Your problem is in your word choice. There are not three persons, there are three hypostases. This is akin to describing the three aspects of time; past, present, and future, or the three dimensions of an object. Each are unique, but wholly a part of the Ousia.
*****Your problem is in your word choice. There are not three persons, there are three hypostases. This is akin to describing the three aspects of time; past, present, and future, or the three dimensions of an object. Each are unique, but wholly a part of the Ousia. *****
Even though the Three Persons are One God, yet they are distinct: for the Father has no origin, He came from no one. But the Son is begotten, He comes from the Father alone. The Holy Spirit comes or proceeds from both the Father and the Son. These different relations of origin tell us there are three distinct Persons, who have one and the same divine nature.
http://www.ewtn.com/faith/teachings/GODA22.htm