Perichoresis! So hot right now.
Actually, so hot all the time. The confession that the persons of the Trinity mutually indwell each other –“I am in the Father and the Father is in me”– is directly evident from Scripture, has been confessed in the church “always, at all times, by everyone” (in Vincent of Lerins’ terms), and is an especially beautiful piece of Christian doctrine. Three cheers for perichoresis! (Exactly three.)
Polanus’ treatment of the doctrine has a number of virtues. First, he keeps the doctrine very close to the confession that the persons of the Trinity have the identical divine nature; in fact, he builds a reference to the unity of nature into his very definition of perichoresis. Second, he brings great verbal resourcefulness to the doctrine, offering a large number of appropriate ways to speak about it –there is something almost playful in the way he moves from one Latin formulation to another. And third, he handles it with a special rhetorical flourish, especially at the conclusion, where he brings the section to a point by borrowing the very words of a conclusion from one of Augustine’s books of On the Trinity.
Here is Ryan Hurd’s translation of this section:
The περιχωρησις or εμπεριχωρησις εναλληλος of divine persons is that tightest union whereby one person is in another, not like an accident is in a subject, but such that one person permeates another whole in all respects and embraces it always and inseparably, thanks to the essence one and the same in number, which the individual persons possess as a whole. “That Word was with God” (John 1:1); “The Father who remains in me, he himself is doing the works. Believe me that I am in the Father and the Father is in me” (10:38; 14:10–11).
The Greeks call this type of absolutely perfect union περιχωρησις, and is the union whereby some thing embraces and permeates another whole—and not the sort of union where one is coupled up with another. The Greek Fathers also call this περιχωρησις of divine persons ιδρυσις (session, sitting, situated-together-with); μονη (dwelling); and likewise εμμονη εναλληλος (mutual indwelling), whereby the divine persons always co-exist and dwell one in the other. The Latin Fathers and scholastics call it the circumincessio (circuminsession); influentia mutua (mutual in-flowing) of persons; immanentia mutua (mutual immanence); immeatio (“passing through”); commeatio (“co-passing-through”); or permeatio (permeation), and likewise circumplexum (circumplexion).
Thanks to this περιχωρησις and the identity of or the absolutely singular, maximally one unity of the essence in the persons, the persons are ενυποστατοι: the Father is in the Son, the Son is in the Father, and the Holy Spirit is in the Father and Son, whereof there is essential virtue and ενυποστατος to each, in such a way that despite this the persons and their personal properties are not confounded between themselves. With this, not the distinction but the disjunction of the persons is excluded.
Due to this περιχωρησις εναλληλος, these three persons are absolutely always simultaneous both in every single place and in every single thing and each always in themselves, such that wherever one of the persons is in actual reality, likewise also the other is present there in actual reality.
Father, Son, and Holy Spirit are the essence one in number; therefore, one divine person is necessarily in another.
Hilary deals with this mystery, as does Ambrose and also Augustine, where the latter concludes Book Six of On the Trinity this way:
“Thus they are each in each, all in each, each in all, all in all, and all are one. Let him who sees this either partly or through a mirror and darkly rejoice because he is knowing God, and so let him honor God and give him thanks. But he who does not see this, let him strive by piety to see, not by blindness to berate: for God is one, but still Trinity. Do not take this in a confused way: ‘From whom all things, through whom all things, in whom all things,’ as meaning many gods, but let glory be to Him forever and ever.”
 Hilary of Poitiers, On the Trinity, IV.
 Ambrosiaster, on 2 Corinthians 13:13.
 Augustine, On the Trinity VI:12.
And here is our conversation about it:
Just a couple of links here on the three sources Polanus cites:
Hilary of Poitiers, On the Trinity, Book IV. Probably the section Polanus has in mind is section 40, where Hilary makes his aggressively anti-Arian point thus: “Thus God is in God, and it is God in Whom God dwells. But how is ‘There is no God beside You’ true, if God be within Him? Heretic!”
Ambrosiaster, on 2 Corinthians 13. Polanus identifies this author as Ambrose, so he could mean either Ambrose of Milan (who says, “If there is one grace, one peace, one love and one fellowship on the part of the Father and of the Son and of the Holy Spirit, surely there is one operation, and where there is one operation, certainly the power cannot be divided or the substance separated.” But he might also mean the commentator we now call Ambrosiaster. Since 2009, you can read Ambrosiaster’s commentary on Paul in this swell edition. On this same passage, Ambrosiaster says, “Here is the intertwining of the Trinity and the unity of power which brings all salvation to fulfillment. The love of God has sent us Jesus the Savior, by whose grace we have been saved. The fellowship of the Holy Spirit makes it possible for us to possess the grace of salvation, for he guards those who are loved by God and saved by the grace of Christ, so that the completeness of the Three may be the saving fulfillment of mankind. ” I’m guessing that Polanus has this latter quote in mind.
Augustine, On the Trinity VI:12. Polanus quotes a chunk of text from the end of the sixth book of Augustine’s De Trinitate. Here’s a link to the Haddan translation of it; scroll to the bottom.