James Burgh's Quaternity

Over a decade ago I found a passage written by James Burgh (in "Crito") wherein he gives an account of his Arianism. Burgh was an English Whig writer who influenced America's founders. Among other things, he arguably served as the intellectual intermediary between Roger Williams and Thomas Jefferson regarding the term "separation of church and state." Jefferson got it from Burgh; Burgh got it from Williams.

I found of interest Burgh's use of the term "quaternity." As he wrote:

... The papists have thought proper to put the Virgin Mary into the Tr---ty, and call her the complement, or completing of it. That is, the F----r, the S-n, the H--y Gh--t, and the Virgin Mary, the undivided mystical four, or three, which is the same (for in a mystery, three is the same as four, and four the same as one; finite the same as infinite; human the same as divine) the mystical four, I say, are the tr---ty, or rather quaternity, that is, four different beings, some infinite, some finite, some mortal, some immortal, are only three beings, and these three-four beings, are the One, indivisible, simple, unoriginated Spirit, the first cause and fountain of being. 

No Protestant holds the Virgin Mary, who has these many ages been dead and rotten, to be any part of the immortal God. This is out of the question. But I would imagine, that to a person who denies the Athanasian doctrine, it should not appear a whit more absurd to put the Virgin Mary into the Tr---ty, or Godhead, than any other being whatever. All beings are equally different from and inferior to the Supreme; the S-n as much as the virgin; the virgin as much as a worm. ...

This old school, Enlightenment era, unitarian logic argues Roman Catholic doctrine is responsible for the error of Trinitarianism and sees a connection between Marianism and Trinitarianism. It argues the Trinity is as logically sound as the Quaternity. With Mary of course as the 4th Person in the Godhead. A short time later John Adams would write: 

The Trinity was carried in a general council by one vote against a quaternity; the Virgin Mary lost an equality with the Father, Son, and Spirit only by a single suffrage.

-- John Adams to Benjamin Rush, June 12, 1812. 

I would bet Adams got this sentiment from Burgh.