G. Reale, A History of Ancient Philosophy: The Schools of the Imperial Age, trans. John R. Catan (Albany: State University of New York Press, 1990) 266.
Numenius of Apamea lived in the second century C.E., and he was a forerunner of the Neo-Platonists. He had a conception of God that Reale calls "trinitarian." According to Proclus, "Numenius proclaimed three Gods and calls the first 'Father'; the second 'Creator'; the third 'Creation'; in fact according to him, the Cosmos is the third God."
I don't profess to understand the intricacies of Numenius' trinity, but what I got from the chapter was the following:
There is the "first God," who is transcendent and thinks about the eternal forms. According to Plato, what exists on earth is an imperfect reflection of the eternal forms in heaven. On earth, we see a horse, for example. In heaven, there's an idea of the perfect horse, the "horse form." Horses on earth may differ from one another, but they all reflect the "horse form," the definition of "horse" that exists in heaven.
There is the "second God," the Demiurge, who organized matter according to the first God's forms, thereby creating the Cosmos.
Then there's the Cosmos, which has a "soul" that's reasonable. At the same time, the matter that the Demiurge used to fashion the Cosmos is evil and chaotic, and it continually tries to disrupt the order and rationality of the universe. We are a microcosm of this set-up, as we try to tame our inward evil and submit to a good rational order.
There's a lot that I don't understand about this. For example, does the Cosmos consciously try to subordinate chaotic matter? If so, how? Ancient Near Eastern religion, including that of the Israelites, maintained that the deity continually needed to defeat chaos in order to preserve and uphold the order of creation. Does Neo-Pythagoreanism have something similar to this? Does the Demiurge continue to keep order in the universe, or did it retire right after creation?
In some sense, Numenius' trinity resembles that of Christianity, at least from a certain point of view. Armstrongites did not believe in the trinity, but they did maintain that God is a binity of Father and Son. In their view, the Father was utterly transcendent, one whom no one has seen at any time (John 1:18). The Son was the one who created all things, much like the Demiurge (John 1:3; Colossians 1:16; Hebrews 1:2). Moreover, since John 5:37 says regarding the Father that "You have never heard his voice or seen his form," Armstrongites conclude that the "God" we encounter in the Old Testament is actually Jesus Christ, who speaks on God the Father's behalf. And, in the same way that the Demiurge modelled himself after the Father at creation, the Son does what he sees the Father doing (John 5:19, 30).
I'm not sure to what extent the cosmic soul resembles the Holy Spirit. In the Bible, the Spirit plays an important role in creation (Genesis 1:2; Psalm 104:30), as well as other aspects of God's activity on earth, such as empowering people for ministry (Judges 3:10; 6:34; Matthew 12:28; Acts 2). In a sense, God's spirit keeps evil in check, the same way that the rational world soul is in tension with evil matter. Another possible commonality is that both the rational world soul and the Holy Spirit are involved in some way with people's moral behavior: people can choose either to follow rationality or the Holy Spirit, or they can go the way of evil (John 16:8). Moreover, rationality and the Holy Spirit are in the human being (or, actually, the Holy Spirit is in Christians; Romans 8; I Corinthians 2).
The above may not be the only way to conceptualize the Bible's teachings about the Godhead, for the Father is not always utterly transcendent. In Matthew 6, for example, Jesus presents the Father as someone who hears prayer and provides for his children. But some Christians may say that the Father became less transcendent once Jesus reconciled people to him.
I'm not sure if Numenius was copying the Christian trinity. The concept of an intermediary between God and humanity did not originate with Christianity, for Philo's idea of the logos as an intermediary "second God" drew from Greek philosophy. And Plato's concept of the Demiurge existed long before.
Trinities exist in different cultures. A professor of mine once said that Egypt had one. I've heard that Hinduism has one as well. They're not necessarily similar in all aspects to the Christian trinity, but there's obviously something significant about the number "three" to a variety of cultures.