally confessed to be simple and not composite."
St. Augustine: "God is of an uncompounded nature; nothing can be added to Him, and that alone which is Divine has He in His nature…."
St. Augustine: "in God nothing is said to be according to accident, because in Him nothing is changeable…."
St. Cyril of Alexandria: "We are made to [God's] image and likeness. But … we are at an infinite distance. For we are not simple by nature, whereas the divinity, which is perfectly simple and not composite, possesses in itself every perfection, and nothing is lacking to it."
Roman Catholic theologian