Both Uses of

divine

in

1984, by Orwell

Syme, however, had divined what he was about to say.
p. 52.9 *

divined = discovered (figured out)

Everywhere there is the same pyramidal structure, the same worship of semi-divine leader, the same economy existing by and for continuous warfare.
p. 197.2 *

divine = god-like

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)
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.