The following is some rich material on the “divine nature” or the “Godhead” from the Synopsis Purioris Theologiae (1625).
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In using the phrase “divine Essence” we mean that what God is; for “to be” is said of Him (Hebrews 11:6, and ho ōn kai ho ēn, Revelation 4:8). To Him are attributed “nature,” phusis (Galatians 4:8), and “divine nature” (2Peter 1:4; although it is restricted to the divine properties), theotēs, “deity” (Colossians 2:9) and theiotēs, “divinity” (Romans 1:20), and to theion, “the divine” or “the godhead” (Acts 17:29), and morphē theou, “the form of God” (Philippians 2:6); and He is called theos, “God” (Acts 17:24, 29). From and in this divine nature all things are and exist, everything by means of its own way of participation. . .
Now this name for God is exercised in two ways in the Scriptures, either essentially in the proper and usual way, or in an improper way. In the proper way, the word “God” is used either of the essence of the Godhead, when the word is taken generally without specifying the divine persons, as in “God is Spirit” (John 4:24), or personally, when the name of God is attributed to a certain person as subject, as of the Father (Romans 7:25, and 8:3), of the Son (1Timothy 3:16, Acts 20:28), and of the Holy Spirit (Acts 5:4). However, it is appropriated to the Father especially (Romans 1:1), both because of the relation between the persons, as well as because of the economy and plan that was established in order to maintain the mystery of our salvation.
In the improper and wrong sense the name “God” is bestowed on created beings, either by making it common with angels or people, on account of the surpassing dignity, power and management in which God has placed them, and which they carry out towards others. Or, when misapplied to false gods, out of misconception and error (John 10:34; Exodus 22:28; Psalm 82:6; 1 Corinthians 8:4,5); wherefore it happens that the name of God, which is the proper name for signifying his individual essence, has become a common appellative noun. Therefore, in order to set himself apart from all who come by the name “God,” He has defined his own name by means of certain personal properties, as when He calls himself “the God of Abraham, Isaac, and Jacob (or Israel)” (Exodus 3:6); “the God of hosts” (Isaiah 1:24); “God of Gods” (Deuteronomy 10:17); “the true and living God.” So too He calls himself ‘El Shadday (Exodus 6), and simply Shadday, “all-powerful,” from shadad, “he has laid waste,” in the Chaldean plural form; and ‘Adon, “lord,” ‘Adonim, and ‘Adonai, “lords,” again in the plural form; and ‘Eljon, “the exalted.”

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