All 9 Uses

divine
in
The Mayor of Casterbridge
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...she said, glad that he had divined this without her being obliged to express it.
Chpt 10 *

divined = discovered (figured out)
She did not divine the ample explanation of his manner, without personal vanity, that was afforded by the fact of Donald being the depositary of Henchard's confidence in respect of his past treatment of the pale, chastened mother who walked by her side.†
Chpt 14
A seer's spirit took possession of Elizabeth, impelling her to sit down by the fire and divine events so surely from data already her own that they could be held as witnessed.†
Chpt 24
"We both know him," said kind Elizabeth-Jane, to relieve her companion's divined embarrassment.†
Chpt 26
She had divined Man Number One.†
Chpt 30
The truth was that, as may be divined, he had quite intended to effect a grand catastrophe at the end of this drama by reading out the name, he had come to the house with no other thought.†
Chpt 34
But hard fate had ordained that he should be unable to call up this Divine spirit in his need.†
Chpt 41 *
How this woman divined things!†
Chpt 41
Yet she had not divined their whole extremity.†
Chpt 41

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 discover or predict 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)
In the time of Shakespeare, divine was sometimes used as a noun to reference a priest or a person of the church.

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.