Both Uses of

divine
in
The Autobiography of Benjamin Franklin

My father's little library consisted chiefly of books in polemic divinity, most of which I read, and have since often regretted that, at a time when I had such a thirst for knowledge, more proper books had not fallen in my way since it was now resolved I should not be a clergyman.†
*

divinity = the state of being god-like; or of being a god

He liked the tho't, undertook the office, and, with the help of a few hands to measure out the liquor, executed it to satisfaction, and never were prayers more generally and more punctually attended; so that I thought this method preferable to the punishment inflicted by some military laws for non-attendance on divine service.†

Definitions:

(1) (divine as in: to forgive is divine)
wonderful; or god-like or coming from God
(2) (divine as in: divined from tea leaves)
to predict or discover something supernaturally (as if by magic)
(3) (divine as in: divined through intuition)
to discover or guess something -- usually through intuition or reflection
(4) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

In the time of Shakespeare, divine was sometimes used as a noun to reference a priest or a person of the church. (To remember that sense, think of the clergyman as having come from God).

Divinity typically refers to a god or to a school of religion, but on rare occasions, it refers to the name of a kind of soft white candy. To remember that sense, you might think of it as tasting divine/wonderful.