The Persons of the Godhead are a distinction and not a division. Augustine speaks clearly of the distinctions within the Godhead meaning as they belong to the Persons of the Trinity, when he says,

“Christ with respect to himself is called God; with respect to the Father, Son. Again, the Father with respect to himself is called God; with respect to the Son, Father. In so far as he is called Father with respect to the Son, he is not the Son; in so far as he is called the Son with respect to the Father, he is not the Father; in so far as he is called both Father with respect to himself, and Son with respect to himself, he is the same God.”