What do 'fain' and 'unfained' mean in this paragraph from Milton's "The Doctrine & Discipline of Divorce"?

Question

In book one, chapter VI, of The Doctrine & Discipline of Divorce, it is written:

Fourthly, Mariage is a cov’nant the very beeing wherof consists, not in a forc’t cohabitation, and counterfet performance of duties, but in unfained love and peace. And of matrimoniall love no doubt but that was chiefly meant, which by the ancient Sages was thus parabl’d, That Love, if he be not twin-born, yet hath a brother wondrous like him, call’d Anteros: whom while he seeks all about, his chance is to meet with many fals and faining Desires that wander singly up and down in his likenes.

I tried to decode the meaning of fain and unfained in Milton's writing but to no avail. Are these just alternative spellings of fine (meaning to diminish) and unfined?

Answer 1

The appropriate (adjectival) meaning is summarised and exemplified in M-W as

Merriam-Webster
a: WILLING
he was very fain, for the young widow was "altogether fair and lovely …
b: being obliged or constrained : COMPELLED
Great Britain was fain to devote its whole energy … to the business of slaying and being slain

This is consistent with an Oxford Languages definition (which I cannot reference because of pay-wall) quoted by Google search for fain as:

1. pleased or willing under the circumstances.
   "the traveller was fain to proceed"
2. compelled by the circumstances; obliged.
   "he was fain to acknowledge that the agreement was sacrosanct"

Hence, we may understand
but in unfained love and peace
as
in unconstrained (unforced, willingly accepted etc) love and peace

and understand
to meet with many fals and faining Desires
as
to meet with many fals (false) and faining (restricting, compelling, forcing, unwillingly demanding etc) desires

Fain and feign are sometimes confused:

Grammarist
Fain is (1) an adjective meaning glad or content to do something, and (2) an adverb meaning willingly or gladly. It’s mostly archaic. It still appears occasionally, but in most modern examples we can find, the word is used to affect an archaic tone. Feign is a verb meaning to pretend, to give a false appearance of, or to imitate.