Wait. I do recall being frustrated when people threw statements out without backing it up so I follow up here:
In
The Marrow of Theology, Book 1, Chapter 5 ("The Subsistence of God"), Ames writes precisely this:
They are distinguished from each other as things connected by certain relative properties... The relative property of the Father is to beget... The relative property of the Son is to be begotten... The property of the Holy Spirit is to be breathed."
Coxe wasn't making up new, less-precise vocabulary. He was quoting Ames word-for-word.
Let's pull Turretin off the shelf. In
Institutes of Elenctic Theology (Topic 3, Question 27), Turretin explicitly equates the properties with the relations. Turretin writes that the divine persons are distinguished not by their essence (which is one), but by their
"personal properties" (
proprietates personales), which he explicitly defines as
"relations" (
relationes).
... the Son is said to be from the Father by generation; not with respect to essence and absolutely as God, but with respect to person and reduplicatively as Son. The Holy Spirit is from the Father and the Son by spiration; for generation and spiration are communicative of the essence to the term of personality.
XVIII. Because these personal and characteristic properties are usually expressed by the relative names of the Father, Son, and Holy Spirit, it happens that they may well be said also to be distinguished from each other by relations... For as to each person there is a peculiar subsistence and a peculiar property, so also to them singly there is a peculiar relation.
Turretin teaches that in God, an incommunicable property
is a relation. Therefore, when Coxe (and Ames) use the English phrase "relative property," they are progenitors of Turretin’s precise theological concept: the property that constitutes the relation of origin (again, a phrase directly stated by Coxe).
Owen says this also in his
Brief Declaration and Vindication of the Doctrine of the Trinity, but I am having a hard time tracking it down in my Kindle.